%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP623+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 : n006.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 08:42:03 AM UTC 2026
% Result : Theorem 100.65s 100.92s
% Output : Proof 100.78s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t14_autgroup,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> r1_tarski(k4_autgroup(A),k1_autgroup(A)) ),
file('theBenchmark.p',t14_autgroup) ).
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_fraenkel,axiom,
! [A] :
( v1_fraenkel(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_funct_1(B)
& v1_relat_1(B) ) ) ),
file('theBenchmark.p',cc1_fraenkel) ).
fof(cc1_funct_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_funct_1(A) ),
file('theBenchmark.p',cc1_funct_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(cc1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> ( ( v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( v2_group_1(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc1_group_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(cc2_funct_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) )
=> ( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(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(d3_tarski,axiom,
! [A,B] :
( r1_tarski(A,B)
<=> ! [C] :
( r2_hidden(C,A)
=> r2_hidden(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
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_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k1_autgroup) ).
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_k4_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_fraenkel(k4_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k4_autgroup) ).
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_fraenkel,axiom,
! [A,B,C] :
( m1_fraenkel(C,A,B)
=> ( v1_fraenkel(C)
& ~ v1_xboole_0(C) ) ),
file('theBenchmark.p',dt_m1_fraenkel) ).
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_fraenkel,axiom,
! [A,B,C] :
( ( m1_fraenkel(C,A,B)
& ~ v1_xboole_0(B) )
=> ! [D] :
( m2_fraenkel(D,A,B,C)
=> ( m2_relset_1(D,A,B)
& v1_funct_2(D,A,B)
& v1_funct_1(D) ) ) ),
file('theBenchmark.p',dt_m2_fraenkel) ).
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_fraenkel,axiom,
! [A,B] :
? [C] : m1_fraenkel(C,A,B),
file('theBenchmark.p',existence_m1_fraenkel) ).
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_fraenkel,axiom,
! [A,B,C] :
( ( m1_fraenkel(C,A,B)
& ~ v1_xboole_0(B) )
=> ? [D] : m2_fraenkel(D,A,B,C) ),
file('theBenchmark.p',existence_m2_fraenkel) ).
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_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)
& ~ v1_xboole_0(A) )
=> ( v1_group_1(g1_group_1(A,B))
& ~ v3_struct_0(g1_group_1(A,B)) ) ),
file('theBenchmark.p',fc1_group_1) ).
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_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
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_fraenkel,axiom,
? [A] :
( v1_fraenkel(A)
& ~ v1_xboole_0(A) ),
file('theBenchmark.p',rc1_fraenkel) ).
fof(rc1_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc1_funct_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_group_1,axiom,
? [A] :
( v1_group_1(A)
& l1_group_1(A) ),
file('theBenchmark.p',rc1_group_1) ).
fof(rc1_partfun1,axiom,
? [A] :
( v1_xboole_0(A)
& v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc1_partfun1) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_group_1,axiom,
? [A] :
( v1_group_1(A)
& ~ v3_struct_0(A)
& l1_group_1(A) ),
file('theBenchmark.p',rc2_group_1) ).
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_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_funct_1,axiom,
? [A] :
( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_group_1,axiom,
? [A] :
( v4_group_1(A)
& v3_group_1(A)
& v2_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A)
& l1_group_1(A) ),
file('theBenchmark.p',rc3_group_1) ).
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_fraenkel,axiom,
! [A,B,C] :
( ( m1_fraenkel(C,A,B)
& ~ v1_xboole_0(B) )
=> ! [D] :
( m2_fraenkel(D,A,B,C)
<=> m1_subset_1(D,C) ) ),
file('theBenchmark.p',redefinition_m2_fraenkel) ).
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(t13_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ),
file('theBenchmark.p',t13_autgroup) ).
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)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> r1_tarski(k4_autgroup(A),k1_autgroup(A)) ),
inference(negate,[status(cth)],[t14_autgroup]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ~ r1_tarski(k4_autgroup(A),k1_autgroup(A))
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_0] :
( ~ r1_tarski(k4_autgroup(U_0),k1_autgroup(U_0))
& l1_group_1(U_0)
& v4_group_1(U_0)
& v3_group_1(U_0)
& v1_group_1(U_0)
& ~ v3_struct_0(U_0) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ~ r1_tarski(k4_autgroup(sK1),k1_autgroup(sK1))
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& v1_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1)],[f_1_3]) ).
cnf(f_1_5,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,negated_conjecture,
v1_group_1(sK1),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,negated_conjecture,
v3_group_1(sK1),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_8,negated_conjecture,
v4_group_1(sK1),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_9,negated_conjecture,
l1_group_1(sK1),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_10,negated_conjecture,
~ r1_tarski(k4_autgroup(sK1),k1_autgroup(sK1)),
inference(clausify,[status(thm)],[f_1_4]) ).
