%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP640+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 : n008.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 08:42:07 AM UTC 2026
% Result : Theorem 136.05s 136.38s
% Output : Proof 136.64s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t13_latsubgr,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_group_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> ! [E] :
( ( m2_relset_1(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(E) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ( F = k2_xboole_0(u1_struct_0(C),u1_struct_0(D))
=> k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k8_group_4(A,C,D))) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k5_group_4(A,F))) ) ) ) ) ) ) ),
file('theBenchmark.p',t13_latsubgr) ).
fof(free_g1_group_1,axiom,
! [A,B] :
( ( m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(B) )
=> ! [C,D] :
( g1_group_1(A,B) = g1_group_1(C,D)
=> ( B = D
& A = C ) ) ),
file('theBenchmark.p',free_g1_group_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(dt_g1_group_1,axiom,
! [A,B] :
( ( m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(B) )
=> ( l1_group_1(g1_group_1(A,B))
& v1_group_1(g1_group_1(A,B)) ) ),
file('theBenchmark.p',dt_g1_group_1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_u1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> ( m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_group_1(A)) ) ),
file('theBenchmark.p',dt_u1_group_1) ).
fof(cc1_funct_2,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> ( ( v1_partfun1(C,A,B)
& v1_funct_1(C) )
=> ( v1_funct_2(C,A,B)
& v1_funct_1(C) ) ) ),
file('theBenchmark.p',cc1_funct_2) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
fof(rc1_funct_2,axiom,
! [A,B] :
? [C] :
( v1_funct_2(C,A,B)
& v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
file('theBenchmark.p',rc1_funct_2) ).
fof(rc2_partfun1,axiom,
! [A,B] :
? [C] :
( v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
file('theBenchmark.p',rc2_partfun1) ).
fof(t1_boole,axiom,
! [A] : k2_xboole_0(A,k1_xboole_0) = A,
file('theBenchmark.p',t1_boole) ).
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(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(abstractness_v1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> ( v1_group_1(A)
=> A = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ),
file('theBenchmark.p',abstractness_v1_group_1) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k9_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k9_relat_1) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_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(cc5_funct_2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_2(C,A,B)
& v1_funct_1(C) )
=> ( v1_funct_2(C,A,B)
& v1_partfun1(C,A,B)
& v1_funct_1(C) ) ) ) ),
file('theBenchmark.p',cc5_funct_2) ).
fof(cc6_funct_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(A) )
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_2(C,A,B)
& v1_funct_1(C) )
=> ( v1_funct_2(C,A,B)
& v1_partfun1(C,A,B)
& ~ v1_xboole_0(C)
& v1_funct_1(C) ) ) ) ),
file('theBenchmark.p',cc6_funct_2) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ v1_xboole_0(A)
=> ~ v1_xboole_0(k2_xboole_0(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ v1_xboole_0(A)
=> ~ v1_xboole_0(k2_xboole_0(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(A) )
=> ~ v1_xboole_0(k2_zfmisc_1(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc5_struct_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(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(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& A != B
& v1_xboole_0(A) ),
file('theBenchmark.p',t8_boole) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : k2_xboole_0(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(symmetry_r1_group_2,axiom,
! [A,B,C] :
( ( m1_group_2(C,A)
& v1_group_1(C)
& m1_group_2(B,A)
& v1_group_1(B)
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( r1_group_2(A,B,C)
=> r1_group_2(A,C,B) ) ),
file('theBenchmark.p',symmetry_r1_group_2) ).
fof(reflexivity_r1_group_2,axiom,
! [A,B,C] :
( ( m1_group_2(C,A)
& v1_group_1(C)
& m1_group_2(B,A)
& v1_group_1(B)
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> r1_group_2(A,B,B) ),
file('theBenchmark.p',reflexivity_r1_group_2) ).
fof(existence_l1_group_1,axiom,
? [A] : l1_group_1(A),
file('theBenchmark.p',existence_l1_group_1) ).
fof(existence_m1_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ? [B] : m1_group_2(B,A) ),
file('theBenchmark.p',existence_m1_group_2) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_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_k2_funct_2,axiom,
! [A,B,C,D] :
( ( m1_relset_1(C,A,B)
& v1_funct_2(C,A,B)
& v1_funct_1(C) )
=> k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ),
file('theBenchmark.p',redefinition_k2_funct_2) ).
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(redefinition_r1_group_2,axiom,
! [A,B,C] :
( ( m1_group_2(C,A)
& v1_group_1(C)
& m1_group_2(B,A)
& v1_group_1(B)
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( r1_group_2(A,B,C)
<=> B = C ) ),
file('theBenchmark.p',redefinition_r1_group_2) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_funct_2,axiom,
! [A,B,C,D] :
( ( m1_relset_1(C,A,B)
& v1_funct_2(C,A,B)
& v1_funct_1(C) )
=> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ),
file('theBenchmark.p',dt_k2_funct_2) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_k5_group_4,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( m1_group_2(k5_group_4(A,B),A)
& v1_group_1(k5_group_4(A,B)) ) ),
file('theBenchmark.p',dt_k5_group_4) ).
fof(dt_k8_group_4,axiom,
! [A,B,C] :
( ( m1_group_2(C,A)
& m1_group_2(B,A)
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( m1_group_2(k8_group_4(A,B,C),A)
& v1_group_1(k8_group_4(A,B,C)) ) ),
file('theBenchmark.p',dt_k8_group_4) ).
fof(dt_l1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_group_1) ).
fof(dt_m1_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) ) ) ),
file('theBenchmark.p',dt_m1_group_2) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_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_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_latsubgr,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( m1_group_2(C,A)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( D = k2_xboole_0(u1_struct_0(B),u1_struct_0(C))
=> r1_group_2(A,k8_group_4(A,B,C),k5_group_4(A,D)) ) ) ) ) ),
file('theBenchmark.p',t4_latsubgr) ).
