%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LAT337+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:48:16 AM UTC 2026
% Result : Theorem 183.06s 183.39s
% Output : Proof 183.25s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t87_filter_2,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r3_lattices(A,B,C)
& l3_lattices(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v17_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& ~ v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C))) ) ) ) ) ),
file('theBenchmark.p',t87_filter_2) ).
fof(abstractness_v3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( v3_lattices(A)
=> A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ),
file('theBenchmark.p',abstractness_v3_lattices) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_funct_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_funct_1(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc1_lattices) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) )
=> ( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(cc2_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) )
=> ( v10_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc2_lattices) ).
fof(cc3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v14_lattices(A)
& v13_lattices(A)
& ~ v3_struct_0(A) )
=> ( v15_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc3_lattices) ).
fof(cc4_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v15_lattices(A)
& ~ v3_struct_0(A) )
=> ( v14_lattices(A)
& v13_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc4_lattices) ).
fof(cc5_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v17_lattices(A)
& ~ v3_struct_0(A) )
=> ( v16_lattices(A)
& v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v11_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc5_lattices) ).
fof(cc6_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v16_lattices(A)
& v15_lattices(A)
& v11_lattices(A)
& ~ v3_struct_0(A) )
=> ( v17_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc6_lattices) ).
fof(cc7_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v11_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v12_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc7_lattices) ).
fof(dt_g3_lattices,axiom,
! [A,B,C] :
( ( m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(B) )
=> ( l3_lattices(g3_lattices(A,B,C))
& v3_lattices(g3_lattices(A,B,C)) ) ),
file('theBenchmark.p',dt_g3_lattices) ).
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_k22_filter_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( m2_lattice4(k22_filter_2(A,B,C),A)
& ~ v1_xboole_0(k22_filter_2(A,B,C)) ) ),
file('theBenchmark.p',dt_k22_filter_2) ).
fof(dt_k23_filter_2,axiom,
! [A,B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> m2_nat_lat(k23_filter_2(A,B),A) ),
file('theBenchmark.p',dt_k23_filter_2) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_l1_lattices,axiom,
! [A] :
( l1_lattices(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_lattices) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_l2_lattices,axiom,
! [A] :
( l2_lattices(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l2_lattices) ).
fof(dt_l3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( l2_lattices(A)
& l1_lattices(A) ) ),
file('theBenchmark.p',dt_l3_lattices) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_lattice4,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_lattice4(B,A)
=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',dt_m2_lattice4) ).
fof(dt_m2_nat_lat,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_nat_lat(B,A)
=> ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B) ) ) ),
file('theBenchmark.p',dt_m2_nat_lat) ).
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_lattices,axiom,
! [A] :
( l1_lattices(A)
=> ( m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_lattices(A)) ) ),
file('theBenchmark.p',dt_u1_lattices) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(dt_u2_lattices,axiom,
! [A] :
( l2_lattices(A)
=> ( m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u2_lattices(A)) ) ),
file('theBenchmark.p',dt_u2_lattices) ).
fof(existence_l1_lattices,axiom,
? [A] : l1_lattices(A),
file('theBenchmark.p',existence_l1_lattices) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l2_lattices,axiom,
? [A] : l2_lattices(A),
file('theBenchmark.p',existence_l2_lattices) ).
fof(existence_l3_lattices,axiom,
? [A] : l3_lattices(A),
file('theBenchmark.p',existence_l3_lattices) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_lattice4,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] : m2_lattice4(B,A) ),
file('theBenchmark.p',existence_m2_lattice4) ).
fof(existence_m2_nat_lat,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] : m2_nat_lat(B,A) ),
file('theBenchmark.p',existence_m2_nat_lat) ).
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_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_lattice2,axiom,
! [A] :
( ( l2_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) )
=> ( v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_binop_1(u2_lattices(A),u1_struct_0(A))
& v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u2_lattices(A))
& v1_relat_1(u2_lattices(A)) ) ),
file('theBenchmark.p',fc2_lattice2) ).
fof(fc3_lattice2,axiom,
! [A] :
( ( l2_lattices(A)
& v5_lattices(A)
& ~ v3_struct_0(A) )
=> ( v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v2_binop_1(u2_lattices(A),u1_struct_0(A))
& v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u2_lattices(A))
& v1_relat_1(u2_lattices(A)) ) ),
file('theBenchmark.p',fc3_lattice2) ).
fof(fc3_lattices,axiom,
! [A,B,C] :
( ( m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(B)
& ~ v1_xboole_0(A) )
=> ( v3_lattices(g3_lattices(A,B,C))
& ~ v3_struct_0(g3_lattices(A,B,C)) ) ),
file('theBenchmark.p',fc3_lattices) ).
fof(fc4_lattice2,axiom,
! [A] :
( ( l1_lattices(A)
& v6_lattices(A)
& ~ v3_struct_0(A) )
=> ( v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_binop_1(u1_lattices(A),u1_struct_0(A))
& v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_lattices(A))
& v1_relat_1(u1_lattices(A)) ) ),
file('theBenchmark.p',fc4_lattice2) ).
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(fc5_filter_2,axiom,
! [A,B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v10_lattices(k23_filter_2(A,B))
& v9_lattices(k23_filter_2(A,B))
& v8_lattices(k23_filter_2(A,B))
& v7_lattices(k23_filter_2(A,B))
& v6_lattices(k23_filter_2(A,B))
& v5_lattices(k23_filter_2(A,B))
& v4_lattices(k23_filter_2(A,B))
& v3_lattices(k23_filter_2(A,B))
& ~ v3_struct_0(k23_filter_2(A,B)) ) ),
file('theBenchmark.p',fc5_filter_2) ).
fof(fc5_lattice2,axiom,
! [A] :
( ( l1_lattices(A)
& v7_lattices(A)
& ~ v3_struct_0(A) )
=> ( v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v2_binop_1(u1_lattices(A),u1_struct_0(A))
& v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_lattices(A))
& v1_relat_1(u1_lattices(A)) ) ),
file('theBenchmark.p',fc5_lattice2) ).
fof(free_g3_lattices,axiom,
! [A,B,C] :
( ( m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(B) )
=> ! [D,E,F] :
( g3_lattices(A,B,C) = g3_lattices(D,E,F)
=> ( C = F
& B = E
& A = D ) ) ),
file('theBenchmark.p',free_g3_lattices) ).
fof(rc10_lattices,axiom,
? [A] :
( v14_lattices(A)
& v13_lattices(A)
& v12_lattices(A)
& v11_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
file('theBenchmark.p',rc10_lattices) ).
fof(rc11_lattices,axiom,
? [A] :
( v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
file('theBenchmark.p',rc11_lattices) ).
fof(rc12_lattices,axiom,
? [A] :
( v16_lattices(A)
& v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
file('theBenchmark.p',rc12_lattices) ).
fof(rc13_lattices,axiom,
? [A] :
( v17_lattices(A)
& v16_lattices(A)
& v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v11_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
file('theBenchmark.p',rc13_lattices) ).
fof(rc1_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_lattice4,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( ~ v1_xboole_0(B)
& m2_lattice4(B,A) ) ),
file('theBenchmark.p',rc1_lattice4) ).
fof(rc1_nat_lat,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( v10_lattices(B)
& v9_lattices(B)
& v8_lattices(B)
& v7_lattices(B)
& v6_lattices(B)
& v5_lattices(B)
& v4_lattices(B)
& v3_lattices(B)
& ~ v3_struct_0(B)
& m2_nat_lat(B,A) ) ),
file('theBenchmark.p',rc1_nat_lat) ).
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_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc2_funct_1) ).
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_funct_1,axiom,
? [A] :
( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_lattices,axiom,
? [A] :
( v3_lattices(A)
& l3_lattices(A) ),
file('theBenchmark.p',rc3_lattices) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc5_struct_0) ).
fof(rc6_lattices,axiom,
? [A] :
( v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
file('theBenchmark.p',rc6_lattices) ).
fof(rc9_lattices,axiom,
? [A] :
( v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
file('theBenchmark.p',rc9_lattices) ).
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(redefinition_r3_lattices,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v6_lattices(A)
& ~ v3_struct_0(A) )
=> ( r3_lattices(A,B,C)
<=> r1_lattices(A,B,C) ) ),
file('theBenchmark.p',redefinition_r3_lattices) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(reflexivity_r3_lattices,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v6_lattices(A)
& ~ v3_struct_0(A) )
=> r3_lattices(A,B,B) ),
file('theBenchmark.p',reflexivity_r3_lattices) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(t78_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) )
=> ( v11_lattices(A)
=> v11_lattices(k23_filter_2(A,B)) ) ) ),
file('theBenchmark.p',t78_filter_2) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t86_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r3_lattices(A,B,C)
& v12_lattices(A)
& l3_lattices(A)
& v16_lattices(A)
& v15_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v16_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v15_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& ~ v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C))) ) ) ) ) ),
file('theBenchmark.p',t86_filter_2) ).