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_1] :
( U_1 = g1_group_1(u1_struct_0(U_1),u1_group_1(U_1))
| ~ v1_group_1(U_1)
| ~ l1_group_1(U_1) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( U_1 = g1_group_1(u1_struct_0(U_1),u1_group_1(U_1))
| ~ v1_group_1(U_1)
| ~ l1_group_1(U_1) ),
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_3,U_2] :
( ~ r2_hidden(U_2,U_3)
| ~ r2_hidden(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ r2_hidden(U_2,U_3)
| ~ r2_hidden(U_3,U_2) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ! [B] :
( ( v1_funct_1(B)
& v1_relat_1(B) )
| ~ m1_subset_1(B,A) )
| ~ v1_fraenkel(A) ),
inference(fof_nnf,[status(thm)],[cc1_fraenkel]) ).
fof(f_4_2,plain,
! [U_5] :
( ! [U_4] :
( ( v1_funct_1(U_4)
& v1_relat_1(U_4) )
| ~ m1_subset_1(U_4,U_5) )
| ~ v1_fraenkel(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v1_relat_1(U_4)
| ~ m1_subset_1(U_4,U_5)
| ~ v1_fraenkel(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( v1_funct_1(U_4)
| ~ m1_subset_1(U_4,U_5)
| ~ v1_fraenkel(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( v1_funct_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_5_2,plain,
! [U_6] :
( v1_funct_1(U_6)
| ~ v1_xboole_0(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( v1_funct_1(U_6)
| ~ v1_xboole_0(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_9,U_8,U_7] :
( ( v1_funct_2(U_7,U_9,U_8)
& v1_funct_1(U_7) )
| ~ v1_partfun1(U_7,U_9,U_8)
| ~ v1_funct_1(U_7)
| ~ m1_relset_1(U_7,U_9,U_8) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( v1_funct_1(U_7)
| ~ v1_partfun1(U_7,U_9,U_8)
| ~ v1_funct_1(U_7)
| ~ m1_relset_1(U_7,U_9,U_8) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( v1_funct_2(U_7,U_9,U_8)
| ~ v1_partfun1(U_7,U_9,U_8)
| ~ v1_funct_1(U_7)
| ~ m1_relset_1(U_7,U_9,U_8) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ( v2_group_1(A)
& ~ v3_struct_0(A) )
| ~ v3_group_1(A)
| v3_struct_0(A)
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[cc1_group_1]) ).
fof(f_7_2,plain,
! [U_10] :
( ( v2_group_1(U_10)
& ~ v3_struct_0(U_10) )
| ~ v3_group_1(U_10)
| v3_struct_0(U_10)
| ~ l1_group_1(U_10) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( ~ v3_struct_0(U_10)
| ~ v3_group_1(U_10)
| v3_struct_0(U_10)
| ~ l1_group_1(U_10) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( v2_group_1(U_10)
| ~ v3_group_1(U_10)
| v3_struct_0(U_10)
| ~ l1_group_1(U_10) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_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_8_2,plain,
! [U_13,U_12,U_11] :
( v1_relat_1(U_11)
| ~ m1_subset_1(U_11,k1_zfmisc_1(k2_zfmisc_1(U_13,U_12))) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( v1_relat_1(U_11)
| ~ m1_subset_1(U_11,k1_zfmisc_1(k2_zfmisc_1(U_13,U_12))) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] :
( ( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) )
| ~ v1_funct_1(A)
| ~ v1_xboole_0(A)
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_9_2,plain,
! [U_14] :
( ( v2_funct_1(U_14)
& v1_funct_1(U_14)
& v1_relat_1(U_14) )
| ~ v1_funct_1(U_14)
| ~ v1_xboole_0(U_14)
| ~ v1_relat_1(U_14) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( v1_relat_1(U_14)
| ~ v1_funct_1(U_14)
| ~ v1_xboole_0(U_14)
| ~ v1_relat_1(U_14) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( v1_funct_1(U_14)
| ~ v1_funct_1(U_14)
| ~ v1_xboole_0(U_14)
| ~ v1_relat_1(U_14) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_5,plain,
( v2_funct_1(U_14)
| ~ v1_funct_1(U_14)
| ~ v1_xboole_0(U_14)
| ~ v1_relat_1(U_14) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_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_10_2,plain,
! [U_17,U_16] :
( ! [U_15] :
( ( v1_funct_2(U_15,U_17,U_16)
& v1_partfun1(U_15,U_17,U_16)
& v1_funct_1(U_15) )
| ~ v1_funct_2(U_15,U_17,U_16)
| ~ v1_funct_1(U_15)
| ~ m1_relset_1(U_15,U_17,U_16) )
| v1_xboole_0(U_16) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( v1_funct_1(U_15)
| ~ v1_funct_2(U_15,U_17,U_16)
| ~ v1_funct_1(U_15)
| ~ m1_relset_1(U_15,U_17,U_16)
| v1_xboole_0(U_16) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( v1_partfun1(U_15,U_17,U_16)
| ~ v1_funct_2(U_15,U_17,U_16)
| ~ v1_funct_1(U_15)
| ~ m1_relset_1(U_15,U_17,U_16)
| v1_xboole_0(U_16) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_5,plain,