fof(f_1_1,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_group_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> ! [E] :
( ( m2_relset_1(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(E) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ( F = k2_xboole_0(u1_struct_0(C),u1_struct_0(D))
=> k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k8_group_4(A,C,D))) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k5_group_4(A,F))) ) ) ) ) ) ) ),
inference(negate,[status(cth)],[t13_latsubgr]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k8_group_4(A,C,D))) != k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k5_group_4(A,F)))
& F = k2_xboole_0(u1_struct_0(C),u1_struct_0(D))
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) )
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(E) )
& m1_group_2(D,A) )
& m1_group_2(C,A) )
& l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_5] :
( ? [U_4] :
( ? [U_3] :
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( k2_funct_2(u1_struct_0(U_5),u1_struct_0(U_4),U_1,u1_struct_0(k8_group_4(U_5,U_3,U_2))) != k2_funct_2(u1_struct_0(U_5),u1_struct_0(U_4),U_1,u1_struct_0(k5_group_4(U_5,U_0)))
& U_0 = k2_xboole_0(u1_struct_0(U_3),u1_struct_0(U_2))
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(U_5))) )
& m2_relset_1(U_1,u1_struct_0(U_5),u1_struct_0(U_4))
& v1_funct_2(U_1,u1_struct_0(U_5),u1_struct_0(U_4))
& v1_funct_1(U_1) )
& m1_group_2(U_2,U_5) )
& m1_group_2(U_3,U_5) )
& l1_group_1(U_4)
& v4_group_1(U_4)
& v3_group_1(U_4)
& ~ v3_struct_0(U_4) )
& l1_group_1(U_5)
& v4_group_1(U_5)
& v3_group_1(U_5)
& ~ v3_struct_0(U_5) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_4] :
( ? [U_3] :
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( k2_funct_2(u1_struct_0(sK1),u1_struct_0(U_4),U_1,u1_struct_0(k8_group_4(sK1,U_3,U_2))) != k2_funct_2(u1_struct_0(sK1),u1_struct_0(U_4),U_1,u1_struct_0(k5_group_4(sK1,U_0)))
& U_0 = k2_xboole_0(u1_struct_0(U_3),u1_struct_0(U_2))
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(sK1))) )
& m2_relset_1(U_1,u1_struct_0(sK1),u1_struct_0(U_4))
& v1_funct_2(U_1,u1_struct_0(sK1),u1_struct_0(U_4))
& v1_funct_1(U_1) )
& m1_group_2(U_2,sK1) )
& m1_group_2(U_3,sK1) )
& l1_group_1(U_4)
& v4_group_1(U_4)
& v3_group_1(U_4)
& ~ v3_struct_0(U_4) )
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_3] :
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),U_1,u1_struct_0(k8_group_4(sK1,U_3,U_2))) != k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),U_1,u1_struct_0(k5_group_4(sK1,U_0)))
& U_0 = k2_xboole_0(u1_struct_0(U_3),u1_struct_0(U_2))
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(sK1))) )
& m2_relset_1(U_1,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_2(U_1,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_1(U_1) )
& m1_group_2(U_2,sK1) )
& m1_group_2(U_3,sK1) )
& l1_group_1(sK2)
& v4_group_1(sK2)
& v3_group_1(sK2)
& ~ v3_struct_0(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),U_1,u1_struct_0(k8_group_4(sK1,sK3,U_2))) != k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),U_1,u1_struct_0(k5_group_4(sK1,U_0)))
& U_0 = k2_xboole_0(u1_struct_0(sK3),u1_struct_0(U_2))
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(sK1))) )
& m2_relset_1(U_1,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_2(U_1,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_1(U_1) )
& m1_group_2(U_2,sK1) )
& m1_group_2(sK3,sK1)
& l1_group_1(sK2)
& v4_group_1(sK2)
& v3_group_1(sK2)
& ~ v3_struct_0(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_3,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ? [U_1] :
( ? [U_0] :
( k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),U_1,u1_struct_0(k8_group_4(sK1,sK3,sK4))) != k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),U_1,u1_struct_0(k5_group_4(sK1,U_0)))
& U_0 = k2_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(sK1))) )
& m2_relset_1(U_1,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_2(U_1,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_1(U_1) )
& m1_group_2(sK4,sK1)
& m1_group_2(sK3,sK1)
& l1_group_1(sK2)
& v4_group_1(sK2)
& v3_group_1(sK2)
& ~ v3_struct_0(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_2,sK4)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ? [U_0] :
( k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),sK5,u1_struct_0(k8_group_4(sK1,sK3,sK4))) != k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),sK5,u1_struct_0(k5_group_4(sK1,U_0)))
& U_0 = k2_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(sK1))) )
& m2_relset_1(sK5,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_2(sK5,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_1(sK5)
& m1_group_2(sK4,sK1)
& m1_group_2(sK3,sK1)
& l1_group_1(sK2)
& v4_group_1(sK2)
& v3_group_1(sK2)
& ~ v3_struct_0(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_1,sK5)],[f_1_7]) ).
fof(f_1_9,negated_conjecture,
( k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),sK5,u1_struct_0(k8_group_4(sK1,sK3,sK4))) != k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),sK5,u1_struct_0(k5_group_4(sK1,sK6)))
& sK6 = k2_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))
& m1_subset_1(sK6,k1_zfmisc_1(u1_struct_0(sK1)))
& m2_relset_1(sK5,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_2(sK5,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_1(sK5)
& m1_group_2(sK4,sK1)
& m1_group_2(sK3,sK1)
& l1_group_1(sK2)
& v4_group_1(sK2)
& v3_group_1(sK2)
& ~ v3_struct_0(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_0,sK6)],[f_1_8]) ).
fof(f_1_10,negated_conjecture,
( k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),sK5,u1_struct_0(k8_group_4(sK1,sK3,sK4))) != k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),sK5,u1_struct_0(k5_group_4(sK1,sK6)))
& sK6 = k2_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))
& m1_subset_1(sK6,k1_zfmisc_1(u1_struct_0(sK1)))
& m2_relset_1(sK5,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_2(sK5,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_1(sK5)
& m1_group_2(sK4,sK1)
& m1_group_2(sK3,sK1)
& l1_group_1(sK2)
& v4_group_1(sK2)
& v3_group_1(sK2)
& ~ v3_struct_0(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(definitional_conversion,[status(esa)],[f_1_9]) ).
cnf(f_1_11,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_12,negated_conjecture,
v3_group_1(sK1),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_13,negated_conjecture,
v4_group_1(sK1),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_14,negated_conjecture,
l1_group_1(sK1),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_15,negated_conjecture,
~ v3_struct_0(sK2),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_16,negated_conjecture,
v3_group_1(sK2),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_17,negated_conjecture,
v4_group_1(sK2),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_18,negated_conjecture,
l1_group_1(sK2),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_19,negated_conjecture,
m1_group_2(sK3,sK1),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_20,negated_conjecture,
m1_group_2(sK4,sK1),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_21,negated_conjecture,
v1_funct_1(sK5),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_22,negated_conjecture,
v1_funct_2(sK5,u1_struct_0(sK1),u1_struct_0(sK2)),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_23,negated_conjecture,
m2_relset_1(sK5,u1_struct_0(sK1),u1_struct_0(sK2)),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_24,negated_conjecture,
m1_subset_1(sK6,k1_zfmisc_1(u1_struct_0(sK1))),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_25,negated_conjecture,
sK6 = k2_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_26,negated_conjecture,
k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),sK5,u1_struct_0(k8_group_4(sK1,sK3,sK4))) != k2_funct_2(u1_struct_0(sK1),u1_struct_0(sK2),sK5,u1_struct_0(k5_group_4(sK1,sK6))),
inference(clausify,[status(thm)],[f_1_10]) ).