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_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r3_lattices(A,B,C)
& l3_lattices(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v17_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& ~ v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C))) ) ) ) ) ),
inference(negate,[status(cth)],[t87_filter_2]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ( ~ l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
| ~ v17_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
| ~ v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
| v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C))) )
& r3_lattices(A,B,C)
& l3_lattices(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A)
& m1_subset_1(C,u1_struct_0(A)) )
& m1_subset_1(B,u1_struct_0(A)) )
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ( ~ l3_lattices(k23_filter_2(U_2,k22_filter_2(U_2,U_1,U_0)))
| ~ v17_lattices(k23_filter_2(U_2,k22_filter_2(U_2,U_1,U_0)))
| ~ v10_lattices(k23_filter_2(U_2,k22_filter_2(U_2,U_1,U_0)))
| v3_struct_0(k23_filter_2(U_2,k22_filter_2(U_2,U_1,U_0))) )
& r3_lattices(U_2,U_1,U_0)
& l3_lattices(U_2)
& v17_lattices(U_2)
& v10_lattices(U_2)
& ~ v3_struct_0(U_2)
& m1_subset_1(U_0,u1_struct_0(U_2)) )
& m1_subset_1(U_1,u1_struct_0(U_2)) )
& l3_lattices(U_2)
& v10_lattices(U_2)
& ~ v3_struct_0(U_2) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_1] :
( ? [U_0] :
( ( ~ l3_lattices(k23_filter_2(sK1,k22_filter_2(sK1,U_1,U_0)))
| ~ v17_lattices(k23_filter_2(sK1,k22_filter_2(sK1,U_1,U_0)))
| ~ v10_lattices(k23_filter_2(sK1,k22_filter_2(sK1,U_1,U_0)))
| v3_struct_0(k23_filter_2(sK1,k22_filter_2(sK1,U_1,U_0))) )
& r3_lattices(sK1,U_1,U_0)
& l3_lattices(sK1)
& v17_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1)
& m1_subset_1(U_0,u1_struct_0(sK1)) )
& m1_subset_1(U_1,u1_struct_0(sK1)) )
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_0] :
( ( ~ l3_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,U_0)))
| ~ v17_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,U_0)))
| ~ v10_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,U_0)))
| v3_struct_0(k23_filter_2(sK1,k22_filter_2(sK1,sK2,U_0))) )
& r3_lattices(sK1,sK2,U_0)
& l3_lattices(sK1)
& v17_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1)
& m1_subset_1(U_0,u1_struct_0(sK1)) )
& m1_subset_1(sK2,u1_struct_0(sK1))
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( ~ l3_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3)))
| ~ v17_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3)))
| ~ v10_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3)))
| v3_struct_0(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3))) )
& r3_lattices(sK1,sK2,sK3)
& l3_lattices(sK1)
& v17_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1)
& m1_subset_1(sK3,u1_struct_0(sK1))
& m1_subset_1(sK2,u1_struct_0(sK1))
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_0,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ( ~ l3_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3)))
| ~ v17_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3)))
| ~ v10_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3)))
| v3_struct_0(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3))) )
& r3_lattices(sK1,sK2,sK3)
& l3_lattices(sK1)
& v17_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1)
& m1_subset_1(sK3,u1_struct_0(sK1))
& m1_subset_1(sK2,u1_struct_0(sK1))
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(definitional_conversion,[status(esa)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
v10_lattices(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_10,negated_conjecture,
l3_lattices(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_11,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_12,negated_conjecture,
m1_subset_1(sK3,u1_struct_0(sK1)),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_13,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_14,negated_conjecture,
v10_lattices(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_15,negated_conjecture,
v17_lattices(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_16,negated_conjecture,
l3_lattices(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_17,negated_conjecture,
r3_lattices(sK1,sK2,sK3),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_18,negated_conjecture,
( ~ l3_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3)))
| ~ v17_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3)))
| ~ v10_lattices(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3)))
| v3_struct_0(k23_filter_2(sK1,k22_filter_2(sK1,sK2,sK3))) ),
inference(clausify,[status(thm)],[f_1_7]) ).
fof(f_2_1,plain,
! [A] :
( A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A))
| ~ v3_lattices(A)
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[abstractness_v3_lattices]) ).
fof(f_2_2,plain,
! [U_3] :
( U_3 = g3_lattices(u1_struct_0(U_3),u2_lattices(U_3),u1_lattices(U_3))
| ~ v3_lattices(U_3)
| ~ l3_lattices(U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( U_3 = g3_lattices(u1_struct_0(U_3),u2_lattices(U_3),u1_lattices(U_3))
| ~ v3_lattices(U_3)
| ~ l3_lattices(U_3) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_3_2,plain,
! [U_5,U_4] :
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( v1_funct_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_4_2,plain,
! [U_6] :
( v1_funct_1(U_6)
| ~ v1_xboole_0(U_6) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v1_funct_1(U_6)
| ~ v1_xboole_0(U_6) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ( v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) )
| ~ v10_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[cc1_lattices]) ).
fof(f_5_2,plain,
! [U_7] :
( ( v9_lattices(U_7)
& v8_lattices(U_7)
& v7_lattices(U_7)
& v6_lattices(U_7)
& v5_lattices(U_7)
& v4_lattices(U_7)
& ~ v3_struct_0(U_7) )
| ~ v10_lattices(U_7)
| v3_struct_0(U_7)
| ~ l3_lattices(U_7) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( ~ v3_struct_0(U_7)
| ~ v10_lattices(U_7)
| v3_struct_0(U_7)
| ~ l3_lattices(U_7) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( v4_lattices(U_7)
| ~ v10_lattices(U_7)
| v3_struct_0(U_7)
| ~ l3_lattices(U_7) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( v5_lattices(U_7)
| ~ v10_lattices(U_7)
| v3_struct_0(U_7)
| ~ l3_lattices(U_7) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_6,plain,
( v6_lattices(U_7)
| ~ v10_lattices(U_7)
| v3_struct_0(U_7)
| ~ l3_lattices(U_7) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_7,plain,
( v7_lattices(U_7)
| ~ v10_lattices(U_7)
| v3_struct_0(U_7)
| ~ l3_lattices(U_7) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_8,plain,
( v8_lattices(U_7)
| ~ v10_lattices(U_7)
| v3_struct_0(U_7)
| ~ l3_lattices(U_7) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_9,plain,
( v9_lattices(U_7)
| ~ v10_lattices(U_7)
| v3_struct_0(U_7)
| ~ l3_lattices(U_7) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_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_6_1]) ).
cnf(f_6_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_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) )
| ~ v1_funct_1(A)
| ~ v1_xboole_0(A)
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_7_2,plain,
! [U_11] :
( ( v2_funct_1(U_11)
& v1_funct_1(U_11)
& v1_relat_1(U_11) )
| ~ v1_funct_1(U_11)
| ~ v1_xboole_0(U_11)
| ~ v1_relat_1(U_11) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( v1_relat_1(U_11)
| ~ v1_funct_1(U_11)
| ~ v1_xboole_0(U_11)
| ~ v1_relat_1(U_11) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( v1_funct_1(U_11)
| ~ v1_funct_1(U_11)
| ~ v1_xboole_0(U_11)
| ~ v1_relat_1(U_11) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_5,plain,
( v2_funct_1(U_11)
| ~ v1_funct_1(U_11)
| ~ v1_xboole_0(U_11)
| ~ v1_relat_1(U_11) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ( v10_lattices(A)
& ~ v3_struct_0(A) )
| ~ v9_lattices(A)
| ~ v8_lattices(A)
| ~ v7_lattices(A)
| ~ v6_lattices(A)
| ~ v5_lattices(A)
| ~ v4_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[cc2_lattices]) ).
fof(f_8_2,plain,
! [U_12] :
( ( v10_lattices(U_12)
& ~ v3_struct_0(U_12) )
| ~ v9_lattices(U_12)
| ~ v8_lattices(U_12)
| ~ v7_lattices(U_12)
| ~ v6_lattices(U_12)
| ~ v5_lattices(U_12)
| ~ v4_lattices(U_12)
| v3_struct_0(U_12)
| ~ l3_lattices(U_12) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( ~ v3_struct_0(U_12)
| ~ v9_lattices(U_12)
| ~ v8_lattices(U_12)
| ~ v7_lattices(U_12)
| ~ v6_lattices(U_12)
| ~ v5_lattices(U_12)
| ~ v4_lattices(U_12)
| v3_struct_0(U_12)
| ~ l3_lattices(U_12) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( v10_lattices(U_12)
| ~ v9_lattices(U_12)
| ~ v8_lattices(U_12)
| ~ v7_lattices(U_12)
| ~ v6_lattices(U_12)
| ~ v5_lattices(U_12)
| ~ v4_lattices(U_12)
| v3_struct_0(U_12)
| ~ l3_lattices(U_12) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] :
( ( v15_lattices(A)
& ~ v3_struct_0(A) )
| ~ v14_lattices(A)
| ~ v13_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[cc3_lattices]) ).
fof(f_9_2,plain,
! [U_13] :
( ( v15_lattices(U_13)
& ~ v3_struct_0(U_13) )
| ~ v14_lattices(U_13)
| ~ v13_lattices(U_13)
| v3_struct_0(U_13)
| ~ l3_lattices(U_13) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( ~ v3_struct_0(U_13)
| ~ v14_lattices(U_13)
| ~ v13_lattices(U_13)
| v3_struct_0(U_13)
| ~ l3_lattices(U_13) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( v15_lattices(U_13)
| ~ v14_lattices(U_13)
| ~ v13_lattices(U_13)
| v3_struct_0(U_13)
| ~ l3_lattices(U_13) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] :
( ( v14_lattices(A)
& v13_lattices(A)
& ~ v3_struct_0(A) )
| ~ v15_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[cc4_lattices]) ).
fof(f_10_2,plain,
! [U_14] :
( ( v14_lattices(U_14)
& v13_lattices(U_14)
& ~ v3_struct_0(U_14) )
| ~ v15_lattices(U_14)
| v3_struct_0(U_14)
| ~ l3_lattices(U_14) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( ~ v3_struct_0(U_14)
| ~ v15_lattices(U_14)
| v3_struct_0(U_14)
| ~ l3_lattices(U_14) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( v13_lattices(U_14)
| ~ v15_lattices(U_14)
| v3_struct_0(U_14)
| ~ l3_lattices(U_14) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_5,plain,
( v14_lattices(U_14)
| ~ v15_lattices(U_14)
| v3_struct_0(U_14)
| ~ l3_lattices(U_14) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] :
( ( v16_lattices(A)
& v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v11_lattices(A)
& ~ v3_struct_0(A) )
| ~ v17_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[cc5_lattices]) ).
fof(f_11_2,plain,
! [U_15] :
( ( v16_lattices(U_15)
& v15_lattices(U_15)
& v14_lattices(U_15)
& v13_lattices(U_15)
& v11_lattices(U_15)
& ~ v3_struct_0(U_15) )
| ~ v17_lattices(U_15)
| v3_struct_0(U_15)
| ~ l3_lattices(U_15) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( ~ v3_struct_0(U_15)
| ~ v17_lattices(U_15)
| v3_struct_0(U_15)
| ~ l3_lattices(U_15) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( v11_lattices(U_15)
| ~ v17_lattices(U_15)
| v3_struct_0(U_15)
| ~ l3_lattices(U_15) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_5,plain,
( v13_lattices(U_15)
| ~ v17_lattices(U_15)
| v3_struct_0(U_15)
| ~ l3_lattices(U_15) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_6,plain,
( v14_lattices(U_15)
| ~ v17_lattices(U_15)
| v3_struct_0(U_15)
| ~ l3_lattices(U_15) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_7,plain,
( v15_lattices(U_15)
| ~ v17_lattices(U_15)
| v3_struct_0(U_15)
| ~ l3_lattices(U_15) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_8,plain,
( v16_lattices(U_15)
| ~ v17_lattices(U_15)
| v3_struct_0(U_15)
| ~ l3_lattices(U_15) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] :
( ( v17_lattices(A)
& ~ v3_struct_0(A) )
| ~ v16_lattices(A)
| ~ v15_lattices(A)
| ~ v11_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[cc6_lattices]) ).
fof(f_12_2,plain,
! [U_16] :
( ( v17_lattices(U_16)
& ~ v3_struct_0(U_16) )
| ~ v16_lattices(U_16)
| ~ v15_lattices(U_16)
| ~ v11_lattices(U_16)
| v3_struct_0(U_16)
| ~ l3_lattices(U_16) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( ~ v3_struct_0(U_16)
| ~ v16_lattices(U_16)
| ~ v15_lattices(U_16)
| ~ v11_lattices(U_16)
| v3_struct_0(U_16)
| ~ l3_lattices(U_16) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( v17_lattices(U_16)
| ~ v16_lattices(U_16)
| ~ v15_lattices(U_16)
| ~ v11_lattices(U_16)
| v3_struct_0(U_16)
| ~ l3_lattices(U_16) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A] :
( ( v12_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) )
| ~ v11_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[cc7_lattices]) ).
