%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP618+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 08:42:01 AM UTC 2026
% Result : Theorem 2.65s 2.90s
% Output : Proof 2.65s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t1_autgroup,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( m1_subset_1(D,u1_struct_0(B))
=> r1_rlvect_1(B,k2_group_3(A,D,C)) ) ) )
<=> v1_group_3(B,A) ) ) ),
file('theBenchmark.p',t1_autgroup) ).
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(rc3_funct_1,axiom,
? [A] :
( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) )
=> ( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_funct_2,axiom,
! [A,B] :
? [C] :
( v1_funct_2(C,A,B)
& v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
file('theBenchmark.p',rc1_funct_2) ).
fof(rc2_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc2_funct_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(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
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(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(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_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(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_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(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_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(cc1_funct_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_funct_1(A) ),
file('theBenchmark.p',cc1_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(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(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(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(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(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A),
file('theBenchmark.p',existence_l1_struct_0) ).
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_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_u1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> ( m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_group_1(A)) ) ),
file('theBenchmark.p',dt_u1_group_1) ).
fof(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(rc1_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( v4_group_1(B)
& v3_group_1(B)
& v2_group_1(B)
& v1_group_1(B)
& ~ v3_struct_0(B)
& m1_group_2(B,A) ) ),
file('theBenchmark.p',rc1_group_2) ).
fof(rc1_group_3,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( v1_group_3(B,A)
& v4_group_1(B)
& v3_group_1(B)
& v2_group_1(B)
& v1_group_1(B)
& ~ v3_struct_0(B)
& m1_group_2(B,A) ) ),
file('theBenchmark.p',rc1_group_3) ).
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(abstractness_v1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> ( v1_group_1(A)
=> A = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ),
file('theBenchmark.p',abstractness_v1_group_1) ).
fof(existence_l1_group_1,axiom,
? [A] : l1_group_1(A),
file('theBenchmark.p',existence_l1_group_1) ).
fof(existence_m1_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ? [B] : m1_group_2(B,A) ),
file('theBenchmark.p',existence_m1_group_2) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(dt_k2_group_3,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k2_group_3(A,B,C),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k2_group_3) ).
fof(dt_l1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_group_1) ).
fof(dt_m1_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) ) ) ),
file('theBenchmark.p',dt_m1_group_2) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
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_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> v4_group_1(B) ) ),
file('theBenchmark.p',cc1_group_2) ).
fof(rc1_group_1,axiom,
? [A] :
( v1_group_1(A)
& l1_group_1(A) ),
file('theBenchmark.p',rc1_group_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(l1_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( m1_subset_1(D,u1_struct_0(B))
=> r1_rlvect_1(B,k2_group_3(A,D,C)) ) ) )
=> v1_group_3(B,A) ) ) ),
file('theBenchmark.p',l1_autgroup) ).
fof(l2_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( v1_group_3(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( m1_subset_1(D,u1_struct_0(B))
=> r1_rlvect_1(B,k2_group_3(A,D,C)) ) ) ) ) ) ),
file('theBenchmark.p',l2_autgroup) ).
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) )
=> ! [B] :
( m1_group_2(B,A)
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( m1_subset_1(D,u1_struct_0(B))
=> r1_rlvect_1(B,k2_group_3(A,D,C)) ) ) )
<=> v1_group_3(B,A) ) ) ),
inference(negate,[status(cth)],[t1_autgroup]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ( ( ? [C] :
( ? [D] :
( ~ r1_rlvect_1(B,k2_group_3(A,D,C))
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(A)) )
& m1_subset_1(C,u1_struct_0(A)) )
& v1_group_3(B,A) )
| ( ~ v1_group_3(B,A)
& ! [C] :
( ! [D] :
( r1_rlvect_1(B,k2_group_3(A,D,C))
| ~ m1_subset_1(D,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(A)) )
| ~ m1_subset_1(C,u1_struct_0(A)) ) ) )
& m1_group_2(B,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_5] :
( ? [U_4] :
( ( ( ? [U_3] :
( ? [U_2] :
( ~ r1_rlvect_1(U_4,k2_group_3(U_5,U_2,U_3))
& m1_subset_1(U_2,u1_struct_0(U_4))
& m1_subset_1(U_2,u1_struct_0(U_5)) )
& m1_subset_1(U_3,u1_struct_0(U_5)) )
& v1_group_3(U_4,U_5) )
| ( ~ v1_group_3(U_4,U_5)
& ! [U_1] :
( ! [U_0] :
( r1_rlvect_1(U_4,k2_group_3(U_5,U_0,U_1))
| ~ m1_subset_1(U_0,u1_struct_0(U_4))
| ~ m1_subset_1(U_0,u1_struct_0(U_5)) )
| ~ m1_subset_1(U_1,u1_struct_0(U_5)) ) ) )
& m1_group_2(U_4,U_5) )
& l1_group_1(U_5)
& v4_group_1(U_5)
& v3_group_1(U_5)
& v1_group_1(U_5)
& ~ v3_struct_0(U_5) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_4] :
( ( ( ? [U_3] :
( ? [U_2] :
( ~ r1_rlvect_1(U_4,k2_group_3(sK1,U_2,U_3))
& m1_subset_1(U_2,u1_struct_0(U_4))
& m1_subset_1(U_2,u1_struct_0(sK1)) )
& m1_subset_1(U_3,u1_struct_0(sK1)) )
& v1_group_3(U_4,sK1) )
| ( ~ v1_group_3(U_4,sK1)
& ! [U_1] :
( ! [U_0] :
( r1_rlvect_1(U_4,k2_group_3(sK1,U_0,U_1))
| ~ m1_subset_1(U_0,u1_struct_0(U_4))
| ~ m1_subset_1(U_0,u1_struct_0(sK1)) )
| ~ m1_subset_1(U_1,u1_struct_0(sK1)) ) ) )
