%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LAT301+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:48:07 AM UTC 2026
% Result : Theorem 285.15s 285.42s
% Output : Proof 285.60s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t25_filter_2,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( v13_lattices(A)
=> r2_hidden(k5_lattices(A),B) ) ) ),
file('theBenchmark.p',t25_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(d2_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> k1_lattice2(A) = g3_lattices(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ),
file('theBenchmark.p',d2_lattice2) ).
fof(d6_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k7_filter_2(A,B) = B ) ),
file('theBenchmark.p',d6_filter_2) ).
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_k15_filter_2,axiom,
! [A,B] :
( ( m2_filter_2(B,A)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> m1_filter_2(k15_filter_2(A,B),k1_lattice2(A)) ),
file('theBenchmark.p',dt_k15_filter_2) ).
fof(dt_k1_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> ( l3_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) ) ),
file('theBenchmark.p',dt_k1_lattice2) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k5_lattices,axiom,
! [A] :
( ( l1_lattices(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k5_lattices(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k5_lattices) ).
fof(dt_k6_lattices,axiom,
! [A] :
( ( l2_lattices(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k6_lattices(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k6_lattices) ).
fof(dt_k7_filter_2,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k7_filter_2(A,B),k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) ),
file('theBenchmark.p',dt_k7_filter_2) ).
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_filter_0,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) ) ) ),
file('theBenchmark.p',dt_m1_filter_0) ).
fof(dt_m1_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_filter_2(B,A)
=> ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) ) ) ),
file('theBenchmark.p',dt_m1_filter_2) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) ) ) ),
file('theBenchmark.p',dt_m2_filter_2) ).
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_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_filter_0,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] : m1_filter_0(B,A) ),
file('theBenchmark.p',existence_m1_filter_0) ).
fof(existence_m1_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] : m1_filter_2(B,A) ),
file('theBenchmark.p',existence_m1_filter_2) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] : m2_filter_2(B,A) ),
file('theBenchmark.p',existence_m2_filter_2) ).
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_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(fc1_filter_2,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(k7_filter_2(A,B)) ),
file('theBenchmark.p',fc1_filter_2) ).
fof(fc1_lattice2,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_struct_0(A) )
=> ( v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ),
file('theBenchmark.p',fc1_lattice2) ).
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_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(fc6_lattice2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v10_lattices(k1_lattice2(A))
& v9_lattices(k1_lattice2(A))
& v8_lattices(k1_lattice2(A))
& v7_lattices(k1_lattice2(A))
& v6_lattices(k1_lattice2(A))
& v5_lattices(k1_lattice2(A))
& v4_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ),
file('theBenchmark.p',fc6_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(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(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_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_k15_filter_2,axiom,
! [A,B] :
( ( m2_filter_2(B,A)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k15_filter_2(A,B) = k7_filter_2(A,B) ),
file('theBenchmark.p',redefinition_k15_filter_2) ).
fof(redefinition_m1_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_filter_2(B,A)
<=> m1_filter_0(B,A) ) ),
file('theBenchmark.p',redefinition_m1_filter_2) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t12_filter_0,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ( ( l3_lattices(A)
& v14_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> r2_hidden(k6_lattices(A),B) ) ) ),
file('theBenchmark.p',t12_filter_0) ).
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(t63_lattice2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v13_lattices(A)
<=> v14_lattices(k1_lattice2(A)) ) ),
file('theBenchmark.p',t63_lattice2) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(t78_lattice2,axiom,
! [A] :
( ( l3_lattices(A)
& v13_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k5_lattices(A) = k6_lattices(k1_lattice2(A)) ),
file('theBenchmark.p',t78_lattice2) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& A != B
& v1_xboole_0(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( v13_lattices(A)
=> r2_hidden(k5_lattices(A),B) ) ) ),
inference(negate,[status(cth)],[t25_filter_2]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ~ r2_hidden(k5_lattices(A),B)
& v13_lattices(A)
& m2_filter_2(B,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_1] :
( ? [U_0] :
( ~ r2_hidden(k5_lattices(U_1),U_0)
& v13_lattices(U_1)
& m2_filter_2(U_0,U_1) )
& l3_lattices(U_1)
& v10_lattices(U_1)
& ~ v3_struct_0(U_1) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_0] :
( ~ r2_hidden(k5_lattices(sK1),U_0)
& v13_lattices(sK1)
& m2_filter_2(U_0,sK1) )
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ~ r2_hidden(k5_lattices(sK1),sK2)
& v13_lattices(sK1)
& m2_filter_2(sK2,sK1)
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_0,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ~ r2_hidden(k5_lattices(sK1),sK2)
& v13_lattices(sK1)
& m2_filter_2(sK2,sK1)
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(definitional_conversion,[status(esa)],[f_1_5]) ).
