%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ALG214+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 08:11:49 AM UTC 2026
% Result : Theorem 2.77s 3.14s
% Output : Proof 2.87s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t2_rmod_5,conjecture,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v1_rmod_5(D,A,B)
& r1_tarski(C,D) )
=> v1_rmod_5(C,A,B) ) ) ) ) ),
file('theBenchmark.p',t2_rmod_5) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
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(d1_rmod_5,axiom,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( v1_rmod_5(C,A,B)
<=> ! [D] :
( m2_rmod_4(D,A,B,C)
=> ( k5_rmod_4(A,B,D) = k1_rlvect_1(B)
=> k2_rmod_4(A,B,D) = k1_xboole_0 ) ) ) ) ) ),
file('theBenchmark.p',d1_rmod_5) ).
fof(d5_rmod_4,axiom,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_rmod_4(C,A,B)
=> k2_rmod_4(A,B,C) = a_3_0_rmod_4(A,B,C) ) ) ),
file('theBenchmark.p',d5_rmod_4) ).
fof(dt_k1_fraenkel,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> m1_fraenkel(k1_fraenkel(A,B),A,B) ),
file('theBenchmark.p',dt_k1_fraenkel) ).
fof(dt_k1_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
fof(dt_k1_funct_2,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_2) ).
fof(dt_k1_rlvect_1,axiom,
! [A] :
( l2_struct_0(A)
=> m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k1_rlvect_1) ).
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_rmod_4,axiom,
! [A,B,C] :
( ( m1_rmod_4(C,A,B)
& l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ( m1_subset_1(k2_rmod_4(A,B,C),k1_zfmisc_1(u1_struct_0(B)))
& v1_finset_1(k2_rmod_4(A,B,C)) ) ),
file('theBenchmark.p',dt_k2_rmod_4) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k5_rmod_4,axiom,
! [A,B,C] :
( ( m1_rmod_4(C,A,B)
& l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k5_rmod_4(A,B,C),u1_struct_0(B)) ),
file('theBenchmark.p',dt_k5_rmod_4) ).
fof(dt_k8_funct_2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(D,A)
& m1_relset_1(C,A,B)
& v1_funct_2(C,A,B)
& v1_funct_1(C)
& ~ v1_xboole_0(A) )
=> m1_subset_1(k8_funct_2(A,B,C,D),B) ),
file('theBenchmark.p',dt_k8_funct_2) ).
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_rlvect_1,axiom,
! [A] :
( l1_rlvect_1(A)
=> l2_struct_0(A) ),
file('theBenchmark.p',dt_l1_rlvect_1) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_l1_vectsp_1,axiom,
! [A] :
( l1_vectsp_1(A)
=> l1_group_1(A) ),
file('theBenchmark.p',dt_l1_vectsp_1) ).
fof(dt_l1_vectsp_2,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_vectsp_2(B,A)
=> l1_rlvect_1(B) ) ),
file('theBenchmark.p',dt_l1_vectsp_2) ).
fof(dt_l2_struct_0,axiom,
! [A] :
( l2_struct_0(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l2_struct_0) ).
fof(dt_l2_vectsp_1,axiom,
! [A] :
( l2_vectsp_1(A)
=> ( l2_struct_0(A)
& l1_vectsp_1(A) ) ),
file('theBenchmark.p',dt_l2_vectsp_1) ).
fof(dt_l3_vectsp_1,axiom,
! [A] :
( l3_vectsp_1(A)
=> ( l2_vectsp_1(A)
& l1_rlvect_1(A) ) ),
file('theBenchmark.p',dt_l3_vectsp_1) ).
fof(dt_m1_fraenkel,axiom,
! [A,B,C] :
( m1_fraenkel(C,A,B)
=> ( v1_fraenkel(C)
& ~ v1_xboole_0(C) ) ),
file('theBenchmark.p',dt_m1_fraenkel) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_rmod_4,axiom,
! [A,B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [C] :
( m1_rmod_4(C,A,B)
=> m2_fraenkel(C,u1_struct_0(B),u1_struct_0(A),k1_fraenkel(u1_struct_0(B),u1_struct_0(A))) ) ),
file('theBenchmark.p',dt_m1_rmod_4) ).
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_m2_rmod_4,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [D] :
( m2_rmod_4(D,A,B,C)
=> m1_rmod_4(D,A,B) ) ),
file('theBenchmark.p',dt_m2_rmod_4) ).
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_rlvect_1,axiom,
? [A] : l1_rlvect_1(A),
file('theBenchmark.p',existence_l1_rlvect_1) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l1_vectsp_1,axiom,
? [A] : l1_vectsp_1(A),
file('theBenchmark.p',existence_l1_vectsp_1) ).
fof(existence_l1_vectsp_2,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] : l1_vectsp_2(B,A) ),
file('theBenchmark.p',existence_l1_vectsp_2) ).
fof(existence_l2_struct_0,axiom,
? [A] : l2_struct_0(A),
file('theBenchmark.p',existence_l2_struct_0) ).
fof(existence_l2_vectsp_1,axiom,
? [A] : l2_vectsp_1(A),
file('theBenchmark.p',existence_l2_vectsp_1) ).
fof(existence_l3_vectsp_1,axiom,
? [A] : l3_vectsp_1(A),
file('theBenchmark.p',existence_l3_vectsp_1) ).
fof(existence_m1_fraenkel,axiom,
! [A,B] :
? [C] : m1_fraenkel(C,A,B),
file('theBenchmark.p',existence_m1_fraenkel) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_rmod_4,axiom,
! [A,B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ? [C] : m1_rmod_4(C,A,B) ),
file('theBenchmark.p',existence_m1_rmod_4) ).
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(existence_m2_rmod_4,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ? [D] : m2_rmod_4(D,A,B,C) ),
file('theBenchmark.p',existence_m2_rmod_4) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(A) )
=> ~ v1_xboole_0(k2_zfmisc_1(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(fraenkel_a_3_0_rmod_4,axiom,
! [A,B,C,D] :
( ( m1_rmod_4(D,B,C)
& l1_vectsp_2(C,B)
& v5_vectsp_2(C,B)
& v6_rlvect_1(C)
& v5_rlvect_1(C)
& v4_rlvect_1(C)
& v3_rlvect_1(C)
& ~ v3_struct_0(C)
& l3_vectsp_1(B)
& v8_vectsp_1(B)
& v7_vectsp_1(B)
& v6_vectsp_1(B)
& v4_group_1(B)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ( r2_hidden(A,a_3_0_rmod_4(B,C,D))
<=> ? [E] :
( k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,E) != k1_rlvect_1(B)
& A = E
& m1_subset_1(E,u1_struct_0(C)) ) ) ),
file('theBenchmark.p',fraenkel_a_3_0_rmod_4) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_rlvect_2,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( v1_finset_1(B)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc2_rlvect_2) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc4_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l2_struct_0(A) ),
file('theBenchmark.p',rc4_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(rc9_vectsp_2,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( ~ v3_struct_0(B)
& l1_vectsp_2(B,A) ) ),
file('theBenchmark.p',rc9_vectsp_2) ).
fof(redefinition_k1_fraenkel,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> k1_fraenkel(A,B) = k1_funct_2(A,B) ),
file('theBenchmark.p',redefinition_k1_fraenkel) ).
fof(redefinition_k8_funct_2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(D,A)
& m1_relset_1(C,A,B)
& v1_funct_2(C,A,B)
& v1_funct_1(C)
& ~ v1_xboole_0(A) )
=> k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ),
file('theBenchmark.p',redefinition_k8_funct_2) ).
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(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t25_rmod_4,axiom,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ! [E] :
( m2_rmod_4(E,A,B,C)
=> ( r1_tarski(C,D)
=> m2_rmod_4(E,A,B,D) ) ) ) ) ) ),
file('theBenchmark.p',t25_rmod_4) ).