& m1_group_2(U_4,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_5,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ( ( ? [U_3] :
( ? [U_2] :
( ~ r1_rlvect_1(sK2,k2_group_3(sK1,U_2,U_3))
& m1_subset_1(U_2,u1_struct_0(sK2))
& m1_subset_1(U_2,u1_struct_0(sK1)) )
& m1_subset_1(U_3,u1_struct_0(sK1)) )
& v1_group_3(sK2,sK1) )
| ( ~ v1_group_3(sK2,sK1)
& ! [U_1] :
( ! [U_0] :
( r1_rlvect_1(sK2,k2_group_3(sK1,U_0,U_1))
| ~ m1_subset_1(U_0,u1_struct_0(sK2))
| ~ m1_subset_1(U_0,u1_struct_0(sK1)) )
| ~ m1_subset_1(U_1,u1_struct_0(sK1)) ) ) )
& m1_group_2(sK2,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,[sK2]),skolemize(U_4,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( ( ? [U_2] :
( ~ r1_rlvect_1(sK2,k2_group_3(sK1,U_2,sK3))
& m1_subset_1(U_2,u1_struct_0(sK2))
& m1_subset_1(U_2,u1_struct_0(sK1)) )
& m1_subset_1(sK3,u1_struct_0(sK1))
& v1_group_3(sK2,sK1) )
| ( ~ v1_group_3(sK2,sK1)
& ! [U_1] :
( ! [U_0] :
( r1_rlvect_1(sK2,k2_group_3(sK1,U_0,U_1))
| ~ m1_subset_1(U_0,u1_struct_0(sK2))
| ~ m1_subset_1(U_0,u1_struct_0(sK1)) )
| ~ m1_subset_1(U_1,u1_struct_0(sK1)) ) ) )
& m1_group_2(sK2,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,[sK3]),skolemize(U_3,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ( ( ~ r1_rlvect_1(sK2,k2_group_3(sK1,sK4,sK3))
& m1_subset_1(sK4,u1_struct_0(sK2))
& m1_subset_1(sK4,u1_struct_0(sK1))
& m1_subset_1(sK3,u1_struct_0(sK1))
& v1_group_3(sK2,sK1) )
| ( ~ v1_group_3(sK2,sK1)
& ! [U_1] :
( ! [U_0] :
( r1_rlvect_1(sK2,k2_group_3(sK1,U_0,U_1))
| ~ m1_subset_1(U_0,u1_struct_0(sK2))
| ~ m1_subset_1(U_0,u1_struct_0(sK1)) )
| ~ m1_subset_1(U_1,u1_struct_0(sK1)) ) ) )
& m1_group_2(sK2,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,[sK4]),skolemize(U_2,sK4)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ( ~ r1_rlvect_1(sK2,k2_group_3(sK1,sK4,sK3))
| ~ sP1 )
& ( m1_subset_1(sK4,u1_struct_0(sK2))
| ~ sP1 )
& ( m1_subset_1(sK4,u1_struct_0(sK1))
| ~ sP1 )
& ( m1_subset_1(sK3,u1_struct_0(sK1))
| ~ sP1 )
& ( v1_group_3(sK2,sK1)
| ~ sP1 )
& ! [U_0,U_1] :
( ~ v1_group_3(sK2,sK1)
| ~ sP0(U_0,U_1) )
& ! [U_0,U_1] :
( r1_rlvect_1(sK2,k2_group_3(sK1,U_0,U_1))
| ~ m1_subset_1(U_0,u1_struct_0(sK2))
| ~ m1_subset_1(U_0,u1_struct_0(sK1))
| ~ m1_subset_1(U_1,u1_struct_0(sK1))
| ~ sP0(U_0,U_1) )
& ! [U_0,U_1] :
( sP1
| sP0(U_0,U_1) )
& m1_group_2(sK2,sK1)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& v1_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_10,negated_conjecture,
v1_group_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_11,negated_conjecture,
v3_group_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_12,negated_conjecture,
v4_group_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_13,negated_conjecture,
l1_group_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_14,negated_conjecture,
m1_group_2(sK2,sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_15,negated_conjecture,
( sP1
| sP0(U_0,U_1) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_16,negated_conjecture,
( r1_rlvect_1(sK2,k2_group_3(sK1,U_0,U_1))
| ~ m1_subset_1(U_0,u1_struct_0(sK2))
| ~ m1_subset_1(U_0,u1_struct_0(sK1))
| ~ m1_subset_1(U_1,u1_struct_0(sK1))
| ~ sP0(U_0,U_1) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_17,negated_conjecture,
( ~ v1_group_3(sK2,sK1)
| ~ sP0(U_0,U_1) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_18,negated_conjecture,
( v1_group_3(sK2,sK1)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_19,negated_conjecture,
( m1_subset_1(sK3,u1_struct_0(sK1))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_20,negated_conjecture,
( m1_subset_1(sK4,u1_struct_0(sK1))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_21,negated_conjecture,
( m1_subset_1(sK4,u1_struct_0(sK2))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_22,negated_conjecture,
( ~ r1_rlvect_1(sK2,k2_group_3(sK1,sK4,sK3))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_1_8]) ).
fof(f_2_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_2_2,plain,
? [U_6] :
( v1_xboole_0(U_6)
& v2_funct_1(U_6)
& v1_funct_1(U_6)
& v1_relat_1(U_6) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( v1_xboole_0(sK5)
& v2_funct_1(sK5)
& v1_funct_1(sK5)
& v1_relat_1(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_6,sK5)],[f_2_2]) ).
cnf(f_2_4,plain,
v1_relat_1(sK5),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
v1_funct_1(sK5),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
v2_funct_1(sK5),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_7,plain,
v1_xboole_0(sK5),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_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_3_2,plain,
? [U_7] :
( v2_funct_1(U_7)
& v1_funct_1(U_7)
& v1_relat_1(U_7) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( v2_funct_1(sK6)
& v1_funct_1(sK6)
& v1_relat_1(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_7,sK6)],[f_3_2]) ).
cnf(f_3_4,plain,
v1_relat_1(sK6),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
v1_funct_1(sK6),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
v2_funct_1(sK6),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_4_2,plain,
! [U_9,U_8] : r1_tarski(U_9,U_9),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_9] : r1_tarski(U_9,U_9),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
r1_tarski(U_9,U_9),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_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_5_2,plain,
! [U_10] :
( ( v2_funct_1(U_10)
& v1_funct_1(U_10)
& v1_relat_1(U_10) )
| ~ v1_funct_1(U_10)
| ~ v1_xboole_0(U_10)
| ~ v1_relat_1(U_10) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( v1_relat_1(U_10)
| ~ v1_funct_1(U_10)
| ~ v1_xboole_0(U_10)
| ~ v1_relat_1(U_10) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( v1_funct_1(U_10)
| ~ v1_funct_1(U_10)
| ~ v1_xboole_0(U_10)
| ~ v1_relat_1(U_10) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( v2_funct_1(U_10)
| ~ v1_funct_1(U_10)
| ~ v1_xboole_0(U_10)
| ~ v1_relat_1(U_10) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_6_2,plain,
? [U_11] :
( v1_funct_1(U_11)
& v1_relat_1(U_11) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( v1_funct_1(sK7)
& v1_relat_1(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_11,sK7)],[f_6_2]) ).
