%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP628+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 : n015.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 08:42:04 AM UTC 2026
% Result : Theorem 12.94s 13.23s
% Output : Proof 13.08s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t22_autgroup,conjecture,
! [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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_autgroup(A)))
=> ( B = C
=> k2_funct_1(B) = k3_group_1(k5_autgroup(A),C) ) ) ) ),
file('theBenchmark.p',t22_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_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(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_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> k3_autgroup(A) = g1_group_1(k1_autgroup(A),k2_autgroup(A)) ),
file('theBenchmark.p',d3_autgroup) ).
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_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ( m2_relset_1(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_2(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_1(k2_autgroup(A)) ) ),
file('theBenchmark.p',dt_k2_autgroup) ).
fof(dt_k2_funct_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_relat_1(A) )
=> ( v1_funct_1(k2_funct_1(A))
& v1_relat_1(k2_funct_1(A)) ) ),
file('theBenchmark.p',dt_k2_funct_1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ( l1_group_1(k3_autgroup(A))
& v4_group_1(k3_autgroup(A))
& v3_group_1(k3_autgroup(A))
& v1_group_1(k3_autgroup(A))
& ~ v3_struct_0(k3_autgroup(A)) ) ),
file('theBenchmark.p',dt_k3_autgroup) ).
fof(dt_k3_group_1,axiom,
! [A,B] :
( ( 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(k3_group_1(A,B),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k3_group_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_k5_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ( m1_group_2(k5_autgroup(A),k3_autgroup(A))
& v1_group_3(k5_autgroup(A),k3_autgroup(A))
& v1_group_1(k5_autgroup(A)) ) ),
file('theBenchmark.p',dt_k5_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_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) ) ) ),
file('theBenchmark.p',dt_m1_group_2) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_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_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ? [B] : m1_group_2(B,A) ),
file('theBenchmark.p',existence_m1_group_2) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_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_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(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(t11_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),k1_autgroup(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_autgroup(A)))
=> ( B = C
=> k2_funct_1(B) = k3_group_1(k3_autgroup(A),C) ) ) ) ),
file('theBenchmark.p',t11_autgroup) ).
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(t51_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(A)) ) ) ),
file('theBenchmark.p',t51_group_2) ).
fof(t57_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_group_2(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( D = B
=> k3_group_1(C,D) = k3_group_1(A,B) ) ) ) ) ),
file('theBenchmark.p',t57_group_2) ).
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) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_autgroup(A)))
=> ( B = C
=> k2_funct_1(B) = k3_group_1(k5_autgroup(A),C) ) ) ) ),
inference(negate,[status(cth)],[t22_autgroup]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( k2_funct_1(B) != k3_group_1(k5_autgroup(A),C)
& B = C
& m1_subset_1(C,u1_struct_0(k5_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)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_2] :
( ? [U_1] :
( ? [U_0] :
( k2_funct_1(U_1) != k3_group_1(k5_autgroup(U_2),U_0)
& U_1 = U_0
& m1_subset_1(U_0,u1_struct_0(k5_autgroup(U_2))) )
& m2_fraenkel(U_1,u1_struct_0(U_2),u1_struct_0(U_2),k4_autgroup(U_2)) )
& l1_group_1(U_2)
& v4_group_1(U_2)
& v3_group_1(U_2)
& v1_group_1(U_2)
& ~ v3_struct_0(U_2) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_1] :
( ? [U_0] :
( k2_funct_1(U_1) != k3_group_1(k5_autgroup(sK1),U_0)
& U_1 = U_0
& m1_subset_1(U_0,u1_struct_0(k5_autgroup(sK1))) )
& m2_fraenkel(U_1,u1_struct_0(sK1),u1_struct_0(sK1),k4_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_2,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_0] :
( k2_funct_1(sK2) != k3_group_1(k5_autgroup(sK1),U_0)
& sK2 = U_0
& m1_subset_1(U_0,u1_struct_0(k5_autgroup(sK1))) )
& m2_fraenkel(sK2,u1_struct_0(sK1),u1_struct_0(sK1),k4_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,[sK2]),skolemize(U_1,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( k2_funct_1(sK2) != k3_group_1(k5_autgroup(sK1),sK3)
& sK2 = sK3
& m1_subset_1(sK3,u1_struct_0(k5_autgroup(sK1)))
& m2_fraenkel(sK2,u1_struct_0(sK1),u1_struct_0(sK1),k4_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,[sK3]),skolemize(U_0,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( k2_funct_1(sK2) != k3_group_1(k5_autgroup(sK1),sK3)
& sK2 = sK3
& m1_subset_1(sK3,u1_struct_0(k5_autgroup(sK1)))
& m2_fraenkel(sK2,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(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)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
v1_group_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_10,negated_conjecture,
v3_group_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_11,negated_conjecture,
v4_group_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_12,negated_conjecture,
l1_group_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_13,negated_conjecture,
m2_fraenkel(sK2,u1_struct_0(sK1),u1_struct_0(sK1),k4_autgroup(sK1)),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_14,negated_conjecture,
m1_subset_1(sK3,u1_struct_0(k5_autgroup(sK1))),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_15,negated_conjecture,
sK2 = sK3,
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_16,negated_conjecture,
k2_funct_1(sK2) != k3_group_1(k5_autgroup(sK1),sK3),
inference(clausify,[status(thm)],[f_1_7]) ).
