%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP642+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 167.05s 167.39s
% Output : Proof 167.82s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t20_latsubgr,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0 ) ),
file('theBenchmark.p',t20_latsubgr) ).
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(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
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(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(d1_latsubgr,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(B) )
=> ( B = k1_latsubgr(A)
<=> ! [C] :
( ( m1_group_2(C,A)
& v1_group_1(C) )
=> k1_funct_1(B,C) = u1_struct_0(C) ) ) ) ),
file('theBenchmark.p',d1_latsubgr) ).
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_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
fof(dt_k1_group_3,axiom,
$true,
file('theBenchmark.p',dt_k1_group_3) ).
fof(dt_k1_latsubgr,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(k1_latsubgr(A)) ) ),
file('theBenchmark.p',dt_k1_latsubgr) ).
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_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_l1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_group_1) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
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_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
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_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(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(existence_l1_group_1,axiom,
? [A] : l1_group_1(A),
file('theBenchmark.p',existence_l1_group_1) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A),
file('theBenchmark.p',existence_l1_struct_0) ).
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_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
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(fc1_group_3,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(k1_group_3(A)) ),
file('theBenchmark.p',fc1_group_3) ).
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(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_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(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(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(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_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(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(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(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_subset) ).
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(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(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(f_1_1,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0 ) ),
inference(negate,[status(cth)],[t20_latsubgr]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( k1_funct_1(k1_latsubgr(A),B) = k1_xboole_0
& 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)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_1] :
( ? [U_0] :
( k1_funct_1(k1_latsubgr(U_1),U_0) = k1_xboole_0
& m1_group_2(U_0,U_1)
& v1_group_1(U_0) )
& l1_group_1(U_1)
& v4_group_1(U_1)
& v3_group_1(U_1)
& ~ v3_struct_0(U_1) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_0] :
( k1_funct_1(k1_latsubgr(sK1),U_0) = k1_xboole_0
& m1_group_2(U_0,sK1)
& v1_group_1(U_0) )
& 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_1,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( k1_funct_1(k1_latsubgr(sK1),sK2) = k1_xboole_0
& m1_group_2(sK2,sK1)
& v1_group_1(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_0,sK2)],[f_1_4]) ).
cnf(f_1_6,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_7,negated_conjecture,
v3_group_1(sK1),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_8,negated_conjecture,
v4_group_1(sK1),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_9,negated_conjecture,
l1_group_1(sK1),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_10,negated_conjecture,
