%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : CAT033+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:14:14 AM UTC 2026
% Result : Theorem 47.32s 47.68s
% Output : Proof 47.94s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t2_yoneda_1,conjecture,
! [A] :
( ( l1_cat_1(A)
& v2_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> m2_cat_1(k20_ens_1(A,B),A,k1_yoneda_1(A)) ) ),
file('theBenchmark.p',t2_yoneda_1) ).
fof(rc3_funct_1,axiom,
? [A] :
( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) )
=> ( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc2_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(free_g1_cat_1,axiom,
! [A,B,C,D,E,F] :
( ( m1_relset_1(F,A,B)
& v1_funct_2(F,A,B)
& v1_funct_1(F)
& m1_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(E)
& m1_relset_1(D,B,A)
& v1_funct_2(D,B,A)
& v1_funct_1(D)
& m1_relset_1(C,B,A)
& v1_funct_2(C,B,A)
& v1_funct_1(C)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(A) )
=> ! [G,H,I,J,K,L] :
( g1_cat_1(A,B,C,D,E,F) = g1_cat_1(G,H,I,J,K,L)
=> ( F = L
& E = K
& D = J
& C = I
& B = H
& A = G ) ) ),
file('theBenchmark.p',free_g1_cat_1) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(dt_g1_cat_1,axiom,
! [A,B,C,D,E,F] :
( ( m1_relset_1(F,A,B)
& v1_funct_2(F,A,B)
& v1_funct_1(F)
& m1_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(E)
& m1_relset_1(D,B,A)
& v1_funct_2(D,B,A)
& v1_funct_1(D)
& m1_relset_1(C,B,A)
& v1_funct_2(C,B,A)
& v1_funct_1(C)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(A) )
=> ( l1_cat_1(g1_cat_1(A,B,C,D,E,F))
& v1_cat_1(g1_cat_1(A,B,C,D,E,F)) ) ),
file('theBenchmark.p',dt_g1_cat_1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_u3_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A))
& v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A))
& v1_funct_1(u3_cat_1(A)) ) ),
file('theBenchmark.p',dt_u3_cat_1) ).
fof(dt_u4_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A))
& v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A))
& v1_funct_1(u4_cat_1(A)) ) ),
file('theBenchmark.p',dt_u4_cat_1) ).
fof(dt_u5_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( m2_relset_1(u5_cat_1(A),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(A)),u2_cat_1(A))
& v1_funct_1(u5_cat_1(A)) ) ),
file('theBenchmark.p',dt_u5_cat_1) ).
fof(dt_u6_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A))
& v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A))
& v1_funct_1(u6_cat_1(A)) ) ),
file('theBenchmark.p',dt_u6_cat_1) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(abstractness_v1_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( v1_cat_1(A)
=> A = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ),
file('theBenchmark.p',abstractness_v1_cat_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_ens_1,axiom,
$true,
file('theBenchmark.p',dt_k2_ens_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(dt_u2_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ~ v1_xboole_0(u2_cat_1(A)) ),
file('theBenchmark.p',dt_u2_cat_1) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_ens_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ~ v1_xboole_0(k2_ens_1(A)) ),
file('theBenchmark.p',fc2_ens_1) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& A != B
& v1_xboole_0(A) ),
file('theBenchmark.p',t8_boole) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(existence_l1_cat_1,axiom,
? [A] : l1_cat_1(A),
file('theBenchmark.p',existence_l1_cat_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_cat_1,axiom,
! [A,B] :
( ( l1_cat_1(B)
& v2_cat_1(B)
& l1_cat_1(A)
& v2_cat_1(A) )
=> ? [C] : m2_cat_1(C,A,B) ),
file('theBenchmark.p',existence_m2_cat_1) ).
fof(dt_k12_ens_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> l1_cat_1(k12_ens_1(A)) ),
file('theBenchmark.p',dt_k12_ens_1) ).
fof(dt_k17_ens_1,axiom,
$true,
file('theBenchmark.p',dt_k17_ens_1) ).
fof(dt_k1_yoneda_1,axiom,
! [A] :
( ( l1_cat_1(A)
& v2_cat_1(A) )
=> ( l1_cat_1(k1_yoneda_1(A))
& v2_cat_1(k1_yoneda_1(A)) ) ),
file('theBenchmark.p',dt_k1_yoneda_1) ).
fof(dt_k20_ens_1,axiom,
! [A,B] :
( ( m1_subset_1(B,u1_cat_1(A))
& l1_cat_1(A)
& v2_cat_1(A) )
=> ( m2_relset_1(k20_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A)))
& v1_funct_2(k20_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A)))
& v1_funct_1(k20_ens_1(A,B)) ) ),
file('theBenchmark.p',dt_k20_ens_1) ).
fof(dt_l1_cat_1,axiom,
$true,
file('theBenchmark.p',dt_l1_cat_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_cat_1,axiom,
! [A,B] :
( ( l1_cat_1(B)
& v2_cat_1(B)
& l1_cat_1(A)
& v2_cat_1(A) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ( m2_relset_1(C,u2_cat_1(A),u2_cat_1(B))
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& v1_funct_1(C) ) ) ),
file('theBenchmark.p',dt_m2_cat_1) ).
fof(dt_u1_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ~ v1_xboole_0(u1_cat_1(A)) ),
file('theBenchmark.p',dt_u1_cat_1) ).
fof(cc1_funct_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_funct_1(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(fc4_ens_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( v2_cat_1(k12_ens_1(A))
& v1_cat_1(k12_ens_1(A)) ) ),
file('theBenchmark.p',fc4_ens_1) ).
fof(fc5_ens_1,axiom,
! [A] :
( ( l1_cat_1(A)
& v2_cat_1(A) )
=> ~ v1_xboole_0(k17_ens_1(A)) ),
file('theBenchmark.p',fc5_ens_1) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(d1_yoneda_1,axiom,
! [A] :
( ( l1_cat_1(A)
& v2_cat_1(A) )
=> k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)) ),
file('theBenchmark.p',d1_yoneda_1) ).
fof(t49_ens_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( l1_cat_1(B)
& v2_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ( r1_tarski(k17_ens_1(B),A)
=> m2_cat_1(k20_ens_1(B,C),B,k12_ens_1(A)) ) ) ) ),
file('theBenchmark.p',t49_ens_1) ).
