% Mizar problem: e12_16_1_1_1_2,arytm_3,329,37 
include('Axioms/SET010^0.ax').
thf(c1_16_type,type,( c1_16__arytm_3: $i )).
thf(c2_16_type,type,( c2_16__arytm_3: $i )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r2_arytm_3_type,type,( r2_arytm_3: $i > $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(reflexivity_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( r1_ordinal1 @ A @ A ) ) ),file(ordinal1,r1_ordinal1)).
thf(connectedness_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) | ( r1_ordinal1 @ B @ A ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(reflexivity_r2_arytm_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( r2_arytm_3 @ A @ A ) ) ),file(arytm_3,r2_arytm_3)).
thf(redefinition_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) <=> ( r1_tarski @ A @ B ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(dt_c1_16__arytm_3,axiom,( ( v3_ordinal1 @ c1_16__arytm_3 ) & ( v7_ordinal1 @ c1_16__arytm_3 ) ),file(arytm_3,c1_16__arytm_3)).
thf(dt_c2_16__arytm_3,axiom,( ( v3_ordinal1 @ c2_16__arytm_3 ) & ( v7_ordinal1 @ c2_16__arytm_3 ) ),file(arytm_3,c2_16__arytm_3)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(e11_16_1_1_1_2__arytm_3,axiom,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( v7_ordinal1 @ B ) & ( = @ A @ B ) & ( r2_arytm_3 @ c1_16__arytm_3 @ B ) & ( r2_arytm_3 @ c2_16__arytm_3 @ B ) & ( r1_ordinal1 @ c1_16__arytm_3 @ B ) ) ) ),file(arytm_3,e11_16_1_1_1_2__arytm_3)).
thf(s1_ordinal1,axiom,( ! [A: $i > $o] : ( ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( A @ B ) ) => ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( A @ B ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( A @ C ) => ( r1_ordinal1 @ B @ C ) ) ) ) ) ),file(ordinal1,s1_ordinal1)).
thf(e12_16_1_1_1_2__arytm_3,conjecture,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( v7_ordinal1 @ B ) & ( = @ A @ B ) & ( r2_arytm_3 @ c1_16__arytm_3 @ B ) & ( r2_arytm_3 @ c2_16__arytm_3 @ B ) & ( r1_ordinal1 @ c1_16__arytm_3 @ B ) ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ? [C: $i] : ( ( v3_ordinal1 @ C ) & ( v7_ordinal1 @ C ) & ( = @ B @ C ) & ( r2_arytm_3 @ c1_16__arytm_3 @ C ) & ( r2_arytm_3 @ c2_16__arytm_3 @ C ) & ( r1_ordinal1 @ c1_16__arytm_3 @ C ) ) => ( r1_ordinal1 @ A @ B ) ) ) ) ),file(arytm_3,e12_16_1_1_1_2__arytm_3)).