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(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( r2_hidden(C,A)
<=> r2_hidden(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& A != B
& v1_xboole_0(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,negated_conjecture,
~ ! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v1_rmod_5(D,A,B)
& r1_tarski(C,D) )
=> v1_rmod_5(C,A,B) ) ) ) ) ),
inference(negate,[status(cth)],[t2_rmod_5]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ~ v1_rmod_5(C,A,B)
& v1_rmod_5(D,A,B)
& r1_tarski(C,D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
& l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_3] :
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ~ v1_rmod_5(U_1,U_3,U_2)
& v1_rmod_5(U_0,U_3,U_2)
& r1_tarski(U_1,U_0)
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(U_2))) )
& m1_subset_1(U_1,k1_zfmisc_1(u1_struct_0(U_2))) )
& l1_vectsp_2(U_2,U_3)
& v5_vectsp_2(U_2,U_3)
& v6_rlvect_1(U_2)
& v5_rlvect_1(U_2)
& v4_rlvect_1(U_2)
& v3_rlvect_1(U_2)
& ~ v3_struct_0(U_2) )
& l3_vectsp_1(U_3)
& v8_vectsp_1(U_3)
& v7_vectsp_1(U_3)
& v6_vectsp_1(U_3)
& v4_group_1(U_3)
& v6_rlvect_1(U_3)
& v5_rlvect_1(U_3)
& v4_rlvect_1(U_3)
& v3_rlvect_1(U_3)
& ~ v3_struct_0(U_3) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ~ v1_rmod_5(U_1,sK1,U_2)
& v1_rmod_5(U_0,sK1,U_2)
& r1_tarski(U_1,U_0)
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(U_2))) )
& m1_subset_1(U_1,k1_zfmisc_1(u1_struct_0(U_2))) )
& l1_vectsp_2(U_2,sK1)
& v5_vectsp_2(U_2,sK1)
& v6_rlvect_1(U_2)
& v5_rlvect_1(U_2)
& v4_rlvect_1(U_2)
& v3_rlvect_1(U_2)
& ~ v3_struct_0(U_2) )
& l3_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v4_group_1(sK1)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_1] :
( ? [U_0] :
( ~ v1_rmod_5(U_1,sK1,sK2)
& v1_rmod_5(U_0,sK1,sK2)
& r1_tarski(U_1,U_0)
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(sK2))) )
& m1_subset_1(U_1,k1_zfmisc_1(u1_struct_0(sK2))) )
& l1_vectsp_2(sK2,sK1)
& v5_vectsp_2(sK2,sK1)
& v6_rlvect_1(sK2)
& v5_rlvect_1(sK2)
& v4_rlvect_1(sK2)
& v3_rlvect_1(sK2)
& ~ v3_struct_0(sK2)
& l3_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v4_group_1(sK1)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_2,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ? [U_0] :
( ~ v1_rmod_5(sK3,sK1,sK2)
& v1_rmod_5(U_0,sK1,sK2)
& r1_tarski(sK3,U_0)
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(sK2))) )
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK2)))
& l1_vectsp_2(sK2,sK1)
& v5_vectsp_2(sK2,sK1)
& v6_rlvect_1(sK2)
& v5_rlvect_1(sK2)
& v4_rlvect_1(sK2)
& v3_rlvect_1(sK2)
& ~ v3_struct_0(sK2)
& l3_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v4_group_1(sK1)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_1,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ~ v1_rmod_5(sK3,sK1,sK2)
& v1_rmod_5(sK4,sK1,sK2)
& r1_tarski(sK3,sK4)
& m1_subset_1(sK4,k1_zfmisc_1(u1_struct_0(sK2)))
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK2)))
& l1_vectsp_2(sK2,sK1)
& v5_vectsp_2(sK2,sK1)
& v6_rlvect_1(sK2)
& v5_rlvect_1(sK2)
& v4_rlvect_1(sK2)
& v3_rlvect_1(sK2)
& ~ v3_struct_0(sK2)
& l3_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v4_group_1(sK1)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_0,sK4)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ~ v1_rmod_5(sK3,sK1,sK2)
& v1_rmod_5(sK4,sK1,sK2)
& r1_tarski(sK3,sK4)
& m1_subset_1(sK4,k1_zfmisc_1(u1_struct_0(sK2)))
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK2)))
& l1_vectsp_2(sK2,sK1)
& v5_vectsp_2(sK2,sK1)
& v6_rlvect_1(sK2)
& v5_rlvect_1(sK2)
& v4_rlvect_1(sK2)
& v3_rlvect_1(sK2)
& ~ v3_struct_0(sK2)
& l3_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v4_group_1(sK1)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(definitional_conversion,[status(esa)],[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,
v3_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_11,negated_conjecture,
v4_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_12,negated_conjecture,
v5_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_13,negated_conjecture,
v6_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_14,negated_conjecture,
v4_group_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_15,negated_conjecture,
v6_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_16,negated_conjecture,
v7_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_17,negated_conjecture,
v8_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_18,negated_conjecture,
l3_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_19,negated_conjecture,
~ v3_struct_0(sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_20,negated_conjecture,
v3_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_21,negated_conjecture,
v4_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_22,negated_conjecture,
v5_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_23,negated_conjecture,
v6_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_24,negated_conjecture,
v5_vectsp_2(sK2,sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_25,negated_conjecture,
l1_vectsp_2(sK2,sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_26,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK2))),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_27,negated_conjecture,
m1_subset_1(sK4,k1_zfmisc_1(u1_struct_0(sK2))),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_28,negated_conjecture,
r1_tarski(sK3,sK4),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_29,negated_conjecture,
v1_rmod_5(sK4,sK1,sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_30,negated_conjecture,
~ v1_rmod_5(sK3,sK1,sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_2_2,plain,
! [U_5,U_4] :
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_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_3_2,plain,
! [U_8,U_7,U_6] :
( v1_relat_1(U_6)
| ~ m1_subset_1(U_6,k1_zfmisc_1(k2_zfmisc_1(U_8,U_7))) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( v1_relat_1(U_6)
| ~ m1_subset_1(U_6,k1_zfmisc_1(k2_zfmisc_1(U_8,U_7))) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( v1_rmod_5(C,A,B)
| ? [D] :
( k2_rmod_4(A,B,D) != k1_xboole_0
& k5_rmod_4(A,B,D) = k1_rlvect_1(B)
& m2_rmod_4(D,A,B,C) ) )
& ( ! [D] :
( k2_rmod_4(A,B,D) = k1_xboole_0
| k5_rmod_4(A,B,D) != k1_rlvect_1(B)
| ~ m2_rmod_4(D,A,B,C) )
| ~ v1_rmod_5(C,A,B) ) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[d1_rmod_5]) ).
fof(f_4_2,plain,
! [U_13] :
( ! [U_12] :
( ! [U_11] :
( ( ( v1_rmod_5(U_11,U_13,U_12)
| ? [U_10] :
( k2_rmod_4(U_13,U_12,U_10) != k1_xboole_0
& k5_rmod_4(U_13,U_12,U_10) = k1_rlvect_1(U_12)
& m2_rmod_4(U_10,U_13,U_12,U_11) ) )
& ( ! [U_9] :
( k2_rmod_4(U_13,U_12,U_9) = k1_xboole_0
| k5_rmod_4(U_13,U_12,U_9) != k1_rlvect_1(U_12)
| ~ m2_rmod_4(U_9,U_13,U_12,U_11) )
| ~ v1_rmod_5(U_11,U_13,U_12) ) )
| ~ m1_subset_1(U_11,k1_zfmisc_1(u1_struct_0(U_12))) )
| ~ l1_vectsp_2(U_12,U_13)
| ~ v5_vectsp_2(U_12,U_13)
| ~ v6_rlvect_1(U_12)
| ~ v5_rlvect_1(U_12)
| ~ v4_rlvect_1(U_12)
| ~ v3_rlvect_1(U_12)
| v3_struct_0(U_12) )
| ~ l3_vectsp_1(U_13)
| ~ v8_vectsp_1(U_13)
| ~ v7_vectsp_1(U_13)
| ~ v6_vectsp_1(U_13)
| ~ v4_group_1(U_13)
| ~ v6_rlvect_1(U_13)
| ~ v5_rlvect_1(U_13)
| ~ v4_rlvect_1(U_13)
| ~ v3_rlvect_1(U_13)
| v3_struct_0(U_13) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_13] :
( ! [U_12] :
( ! [U_11] :
( ( ( v1_rmod_5(U_11,U_13,U_12)
| ( k2_rmod_4(U_13,U_12,sK5(U_13,U_12,U_11)) != k1_xboole_0
& k5_rmod_4(U_13,U_12,sK5(U_13,U_12,U_11)) = k1_rlvect_1(U_12)
& m2_rmod_4(sK5(U_13,U_12,U_11),U_13,U_12,U_11) ) )
& ( ! [U_9] :
( k2_rmod_4(U_13,U_12,U_9) = k1_xboole_0
| k5_rmod_4(U_13,U_12,U_9) != k1_rlvect_1(U_12)
| ~ m2_rmod_4(U_9,U_13,U_12,U_11) )
| ~ v1_rmod_5(U_11,U_13,U_12) ) )
| ~ m1_subset_1(U_11,k1_zfmisc_1(u1_struct_0(U_12))) )
| ~ l1_vectsp_2(U_12,U_13)
| ~ v5_vectsp_2(U_12,U_13)
| ~ v6_rlvect_1(U_12)
| ~ v5_rlvect_1(U_12)
| ~ v4_rlvect_1(U_12)
| ~ v3_rlvect_1(U_12)
| v3_struct_0(U_12) )
| ~ l3_vectsp_1(U_13)
| ~ v8_vectsp_1(U_13)
| ~ v7_vectsp_1(U_13)
| ~ v6_vectsp_1(U_13)
| ~ v4_group_1(U_13)
| ~ v6_rlvect_1(U_13)
| ~ v5_rlvect_1(U_13)
| ~ v4_rlvect_1(U_13)
| ~ v3_rlvect_1(U_13)
| v3_struct_0(U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_10,sK5(U_13,U_12,U_11))],[f_4_2]) ).
cnf(f_4_4,plain,
( k2_rmod_4(U_13,U_12,U_9) = k1_xboole_0
| k5_rmod_4(U_13,U_12,U_9) != k1_rlvect_1(U_12)
| ~ m2_rmod_4(U_9,U_13,U_12,U_11)
| ~ v1_rmod_5(U_11,U_13,U_12)
| ~ m1_subset_1(U_11,k1_zfmisc_1(u1_struct_0(U_12)))
| ~ l1_vectsp_2(U_12,U_13)
| ~ v5_vectsp_2(U_12,U_13)
| ~ v6_rlvect_1(U_12)
| ~ v5_rlvect_1(U_12)
| ~ v4_rlvect_1(U_12)
| ~ v3_rlvect_1(U_12)
| v3_struct_0(U_12)
| ~ l3_vectsp_1(U_13)
| ~ v8_vectsp_1(U_13)
| ~ v7_vectsp_1(U_13)
| ~ v6_vectsp_1(U_13)
| ~ v4_group_1(U_13)
| ~ v6_rlvect_1(U_13)
| ~ v5_rlvect_1(U_13)
| ~ v4_rlvect_1(U_13)
| ~ v3_rlvect_1(U_13)
| v3_struct_0(U_13) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( m2_rmod_4(sK5(U_13,U_12,U_11),U_13,U_12,U_11)
| v1_rmod_5(U_11,U_13,U_12)
| ~ m1_subset_1(U_11,k1_zfmisc_1(u1_struct_0(U_12)))
| ~ l1_vectsp_2(U_12,U_13)
| ~ v5_vectsp_2(U_12,U_13)
| ~ v6_rlvect_1(U_12)
| ~ v5_rlvect_1(U_12)
| ~ v4_rlvect_1(U_12)
| ~ v3_rlvect_1(U_12)
| v3_struct_0(U_12)
| ~ l3_vectsp_1(U_13)
| ~ v8_vectsp_1(U_13)
| ~ v7_vectsp_1(U_13)
| ~ v6_vectsp_1(U_13)
| ~ v4_group_1(U_13)
| ~ v6_rlvect_1(U_13)
| ~ v5_rlvect_1(U_13)
| ~ v4_rlvect_1(U_13)
| ~ v3_rlvect_1(U_13)
| v3_struct_0(U_13) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( k5_rmod_4(U_13,U_12,sK5(U_13,U_12,U_11)) = k1_rlvect_1(U_12)
| v1_rmod_5(U_11,U_13,U_12)
| ~ m1_subset_1(U_11,k1_zfmisc_1(u1_struct_0(U_12)))
| ~ l1_vectsp_2(U_12,U_13)
| ~ v5_vectsp_2(U_12,U_13)
| ~ v6_rlvect_1(U_12)
| ~ v5_rlvect_1(U_12)
| ~ v4_rlvect_1(U_12)
| ~ v3_rlvect_1(U_12)
| v3_struct_0(U_12)
| ~ l3_vectsp_1(U_13)
| ~ v8_vectsp_1(U_13)
| ~ v7_vectsp_1(U_13)
| ~ v6_vectsp_1(U_13)
| ~ v4_group_1(U_13)
| ~ v6_rlvect_1(U_13)
| ~ v5_rlvect_1(U_13)
| ~ v4_rlvect_1(U_13)
| ~ v3_rlvect_1(U_13)
| v3_struct_0(U_13) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_7,plain,
( k2_rmod_4(U_13,U_12,sK5(U_13,U_12,U_11)) != k1_xboole_0
| v1_rmod_5(U_11,U_13,U_12)
| ~ m1_subset_1(U_11,k1_zfmisc_1(u1_struct_0(U_12)))
| ~ l1_vectsp_2(U_12,U_13)
| ~ v5_vectsp_2(U_12,U_13)
| ~ v6_rlvect_1(U_12)
| ~ v5_rlvect_1(U_12)
| ~ v4_rlvect_1(U_12)
| ~ v3_rlvect_1(U_12)
| v3_struct_0(U_12)
| ~ l3_vectsp_1(U_13)
| ~ v8_vectsp_1(U_13)
| ~ v7_vectsp_1(U_13)
| ~ v6_vectsp_1(U_13)
| ~ v4_group_1(U_13)
| ~ v6_rlvect_1(U_13)
| ~ v5_rlvect_1(U_13)
| ~ v4_rlvect_1(U_13)
| ~ v3_rlvect_1(U_13)
| v3_struct_0(U_13) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( k2_rmod_4(A,B,C) = a_3_0_rmod_4(A,B,C)
| ~ m1_rmod_4(C,A,B) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[d5_rmod_4]) ).