fof(f_1_1,negated_conjecture,
~ ! [A] :
( ( l1_cat_1(A)
& v2_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> m2_cat_1(k20_ens_1(A,B),A,k1_yoneda_1(A)) ) ),
inference(negate,[status(cth)],[t2_yoneda_1]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ~ m2_cat_1(k20_ens_1(A,B),A,k1_yoneda_1(A))
& m1_subset_1(B,u1_cat_1(A)) )
& l1_cat_1(A)
& v2_cat_1(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_1] :
( ? [U_0] :
( ~ m2_cat_1(k20_ens_1(U_1,U_0),U_1,k1_yoneda_1(U_1))
& m1_subset_1(U_0,u1_cat_1(U_1)) )
& l1_cat_1(U_1)
& v2_cat_1(U_1) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_0] :
( ~ m2_cat_1(k20_ens_1(sK1,U_0),sK1,k1_yoneda_1(sK1))
& m1_subset_1(U_0,u1_cat_1(sK1)) )
& l1_cat_1(sK1)
& v2_cat_1(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ~ m2_cat_1(k20_ens_1(sK1,sK2),sK1,k1_yoneda_1(sK1))
& m1_subset_1(sK2,u1_cat_1(sK1))
& l1_cat_1(sK1)
& v2_cat_1(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_0,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ~ m2_cat_1(k20_ens_1(sK1,sK2),sK1,k1_yoneda_1(sK1))
& m1_subset_1(sK2,u1_cat_1(sK1))
& l1_cat_1(sK1)
& v2_cat_1(sK1) ),
inference(definitional_conversion,[status(esa)],[f_1_5]) ).
cnf(f_1_7,negated_conjecture,
v2_cat_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
l1_cat_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_9,negated_conjecture,
m1_subset_1(sK2,u1_cat_1(sK1)),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_10,negated_conjecture,
~ m2_cat_1(k20_ens_1(sK1,sK2),sK1,k1_yoneda_1(sK1)),
inference(clausify,[status(thm)],[f_1_6]) ).
fof(f_2_1,plain,
? [A] :
( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_2_2,plain,
? [U_2] :
( v2_funct_1(U_2)
& v1_funct_1(U_2)
& v1_relat_1(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( v2_funct_1(sK3)
& v1_funct_1(sK3)
& v1_relat_1(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_2,sK3)],[f_2_2]) ).
fof(f_2_4,plain,
( v2_funct_1(sK3)
& v1_funct_1(sK3)
& v1_relat_1(sK3) ),
inference(definitional_conversion,[status(esa)],[f_2_3]) ).
cnf(f_2_5,plain,
v1_relat_1(sK3),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
v1_funct_1(sK3),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
v2_funct_1(sK3),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
! [A] :
( ( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) )
| ~ v1_funct_1(A)
| ~ v1_xboole_0(A)
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_3_2,plain,
! [U_3] :
( ( v2_funct_1(U_3)
& v1_funct_1(U_3)
& v1_relat_1(U_3) )
| ~ v1_funct_1(U_3)
| ~ v1_xboole_0(U_3)
| ~ v1_relat_1(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_3] :
( v2_funct_1(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( v1_funct_1(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( v1_relat_1(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( sP0(U_3)
| ~ v1_funct_1(U_3)
| ~ v1_xboole_0(U_3)
| ~ v1_relat_1(U_3) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_2]) ).
cnf(f_3_4,plain,
( sP0(U_3)
| ~ v1_funct_1(U_3)
| ~ v1_xboole_0(U_3)
| ~ v1_relat_1(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( v1_relat_1(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( v1_funct_1(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_7,plain,
( v2_funct_1(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_4_2,plain,
? [U_4] :
( v1_funct_1(U_4)
& v1_relat_1(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( v1_funct_1(sK4)
& v1_relat_1(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_4,sK4)],[f_4_2]) ).
fof(f_4_4,plain,
( v1_funct_1(sK4)
& v1_relat_1(sK4) ),
inference(definitional_conversion,[status(esa)],[f_4_3]) ).
cnf(f_4_5,plain,
v1_relat_1(sK4),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
v1_funct_1(sK4),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_5_2,plain,
? [U_5] :
( v1_funct_1(U_5)
& v1_xboole_0(U_5)
& v1_relat_1(U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( v1_funct_1(sK5)
& v1_xboole_0(sK5)
& v1_relat_1(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_5,sK5)],[f_5_2]) ).
fof(f_5_4,plain,
( v1_funct_1(sK5)
& v1_xboole_0(sK5)
& v1_relat_1(sK5) ),
inference(definitional_conversion,[status(esa)],[f_5_3]) ).
cnf(f_5_5,plain,
v1_relat_1(sK5),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
v1_xboole_0(sK5),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
v1_funct_1(sK5),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
! [A,B,C,D,E,F] :
( ! [G,H,I,J,K,L] :
( ( F = L
& E = K
& D = J
& C = I
& B = H
& A = G )
| g1_cat_1(A,B,C,D,E,F) != g1_cat_1(G,H,I,J,K,L) )
| ~ m1_relset_1(F,A,B)
| ~ v1_funct_2(F,A,B)
| ~ v1_funct_1(F)
| ~ m1_relset_1(E,k2_zfmisc_1(B,B),B)
| ~ v1_funct_1(E)
| ~ m1_relset_1(D,B,A)
| ~ v1_funct_2(D,B,A)
| ~ v1_funct_1(D)
| ~ m1_relset_1(C,B,A)
| ~ v1_funct_2(C,B,A)
| ~ v1_funct_1(C)
| v1_xboole_0(B)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[free_g1_cat_1]) ).
fof(f_6_2,plain,
! [U_17,U_16,U_15,U_14,U_13,U_12] :
( ! [U_11,U_10,U_9,U_8,U_7,U_6] :
( ( U_12 = U_6
& U_13 = U_7
& U_14 = U_8
& U_15 = U_9
& U_16 = U_10
& U_17 = U_11 )
| g1_cat_1(U_17,U_16,U_15,U_14,U_13,U_12) != g1_cat_1(U_11,U_10,U_9,U_8,U_7,U_6) )
| ~ m1_relset_1(U_12,U_17,U_16)
| ~ v1_funct_2(U_12,U_17,U_16)
| ~ v1_funct_1(U_12)
| ~ m1_relset_1(U_13,k2_zfmisc_1(U_16,U_16),U_16)
| ~ v1_funct_1(U_13)
| ~ m1_relset_1(U_14,U_16,U_17)
| ~ v1_funct_2(U_14,U_16,U_17)
| ~ v1_funct_1(U_14)
| ~ m1_relset_1(U_15,U_16,U_17)
| ~ v1_funct_2(U_15,U_16,U_17)
| ~ v1_funct_1(U_15)
| v1_xboole_0(U_16)
| v1_xboole_0(U_17) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17] :
( U_12 = U_6
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) )
& ! [U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17] :
( U_13 = U_7
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) )
& ! [U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17] :
( U_14 = U_8
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) )
& ! [U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17] :
( U_15 = U_9
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) )
& ! [U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17] :
( U_16 = U_10
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) )
& ! [U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17] :
( U_17 = U_11
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) )
& ! [U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17] :
( sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17)
| g1_cat_1(U_17,U_16,U_15,U_14,U_13,U_12) != g1_cat_1(U_11,U_10,U_9,U_8,U_7,U_6)
| ~ m1_relset_1(U_12,U_17,U_16)
| ~ v1_funct_2(U_12,U_17,U_16)
| ~ v1_funct_1(U_12)
| ~ m1_relset_1(U_13,k2_zfmisc_1(U_16,U_16),U_16)
| ~ v1_funct_1(U_13)
| ~ m1_relset_1(U_14,U_16,U_17)
| ~ v1_funct_2(U_14,U_16,U_17)
| ~ v1_funct_1(U_14)
| ~ m1_relset_1(U_15,U_16,U_17)
| ~ v1_funct_2(U_15,U_16,U_17)
| ~ v1_funct_1(U_15)
| v1_xboole_0(U_16)
| v1_xboole_0(U_17) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17)
| g1_cat_1(U_17,U_16,U_15,U_14,U_13,U_12) != g1_cat_1(U_11,U_10,U_9,U_8,U_7,U_6)
| ~ m1_relset_1(U_12,U_17,U_16)
| ~ v1_funct_2(U_12,U_17,U_16)
| ~ v1_funct_1(U_12)
| ~ m1_relset_1(U_13,k2_zfmisc_1(U_16,U_16),U_16)
| ~ v1_funct_1(U_13)
| ~ m1_relset_1(U_14,U_16,U_17)
| ~ v1_funct_2(U_14,U_16,U_17)
| ~ v1_funct_1(U_14)
| ~ m1_relset_1(U_15,U_16,U_17)
| ~ v1_funct_2(U_15,U_16,U_17)
| ~ v1_funct_1(U_15)
| v1_xboole_0(U_16)
| v1_xboole_0(U_17) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( U_17 = U_11
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( U_16 = U_10
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( U_15 = U_9
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_8,plain,
( U_14 = U_8
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_9,plain,
( U_13 = U_7
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_10,plain,
( U_12 = U_6
| ~ sP1(U_7,U_8,U_9,U_10,U_11,U_12,U_6,U_13,U_14,U_15,U_16,U_17) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_7_2,plain,
! [U_20,U_19] :
? [U_18] : m1_relset_1(U_18,U_20,U_19),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_20,U_19] : m1_relset_1(sK6(U_20,U_19),U_20,U_19),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_18,sK6(U_20,U_19))],[f_7_2]) ).