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_3] :
( U_3 = g1_group_1(u1_struct_0(U_3),u1_group_1(U_3))
| ~ v1_group_1(U_3)
| ~ l1_group_1(U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( U_3 = g1_group_1(u1_struct_0(U_3),u1_group_1(U_3))
| ~ v1_group_1(U_3)
| ~ l1_group_1(U_3) ),
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_5,U_4] :
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
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_7] :
( ! [U_6] :
( ( v1_funct_1(U_6)
& v1_relat_1(U_6) )
| ~ m1_subset_1(U_6,U_7) )
| ~ v1_fraenkel(U_7) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v1_relat_1(U_6)
| ~ m1_subset_1(U_6,U_7)
| ~ v1_fraenkel(U_7) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( v1_funct_1(U_6)
| ~ m1_subset_1(U_6,U_7)
| ~ v1_fraenkel(U_7) ),
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_8] :
( v1_funct_1(U_8)
| ~ v1_xboole_0(U_8) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( v1_funct_1(U_8)
| ~ v1_xboole_0(U_8) ),
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_11,U_10,U_9] :
( ( v1_funct_2(U_9,U_11,U_10)
& v1_funct_1(U_9) )
| ~ v1_partfun1(U_9,U_11,U_10)
| ~ v1_funct_1(U_9)
| ~ m1_relset_1(U_9,U_11,U_10) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( v1_funct_1(U_9)
| ~ v1_partfun1(U_9,U_11,U_10)
| ~ v1_funct_1(U_9)
| ~ m1_relset_1(U_9,U_11,U_10) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( v1_funct_2(U_9,U_11,U_10)
| ~ v1_partfun1(U_9,U_11,U_10)
| ~ v1_funct_1(U_9)
| ~ m1_relset_1(U_9,U_11,U_10) ),
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_12] :
( ( v2_group_1(U_12)
& ~ v3_struct_0(U_12) )
| ~ v3_group_1(U_12)
| v3_struct_0(U_12)
| ~ l1_group_1(U_12) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( ~ v3_struct_0(U_12)
| ~ v3_group_1(U_12)
| v3_struct_0(U_12)
| ~ l1_group_1(U_12) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( v2_group_1(U_12)
| ~ v3_group_1(U_12)
| v3_struct_0(U_12)
| ~ l1_group_1(U_12) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_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_8_2,plain,
! [U_14] :
( ! [U_13] :
( v4_group_1(U_13)
| ~ m1_group_2(U_13,U_14) )
| ~ l1_group_1(U_14)
| ~ v4_group_1(U_14)
| ~ v3_group_1(U_14)
| v3_struct_0(U_14) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( v4_group_1(U_13)
| ~ m1_group_2(U_13,U_14)
| ~ l1_group_1(U_14)
| ~ v4_group_1(U_14)
| ~ v3_group_1(U_14)
| v3_struct_0(U_14) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_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_9_2,plain,
! [U_17,U_16,U_15] :
( v1_relat_1(U_15)
| ~ m1_subset_1(U_15,k1_zfmisc_1(k2_zfmisc_1(U_17,U_16))) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( v1_relat_1(U_15)
| ~ m1_subset_1(U_15,k1_zfmisc_1(k2_zfmisc_1(U_17,U_16))) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_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_10_2,plain,
! [U_18] :
( ( v2_funct_1(U_18)
& v1_funct_1(U_18)
& v1_relat_1(U_18) )
| ~ v1_funct_1(U_18)
| ~ v1_xboole_0(U_18)
| ~ v1_relat_1(U_18) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( v1_relat_1(U_18)
| ~ v1_funct_1(U_18)
| ~ v1_xboole_0(U_18)
| ~ v1_relat_1(U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( v1_funct_1(U_18)
| ~ v1_funct_1(U_18)
| ~ v1_xboole_0(U_18)
| ~ v1_relat_1(U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_5,plain,
( v2_funct_1(U_18)
| ~ v1_funct_1(U_18)
| ~ v1_xboole_0(U_18)
| ~ v1_relat_1(U_18) ),
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_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_11_2,plain,
! [U_21,U_20] :
( ! [U_19] :
( ( v1_funct_2(U_19,U_21,U_20)
& v1_partfun1(U_19,U_21,U_20)
& v1_funct_1(U_19) )
| ~ v1_funct_2(U_19,U_21,U_20)
| ~ v1_funct_1(U_19)
| ~ m1_relset_1(U_19,U_21,U_20) )
| v1_xboole_0(U_20) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( v1_funct_1(U_19)
| ~ v1_funct_2(U_19,U_21,U_20)
| ~ v1_funct_1(U_19)
| ~ m1_relset_1(U_19,U_21,U_20)
| v1_xboole_0(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( v1_partfun1(U_19,U_21,U_20)
| ~ v1_funct_2(U_19,U_21,U_20)
| ~ v1_funct_1(U_19)
| ~ m1_relset_1(U_19,U_21,U_20)
| v1_xboole_0(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_5,plain,
( v1_funct_2(U_19,U_21,U_20)
| ~ v1_funct_2(U_19,U_21,U_20)
| ~ v1_funct_1(U_19)
| ~ m1_relset_1(U_19,U_21,U_20)
| v1_xboole_0(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_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_12_2,plain,
! [U_24,U_23] :
( ! [U_22] :
( ( v1_funct_2(U_22,U_24,U_23)
& v1_partfun1(U_22,U_24,U_23)
& ~ v1_xboole_0(U_22)
& v1_funct_1(U_22) )
| ~ v1_funct_2(U_22,U_24,U_23)
| ~ v1_funct_1(U_22)
| ~ m1_relset_1(U_22,U_24,U_23) )
| v1_xboole_0(U_23)
| v1_xboole_0(U_24) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( v1_funct_1(U_22)
| ~ v1_funct_2(U_22,U_24,U_23)
| ~ v1_funct_1(U_22)
| ~ m1_relset_1(U_22,U_24,U_23)
| v1_xboole_0(U_23)
| v1_xboole_0(U_24) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( ~ v1_xboole_0(U_22)
| ~ v1_funct_2(U_22,U_24,U_23)
| ~ v1_funct_1(U_22)
| ~ m1_relset_1(U_22,U_24,U_23)
| v1_xboole_0(U_23)
| v1_xboole_0(U_24) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_5,plain,
( v1_partfun1(U_22,U_24,U_23)
| ~ v1_funct_2(U_22,U_24,U_23)
| ~ v1_funct_1(U_22)
| ~ m1_relset_1(U_22,U_24,U_23)
| v1_xboole_0(U_23)
| v1_xboole_0(U_24) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_6,plain,
( v1_funct_2(U_22,U_24,U_23)
| ~ v1_funct_2(U_22,U_24,U_23)
| ~ v1_funct_1(U_22)
| ~ m1_relset_1(U_22,U_24,U_23)
| v1_xboole_0(U_23)
| v1_xboole_0(U_24) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A] :
( k3_autgroup(A) = g1_group_1(k1_autgroup(A),k2_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)],[d3_autgroup]) ).
fof(f_13_2,plain,
! [U_25] :
( k3_autgroup(U_25) = g1_group_1(k1_autgroup(U_25),k2_autgroup(U_25))
| ~ l1_group_1(U_25)
| ~ v4_group_1(U_25)
| ~ v3_group_1(U_25)
| ~ v1_group_1(U_25)
| v3_struct_0(U_25) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( k3_autgroup(U_25) = g1_group_1(k1_autgroup(U_25),k2_autgroup(U_25))
| ~ l1_group_1(U_25)
| ~ v4_group_1(U_25)
| ~ v3_group_1(U_25)
| ~ v1_group_1(U_25)
| v3_struct_0(U_25) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_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_14_2,plain,
! [U_27,U_26] :
( ( l1_group_1(g1_group_1(U_27,U_26))
& v1_group_1(g1_group_1(U_27,U_26)) )
| ~ m1_relset_1(U_26,k2_zfmisc_1(U_27,U_27),U_27)
| ~ v1_funct_2(U_26,k2_zfmisc_1(U_27,U_27),U_27)
| ~ v1_funct_1(U_26) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( v1_group_1(g1_group_1(U_27,U_26))
| ~ m1_relset_1(U_26,k2_zfmisc_1(U_27,U_27),U_27)
| ~ v1_funct_2(U_26,k2_zfmisc_1(U_27,U_27),U_27)
| ~ v1_funct_1(U_26) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( l1_group_1(g1_group_1(U_27,U_26))
| ~ m1_relset_1(U_26,k2_zfmisc_1(U_27,U_27),U_27)
| ~ v1_funct_2(U_26,k2_zfmisc_1(U_27,U_27),U_27)
| ~ v1_funct_1(U_26) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_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_15_2,plain,
! [U_28] :
( m1_fraenkel(k1_autgroup(U_28),u1_struct_0(U_28),u1_struct_0(U_28))
| ~ l1_group_1(U_28)
| ~ v4_group_1(U_28)
| ~ v3_group_1(U_28)
| ~ v1_group_1(U_28)
| v3_struct_0(U_28) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( m1_fraenkel(k1_autgroup(U_28),u1_struct_0(U_28),u1_struct_0(U_28))
| ~ l1_group_1(U_28)
| ~ v4_group_1(U_28)
| ~ v3_group_1(U_28)
| ~ v1_group_1(U_28)
| v3_struct_0(U_28) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
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_k1_zfmisc_1]) ).