fof(f_5_2,plain,
! [U_16] :
( ! [U_15] :
( ! [U_14] :
( k2_rmod_4(U_16,U_15,U_14) = a_3_0_rmod_4(U_16,U_15,U_14)
| ~ m1_rmod_4(U_14,U_16,U_15) )
| ~ l1_vectsp_2(U_15,U_16)
| ~ v5_vectsp_2(U_15,U_16)
| ~ v6_rlvect_1(U_15)
| ~ v5_rlvect_1(U_15)
| ~ v4_rlvect_1(U_15)
| ~ v3_rlvect_1(U_15)
| v3_struct_0(U_15) )
| ~ l3_vectsp_1(U_16)
| ~ v8_vectsp_1(U_16)
| ~ v7_vectsp_1(U_16)
| ~ v6_vectsp_1(U_16)
| ~ v4_group_1(U_16)
| ~ v6_rlvect_1(U_16)
| ~ v5_rlvect_1(U_16)
| ~ v4_rlvect_1(U_16)
| ~ v3_rlvect_1(U_16)
| v3_struct_0(U_16) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( k2_rmod_4(U_16,U_15,U_14) = a_3_0_rmod_4(U_16,U_15,U_14)
| ~ m1_rmod_4(U_14,U_16,U_15)
| ~ l1_vectsp_2(U_15,U_16)
| ~ v5_vectsp_2(U_15,U_16)
| ~ v6_rlvect_1(U_15)
| ~ v5_rlvect_1(U_15)
| ~ v4_rlvect_1(U_15)
| ~ v3_rlvect_1(U_15)
| v3_struct_0(U_15)
| ~ l3_vectsp_1(U_16)
| ~ v8_vectsp_1(U_16)
| ~ v7_vectsp_1(U_16)
| ~ v6_vectsp_1(U_16)
| ~ v4_group_1(U_16)
| ~ v6_rlvect_1(U_16)
| ~ v5_rlvect_1(U_16)
| ~ v4_rlvect_1(U_16)
| ~ v3_rlvect_1(U_16)
| v3_struct_0(U_16) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] :
( m1_fraenkel(k1_fraenkel(A,B),A,B)
| v1_xboole_0(B) ),
inference(fof_nnf,[status(thm)],[dt_k1_fraenkel]) ).
fof(f_6_2,plain,
! [U_18,U_17] :
( m1_fraenkel(k1_fraenkel(U_18,U_17),U_18,U_17)
| v1_xboole_0(U_17) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( m1_fraenkel(k1_fraenkel(U_18,U_17),U_18,U_17)
| v1_xboole_0(U_17) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_7_2,plain,
$true,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_2]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
! [A] :
( m1_subset_1(k1_rlvect_1(A),u1_struct_0(A))
| ~ l2_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_rlvect_1]) ).
fof(f_9_2,plain,
! [U_19] :
( m1_subset_1(k1_rlvect_1(U_19),u1_struct_0(U_19))
| ~ l2_struct_0(U_19) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( m1_subset_1(k1_rlvect_1(U_19),u1_struct_0(U_19))
| ~ l2_struct_0(U_19) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
! [A,B,C] :
( ( m1_subset_1(k2_rmod_4(A,B,C),k1_zfmisc_1(u1_struct_0(B)))
& v1_finset_1(k2_rmod_4(A,B,C)) )
| ~ m1_rmod_4(C,A,B)
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B)
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_rmod_4]) ).
fof(f_12_2,plain,
! [U_22,U_21,U_20] :
( ( m1_subset_1(k2_rmod_4(U_22,U_21,U_20),k1_zfmisc_1(u1_struct_0(U_21)))
& v1_finset_1(k2_rmod_4(U_22,U_21,U_20)) )
| ~ m1_rmod_4(U_20,U_22,U_21)
| ~ l1_vectsp_2(U_21,U_22)
| ~ v5_vectsp_2(U_21,U_22)
| ~ v6_rlvect_1(U_21)
| ~ v5_rlvect_1(U_21)
| ~ v4_rlvect_1(U_21)
| ~ v3_rlvect_1(U_21)
| v3_struct_0(U_21)
| ~ l3_vectsp_1(U_22)
| ~ v8_vectsp_1(U_22)
| ~ v7_vectsp_1(U_22)
| ~ v6_vectsp_1(U_22)
| ~ v4_group_1(U_22)
| ~ v6_rlvect_1(U_22)
| ~ v5_rlvect_1(U_22)
| ~ v4_rlvect_1(U_22)
| ~ v3_rlvect_1(U_22)
| v3_struct_0(U_22) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( v1_finset_1(k2_rmod_4(U_22,U_21,U_20))
| ~ m1_rmod_4(U_20,U_22,U_21)
| ~ l1_vectsp_2(U_21,U_22)
| ~ v5_vectsp_2(U_21,U_22)
| ~ v6_rlvect_1(U_21)
| ~ v5_rlvect_1(U_21)
| ~ v4_rlvect_1(U_21)
| ~ v3_rlvect_1(U_21)
| v3_struct_0(U_21)
| ~ l3_vectsp_1(U_22)
| ~ v8_vectsp_1(U_22)
| ~ v7_vectsp_1(U_22)
| ~ v6_vectsp_1(U_22)
| ~ v4_group_1(U_22)
| ~ v6_rlvect_1(U_22)
| ~ v5_rlvect_1(U_22)
| ~ v4_rlvect_1(U_22)
| ~ v3_rlvect_1(U_22)
| v3_struct_0(U_22) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( m1_subset_1(k2_rmod_4(U_22,U_21,U_20),k1_zfmisc_1(u1_struct_0(U_21)))
| ~ m1_rmod_4(U_20,U_22,U_21)
| ~ l1_vectsp_2(U_21,U_22)
| ~ v5_vectsp_2(U_21,U_22)
| ~ v6_rlvect_1(U_21)
| ~ v5_rlvect_1(U_21)
| ~ v4_rlvect_1(U_21)
| ~ v3_rlvect_1(U_21)
| v3_struct_0(U_21)
| ~ l3_vectsp_1(U_22)
| ~ v8_vectsp_1(U_22)
| ~ v7_vectsp_1(U_22)
| ~ v6_vectsp_1(U_22)
| ~ v4_group_1(U_22)
| ~ v6_rlvect_1(U_22)
| ~ v5_rlvect_1(U_22)
| ~ v4_rlvect_1(U_22)
| ~ v3_rlvect_1(U_22)
| v3_struct_0(U_22) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A,B,C] :
( m1_subset_1(k5_rmod_4(A,B,C),u1_struct_0(B))
| ~ m1_rmod_4(C,A,B)
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B)
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_rmod_4]) ).
fof(f_14_2,plain,
! [U_25,U_24,U_23] :
( m1_subset_1(k5_rmod_4(U_25,U_24,U_23),u1_struct_0(U_24))
| ~ m1_rmod_4(U_23,U_25,U_24)
| ~ l1_vectsp_2(U_24,U_25)
| ~ v5_vectsp_2(U_24,U_25)
| ~ v6_rlvect_1(U_24)
| ~ v5_rlvect_1(U_24)
| ~ v4_rlvect_1(U_24)
| ~ v3_rlvect_1(U_24)
| v3_struct_0(U_24)
| ~ l3_vectsp_1(U_25)
| ~ v8_vectsp_1(U_25)
| ~ v7_vectsp_1(U_25)
| ~ v6_vectsp_1(U_25)
| ~ v4_group_1(U_25)
| ~ v6_rlvect_1(U_25)
| ~ v5_rlvect_1(U_25)
| ~ v4_rlvect_1(U_25)
| ~ v3_rlvect_1(U_25)
| v3_struct_0(U_25) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( m1_subset_1(k5_rmod_4(U_25,U_24,U_23),u1_struct_0(U_24))
| ~ m1_rmod_4(U_23,U_25,U_24)
| ~ l1_vectsp_2(U_24,U_25)
| ~ v5_vectsp_2(U_24,U_25)
| ~ v6_rlvect_1(U_24)
| ~ v5_rlvect_1(U_24)
| ~ v4_rlvect_1(U_24)
| ~ v3_rlvect_1(U_24)
| v3_struct_0(U_24)
| ~ l3_vectsp_1(U_25)
| ~ v8_vectsp_1(U_25)
| ~ v7_vectsp_1(U_25)
| ~ v6_vectsp_1(U_25)
| ~ v4_group_1(U_25)
| ~ v6_rlvect_1(U_25)
| ~ v5_rlvect_1(U_25)
| ~ v4_rlvect_1(U_25)
| ~ v3_rlvect_1(U_25)
| v3_struct_0(U_25) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A,B,C,D] :
( m1_subset_1(k8_funct_2(A,B,C,D),B)
| ~ m1_subset_1(D,A)
| ~ m1_relset_1(C,A,B)
| ~ v1_funct_2(C,A,B)
| ~ v1_funct_1(C)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k8_funct_2]) ).
fof(f_15_2,plain,
! [U_29,U_28,U_27,U_26] :
( m1_subset_1(k8_funct_2(U_29,U_28,U_27,U_26),U_28)
| ~ m1_subset_1(U_26,U_29)
| ~ m1_relset_1(U_27,U_29,U_28)
| ~ v1_funct_2(U_27,U_29,U_28)
| ~ v1_funct_1(U_27)
| v1_xboole_0(U_29) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( m1_subset_1(k8_funct_2(U_29,U_28,U_27,U_26),U_28)
| ~ m1_subset_1(U_26,U_29)
| ~ m1_relset_1(U_27,U_29,U_28)
| ~ v1_funct_2(U_27,U_29,U_28)
| ~ v1_funct_1(U_27)
| v1_xboole_0(U_29) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_group_1]) ).