fof(f_2_1,plain,
! [A,B] :
( ! [C,D] :
( ( B = D
& A = C )
| g1_group_1(A,B) != g1_group_1(C,D) )
| ~ m1_relset_1(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(B) ),
inference(fof_nnf,[status(thm)],[free_g1_group_1]) ).
fof(f_2_2,plain,
! [U_9,U_8] :
( ! [U_7,U_6] :
( ( U_8 = U_6
& U_9 = U_7 )
| g1_group_1(U_9,U_8) != g1_group_1(U_7,U_6) )
| ~ m1_relset_1(U_8,k2_zfmisc_1(U_9,U_9),U_9)
| ~ v1_funct_2(U_8,k2_zfmisc_1(U_9,U_9),U_9)
| ~ v1_funct_1(U_8) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( U_9 = U_7
| g1_group_1(U_9,U_8) != g1_group_1(U_7,U_6)
| ~ m1_relset_1(U_8,k2_zfmisc_1(U_9,U_9),U_9)
| ~ v1_funct_2(U_8,k2_zfmisc_1(U_9,U_9),U_9)
| ~ v1_funct_1(U_8) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( U_8 = U_6
| g1_group_1(U_9,U_8) != g1_group_1(U_7,U_6)
| ~ m1_relset_1(U_8,k2_zfmisc_1(U_9,U_9),U_9)
| ~ v1_funct_2(U_8,k2_zfmisc_1(U_9,U_9),U_9)
| ~ v1_funct_1(U_8) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_3_2,plain,
! [U_11,U_10] :
( ~ r2_hidden(U_10,U_11)
| ~ r2_hidden(U_11,U_10) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ r2_hidden(U_10,U_11)
| ~ r2_hidden(U_11,U_10) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] :
( ( l1_group_1(g1_group_1(A,B))
& v1_group_1(g1_group_1(A,B)) )
| ~ m1_relset_1(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(B) ),
inference(fof_nnf,[status(thm)],[dt_g1_group_1]) ).
fof(f_4_2,plain,
! [U_13,U_12] :
( ( l1_group_1(g1_group_1(U_13,U_12))
& v1_group_1(g1_group_1(U_13,U_12)) )
| ~ m1_relset_1(U_12,k2_zfmisc_1(U_13,U_13),U_13)
| ~ v1_funct_2(U_12,k2_zfmisc_1(U_13,U_13),U_13)
| ~ v1_funct_1(U_12) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v1_group_1(g1_group_1(U_13,U_12))
| ~ m1_relset_1(U_12,k2_zfmisc_1(U_13,U_13),U_13)
| ~ v1_funct_2(U_12,k2_zfmisc_1(U_13,U_13),U_13)
| ~ v1_funct_1(U_12) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( l1_group_1(g1_group_1(U_13,U_12))
| ~ m1_relset_1(U_12,k2_zfmisc_1(U_13,U_13),U_13)
| ~ v1_funct_2(U_12,k2_zfmisc_1(U_13,U_13),U_13)
| ~ v1_funct_1(U_12) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
! [A] :
( ( m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_group_1(A)) )
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_group_1]) ).
fof(f_6_2,plain,
! [U_14] :
( ( m2_relset_1(u1_group_1(U_14),k2_zfmisc_1(u1_struct_0(U_14),u1_struct_0(U_14)),u1_struct_0(U_14))
& v1_funct_2(u1_group_1(U_14),k2_zfmisc_1(u1_struct_0(U_14),u1_struct_0(U_14)),u1_struct_0(U_14))
& v1_funct_1(u1_group_1(U_14)) )
| ~ l1_group_1(U_14) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( v1_funct_1(u1_group_1(U_14))
| ~ l1_group_1(U_14) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( v1_funct_2(u1_group_1(U_14),k2_zfmisc_1(u1_struct_0(U_14),u1_struct_0(U_14)),u1_struct_0(U_14))
| ~ l1_group_1(U_14) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( m2_relset_1(u1_group_1(U_14),k2_zfmisc_1(u1_struct_0(U_14),u1_struct_0(U_14)),u1_struct_0(U_14))
| ~ l1_group_1(U_14) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B,C] :
( ( v1_funct_2(C,A,B)
& v1_funct_1(C) )
| ~ v1_partfun1(C,A,B)
| ~ v1_funct_1(C)
| ~ m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[cc1_funct_2]) ).
fof(f_7_2,plain,
! [U_17,U_16,U_15] :
( ( v1_funct_2(U_15,U_17,U_16)
& v1_funct_1(U_15) )
| ~ v1_partfun1(U_15,U_17,U_16)
| ~ v1_funct_1(U_15)
| ~ m1_relset_1(U_15,U_17,U_16) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( v1_funct_1(U_15)
| ~ v1_partfun1(U_15,U_17,U_16)
| ~ v1_funct_1(U_15)
| ~ m1_relset_1(U_15,U_17,U_16) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( v1_funct_2(U_15,U_17,U_16)
| ~ v1_partfun1(U_15,U_17,U_16)
| ~ v1_funct_1(U_15)
| ~ m1_relset_1(U_15,U_17,U_16) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_8_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
! [A,B] :
? [C] :
( v1_funct_2(C,A,B)
& v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[rc1_funct_2]) ).
fof(f_9_2,plain,
! [U_20,U_19] :
? [U_18] :
( v1_funct_2(U_18,U_20,U_19)
& v1_funct_1(U_18)
& v1_relat_1(U_18)
& m1_relset_1(U_18,U_20,U_19) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_20,U_19] :
( v1_funct_2(sK7(U_20,U_19),U_20,U_19)
& v1_funct_1(sK7(U_20,U_19))
& v1_relat_1(sK7(U_20,U_19))
& m1_relset_1(sK7(U_20,U_19),U_20,U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_18,sK7(U_20,U_19))],[f_9_2]) ).
cnf(f_9_4,plain,
m1_relset_1(sK7(U_20,U_19),U_20,U_19),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
v1_relat_1(sK7(U_20,U_19)),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
v1_funct_1(sK7(U_20,U_19)),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_7,plain,
v1_funct_2(sK7(U_20,U_19),U_20,U_19),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B] :
? [C] :
( v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[rc2_partfun1]) ).