v1_group_1(sK2),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_11,negated_conjecture,
m1_group_2(sK2,sK1),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_12,negated_conjecture,
k1_funct_1(k1_latsubgr(sK1),sK2) = k1_xboole_0,
inference(clausify,[status(thm)],[f_1_5]) ).
fof(f_2_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_2_2,plain,
! [U_2] :
( U_2 = g1_group_1(u1_struct_0(U_2),u1_group_1(U_2))
| ~ v1_group_1(U_2)
| ~ l1_group_1(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( U_2 = g1_group_1(u1_struct_0(U_2),u1_group_1(U_2))
| ~ v1_group_1(U_2)
| ~ l1_group_1(U_2) ),
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_4,U_3] :
( ~ r2_hidden(U_3,U_4)
| ~ r2_hidden(U_4,U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ r2_hidden(U_3,U_4)
| ~ r2_hidden(U_4,U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_7,U_6,U_5] :
( ( v1_funct_2(U_5,U_7,U_6)
& v1_funct_1(U_5) )
| ~ v1_partfun1(U_5,U_7,U_6)
| ~ v1_funct_1(U_5)
| ~ m1_relset_1(U_5,U_7,U_6) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v1_funct_1(U_5)
| ~ v1_partfun1(U_5,U_7,U_6)
| ~ v1_funct_1(U_5)
| ~ m1_relset_1(U_5,U_7,U_6) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( v1_funct_2(U_5,U_7,U_6)
| ~ v1_partfun1(U_5,U_7,U_6)
| ~ v1_funct_1(U_5)
| ~ m1_relset_1(U_5,U_7,U_6) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_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_5_2,plain,
! [U_10,U_9,U_8] :
( v1_relat_1(U_8)
| ~ m1_subset_1(U_8,k1_zfmisc_1(k2_zfmisc_1(U_10,U_9))) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( v1_relat_1(U_8)
| ~ m1_subset_1(U_8,k1_zfmisc_1(k2_zfmisc_1(U_10,U_9))) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_13,U_12] :
( ! [U_11] :
( ( v1_funct_2(U_11,U_13,U_12)
& v1_partfun1(U_11,U_13,U_12)
& v1_funct_1(U_11) )
| ~ v1_funct_2(U_11,U_13,U_12)
| ~ v1_funct_1(U_11)
| ~ m1_relset_1(U_11,U_13,U_12) )
| v1_xboole_0(U_12) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( v1_funct_1(U_11)
| ~ v1_funct_2(U_11,U_13,U_12)
| ~ v1_funct_1(U_11)
| ~ m1_relset_1(U_11,U_13,U_12)
| v1_xboole_0(U_12) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( v1_partfun1(U_11,U_13,U_12)
| ~ v1_funct_2(U_11,U_13,U_12)
| ~ v1_funct_1(U_11)
| ~ m1_relset_1(U_11,U_13,U_12)
| v1_xboole_0(U_12) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( v1_funct_2(U_11,U_13,U_12)
| ~ v1_funct_2(U_11,U_13,U_12)
| ~ v1_funct_1(U_11)
| ~ m1_relset_1(U_11,U_13,U_12)
| v1_xboole_0(U_12) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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_7_2,plain,
! [U_16,U_15] :
( ! [U_14] :
( ( v1_funct_2(U_14,U_16,U_15)
& v1_partfun1(U_14,U_16,U_15)
& ~ v1_xboole_0(U_14)
& v1_funct_1(U_14) )
| ~ v1_funct_2(U_14,U_16,U_15)
| ~ v1_funct_1(U_14)
| ~ m1_relset_1(U_14,U_16,U_15) )
| v1_xboole_0(U_15)
| v1_xboole_0(U_16) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( v1_funct_1(U_14)
| ~ v1_funct_2(U_14,U_16,U_15)
| ~ v1_funct_1(U_14)
| ~ m1_relset_1(U_14,U_16,U_15)
| v1_xboole_0(U_15)
| v1_xboole_0(U_16) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( ~ v1_xboole_0(U_14)
| ~ v1_funct_2(U_14,U_16,U_15)
| ~ v1_funct_1(U_14)
| ~ m1_relset_1(U_14,U_16,U_15)
| v1_xboole_0(U_15)
| v1_xboole_0(U_16) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_5,plain,
( v1_partfun1(U_14,U_16,U_15)
| ~ v1_funct_2(U_14,U_16,U_15)
| ~ v1_funct_1(U_14)
| ~ m1_relset_1(U_14,U_16,U_15)
| v1_xboole_0(U_15)
| v1_xboole_0(U_16) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_6,plain,
( v1_funct_2(U_14,U_16,U_15)
| ~ v1_funct_2(U_14,U_16,U_15)
| ~ v1_funct_1(U_14)
| ~ m1_relset_1(U_14,U_16,U_15)
| v1_xboole_0(U_15)
| v1_xboole_0(U_16) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( ( ( B = k1_latsubgr(A)
| ? [C] :
( k1_funct_1(B,C) != u1_struct_0(C)
& m1_group_2(C,A)
& v1_group_1(C) ) )
& ( ! [C] :
( k1_funct_1(B,C) = u1_struct_0(C)
| ~ m1_group_2(C,A)
| ~ v1_group_1(C) )
| B != k1_latsubgr(A) ) )
| ~ m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_1(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[d1_latsubgr]) ).