fof(f_7_4,plain,
! [U_19,U_20] : m1_relset_1(sK6(U_20,U_19),U_20,U_19),
inference(definitional_conversion,[status(esa)],[f_7_3]) ).
cnf(f_7_5,plain,
m1_relset_1(sK6(U_20,U_19),U_20,U_19),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
! [A,B,C,D,E,F] :
( ( l1_cat_1(g1_cat_1(A,B,C,D,E,F))
& v1_cat_1(g1_cat_1(A,B,C,D,E,F)) )
| ~ m1_relset_1(F,A,B)
| ~ v1_funct_2(F,A,B)
| ~ v1_funct_1(F)
| ~ m1_relset_1(E,k2_zfmisc_1(B,B),B)
| ~ v1_funct_1(E)
| ~ m1_relset_1(D,B,A)
| ~ v1_funct_2(D,B,A)
| ~ v1_funct_1(D)
| ~ m1_relset_1(C,B,A)
| ~ v1_funct_2(C,B,A)
| ~ v1_funct_1(C)
| v1_xboole_0(B)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[dt_g1_cat_1]) ).
fof(f_8_2,plain,
! [U_26,U_25,U_24,U_23,U_22,U_21] :
( ( l1_cat_1(g1_cat_1(U_26,U_25,U_24,U_23,U_22,U_21))
& v1_cat_1(g1_cat_1(U_26,U_25,U_24,U_23,U_22,U_21)) )
| ~ m1_relset_1(U_21,U_26,U_25)
| ~ v1_funct_2(U_21,U_26,U_25)
| ~ v1_funct_1(U_21)
| ~ m1_relset_1(U_22,k2_zfmisc_1(U_25,U_25),U_25)
| ~ v1_funct_1(U_22)
| ~ m1_relset_1(U_23,U_25,U_26)
| ~ v1_funct_2(U_23,U_25,U_26)
| ~ v1_funct_1(U_23)
| ~ m1_relset_1(U_24,U_25,U_26)
| ~ v1_funct_2(U_24,U_25,U_26)
| ~ v1_funct_1(U_24)
| v1_xboole_0(U_25)
| v1_xboole_0(U_26) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_22,U_24,U_25,U_21,U_26,U_23] :
( l1_cat_1(g1_cat_1(U_26,U_25,U_24,U_23,U_22,U_21))
| ~ sP2(U_22,U_24,U_25,U_21,U_26,U_23) )
& ! [U_22,U_24,U_25,U_21,U_26,U_23] :
( v1_cat_1(g1_cat_1(U_26,U_25,U_24,U_23,U_22,U_21))
| ~ sP2(U_22,U_24,U_25,U_21,U_26,U_23) )
& ! [U_22,U_24,U_25,U_21,U_26,U_23] :
( sP2(U_22,U_24,U_25,U_21,U_26,U_23)
| ~ m1_relset_1(U_21,U_26,U_25)
| ~ v1_funct_2(U_21,U_26,U_25)
| ~ v1_funct_1(U_21)
| ~ m1_relset_1(U_22,k2_zfmisc_1(U_25,U_25),U_25)
| ~ v1_funct_1(U_22)
| ~ m1_relset_1(U_23,U_25,U_26)
| ~ v1_funct_2(U_23,U_25,U_26)
| ~ v1_funct_1(U_23)
| ~ m1_relset_1(U_24,U_25,U_26)
| ~ v1_funct_2(U_24,U_25,U_26)
| ~ v1_funct_1(U_24)
| v1_xboole_0(U_25)
| v1_xboole_0(U_26) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_8_2]) ).
cnf(f_8_4,plain,
( sP2(U_22,U_24,U_25,U_21,U_26,U_23)
| ~ m1_relset_1(U_21,U_26,U_25)
| ~ v1_funct_2(U_21,U_26,U_25)
| ~ v1_funct_1(U_21)
| ~ m1_relset_1(U_22,k2_zfmisc_1(U_25,U_25),U_25)
| ~ v1_funct_1(U_22)
| ~ m1_relset_1(U_23,U_25,U_26)
| ~ v1_funct_2(U_23,U_25,U_26)
| ~ v1_funct_1(U_23)
| ~ m1_relset_1(U_24,U_25,U_26)
| ~ v1_funct_2(U_24,U_25,U_26)
| ~ v1_funct_1(U_24)
| v1_xboole_0(U_25)
| v1_xboole_0(U_26) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( v1_cat_1(g1_cat_1(U_26,U_25,U_24,U_23,U_22,U_21))
| ~ sP2(U_22,U_24,U_25,U_21,U_26,U_23) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( l1_cat_1(g1_cat_1(U_26,U_25,U_24,U_23,U_22,U_21))
| ~ sP2(U_22,U_24,U_25,U_21,U_26,U_23) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_9_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
$true,
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
fof(f_10_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
$true,
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] :
( ( m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A))
& v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A))
& v1_funct_1(u3_cat_1(A)) )
| ~ l1_cat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_u3_cat_1]) ).