fof(f_16_2,plain,
! [U_30] :
( l1_struct_0(U_30)
| ~ l1_group_1(U_30) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( l1_struct_0(U_30)
| ~ l1_group_1(U_30) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] :
( l2_struct_0(A)
| ~ l1_rlvect_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_rlvect_1]) ).
fof(f_17_2,plain,
! [U_31] :
( l2_struct_0(U_31)
| ~ l1_rlvect_1(U_31) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( l2_struct_0(U_31)
| ~ l1_rlvect_1(U_31) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_18_2,plain,
$true,
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
! [A] :
( l1_group_1(A)
| ~ l1_vectsp_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_vectsp_1]) ).
fof(f_19_2,plain,
! [U_32] :
( l1_group_1(U_32)
| ~ l1_vectsp_1(U_32) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( l1_group_1(U_32)
| ~ l1_vectsp_1(U_32) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A] :
( ! [B] :
( l1_rlvect_1(B)
| ~ l1_vectsp_2(B,A) )
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_vectsp_2]) ).
fof(f_20_2,plain,
! [U_34] :
( ! [U_33] :
( l1_rlvect_1(U_33)
| ~ l1_vectsp_2(U_33,U_34) )
| ~ l1_struct_0(U_34) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( l1_rlvect_1(U_33)
| ~ l1_vectsp_2(U_33,U_34)
| ~ l1_struct_0(U_34) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_struct_0]) ).
fof(f_21_2,plain,
! [U_35] :
( l1_struct_0(U_35)
| ~ l2_struct_0(U_35) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( l1_struct_0(U_35)
| ~ l2_struct_0(U_35) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A] :
( ( l2_struct_0(A)
& l1_vectsp_1(A) )
| ~ l2_vectsp_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_vectsp_1]) ).
fof(f_22_2,plain,
! [U_36] :
( ( l2_struct_0(U_36)
& l1_vectsp_1(U_36) )
| ~ l2_vectsp_1(U_36) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( l1_vectsp_1(U_36)
| ~ l2_vectsp_1(U_36) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( l2_struct_0(U_36)
| ~ l2_vectsp_1(U_36) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A] :
( ( l2_vectsp_1(A)
& l1_rlvect_1(A) )
| ~ l3_vectsp_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l3_vectsp_1]) ).
fof(f_23_2,plain,
! [U_37] :
( ( l2_vectsp_1(U_37)
& l1_rlvect_1(U_37) )
| ~ l3_vectsp_1(U_37) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( l1_rlvect_1(U_37)
| ~ l3_vectsp_1(U_37) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( l2_vectsp_1(U_37)
| ~ l3_vectsp_1(U_37) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_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_24_2,plain,
! [U_40,U_39,U_38] :
( ( v1_fraenkel(U_38)
& ~ v1_xboole_0(U_38) )
| ~ m1_fraenkel(U_38,U_40,U_39) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( ~ v1_xboole_0(U_38)
| ~ m1_fraenkel(U_38,U_40,U_39) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( v1_fraenkel(U_38)
| ~ m1_fraenkel(U_38,U_40,U_39) ),
inference(clausify,[status(thm)],[f_24_2]) ).
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] :
( m2_fraenkel(C,u1_struct_0(B),u1_struct_0(A),k1_fraenkel(u1_struct_0(B),u1_struct_0(A)))
| ~ m1_rmod_4(C,A,B) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B)
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m1_rmod_4]) ).
fof(f_26_2,plain,
! [U_43,U_42] :
( ! [U_41] :
( m2_fraenkel(U_41,u1_struct_0(U_42),u1_struct_0(U_43),k1_fraenkel(u1_struct_0(U_42),u1_struct_0(U_43)))
| ~ m1_rmod_4(U_41,U_43,U_42) )
| ~ l1_vectsp_2(U_42,U_43)
| ~ v5_vectsp_2(U_42,U_43)
| ~ v6_rlvect_1(U_42)
| ~ v5_rlvect_1(U_42)
| ~ v4_rlvect_1(U_42)
| ~ v3_rlvect_1(U_42)
| v3_struct_0(U_42)
| ~ l3_vectsp_1(U_43)
| ~ v8_vectsp_1(U_43)
| ~ v7_vectsp_1(U_43)
| ~ v6_vectsp_1(U_43)
| ~ v4_group_1(U_43)
| ~ v6_rlvect_1(U_43)
| ~ v5_rlvect_1(U_43)
| ~ v4_rlvect_1(U_43)
| ~ v3_rlvect_1(U_43)
| v3_struct_0(U_43) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( m2_fraenkel(U_41,u1_struct_0(U_42),u1_struct_0(U_43),k1_fraenkel(u1_struct_0(U_42),u1_struct_0(U_43)))
| ~ m1_rmod_4(U_41,U_43,U_42)
| ~ l1_vectsp_2(U_42,U_43)
| ~ v5_vectsp_2(U_42,U_43)
| ~ v6_rlvect_1(U_42)
| ~ v5_rlvect_1(U_42)
| ~ v4_rlvect_1(U_42)
| ~ v3_rlvect_1(U_42)
| v3_struct_0(U_42)
| ~ l3_vectsp_1(U_43)
| ~ v8_vectsp_1(U_43)
| ~ v7_vectsp_1(U_43)
| ~ v6_vectsp_1(U_43)
| ~ v4_group_1(U_43)
| ~ v6_rlvect_1(U_43)
| ~ v5_rlvect_1(U_43)
| ~ v4_rlvect_1(U_43)
| ~ v3_rlvect_1(U_43)
| v3_struct_0(U_43) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_27_2,plain,
$true,
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_28_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_28_2,plain,
! [U_47,U_46,U_45] :
( ! [U_44] :
( ( m2_relset_1(U_44,U_47,U_46)
& v1_funct_2(U_44,U_47,U_46)
& v1_funct_1(U_44) )
| ~ m2_fraenkel(U_44,U_47,U_46,U_45) )
| ~ m1_fraenkel(U_45,U_47,U_46)
| v1_xboole_0(U_46) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( v1_funct_1(U_44)
| ~ m2_fraenkel(U_44,U_47,U_46,U_45)
| ~ m1_fraenkel(U_45,U_47,U_46)
| v1_xboole_0(U_46) ),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( v1_funct_2(U_44,U_47,U_46)
| ~ m2_fraenkel(U_44,U_47,U_46,U_45)
| ~ m1_fraenkel(U_45,U_47,U_46)
| v1_xboole_0(U_46) ),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_5,plain,
( m2_relset_1(U_44,U_47,U_46)
| ~ m2_fraenkel(U_44,U_47,U_46,U_45)
| ~ m1_fraenkel(U_45,U_47,U_46)
| v1_xboole_0(U_46) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_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_29_2,plain,
! [U_50,U_49,U_48] :
( m1_subset_1(U_48,k1_zfmisc_1(k2_zfmisc_1(U_50,U_49)))
| ~ m2_relset_1(U_48,U_50,U_49) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( m1_subset_1(U_48,k1_zfmisc_1(k2_zfmisc_1(U_50,U_49)))
| ~ m2_relset_1(U_48,U_50,U_49) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B,C] :
( ! [D] :
( m1_rmod_4(D,A,B)
| ~ m2_rmod_4(D,A,B,C) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B)
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m2_rmod_4]) ).
fof(f_30_2,plain,
! [U_54,U_53,U_52] :
( ! [U_51] :
( m1_rmod_4(U_51,U_54,U_53)
| ~ m2_rmod_4(U_51,U_54,U_53,U_52) )
| ~ m1_subset_1(U_52,k1_zfmisc_1(u1_struct_0(U_53)))
| ~ l1_vectsp_2(U_53,U_54)
| ~ v5_vectsp_2(U_53,U_54)
| ~ v6_rlvect_1(U_53)
| ~ v5_rlvect_1(U_53)
| ~ v4_rlvect_1(U_53)
| ~ v3_rlvect_1(U_53)
| v3_struct_0(U_53)
| ~ l3_vectsp_1(U_54)
| ~ v8_vectsp_1(U_54)
| ~ v7_vectsp_1(U_54)
| ~ v6_vectsp_1(U_54)
| ~ v4_group_1(U_54)
| ~ v6_rlvect_1(U_54)
| ~ v5_rlvect_1(U_54)
| ~ v4_rlvect_1(U_54)
| ~ v3_rlvect_1(U_54)
| v3_struct_0(U_54) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( m1_rmod_4(U_51,U_54,U_53)
| ~ m2_rmod_4(U_51,U_54,U_53,U_52)
| ~ m1_subset_1(U_52,k1_zfmisc_1(u1_struct_0(U_53)))
| ~ l1_vectsp_2(U_53,U_54)
| ~ v5_vectsp_2(U_53,U_54)
| ~ v6_rlvect_1(U_53)
| ~ v5_rlvect_1(U_53)
| ~ v4_rlvect_1(U_53)
| ~ v3_rlvect_1(U_53)
| v3_struct_0(U_53)
| ~ l3_vectsp_1(U_54)
| ~ v8_vectsp_1(U_54)
| ~ v7_vectsp_1(U_54)
| ~ v6_vectsp_1(U_54)
| ~ v4_group_1(U_54)
| ~ v6_rlvect_1(U_54)
| ~ v5_rlvect_1(U_54)
| ~ v4_rlvect_1(U_54)
| ~ v3_rlvect_1(U_54)
| v3_struct_0(U_54) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_31_2,plain,
$true,
inference(clausify,[status(thm)],[f_31_1]) ).
fof(f_32_1,plain,
? [A] : l1_group_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_group_1]) ).
fof(f_32_2,plain,
? [U_55] : l1_group_1(U_55),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
l1_group_1(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_55,sK6)],[f_32_2]) ).
cnf(f_32_4,plain,
l1_group_1(sK6),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] : l1_rlvect_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_rlvect_1]) ).
fof(f_33_2,plain,
? [U_56] : l1_rlvect_1(U_56),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
l1_rlvect_1(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_56,sK7)],[f_33_2]) ).
cnf(f_33_4,plain,
l1_rlvect_1(sK7),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_34_2,plain,
? [U_57] : l1_struct_0(U_57),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
l1_struct_0(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_57,sK8)],[f_34_2]) ).
cnf(f_34_4,plain,
l1_struct_0(sK8),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] : l1_vectsp_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_vectsp_1]) ).
fof(f_35_2,plain,
? [U_58] : l1_vectsp_1(U_58),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
l1_vectsp_1(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_58,sK9)],[f_35_2]) ).