fof(f_8_2,plain,
! [U_20] :
( ! [U_19] :
( ( ( U_19 = k1_latsubgr(U_20)
| ? [U_18] :
( k1_funct_1(U_19,U_18) != u1_struct_0(U_18)
& m1_group_2(U_18,U_20)
& v1_group_1(U_18) ) )
& ( ! [U_17] :
( k1_funct_1(U_19,U_17) = u1_struct_0(U_17)
| ~ m1_group_2(U_17,U_20)
| ~ v1_group_1(U_17) )
| U_19 != k1_latsubgr(U_20) ) )
| ~ m2_relset_1(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_2(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_1(U_19) )
| ~ l1_group_1(U_20)
| ~ v4_group_1(U_20)
| ~ v3_group_1(U_20)
| v3_struct_0(U_20) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_20] :
( ! [U_19] :
( ( ( U_19 = k1_latsubgr(U_20)
| ( k1_funct_1(U_19,sK3(U_20,U_19)) != u1_struct_0(sK3(U_20,U_19))
& m1_group_2(sK3(U_20,U_19),U_20)
& v1_group_1(sK3(U_20,U_19)) ) )
& ( ! [U_17] :
( k1_funct_1(U_19,U_17) = u1_struct_0(U_17)
| ~ m1_group_2(U_17,U_20)
| ~ v1_group_1(U_17) )
| U_19 != k1_latsubgr(U_20) ) )
| ~ m2_relset_1(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_2(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_1(U_19) )
| ~ l1_group_1(U_20)
| ~ v4_group_1(U_20)
| ~ v3_group_1(U_20)
| v3_struct_0(U_20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_18,sK3(U_20,U_19))],[f_8_2]) ).
cnf(f_8_4,plain,
( k1_funct_1(U_19,U_17) = u1_struct_0(U_17)
| ~ m1_group_2(U_17,U_20)
| ~ v1_group_1(U_17)
| U_19 != k1_latsubgr(U_20)
| ~ m2_relset_1(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_2(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_1(U_19)
| ~ l1_group_1(U_20)
| ~ v4_group_1(U_20)
| ~ v3_group_1(U_20)
| v3_struct_0(U_20) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( v1_group_1(sK3(U_20,U_19))
| U_19 = k1_latsubgr(U_20)
| ~ m2_relset_1(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_2(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_1(U_19)
| ~ l1_group_1(U_20)
| ~ v4_group_1(U_20)
| ~ v3_group_1(U_20)
| v3_struct_0(U_20) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( m1_group_2(sK3(U_20,U_19),U_20)
| U_19 = k1_latsubgr(U_20)
| ~ m2_relset_1(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_2(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_1(U_19)
| ~ l1_group_1(U_20)
| ~ v4_group_1(U_20)
| ~ v3_group_1(U_20)
| v3_struct_0(U_20) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_7,plain,
( k1_funct_1(U_19,sK3(U_20,U_19)) != u1_struct_0(sK3(U_20,U_19))
| U_19 = k1_latsubgr(U_20)
| ~ m2_relset_1(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_2(U_19,k1_group_3(U_20),k1_zfmisc_1(u1_struct_0(U_20)))
| ~ v1_funct_1(U_19)
| ~ l1_group_1(U_20)
| ~ v4_group_1(U_20)
| ~ v3_group_1(U_20)
| v3_struct_0(U_20) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_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_9_2,plain,
! [U_22,U_21] :
( ( l1_group_1(g1_group_1(U_22,U_21))
& v1_group_1(g1_group_1(U_22,U_21)) )
| ~ m1_relset_1(U_21,k2_zfmisc_1(U_22,U_22),U_22)
| ~ v1_funct_2(U_21,k2_zfmisc_1(U_22,U_22),U_22)
| ~ v1_funct_1(U_21) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( v1_group_1(g1_group_1(U_22,U_21))
| ~ m1_relset_1(U_21,k2_zfmisc_1(U_22,U_22),U_22)
| ~ v1_funct_2(U_21,k2_zfmisc_1(U_22,U_22),U_22)
| ~ v1_funct_1(U_21) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( l1_group_1(g1_group_1(U_22,U_21))
| ~ m1_relset_1(U_21,k2_zfmisc_1(U_22,U_22),U_22)
| ~ v1_funct_2(U_21,k2_zfmisc_1(U_22,U_22),U_22)
| ~ v1_funct_1(U_21) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_group_3]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
! [A] :
( ( m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(k1_latsubgr(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_latsubgr]) ).