fof(f_13_2,plain,
! [U_17] :
( ( v12_lattices(U_17)
& v10_lattices(U_17)
& v9_lattices(U_17)
& v8_lattices(U_17)
& v7_lattices(U_17)
& v6_lattices(U_17)
& v5_lattices(U_17)
& v4_lattices(U_17)
& ~ v3_struct_0(U_17) )
| ~ v11_lattices(U_17)
| ~ v10_lattices(U_17)
| v3_struct_0(U_17)
| ~ l3_lattices(U_17) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( ~ v3_struct_0(U_17)
| ~ v11_lattices(U_17)
| ~ v10_lattices(U_17)
| v3_struct_0(U_17)
| ~ l3_lattices(U_17) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( v4_lattices(U_17)
| ~ v11_lattices(U_17)
| ~ v10_lattices(U_17)
| v3_struct_0(U_17)
| ~ l3_lattices(U_17) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_5,plain,
( v5_lattices(U_17)
| ~ v11_lattices(U_17)
| ~ v10_lattices(U_17)
| v3_struct_0(U_17)
| ~ l3_lattices(U_17) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_6,plain,
( v6_lattices(U_17)
| ~ v11_lattices(U_17)
| ~ v10_lattices(U_17)
| v3_struct_0(U_17)
| ~ l3_lattices(U_17) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_7,plain,
( v7_lattices(U_17)
| ~ v11_lattices(U_17)
| ~ v10_lattices(U_17)
| v3_struct_0(U_17)
| ~ l3_lattices(U_17) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_8,plain,
( v8_lattices(U_17)
| ~ v11_lattices(U_17)
| ~ v10_lattices(U_17)
| v3_struct_0(U_17)
| ~ l3_lattices(U_17) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_9,plain,
( v9_lattices(U_17)
| ~ v11_lattices(U_17)
| ~ v10_lattices(U_17)
| v3_struct_0(U_17)
| ~ l3_lattices(U_17) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_10,plain,
( v10_lattices(U_17)
| ~ v11_lattices(U_17)
| ~ v10_lattices(U_17)
| v3_struct_0(U_17)
| ~ l3_lattices(U_17) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_11,plain,
( v12_lattices(U_17)
| ~ v11_lattices(U_17)
| ~ v10_lattices(U_17)
| v3_struct_0(U_17)
| ~ l3_lattices(U_17) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A,B,C] :
( ( l3_lattices(g3_lattices(A,B,C))
& v3_lattices(g3_lattices(A,B,C)) )
| ~ m1_relset_1(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(C)
| ~ m1_relset_1(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(B) ),
inference(fof_nnf,[status(thm)],[dt_g3_lattices]) ).
fof(f_14_2,plain,
! [U_20,U_19,U_18] :
( ( l3_lattices(g3_lattices(U_20,U_19,U_18))
& v3_lattices(g3_lattices(U_20,U_19,U_18)) )
| ~ m1_relset_1(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_18)
| ~ m1_relset_1(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_19) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( v3_lattices(g3_lattices(U_20,U_19,U_18))
| ~ m1_relset_1(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_18)
| ~ m1_relset_1(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_19) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( l3_lattices(g3_lattices(U_20,U_19,U_18))
| ~ m1_relset_1(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_18)
| ~ m1_relset_1(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_19) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_16_2,plain,
$true,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
! [A,B,C] :
( ( m2_lattice4(k22_filter_2(A,B,C),A)
& ~ v1_xboole_0(k22_filter_2(A,B,C)) )
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k22_filter_2]) ).
fof(f_17_2,plain,
! [U_23,U_22,U_21] :
( ( m2_lattice4(k22_filter_2(U_23,U_22,U_21),U_23)
& ~ v1_xboole_0(k22_filter_2(U_23,U_22,U_21)) )
| ~ m1_subset_1(U_21,u1_struct_0(U_23))
| ~ m1_subset_1(U_22,u1_struct_0(U_23))
| ~ l3_lattices(U_23)
| ~ v10_lattices(U_23)
| v3_struct_0(U_23) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( ~ v1_xboole_0(k22_filter_2(U_23,U_22,U_21))
| ~ m1_subset_1(U_21,u1_struct_0(U_23))
| ~ m1_subset_1(U_22,u1_struct_0(U_23))
| ~ l3_lattices(U_23)
| ~ v10_lattices(U_23)
| v3_struct_0(U_23) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( m2_lattice4(k22_filter_2(U_23,U_22,U_21),U_23)
| ~ m1_subset_1(U_21,u1_struct_0(U_23))
| ~ m1_subset_1(U_22,u1_struct_0(U_23))
| ~ l3_lattices(U_23)
| ~ v10_lattices(U_23)
| v3_struct_0(U_23) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A,B] :
( m2_nat_lat(k23_filter_2(A,B),A)
| ~ m2_lattice4(B,A)
| v1_xboole_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k23_filter_2]) ).
fof(f_18_2,plain,
! [U_25,U_24] :
( m2_nat_lat(k23_filter_2(U_25,U_24),U_25)
| ~ m2_lattice4(U_24,U_25)
| v1_xboole_0(U_24)
| ~ l3_lattices(U_25)
| ~ v10_lattices(U_25)
| v3_struct_0(U_25) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( m2_nat_lat(k23_filter_2(U_25,U_24),U_25)
| ~ m2_lattice4(U_24,U_25)
| v1_xboole_0(U_24)
| ~ l3_lattices(U_25)
| ~ v10_lattices(U_25)
| v3_struct_0(U_25) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_19_2,plain,
$true,
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_lattices]) ).
fof(f_20_2,plain,
! [U_26] :
( l1_struct_0(U_26)
| ~ l1_lattices(U_26) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( l1_struct_0(U_26)
| ~ l1_lattices(U_26) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_21_2,plain,
$true,
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_lattices]) ).
fof(f_22_2,plain,
! [U_27] :
( l1_struct_0(U_27)
| ~ l2_lattices(U_27) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( l1_struct_0(U_27)
| ~ l2_lattices(U_27) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A] :
( ( l2_lattices(A)
& l1_lattices(A) )
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l3_lattices]) ).
fof(f_23_2,plain,
! [U_28] :
( ( l2_lattices(U_28)
& l1_lattices(U_28) )
| ~ l3_lattices(U_28) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( l1_lattices(U_28)
| ~ l3_lattices(U_28) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( l2_lattices(U_28)
| ~ l3_lattices(U_28) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_24_2,plain,
$true,
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_25_2,plain,
$true,
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
! [A] :
( ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ m2_lattice4(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m2_lattice4]) ).
fof(f_26_2,plain,
! [U_30] :
( ! [U_29] :
( m1_subset_1(U_29,k1_zfmisc_1(u1_struct_0(U_30)))
| ~ m2_lattice4(U_29,U_30) )
| ~ l3_lattices(U_30)
| ~ v10_lattices(U_30)
| v3_struct_0(U_30) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( m1_subset_1(U_29,k1_zfmisc_1(u1_struct_0(U_30)))
| ~ m2_lattice4(U_29,U_30)
| ~ l3_lattices(U_30)
| ~ v10_lattices(U_30)
| v3_struct_0(U_30) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A] :
( ! [B] :
( ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B) )
| ~ m2_nat_lat(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m2_nat_lat]) ).
fof(f_27_2,plain,
! [U_32] :
( ! [U_31] :
( ( l3_lattices(U_31)
& v10_lattices(U_31)
& ~ v3_struct_0(U_31) )
| ~ m2_nat_lat(U_31,U_32) )
| ~ l3_lattices(U_32)
| ~ v10_lattices(U_32)
| v3_struct_0(U_32) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( ~ v3_struct_0(U_31)
| ~ m2_nat_lat(U_31,U_32)
| ~ l3_lattices(U_32)
| ~ v10_lattices(U_32)
| v3_struct_0(U_32) ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( v10_lattices(U_31)
| ~ m2_nat_lat(U_31,U_32)
| ~ l3_lattices(U_32)
| ~ v10_lattices(U_32)
| v3_struct_0(U_32) ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_5,plain,
( l3_lattices(U_31)
| ~ m2_nat_lat(U_31,U_32)
| ~ l3_lattices(U_32)
| ~ v10_lattices(U_32)
| v3_struct_0(U_32) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_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_28_2,plain,
! [U_35,U_34,U_33] :
( m1_subset_1(U_33,k1_zfmisc_1(k2_zfmisc_1(U_35,U_34)))
| ~ m2_relset_1(U_33,U_35,U_34) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( m1_subset_1(U_33,k1_zfmisc_1(k2_zfmisc_1(U_35,U_34)))
| ~ m2_relset_1(U_33,U_35,U_34) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A] :
( ( m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_lattices(A)) )
| ~ l1_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_lattices]) ).
fof(f_29_2,plain,
! [U_36] :
( ( m2_relset_1(u1_lattices(U_36),k2_zfmisc_1(u1_struct_0(U_36),u1_struct_0(U_36)),u1_struct_0(U_36))
& v1_funct_2(u1_lattices(U_36),k2_zfmisc_1(u1_struct_0(U_36),u1_struct_0(U_36)),u1_struct_0(U_36))
& v1_funct_1(u1_lattices(U_36)) )
| ~ l1_lattices(U_36) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( v1_funct_1(u1_lattices(U_36))
| ~ l1_lattices(U_36) ),
inference(clausify,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
( v1_funct_2(u1_lattices(U_36),k2_zfmisc_1(u1_struct_0(U_36),u1_struct_0(U_36)),u1_struct_0(U_36))
| ~ l1_lattices(U_36) ),
inference(clausify,[status(thm)],[f_29_2]) ).
cnf(f_29_5,plain,
( m2_relset_1(u1_lattices(U_36),k2_zfmisc_1(u1_struct_0(U_36),u1_struct_0(U_36)),u1_struct_0(U_36))
| ~ l1_lattices(U_36) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_30_2,plain,
$true,
inference(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_1,plain,
! [A] :
( ( m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u2_lattices(A)) )
| ~ l2_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_u2_lattices]) ).
