%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ALG220+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 08:12:29 AM UTC 2026
% Result : Theorem 175.13s 175.48s
% Output : Proof 175.39s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t16_rmod_5,conjecture,
! [A] :
( ( l3_vectsp_1(A)
& v2_vectsp_2(A)
& ~ v10_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v7_group_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)
& v3_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)))
=> ( ( r1_tarski(C,D)
& k1_rmod_5(A,B,C) = B )
=> k1_rmod_5(A,B,D) = B ) ) ) ) ),
file('theBenchmark.p',t16_rmod_5) ).
fof(abstractness_v3_vectsp_2,axiom,
! [A,B] :
( ( l1_vectsp_2(B,A)
& l1_struct_0(A) )
=> ( v3_vectsp_2(B,A)
=> B = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) ) ),
file('theBenchmark.p',abstractness_v3_vectsp_2) ).
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(cc2_vectsp_2,axiom,
! [A] :
( l1_vectsp_1(A)
=> ( ( v8_vectsp_1(A)
& v7_group_1(A)
& ~ v3_struct_0(A) )
=> ( v8_vectsp_1(A)
& v6_vectsp_1(A)
& v2_group_1(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc2_vectsp_2) ).
fof(cc3_vectsp_2,axiom,
! [A] :
( l1_vectsp_1(A)
=> ( ( v6_vectsp_1(A)
& v7_group_1(A)
& ~ v3_struct_0(A) )
=> ( v8_vectsp_1(A)
& v6_vectsp_1(A)
& v2_group_1(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc3_vectsp_2) ).
fof(dt_g1_vectsp_2,axiom,
! [A,B,C,D,E] :
( ( m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
& v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
& v1_funct_1(E)
& m1_subset_1(D,B)
& m1_relset_1(C,k2_zfmisc_1(B,B),B)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& v1_funct_1(C)
& l1_struct_0(A) )
=> ( l1_vectsp_2(g1_vectsp_2(A,B,C,D,E),A)
& v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A) ) ),
file('theBenchmark.p',dt_g1_vectsp_2) ).
fof(dt_k1_rmod_5,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)
& v2_vectsp_2(A)
& ~ v10_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v7_group_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_rmod_2(k1_rmod_5(A,B,C),A,B)
& v3_vectsp_2(k1_rmod_5(A,B,C),A) ) ),
file('theBenchmark.p',dt_k1_rmod_5) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_l1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_group_1) ).
fof(dt_l1_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_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_rmod_2,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_2(C,A,B)
=> ( l1_vectsp_2(C,A)
& v5_vectsp_2(C,A)
& v6_rlvect_1(C)
& v5_rlvect_1(C)
& v4_rlvect_1(C)
& v3_rlvect_1(C)
& ~ v3_struct_0(C) ) ) ),
file('theBenchmark.p',dt_m1_rmod_2) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(dt_u1_rlvect_1,axiom,
! [A] :
( l1_rlvect_1(A)
=> ( m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_rlvect_1(A)) ) ),
file('theBenchmark.p',dt_u1_rlvect_1) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(dt_u1_vectsp_2,axiom,
! [A,B] :
( ( l1_vectsp_2(B,A)
& l1_struct_0(A) )
=> ( m2_relset_1(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B))
& v1_funct_2(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B))
& v1_funct_1(u1_vectsp_2(A,B)) ) ),
file('theBenchmark.p',dt_u1_vectsp_2) ).
fof(dt_u2_struct_0,axiom,
! [A] :
( l2_struct_0(A)
=> m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_u2_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_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_rmod_2,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_2(C,A,B) ),
file('theBenchmark.p',existence_m1_rmod_2) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(fc1_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_vectsp_2,axiom,
! [A,B,C,D,E] :
( ( m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
& v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
& v1_funct_1(E)
& m1_subset_1(D,B)
& m1_relset_1(C,k2_zfmisc_1(B,B),B)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& v1_funct_1(C)
& ~ v1_xboole_0(B)
& l1_struct_0(A) )
=> ( v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A)
& ~ v3_struct_0(g1_vectsp_2(A,B,C,D,E)) ) ),
file('theBenchmark.p',fc1_vectsp_2) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(A) )
=> ~ v1_xboole_0(k2_zfmisc_1(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(free_g1_vectsp_2,axiom,
! [A,B,C,D,E] :
( ( m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
& v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
& v1_funct_1(E)
& m1_subset_1(D,B)
& m1_relset_1(C,k2_zfmisc_1(B,B),B)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& v1_funct_1(C)
& l1_struct_0(A) )
=> ! [F,G,H,I,J] :
( g1_vectsp_2(A,B,C,D,E) = g1_vectsp_2(F,G,H,I,J)
=> ( E = J
& D = I
& C = H
& B = G
& A = F ) ) ),
file('theBenchmark.p',free_g1_vectsp_2) ).
fof(rc13_vectsp_2,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] :
( v3_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l1_vectsp_2(B,A) ) ),
file('theBenchmark.p',rc13_vectsp_2) ).
fof(rc16_vectsp_2,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] :
( v5_vectsp_2(B,A)
& v3_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l1_vectsp_2(B,A) ) ),
file('theBenchmark.p',rc16_vectsp_2) ).
fof(rc1_rmod_2,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] :
( v5_vectsp_2(C,A)
& v3_vectsp_2(C,A)
& v6_rlvect_1(C)
& v5_rlvect_1(C)
& v4_rlvect_1(C)
& v3_rlvect_1(C)
& ~ v3_struct_0(C)
& m1_rmod_2(C,A,B) ) ),
file('theBenchmark.p',rc1_rmod_2) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_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(rc8_vectsp_2,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( v3_vectsp_2(B,A)
& l1_vectsp_2(B,A) ) ),
file('theBenchmark.p',rc8_vectsp_2) ).
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_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(t15_rmod_5,axiom,
! [A] :
( ( l3_vectsp_1(A)
& v2_vectsp_2(A)
& ~ v10_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v7_group_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)))
=> ( r1_tarski(C,D)
=> m1_rmod_2(k1_rmod_5(A,B,C),A,k1_rmod_5(A,B,D)) ) ) ) ) ),
file('theBenchmark.p',t15_rmod_5) ).
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(t33_rmod_2,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)
& v3_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] :
( ( l1_vectsp_2(C,A)
& v5_vectsp_2(C,A)
& v3_vectsp_2(C,A)
& v6_rlvect_1(C)
& v5_rlvect_1(C)
& v4_rlvect_1(C)
& v3_rlvect_1(C)
& ~ v3_struct_0(C) )
=> ( ( m1_rmod_2(B,A,C)
& m1_rmod_2(C,A,B) )
=> C = B ) ) ) ),
file('theBenchmark.p',t33_rmod_2) ).
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)
& v2_vectsp_2(A)
& ~ v10_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v7_group_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)
& v3_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)))
=> ( ( r1_tarski(C,D)
& k1_rmod_5(A,B,C) = B )
=> k1_rmod_5(A,B,D) = B ) ) ) ) ),
inference(negate,[status(cth)],[t16_rmod_5]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( k1_rmod_5(A,B,D) != B
& r1_tarski(C,D)
& k1_rmod_5(A,B,C) = B
& 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)
& v3_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)
& v2_vectsp_2(A)
& ~ v10_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v7_group_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] :
( k1_rmod_5(U_3,U_2,U_0) != U_2
& r1_tarski(U_1,U_0)
& k1_rmod_5(U_3,U_2,U_1) = U_2
& 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)
& v3_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)
& v2_vectsp_2(U_3)
& ~ v10_vectsp_1(U_3)
& v8_vectsp_1(U_3)
& v7_vectsp_1(U_3)
& v6_vectsp_1(U_3)
& v7_group_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] :
( k1_rmod_5(sK1,U_2,U_0) != U_2
& r1_tarski(U_1,U_0)
& k1_rmod_5(sK1,U_2,U_1) = U_2
& 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)
& v3_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)
& v2_vectsp_2(sK1)
& ~ v10_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v7_group_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] :
( k1_rmod_5(sK1,sK2,U_0) != sK2
& r1_tarski(U_1,U_0)
& k1_rmod_5(sK1,sK2,U_1) = sK2
& 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)
& v3_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)
& v2_vectsp_2(sK1)
& ~ v10_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v7_group_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] :
( k1_rmod_5(sK1,sK2,U_0) != sK2
& r1_tarski(sK3,U_0)
& k1_rmod_5(sK1,sK2,sK3) = sK2
& 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)
& v3_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)
& v2_vectsp_2(sK1)
& ~ v10_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v7_group_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,
( k1_rmod_5(sK1,sK2,sK4) != sK2
& r1_tarski(sK3,sK4)
& k1_rmod_5(sK1,sK2,sK3) = sK2
& 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)
& v3_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)
& v2_vectsp_2(sK1)
& ~ v10_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v7_group_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]) ).
cnf(f_1_8,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
v3_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_10,negated_conjecture,
v4_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_11,negated_conjecture,
v5_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_12,negated_conjecture,
v6_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_13,negated_conjecture,
v4_group_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_14,negated_conjecture,
v7_group_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_15,negated_conjecture,
v6_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_16,negated_conjecture,
v7_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_17,negated_conjecture,
v8_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_18,negated_conjecture,
~ v10_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_19,negated_conjecture,
v2_vectsp_2(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_20,negated_conjecture,
l3_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_21,negated_conjecture,
~ v3_struct_0(sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_22,negated_conjecture,
v3_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_23,negated_conjecture,
v4_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_24,negated_conjecture,
v5_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_25,negated_conjecture,
v6_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_26,negated_conjecture,
v3_vectsp_2(sK2,sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_27,negated_conjecture,
v5_vectsp_2(sK2,sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_28,negated_conjecture,
l1_vectsp_2(sK2,sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_29,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK2))),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_30,negated_conjecture,
m1_subset_1(sK4,k1_zfmisc_1(u1_struct_0(sK2))),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_31,negated_conjecture,
k1_rmod_5(sK1,sK2,sK3) = sK2,
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_32,negated_conjecture,
r1_tarski(sK3,sK4),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_33,negated_conjecture,
k1_rmod_5(sK1,sK2,sK4) != sK2,
inference(clausify,[status(thm)],[f_1_7]) ).