( v1_funct_2(U_15,U_17,U_16)
| ~ v1_funct_2(U_15,U_17,U_16)
| ~ v1_funct_1(U_15)
| ~ m1_relset_1(U_15,U_17,U_16)
| v1_xboole_0(U_16) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_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_11_2,plain,
! [U_20,U_19] :
( ! [U_18] :
( ( v1_funct_2(U_18,U_20,U_19)
& v1_partfun1(U_18,U_20,U_19)
& ~ v1_xboole_0(U_18)
& v1_funct_1(U_18) )
| ~ v1_funct_2(U_18,U_20,U_19)
| ~ v1_funct_1(U_18)
| ~ m1_relset_1(U_18,U_20,U_19) )
| v1_xboole_0(U_19)
| v1_xboole_0(U_20) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( v1_funct_1(U_18)
| ~ v1_funct_2(U_18,U_20,U_19)
| ~ v1_funct_1(U_18)
| ~ m1_relset_1(U_18,U_20,U_19)
| v1_xboole_0(U_19)
| v1_xboole_0(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( ~ v1_xboole_0(U_18)
| ~ v1_funct_2(U_18,U_20,U_19)
| ~ v1_funct_1(U_18)
| ~ m1_relset_1(U_18,U_20,U_19)
| v1_xboole_0(U_19)
| v1_xboole_0(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_5,plain,
( v1_partfun1(U_18,U_20,U_19)
| ~ v1_funct_2(U_18,U_20,U_19)
| ~ v1_funct_1(U_18)
| ~ m1_relset_1(U_18,U_20,U_19)
| v1_xboole_0(U_19)
| v1_xboole_0(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_6,plain,
( v1_funct_2(U_18,U_20,U_19)
| ~ v1_funct_2(U_18,U_20,U_19)
| ~ v1_funct_1(U_18)
| ~ m1_relset_1(U_18,U_20,U_19)
| v1_xboole_0(U_19)
| v1_xboole_0(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B] :
( ( r1_tarski(A,B)
| ? [C] :
( ~ r2_hidden(C,B)
& r2_hidden(C,A) ) )
& ( ! [C] :
( r2_hidden(C,B)
| ~ r2_hidden(C,A) )
| ~ r1_tarski(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_12_2,plain,
! [U_24,U_23] :
( ( r1_tarski(U_24,U_23)
| ? [U_22] :
( ~ r2_hidden(U_22,U_23)
& r2_hidden(U_22,U_24) ) )
& ( ! [U_21] :
( r2_hidden(U_21,U_23)
| ~ r2_hidden(U_21,U_24) )
| ~ r1_tarski(U_24,U_23) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_28,U_26] :
( r1_tarski(U_28,U_26)
| ? [U_22] :
( ~ r2_hidden(U_22,U_26)
& r2_hidden(U_22,U_28) ) )
& ! [U_27,U_25] :
( ! [U_21] :
( r2_hidden(U_21,U_25)
| ~ r2_hidden(U_21,U_27) )
| ~ r1_tarski(U_27,U_25) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_28,U_26] :
( r1_tarski(U_28,U_26)
| ( ~ r2_hidden(sK2(U_28,U_26),U_26)
& r2_hidden(sK2(U_28,U_26),U_28) ) )
& ! [U_27,U_25] :
( ! [U_21] :
( r2_hidden(U_21,U_25)
| ~ r2_hidden(U_21,U_27) )
| ~ r1_tarski(U_27,U_25) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_22,sK2(U_28,U_26))],[f_12_3]) ).
cnf(f_12_5,plain,
( r2_hidden(U_21,U_25)
| ~ r2_hidden(U_21,U_27)
| ~ r1_tarski(U_27,U_25) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_6,plain,
( r2_hidden(sK2(U_28,U_26),U_28)
| r1_tarski(U_28,U_26) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_7,plain,
( ~ r2_hidden(sK2(U_28,U_26),U_26)
| r1_tarski(U_28,U_26) ),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_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_13_2,plain,
! [U_30,U_29] :
( ( l1_group_1(g1_group_1(U_30,U_29))
& v1_group_1(g1_group_1(U_30,U_29)) )
| ~ m1_relset_1(U_29,k2_zfmisc_1(U_30,U_30),U_30)
| ~ v1_funct_2(U_29,k2_zfmisc_1(U_30,U_30),U_30)
| ~ v1_funct_1(U_29) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( v1_group_1(g1_group_1(U_30,U_29))
| ~ m1_relset_1(U_29,k2_zfmisc_1(U_30,U_30),U_30)
| ~ v1_funct_2(U_29,k2_zfmisc_1(U_30,U_30),U_30)
| ~ v1_funct_1(U_29) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( l1_group_1(g1_group_1(U_30,U_29))
| ~ m1_relset_1(U_29,k2_zfmisc_1(U_30,U_30),U_30)
| ~ v1_funct_2(U_29,k2_zfmisc_1(U_30,U_30),U_30)
| ~ v1_funct_1(U_29) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_autgroup]) ).
fof(f_14_2,plain,
! [U_31] :
( m1_fraenkel(k1_autgroup(U_31),u1_struct_0(U_31),u1_struct_0(U_31))
| ~ l1_group_1(U_31)
| ~ v4_group_1(U_31)
| ~ v3_group_1(U_31)
| ~ v1_group_1(U_31)
| v3_struct_0(U_31) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( m1_fraenkel(k1_autgroup(U_31),u1_struct_0(U_31),u1_struct_0(U_31))
| ~ l1_group_1(U_31)
| ~ v4_group_1(U_31)
| ~ v3_group_1(U_31)
| ~ v1_group_1(U_31)
| v3_struct_0(U_31) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_16_2,plain,
$true,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_17_2,plain,
$true,
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A] :
( m1_fraenkel(k4_autgroup(A),u1_struct_0(A),u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_autgroup]) ).