fof(f_10_2,plain,
! [U_23,U_22] :
? [U_21] :
( v1_funct_1(U_21)
& v1_relat_1(U_21)
& m1_relset_1(U_21,U_23,U_22) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_23,U_22] :
( v1_funct_1(sK8(U_23,U_22))
& v1_relat_1(sK8(U_23,U_22))
& m1_relset_1(sK8(U_23,U_22),U_23,U_22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_21,sK8(U_23,U_22))],[f_10_2]) ).
cnf(f_10_4,plain,
m1_relset_1(sK8(U_23,U_22),U_23,U_22),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
v1_relat_1(sK8(U_23,U_22)),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
v1_funct_1(sK8(U_23,U_22)),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] : k2_xboole_0(A,k1_xboole_0) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_11_2,plain,
! [U_24] : k2_xboole_0(U_24,k1_xboole_0) = U_24,
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
k2_xboole_0(U_24,k1_xboole_0) = U_24,
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_12_2,plain,
! [U_26,U_25] :
( m1_subset_1(U_26,U_25)
| ~ r2_hidden(U_26,U_25) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( m1_subset_1(U_26,U_25)
| ~ r2_hidden(U_26,U_25) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_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_13_2,plain,
! [U_29,U_28,U_27] :
( m1_subset_1(U_29,U_27)
| ~ m1_subset_1(U_28,k1_zfmisc_1(U_27))
| ~ r2_hidden(U_29,U_28) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( m1_subset_1(U_29,U_27)
| ~ m1_subset_1(U_28,k1_zfmisc_1(U_27))
| ~ r2_hidden(U_29,U_28) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_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_14_2,plain,
! [U_32,U_31,U_30] :
( ~ v1_xboole_0(U_30)
| ~ m1_subset_1(U_31,k1_zfmisc_1(U_30))
| ~ r2_hidden(U_32,U_31) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_32,U_31] :
( ! [U_30] :
( ~ v1_xboole_0(U_30)
| ~ m1_subset_1(U_31,k1_zfmisc_1(U_30)) )
| ~ r2_hidden(U_32,U_31) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( ~ v1_xboole_0(U_30)
| ~ m1_subset_1(U_31,k1_zfmisc_1(U_30))
| ~ r2_hidden(U_32,U_31) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_15_2,plain,
! [U_34,U_33] : r1_tarski(U_34,U_34),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_34] : r1_tarski(U_34,U_34),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
r1_tarski(U_34,U_34),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A] :
( A = g1_group_1(u1_struct_0(A),u1_group_1(A))
| ~ v1_group_1(A)
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[abstractness_v1_group_1]) ).
fof(f_16_2,plain,
! [U_35] :
( U_35 = g1_group_1(u1_struct_0(U_35),u1_group_1(U_35))
| ~ v1_group_1(U_35)
| ~ l1_group_1(U_35) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( U_35 = g1_group_1(u1_struct_0(U_35),u1_group_1(U_35))
| ~ v1_group_1(U_35)
| ~ l1_group_1(U_35) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_17_2,plain,
? [U_36] : l1_struct_0(U_36),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
l1_struct_0(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_36,sK9)],[f_17_2]) ).
cnf(f_17_4,plain,
l1_struct_0(sK9),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_18_2,plain,
! [U_39,U_38] :
? [U_37] : m1_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] : m1_relset_1(sK10(U_39,U_38),U_39,U_38),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_37,sK10(U_39,U_38))],[f_18_2]) ).
cnf(f_18_4,plain,
m1_relset_1(sK10(U_39,U_38),U_39,U_38),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_19_2,plain,
$true,
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_21_2,plain,
$true,
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_22_2,plain,
$true,
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_23_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_23_2,plain,
! [U_42,U_41,U_40] :
( v1_relat_1(U_40)
| ~ m1_subset_1(U_40,k1_zfmisc_1(k2_zfmisc_1(U_42,U_41))) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( v1_relat_1(U_40)
| ~ m1_subset_1(U_40,k1_zfmisc_1(k2_zfmisc_1(U_42,U_41))) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B] :
( ! [C] :
( ( v1_funct_2(C,A,B)
& v1_partfun1(C,A,B)
& v1_funct_1(C) )
| ~ v1_funct_2(C,A,B)
| ~ v1_funct_1(C)
| ~ m1_relset_1(C,A,B) )
| v1_xboole_0(B) ),
inference(fof_nnf,[status(thm)],[cc5_funct_2]) ).
fof(f_24_2,plain,
! [U_45,U_44] :
( ! [U_43] :
( ( v1_funct_2(U_43,U_45,U_44)
& v1_partfun1(U_43,U_45,U_44)
& v1_funct_1(U_43) )
| ~ v1_funct_2(U_43,U_45,U_44)
| ~ v1_funct_1(U_43)
| ~ m1_relset_1(U_43,U_45,U_44) )
| v1_xboole_0(U_44) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( v1_funct_1(U_43)
| ~ v1_funct_2(U_43,U_45,U_44)
| ~ v1_funct_1(U_43)
| ~ m1_relset_1(U_43,U_45,U_44)
| v1_xboole_0(U_44) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( v1_partfun1(U_43,U_45,U_44)
| ~ v1_funct_2(U_43,U_45,U_44)
| ~ v1_funct_1(U_43)
| ~ m1_relset_1(U_43,U_45,U_44)
| v1_xboole_0(U_44) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_5,plain,
( v1_funct_2(U_43,U_45,U_44)
| ~ v1_funct_2(U_43,U_45,U_44)
| ~ v1_funct_1(U_43)
| ~ m1_relset_1(U_43,U_45,U_44)
| v1_xboole_0(U_44) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A,B] :
( ! [C] :
( ( v1_funct_2(C,A,B)
& v1_partfun1(C,A,B)
& ~ v1_xboole_0(C)
& v1_funct_1(C) )
| ~ v1_funct_2(C,A,B)
| ~ v1_funct_1(C)
| ~ m1_relset_1(C,A,B) )
| v1_xboole_0(B)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc6_funct_2]) ).