fof(f_2_1,plain,
! [A,B] :
( B = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B))
| ~ v3_vectsp_2(B,A)
| ~ l1_vectsp_2(B,A)
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[abstractness_v3_vectsp_2]) ).
fof(f_2_2,plain,
! [U_5,U_4] :
( U_4 = g1_vectsp_2(U_5,u1_struct_0(U_4),u1_rlvect_1(U_4),u2_struct_0(U_4),u1_vectsp_2(U_5,U_4))
| ~ v3_vectsp_2(U_4,U_5)
| ~ l1_vectsp_2(U_4,U_5)
| ~ l1_struct_0(U_5) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( U_4 = g1_vectsp_2(U_5,u1_struct_0(U_4),u1_rlvect_1(U_4),u2_struct_0(U_4),u1_vectsp_2(U_5,U_4))
| ~ v3_vectsp_2(U_4,U_5)
| ~ l1_vectsp_2(U_4,U_5)
| ~ l1_struct_0(U_5) ),
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_7,U_6] :
( ~ r2_hidden(U_6,U_7)
| ~ r2_hidden(U_7,U_6) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ r2_hidden(U_6,U_7)
| ~ r2_hidden(U_7,U_6) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_10,U_9,U_8] :
( v1_relat_1(U_8)
| ~ m1_subset_1(U_8,k1_zfmisc_1(k2_zfmisc_1(U_10,U_9))) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v1_relat_1(U_8)
| ~ m1_subset_1(U_8,k1_zfmisc_1(k2_zfmisc_1(U_10,U_9))) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ( v8_vectsp_1(A)
& v6_vectsp_1(A)
& v2_group_1(A)
& ~ v3_struct_0(A) )
| ~ v8_vectsp_1(A)
| ~ v7_group_1(A)
| v3_struct_0(A)
| ~ l1_vectsp_1(A) ),
inference(fof_nnf,[status(thm)],[cc2_vectsp_2]) ).
fof(f_5_2,plain,
! [U_11] :
( ( v8_vectsp_1(U_11)
& v6_vectsp_1(U_11)
& v2_group_1(U_11)
& ~ v3_struct_0(U_11) )
| ~ v8_vectsp_1(U_11)
| ~ v7_group_1(U_11)
| v3_struct_0(U_11)
| ~ l1_vectsp_1(U_11) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( ~ v3_struct_0(U_11)
| ~ v8_vectsp_1(U_11)
| ~ v7_group_1(U_11)
| v3_struct_0(U_11)
| ~ l1_vectsp_1(U_11) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( v2_group_1(U_11)
| ~ v8_vectsp_1(U_11)
| ~ v7_group_1(U_11)
| v3_struct_0(U_11)
| ~ l1_vectsp_1(U_11) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( v6_vectsp_1(U_11)
| ~ v8_vectsp_1(U_11)
| ~ v7_group_1(U_11)
| v3_struct_0(U_11)
| ~ l1_vectsp_1(U_11) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_6,plain,
( v8_vectsp_1(U_11)
| ~ v8_vectsp_1(U_11)
| ~ v7_group_1(U_11)
| v3_struct_0(U_11)
| ~ l1_vectsp_1(U_11) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ( v8_vectsp_1(A)
& v6_vectsp_1(A)
& v2_group_1(A)
& ~ v3_struct_0(A) )
| ~ v6_vectsp_1(A)
| ~ v7_group_1(A)
| v3_struct_0(A)
| ~ l1_vectsp_1(A) ),
inference(fof_nnf,[status(thm)],[cc3_vectsp_2]) ).
fof(f_6_2,plain,
! [U_12] :
( ( v8_vectsp_1(U_12)
& v6_vectsp_1(U_12)
& v2_group_1(U_12)
& ~ v3_struct_0(U_12) )
| ~ v6_vectsp_1(U_12)
| ~ v7_group_1(U_12)
| v3_struct_0(U_12)
| ~ l1_vectsp_1(U_12) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( ~ v3_struct_0(U_12)
| ~ v6_vectsp_1(U_12)
| ~ v7_group_1(U_12)
| v3_struct_0(U_12)
| ~ l1_vectsp_1(U_12) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( v2_group_1(U_12)
| ~ v6_vectsp_1(U_12)
| ~ v7_group_1(U_12)
| v3_struct_0(U_12)
| ~ l1_vectsp_1(U_12) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( v6_vectsp_1(U_12)
| ~ v6_vectsp_1(U_12)
| ~ v7_group_1(U_12)
| v3_struct_0(U_12)
| ~ l1_vectsp_1(U_12) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_6,plain,
( v8_vectsp_1(U_12)
| ~ v6_vectsp_1(U_12)
| ~ v7_group_1(U_12)
| v3_struct_0(U_12)
| ~ l1_vectsp_1(U_12) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B,C,D,E] :
( ( l1_vectsp_2(g1_vectsp_2(A,B,C,D,E),A)
& v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A) )
| ~ m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
| ~ v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
| ~ v1_funct_1(E)
| ~ m1_subset_1(D,B)
| ~ m1_relset_1(C,k2_zfmisc_1(B,B),B)
| ~ v1_funct_2(C,k2_zfmisc_1(B,B),B)
| ~ v1_funct_1(C)
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_g1_vectsp_2]) ).
fof(f_7_2,plain,
! [U_17,U_16,U_15,U_14,U_13] :
( ( l1_vectsp_2(g1_vectsp_2(U_17,U_16,U_15,U_14,U_13),U_17)
& v3_vectsp_2(g1_vectsp_2(U_17,U_16,U_15,U_14,U_13),U_17) )
| ~ m1_relset_1(U_13,k2_zfmisc_1(U_16,u1_struct_0(U_17)),U_16)
| ~ v1_funct_2(U_13,k2_zfmisc_1(U_16,u1_struct_0(U_17)),U_16)
| ~ v1_funct_1(U_13)
| ~ m1_subset_1(U_14,U_16)
| ~ m1_relset_1(U_15,k2_zfmisc_1(U_16,U_16),U_16)
| ~ v1_funct_2(U_15,k2_zfmisc_1(U_16,U_16),U_16)
| ~ v1_funct_1(U_15)
| ~ l1_struct_0(U_17) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( v3_vectsp_2(g1_vectsp_2(U_17,U_16,U_15,U_14,U_13),U_17)
| ~ m1_relset_1(U_13,k2_zfmisc_1(U_16,u1_struct_0(U_17)),U_16)
| ~ v1_funct_2(U_13,k2_zfmisc_1(U_16,u1_struct_0(U_17)),U_16)
| ~ v1_funct_1(U_13)
| ~ m1_subset_1(U_14,U_16)
| ~ m1_relset_1(U_15,k2_zfmisc_1(U_16,U_16),U_16)
| ~ v1_funct_2(U_15,k2_zfmisc_1(U_16,U_16),U_16)
| ~ v1_funct_1(U_15)
| ~ l1_struct_0(U_17) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( l1_vectsp_2(g1_vectsp_2(U_17,U_16,U_15,U_14,U_13),U_17)
| ~ m1_relset_1(U_13,k2_zfmisc_1(U_16,u1_struct_0(U_17)),U_16)
| ~ v1_funct_2(U_13,k2_zfmisc_1(U_16,u1_struct_0(U_17)),U_16)
| ~ v1_funct_1(U_13)
| ~ m1_subset_1(U_14,U_16)
| ~ m1_relset_1(U_15,k2_zfmisc_1(U_16,U_16),U_16)
| ~ v1_funct_2(U_15,k2_zfmisc_1(U_16,U_16),U_16)
| ~ v1_funct_1(U_15)
| ~ l1_struct_0(U_17) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A,B,C] :
( ( m1_rmod_2(k1_rmod_5(A,B,C),A,B)
& v3_vectsp_2(k1_rmod_5(A,B,C),A) )
| ~ 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)
| ~ v2_vectsp_2(A)
| v10_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v7_group_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_k1_rmod_5]) ).
fof(f_8_2,plain,
! [U_20,U_19,U_18] :
( ( m1_rmod_2(k1_rmod_5(U_20,U_19,U_18),U_20,U_19)
& v3_vectsp_2(k1_rmod_5(U_20,U_19,U_18),U_20) )
| ~ m1_subset_1(U_18,k1_zfmisc_1(u1_struct_0(U_19)))
| ~ l1_vectsp_2(U_19,U_20)
| ~ v5_vectsp_2(U_19,U_20)
| ~ v6_rlvect_1(U_19)
| ~ v5_rlvect_1(U_19)
| ~ v4_rlvect_1(U_19)
| ~ v3_rlvect_1(U_19)
| v3_struct_0(U_19)
| ~ l3_vectsp_1(U_20)
| ~ v2_vectsp_2(U_20)
| v10_vectsp_1(U_20)
| ~ v8_vectsp_1(U_20)
| ~ v7_vectsp_1(U_20)
| ~ v6_vectsp_1(U_20)
| ~ v7_group_1(U_20)
| ~ v4_group_1(U_20)
| ~ v6_rlvect_1(U_20)
| ~ v5_rlvect_1(U_20)
| ~ v4_rlvect_1(U_20)
| ~ v3_rlvect_1(U_20)
| v3_struct_0(U_20) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( v3_vectsp_2(k1_rmod_5(U_20,U_19,U_18),U_20)
| ~ m1_subset_1(U_18,k1_zfmisc_1(u1_struct_0(U_19)))
| ~ l1_vectsp_2(U_19,U_20)
| ~ v5_vectsp_2(U_19,U_20)
| ~ v6_rlvect_1(U_19)
| ~ v5_rlvect_1(U_19)
| ~ v4_rlvect_1(U_19)
| ~ v3_rlvect_1(U_19)
| v3_struct_0(U_19)
| ~ l3_vectsp_1(U_20)
| ~ v2_vectsp_2(U_20)
| v10_vectsp_1(U_20)
| ~ v8_vectsp_1(U_20)
| ~ v7_vectsp_1(U_20)
| ~ v6_vectsp_1(U_20)
| ~ v7_group_1(U_20)
| ~ v4_group_1(U_20)
| ~ v6_rlvect_1(U_20)
| ~ v5_rlvect_1(U_20)
| ~ v4_rlvect_1(U_20)
| ~ v3_rlvect_1(U_20)
| v3_struct_0(U_20) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( m1_rmod_2(k1_rmod_5(U_20,U_19,U_18),U_20,U_19)
| ~ m1_subset_1(U_18,k1_zfmisc_1(u1_struct_0(U_19)))
| ~ l1_vectsp_2(U_19,U_20)
| ~ v5_vectsp_2(U_19,U_20)
| ~ v6_rlvect_1(U_19)
| ~ v5_rlvect_1(U_19)
| ~ v4_rlvect_1(U_19)
| ~ v3_rlvect_1(U_19)
| v3_struct_0(U_19)
| ~ l3_vectsp_1(U_20)
| ~ v2_vectsp_2(U_20)
| v10_vectsp_1(U_20)
| ~ v8_vectsp_1(U_20)
| ~ v7_vectsp_1(U_20)
| ~ v6_vectsp_1(U_20)
| ~ v7_group_1(U_20)
| ~ v4_group_1(U_20)
| ~ v6_rlvect_1(U_20)
| ~ v5_rlvect_1(U_20)
| ~ v4_rlvect_1(U_20)
| ~ v3_rlvect_1(U_20)
| v3_struct_0(U_20) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_group_1]) ).