cnf(f_17_2,plain,
$true,
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A] :
( ( m2_relset_1(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_2(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& v1_funct_1(k2_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)],[dt_k2_autgroup]) ).
fof(f_18_2,plain,
! [U_29] :
( ( m2_relset_1(k2_autgroup(U_29),k2_zfmisc_1(k1_autgroup(U_29),k1_autgroup(U_29)),k1_autgroup(U_29))
& v1_funct_2(k2_autgroup(U_29),k2_zfmisc_1(k1_autgroup(U_29),k1_autgroup(U_29)),k1_autgroup(U_29))
& v1_funct_1(k2_autgroup(U_29)) )
| ~ l1_group_1(U_29)
| ~ v4_group_1(U_29)
| ~ v3_group_1(U_29)
| ~ v1_group_1(U_29)
| v3_struct_0(U_29) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( v1_funct_1(k2_autgroup(U_29))
| ~ l1_group_1(U_29)
| ~ v4_group_1(U_29)
| ~ v3_group_1(U_29)
| ~ v1_group_1(U_29)
| v3_struct_0(U_29) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( v1_funct_2(k2_autgroup(U_29),k2_zfmisc_1(k1_autgroup(U_29),k1_autgroup(U_29)),k1_autgroup(U_29))
| ~ l1_group_1(U_29)
| ~ v4_group_1(U_29)
| ~ v3_group_1(U_29)
| ~ v1_group_1(U_29)
| v3_struct_0(U_29) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_5,plain,
( m2_relset_1(k2_autgroup(U_29),k2_zfmisc_1(k1_autgroup(U_29),k1_autgroup(U_29)),k1_autgroup(U_29))
| ~ l1_group_1(U_29)
| ~ v4_group_1(U_29)
| ~ v3_group_1(U_29)
| ~ v1_group_1(U_29)
| v3_struct_0(U_29) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( ( v1_funct_1(k2_funct_1(A))
& v1_relat_1(k2_funct_1(A)) )
| ~ v1_funct_1(A)
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_funct_1]) ).
fof(f_19_2,plain,
! [U_30] :
( ( v1_funct_1(k2_funct_1(U_30))
& v1_relat_1(k2_funct_1(U_30)) )
| ~ v1_funct_1(U_30)
| ~ v1_relat_1(U_30) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( v1_relat_1(k2_funct_1(U_30))
| ~ v1_funct_1(U_30)
| ~ v1_relat_1(U_30) ),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( v1_funct_1(k2_funct_1(U_30))
| ~ v1_funct_1(U_30)
| ~ v1_relat_1(U_30) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
! [A] :
( ( l1_group_1(k3_autgroup(A))
& v4_group_1(k3_autgroup(A))
& v3_group_1(k3_autgroup(A))
& v1_group_1(k3_autgroup(A))
& ~ v3_struct_0(k3_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)],[dt_k3_autgroup]) ).
fof(f_21_2,plain,
! [U_31] :
( ( l1_group_1(k3_autgroup(U_31))
& v4_group_1(k3_autgroup(U_31))
& v3_group_1(k3_autgroup(U_31))
& v1_group_1(k3_autgroup(U_31))
& ~ v3_struct_0(k3_autgroup(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_21_1]) ).
cnf(f_21_3,plain,
( ~ v3_struct_0(k3_autgroup(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_21_2]) ).
cnf(f_21_4,plain,
( v1_group_1(k3_autgroup(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_21_2]) ).
cnf(f_21_5,plain,
( v3_group_1(k3_autgroup(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_21_2]) ).
cnf(f_21_6,plain,
( v4_group_1(k3_autgroup(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_21_2]) ).
cnf(f_21_7,plain,
( l1_group_1(k3_autgroup(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_21_2]) ).
fof(f_22_1,plain,
! [A,B] :
( m1_subset_1(k3_group_1(A,B),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_k3_group_1]) ).
fof(f_22_2,plain,
! [U_33,U_32] :
( m1_subset_1(k3_group_1(U_33,U_32),u1_struct_0(U_33))
| ~ m1_subset_1(U_32,u1_struct_0(U_33))
| ~ l1_group_1(U_33)
| ~ v4_group_1(U_33)
| ~ v3_group_1(U_33)
| v3_struct_0(U_33) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( m1_subset_1(k3_group_1(U_33,U_32),u1_struct_0(U_33))
| ~ m1_subset_1(U_32,u1_struct_0(U_33))
| ~ l1_group_1(U_33)
| ~ v4_group_1(U_33)
| ~ v3_group_1(U_33)
| v3_struct_0(U_33) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_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_23_2,plain,
! [U_34] :
( m1_fraenkel(k4_autgroup(U_34),u1_struct_0(U_34),u1_struct_0(U_34))
| ~ l1_group_1(U_34)
| ~ v4_group_1(U_34)
| ~ v3_group_1(U_34)
| ~ v1_group_1(U_34)
| v3_struct_0(U_34) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( m1_fraenkel(k4_autgroup(U_34),u1_struct_0(U_34),u1_struct_0(U_34))
| ~ l1_group_1(U_34)
| ~ v4_group_1(U_34)
| ~ v3_group_1(U_34)
| ~ v1_group_1(U_34)
| v3_struct_0(U_34) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A] :
( ( m1_group_2(k5_autgroup(A),k3_autgroup(A))
& v1_group_3(k5_autgroup(A),k3_autgroup(A))
& v1_group_1(k5_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)],[dt_k5_autgroup]) ).
fof(f_24_2,plain,
! [U_35] :
( ( m1_group_2(k5_autgroup(U_35),k3_autgroup(U_35))
& v1_group_3(k5_autgroup(U_35),k3_autgroup(U_35))
& v1_group_1(k5_autgroup(U_35)) )
| ~ l1_group_1(U_35)
| ~ v4_group_1(U_35)
| ~ v3_group_1(U_35)
| ~ v1_group_1(U_35)
| v3_struct_0(U_35) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( v1_group_1(k5_autgroup(U_35))
| ~ l1_group_1(U_35)
| ~ v4_group_1(U_35)
| ~ v3_group_1(U_35)
| ~ v1_group_1(U_35)
| v3_struct_0(U_35) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( v1_group_3(k5_autgroup(U_35),k3_autgroup(U_35))
| ~ l1_group_1(U_35)
| ~ v4_group_1(U_35)
| ~ v3_group_1(U_35)
| ~ v1_group_1(U_35)
| v3_struct_0(U_35) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_5,plain,
( m1_group_2(k5_autgroup(U_35),k3_autgroup(U_35))
| ~ l1_group_1(U_35)
| ~ v4_group_1(U_35)
| ~ v3_group_1(U_35)
| ~ v1_group_1(U_35)
| v3_struct_0(U_35) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_group_1]) ).