cnf(f_35_4,plain,
l1_vectsp_1(sK9),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A] :
( ? [B] : l1_vectsp_2(B,A)
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_l1_vectsp_2]) ).
fof(f_36_2,plain,
! [U_60] :
( ? [U_59] : l1_vectsp_2(U_59,U_60)
| ~ l1_struct_0(U_60) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_60] :
( l1_vectsp_2(sK10(U_60),U_60)
| ~ l1_struct_0(U_60) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_59,sK10(U_60))],[f_36_2]) ).
cnf(f_36_4,plain,
( l1_vectsp_2(sK10(U_60),U_60)
| ~ l1_struct_0(U_60) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
? [A] : l2_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l2_struct_0]) ).
fof(f_37_2,plain,
? [U_61] : l2_struct_0(U_61),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
l2_struct_0(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_61,sK11)],[f_37_2]) ).
cnf(f_37_4,plain,
l2_struct_0(sK11),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
? [A] : l2_vectsp_1(A),
inference(fof_nnf,[status(thm)],[existence_l2_vectsp_1]) ).
fof(f_38_2,plain,
? [U_62] : l2_vectsp_1(U_62),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
l2_vectsp_1(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_62,sK12)],[f_38_2]) ).
cnf(f_38_4,plain,
l2_vectsp_1(sK12),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
? [A] : l3_vectsp_1(A),
inference(fof_nnf,[status(thm)],[existence_l3_vectsp_1]) ).
fof(f_39_2,plain,
? [U_63] : l3_vectsp_1(U_63),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
l3_vectsp_1(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_63,sK13)],[f_39_2]) ).
cnf(f_39_4,plain,
l3_vectsp_1(sK13),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B] :
? [C] : m1_fraenkel(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_fraenkel]) ).
fof(f_40_2,plain,
! [U_66,U_65] :
? [U_64] : m1_fraenkel(U_64,U_66,U_65),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_66,U_65] : m1_fraenkel(sK14(U_66,U_65),U_66,U_65),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_64,sK14(U_66,U_65))],[f_40_2]) ).
cnf(f_40_4,plain,
m1_fraenkel(sK14(U_66,U_65),U_66,U_65),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_41_2,plain,
! [U_69,U_68] :
? [U_67] : m1_relset_1(U_67,U_69,U_68),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_69,U_68] : m1_relset_1(sK15(U_69,U_68),U_69,U_68),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_67,sK15(U_69,U_68))],[f_41_2]) ).
cnf(f_41_4,plain,
m1_relset_1(sK15(U_69,U_68),U_69,U_68),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B] :
( ? [C] : m1_rmod_4(C,A,B)
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B)
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m1_rmod_4]) ).
fof(f_42_2,plain,
! [U_72,U_71] :
( ? [U_70] : m1_rmod_4(U_70,U_72,U_71)
| ~ l1_vectsp_2(U_71,U_72)
| ~ v5_vectsp_2(U_71,U_72)
| ~ v6_rlvect_1(U_71)
| ~ v5_rlvect_1(U_71)
| ~ v4_rlvect_1(U_71)
| ~ v3_rlvect_1(U_71)
| v3_struct_0(U_71)
| ~ l3_vectsp_1(U_72)
| ~ v8_vectsp_1(U_72)
| ~ v7_vectsp_1(U_72)
| ~ v6_vectsp_1(U_72)
| ~ v4_group_1(U_72)
| ~ v6_rlvect_1(U_72)
| ~ v5_rlvect_1(U_72)
| ~ v4_rlvect_1(U_72)
| ~ v3_rlvect_1(U_72)
| v3_struct_0(U_72) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_72,U_71] :
( m1_rmod_4(sK16(U_72,U_71),U_72,U_71)
| ~ l1_vectsp_2(U_71,U_72)
| ~ v5_vectsp_2(U_71,U_72)
| ~ v6_rlvect_1(U_71)
| ~ v5_rlvect_1(U_71)
| ~ v4_rlvect_1(U_71)
| ~ v3_rlvect_1(U_71)
| v3_struct_0(U_71)
| ~ l3_vectsp_1(U_72)
| ~ v8_vectsp_1(U_72)
| ~ v7_vectsp_1(U_72)
| ~ v6_vectsp_1(U_72)
| ~ v4_group_1(U_72)
| ~ v6_rlvect_1(U_72)
| ~ v5_rlvect_1(U_72)
| ~ v4_rlvect_1(U_72)
| ~ v3_rlvect_1(U_72)
| v3_struct_0(U_72) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_70,sK16(U_72,U_71))],[f_42_2]) ).
cnf(f_42_4,plain,
( m1_rmod_4(sK16(U_72,U_71),U_72,U_71)
| ~ l1_vectsp_2(U_71,U_72)
| ~ v5_vectsp_2(U_71,U_72)
| ~ v6_rlvect_1(U_71)
| ~ v5_rlvect_1(U_71)
| ~ v4_rlvect_1(U_71)
| ~ v3_rlvect_1(U_71)
| v3_struct_0(U_71)
| ~ l3_vectsp_1(U_72)
| ~ v8_vectsp_1(U_72)
| ~ v7_vectsp_1(U_72)
| ~ v6_vectsp_1(U_72)
| ~ v4_group_1(U_72)
| ~ v6_rlvect_1(U_72)
| ~ v5_rlvect_1(U_72)
| ~ v4_rlvect_1(U_72)
| ~ v3_rlvect_1(U_72)
| v3_struct_0(U_72) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_43_2,plain,
! [U_74] :
? [U_73] : m1_subset_1(U_73,U_74),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_74] : m1_subset_1(sK17(U_74),U_74),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_73,sK17(U_74))],[f_43_2]) ).
cnf(f_43_4,plain,
m1_subset_1(sK17(U_74),U_74),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_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_44_2,plain,
! [U_78,U_77,U_76] :
( ? [U_75] : m2_fraenkel(U_75,U_78,U_77,U_76)
| ~ m1_fraenkel(U_76,U_78,U_77)
| v1_xboole_0(U_77) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_78,U_77,U_76] :
( m2_fraenkel(sK18(U_78,U_77,U_76),U_78,U_77,U_76)
| ~ m1_fraenkel(U_76,U_78,U_77)
| v1_xboole_0(U_77) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_75,sK18(U_78,U_77,U_76))],[f_44_2]) ).
cnf(f_44_4,plain,
( m2_fraenkel(sK18(U_78,U_77,U_76),U_78,U_77,U_76)
| ~ m1_fraenkel(U_76,U_78,U_77)
| v1_xboole_0(U_77) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_45_2,plain,
! [U_81,U_80] :
? [U_79] : m2_relset_1(U_79,U_81,U_80),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_81,U_80] : m2_relset_1(sK19(U_81,U_80),U_81,U_80),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_79,sK19(U_81,U_80))],[f_45_2]) ).
cnf(f_45_4,plain,
m2_relset_1(sK19(U_81,U_80),U_81,U_80),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [A,B,C] :
( ? [D] : m2_rmod_4(D,A,B,C)
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B)
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m2_rmod_4]) ).
fof(f_46_2,plain,
! [U_85,U_84,U_83] :
( ? [U_82] : m2_rmod_4(U_82,U_85,U_84,U_83)
| ~ m1_subset_1(U_83,k1_zfmisc_1(u1_struct_0(U_84)))
| ~ l1_vectsp_2(U_84,U_85)
| ~ v5_vectsp_2(U_84,U_85)
| ~ v6_rlvect_1(U_84)
| ~ v5_rlvect_1(U_84)
| ~ v4_rlvect_1(U_84)
| ~ v3_rlvect_1(U_84)
| v3_struct_0(U_84)
| ~ l3_vectsp_1(U_85)
| ~ v8_vectsp_1(U_85)
| ~ v7_vectsp_1(U_85)
| ~ v6_vectsp_1(U_85)
| ~ v4_group_1(U_85)
| ~ v6_rlvect_1(U_85)
| ~ v5_rlvect_1(U_85)
| ~ v4_rlvect_1(U_85)
| ~ v3_rlvect_1(U_85)
| v3_struct_0(U_85) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_85,U_84,U_83] :
( m2_rmod_4(sK20(U_85,U_84,U_83),U_85,U_84,U_83)
| ~ m1_subset_1(U_83,k1_zfmisc_1(u1_struct_0(U_84)))
| ~ l1_vectsp_2(U_84,U_85)
| ~ v5_vectsp_2(U_84,U_85)
| ~ v6_rlvect_1(U_84)
| ~ v5_rlvect_1(U_84)
| ~ v4_rlvect_1(U_84)
| ~ v3_rlvect_1(U_84)
| v3_struct_0(U_84)
| ~ l3_vectsp_1(U_85)
| ~ v8_vectsp_1(U_85)
| ~ v7_vectsp_1(U_85)
| ~ v6_vectsp_1(U_85)
| ~ v4_group_1(U_85)
| ~ v6_rlvect_1(U_85)
| ~ v5_rlvect_1(U_85)
| ~ v4_rlvect_1(U_85)
| ~ v3_rlvect_1(U_85)
| v3_struct_0(U_85) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_82,sK20(U_85,U_84,U_83))],[f_46_2]) ).
cnf(f_46_4,plain,
( m2_rmod_4(sK20(U_85,U_84,U_83),U_85,U_84,U_83)
| ~ m1_subset_1(U_83,k1_zfmisc_1(u1_struct_0(U_84)))
| ~ l1_vectsp_2(U_84,U_85)
| ~ v5_vectsp_2(U_84,U_85)
| ~ v6_rlvect_1(U_84)
| ~ v5_rlvect_1(U_84)
| ~ v4_rlvect_1(U_84)
| ~ v3_rlvect_1(U_84)
| v3_struct_0(U_84)
| ~ l3_vectsp_1(U_85)
| ~ v8_vectsp_1(U_85)
| ~ v7_vectsp_1(U_85)
| ~ v6_vectsp_1(U_85)
| ~ v4_group_1(U_85)
| ~ v6_rlvect_1(U_85)
| ~ v5_rlvect_1(U_85)
| ~ v4_rlvect_1(U_85)
| ~ v3_rlvect_1(U_85)
| v3_struct_0(U_85) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_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_47_2,plain,
! [U_86] :
( ~ v1_xboole_0(u1_struct_0(U_86))
| ~ l1_struct_0(U_86)
| v3_struct_0(U_86) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_86))
| ~ l1_struct_0(U_86)
| v3_struct_0(U_86) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_48_2,plain,
! [U_87] : ~ v1_xboole_0(k1_zfmisc_1(U_87)),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
~ v1_xboole_0(k1_zfmisc_1(U_87)),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_49_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_49_1]) ).