fof(f_12_2,plain,
! [U_21] :
( l1_struct_0(U_21)
| ~ l1_group_1(U_21) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( l1_struct_0(U_21)
| ~ l1_group_1(U_21) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A] :
( l2_struct_0(A)
| ~ l1_rlvect_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_rlvect_1]) ).
fof(f_13_2,plain,
! [U_22] :
( l2_struct_0(U_22)
| ~ l1_rlvect_1(U_22) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( l2_struct_0(U_22)
| ~ l1_rlvect_1(U_22) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_14_2,plain,
$true,
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
! [A] :
( l1_group_1(A)
| ~ l1_vectsp_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_vectsp_1]) ).
fof(f_15_2,plain,
! [U_23] :
( l1_group_1(U_23)
| ~ l1_vectsp_1(U_23) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( l1_group_1(U_23)
| ~ l1_vectsp_1(U_23) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_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_16_2,plain,
! [U_25] :
( ! [U_24] :
( l1_rlvect_1(U_24)
| ~ l1_vectsp_2(U_24,U_25) )
| ~ l1_struct_0(U_25) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( l1_rlvect_1(U_24)
| ~ l1_vectsp_2(U_24,U_25)
| ~ l1_struct_0(U_25) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_struct_0]) ).
fof(f_17_2,plain,
! [U_26] :
( l1_struct_0(U_26)
| ~ l2_struct_0(U_26) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( l1_struct_0(U_26)
| ~ l2_struct_0(U_26) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_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_18_2,plain,
! [U_27] :
( ( l2_struct_0(U_27)
& l1_vectsp_1(U_27) )
| ~ l2_vectsp_1(U_27) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( l1_vectsp_1(U_27)
| ~ l2_vectsp_1(U_27) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( l2_struct_0(U_27)
| ~ l2_vectsp_1(U_27) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_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_19_2,plain,
! [U_28] :
( ( l2_vectsp_1(U_28)
& l1_rlvect_1(U_28) )
| ~ l3_vectsp_1(U_28) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( l1_rlvect_1(U_28)
| ~ l3_vectsp_1(U_28) ),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( l2_vectsp_1(U_28)
| ~ l3_vectsp_1(U_28) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
! [A,B] :
( ! [C] :
( ( l1_vectsp_2(C,A)
& v5_vectsp_2(C,A)
& v6_rlvect_1(C)
& v5_rlvect_1(C)
& v4_rlvect_1(C)
& v3_rlvect_1(C)
& ~ v3_struct_0(C) )
| ~ m1_rmod_2(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_2]) ).
fof(f_21_2,plain,
! [U_31,U_30] :
( ! [U_29] :
( ( l1_vectsp_2(U_29,U_31)
& v5_vectsp_2(U_29,U_31)
& v6_rlvect_1(U_29)
& v5_rlvect_1(U_29)
& v4_rlvect_1(U_29)
& v3_rlvect_1(U_29)
& ~ v3_struct_0(U_29) )
| ~ m1_rmod_2(U_29,U_31,U_30) )
| ~ l1_vectsp_2(U_30,U_31)
| ~ v5_vectsp_2(U_30,U_31)
| ~ v6_rlvect_1(U_30)
| ~ v5_rlvect_1(U_30)
| ~ v4_rlvect_1(U_30)
| ~ v3_rlvect_1(U_30)
| v3_struct_0(U_30)
| ~ l3_vectsp_1(U_31)
| ~ v8_vectsp_1(U_31)
| ~ v7_vectsp_1(U_31)
| ~ v6_vectsp_1(U_31)
| ~ v4_group_1(U_31)
| ~ v6_rlvect_1(U_31)
| ~ v5_rlvect_1(U_31)
| ~ v4_rlvect_1(U_31)
| ~ v3_rlvect_1(U_31)
| v3_struct_0(U_31) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( ~ v3_struct_0(U_29)
| ~ m1_rmod_2(U_29,U_31,U_30)
| ~ l1_vectsp_2(U_30,U_31)
| ~ v5_vectsp_2(U_30,U_31)
| ~ v6_rlvect_1(U_30)
| ~ v5_rlvect_1(U_30)
| ~ v4_rlvect_1(U_30)
| ~ v3_rlvect_1(U_30)
| v3_struct_0(U_30)
| ~ l3_vectsp_1(U_31)
| ~ v8_vectsp_1(U_31)
| ~ v7_vectsp_1(U_31)
| ~ v6_vectsp_1(U_31)
| ~ v4_group_1(U_31)
| ~ v6_rlvect_1(U_31)
| ~ v5_rlvect_1(U_31)
| ~ v4_rlvect_1(U_31)
| ~ v3_rlvect_1(U_31)
| v3_struct_0(U_31) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( v3_rlvect_1(U_29)
| ~ m1_rmod_2(U_29,U_31,U_30)
| ~ l1_vectsp_2(U_30,U_31)
| ~ v5_vectsp_2(U_30,U_31)
| ~ v6_rlvect_1(U_30)
| ~ v5_rlvect_1(U_30)
| ~ v4_rlvect_1(U_30)
| ~ v3_rlvect_1(U_30)
| v3_struct_0(U_30)
| ~ l3_vectsp_1(U_31)
| ~ v8_vectsp_1(U_31)
| ~ v7_vectsp_1(U_31)
| ~ v6_vectsp_1(U_31)
| ~ v4_group_1(U_31)
| ~ v6_rlvect_1(U_31)
| ~ v5_rlvect_1(U_31)
| ~ v4_rlvect_1(U_31)
| ~ v3_rlvect_1(U_31)
| v3_struct_0(U_31) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_5,plain,
( v4_rlvect_1(U_29)
| ~ m1_rmod_2(U_29,U_31,U_30)
| ~ l1_vectsp_2(U_30,U_31)
| ~ v5_vectsp_2(U_30,U_31)
| ~ v6_rlvect_1(U_30)
| ~ v5_rlvect_1(U_30)
| ~ v4_rlvect_1(U_30)
| ~ v3_rlvect_1(U_30)
| v3_struct_0(U_30)
| ~ l3_vectsp_1(U_31)
| ~ v8_vectsp_1(U_31)
| ~ v7_vectsp_1(U_31)
| ~ v6_vectsp_1(U_31)
| ~ v4_group_1(U_31)
| ~ v6_rlvect_1(U_31)
| ~ v5_rlvect_1(U_31)
| ~ v4_rlvect_1(U_31)
| ~ v3_rlvect_1(U_31)
| v3_struct_0(U_31) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_6,plain,
( v5_rlvect_1(U_29)
| ~ m1_rmod_2(U_29,U_31,U_30)
| ~ l1_vectsp_2(U_30,U_31)
| ~ v5_vectsp_2(U_30,U_31)
| ~ v6_rlvect_1(U_30)
| ~ v5_rlvect_1(U_30)
| ~ v4_rlvect_1(U_30)
| ~ v3_rlvect_1(U_30)
| v3_struct_0(U_30)
| ~ l3_vectsp_1(U_31)
| ~ v8_vectsp_1(U_31)
| ~ v7_vectsp_1(U_31)
| ~ v6_vectsp_1(U_31)
| ~ v4_group_1(U_31)
| ~ v6_rlvect_1(U_31)
| ~ v5_rlvect_1(U_31)
| ~ v4_rlvect_1(U_31)
| ~ v3_rlvect_1(U_31)
| v3_struct_0(U_31) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_7,plain,
( v6_rlvect_1(U_29)
| ~ m1_rmod_2(U_29,U_31,U_30)
| ~ l1_vectsp_2(U_30,U_31)
| ~ v5_vectsp_2(U_30,U_31)
| ~ v6_rlvect_1(U_30)
| ~ v5_rlvect_1(U_30)
| ~ v4_rlvect_1(U_30)
| ~ v3_rlvect_1(U_30)
| v3_struct_0(U_30)
| ~ l3_vectsp_1(U_31)
| ~ v8_vectsp_1(U_31)
| ~ v7_vectsp_1(U_31)
| ~ v6_vectsp_1(U_31)
| ~ v4_group_1(U_31)
| ~ v6_rlvect_1(U_31)
| ~ v5_rlvect_1(U_31)
| ~ v4_rlvect_1(U_31)
| ~ v3_rlvect_1(U_31)
| v3_struct_0(U_31) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_8,plain,
( v5_vectsp_2(U_29,U_31)
| ~ m1_rmod_2(U_29,U_31,U_30)
| ~ l1_vectsp_2(U_30,U_31)
| ~ v5_vectsp_2(U_30,U_31)
| ~ v6_rlvect_1(U_30)
| ~ v5_rlvect_1(U_30)
| ~ v4_rlvect_1(U_30)
| ~ v3_rlvect_1(U_30)
| v3_struct_0(U_30)
| ~ l3_vectsp_1(U_31)
| ~ v8_vectsp_1(U_31)
| ~ v7_vectsp_1(U_31)
| ~ v6_vectsp_1(U_31)
| ~ v4_group_1(U_31)
| ~ v6_rlvect_1(U_31)
| ~ v5_rlvect_1(U_31)
| ~ v4_rlvect_1(U_31)
| ~ v3_rlvect_1(U_31)
| v3_struct_0(U_31) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_9,plain,
( l1_vectsp_2(U_29,U_31)
| ~ m1_rmod_2(U_29,U_31,U_30)
| ~ l1_vectsp_2(U_30,U_31)
| ~ v5_vectsp_2(U_30,U_31)
| ~ v6_rlvect_1(U_30)
| ~ v5_rlvect_1(U_30)
| ~ v4_rlvect_1(U_30)
| ~ v3_rlvect_1(U_30)
| v3_struct_0(U_30)
| ~ l3_vectsp_1(U_31)
| ~ v8_vectsp_1(U_31)
| ~ v7_vectsp_1(U_31)
| ~ v6_vectsp_1(U_31)
| ~ v4_group_1(U_31)
| ~ v6_rlvect_1(U_31)
| ~ v5_rlvect_1(U_31)
| ~ v4_rlvect_1(U_31)
| ~ v3_rlvect_1(U_31)
| v3_struct_0(U_31) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_22_2,plain,
$true,
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_23_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_23_2,plain,
! [U_34,U_33,U_32] :
( m1_subset_1(U_32,k1_zfmisc_1(k2_zfmisc_1(U_34,U_33)))
| ~ m2_relset_1(U_32,U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( m1_subset_1(U_32,k1_zfmisc_1(k2_zfmisc_1(U_34,U_33)))
| ~ m2_relset_1(U_32,U_34,U_33) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A] :
( ( m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_rlvect_1(A)) )
| ~ l1_rlvect_1(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_rlvect_1]) ).