fof(f_11_2,plain,
! [U_27] :
( ( m2_relset_1(u3_cat_1(U_27),u2_cat_1(U_27),u1_cat_1(U_27))
& v1_funct_2(u3_cat_1(U_27),u2_cat_1(U_27),u1_cat_1(U_27))
& v1_funct_1(u3_cat_1(U_27)) )
| ~ l1_cat_1(U_27) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_27] :
( m2_relset_1(u3_cat_1(U_27),u2_cat_1(U_27),u1_cat_1(U_27))
| ~ sP3(U_27) )
& ! [U_27] :
( v1_funct_2(u3_cat_1(U_27),u2_cat_1(U_27),u1_cat_1(U_27))
| ~ sP3(U_27) )
& ! [U_27] :
( v1_funct_1(u3_cat_1(U_27))
| ~ sP3(U_27) )
& ! [U_27] :
( sP3(U_27)
| ~ l1_cat_1(U_27) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_11_2]) ).
cnf(f_11_4,plain,
( sP3(U_27)
| ~ l1_cat_1(U_27) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( v1_funct_1(u3_cat_1(U_27))
| ~ sP3(U_27) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( v1_funct_2(u3_cat_1(U_27),u2_cat_1(U_27),u1_cat_1(U_27))
| ~ sP3(U_27) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_7,plain,
( m2_relset_1(u3_cat_1(U_27),u2_cat_1(U_27),u1_cat_1(U_27))
| ~ sP3(U_27) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A] :
( ( m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A))
& v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A))
& v1_funct_1(u4_cat_1(A)) )
| ~ l1_cat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_u4_cat_1]) ).
fof(f_12_2,plain,
! [U_28] :
( ( m2_relset_1(u4_cat_1(U_28),u2_cat_1(U_28),u1_cat_1(U_28))
& v1_funct_2(u4_cat_1(U_28),u2_cat_1(U_28),u1_cat_1(U_28))
& v1_funct_1(u4_cat_1(U_28)) )
| ~ l1_cat_1(U_28) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_28] :
( m2_relset_1(u4_cat_1(U_28),u2_cat_1(U_28),u1_cat_1(U_28))
| ~ sP4(U_28) )
& ! [U_28] :
( v1_funct_2(u4_cat_1(U_28),u2_cat_1(U_28),u1_cat_1(U_28))
| ~ sP4(U_28) )
& ! [U_28] :
( v1_funct_1(u4_cat_1(U_28))
| ~ sP4(U_28) )
& ! [U_28] :
( sP4(U_28)
| ~ l1_cat_1(U_28) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_12_2]) ).
cnf(f_12_4,plain,
( sP4(U_28)
| ~ l1_cat_1(U_28) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( v1_funct_1(u4_cat_1(U_28))
| ~ sP4(U_28) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( v1_funct_2(u4_cat_1(U_28),u2_cat_1(U_28),u1_cat_1(U_28))
| ~ sP4(U_28) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_7,plain,
( m2_relset_1(u4_cat_1(U_28),u2_cat_1(U_28),u1_cat_1(U_28))
| ~ sP4(U_28) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A] :
( ( m2_relset_1(u5_cat_1(A),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(A)),u2_cat_1(A))
& v1_funct_1(u5_cat_1(A)) )
| ~ l1_cat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_u5_cat_1]) ).
fof(f_13_2,plain,
! [U_29] :
( ( m2_relset_1(u5_cat_1(U_29),k2_zfmisc_1(u2_cat_1(U_29),u2_cat_1(U_29)),u2_cat_1(U_29))
& v1_funct_1(u5_cat_1(U_29)) )
| ~ l1_cat_1(U_29) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_29] :
( m2_relset_1(u5_cat_1(U_29),k2_zfmisc_1(u2_cat_1(U_29),u2_cat_1(U_29)),u2_cat_1(U_29))
| ~ sP5(U_29) )
& ! [U_29] :
( v1_funct_1(u5_cat_1(U_29))
| ~ sP5(U_29) )
& ! [U_29] :
( sP5(U_29)
| ~ l1_cat_1(U_29) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_13_2]) ).
cnf(f_13_4,plain,
( sP5(U_29)
| ~ l1_cat_1(U_29) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( v1_funct_1(u5_cat_1(U_29))
| ~ sP5(U_29) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( m2_relset_1(u5_cat_1(U_29),k2_zfmisc_1(u2_cat_1(U_29),u2_cat_1(U_29)),u2_cat_1(U_29))
| ~ sP5(U_29) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A] :
( ( m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A))
& v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A))
& v1_funct_1(u6_cat_1(A)) )
| ~ l1_cat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_u6_cat_1]) ).
fof(f_14_2,plain,
! [U_30] :
( ( m2_relset_1(u6_cat_1(U_30),u1_cat_1(U_30),u2_cat_1(U_30))
& v1_funct_2(u6_cat_1(U_30),u1_cat_1(U_30),u2_cat_1(U_30))
& v1_funct_1(u6_cat_1(U_30)) )
| ~ l1_cat_1(U_30) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_30] :
( m2_relset_1(u6_cat_1(U_30),u1_cat_1(U_30),u2_cat_1(U_30))
| ~ sP6(U_30) )
& ! [U_30] :
( v1_funct_2(u6_cat_1(U_30),u1_cat_1(U_30),u2_cat_1(U_30))
| ~ sP6(U_30) )
& ! [U_30] :
( v1_funct_1(u6_cat_1(U_30))
| ~ sP6(U_30) )
& ! [U_30] :
( sP6(U_30)
| ~ l1_cat_1(U_30) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_14_2]) ).
cnf(f_14_4,plain,
( sP6(U_30)
| ~ l1_cat_1(U_30) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( v1_funct_1(u6_cat_1(U_30))
| ~ sP6(U_30) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_6,plain,
( v1_funct_2(u6_cat_1(U_30),u1_cat_1(U_30),u2_cat_1(U_30))
| ~ sP6(U_30) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_7,plain,
( m2_relset_1(u6_cat_1(U_30),u1_cat_1(U_30),u2_cat_1(U_30))
| ~ sP6(U_30) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A,B,C] :
( v1_relat_1(C)
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_15_2,plain,
! [U_33,U_32,U_31] :
( v1_relat_1(U_31)
| ~ m1_subset_1(U_31,k1_zfmisc_1(k2_zfmisc_1(U_33,U_32))) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_33,U_31,U_32] :
( v1_relat_1(U_31)
| ~ m1_subset_1(U_31,k1_zfmisc_1(k2_zfmisc_1(U_33,U_32))) ),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
( v1_relat_1(U_31)
| ~ m1_subset_1(U_31,k1_zfmisc_1(k2_zfmisc_1(U_33,U_32))) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_16_2,plain,
! [U_35,U_34] :
( ~ r2_hidden(U_34,U_35)
| ~ r2_hidden(U_35,U_34) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_35,U_34] :
( ~ r2_hidden(U_34,U_35)
| ~ r2_hidden(U_35,U_34) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( ~ r2_hidden(U_34,U_35)
| ~ r2_hidden(U_35,U_34) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A] :
( A = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
| ~ v1_cat_1(A)
| ~ l1_cat_1(A) ),
inference(fof_nnf,[status(thm)],[abstractness_v1_cat_1]) ).