cnf(f_6_4,plain,
v1_relat_1(sK7),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
v1_funct_1(sK7),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_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_7_2,plain,
! [U_14,U_13] :
? [U_12] :
( v1_funct_2(U_12,U_14,U_13)
& v1_funct_1(U_12)
& v1_relat_1(U_12)
& m1_relset_1(U_12,U_14,U_13) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_14,U_13] :
( v1_funct_2(sK8(U_14,U_13),U_14,U_13)
& v1_funct_1(sK8(U_14,U_13))
& v1_relat_1(sK8(U_14,U_13))
& m1_relset_1(sK8(U_14,U_13),U_14,U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_12,sK8(U_14,U_13))],[f_7_2]) ).
cnf(f_7_4,plain,
m1_relset_1(sK8(U_14,U_13),U_14,U_13),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
v1_relat_1(sK8(U_14,U_13)),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
v1_funct_1(sK8(U_14,U_13)),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
v1_funct_2(sK8(U_14,U_13),U_14,U_13),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_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_8_2,plain,
? [U_15] :
( v1_funct_1(U_15)
& v1_xboole_0(U_15)
& v1_relat_1(U_15) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( v1_funct_1(sK9)
& v1_xboole_0(sK9)
& v1_relat_1(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_15,sK9)],[f_8_2]) ).
cnf(f_8_4,plain,
v1_relat_1(sK9),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
v1_xboole_0(sK9),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
v1_funct_1(sK9),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_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_9_2,plain,
! [U_18,U_17] :
? [U_16] :
( v1_funct_1(U_16)
& v1_relat_1(U_16)
& m1_relset_1(U_16,U_18,U_17) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_18,U_17] :
( v1_funct_1(sK10(U_18,U_17))
& v1_relat_1(sK10(U_18,U_17))
& m1_relset_1(sK10(U_18,U_17),U_18,U_17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_16,sK10(U_18,U_17))],[f_9_2]) ).
cnf(f_9_4,plain,
m1_relset_1(sK10(U_18,U_17),U_18,U_17),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
v1_relat_1(sK10(U_18,U_17)),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
v1_funct_1(sK10(U_18,U_17)),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_10_2,plain,
! [U_20,U_19] :
( ~ r2_hidden(U_19,U_20)
| ~ r2_hidden(U_20,U_19) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( ~ r2_hidden(U_19,U_20)
| ~ r2_hidden(U_20,U_19) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_12_2,plain,
$true,
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_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_13_2,plain,
! [U_23,U_22,U_21] :
( ( v1_funct_2(U_21,U_23,U_22)
& v1_funct_1(U_21) )
| ~ v1_partfun1(U_21,U_23,U_22)
| ~ v1_funct_1(U_21)
| ~ m1_relset_1(U_21,U_23,U_22) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( v1_funct_1(U_21)
| ~ v1_partfun1(U_21,U_23,U_22)
| ~ v1_funct_1(U_21)
| ~ m1_relset_1(U_21,U_23,U_22) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( v1_funct_2(U_21,U_23,U_22)
| ~ v1_partfun1(U_21,U_23,U_22)
| ~ v1_funct_1(U_21)
| ~ m1_relset_1(U_21,U_23,U_22) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_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_14_2,plain,
! [U_26,U_25,U_24] :
( v1_relat_1(U_24)
| ~ m1_subset_1(U_24,k1_zfmisc_1(k2_zfmisc_1(U_26,U_25))) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( v1_relat_1(U_24)
| ~ m1_subset_1(U_24,k1_zfmisc_1(k2_zfmisc_1(U_26,U_25))) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_15_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_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_16_2,plain,
! [U_28] :
( ? [U_27] :
( ~ v1_xboole_0(U_27)
& m1_subset_1(U_27,k1_zfmisc_1(u1_struct_0(U_28))) )
| ~ l1_struct_0(U_28)
| v3_struct_0(U_28) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_28] :
( ( ~ v1_xboole_0(sK11(U_28))
& m1_subset_1(sK11(U_28),k1_zfmisc_1(u1_struct_0(U_28))) )
| ~ l1_struct_0(U_28)
| v3_struct_0(U_28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_27,sK11(U_28))],[f_16_2]) ).
cnf(f_16_4,plain,
( m1_subset_1(sK11(U_28),k1_zfmisc_1(u1_struct_0(U_28)))
| ~ l1_struct_0(U_28)
| v3_struct_0(U_28) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( ~ v1_xboole_0(sK11(U_28))
| ~ l1_struct_0(U_28)
| v3_struct_0(U_28) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_17_2,plain,
! [U_30,U_29] :
( m1_subset_1(U_30,U_29)
| ~ r2_hidden(U_30,U_29) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( m1_subset_1(U_30,U_29)
| ~ r2_hidden(U_30,U_29) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_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_18_2,plain,
! [U_32,U_31] :
( ( m1_subset_1(U_32,k1_zfmisc_1(U_31))
| ~ r1_tarski(U_32,U_31) )
& ( r1_tarski(U_32,U_31)
| ~ m1_subset_1(U_32,k1_zfmisc_1(U_31)) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_36,U_34] :
( m1_subset_1(U_36,k1_zfmisc_1(U_34))
| ~ r1_tarski(U_36,U_34) )
& ! [U_35,U_33] :
( r1_tarski(U_35,U_33)
| ~ m1_subset_1(U_35,k1_zfmisc_1(U_33)) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( r1_tarski(U_35,U_33)
| ~ m1_subset_1(U_35,k1_zfmisc_1(U_33)) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( m1_subset_1(U_36,k1_zfmisc_1(U_34))
| ~ r1_tarski(U_36,U_34) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_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_19_2,plain,
! [U_39,U_38,U_37] :
( m1_subset_1(U_39,U_37)
| ~ m1_subset_1(U_38,k1_zfmisc_1(U_37))
| ~ r2_hidden(U_39,U_38) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( m1_subset_1(U_39,U_37)
| ~ m1_subset_1(U_38,k1_zfmisc_1(U_37))
| ~ r2_hidden(U_39,U_38) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_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_20_2,plain,
! [U_42,U_41,U_40] :
( ~ v1_xboole_0(U_40)
| ~ m1_subset_1(U_41,k1_zfmisc_1(U_40))
| ~ r2_hidden(U_42,U_41) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_42,U_41] :
( ! [U_40] :
( ~ v1_xboole_0(U_40)
| ~ m1_subset_1(U_41,k1_zfmisc_1(U_40)) )
| ~ r2_hidden(U_42,U_41) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( ~ v1_xboole_0(U_40)
| ~ m1_subset_1(U_41,k1_zfmisc_1(U_40))
| ~ r2_hidden(U_42,U_41) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_21_2,plain,
! [U_45,U_44] :
? [U_43] : m1_relset_1(U_43,U_45,U_44),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_45,U_44] : m1_relset_1(sK12(U_45,U_44),U_45,U_44),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_43,sK12(U_45,U_44))],[f_21_2]) ).