fof(f_25_2,plain,
! [U_36] :
( l1_struct_0(U_36)
| ~ l1_group_1(U_36) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( l1_struct_0(U_36)
| ~ l1_group_1(U_36) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_26_2,plain,
$true,
inference(clausify,[status(thm)],[f_26_1]) ).
fof(f_27_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_27_2,plain,
! [U_39,U_38,U_37] :
( ( v1_fraenkel(U_37)
& ~ v1_xboole_0(U_37) )
| ~ m1_fraenkel(U_37,U_39,U_38) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( ~ v1_xboole_0(U_37)
| ~ m1_fraenkel(U_37,U_39,U_38) ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( v1_fraenkel(U_37)
| ~ m1_fraenkel(U_37,U_39,U_38) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_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_28_2,plain,
! [U_41] :
( ! [U_40] :
( ( l1_group_1(U_40)
& v3_group_1(U_40)
& ~ v3_struct_0(U_40) )
| ~ m1_group_2(U_40,U_41) )
| ~ l1_group_1(U_41)
| ~ v3_group_1(U_41)
| v3_struct_0(U_41) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( ~ v3_struct_0(U_40)
| ~ m1_group_2(U_40,U_41)
| ~ l1_group_1(U_41)
| ~ v3_group_1(U_41)
| v3_struct_0(U_41) ),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( v3_group_1(U_40)
| ~ m1_group_2(U_40,U_41)
| ~ l1_group_1(U_41)
| ~ v3_group_1(U_41)
| v3_struct_0(U_41) ),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_5,plain,
( l1_group_1(U_40)
| ~ m1_group_2(U_40,U_41)
| ~ l1_group_1(U_41)
| ~ v3_group_1(U_41)
| v3_struct_0(U_41) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_29_2,plain,
$true,
inference(clausify,[status(thm)],[f_29_1]) ).
fof(f_30_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_30_2,plain,
$true,
inference(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_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_31_2,plain,
! [U_45,U_44,U_43] :
( ! [U_42] :
( ( m2_relset_1(U_42,U_45,U_44)
& v1_funct_2(U_42,U_45,U_44)
& v1_funct_1(U_42) )
| ~ m2_fraenkel(U_42,U_45,U_44,U_43) )
| ~ m1_fraenkel(U_43,U_45,U_44)
| v1_xboole_0(U_44) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( v1_funct_1(U_42)
| ~ m2_fraenkel(U_42,U_45,U_44,U_43)
| ~ m1_fraenkel(U_43,U_45,U_44)
| v1_xboole_0(U_44) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( v1_funct_2(U_42,U_45,U_44)
| ~ m2_fraenkel(U_42,U_45,U_44,U_43)
| ~ m1_fraenkel(U_43,U_45,U_44)
| v1_xboole_0(U_44) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_5,plain,
( m2_relset_1(U_42,U_45,U_44)
| ~ m2_fraenkel(U_42,U_45,U_44,U_43)
| ~ m1_fraenkel(U_43,U_45,U_44)
| v1_xboole_0(U_44) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_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_32_2,plain,
! [U_48,U_47,U_46] :
( m1_subset_1(U_46,k1_zfmisc_1(k2_zfmisc_1(U_48,U_47)))
| ~ m2_relset_1(U_46,U_48,U_47) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( m1_subset_1(U_46,k1_zfmisc_1(k2_zfmisc_1(U_48,U_47)))
| ~ m2_relset_1(U_46,U_48,U_47) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_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_33_2,plain,
! [U_49] :
( ( m2_relset_1(u1_group_1(U_49),k2_zfmisc_1(u1_struct_0(U_49),u1_struct_0(U_49)),u1_struct_0(U_49))
& v1_funct_2(u1_group_1(U_49),k2_zfmisc_1(u1_struct_0(U_49),u1_struct_0(U_49)),u1_struct_0(U_49))
& v1_funct_1(u1_group_1(U_49)) )
| ~ l1_group_1(U_49) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( v1_funct_1(u1_group_1(U_49))
| ~ l1_group_1(U_49) ),
inference(clausify,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( v1_funct_2(u1_group_1(U_49),k2_zfmisc_1(u1_struct_0(U_49),u1_struct_0(U_49)),u1_struct_0(U_49))
| ~ l1_group_1(U_49) ),
inference(clausify,[status(thm)],[f_33_2]) ).
cnf(f_33_5,plain,
( m2_relset_1(u1_group_1(U_49),k2_zfmisc_1(u1_struct_0(U_49),u1_struct_0(U_49)),u1_struct_0(U_49))
| ~ l1_group_1(U_49) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_34_2,plain,
$true,
inference(clausify,[status(thm)],[f_34_1]) ).
fof(f_35_1,plain,
? [A] : l1_group_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_group_1]) ).
fof(f_35_2,plain,
? [U_50] : l1_group_1(U_50),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
l1_group_1(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_50,sK4)],[f_35_2]) ).
cnf(f_35_4,plain,
l1_group_1(sK4),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_36_2,plain,
? [U_51] : l1_struct_0(U_51),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
l1_struct_0(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_51,sK5)],[f_36_2]) ).
cnf(f_36_4,plain,
l1_struct_0(sK5),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B] :
? [C] : m1_fraenkel(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_fraenkel]) ).
fof(f_37_2,plain,
! [U_54,U_53] :
? [U_52] : m1_fraenkel(U_52,U_54,U_53),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_54,U_53] : m1_fraenkel(sK6(U_54,U_53),U_54,U_53),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_52,sK6(U_54,U_53))],[f_37_2]) ).
cnf(f_37_4,plain,
m1_fraenkel(sK6(U_54,U_53),U_54,U_53),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_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_38_2,plain,
! [U_56] :
( ? [U_55] : m1_group_2(U_55,U_56)
| ~ l1_group_1(U_56)
| ~ v3_group_1(U_56)
| v3_struct_0(U_56) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_56] :
( m1_group_2(sK7(U_56),U_56)
| ~ l1_group_1(U_56)
| ~ v3_group_1(U_56)
| v3_struct_0(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_55,sK7(U_56))],[f_38_2]) ).
cnf(f_38_4,plain,
( m1_group_2(sK7(U_56),U_56)
| ~ l1_group_1(U_56)
| ~ v3_group_1(U_56)
| v3_struct_0(U_56) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_39_2,plain,
! [U_59,U_58] :
? [U_57] : m1_relset_1(U_57,U_59,U_58),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_59,U_58] : m1_relset_1(sK8(U_59,U_58),U_59,U_58),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_57,sK8(U_59,U_58))],[f_39_2]) ).