fof(f_24_2,plain,
! [U_35] :
( ( m2_relset_1(u1_rlvect_1(U_35),k2_zfmisc_1(u1_struct_0(U_35),u1_struct_0(U_35)),u1_struct_0(U_35))
& v1_funct_2(u1_rlvect_1(U_35),k2_zfmisc_1(u1_struct_0(U_35),u1_struct_0(U_35)),u1_struct_0(U_35))
& v1_funct_1(u1_rlvect_1(U_35)) )
| ~ l1_rlvect_1(U_35) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( v1_funct_1(u1_rlvect_1(U_35))
| ~ l1_rlvect_1(U_35) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( v1_funct_2(u1_rlvect_1(U_35),k2_zfmisc_1(u1_struct_0(U_35),u1_struct_0(U_35)),u1_struct_0(U_35))
| ~ l1_rlvect_1(U_35) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_5,plain,
( m2_relset_1(u1_rlvect_1(U_35),k2_zfmisc_1(u1_struct_0(U_35),u1_struct_0(U_35)),u1_struct_0(U_35))
| ~ l1_rlvect_1(U_35) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_25_2,plain,
$true,
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
! [A,B] :
( ( m2_relset_1(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B))
& v1_funct_2(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B))
& v1_funct_1(u1_vectsp_2(A,B)) )
| ~ l1_vectsp_2(B,A)
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_vectsp_2]) ).
fof(f_26_2,plain,
! [U_37,U_36] :
( ( m2_relset_1(u1_vectsp_2(U_37,U_36),k2_zfmisc_1(u1_struct_0(U_36),u1_struct_0(U_37)),u1_struct_0(U_36))
& v1_funct_2(u1_vectsp_2(U_37,U_36),k2_zfmisc_1(u1_struct_0(U_36),u1_struct_0(U_37)),u1_struct_0(U_36))
& v1_funct_1(u1_vectsp_2(U_37,U_36)) )
| ~ l1_vectsp_2(U_36,U_37)
| ~ l1_struct_0(U_37) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( v1_funct_1(u1_vectsp_2(U_37,U_36))
| ~ l1_vectsp_2(U_36,U_37)
| ~ l1_struct_0(U_37) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( v1_funct_2(u1_vectsp_2(U_37,U_36),k2_zfmisc_1(u1_struct_0(U_36),u1_struct_0(U_37)),u1_struct_0(U_36))
| ~ l1_vectsp_2(U_36,U_37)
| ~ l1_struct_0(U_37) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_5,plain,
( m2_relset_1(u1_vectsp_2(U_37,U_36),k2_zfmisc_1(u1_struct_0(U_36),u1_struct_0(U_37)),u1_struct_0(U_36))
| ~ l1_vectsp_2(U_36,U_37)
| ~ l1_struct_0(U_37) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A] :
( m1_subset_1(u2_struct_0(A),u1_struct_0(A))
| ~ l2_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_u2_struct_0]) ).
fof(f_27_2,plain,
! [U_38] :
( m1_subset_1(u2_struct_0(U_38),u1_struct_0(U_38))
| ~ l2_struct_0(U_38) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( m1_subset_1(u2_struct_0(U_38),u1_struct_0(U_38))
| ~ l2_struct_0(U_38) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
? [A] : l1_group_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_group_1]) ).
fof(f_28_2,plain,
? [U_39] : l1_group_1(U_39),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
l1_group_1(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_39,sK5)],[f_28_2]) ).
cnf(f_28_4,plain,
l1_group_1(sK5),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] : l1_rlvect_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_rlvect_1]) ).
fof(f_29_2,plain,
? [U_40] : l1_rlvect_1(U_40),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
l1_rlvect_1(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_40,sK6)],[f_29_2]) ).
cnf(f_29_4,plain,
l1_rlvect_1(sK6),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_30_2,plain,
? [U_41] : l1_struct_0(U_41),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
l1_struct_0(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_41,sK7)],[f_30_2]) ).
cnf(f_30_4,plain,
l1_struct_0(sK7),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
? [A] : l1_vectsp_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_vectsp_1]) ).
fof(f_31_2,plain,
? [U_42] : l1_vectsp_1(U_42),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
l1_vectsp_1(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_42,sK8)],[f_31_2]) ).
cnf(f_31_4,plain,
l1_vectsp_1(sK8),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A] :
( ? [B] : l1_vectsp_2(B,A)
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_l1_vectsp_2]) ).
fof(f_32_2,plain,
! [U_44] :
( ? [U_43] : l1_vectsp_2(U_43,U_44)
| ~ l1_struct_0(U_44) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_44] :
( l1_vectsp_2(sK9(U_44),U_44)
| ~ l1_struct_0(U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_43,sK9(U_44))],[f_32_2]) ).
cnf(f_32_4,plain,
( l1_vectsp_2(sK9(U_44),U_44)
| ~ l1_struct_0(U_44) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] : l2_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l2_struct_0]) ).
fof(f_33_2,plain,
? [U_45] : l2_struct_0(U_45),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
l2_struct_0(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_45,sK10)],[f_33_2]) ).
cnf(f_33_4,plain,
l2_struct_0(sK10),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
? [A] : l2_vectsp_1(A),
inference(fof_nnf,[status(thm)],[existence_l2_vectsp_1]) ).
fof(f_34_2,plain,
? [U_46] : l2_vectsp_1(U_46),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
l2_vectsp_1(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_46,sK11)],[f_34_2]) ).
cnf(f_34_4,plain,
l2_vectsp_1(sK11),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] : l3_vectsp_1(A),
inference(fof_nnf,[status(thm)],[existence_l3_vectsp_1]) ).
fof(f_35_2,plain,
? [U_47] : l3_vectsp_1(U_47),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
l3_vectsp_1(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_47,sK12)],[f_35_2]) ).
cnf(f_35_4,plain,
l3_vectsp_1(sK12),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_36_2,plain,
! [U_50,U_49] :
? [U_48] : m1_relset_1(U_48,U_50,U_49),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_50,U_49] : m1_relset_1(sK13(U_50,U_49),U_50,U_49),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_48,sK13(U_50,U_49))],[f_36_2]) ).
cnf(f_36_4,plain,
m1_relset_1(sK13(U_50,U_49),U_50,U_49),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B] :
( ? [C] : m1_rmod_2(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_2]) ).
fof(f_37_2,plain,
! [U_53,U_52] :
( ? [U_51] : m1_rmod_2(U_51,U_53,U_52)
| ~ l1_vectsp_2(U_52,U_53)
| ~ v5_vectsp_2(U_52,U_53)
| ~ v6_rlvect_1(U_52)
| ~ v5_rlvect_1(U_52)
| ~ v4_rlvect_1(U_52)
| ~ v3_rlvect_1(U_52)
| v3_struct_0(U_52)
| ~ l3_vectsp_1(U_53)
| ~ v8_vectsp_1(U_53)
| ~ v7_vectsp_1(U_53)
| ~ v6_vectsp_1(U_53)
| ~ v4_group_1(U_53)
| ~ 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) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_53,U_52] :
( m1_rmod_2(sK14(U_53,U_52),U_53,U_52)
| ~ l1_vectsp_2(U_52,U_53)
| ~ v5_vectsp_2(U_52,U_53)
| ~ v6_rlvect_1(U_52)
| ~ v5_rlvect_1(U_52)
| ~ v4_rlvect_1(U_52)
| ~ v3_rlvect_1(U_52)
| v3_struct_0(U_52)
| ~ l3_vectsp_1(U_53)
| ~ v8_vectsp_1(U_53)
| ~ v7_vectsp_1(U_53)
| ~ v6_vectsp_1(U_53)
| ~ v4_group_1(U_53)
| ~ 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) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_51,sK14(U_53,U_52))],[f_37_2]) ).
cnf(f_37_4,plain,
( m1_rmod_2(sK14(U_53,U_52),U_53,U_52)
| ~ l1_vectsp_2(U_52,U_53)
| ~ v5_vectsp_2(U_52,U_53)
| ~ v6_rlvect_1(U_52)
| ~ v5_rlvect_1(U_52)
| ~ v4_rlvect_1(U_52)
| ~ v3_rlvect_1(U_52)
| v3_struct_0(U_52)
| ~ l3_vectsp_1(U_53)
| ~ v8_vectsp_1(U_53)
| ~ v7_vectsp_1(U_53)
| ~ v6_vectsp_1(U_53)
| ~ v4_group_1(U_53)
| ~ 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) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_38_2,plain,
! [U_55] :
? [U_54] : m1_subset_1(U_54,U_55),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_55] : m1_subset_1(sK15(U_55),U_55),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_54,sK15(U_55))],[f_38_2]) ).