fof(f_18_2,plain,
! [U_32] :
( m1_fraenkel(k4_autgroup(U_32),u1_struct_0(U_32),u1_struct_0(U_32))
| ~ l1_group_1(U_32)
| ~ v4_group_1(U_32)
| ~ v3_group_1(U_32)
| ~ v1_group_1(U_32)
| v3_struct_0(U_32) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( m1_fraenkel(k4_autgroup(U_32),u1_struct_0(U_32),u1_struct_0(U_32))
| ~ l1_group_1(U_32)
| ~ v4_group_1(U_32)
| ~ v3_group_1(U_32)
| ~ v1_group_1(U_32)
| v3_struct_0(U_32) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_group_1]) ).
fof(f_19_2,plain,
! [U_33] :
( l1_struct_0(U_33)
| ~ l1_group_1(U_33) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( l1_struct_0(U_33)
| ~ l1_group_1(U_33) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
! [A,B,C] :
( ( v1_fraenkel(C)
& ~ v1_xboole_0(C) )
| ~ m1_fraenkel(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m1_fraenkel]) ).
fof(f_21_2,plain,
! [U_36,U_35,U_34] :
( ( v1_fraenkel(U_34)
& ~ v1_xboole_0(U_34) )
| ~ m1_fraenkel(U_34,U_36,U_35) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( ~ v1_xboole_0(U_34)
| ~ m1_fraenkel(U_34,U_36,U_35) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( v1_fraenkel(U_34)
| ~ m1_fraenkel(U_34,U_36,U_35) ),
inference(clausify,[status(thm)],[f_21_2]) ).
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,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_23_2,plain,
$true,
inference(clausify,[status(thm)],[f_23_1]) ).
fof(f_24_1,plain,
! [A,B,C] :
( ! [D] :
( ( m2_relset_1(D,A,B)
& v1_funct_2(D,A,B)
& v1_funct_1(D) )
| ~ m2_fraenkel(D,A,B,C) )
| ~ m1_fraenkel(C,A,B)
| v1_xboole_0(B) ),
inference(fof_nnf,[status(thm)],[dt_m2_fraenkel]) ).
fof(f_24_2,plain,
! [U_40,U_39,U_38] :
( ! [U_37] :
( ( m2_relset_1(U_37,U_40,U_39)
& v1_funct_2(U_37,U_40,U_39)
& v1_funct_1(U_37) )
| ~ m2_fraenkel(U_37,U_40,U_39,U_38) )
| ~ m1_fraenkel(U_38,U_40,U_39)
| v1_xboole_0(U_39) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( v1_funct_1(U_37)
| ~ m2_fraenkel(U_37,U_40,U_39,U_38)
| ~ m1_fraenkel(U_38,U_40,U_39)
| v1_xboole_0(U_39) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( v1_funct_2(U_37,U_40,U_39)
| ~ m2_fraenkel(U_37,U_40,U_39,U_38)
| ~ m1_fraenkel(U_38,U_40,U_39)
| v1_xboole_0(U_39) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_5,plain,
( m2_relset_1(U_37,U_40,U_39)
| ~ m2_fraenkel(U_37,U_40,U_39,U_38)
| ~ m1_fraenkel(U_38,U_40,U_39)
| v1_xboole_0(U_39) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_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_25_2,plain,
! [U_43,U_42,U_41] :
( m1_subset_1(U_41,k1_zfmisc_1(k2_zfmisc_1(U_43,U_42)))
| ~ m2_relset_1(U_41,U_43,U_42) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( m1_subset_1(U_41,k1_zfmisc_1(k2_zfmisc_1(U_43,U_42)))
| ~ m2_relset_1(U_41,U_43,U_42) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_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_26_2,plain,
! [U_44] :
( ( m2_relset_1(u1_group_1(U_44),k2_zfmisc_1(u1_struct_0(U_44),u1_struct_0(U_44)),u1_struct_0(U_44))
& v1_funct_2(u1_group_1(U_44),k2_zfmisc_1(u1_struct_0(U_44),u1_struct_0(U_44)),u1_struct_0(U_44))
& v1_funct_1(u1_group_1(U_44)) )
| ~ l1_group_1(U_44) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( v1_funct_1(u1_group_1(U_44))
| ~ l1_group_1(U_44) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( v1_funct_2(u1_group_1(U_44),k2_zfmisc_1(u1_struct_0(U_44),u1_struct_0(U_44)),u1_struct_0(U_44))
| ~ l1_group_1(U_44) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_5,plain,
( m2_relset_1(u1_group_1(U_44),k2_zfmisc_1(u1_struct_0(U_44),u1_struct_0(U_44)),u1_struct_0(U_44))
| ~ l1_group_1(U_44) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_27_2,plain,
$true,
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_28_1,plain,
? [A] : l1_group_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_group_1]) ).
fof(f_28_2,plain,
? [U_45] : l1_group_1(U_45),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
l1_group_1(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_45,sK3)],[f_28_2]) ).
cnf(f_28_4,plain,
l1_group_1(sK3),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_29_2,plain,
? [U_46] : l1_struct_0(U_46),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
l1_struct_0(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_46,sK4)],[f_29_2]) ).
cnf(f_29_4,plain,
l1_struct_0(sK4),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A,B] :
? [C] : m1_fraenkel(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_fraenkel]) ).
fof(f_30_2,plain,
! [U_49,U_48] :
? [U_47] : m1_fraenkel(U_47,U_49,U_48),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_49,U_48] : m1_fraenkel(sK5(U_49,U_48),U_49,U_48),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_47,sK5(U_49,U_48))],[f_30_2]) ).