fof(f_17_2,plain,
! [U_36] :
( U_36 = g1_cat_1(u1_cat_1(U_36),u2_cat_1(U_36),u3_cat_1(U_36),u4_cat_1(U_36),u5_cat_1(U_36),u6_cat_1(U_36))
| ~ v1_cat_1(U_36)
| ~ l1_cat_1(U_36) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_36] :
( U_36 = g1_cat_1(u1_cat_1(U_36),u2_cat_1(U_36),u3_cat_1(U_36),u4_cat_1(U_36),u5_cat_1(U_36),u6_cat_1(U_36))
| ~ v1_cat_1(U_36)
| ~ l1_cat_1(U_36) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( U_36 = g1_cat_1(u1_cat_1(U_36),u2_cat_1(U_36),u3_cat_1(U_36),u4_cat_1(U_36),u5_cat_1(U_36),u6_cat_1(U_36))
| ~ v1_cat_1(U_36)
| ~ l1_cat_1(U_36) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_18_2,plain,
! [U_39,U_38] :
? [U_37] : m2_relset_1(U_37,U_39,U_38),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_39,U_38] : m2_relset_1(sK7(U_39,U_38),U_39,U_38),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_37,sK7(U_39,U_38))],[f_18_2]) ).
fof(f_18_4,plain,
! [U_39,U_38] : m2_relset_1(sK7(U_39,U_38),U_39,U_38),
inference(definitional_conversion,[status(esa)],[f_18_3]) ).
cnf(f_18_5,plain,
m2_relset_1(sK7(U_39,U_38),U_39,U_38),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [A,B,C] :
( ( m2_relset_1(C,A,B)
| ~ m1_relset_1(C,A,B) )
& ( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1]) ).
fof(f_19_2,plain,
! [U_42,U_41,U_40] :
( ( m2_relset_1(U_40,U_42,U_41)
| ~ m1_relset_1(U_40,U_42,U_41) )
& ( m1_relset_1(U_40,U_42,U_41)
| ~ m2_relset_1(U_40,U_42,U_41) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_48,U_46,U_44] :
( m2_relset_1(U_44,U_48,U_46)
| ~ m1_relset_1(U_44,U_48,U_46) )
& ! [U_47,U_45,U_43] :
( m1_relset_1(U_43,U_47,U_45)
| ~ m2_relset_1(U_43,U_47,U_45) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_44,U_48,U_46] :
( m2_relset_1(U_44,U_48,U_46)
| ~ m1_relset_1(U_44,U_48,U_46) )
& ! [U_47,U_43,U_45] :
( m1_relset_1(U_43,U_47,U_45)
| ~ m2_relset_1(U_43,U_47,U_45) ) ),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
( m1_relset_1(U_43,U_47,U_45)
| ~ m2_relset_1(U_43,U_47,U_45) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_6,plain,
( m2_relset_1(U_44,U_48,U_46)
| ~ m1_relset_1(U_44,U_48,U_46) ),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_20_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_20_1]) ).
cnf(f_20_3,plain,
$true,
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_21_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_21_1]) ).
cnf(f_21_3,plain,
$true,
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_ens_1]) ).
fof(f_22_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_22_1]) ).
cnf(f_22_3,plain,
$true,
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m2_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_23_2,plain,
! [U_51,U_50,U_49] :
( m1_subset_1(U_49,k1_zfmisc_1(k2_zfmisc_1(U_51,U_50)))
| ~ m2_relset_1(U_49,U_51,U_50) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_50,U_49,U_51] :
( m1_subset_1(U_49,k1_zfmisc_1(k2_zfmisc_1(U_51,U_50)))
| ~ m2_relset_1(U_49,U_51,U_50) ),
inference(definitional_conversion,[status(esa)],[f_23_2]) ).
cnf(f_23_4,plain,
( m1_subset_1(U_49,k1_zfmisc_1(k2_zfmisc_1(U_51,U_50)))
| ~ m2_relset_1(U_49,U_51,U_50) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
( ~ v1_xboole_0(u2_cat_1(A))
| ~ l1_cat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_u2_cat_1]) ).
fof(f_24_2,plain,
! [U_52] :
( ~ v1_xboole_0(u2_cat_1(U_52))
| ~ l1_cat_1(U_52) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_52] :
( ~ v1_xboole_0(u2_cat_1(U_52))
| ~ l1_cat_1(U_52) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( ~ v1_xboole_0(u2_cat_1(U_52))
| ~ l1_cat_1(U_52) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_25_2,plain,
v1_xboole_0(k1_xboole_0),
inference(definitional_conversion,[status(esa)],[f_25_1]) ).
cnf(f_25_3,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A] :
( ~ v1_xboole_0(k2_ens_1(A))
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[fc2_ens_1]) ).
fof(f_26_2,plain,
! [U_53] :
( ~ v1_xboole_0(k2_ens_1(U_53))
| v1_xboole_0(U_53) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_53] :
( ~ v1_xboole_0(k2_ens_1(U_53))
| v1_xboole_0(U_53) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( ~ v1_xboole_0(k2_ens_1(U_53))
| v1_xboole_0(U_53) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_27_2,plain,
! [U_55,U_54] :
( m1_subset_1(U_55,U_54)
| ~ r2_hidden(U_55,U_54) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_55,U_54] :
( m1_subset_1(U_55,U_54)
| ~ r2_hidden(U_55,U_54) ),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,plain,
( m1_subset_1(U_55,U_54)
| ~ r2_hidden(U_55,U_54) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A,B,C] :
( m1_subset_1(A,C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_28_2,plain,
! [U_58,U_57,U_56] :
( m1_subset_1(U_58,U_56)
| ~ m1_subset_1(U_57,k1_zfmisc_1(U_56))
| ~ r2_hidden(U_58,U_57) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_56,U_57,U_58] :
( m1_subset_1(U_58,U_56)
| ~ m1_subset_1(U_57,k1_zfmisc_1(U_56))
| ~ r2_hidden(U_58,U_57) ),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
( m1_subset_1(U_58,U_56)
| ~ m1_subset_1(U_57,k1_zfmisc_1(U_56))
| ~ r2_hidden(U_58,U_57) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B,C] :
( ~ v1_xboole_0(C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_29_2,plain,
! [U_61,U_60,U_59] :
( ~ v1_xboole_0(U_59)
| ~ m1_subset_1(U_60,k1_zfmisc_1(U_59))
| ~ r2_hidden(U_61,U_60) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_61,U_60] :
( ! [U_59] :
( ~ v1_xboole_0(U_59)
| ~ m1_subset_1(U_60,k1_zfmisc_1(U_59)) )
| ~ r2_hidden(U_61,U_60) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
! [U_60,U_59,U_61] :
( ~ v1_xboole_0(U_59)
| ~ m1_subset_1(U_60,k1_zfmisc_1(U_59))
| ~ r2_hidden(U_61,U_60) ),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
( ~ v1_xboole_0(U_59)
| ~ m1_subset_1(U_60,k1_zfmisc_1(U_59))
| ~ r2_hidden(U_61,U_60) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_30_2,plain,
! [U_63,U_62] :
( ~ v1_xboole_0(U_62)
| U_63 = U_62
| ~ v1_xboole_0(U_63) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_63] :
( ! [U_62] :
( ~ v1_xboole_0(U_62)
| U_63 = U_62 )
| ~ v1_xboole_0(U_63) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
! [U_63,U_62] :
( ~ v1_xboole_0(U_62)
| U_63 = U_62
| ~ v1_xboole_0(U_63) ),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
( ~ v1_xboole_0(U_62)
| U_63 = U_62
| ~ v1_xboole_0(U_63) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_31_2,plain,
! [U_65,U_64] : r1_tarski(U_65,U_65),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_65] : r1_tarski(U_65,U_65),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
! [U_65] : r1_tarski(U_65,U_65),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
r1_tarski(U_65,U_65),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,plain,
? [A] : l1_cat_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_cat_1]) ).