fof(f_25_2,plain,
! [U_48,U_47] :
( ! [U_46] :
( ( v1_funct_2(U_46,U_48,U_47)
& v1_partfun1(U_46,U_48,U_47)
& ~ v1_xboole_0(U_46)
& v1_funct_1(U_46) )
| ~ v1_funct_2(U_46,U_48,U_47)
| ~ v1_funct_1(U_46)
| ~ m1_relset_1(U_46,U_48,U_47) )
| v1_xboole_0(U_47)
| v1_xboole_0(U_48) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( v1_funct_1(U_46)
| ~ v1_funct_2(U_46,U_48,U_47)
| ~ v1_funct_1(U_46)
| ~ m1_relset_1(U_46,U_48,U_47)
| v1_xboole_0(U_47)
| v1_xboole_0(U_48) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( ~ v1_xboole_0(U_46)
| ~ v1_funct_2(U_46,U_48,U_47)
| ~ v1_funct_1(U_46)
| ~ m1_relset_1(U_46,U_48,U_47)
| v1_xboole_0(U_47)
| v1_xboole_0(U_48) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_5,plain,
( v1_partfun1(U_46,U_48,U_47)
| ~ v1_funct_2(U_46,U_48,U_47)
| ~ v1_funct_1(U_46)
| ~ m1_relset_1(U_46,U_48,U_47)
| v1_xboole_0(U_47)
| v1_xboole_0(U_48) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_6,plain,
( v1_funct_2(U_46,U_48,U_47)
| ~ v1_funct_2(U_46,U_48,U_47)
| ~ v1_funct_1(U_46)
| ~ m1_relset_1(U_46,U_48,U_47)
| v1_xboole_0(U_47)
| v1_xboole_0(U_48) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_26_2,plain,
! [U_49] :
( ~ v1_xboole_0(u1_struct_0(U_49))
| ~ l1_struct_0(U_49)
| v3_struct_0(U_49) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_49))
| ~ l1_struct_0(U_49)
| v3_struct_0(U_49) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A,B] :
( ~ v1_xboole_0(k2_xboole_0(A,B))
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_27_2,plain,
! [U_51,U_50] :
( ~ v1_xboole_0(k2_xboole_0(U_51,U_50))
| v1_xboole_0(U_51) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_51] :
( ! [U_50] : ~ v1_xboole_0(k2_xboole_0(U_51,U_50))
| v1_xboole_0(U_51) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( ~ v1_xboole_0(k2_xboole_0(U_51,U_50))
| v1_xboole_0(U_51) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A,B] :
( ~ v1_xboole_0(k2_xboole_0(B,A))
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_28_2,plain,
! [U_53,U_52] :
( ~ v1_xboole_0(k2_xboole_0(U_52,U_53))
| v1_xboole_0(U_53) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_53] :
( ! [U_52] : ~ v1_xboole_0(k2_xboole_0(U_52,U_53))
| v1_xboole_0(U_53) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( ~ v1_xboole_0(k2_xboole_0(U_52,U_53))
| v1_xboole_0(U_53) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B] :
( ~ v1_xboole_0(k2_zfmisc_1(A,B))
| v1_xboole_0(B)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_29_2,plain,
! [U_55,U_54] :
( ~ v1_xboole_0(k2_zfmisc_1(U_55,U_54))
| v1_xboole_0(U_54)
| v1_xboole_0(U_55) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( ~ v1_xboole_0(k2_zfmisc_1(U_55,U_54))
| v1_xboole_0(U_54)
| v1_xboole_0(U_55) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_30_2,plain,
! [U_57] :
( ? [U_56] :
( ~ v1_xboole_0(U_56)
& m1_subset_1(U_56,k1_zfmisc_1(U_57)) )
| v1_xboole_0(U_57) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_57] :
( ( ~ v1_xboole_0(sK11(U_57))
& m1_subset_1(sK11(U_57),k1_zfmisc_1(U_57)) )
| v1_xboole_0(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_56,sK11(U_57))],[f_30_2]) ).
cnf(f_30_4,plain,
( m1_subset_1(sK11(U_57),k1_zfmisc_1(U_57))
| v1_xboole_0(U_57) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( ~ v1_xboole_0(sK11(U_57))
| v1_xboole_0(U_57) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_31_2,plain,
? [U_58] : v1_xboole_0(U_58),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
v1_xboole_0(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_58,sK12)],[f_31_2]) ).
cnf(f_31_4,plain,
v1_xboole_0(sK12),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_32_2,plain,
! [U_60] :
? [U_59] :
( v1_xboole_0(U_59)
& m1_subset_1(U_59,k1_zfmisc_1(U_60)) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_60] :
( v1_xboole_0(sK13(U_60))
& m1_subset_1(sK13(U_60),k1_zfmisc_1(U_60)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_59,sK13(U_60))],[f_32_2]) ).
cnf(f_32_4,plain,
m1_subset_1(sK13(U_60),k1_zfmisc_1(U_60)),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
v1_xboole_0(sK13(U_60)),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_33_2,plain,
? [U_61] : ~ v1_xboole_0(U_61),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
~ v1_xboole_0(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_61,sK14)],[f_33_2]) ).
cnf(f_33_4,plain,
~ v1_xboole_0(sK14),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_34_2,plain,
? [U_62] :
( ~ v3_struct_0(U_62)
& l1_struct_0(U_62) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ~ v3_struct_0(sK15)
& l1_struct_0(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_62,sK15)],[f_34_2]) ).
cnf(f_34_4,plain,
l1_struct_0(sK15),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
~ v3_struct_0(sK15),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc5_struct_0]) ).
fof(f_35_2,plain,
! [U_64] :
( ? [U_63] :
( ~ v1_xboole_0(U_63)
& m1_subset_1(U_63,k1_zfmisc_1(u1_struct_0(U_64))) )
| ~ l1_struct_0(U_64)
| v3_struct_0(U_64) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_64] :
( ( ~ v1_xboole_0(sK16(U_64))
& m1_subset_1(sK16(U_64),k1_zfmisc_1(u1_struct_0(U_64))) )
| ~ l1_struct_0(U_64)
| v3_struct_0(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_63,sK16(U_64))],[f_35_2]) ).
cnf(f_35_4,plain,
( m1_subset_1(sK16(U_64),k1_zfmisc_1(u1_struct_0(U_64)))
| ~ l1_struct_0(U_64)
| v3_struct_0(U_64) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( ~ v1_xboole_0(sK16(U_64))
| ~ l1_struct_0(U_64)
| v3_struct_0(U_64) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_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_36_2,plain,
! [U_66,U_65] :
( r2_hidden(U_66,U_65)
| v1_xboole_0(U_65)
| ~ m1_subset_1(U_66,U_65) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( r2_hidden(U_66,U_65)
| v1_xboole_0(U_65)
| ~ m1_subset_1(U_66,U_65) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_37_2,plain,
! [U_67] :
( U_67 = k1_xboole_0
| ~ v1_xboole_0(U_67) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( U_67 = k1_xboole_0
| ~ v1_xboole_0(U_67) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_38_2,plain,
! [U_69,U_68] :
( ~ v1_xboole_0(U_68)
| ~ r2_hidden(U_69,U_68) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( ~ v1_xboole_0(U_68)
| ~ r2_hidden(U_69,U_68) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_39_2,plain,
! [U_71,U_70] :
( ~ v1_xboole_0(U_70)
| U_71 = U_70
| ~ v1_xboole_0(U_71) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_71] :
( ! [U_70] :
( ~ v1_xboole_0(U_70)
| U_71 = U_70 )
| ~ v1_xboole_0(U_71) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( ~ v1_xboole_0(U_70)
| U_71 = U_70
| ~ v1_xboole_0(U_71) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_40_2,plain,
! [U_73,U_72] : k2_xboole_0(U_73,U_72) = k2_xboole_0(U_72,U_73),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
k2_xboole_0(U_73,U_72) = k2_xboole_0(U_72,U_73),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A,B] : k2_xboole_0(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_41_2,plain,
! [U_75,U_74] : k2_xboole_0(U_75,U_75) = U_75,
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_75] : k2_xboole_0(U_75,U_75) = U_75,
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
k2_xboole_0(U_75,U_75) = U_75,
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B,C] :
( r1_group_2(A,C,B)
| ~ r1_group_2(A,B,C)
| ~ m1_group_2(C,A)
| ~ v1_group_1(C)
| ~ m1_group_2(B,A)
| ~ v1_group_1(B)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_group_2]) ).