cnf(f_21_4,plain,
m1_relset_1(sK12(U_45,U_44),U_45,U_44),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_22_2,plain,
! [U_48,U_47] :
? [U_46] : m2_relset_1(U_46,U_48,U_47),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_48,U_47] : m2_relset_1(sK13(U_48,U_47),U_48,U_47),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_46,sK13(U_48,U_47))],[f_22_2]) ).
cnf(f_22_4,plain,
m2_relset_1(sK13(U_48,U_47),U_48,U_47),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_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_23_2,plain,
! [U_51,U_50,U_49] :
( ( m2_relset_1(U_49,U_51,U_50)
| ~ m1_relset_1(U_49,U_51,U_50) )
& ( m1_relset_1(U_49,U_51,U_50)
| ~ m2_relset_1(U_49,U_51,U_50) ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_57,U_55,U_53] :
( m2_relset_1(U_53,U_57,U_55)
| ~ m1_relset_1(U_53,U_57,U_55) )
& ! [U_56,U_54,U_52] :
( m1_relset_1(U_52,U_56,U_54)
| ~ m2_relset_1(U_52,U_56,U_54) ) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( m1_relset_1(U_52,U_56,U_54)
| ~ m2_relset_1(U_52,U_56,U_54) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( m2_relset_1(U_53,U_57,U_55)
| ~ m1_relset_1(U_53,U_57,U_55) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_24_2,plain,
$true,
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_25_2,plain,
$true,
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_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_26_2,plain,
! [U_60,U_59,U_58] :
( m1_subset_1(U_58,k1_zfmisc_1(k2_zfmisc_1(U_60,U_59)))
| ~ m2_relset_1(U_58,U_60,U_59) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( m1_subset_1(U_58,k1_zfmisc_1(k2_zfmisc_1(U_60,U_59)))
| ~ m2_relset_1(U_58,U_60,U_59) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A] :
( v1_funct_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_27_2,plain,
! [U_61] :
( v1_funct_1(U_61)
| ~ v1_xboole_0(U_61) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( v1_funct_1(U_61)
| ~ v1_xboole_0(U_61) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_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_28_2,plain,
! [U_64,U_63] :
( ! [U_62] :
( ( v1_funct_2(U_62,U_64,U_63)
& v1_partfun1(U_62,U_64,U_63)
& v1_funct_1(U_62) )
| ~ v1_funct_2(U_62,U_64,U_63)
| ~ v1_funct_1(U_62)
| ~ m1_relset_1(U_62,U_64,U_63) )
| v1_xboole_0(U_63) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( v1_funct_1(U_62)
| ~ v1_funct_2(U_62,U_64,U_63)
| ~ v1_funct_1(U_62)
| ~ m1_relset_1(U_62,U_64,U_63)
| v1_xboole_0(U_63) ),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( v1_partfun1(U_62,U_64,U_63)
| ~ v1_funct_2(U_62,U_64,U_63)
| ~ v1_funct_1(U_62)
| ~ m1_relset_1(U_62,U_64,U_63)
| v1_xboole_0(U_63) ),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_5,plain,
( v1_funct_2(U_62,U_64,U_63)
| ~ v1_funct_2(U_62,U_64,U_63)
| ~ v1_funct_1(U_62)
| ~ m1_relset_1(U_62,U_64,U_63)
| v1_xboole_0(U_63) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_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_29_2,plain,
! [U_67,U_66] :
( ! [U_65] :
( ( v1_funct_2(U_65,U_67,U_66)
& v1_partfun1(U_65,U_67,U_66)
& ~ v1_xboole_0(U_65)
& v1_funct_1(U_65) )
| ~ v1_funct_2(U_65,U_67,U_66)
| ~ v1_funct_1(U_65)
| ~ m1_relset_1(U_65,U_67,U_66) )
| v1_xboole_0(U_66)
| v1_xboole_0(U_67) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( v1_funct_1(U_65)
| ~ v1_funct_2(U_65,U_67,U_66)
| ~ v1_funct_1(U_65)
| ~ m1_relset_1(U_65,U_67,U_66)
| v1_xboole_0(U_66)
| v1_xboole_0(U_67) ),
inference(clausify,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
( ~ v1_xboole_0(U_65)
| ~ v1_funct_2(U_65,U_67,U_66)
| ~ v1_funct_1(U_65)
| ~ m1_relset_1(U_65,U_67,U_66)
| v1_xboole_0(U_66)
| v1_xboole_0(U_67) ),
inference(clausify,[status(thm)],[f_29_2]) ).
cnf(f_29_5,plain,
( v1_partfun1(U_65,U_67,U_66)
| ~ v1_funct_2(U_65,U_67,U_66)
| ~ v1_funct_1(U_65)
| ~ m1_relset_1(U_65,U_67,U_66)
| v1_xboole_0(U_66)
| v1_xboole_0(U_67) ),
inference(clausify,[status(thm)],[f_29_2]) ).
cnf(f_29_6,plain,
( v1_funct_2(U_65,U_67,U_66)
| ~ v1_funct_2(U_65,U_67,U_66)
| ~ v1_funct_1(U_65)
| ~ m1_relset_1(U_65,U_67,U_66)
| v1_xboole_0(U_66)
| v1_xboole_0(U_67) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_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_30_2,plain,
! [U_69,U_68] :
( ( v1_group_1(g1_group_1(U_69,U_68))
& ~ v3_struct_0(g1_group_1(U_69,U_68)) )
| ~ m1_relset_1(U_68,k2_zfmisc_1(U_69,U_69),U_69)
| ~ v1_funct_2(U_68,k2_zfmisc_1(U_69,U_69),U_69)
| ~ v1_funct_1(U_68)
| v1_xboole_0(U_69) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( ~ v3_struct_0(g1_group_1(U_69,U_68))
| ~ m1_relset_1(U_68,k2_zfmisc_1(U_69,U_69),U_69)
| ~ v1_funct_2(U_68,k2_zfmisc_1(U_69,U_69),U_69)
| ~ v1_funct_1(U_68)
| v1_xboole_0(U_69) ),
inference(clausify,[status(thm)],[f_30_2]) ).