cnf(f_30_4,plain,
m1_fraenkel(sK5(U_49,U_48),U_49,U_48),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_31_2,plain,
! [U_52,U_51] :
? [U_50] : m1_relset_1(U_50,U_52,U_51),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_52,U_51] : m1_relset_1(sK6(U_52,U_51),U_52,U_51),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_50,sK6(U_52,U_51))],[f_31_2]) ).
cnf(f_31_4,plain,
m1_relset_1(sK6(U_52,U_51),U_52,U_51),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_32_2,plain,
! [U_54] :
? [U_53] : m1_subset_1(U_53,U_54),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_54] : m1_subset_1(sK7(U_54),U_54),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_53,sK7(U_54))],[f_32_2]) ).
cnf(f_32_4,plain,
m1_subset_1(sK7(U_54),U_54),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [A,B,C] :
( ? [D] : m2_fraenkel(D,A,B,C)
| ~ m1_fraenkel(C,A,B)
| v1_xboole_0(B) ),
inference(fof_nnf,[status(thm)],[existence_m2_fraenkel]) ).
fof(f_33_2,plain,
! [U_58,U_57,U_56] :
( ? [U_55] : m2_fraenkel(U_55,U_58,U_57,U_56)
| ~ m1_fraenkel(U_56,U_58,U_57)
| v1_xboole_0(U_57) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_58,U_57,U_56] :
( m2_fraenkel(sK8(U_58,U_57,U_56),U_58,U_57,U_56)
| ~ m1_fraenkel(U_56,U_58,U_57)
| v1_xboole_0(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_55,sK8(U_58,U_57,U_56))],[f_33_2]) ).
cnf(f_33_4,plain,
( m2_fraenkel(sK8(U_58,U_57,U_56),U_58,U_57,U_56)
| ~ m1_fraenkel(U_56,U_58,U_57)
| v1_xboole_0(U_57) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_34_2,plain,
! [U_61,U_60] :
? [U_59] : m2_relset_1(U_59,U_61,U_60),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_61,U_60] : m2_relset_1(sK9(U_61,U_60),U_61,U_60),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_59,sK9(U_61,U_60))],[f_34_2]) ).
cnf(f_34_4,plain,
m2_relset_1(sK9(U_61,U_60),U_61,U_60),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A,B] :
( ( v1_group_1(g1_group_1(A,B))
& ~ v3_struct_0(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)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[fc1_group_1]) ).
fof(f_35_2,plain,
! [U_63,U_62] :
( ( v1_group_1(g1_group_1(U_63,U_62))
& ~ v3_struct_0(g1_group_1(U_63,U_62)) )
| ~ m1_relset_1(U_62,k2_zfmisc_1(U_63,U_63),U_63)
| ~ v1_funct_2(U_62,k2_zfmisc_1(U_63,U_63),U_63)
| ~ v1_funct_1(U_62)
| v1_xboole_0(U_63) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( ~ v3_struct_0(g1_group_1(U_63,U_62))
| ~ m1_relset_1(U_62,k2_zfmisc_1(U_63,U_63),U_63)
| ~ v1_funct_2(U_62,k2_zfmisc_1(U_63,U_63),U_63)
| ~ v1_funct_1(U_62)
| v1_xboole_0(U_63) ),
inference(clausify,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( v1_group_1(g1_group_1(U_63,U_62))
| ~ m1_relset_1(U_62,k2_zfmisc_1(U_63,U_63),U_63)
| ~ v1_funct_2(U_62,k2_zfmisc_1(U_63,U_63),U_63)
| ~ v1_funct_1(U_62)
| v1_xboole_0(U_63) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_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_36_2,plain,
! [U_64] :
( ~ v1_xboole_0(u1_struct_0(U_64))
| ~ l1_struct_0(U_64)
| v3_struct_0(U_64) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_64))
| ~ l1_struct_0(U_64)
| v3_struct_0(U_64) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_37_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_38_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_38_2,plain,
! [U_68,U_67] :
( ! [U_66,U_65] :
( ( U_67 = U_65
& U_68 = U_66 )
| g1_group_1(U_68,U_67) != g1_group_1(U_66,U_65) )
| ~ m1_relset_1(U_67,k2_zfmisc_1(U_68,U_68),U_68)
| ~ v1_funct_2(U_67,k2_zfmisc_1(U_68,U_68),U_68)
| ~ v1_funct_1(U_67) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( U_68 = U_66
| g1_group_1(U_68,U_67) != g1_group_1(U_66,U_65)
| ~ m1_relset_1(U_67,k2_zfmisc_1(U_68,U_68),U_68)
| ~ v1_funct_2(U_67,k2_zfmisc_1(U_68,U_68),U_68)
| ~ v1_funct_1(U_67) ),
inference(clausify,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( U_67 = U_65
| g1_group_1(U_68,U_67) != g1_group_1(U_66,U_65)
| ~ m1_relset_1(U_67,k2_zfmisc_1(U_68,U_68),U_68)
| ~ v1_funct_2(U_67,k2_zfmisc_1(U_68,U_68),U_68)
| ~ v1_funct_1(U_67) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
? [A] :
( v1_fraenkel(A)
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_fraenkel]) ).
fof(f_39_2,plain,
? [U_69] :
( v1_fraenkel(U_69)
& ~ v1_xboole_0(U_69) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( v1_fraenkel(sK10)
& ~ v1_xboole_0(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_69,sK10)],[f_39_2]) ).