fof(f_31_2,plain,
! [U_37] :
( ( m2_relset_1(u2_lattices(U_37),k2_zfmisc_1(u1_struct_0(U_37),u1_struct_0(U_37)),u1_struct_0(U_37))
& v1_funct_2(u2_lattices(U_37),k2_zfmisc_1(u1_struct_0(U_37),u1_struct_0(U_37)),u1_struct_0(U_37))
& v1_funct_1(u2_lattices(U_37)) )
| ~ l2_lattices(U_37) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( v1_funct_1(u2_lattices(U_37))
| ~ l2_lattices(U_37) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( v1_funct_2(u2_lattices(U_37),k2_zfmisc_1(u1_struct_0(U_37),u1_struct_0(U_37)),u1_struct_0(U_37))
| ~ l2_lattices(U_37) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_5,plain,
( m2_relset_1(u2_lattices(U_37),k2_zfmisc_1(u1_struct_0(U_37),u1_struct_0(U_37)),u1_struct_0(U_37))
| ~ l2_lattices(U_37) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
? [A] : l1_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l1_lattices]) ).
fof(f_32_2,plain,
? [U_38] : l1_lattices(U_38),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
l1_lattices(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_38,sK4)],[f_32_2]) ).
cnf(f_32_4,plain,
l1_lattices(sK4),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_33_2,plain,
? [U_39] : l1_struct_0(U_39),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
l1_struct_0(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_39,sK5)],[f_33_2]) ).
cnf(f_33_4,plain,
l1_struct_0(sK5),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
? [A] : l2_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l2_lattices]) ).
fof(f_34_2,plain,
? [U_40] : l2_lattices(U_40),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
l2_lattices(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_40,sK6)],[f_34_2]) ).
cnf(f_34_4,plain,
l2_lattices(sK6),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] : l3_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l3_lattices]) ).
fof(f_35_2,plain,
? [U_41] : l3_lattices(U_41),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
l3_lattices(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_41,sK7)],[f_35_2]) ).
cnf(f_35_4,plain,
l3_lattices(sK7),
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_44,U_43] :
? [U_42] : m1_relset_1(U_42,U_44,U_43),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_44,U_43] : m1_relset_1(sK8(U_44,U_43),U_44,U_43),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_42,sK8(U_44,U_43))],[f_36_2]) ).
cnf(f_36_4,plain,
m1_relset_1(sK8(U_44,U_43),U_44,U_43),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_37_2,plain,
! [U_46] :
? [U_45] : m1_subset_1(U_45,U_46),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_46] : m1_subset_1(sK9(U_46),U_46),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_45,sK9(U_46))],[f_37_2]) ).
cnf(f_37_4,plain,
m1_subset_1(sK9(U_46),U_46),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A] :
( ? [B] : m2_lattice4(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m2_lattice4]) ).
fof(f_38_2,plain,
! [U_48] :
( ? [U_47] : m2_lattice4(U_47,U_48)
| ~ l3_lattices(U_48)
| ~ v10_lattices(U_48)
| v3_struct_0(U_48) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_48] :
( m2_lattice4(sK10(U_48),U_48)
| ~ l3_lattices(U_48)
| ~ v10_lattices(U_48)
| v3_struct_0(U_48) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_47,sK10(U_48))],[f_38_2]) ).
cnf(f_38_4,plain,
( m2_lattice4(sK10(U_48),U_48)
| ~ l3_lattices(U_48)
| ~ v10_lattices(U_48)
| v3_struct_0(U_48) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A] :
( ? [B] : m2_nat_lat(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m2_nat_lat]) ).
fof(f_39_2,plain,
! [U_50] :
( ? [U_49] : m2_nat_lat(U_49,U_50)
| ~ l3_lattices(U_50)
| ~ v10_lattices(U_50)
| v3_struct_0(U_50) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_50] :
( m2_nat_lat(sK11(U_50),U_50)
| ~ l3_lattices(U_50)
| ~ v10_lattices(U_50)
| v3_struct_0(U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_49,sK11(U_50))],[f_39_2]) ).
cnf(f_39_4,plain,
( m2_nat_lat(sK11(U_50),U_50)
| ~ l3_lattices(U_50)
| ~ v10_lattices(U_50)
| v3_struct_0(U_50) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_40_2,plain,
! [U_53,U_52] :
? [U_51] : m2_relset_1(U_51,U_53,U_52),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_53,U_52] : m2_relset_1(sK12(U_53,U_52),U_53,U_52),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_51,sK12(U_53,U_52))],[f_40_2]) ).
cnf(f_40_4,plain,
m2_relset_1(sK12(U_53,U_52),U_53,U_52),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_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_41_2,plain,
! [U_54] :
( ~ v1_xboole_0(u1_struct_0(U_54))
| ~ l1_struct_0(U_54)
| v3_struct_0(U_54) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_54))
| ~ l1_struct_0(U_54)
| v3_struct_0(U_54) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_42_2,plain,
! [U_55] : ~ v1_xboole_0(k1_zfmisc_1(U_55)),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
~ v1_xboole_0(k1_zfmisc_1(U_55)),
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] :
( ( v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_binop_1(u2_lattices(A),u1_struct_0(A))
& v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u2_lattices(A))
& v1_relat_1(u2_lattices(A)) )
| ~ l2_lattices(A)
| ~ v4_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc2_lattice2]) ).
fof(f_44_2,plain,
! [U_56] :
( ( v1_partfun1(u2_lattices(U_56),k2_zfmisc_1(u1_struct_0(U_56),u1_struct_0(U_56)),u1_struct_0(U_56))
& v1_binop_1(u2_lattices(U_56),u1_struct_0(U_56))
& v1_funct_2(u2_lattices(U_56),k2_zfmisc_1(u1_struct_0(U_56),u1_struct_0(U_56)),u1_struct_0(U_56))
& v1_funct_1(u2_lattices(U_56))
& v1_relat_1(u2_lattices(U_56)) )
| ~ l2_lattices(U_56)
| ~ v4_lattices(U_56)
| v3_struct_0(U_56) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( v1_relat_1(u2_lattices(U_56))
| ~ l2_lattices(U_56)
| ~ v4_lattices(U_56)
| v3_struct_0(U_56) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_4,plain,
( v1_funct_1(u2_lattices(U_56))
| ~ l2_lattices(U_56)
| ~ v4_lattices(U_56)
| v3_struct_0(U_56) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_5,plain,
( v1_funct_2(u2_lattices(U_56),k2_zfmisc_1(u1_struct_0(U_56),u1_struct_0(U_56)),u1_struct_0(U_56))
| ~ l2_lattices(U_56)
| ~ v4_lattices(U_56)
| v3_struct_0(U_56) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_6,plain,
( v1_binop_1(u2_lattices(U_56),u1_struct_0(U_56))
| ~ l2_lattices(U_56)
| ~ v4_lattices(U_56)
| v3_struct_0(U_56) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_7,plain,
( v1_partfun1(u2_lattices(U_56),k2_zfmisc_1(u1_struct_0(U_56),u1_struct_0(U_56)),u1_struct_0(U_56))
| ~ l2_lattices(U_56)
| ~ v4_lattices(U_56)
| v3_struct_0(U_56) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [A] :
( ( v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v2_binop_1(u2_lattices(A),u1_struct_0(A))
& v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u2_lattices(A))
& v1_relat_1(u2_lattices(A)) )
| ~ l2_lattices(A)
| ~ v5_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc3_lattice2]) ).
fof(f_45_2,plain,
! [U_57] :
( ( v1_partfun1(u2_lattices(U_57),k2_zfmisc_1(u1_struct_0(U_57),u1_struct_0(U_57)),u1_struct_0(U_57))
& v2_binop_1(u2_lattices(U_57),u1_struct_0(U_57))
& v1_funct_2(u2_lattices(U_57),k2_zfmisc_1(u1_struct_0(U_57),u1_struct_0(U_57)),u1_struct_0(U_57))
& v1_funct_1(u2_lattices(U_57))
& v1_relat_1(u2_lattices(U_57)) )
| ~ l2_lattices(U_57)
| ~ v5_lattices(U_57)
| v3_struct_0(U_57) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( v1_relat_1(u2_lattices(U_57))
| ~ l2_lattices(U_57)
| ~ v5_lattices(U_57)
| v3_struct_0(U_57) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
( v1_funct_1(u2_lattices(U_57))
| ~ l2_lattices(U_57)
| ~ v5_lattices(U_57)
| v3_struct_0(U_57) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_5,plain,
( v1_funct_2(u2_lattices(U_57),k2_zfmisc_1(u1_struct_0(U_57),u1_struct_0(U_57)),u1_struct_0(U_57))
| ~ l2_lattices(U_57)
| ~ v5_lattices(U_57)
| v3_struct_0(U_57) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_6,plain,
( v2_binop_1(u2_lattices(U_57),u1_struct_0(U_57))
| ~ l2_lattices(U_57)
| ~ v5_lattices(U_57)
| v3_struct_0(U_57) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_7,plain,
( v1_partfun1(u2_lattices(U_57),k2_zfmisc_1(u1_struct_0(U_57),u1_struct_0(U_57)),u1_struct_0(U_57))
| ~ l2_lattices(U_57)
| ~ v5_lattices(U_57)
| v3_struct_0(U_57) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [A,B,C] :
( ( v3_lattices(g3_lattices(A,B,C))
& ~ v3_struct_0(g3_lattices(A,B,C)) )
| ~ m1_relset_1(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(C)
| ~ m1_relset_1(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(B)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[fc3_lattices]) ).
fof(f_46_2,plain,
! [U_60,U_59,U_58] :
( ( v3_lattices(g3_lattices(U_60,U_59,U_58))
& ~ v3_struct_0(g3_lattices(U_60,U_59,U_58)) )
| ~ m1_relset_1(U_58,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_2(U_58,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_1(U_58)
| ~ m1_relset_1(U_59,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_2(U_59,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_1(U_59)
| v1_xboole_0(U_60) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( ~ v3_struct_0(g3_lattices(U_60,U_59,U_58))
| ~ m1_relset_1(U_58,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_2(U_58,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_1(U_58)
| ~ m1_relset_1(U_59,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_2(U_59,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_1(U_59)
| v1_xboole_0(U_60) ),
inference(clausify,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( v3_lattices(g3_lattices(U_60,U_59,U_58))
| ~ m1_relset_1(U_58,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_2(U_58,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_1(U_58)
| ~ m1_relset_1(U_59,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_2(U_59,k2_zfmisc_1(U_60,U_60),U_60)
| ~ v1_funct_1(U_59)
| v1_xboole_0(U_60) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [A] :
( ( v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_binop_1(u1_lattices(A),u1_struct_0(A))
& v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_lattices(A))
& v1_relat_1(u1_lattices(A)) )
| ~ l1_lattices(A)
| ~ v6_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc4_lattice2]) ).