fof(f_12_2,plain,
! [U_23] :
( ( m2_relset_1(k1_latsubgr(U_23),k1_group_3(U_23),k1_zfmisc_1(u1_struct_0(U_23)))
& v1_funct_2(k1_latsubgr(U_23),k1_group_3(U_23),k1_zfmisc_1(u1_struct_0(U_23)))
& v1_funct_1(k1_latsubgr(U_23)) )
| ~ l1_group_1(U_23)
| ~ v4_group_1(U_23)
| ~ v3_group_1(U_23)
| v3_struct_0(U_23) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( v1_funct_1(k1_latsubgr(U_23))
| ~ l1_group_1(U_23)
| ~ v4_group_1(U_23)
| ~ v3_group_1(U_23)
| v3_struct_0(U_23) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( v1_funct_2(k1_latsubgr(U_23),k1_group_3(U_23),k1_zfmisc_1(u1_struct_0(U_23)))
| ~ l1_group_1(U_23)
| ~ v4_group_1(U_23)
| ~ v3_group_1(U_23)
| v3_struct_0(U_23) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_5,plain,
( m2_relset_1(k1_latsubgr(U_23),k1_group_3(U_23),k1_zfmisc_1(u1_struct_0(U_23)))
| ~ l1_group_1(U_23)
| ~ v4_group_1(U_23)
| ~ v3_group_1(U_23)
| v3_struct_0(U_23) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_14_2,plain,
$true,
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_group_1]) ).
fof(f_16_2,plain,
! [U_24] :
( l1_struct_0(U_24)
| ~ l1_group_1(U_24) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( l1_struct_0(U_24)
| ~ l1_group_1(U_24) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_17_2,plain,
$true,
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_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_18_2,plain,
! [U_26] :
( ! [U_25] :
( ( l1_group_1(U_25)
& v3_group_1(U_25)
& ~ v3_struct_0(U_25) )
| ~ m1_group_2(U_25,U_26) )
| ~ l1_group_1(U_26)
| ~ v3_group_1(U_26)
| v3_struct_0(U_26) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( ~ v3_struct_0(U_25)
| ~ m1_group_2(U_25,U_26)
| ~ l1_group_1(U_26)
| ~ v3_group_1(U_26)
| v3_struct_0(U_26) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( v3_group_1(U_25)
| ~ m1_group_2(U_25,U_26)
| ~ l1_group_1(U_26)
| ~ v3_group_1(U_26)
| v3_struct_0(U_26) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_5,plain,
( l1_group_1(U_25)
| ~ m1_group_2(U_25,U_26)
| ~ l1_group_1(U_26)
| ~ v3_group_1(U_26)
| v3_struct_0(U_26) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_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_m1_subset_1]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_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_21_2,plain,
! [U_29,U_28,U_27] :
( m1_subset_1(U_27,k1_zfmisc_1(k2_zfmisc_1(U_29,U_28)))
| ~ m2_relset_1(U_27,U_29,U_28) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( m1_subset_1(U_27,k1_zfmisc_1(k2_zfmisc_1(U_29,U_28)))
| ~ m2_relset_1(U_27,U_29,U_28) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_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_22_2,plain,
! [U_30] :
( ( m2_relset_1(u1_group_1(U_30),k2_zfmisc_1(u1_struct_0(U_30),u1_struct_0(U_30)),u1_struct_0(U_30))
& v1_funct_2(u1_group_1(U_30),k2_zfmisc_1(u1_struct_0(U_30),u1_struct_0(U_30)),u1_struct_0(U_30))
& v1_funct_1(u1_group_1(U_30)) )
| ~ l1_group_1(U_30) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( v1_funct_1(u1_group_1(U_30))
| ~ l1_group_1(U_30) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( v1_funct_2(u1_group_1(U_30),k2_zfmisc_1(u1_struct_0(U_30),u1_struct_0(U_30)),u1_struct_0(U_30))
| ~ l1_group_1(U_30) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_5,plain,
( m2_relset_1(u1_group_1(U_30),k2_zfmisc_1(u1_struct_0(U_30),u1_struct_0(U_30)),u1_struct_0(U_30))
| ~ l1_group_1(U_30) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_23_2,plain,
$true,
inference(clausify,[status(thm)],[f_23_1]) ).