cnf(f_39_4,plain,
~ v1_xboole_0(sK10),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
v1_fraenkel(sK10),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_40_2,plain,
? [U_70] :
( v1_funct_1(U_70)
& v1_relat_1(U_70) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( v1_funct_1(sK11)
& v1_relat_1(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_70,sK11)],[f_40_2]) ).
cnf(f_40_4,plain,
v1_relat_1(sK11),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
v1_funct_1(sK11),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_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_41_2,plain,
! [U_73,U_72] :
? [U_71] :
( v1_funct_2(U_71,U_73,U_72)
& v1_funct_1(U_71)
& v1_relat_1(U_71)
& m1_relset_1(U_71,U_73,U_72) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_73,U_72] :
( v1_funct_2(sK12(U_73,U_72),U_73,U_72)
& v1_funct_1(sK12(U_73,U_72))
& v1_relat_1(sK12(U_73,U_72))
& m1_relset_1(sK12(U_73,U_72),U_73,U_72) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_71,sK12(U_73,U_72))],[f_41_2]) ).
cnf(f_41_4,plain,
m1_relset_1(sK12(U_73,U_72),U_73,U_72),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
v1_relat_1(sK12(U_73,U_72)),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_6,plain,
v1_funct_1(sK12(U_73,U_72)),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_7,plain,
v1_funct_2(sK12(U_73,U_72),U_73,U_72),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
? [A] :
( v1_group_1(A)
& l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_group_1]) ).
fof(f_42_2,plain,
? [U_74] :
( v1_group_1(U_74)
& l1_group_1(U_74) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( v1_group_1(sK13)
& l1_group_1(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_74,sK13)],[f_42_2]) ).
cnf(f_42_4,plain,
l1_group_1(sK13),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_5,plain,
v1_group_1(sK13),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
? [A] :
( v1_xboole_0(A)
& v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_partfun1]) ).
fof(f_43_2,plain,
? [U_75] :
( v1_xboole_0(U_75)
& v2_funct_1(U_75)
& v1_funct_1(U_75)
& v1_relat_1(U_75) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( v1_xboole_0(sK14)
& v2_funct_1(sK14)
& v1_funct_1(sK14)
& v1_relat_1(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_75,sK14)],[f_43_2]) ).
cnf(f_43_4,plain,
v1_relat_1(sK14),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
v1_funct_1(sK14),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_6,plain,
v2_funct_1(sK14),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_7,plain,
v1_xboole_0(sK14),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_44_2,plain,
? [U_76] : v1_xboole_0(U_76),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
v1_xboole_0(sK15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_76,sK15)],[f_44_2]) ).
cnf(f_44_4,plain,
v1_xboole_0(sK15),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_45_2,plain,
? [U_77] :
( v1_funct_1(U_77)
& v1_xboole_0(U_77)
& v1_relat_1(U_77) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( v1_funct_1(sK16)
& v1_xboole_0(sK16)
& v1_relat_1(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_77,sK16)],[f_45_2]) ).
cnf(f_45_4,plain,
v1_relat_1(sK16),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_5,plain,
v1_xboole_0(sK16),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_6,plain,
v1_funct_1(sK16),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
? [A] :
( v1_group_1(A)
& ~ v3_struct_0(A)
& l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[rc2_group_1]) ).
fof(f_46_2,plain,
? [U_78] :
( v1_group_1(U_78)
& ~ v3_struct_0(U_78)
& l1_group_1(U_78) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( v1_group_1(sK17)
& ~ v3_struct_0(sK17)
& l1_group_1(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_78,sK17)],[f_46_2]) ).
cnf(f_46_4,plain,
l1_group_1(sK17),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_5,plain,
~ v3_struct_0(sK17),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_6,plain,
v1_group_1(sK17),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_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_47_2,plain,
! [U_81,U_80] :
? [U_79] :
( v1_funct_1(U_79)
& v1_relat_1(U_79)
& m1_relset_1(U_79,U_81,U_80) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_81,U_80] :
( v1_funct_1(sK18(U_81,U_80))
& v1_relat_1(sK18(U_81,U_80))
& m1_relset_1(sK18(U_81,U_80),U_81,U_80) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_79,sK18(U_81,U_80))],[f_47_2]) ).
cnf(f_47_4,plain,
m1_relset_1(sK18(U_81,U_80),U_81,U_80),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_5,plain,
v1_relat_1(sK18(U_81,U_80)),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_6,plain,
v1_funct_1(sK18(U_81,U_80)),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_48_2,plain,
? [U_82] : ~ v1_xboole_0(U_82),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
~ v1_xboole_0(sK19),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_82,sK19)],[f_48_2]) ).
cnf(f_48_4,plain,
~ v1_xboole_0(sK19),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
? [A] :
( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_49_2,plain,
? [U_83] :
( v2_funct_1(U_83)
& v1_funct_1(U_83)
& v1_relat_1(U_83) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( v2_funct_1(sK20)
& v1_funct_1(sK20)
& v1_relat_1(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_83,sK20)],[f_49_2]) ).
cnf(f_49_4,plain,
v1_relat_1(sK20),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
v1_funct_1(sK20),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_6,plain,
v2_funct_1(sK20),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
? [A] :
( v4_group_1(A)
& v3_group_1(A)
& v2_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A)
& l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[rc3_group_1]) ).