fof(f_50_1,plain,
! [A,B] :
( ~ v1_xboole_0(k2_zfmisc_1(A,B))
| v1_xboole_0(B)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_50_2,plain,
! [U_89,U_88] :
( ~ v1_xboole_0(k2_zfmisc_1(U_89,U_88))
| v1_xboole_0(U_88)
| v1_xboole_0(U_89) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( ~ v1_xboole_0(k2_zfmisc_1(U_89,U_88))
| v1_xboole_0(U_88)
| v1_xboole_0(U_89) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [A,B,C,D] :
( ( ( r2_hidden(A,a_3_0_rmod_4(B,C,D))
| ! [E] :
( k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,E) = k1_rlvect_1(B)
| A != E
| ~ m1_subset_1(E,u1_struct_0(C)) ) )
& ( ? [E] :
( k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,E) != k1_rlvect_1(B)
& A = E
& m1_subset_1(E,u1_struct_0(C)) )
| ~ r2_hidden(A,a_3_0_rmod_4(B,C,D)) ) )
| ~ m1_rmod_4(D,B,C)
| ~ l1_vectsp_2(C,B)
| ~ v5_vectsp_2(C,B)
| ~ v6_rlvect_1(C)
| ~ v5_rlvect_1(C)
| ~ v4_rlvect_1(C)
| ~ v3_rlvect_1(C)
| v3_struct_0(C)
| ~ l3_vectsp_1(B)
| ~ v8_vectsp_1(B)
| ~ v7_vectsp_1(B)
| ~ v6_vectsp_1(B)
| ~ v4_group_1(B)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) ),
inference(fof_nnf,[status(thm)],[fraenkel_a_3_0_rmod_4]) ).
fof(f_51_2,plain,
! [U_95,U_94,U_93,U_92] :
( ( ( r2_hidden(U_95,a_3_0_rmod_4(U_94,U_93,U_92))
| ! [U_91] :
( k8_funct_2(u1_struct_0(U_93),u1_struct_0(U_94),U_92,U_91) = k1_rlvect_1(U_94)
| U_95 != U_91
| ~ m1_subset_1(U_91,u1_struct_0(U_93)) ) )
& ( ? [U_90] :
( k8_funct_2(u1_struct_0(U_93),u1_struct_0(U_94),U_92,U_90) != k1_rlvect_1(U_94)
& U_95 = U_90
& m1_subset_1(U_90,u1_struct_0(U_93)) )
| ~ r2_hidden(U_95,a_3_0_rmod_4(U_94,U_93,U_92)) ) )
| ~ m1_rmod_4(U_92,U_94,U_93)
| ~ l1_vectsp_2(U_93,U_94)
| ~ v5_vectsp_2(U_93,U_94)
| ~ v6_rlvect_1(U_93)
| ~ v5_rlvect_1(U_93)
| ~ v4_rlvect_1(U_93)
| ~ v3_rlvect_1(U_93)
| v3_struct_0(U_93)
| ~ l3_vectsp_1(U_94)
| ~ v8_vectsp_1(U_94)
| ~ v7_vectsp_1(U_94)
| ~ v6_vectsp_1(U_94)
| ~ v4_group_1(U_94)
| ~ v6_rlvect_1(U_94)
| ~ v5_rlvect_1(U_94)
| ~ v4_rlvect_1(U_94)
| ~ v3_rlvect_1(U_94)
| v3_struct_0(U_94) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_95,U_94,U_93,U_92] :
( ( ( r2_hidden(U_95,a_3_0_rmod_4(U_94,U_93,U_92))
| ! [U_91] :
( k8_funct_2(u1_struct_0(U_93),u1_struct_0(U_94),U_92,U_91) = k1_rlvect_1(U_94)
| U_95 != U_91
| ~ m1_subset_1(U_91,u1_struct_0(U_93)) ) )
& ( ( k8_funct_2(u1_struct_0(U_93),u1_struct_0(U_94),U_92,sK21(U_95,U_94,U_93,U_92)) != k1_rlvect_1(U_94)
& U_95 = sK21(U_95,U_94,U_93,U_92)
& m1_subset_1(sK21(U_95,U_94,U_93,U_92),u1_struct_0(U_93)) )
| ~ r2_hidden(U_95,a_3_0_rmod_4(U_94,U_93,U_92)) ) )
| ~ m1_rmod_4(U_92,U_94,U_93)
| ~ l1_vectsp_2(U_93,U_94)
| ~ v5_vectsp_2(U_93,U_94)
| ~ v6_rlvect_1(U_93)
| ~ v5_rlvect_1(U_93)
| ~ v4_rlvect_1(U_93)
| ~ v3_rlvect_1(U_93)
| v3_struct_0(U_93)
| ~ l3_vectsp_1(U_94)
| ~ v8_vectsp_1(U_94)
| ~ v7_vectsp_1(U_94)
| ~ v6_vectsp_1(U_94)
| ~ v4_group_1(U_94)
| ~ v6_rlvect_1(U_94)
| ~ v5_rlvect_1(U_94)
| ~ v4_rlvect_1(U_94)
| ~ v3_rlvect_1(U_94)
| v3_struct_0(U_94) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_90,sK21(U_95,U_94,U_93,U_92))],[f_51_2]) ).
cnf(f_51_4,plain,
( m1_subset_1(sK21(U_95,U_94,U_93,U_92),u1_struct_0(U_93))
| ~ r2_hidden(U_95,a_3_0_rmod_4(U_94,U_93,U_92))
| ~ m1_rmod_4(U_92,U_94,U_93)
| ~ l1_vectsp_2(U_93,U_94)
| ~ v5_vectsp_2(U_93,U_94)
| ~ v6_rlvect_1(U_93)
| ~ v5_rlvect_1(U_93)
| ~ v4_rlvect_1(U_93)
| ~ v3_rlvect_1(U_93)
| v3_struct_0(U_93)
| ~ l3_vectsp_1(U_94)
| ~ v8_vectsp_1(U_94)
| ~ v7_vectsp_1(U_94)
| ~ v6_vectsp_1(U_94)
| ~ v4_group_1(U_94)
| ~ v6_rlvect_1(U_94)
| ~ v5_rlvect_1(U_94)
| ~ v4_rlvect_1(U_94)
| ~ v3_rlvect_1(U_94)
| v3_struct_0(U_94) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
( U_95 = sK21(U_95,U_94,U_93,U_92)
| ~ r2_hidden(U_95,a_3_0_rmod_4(U_94,U_93,U_92))
| ~ m1_rmod_4(U_92,U_94,U_93)
| ~ l1_vectsp_2(U_93,U_94)
| ~ v5_vectsp_2(U_93,U_94)
| ~ v6_rlvect_1(U_93)
| ~ v5_rlvect_1(U_93)
| ~ v4_rlvect_1(U_93)
| ~ v3_rlvect_1(U_93)
| v3_struct_0(U_93)
| ~ l3_vectsp_1(U_94)
| ~ v8_vectsp_1(U_94)
| ~ v7_vectsp_1(U_94)
| ~ v6_vectsp_1(U_94)
| ~ v4_group_1(U_94)
| ~ v6_rlvect_1(U_94)
| ~ v5_rlvect_1(U_94)
| ~ v4_rlvect_1(U_94)
| ~ v3_rlvect_1(U_94)
| v3_struct_0(U_94) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_6,plain,
( k8_funct_2(u1_struct_0(U_93),u1_struct_0(U_94),U_92,sK21(U_95,U_94,U_93,U_92)) != k1_rlvect_1(U_94)
| ~ r2_hidden(U_95,a_3_0_rmod_4(U_94,U_93,U_92))
| ~ m1_rmod_4(U_92,U_94,U_93)
| ~ l1_vectsp_2(U_93,U_94)
| ~ v5_vectsp_2(U_93,U_94)
| ~ v6_rlvect_1(U_93)
| ~ v5_rlvect_1(U_93)
| ~ v4_rlvect_1(U_93)
| ~ v3_rlvect_1(U_93)
| v3_struct_0(U_93)
| ~ l3_vectsp_1(U_94)
| ~ v8_vectsp_1(U_94)
| ~ v7_vectsp_1(U_94)
| ~ v6_vectsp_1(U_94)
| ~ v4_group_1(U_94)
| ~ v6_rlvect_1(U_94)
| ~ v5_rlvect_1(U_94)
| ~ v4_rlvect_1(U_94)
| ~ v3_rlvect_1(U_94)
| v3_struct_0(U_94) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_7,plain,
( r2_hidden(U_95,a_3_0_rmod_4(U_94,U_93,U_92))
| k8_funct_2(u1_struct_0(U_93),u1_struct_0(U_94),U_92,U_91) = k1_rlvect_1(U_94)
| U_95 != U_91
| ~ m1_subset_1(U_91,u1_struct_0(U_93))
| ~ m1_rmod_4(U_92,U_94,U_93)
| ~ l1_vectsp_2(U_93,U_94)
| ~ v5_vectsp_2(U_93,U_94)
| ~ v6_rlvect_1(U_93)
| ~ v5_rlvect_1(U_93)
| ~ v4_rlvect_1(U_93)
| ~ v3_rlvect_1(U_93)
| v3_struct_0(U_93)
| ~ l3_vectsp_1(U_94)
| ~ v8_vectsp_1(U_94)
| ~ v7_vectsp_1(U_94)
| ~ v6_vectsp_1(U_94)
| ~ v4_group_1(U_94)
| ~ v6_rlvect_1(U_94)
| ~ v5_rlvect_1(U_94)
| ~ v4_rlvect_1(U_94)
| ~ v3_rlvect_1(U_94)
| v3_struct_0(U_94) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_52_2,plain,
! [U_97] :
( ? [U_96] :
( ~ v1_xboole_0(U_96)
& m1_subset_1(U_96,k1_zfmisc_1(U_97)) )
| v1_xboole_0(U_97) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_97] :
( ( ~ v1_xboole_0(sK22(U_97))
& m1_subset_1(sK22(U_97),k1_zfmisc_1(U_97)) )
| v1_xboole_0(U_97) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_96,sK22(U_97))],[f_52_2]) ).
cnf(f_52_4,plain,
( m1_subset_1(sK22(U_97),k1_zfmisc_1(U_97))
| v1_xboole_0(U_97) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
( ~ v1_xboole_0(sK22(U_97))
| v1_xboole_0(U_97) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_53_2,plain,
? [U_98] : v1_xboole_0(U_98),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
v1_xboole_0(sK23),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_98,sK23)],[f_53_2]) ).
cnf(f_53_4,plain,
v1_xboole_0(sK23),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
! [A] :
( ? [B] :
( v1_finset_1(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)],[rc2_rlvect_2]) ).