cnf(f_30_4,plain,
( v1_group_1(g1_group_1(U_69,U_68))
| ~ m1_relset_1(U_68,k2_zfmisc_1(U_69,U_69),U_69)
| ~ v1_funct_2(U_68,k2_zfmisc_1(U_69,U_69),U_69)
| ~ v1_funct_1(U_68)
| v1_xboole_0(U_69) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_31_2,plain,
? [U_70] : v1_xboole_0(U_70),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
v1_xboole_0(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_70,sK14)],[f_31_2]) ).
cnf(f_31_4,plain,
v1_xboole_0(sK14),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_32_2,plain,
? [U_71] : ~ v1_xboole_0(U_71),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
~ v1_xboole_0(sK15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_71,sK15)],[f_32_2]) ).
cnf(f_32_4,plain,
~ v1_xboole_0(sK15),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_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_33_2,plain,
! [U_73,U_72] :
( r2_hidden(U_73,U_72)
| v1_xboole_0(U_72)
| ~ m1_subset_1(U_73,U_72) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( r2_hidden(U_73,U_72)
| v1_xboole_0(U_72)
| ~ m1_subset_1(U_73,U_72) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_34_2,plain,
! [U_74] :
( U_74 = k1_xboole_0
| ~ v1_xboole_0(U_74) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( U_74 = k1_xboole_0
| ~ v1_xboole_0(U_74) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_35_2,plain,
! [U_76,U_75] :
( ~ v1_xboole_0(U_75)
| ~ r2_hidden(U_76,U_75) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( ~ v1_xboole_0(U_75)
| ~ r2_hidden(U_76,U_75) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_36_2,plain,
! [U_78,U_77] :
( ~ v1_xboole_0(U_77)
| U_78 = U_77
| ~ v1_xboole_0(U_78) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_78] :
( ! [U_77] :
( ~ v1_xboole_0(U_77)
| U_78 = U_77 )
| ~ v1_xboole_0(U_78) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( ~ v1_xboole_0(U_77)
| U_78 = U_77
| ~ v1_xboole_0(U_78) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_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_37_2,plain,
! [U_82,U_81] :
( ! [U_80,U_79] :
( ( U_81 = U_79
& U_82 = U_80 )
| g1_group_1(U_82,U_81) != g1_group_1(U_80,U_79) )
| ~ m1_relset_1(U_81,k2_zfmisc_1(U_82,U_82),U_82)
| ~ v1_funct_2(U_81,k2_zfmisc_1(U_82,U_82),U_82)
| ~ v1_funct_1(U_81) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( U_82 = U_80
| g1_group_1(U_82,U_81) != g1_group_1(U_80,U_79)
| ~ m1_relset_1(U_81,k2_zfmisc_1(U_82,U_82),U_82)
| ~ v1_funct_2(U_81,k2_zfmisc_1(U_82,U_82),U_82)
| ~ v1_funct_1(U_81) ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( U_81 = U_79
| g1_group_1(U_82,U_81) != g1_group_1(U_80,U_79)
| ~ m1_relset_1(U_81,k2_zfmisc_1(U_82,U_82),U_82)
| ~ v1_funct_2(U_81,k2_zfmisc_1(U_82,U_82),U_82)
| ~ v1_funct_1(U_81) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_38_2,plain,
? [U_83] : l1_struct_0(U_83),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
l1_struct_0(sK16),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_83,sK16)],[f_38_2]) ).
cnf(f_38_4,plain,
l1_struct_0(sK16),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_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_39_2,plain,
! [U_85,U_84] :
( ( l1_group_1(g1_group_1(U_85,U_84))
& v1_group_1(g1_group_1(U_85,U_84)) )
| ~ m1_relset_1(U_84,k2_zfmisc_1(U_85,U_85),U_85)
| ~ v1_funct_2(U_84,k2_zfmisc_1(U_85,U_85),U_85)
| ~ v1_funct_1(U_84) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( v1_group_1(g1_group_1(U_85,U_84))
| ~ m1_relset_1(U_84,k2_zfmisc_1(U_85,U_85),U_85)
| ~ v1_funct_2(U_84,k2_zfmisc_1(U_85,U_85),U_85)
| ~ v1_funct_1(U_84) ),
inference(clausify,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( l1_group_1(g1_group_1(U_85,U_84))
| ~ m1_relset_1(U_84,k2_zfmisc_1(U_85,U_85),U_85)
| ~ v1_funct_2(U_84,k2_zfmisc_1(U_85,U_85),U_85)
| ~ v1_funct_1(U_84) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_40_2,plain,
$true,
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_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_41_2,plain,
! [U_86] :
( ( m2_relset_1(u1_group_1(U_86),k2_zfmisc_1(u1_struct_0(U_86),u1_struct_0(U_86)),u1_struct_0(U_86))
& v1_funct_2(u1_group_1(U_86),k2_zfmisc_1(u1_struct_0(U_86),u1_struct_0(U_86)),u1_struct_0(U_86))
& v1_funct_1(u1_group_1(U_86)) )
| ~ l1_group_1(U_86) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( v1_funct_1(u1_group_1(U_86))
| ~ l1_group_1(U_86) ),
inference(clausify,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( v1_funct_2(u1_group_1(U_86),k2_zfmisc_1(u1_struct_0(U_86),u1_struct_0(U_86)),u1_struct_0(U_86))
| ~ l1_group_1(U_86) ),
inference(clausify,[status(thm)],[f_41_2]) ).
cnf(f_41_5,plain,
( m2_relset_1(u1_group_1(U_86),k2_zfmisc_1(u1_struct_0(U_86),u1_struct_0(U_86)),u1_struct_0(U_86))
| ~ l1_group_1(U_86) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_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_42_2,plain,
! [U_87] :
( ~ v1_xboole_0(u1_struct_0(U_87))
| ~ l1_struct_0(U_87)
| v3_struct_0(U_87) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_87))
| ~ l1_struct_0(U_87)
| v3_struct_0(U_87) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A] :
( ? [B] :
( v4_group_1(B)
& v3_group_1(B)
& v2_group_1(B)
& v1_group_1(B)
& ~ v3_struct_0(B)
& m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_group_2]) ).