fof(f_42_2,plain,
! [U_78,U_77,U_76] :
( r1_group_2(U_78,U_76,U_77)
| ~ r1_group_2(U_78,U_77,U_76)
| ~ m1_group_2(U_76,U_78)
| ~ v1_group_1(U_76)
| ~ m1_group_2(U_77,U_78)
| ~ v1_group_1(U_77)
| ~ l1_group_1(U_78)
| ~ v4_group_1(U_78)
| ~ v3_group_1(U_78)
| v3_struct_0(U_78) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( r1_group_2(U_78,U_76,U_77)
| ~ r1_group_2(U_78,U_77,U_76)
| ~ m1_group_2(U_76,U_78)
| ~ v1_group_1(U_76)
| ~ m1_group_2(U_77,U_78)
| ~ v1_group_1(U_77)
| ~ l1_group_1(U_78)
| ~ v4_group_1(U_78)
| ~ v3_group_1(U_78)
| v3_struct_0(U_78) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A,B,C] :
( r1_group_2(A,B,B)
| ~ m1_group_2(C,A)
| ~ v1_group_1(C)
| ~ m1_group_2(B,A)
| ~ v1_group_1(B)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_group_2]) ).
fof(f_43_2,plain,
! [U_81,U_80,U_79] :
( r1_group_2(U_81,U_80,U_80)
| ~ m1_group_2(U_79,U_81)
| ~ v1_group_1(U_79)
| ~ m1_group_2(U_80,U_81)
| ~ v1_group_1(U_80)
| ~ l1_group_1(U_81)
| ~ v4_group_1(U_81)
| ~ v3_group_1(U_81)
| v3_struct_0(U_81) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_81,U_80] :
( ! [U_79] :
( ~ m1_group_2(U_79,U_81)
| ~ v1_group_1(U_79) )
| ~ m1_group_2(U_80,U_81)
| ~ v1_group_1(U_80)
| ~ l1_group_1(U_81)
| ~ v4_group_1(U_81)
| ~ v3_group_1(U_81)
| v3_struct_0(U_81)
| r1_group_2(U_81,U_80,U_80) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( ~ m1_group_2(U_79,U_81)
| ~ v1_group_1(U_79)
| ~ m1_group_2(U_80,U_81)
| ~ v1_group_1(U_80)
| ~ l1_group_1(U_81)
| ~ v4_group_1(U_81)
| ~ v3_group_1(U_81)
| v3_struct_0(U_81)
| r1_group_2(U_81,U_80,U_80) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
? [A] : l1_group_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_group_1]) ).
fof(f_44_2,plain,
? [U_82] : l1_group_1(U_82),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
l1_group_1(sK17),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_82,sK17)],[f_44_2]) ).
cnf(f_44_4,plain,
l1_group_1(sK17),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A] :
( ? [B] : m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m1_group_2]) ).
fof(f_45_2,plain,
! [U_84] :
( ? [U_83] : m1_group_2(U_83,U_84)
| ~ l1_group_1(U_84)
| ~ v3_group_1(U_84)
| v3_struct_0(U_84) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_84] :
( m1_group_2(sK18(U_84),U_84)
| ~ l1_group_1(U_84)
| ~ v3_group_1(U_84)
| v3_struct_0(U_84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_83,sK18(U_84))],[f_45_2]) ).
cnf(f_45_4,plain,
( m1_group_2(sK18(U_84),U_84)
| ~ l1_group_1(U_84)
| ~ v3_group_1(U_84)
| v3_struct_0(U_84) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_46_2,plain,
! [U_86] :
? [U_85] : m1_subset_1(U_85,U_86),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_86] : m1_subset_1(sK19(U_86),U_86),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_85,sK19(U_86))],[f_46_2]) ).
cnf(f_46_4,plain,
m1_subset_1(sK19(U_86),U_86),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_47_2,plain,
! [U_89,U_88] :
? [U_87] : m2_relset_1(U_87,U_89,U_88),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_89,U_88] : m2_relset_1(sK20(U_89,U_88),U_89,U_88),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_87,sK20(U_89,U_88))],[f_47_2]) ).
cnf(f_47_4,plain,
m2_relset_1(sK20(U_89,U_88),U_89,U_88),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A,B,C,D] :
( k2_funct_2(A,B,C,D) = k9_relat_1(C,D)
| ~ m1_relset_1(C,A,B)
| ~ v1_funct_2(C,A,B)
| ~ v1_funct_1(C) ),
inference(fof_nnf,[status(thm)],[redefinition_k2_funct_2]) ).
fof(f_48_2,plain,
! [U_93,U_92,U_91,U_90] :
( k2_funct_2(U_93,U_92,U_91,U_90) = k9_relat_1(U_91,U_90)
| ~ m1_relset_1(U_91,U_93,U_92)
| ~ v1_funct_2(U_91,U_93,U_92)
| ~ v1_funct_1(U_91) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_93,U_92,U_91] :
( ! [U_90] : k2_funct_2(U_93,U_92,U_91,U_90) = k9_relat_1(U_91,U_90)
| ~ m1_relset_1(U_91,U_93,U_92)
| ~ v1_funct_2(U_91,U_93,U_92)
| ~ v1_funct_1(U_91) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
cnf(f_48_4,plain,
( k2_funct_2(U_93,U_92,U_91,U_90) = k9_relat_1(U_91,U_90)
| ~ m1_relset_1(U_91,U_93,U_92)
| ~ v1_funct_2(U_91,U_93,U_92)
| ~ v1_funct_1(U_91) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_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_49_2,plain,
! [U_96,U_95,U_94] :
( ( m2_relset_1(U_94,U_96,U_95)
| ~ m1_relset_1(U_94,U_96,U_95) )
& ( m1_relset_1(U_94,U_96,U_95)
| ~ m2_relset_1(U_94,U_96,U_95) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_102,U_100,U_98] :
( m2_relset_1(U_98,U_102,U_100)
| ~ m1_relset_1(U_98,U_102,U_100) )
& ! [U_101,U_99,U_97] :
( m1_relset_1(U_97,U_101,U_99)
| ~ m2_relset_1(U_97,U_101,U_99) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
( m1_relset_1(U_97,U_101,U_99)
| ~ m2_relset_1(U_97,U_101,U_99) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
( m2_relset_1(U_98,U_102,U_100)
| ~ m1_relset_1(U_98,U_102,U_100) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [A,B,C] :
( ( ( r1_group_2(A,B,C)
| B != C )
& ( B = C
| ~ r1_group_2(A,B,C) ) )
| ~ m1_group_2(C,A)
| ~ v1_group_1(C)
| ~ m1_group_2(B,A)
| ~ v1_group_1(B)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r1_group_2]) ).