fof(f_54_2,plain,
! [U_100] :
( ? [U_99] :
( v1_finset_1(U_99)
& ~ v1_xboole_0(U_99)
& m1_subset_1(U_99,k1_zfmisc_1(u1_struct_0(U_100))) )
| ~ l1_struct_0(U_100)
| v3_struct_0(U_100) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_100] :
( ( v1_finset_1(sK24(U_100))
& ~ v1_xboole_0(sK24(U_100))
& m1_subset_1(sK24(U_100),k1_zfmisc_1(u1_struct_0(U_100))) )
| ~ l1_struct_0(U_100)
| v3_struct_0(U_100) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_99,sK24(U_100))],[f_54_2]) ).
cnf(f_54_4,plain,
( m1_subset_1(sK24(U_100),k1_zfmisc_1(u1_struct_0(U_100)))
| ~ l1_struct_0(U_100)
| v3_struct_0(U_100) ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_5,plain,
( ~ v1_xboole_0(sK24(U_100))
| ~ l1_struct_0(U_100)
| v3_struct_0(U_100) ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_6,plain,
( v1_finset_1(sK24(U_100))
| ~ l1_struct_0(U_100)
| v3_struct_0(U_100) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_55_2,plain,
! [U_102] :
? [U_101] :
( v1_xboole_0(U_101)
& m1_subset_1(U_101,k1_zfmisc_1(U_102)) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_102] :
( v1_xboole_0(sK25(U_102))
& m1_subset_1(sK25(U_102),k1_zfmisc_1(U_102)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_101,sK25(U_102))],[f_55_2]) ).
cnf(f_55_4,plain,
m1_subset_1(sK25(U_102),k1_zfmisc_1(U_102)),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_5,plain,
v1_xboole_0(sK25(U_102)),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_56_2,plain,
? [U_103] : ~ v1_xboole_0(U_103),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
~ v1_xboole_0(sK26),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_103,sK26)],[f_56_2]) ).
cnf(f_56_4,plain,
~ v1_xboole_0(sK26),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_57_2,plain,
? [U_104] :
( ~ v3_struct_0(U_104)
& l1_struct_0(U_104) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ~ v3_struct_0(sK27)
& l1_struct_0(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_104,sK27)],[f_57_2]) ).
cnf(f_57_4,plain,
l1_struct_0(sK27),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
~ v3_struct_0(sK27),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l2_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc4_struct_0]) ).
fof(f_58_2,plain,
? [U_105] :
( ~ v3_struct_0(U_105)
& l2_struct_0(U_105) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ~ v3_struct_0(sK28)
& l2_struct_0(sK28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_105,sK28)],[f_58_2]) ).
cnf(f_58_4,plain,
l2_struct_0(sK28),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
~ v3_struct_0(sK28),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_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_59_2,plain,
! [U_107] :
( ? [U_106] :
( ~ v1_xboole_0(U_106)
& m1_subset_1(U_106,k1_zfmisc_1(u1_struct_0(U_107))) )
| ~ l1_struct_0(U_107)
| v3_struct_0(U_107) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_107] :
( ( ~ v1_xboole_0(sK29(U_107))
& m1_subset_1(sK29(U_107),k1_zfmisc_1(u1_struct_0(U_107))) )
| ~ l1_struct_0(U_107)
| v3_struct_0(U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_106,sK29(U_107))],[f_59_2]) ).
cnf(f_59_4,plain,
( m1_subset_1(sK29(U_107),k1_zfmisc_1(u1_struct_0(U_107)))
| ~ l1_struct_0(U_107)
| v3_struct_0(U_107) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_5,plain,
( ~ v1_xboole_0(sK29(U_107))
| ~ l1_struct_0(U_107)
| v3_struct_0(U_107) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [A] :
( ? [B] :
( ~ v3_struct_0(B)
& l1_vectsp_2(B,A) )
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc9_vectsp_2]) ).
fof(f_60_2,plain,
! [U_109] :
( ? [U_108] :
( ~ v3_struct_0(U_108)
& l1_vectsp_2(U_108,U_109) )
| ~ l1_struct_0(U_109) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_109] :
( ( ~ v3_struct_0(sK30(U_109))
& l1_vectsp_2(sK30(U_109),U_109) )
| ~ l1_struct_0(U_109) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_108,sK30(U_109))],[f_60_2]) ).
cnf(f_60_4,plain,
( l1_vectsp_2(sK30(U_109),U_109)
| ~ l1_struct_0(U_109) ),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_5,plain,
( ~ v3_struct_0(sK30(U_109))
| ~ l1_struct_0(U_109) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [A,B] :
( k1_fraenkel(A,B) = k1_funct_2(A,B)
| v1_xboole_0(B) ),
inference(fof_nnf,[status(thm)],[redefinition_k1_fraenkel]) ).
fof(f_61_2,plain,
! [U_111,U_110] :
( k1_fraenkel(U_111,U_110) = k1_funct_2(U_111,U_110)
| v1_xboole_0(U_110) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( k1_fraenkel(U_111,U_110) = k1_funct_2(U_111,U_110)
| v1_xboole_0(U_110) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [A,B,C,D] :
( k8_funct_2(A,B,C,D) = k1_funct_1(C,D)
| ~ m1_subset_1(D,A)
| ~ m1_relset_1(C,A,B)
| ~ v1_funct_2(C,A,B)
| ~ v1_funct_1(C)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k8_funct_2]) ).
fof(f_62_2,plain,
! [U_115,U_114,U_113,U_112] :
( k8_funct_2(U_115,U_114,U_113,U_112) = k1_funct_1(U_113,U_112)
| ~ m1_subset_1(U_112,U_115)
| ~ m1_relset_1(U_113,U_115,U_114)
| ~ v1_funct_2(U_113,U_115,U_114)
| ~ v1_funct_1(U_113)
| v1_xboole_0(U_115) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( k8_funct_2(U_115,U_114,U_113,U_112) = k1_funct_1(U_113,U_112)
| ~ m1_subset_1(U_112,U_115)
| ~ m1_relset_1(U_113,U_115,U_114)
| ~ v1_funct_2(U_113,U_115,U_114)
| ~ v1_funct_1(U_113)
| v1_xboole_0(U_115) ),
inference(clausify,[status(thm)],[f_62_2]) ).
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_119,U_118,U_117] :
( ! [U_116] :
( ( m2_fraenkel(U_116,U_119,U_118,U_117)
| ~ m1_subset_1(U_116,U_117) )
& ( m1_subset_1(U_116,U_117)
| ~ m2_fraenkel(U_116,U_119,U_118,U_117) ) )
| ~ m1_fraenkel(U_117,U_119,U_118)
| v1_xboole_0(U_118) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_119,U_118,U_117] :
( ( ! [U_121] :
( m2_fraenkel(U_121,U_119,U_118,U_117)
| ~ m1_subset_1(U_121,U_117) )
& ! [U_120] :
( m1_subset_1(U_120,U_117)
| ~ m2_fraenkel(U_120,U_119,U_118,U_117) ) )
| ~ m1_fraenkel(U_117,U_119,U_118)
| v1_xboole_0(U_118) ),
inference(miniscope,[status(thm)],[f_63_2]) ).
cnf(f_63_4,plain,
( m1_subset_1(U_120,U_117)
| ~ m2_fraenkel(U_120,U_119,U_118,U_117)
| ~ m1_fraenkel(U_117,U_119,U_118)
| v1_xboole_0(U_118) ),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_5,plain,
( m2_fraenkel(U_121,U_119,U_118,U_117)
| ~ m1_subset_1(U_121,U_117)
| ~ m1_fraenkel(U_117,U_119,U_118)
| v1_xboole_0(U_118) ),
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_124,U_123,U_122] :
( ( m2_relset_1(U_122,U_124,U_123)
| ~ m1_relset_1(U_122,U_124,U_123) )
& ( m1_relset_1(U_122,U_124,U_123)
| ~ m2_relset_1(U_122,U_124,U_123) ) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( ! [U_130,U_128,U_126] :
( m2_relset_1(U_126,U_130,U_128)
| ~ m1_relset_1(U_126,U_130,U_128) )
& ! [U_129,U_127,U_125] :
( m1_relset_1(U_125,U_129,U_127)
| ~ m2_relset_1(U_125,U_129,U_127) ) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
cnf(f_64_4,plain,
( m1_relset_1(U_125,U_129,U_127)
| ~ m2_relset_1(U_125,U_129,U_127) ),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_5,plain,
( m2_relset_1(U_126,U_130,U_128)
| ~ m1_relset_1(U_126,U_130,U_128) ),
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_132,U_131] : r1_tarski(U_132,U_132),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_132] : r1_tarski(U_132,U_132),
inference(miniscope,[status(thm)],[f_65_2]) ).
cnf(f_65_4,plain,
r1_tarski(U_132,U_132),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_66_2,plain,
! [U_134,U_133] :
( m1_subset_1(U_134,U_133)
| ~ r2_hidden(U_134,U_133) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
( m1_subset_1(U_134,U_133)
| ~ r2_hidden(U_134,U_133) ),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( m2_rmod_4(E,A,B,D)
| ~ r1_tarski(C,D)
| ~ m2_rmod_4(E,A,B,C) )
| ~ m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t25_rmod_4]) ).