fof(f_43_2,plain,
! [U_89] :
( ? [U_88] :
( v4_group_1(U_88)
& v3_group_1(U_88)
& v2_group_1(U_88)
& v1_group_1(U_88)
& ~ v3_struct_0(U_88)
& m1_group_2(U_88,U_89) )
| ~ l1_group_1(U_89)
| ~ v4_group_1(U_89)
| ~ v3_group_1(U_89)
| v3_struct_0(U_89) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_89] :
( ( v4_group_1(sK17(U_89))
& v3_group_1(sK17(U_89))
& v2_group_1(sK17(U_89))
& v1_group_1(sK17(U_89))
& ~ v3_struct_0(sK17(U_89))
& m1_group_2(sK17(U_89),U_89) )
| ~ l1_group_1(U_89)
| ~ v4_group_1(U_89)
| ~ v3_group_1(U_89)
| v3_struct_0(U_89) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_88,sK17(U_89))],[f_43_2]) ).
cnf(f_43_4,plain,
( m1_group_2(sK17(U_89),U_89)
| ~ l1_group_1(U_89)
| ~ v4_group_1(U_89)
| ~ v3_group_1(U_89)
| v3_struct_0(U_89) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
( ~ v3_struct_0(sK17(U_89))
| ~ l1_group_1(U_89)
| ~ v4_group_1(U_89)
| ~ v3_group_1(U_89)
| v3_struct_0(U_89) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_6,plain,
( v1_group_1(sK17(U_89))
| ~ l1_group_1(U_89)
| ~ v4_group_1(U_89)
| ~ v3_group_1(U_89)
| v3_struct_0(U_89) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_7,plain,
( v2_group_1(sK17(U_89))
| ~ l1_group_1(U_89)
| ~ v4_group_1(U_89)
| ~ v3_group_1(U_89)
| v3_struct_0(U_89) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_8,plain,
( v3_group_1(sK17(U_89))
| ~ l1_group_1(U_89)
| ~ v4_group_1(U_89)
| ~ v3_group_1(U_89)
| v3_struct_0(U_89) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_9,plain,
( v4_group_1(sK17(U_89))
| ~ l1_group_1(U_89)
| ~ v4_group_1(U_89)
| ~ v3_group_1(U_89)
| v3_struct_0(U_89) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A] :
( ? [B] :
( v1_group_3(B,A)
& v4_group_1(B)
& v3_group_1(B)
& v2_group_1(B)
& v1_group_1(B)
& ~ v3_struct_0(B)
& m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_group_3]) ).
fof(f_44_2,plain,
! [U_91] :
( ? [U_90] :
( v1_group_3(U_90,U_91)
& v4_group_1(U_90)
& v3_group_1(U_90)
& v2_group_1(U_90)
& v1_group_1(U_90)
& ~ v3_struct_0(U_90)
& m1_group_2(U_90,U_91) )
| ~ l1_group_1(U_91)
| ~ v4_group_1(U_91)
| ~ v3_group_1(U_91)
| v3_struct_0(U_91) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_91] :
( ( v1_group_3(sK18(U_91),U_91)
& v4_group_1(sK18(U_91))
& v3_group_1(sK18(U_91))
& v2_group_1(sK18(U_91))
& v1_group_1(sK18(U_91))
& ~ v3_struct_0(sK18(U_91))
& m1_group_2(sK18(U_91),U_91) )
| ~ l1_group_1(U_91)
| ~ v4_group_1(U_91)
| ~ v3_group_1(U_91)
| v3_struct_0(U_91) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_90,sK18(U_91))],[f_44_2]) ).
cnf(f_44_4,plain,
( m1_group_2(sK18(U_91),U_91)
| ~ l1_group_1(U_91)
| ~ v4_group_1(U_91)
| ~ v3_group_1(U_91)
| v3_struct_0(U_91) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_5,plain,
( ~ v3_struct_0(sK18(U_91))
| ~ l1_group_1(U_91)
| ~ v4_group_1(U_91)
| ~ v3_group_1(U_91)
| v3_struct_0(U_91) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_6,plain,
( v1_group_1(sK18(U_91))
| ~ l1_group_1(U_91)
| ~ v4_group_1(U_91)
| ~ v3_group_1(U_91)
| v3_struct_0(U_91) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_7,plain,
( v2_group_1(sK18(U_91))
| ~ l1_group_1(U_91)
| ~ v4_group_1(U_91)
| ~ v3_group_1(U_91)
| v3_struct_0(U_91) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_8,plain,
( v3_group_1(sK18(U_91))
| ~ l1_group_1(U_91)
| ~ v4_group_1(U_91)
| ~ v3_group_1(U_91)
| v3_struct_0(U_91) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_9,plain,
( v4_group_1(sK18(U_91))
| ~ l1_group_1(U_91)
| ~ v4_group_1(U_91)
| ~ v3_group_1(U_91)
| v3_struct_0(U_91) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_10,plain,
( v1_group_3(sK18(U_91),U_91)
| ~ l1_group_1(U_91)
| ~ v4_group_1(U_91)
| ~ v3_group_1(U_91)
| v3_struct_0(U_91) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_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_45_2,plain,
? [U_92] :
( v4_group_1(U_92)
& v3_group_1(U_92)
& v2_group_1(U_92)
& v1_group_1(U_92)
& ~ v3_struct_0(U_92)
& l1_group_1(U_92) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( v4_group_1(sK19)
& v3_group_1(sK19)
& v2_group_1(sK19)
& v1_group_1(sK19)
& ~ v3_struct_0(sK19)
& l1_group_1(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_92,sK19)],[f_45_2]) ).
cnf(f_45_4,plain,
l1_group_1(sK19),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_5,plain,
~ v3_struct_0(sK19),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_6,plain,
v1_group_1(sK19),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_7,plain,
v2_group_1(sK19),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_8,plain,
v3_group_1(sK19),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_9,plain,
v4_group_1(sK19),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_46_2,plain,
? [U_93] :
( ~ v3_struct_0(U_93)
& l1_struct_0(U_93) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( ~ v3_struct_0(sK20)
& l1_struct_0(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_93,sK20)],[f_46_2]) ).