cnf(f_39_4,plain,
m1_relset_1(sK8(U_59,U_58),U_59,U_58),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_40_2,plain,
! [U_61] :
? [U_60] : m1_subset_1(U_60,U_61),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_61] : m1_subset_1(sK9(U_61),U_61),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_60,sK9(U_61))],[f_40_2]) ).
cnf(f_40_4,plain,
m1_subset_1(sK9(U_61),U_61),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_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_41_2,plain,
! [U_65,U_64,U_63] :
( ? [U_62] : m2_fraenkel(U_62,U_65,U_64,U_63)
| ~ m1_fraenkel(U_63,U_65,U_64)
| v1_xboole_0(U_64) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_65,U_64,U_63] :
( m2_fraenkel(sK10(U_65,U_64,U_63),U_65,U_64,U_63)
| ~ m1_fraenkel(U_63,U_65,U_64)
| v1_xboole_0(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_62,sK10(U_65,U_64,U_63))],[f_41_2]) ).
cnf(f_41_4,plain,
( m2_fraenkel(sK10(U_65,U_64,U_63),U_65,U_64,U_63)
| ~ m1_fraenkel(U_63,U_65,U_64)
| v1_xboole_0(U_64) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_42_2,plain,
! [U_68,U_67] :
? [U_66] : m2_relset_1(U_66,U_68,U_67),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_68,U_67] : m2_relset_1(sK11(U_68,U_67),U_68,U_67),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_66,sK11(U_68,U_67))],[f_42_2]) ).
cnf(f_42_4,plain,
m2_relset_1(sK11(U_68,U_67),U_68,U_67),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_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_43_2,plain,
! [U_70,U_69] :
( ( v1_group_1(g1_group_1(U_70,U_69))
& ~ v3_struct_0(g1_group_1(U_70,U_69)) )
| ~ m1_relset_1(U_69,k2_zfmisc_1(U_70,U_70),U_70)
| ~ v1_funct_2(U_69,k2_zfmisc_1(U_70,U_70),U_70)
| ~ v1_funct_1(U_69)
| v1_xboole_0(U_70) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( ~ v3_struct_0(g1_group_1(U_70,U_69))
| ~ m1_relset_1(U_69,k2_zfmisc_1(U_70,U_70),U_70)
| ~ v1_funct_2(U_69,k2_zfmisc_1(U_70,U_70),U_70)
| ~ v1_funct_1(U_69)
| v1_xboole_0(U_70) ),
inference(clausify,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( v1_group_1(g1_group_1(U_70,U_69))
| ~ m1_relset_1(U_69,k2_zfmisc_1(U_70,U_70),U_70)
| ~ v1_funct_2(U_69,k2_zfmisc_1(U_70,U_70),U_70)
| ~ v1_funct_1(U_69)
| v1_xboole_0(U_70) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_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_44_2,plain,
! [U_71] :
( ~ v1_xboole_0(u1_struct_0(U_71))
| ~ l1_struct_0(U_71)
| v3_struct_0(U_71) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_71))
| ~ l1_struct_0(U_71)
| v3_struct_0(U_71) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_45_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_45_1]) ).
fof(f_46_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_46_2,plain,
! [U_75,U_74] :
( ! [U_73,U_72] :
( ( U_74 = U_72
& U_75 = U_73 )
| g1_group_1(U_75,U_74) != g1_group_1(U_73,U_72) )
| ~ m1_relset_1(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_2(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_1(U_74) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( U_75 = U_73
| g1_group_1(U_75,U_74) != g1_group_1(U_73,U_72)
| ~ m1_relset_1(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_2(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_1(U_74) ),
inference(clausify,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( U_74 = U_72
| g1_group_1(U_75,U_74) != g1_group_1(U_73,U_72)
| ~ m1_relset_1(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_2(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_1(U_74) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
? [A] :
( v1_fraenkel(A)
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_fraenkel]) ).
fof(f_47_2,plain,
? [U_76] :
( v1_fraenkel(U_76)
& ~ v1_xboole_0(U_76) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
( v1_fraenkel(sK12)
& ~ v1_xboole_0(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_76,sK12)],[f_47_2]) ).
cnf(f_47_4,plain,
~ v1_xboole_0(sK12),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_5,plain,
v1_fraenkel(sK12),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_48_2,plain,
? [U_77] :
( v1_funct_1(U_77)
& v1_relat_1(U_77) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
( v1_funct_1(sK13)
& v1_relat_1(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_77,sK13)],[f_48_2]) ).
cnf(f_48_4,plain,
v1_relat_1(sK13),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_5,plain,
v1_funct_1(sK13),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_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_49_2,plain,
! [U_80,U_79] :
? [U_78] :
( v1_funct_2(U_78,U_80,U_79)
& v1_funct_1(U_78)
& v1_relat_1(U_78)
& m1_relset_1(U_78,U_80,U_79) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_80,U_79] :
( v1_funct_2(sK14(U_80,U_79),U_80,U_79)
& v1_funct_1(sK14(U_80,U_79))
& v1_relat_1(sK14(U_80,U_79))
& m1_relset_1(sK14(U_80,U_79),U_80,U_79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_78,sK14(U_80,U_79))],[f_49_2]) ).
cnf(f_49_4,plain,
m1_relset_1(sK14(U_80,U_79),U_80,U_79),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
v1_relat_1(sK14(U_80,U_79)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_6,plain,
v1_funct_1(sK14(U_80,U_79)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_7,plain,
v1_funct_2(sK14(U_80,U_79),U_80,U_79),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
? [A] :
( v1_group_1(A)
& l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_group_1]) ).
fof(f_50_2,plain,
? [U_81] :
( v1_group_1(U_81)
& l1_group_1(U_81) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
( v1_group_1(sK15)
& l1_group_1(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_81,sK15)],[f_50_2]) ).
cnf(f_50_4,plain,
l1_group_1(sK15),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_5,plain,
v1_group_1(sK15),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_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_51_2,plain,
! [U_83] :
( ? [U_82] :
( v4_group_1(U_82)
& v3_group_1(U_82)
& v2_group_1(U_82)
& v1_group_1(U_82)
& ~ v3_struct_0(U_82)
& m1_group_2(U_82,U_83) )
| ~ l1_group_1(U_83)
| ~ v4_group_1(U_83)
| ~ v3_group_1(U_83)
| v3_struct_0(U_83) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_83] :
( ( v4_group_1(sK16(U_83))
& v3_group_1(sK16(U_83))
& v2_group_1(sK16(U_83))
& v1_group_1(sK16(U_83))
& ~ v3_struct_0(sK16(U_83))
& m1_group_2(sK16(U_83),U_83) )
| ~ l1_group_1(U_83)
| ~ v4_group_1(U_83)
| ~ v3_group_1(U_83)
| v3_struct_0(U_83) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_82,sK16(U_83))],[f_51_2]) ).