fof(f_47_2,plain,
! [U_61] :
( ( v1_partfun1(u1_lattices(U_61),k2_zfmisc_1(u1_struct_0(U_61),u1_struct_0(U_61)),u1_struct_0(U_61))
& v1_binop_1(u1_lattices(U_61),u1_struct_0(U_61))
& v1_funct_2(u1_lattices(U_61),k2_zfmisc_1(u1_struct_0(U_61),u1_struct_0(U_61)),u1_struct_0(U_61))
& v1_funct_1(u1_lattices(U_61))
& v1_relat_1(u1_lattices(U_61)) )
| ~ l1_lattices(U_61)
| ~ v6_lattices(U_61)
| v3_struct_0(U_61) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( v1_relat_1(u1_lattices(U_61))
| ~ l1_lattices(U_61)
| ~ v6_lattices(U_61)
| v3_struct_0(U_61) ),
inference(clausify,[status(thm)],[f_47_2]) ).
cnf(f_47_4,plain,
( v1_funct_1(u1_lattices(U_61))
| ~ l1_lattices(U_61)
| ~ v6_lattices(U_61)
| v3_struct_0(U_61) ),
inference(clausify,[status(thm)],[f_47_2]) ).
cnf(f_47_5,plain,
( v1_funct_2(u1_lattices(U_61),k2_zfmisc_1(u1_struct_0(U_61),u1_struct_0(U_61)),u1_struct_0(U_61))
| ~ l1_lattices(U_61)
| ~ v6_lattices(U_61)
| v3_struct_0(U_61) ),
inference(clausify,[status(thm)],[f_47_2]) ).
cnf(f_47_6,plain,
( v1_binop_1(u1_lattices(U_61),u1_struct_0(U_61))
| ~ l1_lattices(U_61)
| ~ v6_lattices(U_61)
| v3_struct_0(U_61) ),
inference(clausify,[status(thm)],[f_47_2]) ).
cnf(f_47_7,plain,
( v1_partfun1(u1_lattices(U_61),k2_zfmisc_1(u1_struct_0(U_61),u1_struct_0(U_61)),u1_struct_0(U_61))
| ~ l1_lattices(U_61)
| ~ v6_lattices(U_61)
| v3_struct_0(U_61) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_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_48_2,plain,
! [U_63,U_62] :
( ~ v1_xboole_0(k2_zfmisc_1(U_63,U_62))
| v1_xboole_0(U_62)
| v1_xboole_0(U_63) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( ~ v1_xboole_0(k2_zfmisc_1(U_63,U_62))
| v1_xboole_0(U_62)
| v1_xboole_0(U_63) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
! [A,B] :
( ( v10_lattices(k23_filter_2(A,B))
& v9_lattices(k23_filter_2(A,B))
& v8_lattices(k23_filter_2(A,B))
& v7_lattices(k23_filter_2(A,B))
& v6_lattices(k23_filter_2(A,B))
& v5_lattices(k23_filter_2(A,B))
& v4_lattices(k23_filter_2(A,B))
& v3_lattices(k23_filter_2(A,B))
& ~ v3_struct_0(k23_filter_2(A,B)) )
| ~ m2_lattice4(B,A)
| v1_xboole_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc5_filter_2]) ).
fof(f_49_2,plain,
! [U_65,U_64] :
( ( v10_lattices(k23_filter_2(U_65,U_64))
& v9_lattices(k23_filter_2(U_65,U_64))
& v8_lattices(k23_filter_2(U_65,U_64))
& v7_lattices(k23_filter_2(U_65,U_64))
& v6_lattices(k23_filter_2(U_65,U_64))
& v5_lattices(k23_filter_2(U_65,U_64))
& v4_lattices(k23_filter_2(U_65,U_64))
& v3_lattices(k23_filter_2(U_65,U_64))
& ~ v3_struct_0(k23_filter_2(U_65,U_64)) )
| ~ m2_lattice4(U_64,U_65)
| v1_xboole_0(U_64)
| ~ l3_lattices(U_65)
| ~ v10_lattices(U_65)
| v3_struct_0(U_65) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( ~ v3_struct_0(k23_filter_2(U_65,U_64))
| ~ m2_lattice4(U_64,U_65)
| v1_xboole_0(U_64)
| ~ l3_lattices(U_65)
| ~ v10_lattices(U_65)
| v3_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
( v3_lattices(k23_filter_2(U_65,U_64))
| ~ m2_lattice4(U_64,U_65)
| v1_xboole_0(U_64)
| ~ l3_lattices(U_65)
| ~ v10_lattices(U_65)
| v3_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_5,plain,
( v4_lattices(k23_filter_2(U_65,U_64))
| ~ m2_lattice4(U_64,U_65)
| v1_xboole_0(U_64)
| ~ l3_lattices(U_65)
| ~ v10_lattices(U_65)
| v3_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_6,plain,
( v5_lattices(k23_filter_2(U_65,U_64))
| ~ m2_lattice4(U_64,U_65)
| v1_xboole_0(U_64)
| ~ l3_lattices(U_65)
| ~ v10_lattices(U_65)
| v3_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_7,plain,
( v6_lattices(k23_filter_2(U_65,U_64))
| ~ m2_lattice4(U_64,U_65)
| v1_xboole_0(U_64)
| ~ l3_lattices(U_65)
| ~ v10_lattices(U_65)
| v3_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_8,plain,
( v7_lattices(k23_filter_2(U_65,U_64))
| ~ m2_lattice4(U_64,U_65)
| v1_xboole_0(U_64)
| ~ l3_lattices(U_65)
| ~ v10_lattices(U_65)
| v3_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_9,plain,
( v8_lattices(k23_filter_2(U_65,U_64))
| ~ m2_lattice4(U_64,U_65)
| v1_xboole_0(U_64)
| ~ l3_lattices(U_65)
| ~ v10_lattices(U_65)
| v3_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_10,plain,
( v9_lattices(k23_filter_2(U_65,U_64))
| ~ m2_lattice4(U_64,U_65)
| v1_xboole_0(U_64)
| ~ l3_lattices(U_65)
| ~ v10_lattices(U_65)
| v3_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_11,plain,
( v10_lattices(k23_filter_2(U_65,U_64))
| ~ m2_lattice4(U_64,U_65)
| v1_xboole_0(U_64)
| ~ l3_lattices(U_65)
| ~ v10_lattices(U_65)
| v3_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [A] :
( ( v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v2_binop_1(u1_lattices(A),u1_struct_0(A))
& v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_lattices(A))
& v1_relat_1(u1_lattices(A)) )
| ~ l1_lattices(A)
| ~ v7_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc5_lattice2]) ).
fof(f_50_2,plain,
! [U_66] :
( ( v1_partfun1(u1_lattices(U_66),k2_zfmisc_1(u1_struct_0(U_66),u1_struct_0(U_66)),u1_struct_0(U_66))
& v2_binop_1(u1_lattices(U_66),u1_struct_0(U_66))
& v1_funct_2(u1_lattices(U_66),k2_zfmisc_1(u1_struct_0(U_66),u1_struct_0(U_66)),u1_struct_0(U_66))
& v1_funct_1(u1_lattices(U_66))
& v1_relat_1(u1_lattices(U_66)) )
| ~ l1_lattices(U_66)
| ~ v7_lattices(U_66)
| v3_struct_0(U_66) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( v1_relat_1(u1_lattices(U_66))
| ~ l1_lattices(U_66)
| ~ v7_lattices(U_66)
| v3_struct_0(U_66) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_4,plain,
( v1_funct_1(u1_lattices(U_66))
| ~ l1_lattices(U_66)
| ~ v7_lattices(U_66)
| v3_struct_0(U_66) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_5,plain,
( v1_funct_2(u1_lattices(U_66),k2_zfmisc_1(u1_struct_0(U_66),u1_struct_0(U_66)),u1_struct_0(U_66))
| ~ l1_lattices(U_66)
| ~ v7_lattices(U_66)
| v3_struct_0(U_66) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_6,plain,
( v2_binop_1(u1_lattices(U_66),u1_struct_0(U_66))
| ~ l1_lattices(U_66)
| ~ v7_lattices(U_66)
| v3_struct_0(U_66) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_7,plain,
( v1_partfun1(u1_lattices(U_66),k2_zfmisc_1(u1_struct_0(U_66),u1_struct_0(U_66)),u1_struct_0(U_66))
| ~ l1_lattices(U_66)
| ~ v7_lattices(U_66)
| v3_struct_0(U_66) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [A,B,C] :
( ! [D,E,F] :
( ( C = F
& B = E
& A = D )
| g3_lattices(A,B,C) != g3_lattices(D,E,F) )
| ~ m1_relset_1(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(C)
| ~ m1_relset_1(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(B) ),
inference(fof_nnf,[status(thm)],[free_g3_lattices]) ).
fof(f_51_2,plain,
! [U_72,U_71,U_70] :
( ! [U_69,U_68,U_67] :
( ( U_70 = U_67
& U_71 = U_68
& U_72 = U_69 )
| g3_lattices(U_72,U_71,U_70) != g3_lattices(U_69,U_68,U_67) )
| ~ m1_relset_1(U_70,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_70,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_70)
| ~ m1_relset_1(U_71,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_71,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_71) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( U_72 = U_69
| g3_lattices(U_72,U_71,U_70) != g3_lattices(U_69,U_68,U_67)
| ~ m1_relset_1(U_70,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_70,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_70)
| ~ m1_relset_1(U_71,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_71,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_71) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
( U_71 = U_68
| g3_lattices(U_72,U_71,U_70) != g3_lattices(U_69,U_68,U_67)
| ~ m1_relset_1(U_70,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_70,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_70)
| ~ m1_relset_1(U_71,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_71,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_71) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_5,plain,
( U_70 = U_67
| g3_lattices(U_72,U_71,U_70) != g3_lattices(U_69,U_68,U_67)
| ~ m1_relset_1(U_70,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_70,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_70)
| ~ m1_relset_1(U_71,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_71,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_71) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
? [A] :
( v14_lattices(A)
& v13_lattices(A)
& v12_lattices(A)
& v11_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[rc10_lattices]) ).
fof(f_52_2,plain,
? [U_73] :
( v14_lattices(U_73)
& v13_lattices(U_73)
& v12_lattices(U_73)
& v11_lattices(U_73)
& v10_lattices(U_73)
& v9_lattices(U_73)
& v8_lattices(U_73)
& v7_lattices(U_73)
& v6_lattices(U_73)
& v5_lattices(U_73)
& v4_lattices(U_73)
& v3_lattices(U_73)
& ~ v3_struct_0(U_73)
& l3_lattices(U_73) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( v14_lattices(sK13)
& v13_lattices(sK13)
& v12_lattices(sK13)
& v11_lattices(sK13)
& v10_lattices(sK13)
& v9_lattices(sK13)
& v8_lattices(sK13)
& v7_lattices(sK13)
& v6_lattices(sK13)
& v5_lattices(sK13)
& v4_lattices(sK13)
& v3_lattices(sK13)
& ~ v3_struct_0(sK13)
& l3_lattices(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_73,sK13)],[f_52_2]) ).