fof(f_67_2,plain,
! [U_139] :
( ! [U_138] :
( ! [U_137] :
( ! [U_136] :
( ! [U_135] :
( m2_rmod_4(U_135,U_139,U_138,U_136)
| ~ r1_tarski(U_137,U_136)
| ~ m2_rmod_4(U_135,U_139,U_138,U_137) )
| ~ m1_subset_1(U_136,k1_zfmisc_1(u1_struct_0(U_138))) )
| ~ m1_subset_1(U_137,k1_zfmisc_1(u1_struct_0(U_138))) )
| ~ l1_vectsp_2(U_138,U_139)
| ~ v5_vectsp_2(U_138,U_139)
| ~ v6_rlvect_1(U_138)
| ~ v5_rlvect_1(U_138)
| ~ v4_rlvect_1(U_138)
| ~ v3_rlvect_1(U_138)
| v3_struct_0(U_138) )
| ~ l3_vectsp_1(U_139)
| ~ v8_vectsp_1(U_139)
| ~ v7_vectsp_1(U_139)
| ~ v6_vectsp_1(U_139)
| ~ v4_group_1(U_139)
| ~ v6_rlvect_1(U_139)
| ~ v5_rlvect_1(U_139)
| ~ v4_rlvect_1(U_139)
| ~ v3_rlvect_1(U_139)
| v3_struct_0(U_139) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( m2_rmod_4(U_135,U_139,U_138,U_136)
| ~ r1_tarski(U_137,U_136)
| ~ m2_rmod_4(U_135,U_139,U_138,U_137)
| ~ m1_subset_1(U_136,k1_zfmisc_1(u1_struct_0(U_138)))
| ~ m1_subset_1(U_137,k1_zfmisc_1(u1_struct_0(U_138)))
| ~ l1_vectsp_2(U_138,U_139)
| ~ v5_vectsp_2(U_138,U_139)
| ~ v6_rlvect_1(U_138)
| ~ v5_rlvect_1(U_138)
| ~ v4_rlvect_1(U_138)
| ~ v3_rlvect_1(U_138)
| v3_struct_0(U_138)
| ~ l3_vectsp_1(U_139)
| ~ v8_vectsp_1(U_139)
| ~ v7_vectsp_1(U_139)
| ~ v6_vectsp_1(U_139)
| ~ v4_group_1(U_139)
| ~ v6_rlvect_1(U_139)
| ~ v5_rlvect_1(U_139)
| ~ v4_rlvect_1(U_139)
| ~ v3_rlvect_1(U_139)
| v3_struct_0(U_139) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_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_68_2,plain,
! [U_141,U_140] :
( r2_hidden(U_141,U_140)
| v1_xboole_0(U_140)
| ~ m1_subset_1(U_141,U_140) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( r2_hidden(U_141,U_140)
| v1_xboole_0(U_140)
| ~ m1_subset_1(U_141,U_140) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ r2_hidden(C,A)
& r2_hidden(C,B) )
| ( ~ r2_hidden(C,B)
& r2_hidden(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_69_2,plain,
! [U_144,U_143] :
( U_144 = U_143
| ? [U_142] :
( ( ~ r2_hidden(U_142,U_144)
& r2_hidden(U_142,U_143) )
| ( ~ r2_hidden(U_142,U_143)
& r2_hidden(U_142,U_144) ) ) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_144,U_143] :
( U_144 = U_143
| ? [U_146] :
( ~ r2_hidden(U_146,U_144)
& r2_hidden(U_146,U_143) )
| ? [U_145] :
( ~ r2_hidden(U_145,U_143)
& r2_hidden(U_145,U_144) ) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
fof(f_69_4,plain,
! [U_144,U_143] :
( U_144 = U_143
| ? [U_146] :
( ~ r2_hidden(U_146,U_144)
& r2_hidden(U_146,U_143) )
| ( ~ r2_hidden(sK31(U_144,U_143),U_143)
& r2_hidden(sK31(U_144,U_143),U_144) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_145,sK31(U_144,U_143))],[f_69_3]) ).
fof(f_69_5,plain,
! [U_144,U_143] :
( U_144 = U_143
| ( ~ r2_hidden(sK32(U_144,U_143),U_144)
& r2_hidden(sK32(U_144,U_143),U_143) )
| ( ~ r2_hidden(sK31(U_144,U_143),U_143)
& r2_hidden(sK31(U_144,U_143),U_144) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_146,sK32(U_144,U_143))],[f_69_4]) ).
cnf(f_69_6,plain,
( r2_hidden(sK32(U_144,U_143),U_143)
| r2_hidden(sK31(U_144,U_143),U_144)
| U_144 = U_143 ),
inference(clausify,[status(thm)],[f_69_5]) ).
cnf(f_69_7,plain,
( ~ r2_hidden(sK32(U_144,U_143),U_144)
| r2_hidden(sK31(U_144,U_143),U_144)
| U_144 = U_143 ),
inference(clausify,[status(thm)],[f_69_5]) ).
cnf(f_69_8,plain,
( r2_hidden(sK32(U_144,U_143),U_143)
| ~ r2_hidden(sK31(U_144,U_143),U_143)
| U_144 = U_143 ),
inference(clausify,[status(thm)],[f_69_5]) ).
cnf(f_69_9,plain,
( ~ r2_hidden(sK32(U_144,U_143),U_144)
| ~ r2_hidden(sK31(U_144,U_143),U_143)
| U_144 = U_143 ),
inference(clausify,[status(thm)],[f_69_5]) ).
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_148,U_147] :
( ( m1_subset_1(U_148,k1_zfmisc_1(U_147))
| ~ r1_tarski(U_148,U_147) )
& ( r1_tarski(U_148,U_147)
| ~ m1_subset_1(U_148,k1_zfmisc_1(U_147)) ) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
( ! [U_152,U_150] :
( m1_subset_1(U_152,k1_zfmisc_1(U_150))
| ~ r1_tarski(U_152,U_150) )
& ! [U_151,U_149] :
( r1_tarski(U_151,U_149)
| ~ m1_subset_1(U_151,k1_zfmisc_1(U_149)) ) ),
inference(miniscope,[status(thm)],[f_70_2]) ).
cnf(f_70_4,plain,
( r1_tarski(U_151,U_149)
| ~ m1_subset_1(U_151,k1_zfmisc_1(U_149)) ),
inference(clausify,[status(thm)],[f_70_3]) ).
cnf(f_70_5,plain,
( m1_subset_1(U_152,k1_zfmisc_1(U_150))
| ~ r1_tarski(U_152,U_150) ),
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_155,U_154,U_153] :
( m1_subset_1(U_155,U_153)
| ~ m1_subset_1(U_154,k1_zfmisc_1(U_153))
| ~ r2_hidden(U_155,U_154) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( m1_subset_1(U_155,U_153)
| ~ m1_subset_1(U_154,k1_zfmisc_1(U_153))
| ~ r2_hidden(U_155,U_154) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_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_72_2,plain,
! [U_158,U_157,U_156] :
( ~ v1_xboole_0(U_156)
| ~ m1_subset_1(U_157,k1_zfmisc_1(U_156))
| ~ r2_hidden(U_158,U_157) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_158,U_157] :
( ! [U_156] :
( ~ v1_xboole_0(U_156)
| ~ m1_subset_1(U_157,k1_zfmisc_1(U_156)) )
| ~ r2_hidden(U_158,U_157) ),
inference(miniscope,[status(thm)],[f_72_2]) ).
cnf(f_72_4,plain,
( ~ v1_xboole_0(U_156)
| ~ m1_subset_1(U_157,k1_zfmisc_1(U_156))
| ~ r2_hidden(U_158,U_157) ),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_73_2,plain,
! [U_159] :
( U_159 = k1_xboole_0
| ~ v1_xboole_0(U_159) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( U_159 = k1_xboole_0
| ~ v1_xboole_0(U_159) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_74_2,plain,
! [U_161,U_160] :
( ~ v1_xboole_0(U_160)
| ~ r2_hidden(U_161,U_160) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( ~ v1_xboole_0(U_160)
| ~ r2_hidden(U_161,U_160) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_75_2,plain,
! [U_163,U_162] :
( ~ v1_xboole_0(U_162)
| U_163 = U_162
| ~ v1_xboole_0(U_163) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_163] :
( ! [U_162] :
( ~ v1_xboole_0(U_162)
| U_163 = U_162 )
| ~ v1_xboole_0(U_163) ),
inference(miniscope,[status(thm)],[f_75_2]) ).
cnf(f_75_4,plain,
( ~ v1_xboole_0(U_162)
| U_163 = U_162
| ~ v1_xboole_0(U_163) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_7_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_2]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(f_18_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_2]) ).
cnf(f_25_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_2]) ).
cnf(f_27_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_27_2]) ).
cnf(f_31_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_31_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( u1_struct_0(Eq_x_0) = u1_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k1_zfmisc_1(Eq_x_0) = k1_zfmisc_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( k2_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,
( k5_rmod_4(Eq_x_0,Eq_x_1,Eq_x_2) = k5_rmod_4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( k1_rlvect_1(Eq_x_0) = k1_rlvect_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( k2_rmod_4(Eq_x_0,Eq_x_1,Eq_x_2) = k2_rmod_4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( a_3_0_rmod_4(Eq_x_0,Eq_x_1,Eq_x_2) = a_3_0_rmod_4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( k1_fraenkel(Eq_x_0,Eq_x_1) = k1_fraenkel(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,
( k8_funct_2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = k8_funct_2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( k1_funct_2(Eq_x_0,Eq_x_1) = k1_funct_2(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,
( k1_funct_1(Eq_x_0,Eq_x_1) = k1_funct_1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_18,axiom,
( sK15(Eq_x_0,Eq_x_1) = sK15(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,
( sK16(Eq_x_0,Eq_x_1) = sK16(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,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(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_22,axiom,
( sK19(Eq_x_0,Eq_x_1) = sK19(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,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(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_24,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( sK22(Eq_x_0) = sK22(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( sK24(Eq_x_0) = sK24(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( sK25(Eq_x_0) = sK25(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( sK29(Eq_x_0) = sK29(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( sK30(Eq_x_0) = sK30(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( sK31(Eq_x_0,Eq_x_1) = sK31(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,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_33,axiom,
( v3_rlvect_1(Eq_y_0)
| ~ v3_rlvect_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( v4_rlvect_1(Eq_y_0)
| ~ v4_rlvect_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( v5_rlvect_1(Eq_y_0)
| ~ v5_rlvect_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( v6_rlvect_1(Eq_y_0)
| ~ v6_rlvect_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,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_38,axiom,
( v6_vectsp_1(Eq_y_0)
| ~ v6_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( v7_vectsp_1(Eq_y_0)
| ~ v7_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( v8_vectsp_1(Eq_y_0)
| ~ v8_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( l3_vectsp_1(Eq_y_0)
| ~ l3_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( v5_vectsp_2(Eq_y_0,Eq_y_1)
| ~ v5_vectsp_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_43,axiom,
( l1_vectsp_2(Eq_y_0,Eq_y_1)
| ~ l1_vectsp_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,
( 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_45,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_46,axiom,
( v1_rmod_5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ v1_rmod_5(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,
( 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_48,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_49,axiom,
( m2_rmod_4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ m2_rmod_4(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_50,axiom,
( m1_rmod_4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m1_rmod_4(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_51,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_52,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_53,axiom,
( l2_struct_0(Eq_y_0)
| ~ l2_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( v1_finset_1(Eq_y_0)
| ~ v1_finset_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,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_56,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_57,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_58,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_59,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_60,axiom,
( l1_rlvect_1(Eq_y_0)
| ~ l1_rlvect_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_61,axiom,
( l1_vectsp_1(Eq_y_0)
| ~ l1_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( l2_vectsp_1(Eq_y_0)
| ~ l2_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,axiom,
( v1_fraenkel(Eq_y_0)
| ~ v1_fraenkel(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_64,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_65,axiom,
( m2_relset_1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m2_relset_1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG214+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n015.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 20 09:49:06 UTC 2026
% 0.18/0.45 % CPUTime :
% 2.77/3.14 % SZS status Theorem for theBenchmark
% 2.77/3.14 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------