cnf(f_46_4,plain,
l1_struct_0(sK20),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_5,plain,
~ v3_struct_0(sK20),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_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_47_2,plain,
! [U_94] :
( U_94 = g1_group_1(u1_struct_0(U_94),u1_group_1(U_94))
| ~ v1_group_1(U_94)
| ~ l1_group_1(U_94) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( U_94 = g1_group_1(u1_struct_0(U_94),u1_group_1(U_94))
| ~ v1_group_1(U_94)
| ~ l1_group_1(U_94) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
? [A] : l1_group_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_group_1]) ).
fof(f_48_2,plain,
? [U_95] : l1_group_1(U_95),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
l1_group_1(sK21),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_95,sK21)],[f_48_2]) ).
cnf(f_48_4,plain,
l1_group_1(sK21),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_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_49_2,plain,
! [U_97] :
( ? [U_96] : m1_group_2(U_96,U_97)
| ~ l1_group_1(U_97)
| ~ v3_group_1(U_97)
| v3_struct_0(U_97) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_97] :
( m1_group_2(sK22(U_97),U_97)
| ~ l1_group_1(U_97)
| ~ v3_group_1(U_97)
| v3_struct_0(U_97) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_96,sK22(U_97))],[f_49_2]) ).
cnf(f_49_4,plain,
( m1_group_2(sK22(U_97),U_97)
| ~ l1_group_1(U_97)
| ~ v3_group_1(U_97)
| v3_struct_0(U_97) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_50_2,plain,
! [U_99] :
? [U_98] : m1_subset_1(U_98,U_99),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_99] : m1_subset_1(sK23(U_99),U_99),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_98,sK23(U_99))],[f_50_2]) ).
cnf(f_50_4,plain,
m1_subset_1(sK23(U_99),U_99),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [A,B,C] :
( m1_subset_1(k2_group_3(A,B,C),u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_group_3]) ).
fof(f_51_2,plain,
! [U_102,U_101,U_100] :
( m1_subset_1(k2_group_3(U_102,U_101,U_100),u1_struct_0(U_102))
| ~ m1_subset_1(U_100,u1_struct_0(U_102))
| ~ m1_subset_1(U_101,u1_struct_0(U_102))
| ~ l1_group_1(U_102)
| ~ v4_group_1(U_102)
| ~ v3_group_1(U_102)
| v3_struct_0(U_102) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( m1_subset_1(k2_group_3(U_102,U_101,U_100),u1_struct_0(U_102))
| ~ m1_subset_1(U_100,u1_struct_0(U_102))
| ~ m1_subset_1(U_101,u1_struct_0(U_102))
| ~ l1_group_1(U_102)
| ~ v4_group_1(U_102)
| ~ v3_group_1(U_102)
| v3_struct_0(U_102) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_group_1]) ).
fof(f_52_2,plain,
! [U_103] :
( l1_struct_0(U_103)
| ~ l1_group_1(U_103) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( l1_struct_0(U_103)
| ~ l1_group_1(U_103) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_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_53_2,plain,
! [U_105] :
( ! [U_104] :
( ( l1_group_1(U_104)
& v3_group_1(U_104)
& ~ v3_struct_0(U_104) )
| ~ m1_group_2(U_104,U_105) )
| ~ l1_group_1(U_105)
| ~ v3_group_1(U_105)
| v3_struct_0(U_105) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( ~ v3_struct_0(U_104)
| ~ m1_group_2(U_104,U_105)
| ~ l1_group_1(U_105)
| ~ v3_group_1(U_105)
| v3_struct_0(U_105) ),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_53_4,plain,
( v3_group_1(U_104)
| ~ m1_group_2(U_104,U_105)
| ~ l1_group_1(U_105)
| ~ v3_group_1(U_105)
| v3_struct_0(U_105) ),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_53_5,plain,
( l1_group_1(U_104)
| ~ m1_group_2(U_104,U_105)
| ~ l1_group_1(U_105)
| ~ v3_group_1(U_105)
| v3_struct_0(U_105) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_54_2,plain,
$true,
inference(clausify,[status(thm)],[f_54_1]) ).
fof(f_55_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_55_2,plain,
$true,
inference(clausify,[status(thm)],[f_55_1]) ).
fof(f_56_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_56_2,plain,
! [U_106] :
( ( v2_group_1(U_106)
& ~ v3_struct_0(U_106) )
| ~ v3_group_1(U_106)
| v3_struct_0(U_106)
| ~ l1_group_1(U_106) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( ~ v3_struct_0(U_106)
| ~ v3_group_1(U_106)
| v3_struct_0(U_106)
| ~ l1_group_1(U_106) ),
inference(clausify,[status(thm)],[f_56_2]) ).
cnf(f_56_4,plain,
( v2_group_1(U_106)
| ~ v3_group_1(U_106)
| v3_struct_0(U_106)
| ~ l1_group_1(U_106) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [A] :
( ! [B] :
( v4_group_1(B)
| ~ m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_group_2]) ).
fof(f_57_2,plain,
! [U_108] :
( ! [U_107] :
( v4_group_1(U_107)
| ~ m1_group_2(U_107,U_108) )
| ~ l1_group_1(U_108)
| ~ v4_group_1(U_108)
| ~ v3_group_1(U_108)
| v3_struct_0(U_108) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( v4_group_1(U_107)
| ~ m1_group_2(U_107,U_108)
| ~ l1_group_1(U_108)
| ~ v4_group_1(U_108)
| ~ v3_group_1(U_108)
| v3_struct_0(U_108) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
? [A] :
( v1_group_1(A)
& l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_group_1]) ).
fof(f_58_2,plain,
? [U_109] :
( v1_group_1(U_109)
& l1_group_1(U_109) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( v1_group_1(sK24)
& l1_group_1(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_109,sK24)],[f_58_2]) ).
cnf(f_58_4,plain,
l1_group_1(sK24),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
v1_group_1(sK24),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_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_59_2,plain,
? [U_110] :
( v1_group_1(U_110)
& ~ v3_struct_0(U_110)
& l1_group_1(U_110) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( v1_group_1(sK25)
& ~ v3_struct_0(sK25)
& l1_group_1(sK25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_110,sK25)],[f_59_2]) ).
cnf(f_59_4,plain,
l1_group_1(sK25),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_5,plain,
~ v3_struct_0(sK25),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_6,plain,
v1_group_1(sK25),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [A] :
( ! [B] :
( v1_group_3(B,A)
| ? [C] :
( ? [D] :
( ~ r1_rlvect_1(B,k2_group_3(A,D,C))
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(A)) )
& m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_group_2(B,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)],[l1_autgroup]) ).