cnf(f_51_4,plain,
( m1_group_2(sK16(U_83),U_83)
| ~ l1_group_1(U_83)
| ~ v4_group_1(U_83)
| ~ v3_group_1(U_83)
| v3_struct_0(U_83) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
( ~ v3_struct_0(sK16(U_83))
| ~ l1_group_1(U_83)
| ~ v4_group_1(U_83)
| ~ v3_group_1(U_83)
| v3_struct_0(U_83) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_6,plain,
( v1_group_1(sK16(U_83))
| ~ l1_group_1(U_83)
| ~ v4_group_1(U_83)
| ~ v3_group_1(U_83)
| v3_struct_0(U_83) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_7,plain,
( v2_group_1(sK16(U_83))
| ~ l1_group_1(U_83)
| ~ v4_group_1(U_83)
| ~ v3_group_1(U_83)
| v3_struct_0(U_83) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_8,plain,
( v3_group_1(sK16(U_83))
| ~ l1_group_1(U_83)
| ~ v4_group_1(U_83)
| ~ v3_group_1(U_83)
| v3_struct_0(U_83) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_9,plain,
( v4_group_1(sK16(U_83))
| ~ l1_group_1(U_83)
| ~ v4_group_1(U_83)
| ~ v3_group_1(U_83)
| v3_struct_0(U_83) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_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_52_2,plain,
! [U_85] :
( ? [U_84] :
( v1_group_3(U_84,U_85)
& 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)
& m1_group_2(U_84,U_85) )
| ~ l1_group_1(U_85)
| ~ v4_group_1(U_85)
| ~ v3_group_1(U_85)
| v3_struct_0(U_85) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_85] :
( ( v1_group_3(sK17(U_85),U_85)
& v4_group_1(sK17(U_85))
& v3_group_1(sK17(U_85))
& v2_group_1(sK17(U_85))
& v1_group_1(sK17(U_85))
& ~ v3_struct_0(sK17(U_85))
& m1_group_2(sK17(U_85),U_85) )
| ~ l1_group_1(U_85)
| ~ v4_group_1(U_85)
| ~ v3_group_1(U_85)
| v3_struct_0(U_85) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_84,sK17(U_85))],[f_52_2]) ).
cnf(f_52_4,plain,
( m1_group_2(sK17(U_85),U_85)
| ~ l1_group_1(U_85)
| ~ v4_group_1(U_85)
| ~ v3_group_1(U_85)
| v3_struct_0(U_85) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
( ~ v3_struct_0(sK17(U_85))
| ~ l1_group_1(U_85)
| ~ v4_group_1(U_85)
| ~ v3_group_1(U_85)
| v3_struct_0(U_85) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_6,plain,
( v1_group_1(sK17(U_85))
| ~ l1_group_1(U_85)
| ~ v4_group_1(U_85)
| ~ v3_group_1(U_85)
| v3_struct_0(U_85) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_7,plain,
( v2_group_1(sK17(U_85))
| ~ l1_group_1(U_85)
| ~ v4_group_1(U_85)
| ~ v3_group_1(U_85)
| v3_struct_0(U_85) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_8,plain,
( v3_group_1(sK17(U_85))
| ~ l1_group_1(U_85)
| ~ v4_group_1(U_85)
| ~ v3_group_1(U_85)
| v3_struct_0(U_85) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_9,plain,
( v4_group_1(sK17(U_85))
| ~ l1_group_1(U_85)
| ~ v4_group_1(U_85)
| ~ v3_group_1(U_85)
| v3_struct_0(U_85) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_10,plain,
( v1_group_3(sK17(U_85),U_85)
| ~ l1_group_1(U_85)
| ~ v4_group_1(U_85)
| ~ v3_group_1(U_85)
| v3_struct_0(U_85) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_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_53_2,plain,
? [U_86] :
( v1_xboole_0(U_86)
& v2_funct_1(U_86)
& v1_funct_1(U_86)
& v1_relat_1(U_86) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( v1_xboole_0(sK18)
& v2_funct_1(sK18)
& v1_funct_1(sK18)
& v1_relat_1(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_86,sK18)],[f_53_2]) ).
cnf(f_53_4,plain,
v1_relat_1(sK18),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_5,plain,
v1_funct_1(sK18),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_6,plain,
v2_funct_1(sK18),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_7,plain,
v1_xboole_0(sK18),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_54_2,plain,
? [U_87] : v1_xboole_0(U_87),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
v1_xboole_0(sK19),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_87,sK19)],[f_54_2]) ).
cnf(f_54_4,plain,
v1_xboole_0(sK19),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_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_55_2,plain,
? [U_88] :
( v1_funct_1(U_88)
& v1_xboole_0(U_88)
& v1_relat_1(U_88) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( v1_funct_1(sK20)
& v1_xboole_0(sK20)
& v1_relat_1(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_88,sK20)],[f_55_2]) ).
cnf(f_55_4,plain,
v1_relat_1(sK20),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_5,plain,
v1_xboole_0(sK20),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_6,plain,
v1_funct_1(sK20),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_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_56_2,plain,
? [U_89] :
( v1_group_1(U_89)
& ~ v3_struct_0(U_89)
& l1_group_1(U_89) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( v1_group_1(sK21)
& ~ v3_struct_0(sK21)
& l1_group_1(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_89,sK21)],[f_56_2]) ).
cnf(f_56_4,plain,
l1_group_1(sK21),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
~ v3_struct_0(sK21),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_6,plain,
v1_group_1(sK21),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_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_57_2,plain,
! [U_92,U_91] :
? [U_90] :
( v1_funct_1(U_90)
& v1_relat_1(U_90)
& m1_relset_1(U_90,U_92,U_91) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_92,U_91] :
( v1_funct_1(sK22(U_92,U_91))
& v1_relat_1(sK22(U_92,U_91))
& m1_relset_1(sK22(U_92,U_91),U_92,U_91) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_90,sK22(U_92,U_91))],[f_57_2]) ).
cnf(f_57_4,plain,
m1_relset_1(sK22(U_92,U_91),U_92,U_91),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
v1_relat_1(sK22(U_92,U_91)),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_6,plain,
v1_funct_1(sK22(U_92,U_91)),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_58_2,plain,
? [U_93] : ~ v1_xboole_0(U_93),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
~ v1_xboole_0(sK23),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_93,sK23)],[f_58_2]) ).
cnf(f_58_4,plain,
~ v1_xboole_0(sK23),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_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_59_2,plain,
? [U_94] :
( v2_funct_1(U_94)
& v1_funct_1(U_94)
& v1_relat_1(U_94) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( v2_funct_1(sK24)
& v1_funct_1(sK24)
& v1_relat_1(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_94,sK24)],[f_59_2]) ).
cnf(f_59_4,plain,
v1_relat_1(sK24),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_5,plain,
v1_funct_1(sK24),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_6,plain,
v2_funct_1(sK24),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_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_60_2,plain,
? [U_95] :
( v4_group_1(U_95)
& v3_group_1(U_95)
& v2_group_1(U_95)
& v1_group_1(U_95)
& ~ v3_struct_0(U_95)
& l1_group_1(U_95) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
( v4_group_1(sK25)
& v3_group_1(sK25)
& v2_group_1(sK25)
& v1_group_1(sK25)
& ~ v3_struct_0(sK25)
& l1_group_1(sK25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_95,sK25)],[f_60_2]) ).