cnf(f_38_4,plain,
m1_subset_1(sK15(U_55),U_55),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_39_2,plain,
! [U_58,U_57] :
? [U_56] : m2_relset_1(U_56,U_58,U_57),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_58,U_57] : m2_relset_1(sK16(U_58,U_57),U_58,U_57),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_56,sK16(U_58,U_57))],[f_39_2]) ).
cnf(f_39_4,plain,
m2_relset_1(sK16(U_58,U_57),U_58,U_57),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_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_40_2,plain,
! [U_59] :
( ~ v1_xboole_0(u1_struct_0(U_59))
| ~ l1_struct_0(U_59)
| v3_struct_0(U_59) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_59))
| ~ l1_struct_0(U_59)
| v3_struct_0(U_59) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_41_2,plain,
! [U_60] : ~ v1_xboole_0(k1_zfmisc_1(U_60)),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
~ v1_xboole_0(k1_zfmisc_1(U_60)),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A,B,C,D,E] :
( ( v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A)
& ~ v3_struct_0(g1_vectsp_2(A,B,C,D,E)) )
| ~ m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
| ~ v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
| ~ v1_funct_1(E)
| ~ m1_subset_1(D,B)
| ~ m1_relset_1(C,k2_zfmisc_1(B,B),B)
| ~ v1_funct_2(C,k2_zfmisc_1(B,B),B)
| ~ v1_funct_1(C)
| v1_xboole_0(B)
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc1_vectsp_2]) ).
fof(f_42_2,plain,
! [U_65,U_64,U_63,U_62,U_61] :
( ( v3_vectsp_2(g1_vectsp_2(U_65,U_64,U_63,U_62,U_61),U_65)
& ~ v3_struct_0(g1_vectsp_2(U_65,U_64,U_63,U_62,U_61)) )
| ~ m1_relset_1(U_61,k2_zfmisc_1(U_64,u1_struct_0(U_65)),U_64)
| ~ v1_funct_2(U_61,k2_zfmisc_1(U_64,u1_struct_0(U_65)),U_64)
| ~ v1_funct_1(U_61)
| ~ m1_subset_1(U_62,U_64)
| ~ m1_relset_1(U_63,k2_zfmisc_1(U_64,U_64),U_64)
| ~ v1_funct_2(U_63,k2_zfmisc_1(U_64,U_64),U_64)
| ~ v1_funct_1(U_63)
| v1_xboole_0(U_64)
| ~ l1_struct_0(U_65) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( ~ v3_struct_0(g1_vectsp_2(U_65,U_64,U_63,U_62,U_61))
| ~ m1_relset_1(U_61,k2_zfmisc_1(U_64,u1_struct_0(U_65)),U_64)
| ~ v1_funct_2(U_61,k2_zfmisc_1(U_64,u1_struct_0(U_65)),U_64)
| ~ v1_funct_1(U_61)
| ~ m1_subset_1(U_62,U_64)
| ~ m1_relset_1(U_63,k2_zfmisc_1(U_64,U_64),U_64)
| ~ v1_funct_2(U_63,k2_zfmisc_1(U_64,U_64),U_64)
| ~ v1_funct_1(U_63)
| v1_xboole_0(U_64)
| ~ l1_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( v3_vectsp_2(g1_vectsp_2(U_65,U_64,U_63,U_62,U_61),U_65)
| ~ m1_relset_1(U_61,k2_zfmisc_1(U_64,u1_struct_0(U_65)),U_64)
| ~ v1_funct_2(U_61,k2_zfmisc_1(U_64,u1_struct_0(U_65)),U_64)
| ~ v1_funct_1(U_61)
| ~ m1_subset_1(U_62,U_64)
| ~ m1_relset_1(U_63,k2_zfmisc_1(U_64,U_64),U_64)
| ~ v1_funct_2(U_63,k2_zfmisc_1(U_64,U_64),U_64)
| ~ v1_funct_1(U_63)
| v1_xboole_0(U_64)
| ~ l1_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_43_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_44_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_44_2,plain,
! [U_67,U_66] :
( ~ v1_xboole_0(k2_zfmisc_1(U_67,U_66))
| v1_xboole_0(U_66)
| v1_xboole_0(U_67) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( ~ v1_xboole_0(k2_zfmisc_1(U_67,U_66))
| v1_xboole_0(U_66)
| v1_xboole_0(U_67) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [A,B,C,D,E] :
( ! [F,G,H,I,J] :
( ( E = J
& D = I
& C = H
& B = G
& A = F )
| g1_vectsp_2(A,B,C,D,E) != g1_vectsp_2(F,G,H,I,J) )
| ~ m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
| ~ v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
| ~ v1_funct_1(E)
| ~ m1_subset_1(D,B)
| ~ m1_relset_1(C,k2_zfmisc_1(B,B),B)
| ~ v1_funct_2(C,k2_zfmisc_1(B,B),B)
| ~ v1_funct_1(C)
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[free_g1_vectsp_2]) ).
fof(f_45_2,plain,
! [U_77,U_76,U_75,U_74,U_73] :
( ! [U_72,U_71,U_70,U_69,U_68] :
( ( U_73 = U_68
& U_74 = U_69
& U_75 = U_70
& U_76 = U_71
& U_77 = U_72 )
| g1_vectsp_2(U_77,U_76,U_75,U_74,U_73) != g1_vectsp_2(U_72,U_71,U_70,U_69,U_68) )
| ~ m1_relset_1(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_2(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_1(U_73)
| ~ m1_subset_1(U_74,U_76)
| ~ m1_relset_1(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_2(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_1(U_75)
| ~ l1_struct_0(U_77) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( U_77 = U_72
| g1_vectsp_2(U_77,U_76,U_75,U_74,U_73) != g1_vectsp_2(U_72,U_71,U_70,U_69,U_68)
| ~ m1_relset_1(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_2(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_1(U_73)
| ~ m1_subset_1(U_74,U_76)
| ~ m1_relset_1(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_2(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_1(U_75)
| ~ l1_struct_0(U_77) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
( U_76 = U_71
| g1_vectsp_2(U_77,U_76,U_75,U_74,U_73) != g1_vectsp_2(U_72,U_71,U_70,U_69,U_68)
| ~ m1_relset_1(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_2(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_1(U_73)
| ~ m1_subset_1(U_74,U_76)
| ~ m1_relset_1(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_2(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_1(U_75)
| ~ l1_struct_0(U_77) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_5,plain,
( U_75 = U_70
| g1_vectsp_2(U_77,U_76,U_75,U_74,U_73) != g1_vectsp_2(U_72,U_71,U_70,U_69,U_68)
| ~ m1_relset_1(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_2(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_1(U_73)
| ~ m1_subset_1(U_74,U_76)
| ~ m1_relset_1(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_2(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_1(U_75)
| ~ l1_struct_0(U_77) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_6,plain,
( U_74 = U_69
| g1_vectsp_2(U_77,U_76,U_75,U_74,U_73) != g1_vectsp_2(U_72,U_71,U_70,U_69,U_68)
| ~ m1_relset_1(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_2(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_1(U_73)
| ~ m1_subset_1(U_74,U_76)
| ~ m1_relset_1(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_2(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_1(U_75)
| ~ l1_struct_0(U_77) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_7,plain,
( U_73 = U_68
| g1_vectsp_2(U_77,U_76,U_75,U_74,U_73) != g1_vectsp_2(U_72,U_71,U_70,U_69,U_68)
| ~ m1_relset_1(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_2(U_73,k2_zfmisc_1(U_76,u1_struct_0(U_77)),U_76)
| ~ v1_funct_1(U_73)
| ~ m1_subset_1(U_74,U_76)
| ~ m1_relset_1(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_2(U_75,k2_zfmisc_1(U_76,U_76),U_76)
| ~ v1_funct_1(U_75)
| ~ l1_struct_0(U_77) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [A] :
( ? [B] :
( v3_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l1_vectsp_2(B,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) ),
inference(fof_nnf,[status(thm)],[rc13_vectsp_2]) ).
fof(f_46_2,plain,
! [U_79] :
( ? [U_78] :
( v3_vectsp_2(U_78,U_79)
& v6_rlvect_1(U_78)
& v5_rlvect_1(U_78)
& v4_rlvect_1(U_78)
& v3_rlvect_1(U_78)
& ~ v3_struct_0(U_78)
& l1_vectsp_2(U_78,U_79) )
| ~ l3_vectsp_1(U_79)
| ~ v8_vectsp_1(U_79)
| ~ v7_vectsp_1(U_79)
| ~ v6_vectsp_1(U_79)
| ~ v4_group_1(U_79)
| ~ v6_rlvect_1(U_79)
| ~ v5_rlvect_1(U_79)
| ~ v4_rlvect_1(U_79)
| ~ v3_rlvect_1(U_79)
| v3_struct_0(U_79) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_79] :
( ( v3_vectsp_2(sK17(U_79),U_79)
& v6_rlvect_1(sK17(U_79))
& v5_rlvect_1(sK17(U_79))
& v4_rlvect_1(sK17(U_79))
& v3_rlvect_1(sK17(U_79))
& ~ v3_struct_0(sK17(U_79))
& l1_vectsp_2(sK17(U_79),U_79) )
| ~ l3_vectsp_1(U_79)
| ~ v8_vectsp_1(U_79)
| ~ v7_vectsp_1(U_79)
| ~ v6_vectsp_1(U_79)
| ~ v4_group_1(U_79)
| ~ v6_rlvect_1(U_79)
| ~ v5_rlvect_1(U_79)
| ~ v4_rlvect_1(U_79)
| ~ v3_rlvect_1(U_79)
| v3_struct_0(U_79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_78,sK17(U_79))],[f_46_2]) ).