fof(f_24_1,plain,
? [A] : l1_group_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_group_1]) ).
fof(f_24_2,plain,
? [U_31] : l1_group_1(U_31),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
l1_group_1(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_31,sK4)],[f_24_2]) ).
cnf(f_24_4,plain,
l1_group_1(sK4),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_25_2,plain,
? [U_32] : l1_struct_0(U_32),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
l1_struct_0(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_32,sK5)],[f_25_2]) ).
cnf(f_25_4,plain,
l1_struct_0(sK5),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_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_26_2,plain,
! [U_34] :
( ? [U_33] : m1_group_2(U_33,U_34)
| ~ l1_group_1(U_34)
| ~ v3_group_1(U_34)
| v3_struct_0(U_34) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_34] :
( m1_group_2(sK6(U_34),U_34)
| ~ l1_group_1(U_34)
| ~ v3_group_1(U_34)
| v3_struct_0(U_34) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_33,sK6(U_34))],[f_26_2]) ).
cnf(f_26_4,plain,
( m1_group_2(sK6(U_34),U_34)
| ~ l1_group_1(U_34)
| ~ v3_group_1(U_34)
| v3_struct_0(U_34) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_27_2,plain,
! [U_37,U_36] :
? [U_35] : m1_relset_1(U_35,U_37,U_36),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_37,U_36] : m1_relset_1(sK7(U_37,U_36),U_37,U_36),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_35,sK7(U_37,U_36))],[f_27_2]) ).
cnf(f_27_4,plain,
m1_relset_1(sK7(U_37,U_36),U_37,U_36),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_28_2,plain,
! [U_39] :
? [U_38] : m1_subset_1(U_38,U_39),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_39] : m1_subset_1(sK8(U_39),U_39),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_38,sK8(U_39))],[f_28_2]) ).
cnf(f_28_4,plain,
m1_subset_1(sK8(U_39),U_39),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_29_2,plain,
! [U_42,U_41] :
? [U_40] : m2_relset_1(U_40,U_42,U_41),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_42,U_41] : m2_relset_1(sK9(U_42,U_41),U_42,U_41),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_40,sK9(U_42,U_41))],[f_29_2]) ).
cnf(f_29_4,plain,
m2_relset_1(sK9(U_42,U_41),U_42,U_41),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A] :
( ~ v1_xboole_0(k1_group_3(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc1_group_3]) ).
fof(f_30_2,plain,
! [U_43] :
( ~ v1_xboole_0(k1_group_3(U_43))
| ~ l1_group_1(U_43)
| ~ v4_group_1(U_43)
| ~ v3_group_1(U_43)
| v3_struct_0(U_43) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( ~ v1_xboole_0(k1_group_3(U_43))
| ~ l1_group_1(U_43)
| ~ v4_group_1(U_43)
| ~ v3_group_1(U_43)
| v3_struct_0(U_43) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_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_31_2,plain,
! [U_44] :
( ~ v1_xboole_0(u1_struct_0(U_44))
| ~ l1_struct_0(U_44)
| v3_struct_0(U_44) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_44))
| ~ l1_struct_0(U_44)
| v3_struct_0(U_44) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_32_2,plain,
! [U_45] : ~ v1_xboole_0(k1_zfmisc_1(U_45)),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
~ v1_xboole_0(k1_zfmisc_1(U_45)),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_33_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_33_1]) ).