cnf(f_60_4,plain,
l1_group_1(sK25),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_5,plain,
~ v3_struct_0(sK25),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_6,plain,
v1_group_1(sK25),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_7,plain,
v2_group_1(sK25),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_8,plain,
v3_group_1(sK25),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_9,plain,
v4_group_1(sK25),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_61_2,plain,
? [U_96] :
( ~ v3_struct_0(U_96)
& l1_struct_0(U_96) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( ~ v3_struct_0(sK26)
& l1_struct_0(sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_96,sK26)],[f_61_2]) ).
cnf(f_61_4,plain,
l1_struct_0(sK26),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_5,plain,
~ v3_struct_0(sK26),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_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_62_2,plain,
! [U_98] :
( ? [U_97] :
( ~ v1_xboole_0(U_97)
& m1_subset_1(U_97,k1_zfmisc_1(u1_struct_0(U_98))) )
| ~ l1_struct_0(U_98)
| v3_struct_0(U_98) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_98] :
( ( ~ v1_xboole_0(sK27(U_98))
& m1_subset_1(sK27(U_98),k1_zfmisc_1(u1_struct_0(U_98))) )
| ~ l1_struct_0(U_98)
| v3_struct_0(U_98) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_97,sK27(U_98))],[f_62_2]) ).
cnf(f_62_4,plain,
( m1_subset_1(sK27(U_98),k1_zfmisc_1(u1_struct_0(U_98)))
| ~ l1_struct_0(U_98)
| v3_struct_0(U_98) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_5,plain,
( ~ v1_xboole_0(sK27(U_98))
| ~ l1_struct_0(U_98)
| v3_struct_0(U_98) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_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_63_2,plain,
! [U_102,U_101,U_100] :
( ! [U_99] :
( ( m2_fraenkel(U_99,U_102,U_101,U_100)
| ~ m1_subset_1(U_99,U_100) )
& ( m1_subset_1(U_99,U_100)
| ~ m2_fraenkel(U_99,U_102,U_101,U_100) ) )
| ~ m1_fraenkel(U_100,U_102,U_101)
| v1_xboole_0(U_101) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_102,U_101,U_100] :
( ( ! [U_104] :
( m2_fraenkel(U_104,U_102,U_101,U_100)
| ~ m1_subset_1(U_104,U_100) )
& ! [U_103] :
( m1_subset_1(U_103,U_100)
| ~ m2_fraenkel(U_103,U_102,U_101,U_100) ) )
| ~ m1_fraenkel(U_100,U_102,U_101)
| v1_xboole_0(U_101) ),
inference(miniscope,[status(thm)],[f_63_2]) ).
cnf(f_63_4,plain,
( m1_subset_1(U_103,U_100)
| ~ m2_fraenkel(U_103,U_102,U_101,U_100)
| ~ m1_fraenkel(U_100,U_102,U_101)
| v1_xboole_0(U_101) ),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_5,plain,
( m2_fraenkel(U_104,U_102,U_101,U_100)
| ~ m1_subset_1(U_104,U_100)
| ~ m1_fraenkel(U_100,U_102,U_101)
| v1_xboole_0(U_101) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_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_64_2,plain,
! [U_107,U_106,U_105] :
( ( m2_relset_1(U_105,U_107,U_106)
| ~ m1_relset_1(U_105,U_107,U_106) )
& ( m1_relset_1(U_105,U_107,U_106)
| ~ m2_relset_1(U_105,U_107,U_106) ) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( ! [U_113,U_111,U_109] :
( m2_relset_1(U_109,U_113,U_111)
| ~ m1_relset_1(U_109,U_113,U_111) )
& ! [U_112,U_110,U_108] :
( m1_relset_1(U_108,U_112,U_110)
| ~ m2_relset_1(U_108,U_112,U_110) ) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
cnf(f_64_4,plain,
( m1_relset_1(U_108,U_112,U_110)
| ~ m2_relset_1(U_108,U_112,U_110) ),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_5,plain,
( m2_relset_1(U_109,U_113,U_111)
| ~ m1_relset_1(U_109,U_113,U_111) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_65_2,plain,
! [U_115,U_114] : r1_tarski(U_115,U_115),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_115] : r1_tarski(U_115,U_115),
inference(miniscope,[status(thm)],[f_65_2]) ).
cnf(f_65_4,plain,
r1_tarski(U_115,U_115),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( k2_funct_1(B) = k3_group_1(k3_autgroup(A),C)
| B != C
| ~ m1_subset_1(C,u1_struct_0(k3_autgroup(A))) )
| ~ m2_fraenkel(B,u1_struct_0(A),u1_struct_0(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)],[t11_autgroup]) ).
fof(f_66_2,plain,
! [U_118] :
( ! [U_117] :
( ! [U_116] :
( k2_funct_1(U_117) = k3_group_1(k3_autgroup(U_118),U_116)
| U_117 != U_116
| ~ m1_subset_1(U_116,u1_struct_0(k3_autgroup(U_118))) )
| ~ m2_fraenkel(U_117,u1_struct_0(U_118),u1_struct_0(U_118),k1_autgroup(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_66_1]) ).
cnf(f_66_3,plain,
( k2_funct_1(U_117) = k3_group_1(k3_autgroup(U_118),U_116)
| U_117 != U_116
| ~ m1_subset_1(U_116,u1_struct_0(k3_autgroup(U_118)))
| ~ m2_fraenkel(U_117,u1_struct_0(U_118),u1_struct_0(U_118),k1_autgroup(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_66_2]) ).
fof(f_67_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_67_2,plain,
! [U_120] :
( ! [U_119] :
( m2_fraenkel(U_119,u1_struct_0(U_120),u1_struct_0(U_120),k1_autgroup(U_120))
| ~ m2_fraenkel(U_119,u1_struct_0(U_120),u1_struct_0(U_120),k4_autgroup(U_120)) )
| ~ l1_group_1(U_120)
| ~ v4_group_1(U_120)
| ~ v3_group_1(U_120)
| ~ v1_group_1(U_120)
| v3_struct_0(U_120) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( m2_fraenkel(U_119,u1_struct_0(U_120),u1_struct_0(U_120),k1_autgroup(U_120))
| ~ m2_fraenkel(U_119,u1_struct_0(U_120),u1_struct_0(U_120),k4_autgroup(U_120))
| ~ l1_group_1(U_120)
| ~ v4_group_1(U_120)
| ~ v3_group_1(U_120)
| ~ v1_group_1(U_120)
| v3_struct_0(U_120) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_68_2,plain,
! [U_122,U_121] :
( m1_subset_1(U_122,U_121)
| ~ r2_hidden(U_122,U_121) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( m1_subset_1(U_122,U_121)
| ~ r2_hidden(U_122,U_121) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_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_69_2,plain,
! [U_124,U_123] :
( r2_hidden(U_124,U_123)
| v1_xboole_0(U_123)
| ~ m1_subset_1(U_124,U_123) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( r2_hidden(U_124,U_123)
| v1_xboole_0(U_123)
| ~ m1_subset_1(U_124,U_123) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_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_70_2,plain,
! [U_126,U_125] :
( ( m1_subset_1(U_126,k1_zfmisc_1(U_125))
| ~ r1_tarski(U_126,U_125) )
& ( r1_tarski(U_126,U_125)
| ~ m1_subset_1(U_126,k1_zfmisc_1(U_125)) ) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
( ! [U_130,U_128] :
( m1_subset_1(U_130,k1_zfmisc_1(U_128))
| ~ r1_tarski(U_130,U_128) )
& ! [U_129,U_127] :
( r1_tarski(U_129,U_127)
| ~ m1_subset_1(U_129,k1_zfmisc_1(U_127)) ) ),
inference(miniscope,[status(thm)],[f_70_2]) ).