cnf(f_52_4,plain,
l3_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
~ v3_struct_0(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_6,plain,
v3_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_7,plain,
v4_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_8,plain,
v5_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_9,plain,
v6_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_10,plain,
v7_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_11,plain,
v8_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_12,plain,
v9_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_13,plain,
v10_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_14,plain,
v11_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_15,plain,
v12_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_16,plain,
v13_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_17,plain,
v14_lattices(sK13),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
? [A] :
( v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[rc11_lattices]) ).
fof(f_53_2,plain,
? [U_74] :
( v15_lattices(U_74)
& v14_lattices(U_74)
& v13_lattices(U_74)
& v10_lattices(U_74)
& v9_lattices(U_74)
& v8_lattices(U_74)
& v7_lattices(U_74)
& v6_lattices(U_74)
& v5_lattices(U_74)
& v4_lattices(U_74)
& v3_lattices(U_74)
& ~ v3_struct_0(U_74)
& l3_lattices(U_74) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( v15_lattices(sK14)
& v14_lattices(sK14)
& v13_lattices(sK14)
& v10_lattices(sK14)
& v9_lattices(sK14)
& v8_lattices(sK14)
& v7_lattices(sK14)
& v6_lattices(sK14)
& v5_lattices(sK14)
& v4_lattices(sK14)
& v3_lattices(sK14)
& ~ v3_struct_0(sK14)
& l3_lattices(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_74,sK14)],[f_53_2]) ).
cnf(f_53_4,plain,
l3_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_5,plain,
~ v3_struct_0(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_6,plain,
v3_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_7,plain,
v4_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_8,plain,
v5_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_9,plain,
v6_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_10,plain,
v7_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_11,plain,
v8_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_12,plain,
v9_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_13,plain,
v10_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_14,plain,
v13_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_15,plain,
v14_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_16,plain,
v15_lattices(sK14),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
? [A] :
( v16_lattices(A)
& v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[rc12_lattices]) ).
fof(f_54_2,plain,
? [U_75] :
( v16_lattices(U_75)
& v15_lattices(U_75)
& v14_lattices(U_75)
& v13_lattices(U_75)
& v10_lattices(U_75)
& v9_lattices(U_75)
& v8_lattices(U_75)
& v7_lattices(U_75)
& v6_lattices(U_75)
& v5_lattices(U_75)
& v4_lattices(U_75)
& v3_lattices(U_75)
& ~ v3_struct_0(U_75)
& l3_lattices(U_75) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( v16_lattices(sK15)
& v15_lattices(sK15)
& v14_lattices(sK15)
& v13_lattices(sK15)
& v10_lattices(sK15)
& v9_lattices(sK15)
& v8_lattices(sK15)
& v7_lattices(sK15)
& v6_lattices(sK15)
& v5_lattices(sK15)
& v4_lattices(sK15)
& v3_lattices(sK15)
& ~ v3_struct_0(sK15)
& l3_lattices(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_75,sK15)],[f_54_2]) ).
cnf(f_54_4,plain,
l3_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_5,plain,
~ v3_struct_0(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_6,plain,
v3_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_7,plain,
v4_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_8,plain,
v5_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_9,plain,
v6_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_10,plain,
v7_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_11,plain,
v8_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_12,plain,
v9_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_13,plain,
v10_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_14,plain,
v13_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_15,plain,
v14_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_16,plain,
v15_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_17,plain,
v16_lattices(sK15),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
? [A] :
( v17_lattices(A)
& v16_lattices(A)
& v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v11_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[rc13_lattices]) ).
fof(f_55_2,plain,
? [U_76] :
( v17_lattices(U_76)
& v16_lattices(U_76)
& v15_lattices(U_76)
& v14_lattices(U_76)
& v13_lattices(U_76)
& v11_lattices(U_76)
& v10_lattices(U_76)
& v9_lattices(U_76)
& v8_lattices(U_76)
& v7_lattices(U_76)
& v6_lattices(U_76)
& v5_lattices(U_76)
& v4_lattices(U_76)
& v3_lattices(U_76)
& ~ v3_struct_0(U_76)
& l3_lattices(U_76) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( v17_lattices(sK16)
& v16_lattices(sK16)
& v15_lattices(sK16)
& v14_lattices(sK16)
& v13_lattices(sK16)
& v11_lattices(sK16)
& v10_lattices(sK16)
& v9_lattices(sK16)
& v8_lattices(sK16)
& v7_lattices(sK16)
& v6_lattices(sK16)
& v5_lattices(sK16)
& v4_lattices(sK16)
& v3_lattices(sK16)
& ~ v3_struct_0(sK16)
& l3_lattices(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_76,sK16)],[f_55_2]) ).
cnf(f_55_4,plain,
l3_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_5,plain,
~ v3_struct_0(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_6,plain,
v3_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_7,plain,
v4_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_8,plain,
v5_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_9,plain,
v6_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_10,plain,
v7_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_11,plain,
v8_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_12,plain,
v9_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_13,plain,
v10_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_14,plain,
v11_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_15,plain,
v13_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_16,plain,
v14_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_17,plain,
v15_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_18,plain,
v16_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_19,plain,
v17_lattices(sK16),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_56_2,plain,
? [U_77] :
( v1_funct_1(U_77)
& v1_relat_1(U_77) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( v1_funct_1(sK17)
& v1_relat_1(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_77,sK17)],[f_56_2]) ).
cnf(f_56_4,plain,
v1_relat_1(sK17),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
v1_funct_1(sK17),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m2_lattice4(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_lattice4]) ).
fof(f_57_2,plain,
! [U_79] :
( ? [U_78] :
( ~ v1_xboole_0(U_78)
& m2_lattice4(U_78,U_79) )
| ~ l3_lattices(U_79)
| ~ v10_lattices(U_79)
| v3_struct_0(U_79) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_79] :
( ( ~ v1_xboole_0(sK18(U_79))
& m2_lattice4(sK18(U_79),U_79) )
| ~ l3_lattices(U_79)
| ~ v10_lattices(U_79)
| v3_struct_0(U_79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_78,sK18(U_79))],[f_57_2]) ).
cnf(f_57_4,plain,
( m2_lattice4(sK18(U_79),U_79)
| ~ l3_lattices(U_79)
| ~ v10_lattices(U_79)
| v3_struct_0(U_79) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
( ~ v1_xboole_0(sK18(U_79))
| ~ l3_lattices(U_79)
| ~ v10_lattices(U_79)
| v3_struct_0(U_79) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A] :
( ? [B] :
( v10_lattices(B)
& v9_lattices(B)
& v8_lattices(B)
& v7_lattices(B)
& v6_lattices(B)
& v5_lattices(B)
& v4_lattices(B)
& v3_lattices(B)
& ~ v3_struct_0(B)
& m2_nat_lat(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_nat_lat]) ).
fof(f_58_2,plain,
! [U_81] :
( ? [U_80] :
( v10_lattices(U_80)
& v9_lattices(U_80)
& v8_lattices(U_80)
& v7_lattices(U_80)
& v6_lattices(U_80)
& v5_lattices(U_80)
& v4_lattices(U_80)
& v3_lattices(U_80)
& ~ v3_struct_0(U_80)
& m2_nat_lat(U_80,U_81) )
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_81] :
( ( v10_lattices(sK19(U_81))
& v9_lattices(sK19(U_81))
& v8_lattices(sK19(U_81))
& v7_lattices(sK19(U_81))
& v6_lattices(sK19(U_81))
& v5_lattices(sK19(U_81))
& v4_lattices(sK19(U_81))
& v3_lattices(sK19(U_81))
& ~ v3_struct_0(sK19(U_81))
& m2_nat_lat(sK19(U_81),U_81) )
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_80,sK19(U_81))],[f_58_2]) ).
cnf(f_58_4,plain,
( m2_nat_lat(sK19(U_81),U_81)
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
( ~ v3_struct_0(sK19(U_81))
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_6,plain,
( v3_lattices(sK19(U_81))
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_7,plain,
( v4_lattices(sK19(U_81))
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_8,plain,
( v5_lattices(sK19(U_81))
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_9,plain,
( v6_lattices(sK19(U_81))
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_10,plain,
( v7_lattices(sK19(U_81))
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_11,plain,
( v8_lattices(sK19(U_81))
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_12,plain,
( v9_lattices(sK19(U_81))
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_13,plain,
( v10_lattices(sK19(U_81))
| ~ l3_lattices(U_81)
| ~ v10_lattices(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_59_2,plain,
! [U_83] :
( ? [U_82] :
( ~ v1_xboole_0(U_82)
& m1_subset_1(U_82,k1_zfmisc_1(U_83)) )
| v1_xboole_0(U_83) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_83] :
( ( ~ v1_xboole_0(sK20(U_83))
& m1_subset_1(sK20(U_83),k1_zfmisc_1(U_83)) )
| v1_xboole_0(U_83) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_82,sK20(U_83))],[f_59_2]) ).
cnf(f_59_4,plain,
( m1_subset_1(sK20(U_83),k1_zfmisc_1(U_83))
| v1_xboole_0(U_83) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_5,plain,
( ~ v1_xboole_0(sK20(U_83))
| v1_xboole_0(U_83) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_60_2,plain,
? [U_84] : v1_xboole_0(U_84),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
v1_xboole_0(sK21),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_84,sK21)],[f_60_2]) ).
cnf(f_60_4,plain,
v1_xboole_0(sK21),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_61_2,plain,
? [U_85] :
( v1_funct_1(U_85)
& v1_xboole_0(U_85)
& v1_relat_1(U_85) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( v1_funct_1(sK22)
& v1_xboole_0(sK22)
& v1_relat_1(sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_85,sK22)],[f_61_2]) ).
cnf(f_61_4,plain,
v1_relat_1(sK22),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_5,plain,
v1_xboole_0(sK22),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_6,plain,
v1_funct_1(sK22),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_62_2,plain,
! [U_87] :
? [U_86] :
( v1_xboole_0(U_86)
& m1_subset_1(U_86,k1_zfmisc_1(U_87)) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_87] :
( v1_xboole_0(sK23(U_87))
& m1_subset_1(sK23(U_87),k1_zfmisc_1(U_87)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_86,sK23(U_87))],[f_62_2]) ).
cnf(f_62_4,plain,
m1_subset_1(sK23(U_87),k1_zfmisc_1(U_87)),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_5,plain,
v1_xboole_0(sK23(U_87)),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_63_2,plain,
? [U_88] : ~ v1_xboole_0(U_88),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
~ v1_xboole_0(sK24),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_88,sK24)],[f_63_2]) ).
cnf(f_63_4,plain,
~ v1_xboole_0(sK24),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
? [A] :
( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_64_2,plain,
? [U_89] :
( v2_funct_1(U_89)
& v1_funct_1(U_89)
& v1_relat_1(U_89) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( v2_funct_1(sK25)
& v1_funct_1(sK25)
& v1_relat_1(sK25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_89,sK25)],[f_64_2]) ).