cnf(f_46_4,plain,
( l1_vectsp_2(sK17(U_79),U_79)
| ~ l3_vectsp_1(U_79)
| ~ v8_vectsp_1(U_79)
| ~ v7_vectsp_1(U_79)
| ~ v6_vectsp_1(U_79)
| ~ v4_group_1(U_79)
| ~ v6_rlvect_1(U_79)
| ~ v5_rlvect_1(U_79)
| ~ v4_rlvect_1(U_79)
| ~ v3_rlvect_1(U_79)
| v3_struct_0(U_79) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_5,plain,
( ~ v3_struct_0(sK17(U_79))
| ~ l3_vectsp_1(U_79)
| ~ v8_vectsp_1(U_79)
| ~ v7_vectsp_1(U_79)
| ~ v6_vectsp_1(U_79)
| ~ v4_group_1(U_79)
| ~ v6_rlvect_1(U_79)
| ~ v5_rlvect_1(U_79)
| ~ v4_rlvect_1(U_79)
| ~ v3_rlvect_1(U_79)
| v3_struct_0(U_79) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_6,plain,
( v3_rlvect_1(sK17(U_79))
| ~ l3_vectsp_1(U_79)
| ~ v8_vectsp_1(U_79)
| ~ v7_vectsp_1(U_79)
| ~ v6_vectsp_1(U_79)
| ~ v4_group_1(U_79)
| ~ v6_rlvect_1(U_79)
| ~ v5_rlvect_1(U_79)
| ~ v4_rlvect_1(U_79)
| ~ v3_rlvect_1(U_79)
| v3_struct_0(U_79) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_7,plain,
( v4_rlvect_1(sK17(U_79))
| ~ l3_vectsp_1(U_79)
| ~ v8_vectsp_1(U_79)
| ~ v7_vectsp_1(U_79)
| ~ v6_vectsp_1(U_79)
| ~ v4_group_1(U_79)
| ~ v6_rlvect_1(U_79)
| ~ v5_rlvect_1(U_79)
| ~ v4_rlvect_1(U_79)
| ~ v3_rlvect_1(U_79)
| v3_struct_0(U_79) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_8,plain,
( v5_rlvect_1(sK17(U_79))
| ~ l3_vectsp_1(U_79)
| ~ v8_vectsp_1(U_79)
| ~ v7_vectsp_1(U_79)
| ~ v6_vectsp_1(U_79)
| ~ v4_group_1(U_79)
| ~ v6_rlvect_1(U_79)
| ~ v5_rlvect_1(U_79)
| ~ v4_rlvect_1(U_79)
| ~ v3_rlvect_1(U_79)
| v3_struct_0(U_79) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_9,plain,
( v6_rlvect_1(sK17(U_79))
| ~ l3_vectsp_1(U_79)
| ~ v8_vectsp_1(U_79)
| ~ v7_vectsp_1(U_79)
| ~ v6_vectsp_1(U_79)
| ~ v4_group_1(U_79)
| ~ v6_rlvect_1(U_79)
| ~ v5_rlvect_1(U_79)
| ~ v4_rlvect_1(U_79)
| ~ v3_rlvect_1(U_79)
| v3_struct_0(U_79) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_10,plain,
( v3_vectsp_2(sK17(U_79),U_79)
| ~ l3_vectsp_1(U_79)
| ~ v8_vectsp_1(U_79)
| ~ v7_vectsp_1(U_79)
| ~ v6_vectsp_1(U_79)
| ~ v4_group_1(U_79)
| ~ v6_rlvect_1(U_79)
| ~ v5_rlvect_1(U_79)
| ~ v4_rlvect_1(U_79)
| ~ v3_rlvect_1(U_79)
| v3_struct_0(U_79) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [A] :
( ? [B] :
( v5_vectsp_2(B,A)
& v3_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l1_vectsp_2(B,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) ),
inference(fof_nnf,[status(thm)],[rc16_vectsp_2]) ).
fof(f_47_2,plain,
! [U_81] :
( ? [U_80] :
( v5_vectsp_2(U_80,U_81)
& v3_vectsp_2(U_80,U_81)
& v6_rlvect_1(U_80)
& v5_rlvect_1(U_80)
& v4_rlvect_1(U_80)
& v3_rlvect_1(U_80)
& ~ v3_struct_0(U_80)
& l1_vectsp_2(U_80,U_81) )
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_81] :
( ( v5_vectsp_2(sK18(U_81),U_81)
& v3_vectsp_2(sK18(U_81),U_81)
& v6_rlvect_1(sK18(U_81))
& v5_rlvect_1(sK18(U_81))
& v4_rlvect_1(sK18(U_81))
& v3_rlvect_1(sK18(U_81))
& ~ v3_struct_0(sK18(U_81))
& l1_vectsp_2(sK18(U_81),U_81) )
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_80,sK18(U_81))],[f_47_2]) ).
cnf(f_47_4,plain,
( l1_vectsp_2(sK18(U_81),U_81)
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_5,plain,
( ~ v3_struct_0(sK18(U_81))
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_6,plain,
( v3_rlvect_1(sK18(U_81))
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_7,plain,
( v4_rlvect_1(sK18(U_81))
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_8,plain,
( v5_rlvect_1(sK18(U_81))
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_9,plain,
( v6_rlvect_1(sK18(U_81))
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_10,plain,
( v3_vectsp_2(sK18(U_81),U_81)
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_11,plain,
( v5_vectsp_2(sK18(U_81),U_81)
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A,B] :
( ? [C] :
( v5_vectsp_2(C,A)
& v3_vectsp_2(C,A)
& v6_rlvect_1(C)
& v5_rlvect_1(C)
& v4_rlvect_1(C)
& v3_rlvect_1(C)
& ~ v3_struct_0(C)
& m1_rmod_2(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)],[rc1_rmod_2]) ).
fof(f_48_2,plain,
! [U_84,U_83] :
( ? [U_82] :
( v5_vectsp_2(U_82,U_84)
& v3_vectsp_2(U_82,U_84)
& v6_rlvect_1(U_82)
& v5_rlvect_1(U_82)
& v4_rlvect_1(U_82)
& v3_rlvect_1(U_82)
& ~ v3_struct_0(U_82)
& m1_rmod_2(U_82,U_84,U_83) )
| ~ l1_vectsp_2(U_83,U_84)
| ~ v5_vectsp_2(U_83,U_84)
| ~ v6_rlvect_1(U_83)
| ~ v5_rlvect_1(U_83)
| ~ v4_rlvect_1(U_83)
| ~ v3_rlvect_1(U_83)
| v3_struct_0(U_83)
| ~ l3_vectsp_1(U_84)
| ~ v8_vectsp_1(U_84)
| ~ v7_vectsp_1(U_84)
| ~ v6_vectsp_1(U_84)
| ~ v4_group_1(U_84)
| ~ 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) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_84,U_83] :
( ( v5_vectsp_2(sK19(U_84,U_83),U_84)
& v3_vectsp_2(sK19(U_84,U_83),U_84)
& v6_rlvect_1(sK19(U_84,U_83))
& v5_rlvect_1(sK19(U_84,U_83))
& v4_rlvect_1(sK19(U_84,U_83))
& v3_rlvect_1(sK19(U_84,U_83))
& ~ v3_struct_0(sK19(U_84,U_83))
& m1_rmod_2(sK19(U_84,U_83),U_84,U_83) )
| ~ l1_vectsp_2(U_83,U_84)
| ~ v5_vectsp_2(U_83,U_84)
| ~ v6_rlvect_1(U_83)
| ~ v5_rlvect_1(U_83)
| ~ v4_rlvect_1(U_83)
| ~ v3_rlvect_1(U_83)
| v3_struct_0(U_83)
| ~ l3_vectsp_1(U_84)
| ~ v8_vectsp_1(U_84)
| ~ v7_vectsp_1(U_84)
| ~ v6_vectsp_1(U_84)
| ~ v4_group_1(U_84)
| ~ 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) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_82,sK19(U_84,U_83))],[f_48_2]) ).