fof(f_50_2,plain,
! [U_105,U_104,U_103] :
( ( ( r1_group_2(U_105,U_104,U_103)
| U_104 != U_103 )
& ( U_104 = U_103
| ~ r1_group_2(U_105,U_104,U_103) ) )
| ~ m1_group_2(U_103,U_105)
| ~ v1_group_1(U_103)
| ~ m1_group_2(U_104,U_105)
| ~ v1_group_1(U_104)
| ~ l1_group_1(U_105)
| ~ v4_group_1(U_105)
| ~ v3_group_1(U_105)
| v3_struct_0(U_105) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( U_104 = U_103
| ~ r1_group_2(U_105,U_104,U_103)
| ~ m1_group_2(U_103,U_105)
| ~ v1_group_1(U_103)
| ~ m1_group_2(U_104,U_105)
| ~ v1_group_1(U_104)
| ~ l1_group_1(U_105)
| ~ v4_group_1(U_105)
| ~ v3_group_1(U_105)
| v3_struct_0(U_105) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_4,plain,
( r1_group_2(U_105,U_104,U_103)
| U_104 != U_103
| ~ m1_group_2(U_103,U_105)
| ~ v1_group_1(U_103)
| ~ m1_group_2(U_104,U_105)
| ~ v1_group_1(U_104)
| ~ l1_group_1(U_105)
| ~ v4_group_1(U_105)
| ~ v3_group_1(U_105)
| v3_struct_0(U_105) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_51_2,plain,
$true,
inference(clausify,[status(thm)],[f_51_1]) ).
fof(f_52_1,plain,
! [A,B,C,D] :
( m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B))
| ~ m1_relset_1(C,A,B)
| ~ v1_funct_2(C,A,B)
| ~ v1_funct_1(C) ),
inference(fof_nnf,[status(thm)],[dt_k2_funct_2]) ).
fof(f_52_2,plain,
! [U_109,U_108,U_107,U_106] :
( m1_subset_1(k2_funct_2(U_109,U_108,U_107,U_106),k1_zfmisc_1(U_108))
| ~ m1_relset_1(U_107,U_109,U_108)
| ~ v1_funct_2(U_107,U_109,U_108)
| ~ v1_funct_1(U_107) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_109,U_108,U_107] :
( ! [U_106] : m1_subset_1(k2_funct_2(U_109,U_108,U_107,U_106),k1_zfmisc_1(U_108))
| ~ m1_relset_1(U_107,U_109,U_108)
| ~ v1_funct_2(U_107,U_109,U_108)
| ~ v1_funct_1(U_107) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
cnf(f_52_4,plain,
( m1_subset_1(k2_funct_2(U_109,U_108,U_107,U_106),k1_zfmisc_1(U_108))
| ~ m1_relset_1(U_107,U_109,U_108)
| ~ v1_funct_2(U_107,U_109,U_108)
| ~ v1_funct_1(U_107) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_53_2,plain,
$true,
inference(clausify,[status(thm)],[f_53_1]) ).
fof(f_54_1,plain,
! [A,B] :
( ( m1_group_2(k5_group_4(A,B),A)
& v1_group_1(k5_group_4(A,B)) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_group_4]) ).
fof(f_54_2,plain,
! [U_111,U_110] :
( ( m1_group_2(k5_group_4(U_111,U_110),U_111)
& v1_group_1(k5_group_4(U_111,U_110)) )
| ~ m1_subset_1(U_110,k1_zfmisc_1(u1_struct_0(U_111)))
| ~ l1_group_1(U_111)
| ~ v4_group_1(U_111)
| ~ v3_group_1(U_111)
| v3_struct_0(U_111) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( v1_group_1(k5_group_4(U_111,U_110))
| ~ m1_subset_1(U_110,k1_zfmisc_1(u1_struct_0(U_111)))
| ~ l1_group_1(U_111)
| ~ v4_group_1(U_111)
| ~ v3_group_1(U_111)
| v3_struct_0(U_111) ),
inference(clausify,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
( m1_group_2(k5_group_4(U_111,U_110),U_111)
| ~ m1_subset_1(U_110,k1_zfmisc_1(u1_struct_0(U_111)))
| ~ l1_group_1(U_111)
| ~ v4_group_1(U_111)
| ~ v3_group_1(U_111)
| v3_struct_0(U_111) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
! [A,B,C] :
( ( m1_group_2(k8_group_4(A,B,C),A)
& v1_group_1(k8_group_4(A,B,C)) )
| ~ m1_group_2(C,A)
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k8_group_4]) ).
fof(f_55_2,plain,
! [U_114,U_113,U_112] :
( ( m1_group_2(k8_group_4(U_114,U_113,U_112),U_114)
& v1_group_1(k8_group_4(U_114,U_113,U_112)) )
| ~ m1_group_2(U_112,U_114)
| ~ m1_group_2(U_113,U_114)
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| v3_struct_0(U_114) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( v1_group_1(k8_group_4(U_114,U_113,U_112))
| ~ m1_group_2(U_112,U_114)
| ~ m1_group_2(U_113,U_114)
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| v3_struct_0(U_114) ),
inference(clausify,[status(thm)],[f_55_2]) ).
cnf(f_55_4,plain,
( m1_group_2(k8_group_4(U_114,U_113,U_112),U_114)
| ~ m1_group_2(U_112,U_114)
| ~ m1_group_2(U_113,U_114)
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| v3_struct_0(U_114) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_group_1]) ).
fof(f_56_2,plain,
! [U_115] :
( l1_struct_0(U_115)
| ~ l1_group_1(U_115) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( l1_struct_0(U_115)
| ~ l1_group_1(U_115) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [A] :
( ! [B] :
( ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
| ~ m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m1_group_2]) ).