cnf(f_64_4,plain,
v1_relat_1(sK25),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_5,plain,
v1_funct_1(sK25),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_6,plain,
v2_funct_1(sK25),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
? [A] :
( v3_lattices(A)
& l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[rc3_lattices]) ).
fof(f_65_2,plain,
? [U_90] :
( v3_lattices(U_90)
& l3_lattices(U_90) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
( v3_lattices(sK26)
& l3_lattices(sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_90,sK26)],[f_65_2]) ).
cnf(f_65_4,plain,
l3_lattices(sK26),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_65_5,plain,
v3_lattices(sK26),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_66_2,plain,
? [U_91] :
( ~ v3_struct_0(U_91)
& l1_struct_0(U_91) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
( ~ v3_struct_0(sK27)
& l1_struct_0(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_91,sK27)],[f_66_2]) ).
cnf(f_66_4,plain,
l1_struct_0(sK27),
inference(clausify,[status(thm)],[f_66_3]) ).
cnf(f_66_5,plain,
~ v3_struct_0(sK27),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_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_67_2,plain,
! [U_93] :
( ? [U_92] :
( ~ v1_xboole_0(U_92)
& m1_subset_1(U_92,k1_zfmisc_1(u1_struct_0(U_93))) )
| ~ l1_struct_0(U_93)
| v3_struct_0(U_93) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_93] :
( ( ~ v1_xboole_0(sK28(U_93))
& m1_subset_1(sK28(U_93),k1_zfmisc_1(u1_struct_0(U_93))) )
| ~ l1_struct_0(U_93)
| v3_struct_0(U_93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_92,sK28(U_93))],[f_67_2]) ).
cnf(f_67_4,plain,
( m1_subset_1(sK28(U_93),k1_zfmisc_1(u1_struct_0(U_93)))
| ~ l1_struct_0(U_93)
| v3_struct_0(U_93) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_5,plain,
( ~ v1_xboole_0(sK28(U_93))
| ~ l1_struct_0(U_93)
| v3_struct_0(U_93) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
? [A] :
( v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[rc6_lattices]) ).
fof(f_68_2,plain,
? [U_94] :
( v3_lattices(U_94)
& ~ v3_struct_0(U_94)
& l3_lattices(U_94) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
( v3_lattices(sK29)
& ~ v3_struct_0(sK29)
& l3_lattices(sK29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_94,sK29)],[f_68_2]) ).
cnf(f_68_4,plain,
l3_lattices(sK29),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_5,plain,
~ v3_struct_0(sK29),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_6,plain,
v3_lattices(sK29),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
? [A] :
( v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[rc9_lattices]) ).
fof(f_69_2,plain,
? [U_95] :
( v10_lattices(U_95)
& v9_lattices(U_95)
& v8_lattices(U_95)
& v7_lattices(U_95)
& v6_lattices(U_95)
& v5_lattices(U_95)
& v4_lattices(U_95)
& v3_lattices(U_95)
& ~ v3_struct_0(U_95)
& l3_lattices(U_95) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
( v10_lattices(sK30)
& v9_lattices(sK30)
& v8_lattices(sK30)
& v7_lattices(sK30)
& v6_lattices(sK30)
& v5_lattices(sK30)
& v4_lattices(sK30)
& v3_lattices(sK30)
& ~ v3_struct_0(sK30)
& l3_lattices(sK30) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_95,sK30)],[f_69_2]) ).
cnf(f_69_4,plain,
l3_lattices(sK30),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_5,plain,
~ v3_struct_0(sK30),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_6,plain,
v3_lattices(sK30),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_7,plain,
v4_lattices(sK30),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_8,plain,
v5_lattices(sK30),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_9,plain,
v6_lattices(sK30),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_10,plain,
v7_lattices(sK30),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_11,plain,
v8_lattices(sK30),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_12,plain,
v9_lattices(sK30),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_13,plain,
v10_lattices(sK30),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_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_70_2,plain,
! [U_98,U_97,U_96] :
( ( m2_relset_1(U_96,U_98,U_97)
| ~ m1_relset_1(U_96,U_98,U_97) )
& ( m1_relset_1(U_96,U_98,U_97)
| ~ m2_relset_1(U_96,U_98,U_97) ) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
( ! [U_104,U_102,U_100] :
( m2_relset_1(U_100,U_104,U_102)
| ~ m1_relset_1(U_100,U_104,U_102) )
& ! [U_103,U_101,U_99] :
( m1_relset_1(U_99,U_103,U_101)
| ~ m2_relset_1(U_99,U_103,U_101) ) ),
inference(miniscope,[status(thm)],[f_70_2]) ).
cnf(f_70_4,plain,
( m1_relset_1(U_99,U_103,U_101)
| ~ m2_relset_1(U_99,U_103,U_101) ),
inference(clausify,[status(thm)],[f_70_3]) ).
cnf(f_70_5,plain,
( m2_relset_1(U_100,U_104,U_102)
| ~ m1_relset_1(U_100,U_104,U_102) ),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_1,plain,
! [A,B,C] :
( ( ( r3_lattices(A,B,C)
| ~ r1_lattices(A,B,C) )
& ( r1_lattices(A,B,C)
| ~ r3_lattices(A,B,C) ) )
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v9_lattices(A)
| ~ v8_lattices(A)
| ~ v6_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r3_lattices]) ).
fof(f_71_2,plain,
! [U_107,U_106,U_105] :
( ( ( r3_lattices(U_107,U_106,U_105)
| ~ r1_lattices(U_107,U_106,U_105) )
& ( r1_lattices(U_107,U_106,U_105)
| ~ r3_lattices(U_107,U_106,U_105) ) )
| ~ m1_subset_1(U_105,u1_struct_0(U_107))
| ~ m1_subset_1(U_106,u1_struct_0(U_107))
| ~ l3_lattices(U_107)
| ~ v9_lattices(U_107)
| ~ v8_lattices(U_107)
| ~ v6_lattices(U_107)
| v3_struct_0(U_107) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( r1_lattices(U_107,U_106,U_105)
| ~ r3_lattices(U_107,U_106,U_105)
| ~ m1_subset_1(U_105,u1_struct_0(U_107))
| ~ m1_subset_1(U_106,u1_struct_0(U_107))
| ~ l3_lattices(U_107)
| ~ v9_lattices(U_107)
| ~ v8_lattices(U_107)
| ~ v6_lattices(U_107)
| v3_struct_0(U_107) ),
inference(clausify,[status(thm)],[f_71_2]) ).
cnf(f_71_4,plain,
( r3_lattices(U_107,U_106,U_105)
| ~ r1_lattices(U_107,U_106,U_105)
| ~ m1_subset_1(U_105,u1_struct_0(U_107))
| ~ m1_subset_1(U_106,u1_struct_0(U_107))
| ~ l3_lattices(U_107)
| ~ v9_lattices(U_107)
| ~ v8_lattices(U_107)
| ~ v6_lattices(U_107)
| v3_struct_0(U_107) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_72_2,plain,
! [U_109,U_108] : r1_tarski(U_109,U_109),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_109] : r1_tarski(U_109,U_109),
inference(miniscope,[status(thm)],[f_72_2]) ).
cnf(f_72_4,plain,
r1_tarski(U_109,U_109),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_1,plain,
! [A,B,C] :
( r3_lattices(A,B,B)
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v9_lattices(A)
| ~ v8_lattices(A)
| ~ v6_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r3_lattices]) ).
fof(f_73_2,plain,
! [U_112,U_111,U_110] :
( r3_lattices(U_112,U_111,U_111)
| ~ m1_subset_1(U_110,u1_struct_0(U_112))
| ~ m1_subset_1(U_111,u1_struct_0(U_112))
| ~ l3_lattices(U_112)
| ~ v9_lattices(U_112)
| ~ v8_lattices(U_112)
| ~ v6_lattices(U_112)
| v3_struct_0(U_112) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_112,U_111] :
( ! [U_110] : ~ m1_subset_1(U_110,u1_struct_0(U_112))
| ~ m1_subset_1(U_111,u1_struct_0(U_112))
| ~ l3_lattices(U_112)
| ~ v9_lattices(U_112)
| ~ v8_lattices(U_112)
| ~ v6_lattices(U_112)
| v3_struct_0(U_112)
| r3_lattices(U_112,U_111,U_111) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
cnf(f_73_4,plain,
( ~ m1_subset_1(U_110,u1_struct_0(U_112))
| ~ m1_subset_1(U_111,u1_struct_0(U_112))
| ~ l3_lattices(U_112)
| ~ v9_lattices(U_112)
| ~ v8_lattices(U_112)
| ~ v6_lattices(U_112)
| v3_struct_0(U_112)
| r3_lattices(U_112,U_111,U_111) ),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_74_2,plain,
! [U_114,U_113] :
( m1_subset_1(U_114,U_113)
| ~ r2_hidden(U_114,U_113) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( m1_subset_1(U_114,U_113)
| ~ r2_hidden(U_114,U_113) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_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_75_2,plain,
! [U_116,U_115] :
( r2_hidden(U_116,U_115)
| v1_xboole_0(U_115)
| ~ m1_subset_1(U_116,U_115) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( r2_hidden(U_116,U_115)
| v1_xboole_0(U_115)
| ~ m1_subset_1(U_116,U_115) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_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_76_2,plain,
! [U_118,U_117] :
( ( m1_subset_1(U_118,k1_zfmisc_1(U_117))
| ~ r1_tarski(U_118,U_117) )
& ( r1_tarski(U_118,U_117)
| ~ m1_subset_1(U_118,k1_zfmisc_1(U_117)) ) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
( ! [U_122,U_120] :
( m1_subset_1(U_122,k1_zfmisc_1(U_120))
| ~ r1_tarski(U_122,U_120) )
& ! [U_121,U_119] :
( r1_tarski(U_121,U_119)
| ~ m1_subset_1(U_121,k1_zfmisc_1(U_119)) ) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
cnf(f_76_4,plain,
( r1_tarski(U_121,U_119)
| ~ m1_subset_1(U_121,k1_zfmisc_1(U_119)) ),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_5,plain,
( m1_subset_1(U_122,k1_zfmisc_1(U_120))
| ~ r1_tarski(U_122,U_120) ),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_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_77_2,plain,
! [U_125,U_124,U_123] :
( m1_subset_1(U_125,U_123)
| ~ m1_subset_1(U_124,k1_zfmisc_1(U_123))
| ~ r2_hidden(U_125,U_124) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( m1_subset_1(U_125,U_123)
| ~ m1_subset_1(U_124,k1_zfmisc_1(U_123))
| ~ r2_hidden(U_125,U_124) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_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_78_2,plain,
! [U_128,U_127,U_126] :
( ~ v1_xboole_0(U_126)
| ~ m1_subset_1(U_127,k1_zfmisc_1(U_126))
| ~ r2_hidden(U_128,U_127) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_128,U_127] :
( ! [U_126] :
( ~ v1_xboole_0(U_126)
| ~ m1_subset_1(U_127,k1_zfmisc_1(U_126)) )
| ~ r2_hidden(U_128,U_127) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
cnf(f_78_4,plain,
( ~ v1_xboole_0(U_126)
| ~ m1_subset_1(U_127,k1_zfmisc_1(U_126))
| ~ r2_hidden(U_128,U_127) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_79_2,plain,
! [U_129] :
( U_129 = k1_xboole_0
| ~ v1_xboole_0(U_129) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( U_129 = k1_xboole_0
| ~ v1_xboole_0(U_129) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [A] :
( ! [B] :
( v11_lattices(k23_filter_2(A,B))
| ~ v11_lattices(A)
| ~ m2_lattice4(B,A)
| v1_xboole_0(B) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t78_filter_2]) ).