cnf(f_48_4,plain,
( m1_rmod_2(sK19(U_84,U_83),U_84,U_83)
| ~ l1_vectsp_2(U_83,U_84)
| ~ v5_vectsp_2(U_83,U_84)
| ~ v6_rlvect_1(U_83)
| ~ v5_rlvect_1(U_83)
| ~ v4_rlvect_1(U_83)
| ~ v3_rlvect_1(U_83)
| v3_struct_0(U_83)
| ~ l3_vectsp_1(U_84)
| ~ v8_vectsp_1(U_84)
| ~ v7_vectsp_1(U_84)
| ~ v6_vectsp_1(U_84)
| ~ v4_group_1(U_84)
| ~ 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) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_5,plain,
( ~ v3_struct_0(sK19(U_84,U_83))
| ~ l1_vectsp_2(U_83,U_84)
| ~ v5_vectsp_2(U_83,U_84)
| ~ v6_rlvect_1(U_83)
| ~ v5_rlvect_1(U_83)
| ~ v4_rlvect_1(U_83)
| ~ v3_rlvect_1(U_83)
| v3_struct_0(U_83)
| ~ l3_vectsp_1(U_84)
| ~ v8_vectsp_1(U_84)
| ~ v7_vectsp_1(U_84)
| ~ v6_vectsp_1(U_84)
| ~ v4_group_1(U_84)
| ~ 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) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_6,plain,
( v3_rlvect_1(sK19(U_84,U_83))
| ~ l1_vectsp_2(U_83,U_84)
| ~ v5_vectsp_2(U_83,U_84)
| ~ v6_rlvect_1(U_83)
| ~ v5_rlvect_1(U_83)
| ~ v4_rlvect_1(U_83)
| ~ v3_rlvect_1(U_83)
| v3_struct_0(U_83)
| ~ l3_vectsp_1(U_84)
| ~ v8_vectsp_1(U_84)
| ~ v7_vectsp_1(U_84)
| ~ v6_vectsp_1(U_84)
| ~ v4_group_1(U_84)
| ~ 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) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_7,plain,
( v4_rlvect_1(sK19(U_84,U_83))
| ~ l1_vectsp_2(U_83,U_84)
| ~ v5_vectsp_2(U_83,U_84)
| ~ v6_rlvect_1(U_83)
| ~ v5_rlvect_1(U_83)
| ~ v4_rlvect_1(U_83)
| ~ v3_rlvect_1(U_83)
| v3_struct_0(U_83)
| ~ l3_vectsp_1(U_84)
| ~ v8_vectsp_1(U_84)
| ~ v7_vectsp_1(U_84)
| ~ v6_vectsp_1(U_84)
| ~ v4_group_1(U_84)
| ~ 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) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_8,plain,
( v5_rlvect_1(sK19(U_84,U_83))
| ~ l1_vectsp_2(U_83,U_84)
| ~ v5_vectsp_2(U_83,U_84)
| ~ v6_rlvect_1(U_83)
| ~ v5_rlvect_1(U_83)
| ~ v4_rlvect_1(U_83)
| ~ v3_rlvect_1(U_83)
| v3_struct_0(U_83)
| ~ l3_vectsp_1(U_84)
| ~ v8_vectsp_1(U_84)
| ~ v7_vectsp_1(U_84)
| ~ v6_vectsp_1(U_84)
| ~ v4_group_1(U_84)
| ~ 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) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_9,plain,
( v6_rlvect_1(sK19(U_84,U_83))
| ~ l1_vectsp_2(U_83,U_84)
| ~ v5_vectsp_2(U_83,U_84)
| ~ v6_rlvect_1(U_83)
| ~ v5_rlvect_1(U_83)
| ~ v4_rlvect_1(U_83)
| ~ v3_rlvect_1(U_83)
| v3_struct_0(U_83)
| ~ l3_vectsp_1(U_84)
| ~ v8_vectsp_1(U_84)
| ~ v7_vectsp_1(U_84)
| ~ v6_vectsp_1(U_84)
| ~ v4_group_1(U_84)
| ~ 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) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_10,plain,
( v3_vectsp_2(sK19(U_84,U_83),U_84)
| ~ l1_vectsp_2(U_83,U_84)
| ~ v5_vectsp_2(U_83,U_84)
| ~ v6_rlvect_1(U_83)
| ~ v5_rlvect_1(U_83)
| ~ v4_rlvect_1(U_83)
| ~ v3_rlvect_1(U_83)
| v3_struct_0(U_83)
| ~ l3_vectsp_1(U_84)
| ~ v8_vectsp_1(U_84)
| ~ v7_vectsp_1(U_84)
| ~ v6_vectsp_1(U_84)
| ~ v4_group_1(U_84)
| ~ 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) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_11,plain,
( v5_vectsp_2(sK19(U_84,U_83),U_84)
| ~ l1_vectsp_2(U_83,U_84)
| ~ v5_vectsp_2(U_83,U_84)
| ~ v6_rlvect_1(U_83)
| ~ v5_rlvect_1(U_83)
| ~ v4_rlvect_1(U_83)
| ~ v3_rlvect_1(U_83)
| v3_struct_0(U_83)
| ~ l3_vectsp_1(U_84)
| ~ v8_vectsp_1(U_84)
| ~ v7_vectsp_1(U_84)
| ~ v6_vectsp_1(U_84)
| ~ v4_group_1(U_84)
| ~ 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) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_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_49_2,plain,
! [U_86] :
( ? [U_85] :
( ~ v1_xboole_0(U_85)
& m1_subset_1(U_85,k1_zfmisc_1(U_86)) )
| v1_xboole_0(U_86) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_86] :
( ( ~ v1_xboole_0(sK20(U_86))
& m1_subset_1(sK20(U_86),k1_zfmisc_1(U_86)) )
| v1_xboole_0(U_86) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_85,sK20(U_86))],[f_49_2]) ).
cnf(f_49_4,plain,
( m1_subset_1(sK20(U_86),k1_zfmisc_1(U_86))
| v1_xboole_0(U_86) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
( ~ v1_xboole_0(sK20(U_86))
| v1_xboole_0(U_86) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_50_2,plain,
? [U_87] : v1_xboole_0(U_87),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
v1_xboole_0(sK21),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_87,sK21)],[f_50_2]) ).
cnf(f_50_4,plain,
v1_xboole_0(sK21),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_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_51_2,plain,
! [U_89] :
? [U_88] :
( v1_xboole_0(U_88)
& m1_subset_1(U_88,k1_zfmisc_1(U_89)) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_89] :
( v1_xboole_0(sK22(U_89))
& m1_subset_1(sK22(U_89),k1_zfmisc_1(U_89)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_88,sK22(U_89))],[f_51_2]) ).
cnf(f_51_4,plain,
m1_subset_1(sK22(U_89),k1_zfmisc_1(U_89)),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
v1_xboole_0(sK22(U_89)),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_52_2,plain,
? [U_90] : ~ v1_xboole_0(U_90),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
~ v1_xboole_0(sK23),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_90,sK23)],[f_52_2]) ).
cnf(f_52_4,plain,
~ v1_xboole_0(sK23),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_53_2,plain,
? [U_91] :
( ~ v3_struct_0(U_91)
& l1_struct_0(U_91) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( ~ v3_struct_0(sK24)
& l1_struct_0(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_91,sK24)],[f_53_2]) ).
cnf(f_53_4,plain,
l1_struct_0(sK24),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_5,plain,
~ v3_struct_0(sK24),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l2_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc4_struct_0]) ).
fof(f_54_2,plain,
? [U_92] :
( ~ v3_struct_0(U_92)
& l2_struct_0(U_92) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ~ v3_struct_0(sK25)
& l2_struct_0(sK25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_92,sK25)],[f_54_2]) ).
cnf(f_54_4,plain,
l2_struct_0(sK25),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_5,plain,
~ v3_struct_0(sK25),
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(u1_struct_0(A))) )
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc5_struct_0]) ).
fof(f_55_2,plain,
! [U_94] :
( ? [U_93] :
( ~ v1_xboole_0(U_93)
& m1_subset_1(U_93,k1_zfmisc_1(u1_struct_0(U_94))) )
| ~ l1_struct_0(U_94)
| v3_struct_0(U_94) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_94] :
( ( ~ v1_xboole_0(sK26(U_94))
& m1_subset_1(sK26(U_94),k1_zfmisc_1(u1_struct_0(U_94))) )
| ~ l1_struct_0(U_94)
| v3_struct_0(U_94) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_93,sK26(U_94))],[f_55_2]) ).
cnf(f_55_4,plain,
( m1_subset_1(sK26(U_94),k1_zfmisc_1(u1_struct_0(U_94)))
| ~ l1_struct_0(U_94)
| v3_struct_0(U_94) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_5,plain,
( ~ v1_xboole_0(sK26(U_94))
| ~ l1_struct_0(U_94)
| v3_struct_0(U_94) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [A] :
( ? [B] :
( v3_vectsp_2(B,A)
& l1_vectsp_2(B,A) )
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc8_vectsp_2]) ).
fof(f_56_2,plain,
! [U_96] :
( ? [U_95] :
( v3_vectsp_2(U_95,U_96)
& l1_vectsp_2(U_95,U_96) )
| ~ l1_struct_0(U_96) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_96] :
( ( v3_vectsp_2(sK27(U_96),U_96)
& l1_vectsp_2(sK27(U_96),U_96) )
| ~ l1_struct_0(U_96) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_95,sK27(U_96))],[f_56_2]) ).
cnf(f_56_4,plain,
( l1_vectsp_2(sK27(U_96),U_96)
| ~ l1_struct_0(U_96) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
( v3_vectsp_2(sK27(U_96),U_96)
| ~ l1_struct_0(U_96) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_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_57_2,plain,
! [U_98] :
( ? [U_97] :
( ~ v3_struct_0(U_97)
& l1_vectsp_2(U_97,U_98) )
| ~ l1_struct_0(U_98) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_98] :
( ( ~ v3_struct_0(sK28(U_98))
& l1_vectsp_2(sK28(U_98),U_98) )
| ~ l1_struct_0(U_98) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_97,sK28(U_98))],[f_57_2]) ).
cnf(f_57_4,plain,
( l1_vectsp_2(sK28(U_98),U_98)
| ~ l1_struct_0(U_98) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
( ~ v3_struct_0(sK28(U_98))
| ~ l1_struct_0(U_98) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_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_58_2,plain,
! [U_101,U_100,U_99] :
( ( m2_relset_1(U_99,U_101,U_100)
| ~ m1_relset_1(U_99,U_101,U_100) )
& ( m1_relset_1(U_99,U_101,U_100)
| ~ m2_relset_1(U_99,U_101,U_100) ) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ! [U_107,U_105,U_103] :
( m2_relset_1(U_103,U_107,U_105)
| ~ m1_relset_1(U_103,U_107,U_105) )
& ! [U_106,U_104,U_102] :
( m1_relset_1(U_102,U_106,U_104)
| ~ m2_relset_1(U_102,U_106,U_104) ) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
cnf(f_58_4,plain,
( m1_relset_1(U_102,U_106,U_104)
| ~ m2_relset_1(U_102,U_106,U_104) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
( m2_relset_1(U_103,U_107,U_105)
| ~ m1_relset_1(U_103,U_107,U_105) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_59_2,plain,
! [U_109,U_108] : r1_tarski(U_109,U_109),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_109] : r1_tarski(U_109,U_109),
inference(miniscope,[status(thm)],[f_59_2]) ).
cnf(f_59_4,plain,
r1_tarski(U_109,U_109),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( m1_rmod_2(k1_rmod_5(A,B,C),A,k1_rmod_5(A,B,D))
| ~ 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)
| ~ v2_vectsp_2(A)
| v10_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v7_group_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)],[t15_rmod_5]) ).