fof(f_50_2,plain,
? [U_84] :
( v4_group_1(U_84)
& v3_group_1(U_84)
& v2_group_1(U_84)
& v1_group_1(U_84)
& ~ v3_struct_0(U_84)
& l1_group_1(U_84) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
( v4_group_1(sK21)
& v3_group_1(sK21)
& v2_group_1(sK21)
& v1_group_1(sK21)
& ~ v3_struct_0(sK21)
& l1_group_1(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_84,sK21)],[f_50_2]) ).
cnf(f_50_4,plain,
l1_group_1(sK21),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_5,plain,
~ v3_struct_0(sK21),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_6,plain,
v1_group_1(sK21),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_7,plain,
v2_group_1(sK21),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_8,plain,
v3_group_1(sK21),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_9,plain,
v4_group_1(sK21),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_51_2,plain,
? [U_85] :
( ~ v3_struct_0(U_85)
& l1_struct_0(U_85) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ~ v3_struct_0(sK22)
& l1_struct_0(sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_85,sK22)],[f_51_2]) ).
cnf(f_51_4,plain,
l1_struct_0(sK22),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
~ v3_struct_0(sK22),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_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_52_2,plain,
! [U_87] :
( ? [U_86] :
( ~ v1_xboole_0(U_86)
& m1_subset_1(U_86,k1_zfmisc_1(u1_struct_0(U_87))) )
| ~ l1_struct_0(U_87)
| v3_struct_0(U_87) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_87] :
( ( ~ v1_xboole_0(sK23(U_87))
& m1_subset_1(sK23(U_87),k1_zfmisc_1(u1_struct_0(U_87))) )
| ~ l1_struct_0(U_87)
| v3_struct_0(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_86,sK23(U_87))],[f_52_2]) ).
cnf(f_52_4,plain,
( m1_subset_1(sK23(U_87),k1_zfmisc_1(u1_struct_0(U_87)))
| ~ l1_struct_0(U_87)
| v3_struct_0(U_87) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
( ~ v1_xboole_0(sK23(U_87))
| ~ l1_struct_0(U_87)
| v3_struct_0(U_87) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [A,B,C] :
( ! [D] :
( ( m2_fraenkel(D,A,B,C)
| ~ m1_subset_1(D,C) )
& ( m1_subset_1(D,C)
| ~ m2_fraenkel(D,A,B,C) ) )
| ~ m1_fraenkel(C,A,B)
| v1_xboole_0(B) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_fraenkel]) ).
fof(f_53_2,plain,
! [U_91,U_90,U_89] :
( ! [U_88] :
( ( m2_fraenkel(U_88,U_91,U_90,U_89)
| ~ m1_subset_1(U_88,U_89) )
& ( m1_subset_1(U_88,U_89)
| ~ m2_fraenkel(U_88,U_91,U_90,U_89) ) )
| ~ m1_fraenkel(U_89,U_91,U_90)
| v1_xboole_0(U_90) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_91,U_90,U_89] :
( ( ! [U_93] :
( m2_fraenkel(U_93,U_91,U_90,U_89)
| ~ m1_subset_1(U_93,U_89) )
& ! [U_92] :
( m1_subset_1(U_92,U_89)
| ~ m2_fraenkel(U_92,U_91,U_90,U_89) ) )
| ~ m1_fraenkel(U_89,U_91,U_90)
| v1_xboole_0(U_90) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
cnf(f_53_4,plain,
( m1_subset_1(U_92,U_89)
| ~ m2_fraenkel(U_92,U_91,U_90,U_89)
| ~ m1_fraenkel(U_89,U_91,U_90)
| v1_xboole_0(U_90) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_5,plain,
( m2_fraenkel(U_93,U_91,U_90,U_89)
| ~ m1_subset_1(U_93,U_89)
| ~ m1_fraenkel(U_89,U_91,U_90)
| v1_xboole_0(U_90) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_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_54_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_54_1]) ).
fof(f_54_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_54_2]) ).
cnf(f_54_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_54_3]) ).
cnf(f_54_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_54_3]) ).
fof(f_55_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_55_2,plain,
! [U_104,U_103] : r1_tarski(U_104,U_104),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_104] : r1_tarski(U_104,U_104),
inference(miniscope,[status(thm)],[f_55_2]) ).
cnf(f_55_4,plain,
r1_tarski(U_104,U_104),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [A] :
( ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
| ~ m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t13_autgroup]) ).