fof(f_34_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_34_2,plain,
! [U_47,U_46] :
( ~ v1_xboole_0(k2_zfmisc_1(U_47,U_46))
| v1_xboole_0(U_46)
| v1_xboole_0(U_47) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( ~ v1_xboole_0(k2_zfmisc_1(U_47,U_46))
| v1_xboole_0(U_46)
| v1_xboole_0(U_47) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_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_35_2,plain,
! [U_51,U_50] :
( ! [U_49,U_48] :
( ( U_50 = U_48
& U_51 = U_49 )
| g1_group_1(U_51,U_50) != g1_group_1(U_49,U_48) )
| ~ m1_relset_1(U_50,k2_zfmisc_1(U_51,U_51),U_51)
| ~ v1_funct_2(U_50,k2_zfmisc_1(U_51,U_51),U_51)
| ~ v1_funct_1(U_50) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( U_51 = U_49
| g1_group_1(U_51,U_50) != g1_group_1(U_49,U_48)
| ~ m1_relset_1(U_50,k2_zfmisc_1(U_51,U_51),U_51)
| ~ v1_funct_2(U_50,k2_zfmisc_1(U_51,U_51),U_51)
| ~ v1_funct_1(U_50) ),
inference(clausify,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( U_50 = U_48
| g1_group_1(U_51,U_50) != g1_group_1(U_49,U_48)
| ~ m1_relset_1(U_50,k2_zfmisc_1(U_51,U_51),U_51)
| ~ v1_funct_2(U_50,k2_zfmisc_1(U_51,U_51),U_51)
| ~ v1_funct_1(U_50) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_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_36_2,plain,
! [U_54,U_53] :
? [U_52] :
( v1_funct_2(U_52,U_54,U_53)
& v1_funct_1(U_52)
& v1_relat_1(U_52)
& m1_relset_1(U_52,U_54,U_53) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_54,U_53] :
( v1_funct_2(sK10(U_54,U_53),U_54,U_53)
& v1_funct_1(sK10(U_54,U_53))
& v1_relat_1(sK10(U_54,U_53))
& m1_relset_1(sK10(U_54,U_53),U_54,U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_52,sK10(U_54,U_53))],[f_36_2]) ).
cnf(f_36_4,plain,
m1_relset_1(sK10(U_54,U_53),U_54,U_53),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
v1_relat_1(sK10(U_54,U_53)),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_6,plain,
v1_funct_1(sK10(U_54,U_53)),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_7,plain,
v1_funct_2(sK10(U_54,U_53),U_54,U_53),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_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_37_2,plain,
! [U_56] :
( ? [U_55] :
( ~ v1_xboole_0(U_55)
& m1_subset_1(U_55,k1_zfmisc_1(U_56)) )
| v1_xboole_0(U_56) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_56] :
( ( ~ v1_xboole_0(sK11(U_56))
& m1_subset_1(sK11(U_56),k1_zfmisc_1(U_56)) )
| v1_xboole_0(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_55,sK11(U_56))],[f_37_2]) ).
cnf(f_37_4,plain,
( m1_subset_1(sK11(U_56),k1_zfmisc_1(U_56))
| v1_xboole_0(U_56) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( ~ v1_xboole_0(sK11(U_56))
| v1_xboole_0(U_56) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_38_2,plain,
? [U_57] : v1_xboole_0(U_57),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
v1_xboole_0(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_57,sK12)],[f_38_2]) ).
cnf(f_38_4,plain,
v1_xboole_0(sK12),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_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_39_2,plain,
! [U_60,U_59] :
? [U_58] :
( v1_funct_1(U_58)
& v1_relat_1(U_58)
& m1_relset_1(U_58,U_60,U_59) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_60,U_59] :
( v1_funct_1(sK13(U_60,U_59))
& v1_relat_1(sK13(U_60,U_59))
& m1_relset_1(sK13(U_60,U_59),U_60,U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_58,sK13(U_60,U_59))],[f_39_2]) ).