fof(f_60_2,plain,
! [U_113] :
( ! [U_112] :
( ! [U_111] :
( ! [U_110] :
( m1_rmod_2(k1_rmod_5(U_113,U_112,U_111),U_113,k1_rmod_5(U_113,U_112,U_110))
| ~ r1_tarski(U_111,U_110)
| ~ m1_subset_1(U_110,k1_zfmisc_1(u1_struct_0(U_112))) )
| ~ m1_subset_1(U_111,k1_zfmisc_1(u1_struct_0(U_112))) )
| ~ l1_vectsp_2(U_112,U_113)
| ~ v5_vectsp_2(U_112,U_113)
| ~ v6_rlvect_1(U_112)
| ~ v5_rlvect_1(U_112)
| ~ v4_rlvect_1(U_112)
| ~ v3_rlvect_1(U_112)
| v3_struct_0(U_112) )
| ~ l3_vectsp_1(U_113)
| ~ v2_vectsp_2(U_113)
| v10_vectsp_1(U_113)
| ~ v8_vectsp_1(U_113)
| ~ v7_vectsp_1(U_113)
| ~ v6_vectsp_1(U_113)
| ~ v7_group_1(U_113)
| ~ v4_group_1(U_113)
| ~ v6_rlvect_1(U_113)
| ~ v5_rlvect_1(U_113)
| ~ v4_rlvect_1(U_113)
| ~ v3_rlvect_1(U_113)
| v3_struct_0(U_113) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
( m1_rmod_2(k1_rmod_5(U_113,U_112,U_111),U_113,k1_rmod_5(U_113,U_112,U_110))
| ~ r1_tarski(U_111,U_110)
| ~ m1_subset_1(U_110,k1_zfmisc_1(u1_struct_0(U_112)))
| ~ m1_subset_1(U_111,k1_zfmisc_1(u1_struct_0(U_112)))
| ~ l1_vectsp_2(U_112,U_113)
| ~ v5_vectsp_2(U_112,U_113)
| ~ v6_rlvect_1(U_112)
| ~ v5_rlvect_1(U_112)
| ~ v4_rlvect_1(U_112)
| ~ v3_rlvect_1(U_112)
| v3_struct_0(U_112)
| ~ l3_vectsp_1(U_113)
| ~ v2_vectsp_2(U_113)
| v10_vectsp_1(U_113)
| ~ v8_vectsp_1(U_113)
| ~ v7_vectsp_1(U_113)
| ~ v6_vectsp_1(U_113)
| ~ v7_group_1(U_113)
| ~ v4_group_1(U_113)
| ~ v6_rlvect_1(U_113)
| ~ v5_rlvect_1(U_113)
| ~ v4_rlvect_1(U_113)
| ~ v3_rlvect_1(U_113)
| v3_struct_0(U_113) ),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_61_2,plain,
! [U_115,U_114] :
( m1_subset_1(U_115,U_114)
| ~ r2_hidden(U_115,U_114) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( m1_subset_1(U_115,U_114)
| ~ r2_hidden(U_115,U_114) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_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_62_2,plain,
! [U_117,U_116] :
( r2_hidden(U_117,U_116)
| v1_xboole_0(U_116)
| ~ m1_subset_1(U_117,U_116) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( r2_hidden(U_117,U_116)
| v1_xboole_0(U_116)
| ~ m1_subset_1(U_117,U_116) ),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( C = B
| ~ m1_rmod_2(B,A,C)
| ~ m1_rmod_2(C,A,B)
| ~ l1_vectsp_2(C,A)
| ~ v5_vectsp_2(C,A)
| ~ v3_vectsp_2(C,A)
| ~ v6_rlvect_1(C)
| ~ v5_rlvect_1(C)
| ~ v4_rlvect_1(C)
| ~ v3_rlvect_1(C)
| v3_struct_0(C) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v3_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)],[t33_rmod_2]) ).
fof(f_63_2,plain,
! [U_120] :
( ! [U_119] :
( ! [U_118] :
( U_118 = U_119
| ~ m1_rmod_2(U_119,U_120,U_118)
| ~ m1_rmod_2(U_118,U_120,U_119)
| ~ l1_vectsp_2(U_118,U_120)
| ~ v5_vectsp_2(U_118,U_120)
| ~ v3_vectsp_2(U_118,U_120)
| ~ v6_rlvect_1(U_118)
| ~ v5_rlvect_1(U_118)
| ~ v4_rlvect_1(U_118)
| ~ v3_rlvect_1(U_118)
| v3_struct_0(U_118) )
| ~ l1_vectsp_2(U_119,U_120)
| ~ v5_vectsp_2(U_119,U_120)
| ~ v3_vectsp_2(U_119,U_120)
| ~ v6_rlvect_1(U_119)
| ~ v5_rlvect_1(U_119)
| ~ v4_rlvect_1(U_119)
| ~ v3_rlvect_1(U_119)
| v3_struct_0(U_119) )
| ~ l3_vectsp_1(U_120)
| ~ v8_vectsp_1(U_120)
| ~ v7_vectsp_1(U_120)
| ~ v6_vectsp_1(U_120)
| ~ v4_group_1(U_120)
| ~ v6_rlvect_1(U_120)
| ~ v5_rlvect_1(U_120)
| ~ v4_rlvect_1(U_120)
| ~ v3_rlvect_1(U_120)
| v3_struct_0(U_120) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( U_118 = U_119
| ~ m1_rmod_2(U_119,U_120,U_118)
| ~ m1_rmod_2(U_118,U_120,U_119)
| ~ l1_vectsp_2(U_118,U_120)
| ~ v5_vectsp_2(U_118,U_120)
| ~ v3_vectsp_2(U_118,U_120)
| ~ v6_rlvect_1(U_118)
| ~ v5_rlvect_1(U_118)
| ~ v4_rlvect_1(U_118)
| ~ v3_rlvect_1(U_118)
| v3_struct_0(U_118)
| ~ l1_vectsp_2(U_119,U_120)
| ~ v5_vectsp_2(U_119,U_120)
| ~ v3_vectsp_2(U_119,U_120)
| ~ v6_rlvect_1(U_119)
| ~ v5_rlvect_1(U_119)
| ~ v4_rlvect_1(U_119)
| ~ v3_rlvect_1(U_119)
| v3_struct_0(U_119)
| ~ l3_vectsp_1(U_120)
| ~ v8_vectsp_1(U_120)
| ~ v7_vectsp_1(U_120)
| ~ v6_vectsp_1(U_120)
| ~ v4_group_1(U_120)
| ~ v6_rlvect_1(U_120)
| ~ v5_rlvect_1(U_120)
| ~ v4_rlvect_1(U_120)
| ~ v3_rlvect_1(U_120)
| v3_struct_0(U_120) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_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_64_2,plain,
! [U_122,U_121] :
( ( m1_subset_1(U_122,k1_zfmisc_1(U_121))
| ~ r1_tarski(U_122,U_121) )
& ( r1_tarski(U_122,U_121)
| ~ m1_subset_1(U_122,k1_zfmisc_1(U_121)) ) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( ! [U_126,U_124] :
( m1_subset_1(U_126,k1_zfmisc_1(U_124))
| ~ r1_tarski(U_126,U_124) )
& ! [U_125,U_123] :
( r1_tarski(U_125,U_123)
| ~ m1_subset_1(U_125,k1_zfmisc_1(U_123)) ) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
cnf(f_64_4,plain,
( r1_tarski(U_125,U_123)
| ~ m1_subset_1(U_125,k1_zfmisc_1(U_123)) ),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_5,plain,
( m1_subset_1(U_126,k1_zfmisc_1(U_124))
| ~ r1_tarski(U_126,U_124) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_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_65_2,plain,
! [U_129,U_128,U_127] :
( m1_subset_1(U_129,U_127)
| ~ m1_subset_1(U_128,k1_zfmisc_1(U_127))
| ~ r2_hidden(U_129,U_128) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( m1_subset_1(U_129,U_127)
| ~ m1_subset_1(U_128,k1_zfmisc_1(U_127))
| ~ r2_hidden(U_129,U_128) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_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_66_2,plain,
! [U_132,U_131,U_130] :
( ~ v1_xboole_0(U_130)
| ~ m1_subset_1(U_131,k1_zfmisc_1(U_130))
| ~ r2_hidden(U_132,U_131) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_132,U_131] :
( ! [U_130] :
( ~ v1_xboole_0(U_130)
| ~ m1_subset_1(U_131,k1_zfmisc_1(U_130)) )
| ~ r2_hidden(U_132,U_131) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
cnf(f_66_4,plain,
( ~ v1_xboole_0(U_130)
| ~ m1_subset_1(U_131,k1_zfmisc_1(U_130))
| ~ r2_hidden(U_132,U_131) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_67_2,plain,
! [U_133] :
( U_133 = k1_xboole_0
| ~ v1_xboole_0(U_133) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( U_133 = k1_xboole_0
| ~ v1_xboole_0(U_133) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_68_2,plain,
! [U_135,U_134] :
( ~ v1_xboole_0(U_134)
| ~ r2_hidden(U_135,U_134) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( ~ v1_xboole_0(U_134)
| ~ r2_hidden(U_135,U_134) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_69_2,plain,
! [U_137,U_136] :
( ~ v1_xboole_0(U_136)
| U_137 = U_136
| ~ v1_xboole_0(U_137) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_137] :
( ! [U_136] :
( ~ v1_xboole_0(U_136)
| U_137 = U_136 )
| ~ v1_xboole_0(U_137) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
cnf(f_69_4,plain,
( ~ v1_xboole_0(U_136)
| U_137 = U_136
| ~ v1_xboole_0(U_137) ),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_5_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_6]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_6_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_5]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_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_14_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(f_22_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_22_2]) ).
cnf(f_25_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_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,
( k1_rmod_5(Eq_x_0,Eq_x_1,Eq_x_2) = k1_rmod_5(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_7,axiom,
( u1_rlvect_1(Eq_x_0) = u1_rlvect_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( u2_struct_0(Eq_x_0) = u2_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( u1_vectsp_2(Eq_x_0,Eq_x_1) = u1_vectsp_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_10,axiom,
( g1_vectsp_2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = g1_vectsp_2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| 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_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,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,axiom,
( sK20(Eq_x_0) = sK20(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK22(Eq_x_0) = sK22(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK26(Eq_x_0) = sK26(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK27(Eq_x_0) = sK27(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( sK28(Eq_x_0) = sK28(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,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_26,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_27,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_28,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_29,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_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,
( v7_group_1(Eq_y_0)
| ~ v7_group_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,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_33,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_34,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_35,axiom,
( v10_vectsp_1(Eq_y_0)
| ~ v10_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( v2_vectsp_2(Eq_y_0)
| ~ v2_vectsp_2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,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_38,axiom,
( v3_vectsp_2(Eq_y_0,Eq_y_1)
| ~ v3_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_39,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_40,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_41,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_42,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_43,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_44,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_45,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_46,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_47,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_48,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_49,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_50,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_51,axiom,
( m1_rmod_2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m1_rmod_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_52,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_53,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_54,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_55,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_56,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_57,axiom,
( v1_xboole_0(Eq_y_0)
| ~ v1_xboole_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG220+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sun Sep 20 09:55:37 UTC 2026
% 0.02/0.31 % CPUTime :
% 175.13/175.48 % SZS status Theorem for theBenchmark
% 175.13/175.48 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------