fof(f_32_2,plain,
? [U_66] : l1_cat_1(U_66),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
l1_cat_1(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_66,sK8)],[f_32_2]) ).
fof(f_32_4,plain,
l1_cat_1(sK8),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
l1_cat_1(sK8),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_33_2,plain,
! [U_68] :
? [U_67] : m1_subset_1(U_67,U_68),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_68] : m1_subset_1(sK9(U_68),U_68),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_67,sK9(U_68))],[f_33_2]) ).
fof(f_33_4,plain,
! [U_68] : m1_subset_1(sK9(U_68),U_68),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
m1_subset_1(sK9(U_68),U_68),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A,B] :
( ? [C] : m2_cat_1(C,A,B)
| ~ l1_cat_1(B)
| ~ v2_cat_1(B)
| ~ l1_cat_1(A)
| ~ v2_cat_1(A) ),
inference(fof_nnf,[status(thm)],[existence_m2_cat_1]) ).
fof(f_34_2,plain,
! [U_71,U_70] :
( ? [U_69] : m2_cat_1(U_69,U_71,U_70)
| ~ l1_cat_1(U_70)
| ~ v2_cat_1(U_70)
| ~ l1_cat_1(U_71)
| ~ v2_cat_1(U_71) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_71,U_70] :
( m2_cat_1(sK10(U_71,U_70),U_71,U_70)
| ~ l1_cat_1(U_70)
| ~ v2_cat_1(U_70)
| ~ l1_cat_1(U_71)
| ~ v2_cat_1(U_71) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_69,sK10(U_71,U_70))],[f_34_2]) ).
fof(f_34_4,plain,
! [U_71,U_70] :
( m2_cat_1(sK10(U_71,U_70),U_71,U_70)
| ~ l1_cat_1(U_70)
| ~ v2_cat_1(U_70)
| ~ l1_cat_1(U_71)
| ~ v2_cat_1(U_71) ),
inference(definitional_conversion,[status(esa)],[f_34_3]) ).
cnf(f_34_5,plain,
( m2_cat_1(sK10(U_71,U_70),U_71,U_70)
| ~ l1_cat_1(U_70)
| ~ v2_cat_1(U_70)
| ~ l1_cat_1(U_71)
| ~ v2_cat_1(U_71) ),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_1,plain,
! [A] :
( l1_cat_1(k12_ens_1(A))
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k12_ens_1]) ).
fof(f_35_2,plain,
! [U_72] :
( l1_cat_1(k12_ens_1(U_72))
| v1_xboole_0(U_72) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_72] :
( l1_cat_1(k12_ens_1(U_72))
| v1_xboole_0(U_72) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( l1_cat_1(k12_ens_1(U_72))
| v1_xboole_0(U_72) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k17_ens_1]) ).
fof(f_36_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_36_1]) ).
cnf(f_36_3,plain,
$true,
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A] :
( ( l1_cat_1(k1_yoneda_1(A))
& v2_cat_1(k1_yoneda_1(A)) )
| ~ l1_cat_1(A)
| ~ v2_cat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_yoneda_1]) ).
fof(f_37_2,plain,
! [U_73] :
( ( l1_cat_1(k1_yoneda_1(U_73))
& v2_cat_1(k1_yoneda_1(U_73)) )
| ~ l1_cat_1(U_73)
| ~ v2_cat_1(U_73) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_73] :
( l1_cat_1(k1_yoneda_1(U_73))
| ~ sP7(U_73) )
& ! [U_73] :
( v2_cat_1(k1_yoneda_1(U_73))
| ~ sP7(U_73) )
& ! [U_73] :
( sP7(U_73)
| ~ l1_cat_1(U_73)
| ~ v2_cat_1(U_73) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_37_2]) ).
cnf(f_37_4,plain,
( sP7(U_73)
| ~ l1_cat_1(U_73)
| ~ v2_cat_1(U_73) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( v2_cat_1(k1_yoneda_1(U_73))
| ~ sP7(U_73) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
( l1_cat_1(k1_yoneda_1(U_73))
| ~ sP7(U_73) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A,B] :
( ( m2_relset_1(k20_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A)))
& v1_funct_2(k20_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A)))
& v1_funct_1(k20_ens_1(A,B)) )
| ~ m1_subset_1(B,u1_cat_1(A))
| ~ l1_cat_1(A)
| ~ v2_cat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_k20_ens_1]) ).
fof(f_38_2,plain,
! [U_75,U_74] :
( ( m2_relset_1(k20_ens_1(U_75,U_74),u2_cat_1(U_75),k2_ens_1(k17_ens_1(U_75)))
& v1_funct_2(k20_ens_1(U_75,U_74),u2_cat_1(U_75),k2_ens_1(k17_ens_1(U_75)))
& v1_funct_1(k20_ens_1(U_75,U_74)) )
| ~ m1_subset_1(U_74,u1_cat_1(U_75))
| ~ l1_cat_1(U_75)
| ~ v2_cat_1(U_75) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_74,U_75] :
( m2_relset_1(k20_ens_1(U_75,U_74),u2_cat_1(U_75),k2_ens_1(k17_ens_1(U_75)))
| ~ sP8(U_74,U_75) )
& ! [U_74,U_75] :
( v1_funct_2(k20_ens_1(U_75,U_74),u2_cat_1(U_75),k2_ens_1(k17_ens_1(U_75)))
| ~ sP8(U_74,U_75) )
& ! [U_74,U_75] :
( v1_funct_1(k20_ens_1(U_75,U_74))
| ~ sP8(U_74,U_75) )
& ! [U_74,U_75] :
( sP8(U_74,U_75)
| ~ m1_subset_1(U_74,u1_cat_1(U_75))
| ~ l1_cat_1(U_75)
| ~ v2_cat_1(U_75) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_38_2]) ).
cnf(f_38_4,plain,
( sP8(U_74,U_75)
| ~ m1_subset_1(U_74,u1_cat_1(U_75))
| ~ l1_cat_1(U_75)
| ~ v2_cat_1(U_75) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
( v1_funct_1(k20_ens_1(U_75,U_74))
| ~ sP8(U_74,U_75) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_6,plain,
( v1_funct_2(k20_ens_1(U_75,U_74),u2_cat_1(U_75),k2_ens_1(k17_ens_1(U_75)))
| ~ sP8(U_74,U_75) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_7,plain,
( m2_relset_1(k20_ens_1(U_75,U_74),u2_cat_1(U_75),k2_ens_1(k17_ens_1(U_75)))
| ~ sP8(U_74,U_75) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_cat_1]) ).