cnf(f_70_4,plain,
( r1_tarski(U_129,U_127)
| ~ m1_subset_1(U_129,k1_zfmisc_1(U_127)) ),
inference(clausify,[status(thm)],[f_70_3]) ).
cnf(f_70_5,plain,
( m1_subset_1(U_130,k1_zfmisc_1(U_128))
| ~ r1_tarski(U_130,U_128) ),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_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_71_2,plain,
! [U_133,U_132,U_131] :
( m1_subset_1(U_133,U_131)
| ~ m1_subset_1(U_132,k1_zfmisc_1(U_131))
| ~ r2_hidden(U_133,U_132) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( m1_subset_1(U_133,U_131)
| ~ m1_subset_1(U_132,k1_zfmisc_1(U_131))
| ~ r2_hidden(U_133,U_132) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(C,u1_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)],[t51_group_2]) ).
fof(f_72_2,plain,
! [U_136] :
( ! [U_135] :
( ! [U_134] :
( m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_134,u1_struct_0(U_135)) )
| ~ m1_group_2(U_135,U_136) )
| ~ l1_group_1(U_136)
| ~ v3_group_1(U_136)
| v3_struct_0(U_136) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_134,u1_struct_0(U_135))
| ~ m1_group_2(U_135,U_136)
| ~ l1_group_1(U_136)
| ~ v3_group_1(U_136)
| v3_struct_0(U_136) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( k3_group_1(C,D) = k3_group_1(A,B)
| D != B
| ~ m1_subset_1(D,u1_struct_0(C)) )
| ~ m1_group_2(C,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)],[t57_group_2]) ).
fof(f_73_2,plain,
! [U_140] :
( ! [U_139] :
( ! [U_138] :
( ! [U_137] :
( k3_group_1(U_138,U_137) = k3_group_1(U_140,U_139)
| U_137 != U_139
| ~ m1_subset_1(U_137,u1_struct_0(U_138)) )
| ~ m1_group_2(U_138,U_140) )
| ~ m1_subset_1(U_139,u1_struct_0(U_140)) )
| ~ l1_group_1(U_140)
| ~ v4_group_1(U_140)
| ~ v3_group_1(U_140)
| v3_struct_0(U_140) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( k3_group_1(U_138,U_137) = k3_group_1(U_140,U_139)
| U_137 != U_139
| ~ m1_subset_1(U_137,u1_struct_0(U_138))
| ~ m1_group_2(U_138,U_140)
| ~ m1_subset_1(U_139,u1_struct_0(U_140))
| ~ l1_group_1(U_140)
| ~ v4_group_1(U_140)
| ~ v3_group_1(U_140)
| v3_struct_0(U_140) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_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_74_2,plain,
! [U_143,U_142,U_141] :
( ~ v1_xboole_0(U_141)
| ~ m1_subset_1(U_142,k1_zfmisc_1(U_141))
| ~ r2_hidden(U_143,U_142) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_143,U_142] :
( ! [U_141] :
( ~ v1_xboole_0(U_141)
| ~ m1_subset_1(U_142,k1_zfmisc_1(U_141)) )
| ~ r2_hidden(U_143,U_142) ),
inference(miniscope,[status(thm)],[f_74_2]) ).
cnf(f_74_4,plain,
( ~ v1_xboole_0(U_141)
| ~ m1_subset_1(U_142,k1_zfmisc_1(U_141))
| ~ r2_hidden(U_143,U_142) ),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_75_2,plain,
! [U_144] :
( U_144 = k1_xboole_0
| ~ v1_xboole_0(U_144) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( U_144 = k1_xboole_0
| ~ v1_xboole_0(U_144) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_76_2,plain,
! [U_146,U_145] :
( ~ v1_xboole_0(U_145)
| ~ r2_hidden(U_146,U_145) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( ~ v1_xboole_0(U_145)
| ~ r2_hidden(U_146,U_145) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_77_2,plain,
! [U_148,U_147] :
( ~ v1_xboole_0(U_147)
| U_148 = U_147
| ~ v1_xboole_0(U_148) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_148] :
( ! [U_147] :
( ~ v1_xboole_0(U_147)
| U_148 = U_147 )
| ~ v1_xboole_0(U_148) ),
inference(miniscope,[status(thm)],[f_77_2]) ).
cnf(f_77_4,plain,
( ~ v1_xboole_0(U_147)
| U_148 = U_147
| ~ v1_xboole_0(U_148) ),
inference(clausify,[status(thm)],[f_77_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_10_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_3]) ).
cnf(f_10_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_4]) ).
cnf(f_11_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_3]) ).
cnf(f_11_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_5]) ).
cnf(f_12_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_3]) ).
cnf(f_12_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_6]) ).
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_26_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_26_2]) ).
cnf(f_29_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_2]) ).
cnf(f_30_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_30_2]) ).
cnf(f_34_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_34_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( u1_struct_0(Eq_x_0) = u1_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k4_autgroup(Eq_x_0) = k4_autgroup(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( k5_autgroup(Eq_x_0) = k5_autgroup(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( k2_funct_1(Eq_x_0) = k2_funct_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( k3_group_1(Eq_x_0,Eq_x_1) = k3_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,
( 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_11,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_12,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_13,axiom,
( k3_autgroup(Eq_x_0) = k3_autgroup(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( k1_autgroup(Eq_x_0) = k1_autgroup(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( k2_autgroup(Eq_x_0) = k2_autgroup(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,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_19,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(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_21,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( sK27(Eq_x_0) = sK27(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,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_28,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_29,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_30,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_31,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_32,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_33,axiom,
( m1_subset_1(Eq_y_0,Eq_y_1)
| ~ m1_subset_1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( r2_hidden(Eq_y_0,Eq_y_1)
| ~ r2_hidden(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( v1_fraenkel(Eq_y_0)
| ~ v1_fraenkel(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,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_46,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_47,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_48,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_49,axiom,
( r1_tarski(Eq_y_0,Eq_y_1)
| ~ r1_tarski(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP628+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 09:59:06 UTC 2026
% 0.10/0.39 % CPUTime :
% 12.94/13.23 % SZS status Theorem for theBenchmark
% 12.94/13.23 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------