cnf(f_39_4,plain,
m1_relset_1(sK13(U_60,U_59),U_60,U_59),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
v1_relat_1(sK13(U_60,U_59)),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_6,plain,
v1_funct_1(sK13(U_60,U_59)),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_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_40_2,plain,
! [U_62] :
? [U_61] :
( v1_xboole_0(U_61)
& m1_subset_1(U_61,k1_zfmisc_1(U_62)) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_62] :
( v1_xboole_0(sK14(U_62))
& m1_subset_1(sK14(U_62),k1_zfmisc_1(U_62)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_61,sK14(U_62))],[f_40_2]) ).
cnf(f_40_4,plain,
m1_subset_1(sK14(U_62),k1_zfmisc_1(U_62)),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
v1_xboole_0(sK14(U_62)),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_41_2,plain,
? [U_63] : ~ v1_xboole_0(U_63),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
~ v1_xboole_0(sK15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_63,sK15)],[f_41_2]) ).
cnf(f_41_4,plain,
~ v1_xboole_0(sK15),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_42_2,plain,
? [U_64] :
( ~ v3_struct_0(U_64)
& l1_struct_0(U_64) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ~ v3_struct_0(sK16)
& l1_struct_0(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_64,sK16)],[f_42_2]) ).
cnf(f_42_4,plain,
l1_struct_0(sK16),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_5,plain,
~ v3_struct_0(sK16),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_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_43_2,plain,
! [U_66] :
( ? [U_65] :
( ~ v1_xboole_0(U_65)
& m1_subset_1(U_65,k1_zfmisc_1(u1_struct_0(U_66))) )
| ~ l1_struct_0(U_66)
| v3_struct_0(U_66) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_66] :
( ( ~ v1_xboole_0(sK17(U_66))
& m1_subset_1(sK17(U_66),k1_zfmisc_1(u1_struct_0(U_66))) )
| ~ l1_struct_0(U_66)
| v3_struct_0(U_66) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_65,sK17(U_66))],[f_43_2]) ).
cnf(f_43_4,plain,
( m1_subset_1(sK17(U_66),k1_zfmisc_1(u1_struct_0(U_66)))
| ~ l1_struct_0(U_66)
| v3_struct_0(U_66) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
( ~ v1_xboole_0(sK17(U_66))
| ~ l1_struct_0(U_66)
| v3_struct_0(U_66) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_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_44_2,plain,
! [U_69,U_68,U_67] :
( ( m2_relset_1(U_67,U_69,U_68)
| ~ m1_relset_1(U_67,U_69,U_68) )
& ( m1_relset_1(U_67,U_69,U_68)
| ~ m2_relset_1(U_67,U_69,U_68) ) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ! [U_75,U_73,U_71] :
( m2_relset_1(U_71,U_75,U_73)
| ~ m1_relset_1(U_71,U_75,U_73) )
& ! [U_74,U_72,U_70] :
( m1_relset_1(U_70,U_74,U_72)
| ~ m2_relset_1(U_70,U_74,U_72) ) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
cnf(f_44_4,plain,
( m1_relset_1(U_70,U_74,U_72)
| ~ m2_relset_1(U_70,U_74,U_72) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_5,plain,
( m2_relset_1(U_71,U_75,U_73)
| ~ m1_relset_1(U_71,U_75,U_73) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_45_2,plain,
! [U_77,U_76] : r1_tarski(U_77,U_77),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_77] : r1_tarski(U_77,U_77),
inference(miniscope,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
r1_tarski(U_77,U_77),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_46_2,plain,
! [U_79,U_78] :
( m1_subset_1(U_79,U_78)
| ~ r2_hidden(U_79,U_78) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( m1_subset_1(U_79,U_78)
| ~ r2_hidden(U_79,U_78) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_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_47_2,plain,
! [U_81,U_80] :
( r2_hidden(U_81,U_80)
| v1_xboole_0(U_80)
| ~ m1_subset_1(U_81,U_80) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( r2_hidden(U_81,U_80)
| v1_xboole_0(U_80)
| ~ m1_subset_1(U_81,U_80) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_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_48_2,plain,
! [U_83,U_82] :
( ( m1_subset_1(U_83,k1_zfmisc_1(U_82))
| ~ r1_tarski(U_83,U_82) )
& ( r1_tarski(U_83,U_82)
| ~ m1_subset_1(U_83,k1_zfmisc_1(U_82)) ) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
( ! [U_87,U_85] :
( m1_subset_1(U_87,k1_zfmisc_1(U_85))
| ~ r1_tarski(U_87,U_85) )
& ! [U_86,U_84] :
( r1_tarski(U_86,U_84)