fof(f_56_2,plain,
! [U_106] :
( ! [U_105] :
( m2_fraenkel(U_105,u1_struct_0(U_106),u1_struct_0(U_106),k1_autgroup(U_106))
| ~ m2_fraenkel(U_105,u1_struct_0(U_106),u1_struct_0(U_106),k4_autgroup(U_106)) )
| ~ l1_group_1(U_106)
| ~ v4_group_1(U_106)
| ~ v3_group_1(U_106)
| ~ v1_group_1(U_106)
| v3_struct_0(U_106) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( m2_fraenkel(U_105,u1_struct_0(U_106),u1_struct_0(U_106),k1_autgroup(U_106))
| ~ m2_fraenkel(U_105,u1_struct_0(U_106),u1_struct_0(U_106),k4_autgroup(U_106))
| ~ l1_group_1(U_106)
| ~ v4_group_1(U_106)
| ~ v3_group_1(U_106)
| ~ v1_group_1(U_106)
| v3_struct_0(U_106) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_57_2,plain,
! [U_108,U_107] :
( m1_subset_1(U_108,U_107)
| ~ r2_hidden(U_108,U_107) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( m1_subset_1(U_108,U_107)
| ~ r2_hidden(U_108,U_107) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_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_58_2,plain,
! [U_110,U_109] :
( r2_hidden(U_110,U_109)
| v1_xboole_0(U_109)
| ~ m1_subset_1(U_110,U_109) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( r2_hidden(U_110,U_109)
| v1_xboole_0(U_109)
| ~ m1_subset_1(U_110,U_109) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_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_59_2,plain,
! [U_112,U_111] :
( ( m1_subset_1(U_112,k1_zfmisc_1(U_111))
| ~ r1_tarski(U_112,U_111) )
& ( r1_tarski(U_112,U_111)
| ~ m1_subset_1(U_112,k1_zfmisc_1(U_111)) ) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( ! [U_116,U_114] :
( m1_subset_1(U_116,k1_zfmisc_1(U_114))
| ~ r1_tarski(U_116,U_114) )
& ! [U_115,U_113] :
( r1_tarski(U_115,U_113)
| ~ m1_subset_1(U_115,k1_zfmisc_1(U_113)) ) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
cnf(f_59_4,plain,
( r1_tarski(U_115,U_113)
| ~ m1_subset_1(U_115,k1_zfmisc_1(U_113)) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_5,plain,
( m1_subset_1(U_116,k1_zfmisc_1(U_114))
| ~ r1_tarski(U_116,U_114) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_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_60_2,plain,
! [U_119,U_118,U_117] :
( m1_subset_1(U_119,U_117)
| ~ m1_subset_1(U_118,k1_zfmisc_1(U_117))
| ~ r2_hidden(U_119,U_118) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
( m1_subset_1(U_119,U_117)
| ~ m1_subset_1(U_118,k1_zfmisc_1(U_117))
| ~ r2_hidden(U_119,U_118) ),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_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_61_2,plain,
! [U_122,U_121,U_120] :
( ~ v1_xboole_0(U_120)
| ~ m1_subset_1(U_121,k1_zfmisc_1(U_120))
| ~ r2_hidden(U_122,U_121) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_122,U_121] :
( ! [U_120] :
( ~ v1_xboole_0(U_120)
| ~ m1_subset_1(U_121,k1_zfmisc_1(U_120)) )
| ~ r2_hidden(U_122,U_121) ),
inference(miniscope,[status(thm)],[f_61_2]) ).
cnf(f_61_4,plain,
( ~ v1_xboole_0(U_120)
| ~ m1_subset_1(U_121,k1_zfmisc_1(U_120))
| ~ r2_hidden(U_122,U_121) ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_62_2,plain,
! [U_123] :
( U_123 = k1_xboole_0
| ~ v1_xboole_0(U_123) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( U_123 = k1_xboole_0
| ~ v1_xboole_0(U_123) ),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_63_2,plain,
! [U_125,U_124] :
( ~ v1_xboole_0(U_124)
| ~ r2_hidden(U_125,U_124) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( ~ v1_xboole_0(U_124)
| ~ r2_hidden(U_125,U_124) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_64_2,plain,
! [U_127,U_126] :
( ~ v1_xboole_0(U_126)
| U_127 = U_126
| ~ v1_xboole_0(U_127) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_127] :
( ! [U_126] :
( ~ v1_xboole_0(U_126)
| U_127 = U_126 )
| ~ v1_xboole_0(U_127) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
cnf(f_64_4,plain,
( ~ v1_xboole_0(U_126)
| U_127 = U_126
| ~ v1_xboole_0(U_127) ),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_3]) ).
cnf(f_9_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_4]) ).
cnf(f_10_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_3]) ).
cnf(f_10_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_5]) ).
cnf(f_11_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_3]) ).
cnf(f_11_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_6]) ).
cnf(f_15_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_2]) ).
cnf(f_16_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_2]) ).
cnf(f_17_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(f_22_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_22_2]) ).
cnf(f_23_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_23_2]) ).
cnf(f_27_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_27_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,
( k4_autgroup(Eq_x_0) = k4_autgroup(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k1_autgroup(Eq_x_0) = k1_autgroup(Eq_y_0)
| 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,
( sK2(Eq_x_0,Eq_x_1) = sK2(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,
( sK5(Eq_x_0,Eq_x_1) = sK5(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,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(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_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,
( sK12(Eq_x_0,Eq_x_1) = sK12(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,
( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,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_22,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_23,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_24,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_25,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_26,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_27,axiom,
( v1_fraenkel(Eq_y_0)
| ~ v1_fraenkel(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,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_29,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_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_xboole_0(Eq_y_0)
| ~ v1_xboole_0(Eq_x_0)
| 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,
( 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_34,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_35,axiom,
( v2_group_1(Eq_y_0)
| ~ v2_group_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( v2_funct_1(Eq_y_0)
| ~ v2_funct_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( m1_fraenkel(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m1_fraenkel(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_38,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_39,axiom,
( m2_fraenkel(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ m2_fraenkel(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_40,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP623+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
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 09:53:27 UTC 2026
% 0.13/0.36 % CPUTime :
% 100.65/100.92 % SZS status Theorem for theBenchmark
% 100.65/100.92 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------