% Mizar problem: e2_95_1,mcart_1,1504,41 
include('Axioms/SET010^0.ax').
thf(f1_s1_mcart_1_type,type,( f1_s1_mcart_1: $i )).
thf(f2_s1_mcart_1_type,type,( f2_s1_mcart_1: $i )).
thf(f3_s1_mcart_1_type,type,( f3_s1_mcart_1: $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_xtuple_0_type,type,( k1_xtuple_0: $i > $i )).
thf(k2_xtuple_0_type,type,( k2_xtuple_0: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(p1_s1_mcart_1_type,type,( p1_s1_mcart_1: $i > $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_xtuple_0,axiom,( $true ),file(xtuple_0,k1_xtuple_0)).
thf(dt_k2_xtuple_0,axiom,( $true ),file(xtuple_0,k2_xtuple_0)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_f1_s1_mcart_1,axiom,( $true ),file(mcart_1,f1_s1_mcart_1)).
thf(dt_f2_s1_mcart_1,axiom,( $true ),file(mcart_1,f2_s1_mcart_1)).
thf(dt_f3_s1_mcart_1,axiom,( $true ),file(mcart_1,f3_s1_mcart_1)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(e1_95_1__mcart_1,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ f1_s1_mcart_1 ) & ! [B: $i] : ~ ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ f2_s1_mcart_1 @ f3_s1_mcart_1 ) ) & ! [C: $i] : ! [D: $i] : ( ( ( = @ ( k1_xtuple_0 @ B ) @ C ) & ( = @ ( k2_xtuple_0 @ B ) @ D ) ) => ( p1_s1_mcart_1 @ A @ C @ D ) ) ) ) ),file(mcart_1,e1_95_1__mcart_1)).
thf(s5_funct_1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ! [C: $i] : ( ! [D: $i] : ~ ( ( r2_hidden @ D @ C ) & ! [E: $i] : ~ ( ( r2_hidden @ E @ B ) & ( A @ D @ E ) ) ) => ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ ( k9_xtuple_0 @ D ) @ C ) & ( r1_tarski @ ( k10_xtuple_0 @ D ) @ B ) & ! [E: $i] : ( ( r2_hidden @ E @ C ) => ( A @ E @ ( k1_funct_1 @ D @ E ) ) ) ) ) ),file(funct_1,s5_funct_1)).
thf(e2_95_1__mcart_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ f1_s1_mcart_1 ) & ( r1_tarski @ ( k10_xtuple_0 @ A ) @ ( k2_zfmisc_1 @ f2_s1_mcart_1 @ f3_s1_mcart_1 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ f1_s1_mcart_1 ) => ! [C: $i] : ! [D: $i] : ( ( ( = @ ( k1_xtuple_0 @ ( k1_funct_1 @ A @ B ) ) @ C ) & ( = @ ( k2_xtuple_0 @ ( k1_funct_1 @ A @ B ) ) @ D ) ) => ( p1_s1_mcart_1 @ B @ C @ D ) ) ) ) ),file(mcart_1,e2_95_1__mcart_1)).