fof(f_80_2,plain,
! [U_131] :
( ! [U_130] :
( v11_lattices(k23_filter_2(U_131,U_130))
| ~ v11_lattices(U_131)
| ~ m2_lattice4(U_130,U_131)
| v1_xboole_0(U_130) )
| ~ l3_lattices(U_131)
| ~ v10_lattices(U_131)
| v3_struct_0(U_131) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( v11_lattices(k23_filter_2(U_131,U_130))
| ~ v11_lattices(U_131)
| ~ m2_lattice4(U_130,U_131)
| v1_xboole_0(U_130)
| ~ l3_lattices(U_131)
| ~ v10_lattices(U_131)
| v3_struct_0(U_131) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_81_2,plain,
! [U_133,U_132] :
( ~ v1_xboole_0(U_132)
| ~ r2_hidden(U_133,U_132) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( ~ v1_xboole_0(U_132)
| ~ r2_hidden(U_133,U_132) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v16_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v15_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& ~ v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C))) )
| ~ r3_lattices(A,B,C)
| ~ v12_lattices(A)
| ~ l3_lattices(A)
| ~ v16_lattices(A)
| ~ v15_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A)
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t86_filter_2]) ).
fof(f_82_2,plain,
! [U_136] :
( ! [U_135] :
( ! [U_134] :
( ( l3_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
& v16_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
& v15_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
& v10_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
& ~ v3_struct_0(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134))) )
| ~ r3_lattices(U_136,U_135,U_134)
| ~ v12_lattices(U_136)
| ~ l3_lattices(U_136)
| ~ v16_lattices(U_136)
| ~ v15_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136)
| ~ m1_subset_1(U_134,u1_struct_0(U_136)) )
| ~ m1_subset_1(U_135,u1_struct_0(U_136)) )
| ~ l3_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( ~ v3_struct_0(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
| ~ r3_lattices(U_136,U_135,U_134)
| ~ v12_lattices(U_136)
| ~ l3_lattices(U_136)
| ~ v16_lattices(U_136)
| ~ v15_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136)
| ~ m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_135,u1_struct_0(U_136))
| ~ l3_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136) ),
inference(clausify,[status(thm)],[f_82_2]) ).
cnf(f_82_4,plain,
( v10_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
| ~ r3_lattices(U_136,U_135,U_134)
| ~ v12_lattices(U_136)
| ~ l3_lattices(U_136)
| ~ v16_lattices(U_136)
| ~ v15_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136)
| ~ m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_135,u1_struct_0(U_136))
| ~ l3_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136) ),
inference(clausify,[status(thm)],[f_82_2]) ).
cnf(f_82_5,plain,
( v15_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
| ~ r3_lattices(U_136,U_135,U_134)
| ~ v12_lattices(U_136)
| ~ l3_lattices(U_136)
| ~ v16_lattices(U_136)
| ~ v15_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136)
| ~ m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_135,u1_struct_0(U_136))
| ~ l3_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136) ),
inference(clausify,[status(thm)],[f_82_2]) ).
cnf(f_82_6,plain,
( v16_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
| ~ r3_lattices(U_136,U_135,U_134)
| ~ v12_lattices(U_136)
| ~ l3_lattices(U_136)
| ~ v16_lattices(U_136)
| ~ v15_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136)
| ~ m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_135,u1_struct_0(U_136))
| ~ l3_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136) ),
inference(clausify,[status(thm)],[f_82_2]) ).
cnf(f_82_7,plain,
( l3_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
| ~ r3_lattices(U_136,U_135,U_134)
| ~ v12_lattices(U_136)
| ~ l3_lattices(U_136)
| ~ v16_lattices(U_136)
| ~ v15_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136)
| ~ m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_135,u1_struct_0(U_136))
| ~ l3_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_83_2,plain,
! [U_138,U_137] :
( ~ v1_xboole_0(U_137)
| U_138 = U_137
| ~ v1_xboole_0(U_138) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_138] :
( ! [U_137] :
( ~ v1_xboole_0(U_137)
| U_138 = U_137 )
| ~ v1_xboole_0(U_138) ),
inference(miniscope,[status(thm)],[f_83_2]) ).
cnf(f_83_4,plain,
( ~ v1_xboole_0(U_137)
| U_138 = U_137
| ~ v1_xboole_0(U_138) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_7_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_4]) ).
cnf(f_8_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_3]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_3]) ).
cnf(f_10_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_3]) ).
cnf(f_11_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_3]) ).
cnf(f_12_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_3]) ).
cnf(f_13_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_3]) ).
cnf(f_13_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_10]) ).
cnf(f_15_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_2]) ).
cnf(f_16_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_2]) ).
cnf(f_19_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_2]) ).
cnf(f_21_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_2]) ).
cnf(f_24_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_24_2]) ).
cnf(f_25_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_2]) ).
cnf(f_30_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_30_2]) ).
cnf(f_82_3_simplified,plain,
( ~ v3_struct_0(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
| ~ r3_lattices(U_136,U_135,U_134)
| ~ v12_lattices(U_136)
| ~ l3_lattices(U_136)
| ~ v16_lattices(U_136)
| ~ v15_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136)
| ~ m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_135,u1_struct_0(U_136)) ),
inference(simplify_clause,[status(thm)],[f_82_3]) ).
cnf(f_82_4_simplified,plain,
( v10_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
| ~ r3_lattices(U_136,U_135,U_134)
| ~ v12_lattices(U_136)
| ~ l3_lattices(U_136)
| ~ v16_lattices(U_136)
| ~ v15_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136)
| ~ m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_135,u1_struct_0(U_136)) ),
inference(simplify_clause,[status(thm)],[f_82_4]) ).
cnf(f_82_5_simplified,plain,
( v15_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
| ~ r3_lattices(U_136,U_135,U_134)
| ~ v12_lattices(U_136)
| ~ l3_lattices(U_136)
| ~ v16_lattices(U_136)
| ~ v15_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136)
| ~ m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_135,u1_struct_0(U_136)) ),
inference(simplify_clause,[status(thm)],[f_82_5]) ).
cnf(f_82_6_simplified,plain,
( v16_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
| ~ r3_lattices(U_136,U_135,U_134)
| ~ v12_lattices(U_136)
| ~ l3_lattices(U_136)
| ~ v16_lattices(U_136)
| ~ v15_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136)
| ~ m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_135,u1_struct_0(U_136)) ),
inference(simplify_clause,[status(thm)],[f_82_6]) ).
cnf(f_82_7_simplified,plain,
( l3_lattices(k23_filter_2(U_136,k22_filter_2(U_136,U_135,U_134)))
| ~ r3_lattices(U_136,U_135,U_134)
| ~ v12_lattices(U_136)
| ~ l3_lattices(U_136)
| ~ v16_lattices(U_136)
| ~ v15_lattices(U_136)
| ~ v10_lattices(U_136)
| v3_struct_0(U_136)
| ~ m1_subset_1(U_134,u1_struct_0(U_136))
| ~ m1_subset_1(U_135,u1_struct_0(U_136)) ),
inference(simplify_clause,[status(thm)],[f_82_7]) ).
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,
( k22_filter_2(Eq_x_0,Eq_x_1,Eq_x_2) = k22_filter_2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( k23_filter_2(Eq_x_0,Eq_x_1) = k23_filter_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_7,axiom,
( u2_lattices(Eq_x_0) = u2_lattices(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( u1_lattices(Eq_x_0) = u1_lattices(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( g3_lattices(Eq_x_0,Eq_x_1,Eq_x_2) = g3_lattices(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( 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_11,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_12,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK20(Eq_x_0) = sK20(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK28(Eq_x_0) = sK28(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,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_23,axiom,
( v10_lattices(Eq_y_0)
| ~ v10_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( l3_lattices(Eq_y_0)
| ~ l3_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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_26,axiom,
( v17_lattices(Eq_y_0)
| ~ v17_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( r3_lattices(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r3_lattices(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_28,axiom,
( v3_lattices(Eq_y_0)
| ~ v3_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,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_30,axiom,
( v1_xboole_0(Eq_y_0)
| ~ v1_xboole_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( v1_funct_1(Eq_y_0)
| ~ v1_funct_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( v4_lattices(Eq_y_0)
| ~ v4_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( v5_lattices(Eq_y_0)
| ~ v5_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( v6_lattices(Eq_y_0)
| ~ v6_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( v7_lattices(Eq_y_0)
| ~ v7_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( v8_lattices(Eq_y_0)
| ~ v8_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( v9_lattices(Eq_y_0)
| ~ v9_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,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_39,axiom,
( v2_funct_1(Eq_y_0)
| ~ v2_funct_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( v13_lattices(Eq_y_0)
| ~ v13_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( v14_lattices(Eq_y_0)
| ~ v14_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( v15_lattices(Eq_y_0)
| ~ v15_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( v11_lattices(Eq_y_0)
| ~ v11_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( v16_lattices(Eq_y_0)
| ~ v16_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( v12_lattices(Eq_y_0)
| ~ v12_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,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_47,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_48,axiom,
( m2_lattice4(Eq_y_0,Eq_y_1)
| ~ m2_lattice4(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( m2_nat_lat(Eq_y_0,Eq_y_1)
| ~ m2_nat_lat(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( l1_lattices(Eq_y_0)
| ~ l1_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,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_52,axiom,
( l2_lattices(Eq_y_0)
| ~ l2_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,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_54,axiom,
( v1_binop_1(Eq_y_0,Eq_y_1)
| ~ v1_binop_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_55,axiom,
( v1_partfun1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ v1_partfun1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( v2_binop_1(Eq_y_0,Eq_y_1)
| ~ v2_binop_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_57,axiom,
( r1_lattices(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r1_lattices(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( r1_tarski(Eq_y_0,Eq_y_1)
| ~ r1_tarski(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT337+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 13:28:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 183.06/183.39 % SZS status Theorem for theBenchmark
% 183.06/183.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------