fof(f_57_2,plain,
! [U_117] :
( ! [U_116] :
( ( l1_group_1(U_116)
& v3_group_1(U_116)
& ~ v3_struct_0(U_116) )
| ~ m1_group_2(U_116,U_117) )
| ~ l1_group_1(U_117)
| ~ v3_group_1(U_117)
| v3_struct_0(U_117) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( ~ v3_struct_0(U_116)
| ~ m1_group_2(U_116,U_117)
| ~ l1_group_1(U_117)
| ~ v3_group_1(U_117)
| v3_struct_0(U_117) ),
inference(clausify,[status(thm)],[f_57_2]) ).
cnf(f_57_4,plain,
( v3_group_1(U_116)
| ~ m1_group_2(U_116,U_117)
| ~ l1_group_1(U_117)
| ~ v3_group_1(U_117)
| v3_struct_0(U_117) ),
inference(clausify,[status(thm)],[f_57_2]) ).
cnf(f_57_5,plain,
( l1_group_1(U_116)
| ~ m1_group_2(U_116,U_117)
| ~ l1_group_1(U_117)
| ~ v3_group_1(U_117)
| v3_struct_0(U_117) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_58_2,plain,
$true,
inference(clausify,[status(thm)],[f_58_1]) ).
fof(f_59_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_59_2,plain,
! [U_120,U_119,U_118] :
( m1_subset_1(U_118,k1_zfmisc_1(k2_zfmisc_1(U_120,U_119)))
| ~ m2_relset_1(U_118,U_120,U_119) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( m1_subset_1(U_118,k1_zfmisc_1(k2_zfmisc_1(U_120,U_119)))
| ~ m2_relset_1(U_118,U_120,U_119) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_60_2,plain,
$true,
inference(clausify,[status(thm)],[f_60_1]) ).
fof(f_61_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_61_2,plain,
! [U_121] : ~ v1_xboole_0(k1_zfmisc_1(U_121)),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
~ v1_xboole_0(k1_zfmisc_1(U_121)),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_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_62_2,plain,
! [U_123,U_122] :
( ( m1_subset_1(U_123,k1_zfmisc_1(U_122))
| ~ r1_tarski(U_123,U_122) )
& ( r1_tarski(U_123,U_122)
| ~ m1_subset_1(U_123,k1_zfmisc_1(U_122)) ) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
( ! [U_127,U_125] :
( m1_subset_1(U_127,k1_zfmisc_1(U_125))
| ~ r1_tarski(U_127,U_125) )
& ! [U_126,U_124] :
( r1_tarski(U_126,U_124)
| ~ m1_subset_1(U_126,k1_zfmisc_1(U_124)) ) ),
inference(miniscope,[status(thm)],[f_62_2]) ).
cnf(f_62_4,plain,
( r1_tarski(U_126,U_124)
| ~ m1_subset_1(U_126,k1_zfmisc_1(U_124)) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_5,plain,
( m1_subset_1(U_127,k1_zfmisc_1(U_125))
| ~ r1_tarski(U_127,U_125) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( r1_group_2(A,k8_group_4(A,B,C),k5_group_4(A,D))
| D != k2_xboole_0(u1_struct_0(B),u1_struct_0(C))
| ~ m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
| ~ m1_group_2(C,A) )
| ~ m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t4_latsubgr]) ).
fof(f_63_2,plain,
! [U_131] :
( ! [U_130] :
( ! [U_129] :
( ! [U_128] :
( r1_group_2(U_131,k8_group_4(U_131,U_130,U_129),k5_group_4(U_131,U_128))
| U_128 != k2_xboole_0(u1_struct_0(U_130),u1_struct_0(U_129))
| ~ m1_subset_1(U_128,k1_zfmisc_1(u1_struct_0(U_131))) )
| ~ m1_group_2(U_129,U_131) )
| ~ m1_group_2(U_130,U_131) )
| ~ l1_group_1(U_131)
| ~ v4_group_1(U_131)
| ~ v3_group_1(U_131)
| v3_struct_0(U_131) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( r1_group_2(U_131,k8_group_4(U_131,U_130,U_129),k5_group_4(U_131,U_128))
| U_128 != k2_xboole_0(u1_struct_0(U_130),u1_struct_0(U_129))
| ~ m1_subset_1(U_128,k1_zfmisc_1(u1_struct_0(U_131)))
| ~ m1_group_2(U_129,U_131)
| ~ m1_group_2(U_130,U_131)
| ~ l1_group_1(U_131)
| ~ v4_group_1(U_131)
| ~ v3_group_1(U_131)
| v3_struct_0(U_131) ),
inference(clausify,[status(thm)],[f_63_2]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_2]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_19_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(f_21_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_2]) ).
cnf(f_22_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_22_2]) ).
cnf(f_24_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_24_3]) ).
cnf(f_24_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_24_5]) ).
cnf(f_25_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_3]) ).
cnf(f_25_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_6]) ).
cnf(f_51_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_51_2]) ).
cnf(f_53_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_53_2]) ).
cnf(f_58_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_58_2]) ).
cnf(f_60_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_60_2]) ).
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_struct_0(Eq_x_0) = u1_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,axiom,
( k2_xboole_0(Eq_x_0,Eq_x_1) = k2_xboole_0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( k8_group_4(Eq_x_0,Eq_x_1,Eq_x_2) = k8_group_4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( k2_funct_2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = k2_funct_2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| 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,
( k5_group_4(Eq_x_0,Eq_x_1) = k5_group_4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,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_11,axiom,
( g1_group_1(Eq_x_0,Eq_x_1) = g1_group_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_12,axiom,
( u1_group_1(Eq_x_0) = u1_group_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( k9_relat_1(Eq_x_0,Eq_x_1) = k9_relat_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_14,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_15,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( v3_struct_0(Eq_y_0)
| ~ v3_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( v3_group_1(Eq_y_0)
| ~ v3_group_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( v4_group_1(Eq_y_0)
| ~ v4_group_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( l1_group_1(Eq_y_0)
| ~ l1_group_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( m1_group_2(Eq_y_0,Eq_y_1)
| ~ m1_group_2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,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_29,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_30,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_31,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_32,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_33,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_34,axiom,
( v1_group_1(Eq_y_0)
| ~ v1_group_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( v1_partfun1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ v1_partfun1(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_36,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_37,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_38,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_39,axiom,
( l1_struct_0(Eq_y_0)
| ~ l1_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( r1_group_2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r1_group_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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP640+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 : n008.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 : Sat Sep 19 10:02:30 UTC 2026
% 0.10/0.38 % CPUTime :
% 136.05/136.38 % SZS status Theorem for theBenchmark
% 136.05/136.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------