fof(f_39_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_39_1]) ).
cnf(f_39_3,plain,
$true,
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_40_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_40_1]) ).
cnf(f_40_3,plain,
$true,
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A,B] :
( ! [C] :
( ( m2_relset_1(C,u2_cat_1(A),u2_cat_1(B))
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& v1_funct_1(C) )
| ~ m2_cat_1(C,A,B) )
| ~ l1_cat_1(B)
| ~ v2_cat_1(B)
| ~ l1_cat_1(A)
| ~ v2_cat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_m2_cat_1]) ).
fof(f_41_2,plain,
! [U_78,U_77] :
( ! [U_76] :
( ( m2_relset_1(U_76,u2_cat_1(U_78),u2_cat_1(U_77))
& v1_funct_2(U_76,u2_cat_1(U_78),u2_cat_1(U_77))
& v1_funct_1(U_76) )
| ~ m2_cat_1(U_76,U_78,U_77) )
| ~ l1_cat_1(U_77)
| ~ v2_cat_1(U_77)
| ~ l1_cat_1(U_78)
| ~ v2_cat_1(U_78) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_77,U_76,U_78] :
( m2_relset_1(U_76,u2_cat_1(U_78),u2_cat_1(U_77))
| ~ sP9(U_77,U_76,U_78) )
& ! [U_77,U_76,U_78] :
( v1_funct_2(U_76,u2_cat_1(U_78),u2_cat_1(U_77))
| ~ sP9(U_77,U_76,U_78) )
& ! [U_77,U_76,U_78] :
( v1_funct_1(U_76)
| ~ sP9(U_77,U_76,U_78) )
& ! [U_77,U_76,U_78] :
( sP9(U_77,U_76,U_78)
| ~ m2_cat_1(U_76,U_78,U_77)
| ~ l1_cat_1(U_77)
| ~ v2_cat_1(U_77)
| ~ l1_cat_1(U_78)
| ~ v2_cat_1(U_78) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_41_2]) ).
cnf(f_41_4,plain,
( sP9(U_77,U_76,U_78)
| ~ m2_cat_1(U_76,U_78,U_77)
| ~ l1_cat_1(U_77)
| ~ v2_cat_1(U_77)
| ~ l1_cat_1(U_78)
| ~ v2_cat_1(U_78) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
( v1_funct_1(U_76)
| ~ sP9(U_77,U_76,U_78) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_6,plain,
( v1_funct_2(U_76,u2_cat_1(U_78),u2_cat_1(U_77))
| ~ sP9(U_77,U_76,U_78) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_7,plain,
( m2_relset_1(U_76,u2_cat_1(U_78),u2_cat_1(U_77))
| ~ sP9(U_77,U_76,U_78) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A] :
( ~ v1_xboole_0(u1_cat_1(A))
| ~ l1_cat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_cat_1]) ).
fof(f_42_2,plain,
! [U_79] :
( ~ v1_xboole_0(u1_cat_1(U_79))
| ~ l1_cat_1(U_79) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_79] :
( ~ v1_xboole_0(u1_cat_1(U_79))
| ~ l1_cat_1(U_79) ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
( ~ v1_xboole_0(u1_cat_1(U_79))
| ~ l1_cat_1(U_79) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A] :
( v1_funct_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_43_2,plain,
! [U_80] :
( v1_funct_1(U_80)
| ~ v1_xboole_0(U_80) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_80] :
( v1_funct_1(U_80)
| ~ v1_xboole_0(U_80) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( v1_funct_1(U_80)
| ~ v1_xboole_0(U_80) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A] :
( ( v2_cat_1(k12_ens_1(A))
& v1_cat_1(k12_ens_1(A)) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[fc4_ens_1]) ).
fof(f_44_2,plain,
! [U_81] :
( ( v2_cat_1(k12_ens_1(U_81))
& v1_cat_1(k12_ens_1(U_81)) )
| v1_xboole_0(U_81) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ! [U_81] :
( v2_cat_1(k12_ens_1(U_81))
| ~ sP10(U_81) )
& ! [U_81] :
( v1_cat_1(k12_ens_1(U_81))
| ~ sP10(U_81) )
& ! [U_81] :
( sP10(U_81)
| v1_xboole_0(U_81) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_44_2]) ).
cnf(f_44_4,plain,
( sP10(U_81)
| v1_xboole_0(U_81) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_5,plain,
( v1_cat_1(k12_ens_1(U_81))
| ~ sP10(U_81) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_6,plain,
( v2_cat_1(k12_ens_1(U_81))
| ~ sP10(U_81) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A] :
( ~ v1_xboole_0(k17_ens_1(A))
| ~ l1_cat_1(A)
| ~ v2_cat_1(A) ),
inference(fof_nnf,[status(thm)],[fc5_ens_1]) ).
fof(f_45_2,plain,
! [U_82] :
( ~ v1_xboole_0(k17_ens_1(U_82))
| ~ l1_cat_1(U_82)
| ~ v2_cat_1(U_82) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_82] :
( ~ v1_xboole_0(k17_ens_1(U_82))
| ~ l1_cat_1(U_82)
| ~ v2_cat_1(U_82) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
( ~ v1_xboole_0(k17_ens_1(U_82))
| ~ l1_cat_1(U_82)
| ~ v2_cat_1(U_82) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_46_2,plain,
? [U_83] : v1_xboole_0(U_83),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
v1_xboole_0(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_83,sK11)],[f_46_2]) ).
fof(f_46_4,plain,
v1_xboole_0(sK11),
inference(definitional_conversion,[status(esa)],[f_46_3]) ).
cnf(f_46_5,plain,
v1_xboole_0(sK11),
inference(clausify,[status(thm)],[f_46_4]) ).
fof(f_47_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_47_2,plain,
? [U_84] : ~ v1_xboole_0(U_84),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
~ v1_xboole_0(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_84,sK12)],[f_47_2]) ).
fof(f_47_4,plain,
~ v1_xboole_0(sK12),
inference(definitional_conversion,[status(esa)],[f_47_3]) ).
cnf(f_47_5,plain,
~ v1_xboole_0(sK12),
inference(clausify,[status(thm)],[f_47_4]) ).