| ~ m1_subset_1(U_86,k1_zfmisc_1(U_84)) ) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
cnf(f_48_4,plain,
( r1_tarski(U_86,U_84)
| ~ m1_subset_1(U_86,k1_zfmisc_1(U_84)) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_5,plain,
( m1_subset_1(U_87,k1_zfmisc_1(U_85))
| ~ r1_tarski(U_87,U_85) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_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_49_2,plain,
! [U_90,U_89,U_88] :
( m1_subset_1(U_90,U_88)
| ~ m1_subset_1(U_89,k1_zfmisc_1(U_88))
| ~ r2_hidden(U_90,U_89) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( m1_subset_1(U_90,U_88)
| ~ m1_subset_1(U_89,k1_zfmisc_1(U_88))
| ~ r2_hidden(U_90,U_89) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_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_50_2,plain,
! [U_93,U_92,U_91] :
( ~ v1_xboole_0(U_91)
| ~ m1_subset_1(U_92,k1_zfmisc_1(U_91))
| ~ r2_hidden(U_93,U_92) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_93,U_92] :
( ! [U_91] :
( ~ v1_xboole_0(U_91)
| ~ m1_subset_1(U_92,k1_zfmisc_1(U_91)) )
| ~ r2_hidden(U_93,U_92) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
cnf(f_50_4,plain,
( ~ v1_xboole_0(U_91)
| ~ m1_subset_1(U_92,k1_zfmisc_1(U_91))
| ~ r2_hidden(U_93,U_92) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_51_2,plain,
! [U_94] :
( U_94 = k1_xboole_0
| ~ v1_xboole_0(U_94) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( U_94 = k1_xboole_0
| ~ v1_xboole_0(U_94) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_52_2,plain,
! [U_96,U_95] :
( ~ v1_xboole_0(U_95)
| ~ r2_hidden(U_96,U_95) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( ~ v1_xboole_0(U_95)
| ~ r2_hidden(U_96,U_95) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_53_2,plain,
! [U_98,U_97] :
( ~ v1_xboole_0(U_97)
| U_98 = U_97
| ~ v1_xboole_0(U_98) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_98] :
( ! [U_97] :
( ~ v1_xboole_0(U_97)
| U_98 = U_97 )
| ~ v1_xboole_0(U_98) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
cnf(f_53_4,plain,
( ~ v1_xboole_0(U_97)
| U_98 = U_97
| ~ v1_xboole_0(U_98) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_6_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_5]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_7_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_6]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(f_14_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_2]) ).
cnf(f_15_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_2]) ).
cnf(f_17_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_2]) ).
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_23_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_23_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,
( k1_latsubgr(Eq_x_0) = k1_latsubgr(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k1_funct_1(Eq_x_0,Eq_x_1) = k1_funct_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,
( u1_struct_0(Eq_x_0) = u1_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,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_9,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_10,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_11,axiom,
( k1_group_3(Eq_x_0) = k1_group_3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| 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) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(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,
( 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_18,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(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,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,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_23,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_24,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_25,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_26,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_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,
( 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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP642+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.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 10:04:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 167.05/167.39 % SZS status Theorem for theBenchmark
% 167.05/167.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------