fof(f_60_2,plain,
! [U_114] :
( ! [U_113] :
( v1_group_3(U_113,U_114)
| ? [U_112] :
( ? [U_111] :
( ~ r1_rlvect_1(U_113,k2_group_3(U_114,U_111,U_112))
& m1_subset_1(U_111,u1_struct_0(U_113))
& m1_subset_1(U_111,u1_struct_0(U_114)) )
& m1_subset_1(U_112,u1_struct_0(U_114)) )
| ~ m1_group_2(U_113,U_114) )
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| ~ v1_group_1(U_114)
| v3_struct_0(U_114) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_114] :
( ! [U_113] :
( v1_group_3(U_113,U_114)
| ( ? [U_111] :
( ~ r1_rlvect_1(U_113,k2_group_3(U_114,U_111,sK26(U_114,U_113)))
& m1_subset_1(U_111,u1_struct_0(U_113))
& m1_subset_1(U_111,u1_struct_0(U_114)) )
& m1_subset_1(sK26(U_114,U_113),u1_struct_0(U_114)) )
| ~ m1_group_2(U_113,U_114) )
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| ~ v1_group_1(U_114)
| v3_struct_0(U_114) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_112,sK26(U_114,U_113))],[f_60_2]) ).
fof(f_60_4,plain,
! [U_114] :
( ! [U_113] :
( v1_group_3(U_113,U_114)
| ( ~ r1_rlvect_1(U_113,k2_group_3(U_114,sK27(U_114,U_113),sK26(U_114,U_113)))
& m1_subset_1(sK27(U_114,U_113),u1_struct_0(U_113))
& m1_subset_1(sK27(U_114,U_113),u1_struct_0(U_114))
& m1_subset_1(sK26(U_114,U_113),u1_struct_0(U_114)) )
| ~ m1_group_2(U_113,U_114) )
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| ~ v1_group_1(U_114)
| v3_struct_0(U_114) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_111,sK27(U_114,U_113))],[f_60_3]) ).
cnf(f_60_5,plain,
( m1_subset_1(sK26(U_114,U_113),u1_struct_0(U_114))
| v1_group_3(U_113,U_114)
| ~ m1_group_2(U_113,U_114)
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| ~ v1_group_1(U_114)
| v3_struct_0(U_114) ),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_6,plain,
( m1_subset_1(sK27(U_114,U_113),u1_struct_0(U_114))
| v1_group_3(U_113,U_114)
| ~ m1_group_2(U_113,U_114)
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| ~ v1_group_1(U_114)
| v3_struct_0(U_114) ),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_7,plain,
( m1_subset_1(sK27(U_114,U_113),u1_struct_0(U_113))
| v1_group_3(U_113,U_114)
| ~ m1_group_2(U_113,U_114)
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| ~ v1_group_1(U_114)
| v3_struct_0(U_114) ),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_8,plain,
( ~ r1_rlvect_1(U_113,k2_group_3(U_114,sK27(U_114,U_113),sK26(U_114,U_113)))
| v1_group_3(U_113,U_114)
| ~ m1_group_2(U_113,U_114)
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| ~ v1_group_1(U_114)
| v3_struct_0(U_114) ),
inference(clausify,[status(thm)],[f_60_4]) ).
fof(f_61_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( r1_rlvect_1(B,k2_group_3(A,D,C))
| ~ m1_subset_1(D,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(A)) )
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ v1_group_3(B,A)
| ~ m1_group_2(B,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)],[l2_autgroup]) ).
fof(f_61_2,plain,
! [U_118] :
( ! [U_117] :
( ! [U_116] :
( ! [U_115] :
( r1_rlvect_1(U_117,k2_group_3(U_118,U_115,U_116))
| ~ m1_subset_1(U_115,u1_struct_0(U_117))
| ~ m1_subset_1(U_115,u1_struct_0(U_118)) )
| ~ m1_subset_1(U_116,u1_struct_0(U_118)) )
| ~ v1_group_3(U_117,U_118)
| ~ m1_group_2(U_117,U_118) )
| ~ l1_group_1(U_118)
| ~ v4_group_1(U_118)
| ~ v3_group_1(U_118)
| ~ v1_group_1(U_118)
| v3_struct_0(U_118) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( r1_rlvect_1(U_117,k2_group_3(U_118,U_115,U_116))
| ~ m1_subset_1(U_115,u1_struct_0(U_117))
| ~ m1_subset_1(U_115,u1_struct_0(U_118))
| ~ m1_subset_1(U_116,u1_struct_0(U_118))
| ~ v1_group_3(U_117,U_118)
| ~ m1_group_2(U_117,U_118)
| ~ l1_group_1(U_118)
| ~ v4_group_1(U_118)
| ~ v3_group_1(U_118)
| ~ v1_group_1(U_118)
| v3_struct_0(U_118) ),
inference(clausify,[status(thm)],[f_61_2]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_5_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_4]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_12_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_2]) ).
cnf(f_13_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_3]) ).
cnf(f_24_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_24_2]) ).
cnf(f_25_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_2]) ).
cnf(f_28_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_3]) ).
cnf(f_28_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_5]) ).
cnf(f_29_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_3]) ).
cnf(f_29_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_6]) ).
cnf(f_40_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_40_2]) ).
cnf(f_54_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_54_2]) ).
cnf(f_55_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_55_2]) ).
cnf(f_56_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_56_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( u1_struct_0(Eq_x_0) = u1_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k2_group_3(Eq_x_0,Eq_x_1,Eq_x_2) = k2_group_3(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_6,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_7,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_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,
( u1_group_1(Eq_x_0) = u1_group_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,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_15,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK22(Eq_x_0) = sK22(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK26(Eq_x_0,Eq_x_1) = sK26(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,
( sK27(Eq_x_0,Eq_x_1) = sK27(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,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_22,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_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,
( 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_27,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_28,axiom,
( r1_rlvect_1(Eq_y_0,Eq_y_1)
| ~ r1_rlvect_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_group_3(Eq_y_0,Eq_y_1)
| ~ v1_group_3(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,axiom,
( l1_struct_0(Eq_y_0)
| ~ l1_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( 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_41,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_42,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(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 : GRP618+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n011.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 19 09:50:39 UTC 2026
% 0.08/0.37 % CPUTime :
% 2.65/2.90 % SZS status Theorem for theBenchmark
% 2.65/2.90 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------