fof(f_48_1,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_48_2,plain,
! [U_86,U_85] :
( r2_hidden(U_86,U_85)
| v1_xboole_0(U_85)
| ~ m1_subset_1(U_86,U_85) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_86,U_85] :
( r2_hidden(U_86,U_85)
| v1_xboole_0(U_85)
| ~ m1_subset_1(U_86,U_85) ),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
( r2_hidden(U_86,U_85)
| v1_xboole_0(U_85)
| ~ m1_subset_1(U_86,U_85) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A,B] :
( ( m1_subset_1(A,k1_zfmisc_1(B))
| ~ r1_tarski(A,B) )
& ( r1_tarski(A,B)
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_49_2,plain,
! [U_88,U_87] :
( ( m1_subset_1(U_88,k1_zfmisc_1(U_87))
| ~ r1_tarski(U_88,U_87) )
& ( r1_tarski(U_88,U_87)
| ~ m1_subset_1(U_88,k1_zfmisc_1(U_87)) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_92,U_90] :
( m1_subset_1(U_92,k1_zfmisc_1(U_90))
| ~ r1_tarski(U_92,U_90) )
& ! [U_91,U_89] :
( r1_tarski(U_91,U_89)
| ~ m1_subset_1(U_91,k1_zfmisc_1(U_89)) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_92,U_90] :
( m1_subset_1(U_92,k1_zfmisc_1(U_90))
| ~ r1_tarski(U_92,U_90) )
& ! [U_91,U_89] :
( r1_tarski(U_91,U_89)
| ~ m1_subset_1(U_91,k1_zfmisc_1(U_89)) ) ),
inference(definitional_conversion,[status(esa)],[f_49_3]) ).
cnf(f_49_5,plain,
( r1_tarski(U_91,U_89)
| ~ m1_subset_1(U_91,k1_zfmisc_1(U_89)) ),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_6,plain,
( m1_subset_1(U_92,k1_zfmisc_1(U_90))
| ~ r1_tarski(U_92,U_90) ),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_50_2,plain,
! [U_93] :
( U_93 = k1_xboole_0
| ~ v1_xboole_0(U_93) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_93] :
( U_93 = k1_xboole_0
| ~ v1_xboole_0(U_93) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( U_93 = k1_xboole_0
| ~ v1_xboole_0(U_93) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_51_2,plain,
! [U_95,U_94] :
( ~ v1_xboole_0(U_94)
| ~ r2_hidden(U_95,U_94) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_94,U_95] :
( ~ v1_xboole_0(U_94)
| ~ r2_hidden(U_95,U_94) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( ~ v1_xboole_0(U_94)
| ~ r2_hidden(U_95,U_94) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [A] :
( k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))
| ~ l1_cat_1(A)
| ~ v2_cat_1(A) ),
inference(fof_nnf,[status(thm)],[d1_yoneda_1]) ).
fof(f_52_2,plain,
! [U_96] :
( k1_yoneda_1(U_96) = k12_ens_1(k17_ens_1(U_96))
| ~ l1_cat_1(U_96)
| ~ v2_cat_1(U_96) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_96] :
( k1_yoneda_1(U_96) = k12_ens_1(k17_ens_1(U_96))
| ~ l1_cat_1(U_96)
| ~ v2_cat_1(U_96) ),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
( k1_yoneda_1(U_96) = k12_ens_1(k17_ens_1(U_96))
| ~ l1_cat_1(U_96)
| ~ v2_cat_1(U_96) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( m2_cat_1(k20_ens_1(B,C),B,k12_ens_1(A))
| ~ r1_tarski(k17_ens_1(B),A)
| ~ m1_subset_1(C,u1_cat_1(B)) )
| ~ l1_cat_1(B)
| ~ v2_cat_1(B) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t49_ens_1]) ).
fof(f_53_2,plain,
! [U_99] :
( ! [U_98] :
( ! [U_97] :
( m2_cat_1(k20_ens_1(U_98,U_97),U_98,k12_ens_1(U_99))
| ~ r1_tarski(k17_ens_1(U_98),U_99)
| ~ m1_subset_1(U_97,u1_cat_1(U_98)) )
| ~ l1_cat_1(U_98)
| ~ v2_cat_1(U_98) )
| v1_xboole_0(U_99) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_97,U_98,U_99] :
( m2_cat_1(k20_ens_1(U_98,U_97),U_98,k12_ens_1(U_99))
| ~ r1_tarski(k17_ens_1(U_98),U_99)
| ~ m1_subset_1(U_97,u1_cat_1(U_98))
| ~ l1_cat_1(U_98)
| ~ v2_cat_1(U_98)
| v1_xboole_0(U_99) ),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
( m2_cat_1(k20_ens_1(U_98,U_97),U_98,k12_ens_1(U_99))
| ~ r1_tarski(k17_ens_1(U_98),U_99)
| ~ m1_subset_1(U_97,u1_cat_1(U_98))
| ~ l1_cat_1(U_98)
| ~ v2_cat_1(U_98)
| v1_xboole_0(U_99) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_3]) ).
cnf(f_10_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_3]) ).
cnf(f_20_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_3]) ).
cnf(f_21_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_3]) ).
cnf(f_22_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_22_3]) ).
cnf(f_36_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_36_3]) ).
cnf(f_39_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_39_3]) ).
cnf(f_40_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_40_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( u1_cat_1(Eq_x_0) = u1_cat_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k20_ens_1(Eq_x_0,Eq_x_1) = k20_ens_1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( k1_yoneda_1(Eq_x_0) = k1_yoneda_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( k2_zfmisc_1(Eq_x_0,Eq_x_1) = k2_zfmisc_1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( g1_cat_1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = g1_cat_1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( u3_cat_1(Eq_x_0) = u3_cat_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( u2_cat_1(Eq_x_0) = u2_cat_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( u4_cat_1(Eq_x_0) = u4_cat_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( u5_cat_1(Eq_x_0) = u5_cat_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( u6_cat_1(Eq_x_0) = u6_cat_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( k1_zfmisc_1(Eq_x_0) = k1_zfmisc_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( k2_ens_1(Eq_x_0) = k2_ens_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( k12_ens_1(Eq_x_0) = k12_ens_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( k17_ens_1(Eq_x_0) = k17_ens_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( v2_cat_1(Eq_y_0)
| ~ v2_cat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( l1_cat_1(Eq_y_0)
| ~ l1_cat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( m1_subset_1(Eq_y_0,Eq_y_1)
| ~ m1_subset_1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( m2_cat_1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m2_cat_1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( v1_relat_1(Eq_y_0)
| ~ v1_relat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( v1_funct_1(Eq_y_0)
| ~ v1_funct_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( v2_funct_1(Eq_y_0)
| ~ v2_funct_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( v1_xboole_0(Eq_y_0)
| ~ v1_xboole_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( v1_funct_2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ v1_funct_2(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( m1_relset_1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m1_relset_1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( v1_cat_1(Eq_y_0)
| ~ v1_cat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( m2_relset_1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m2_relset_1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( r2_hidden(Eq_y_0,Eq_y_1)
| ~ r2_hidden(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( r1_tarski(Eq_y_0,Eq_y_1)
| ~ r1_tarski(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10,Eq_y_11)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10,Eq_x_11)
| Eq_x_11 != Eq_y_11
| Eq_x_10 != Eq_y_10
| Eq_x_9 != Eq_y_9
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP3(Eq_y_0)
| ~ sP3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP7(Eq_y_0)
| ~ sP7(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sP10(Eq_y_0)
| ~ sP10(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT033+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 14:21:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 47.32/47.68 % SZS status Theorem for theBenchmark
% 47.32/47.68 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------