cnf(f_1_7,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
v10_lattices(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_9,negated_conjecture,
l3_lattices(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_10,negated_conjecture,
m2_filter_2(sK2,sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_11,negated_conjecture,
v13_lattices(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_12,negated_conjecture,
~ r2_hidden(k5_lattices(sK1),sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
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_2] :
( U_2 = g3_lattices(u1_struct_0(U_2),u2_lattices(U_2),u1_lattices(U_2))
| ~ v3_lattices(U_2)
| ~ l3_lattices(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_2] :
( U_2 = g3_lattices(u1_struct_0(U_2),u2_lattices(U_2),u1_lattices(U_2))
| ~ v3_lattices(U_2)
| ~ l3_lattices(U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( U_2 = g3_lattices(u1_struct_0(U_2),u2_lattices(U_2),u1_lattices(U_2))
| ~ v3_lattices(U_2)
| ~ l3_lattices(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
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_4,U_3] :
( ~ r2_hidden(U_3,U_4)
| ~ r2_hidden(U_4,U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_4,U_3] :
( ~ r2_hidden(U_3,U_4)
| ~ r2_hidden(U_4,U_3) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( ~ r2_hidden(U_3,U_4)
| ~ r2_hidden(U_4,U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
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_5] :
( v1_funct_1(U_5)
| ~ v1_xboole_0(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5] :
( v1_funct_1(U_5)
| ~ v1_xboole_0(U_5) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( v1_funct_1(U_5)
| ~ v1_xboole_0(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
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_6] :
( ( v9_lattices(U_6)
& v8_lattices(U_6)
& v7_lattices(U_6)
& v6_lattices(U_6)
& v5_lattices(U_6)
& v4_lattices(U_6)
& ~ v3_struct_0(U_6) )
| ~ v10_lattices(U_6)
| v3_struct_0(U_6)
| ~ l3_lattices(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_6] :
( v9_lattices(U_6)
| ~ sP0(U_6) )
& ! [U_6] :
( v8_lattices(U_6)
| ~ sP0(U_6) )
& ! [U_6] :
( v7_lattices(U_6)
| ~ sP0(U_6) )
& ! [U_6] :
( v6_lattices(U_6)
| ~ sP0(U_6) )
& ! [U_6] :
( v5_lattices(U_6)
| ~ sP0(U_6) )
& ! [U_6] :
( v4_lattices(U_6)
| ~ sP0(U_6) )
& ! [U_6] :
( ~ v3_struct_0(U_6)
| ~ sP0(U_6) )
& ! [U_6] :
( sP0(U_6)
| ~ v10_lattices(U_6)
| v3_struct_0(U_6)
| ~ l3_lattices(U_6) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_5_2]) ).
cnf(f_5_4,plain,
( sP0(U_6)
| ~ v10_lattices(U_6)
| v3_struct_0(U_6)
| ~ l3_lattices(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( ~ v3_struct_0(U_6)
| ~ sP0(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( v4_lattices(U_6)
| ~ sP0(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_7,plain,
( v5_lattices(U_6)
| ~ sP0(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_8,plain,
( v6_lattices(U_6)
| ~ sP0(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_9,plain,
( v7_lattices(U_6)
| ~ sP0(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_10,plain,
( v8_lattices(U_6)
| ~ sP0(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_11,plain,
( v9_lattices(U_6)
| ~ sP0(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
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_9,U_8,U_7] :
( v1_relat_1(U_7)
| ~ m1_subset_1(U_7,k1_zfmisc_1(k2_zfmisc_1(U_9,U_8))) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_7,U_9,U_8] :
( v1_relat_1(U_7)
| ~ m1_subset_1(U_7,k1_zfmisc_1(k2_zfmisc_1(U_9,U_8))) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( v1_relat_1(U_7)
| ~ m1_subset_1(U_7,k1_zfmisc_1(k2_zfmisc_1(U_9,U_8))) ),
inference(clausify,[status(thm)],[f_6_3]) ).
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_10] :
( ( v2_funct_1(U_10)
& v1_funct_1(U_10)
& v1_relat_1(U_10) )
| ~ v1_funct_1(U_10)
| ~ v1_xboole_0(U_10)
| ~ v1_relat_1(U_10) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_10] :
( v2_funct_1(U_10)
| ~ sP1(U_10) )
& ! [U_10] :
( v1_funct_1(U_10)
| ~ sP1(U_10) )
& ! [U_10] :
( v1_relat_1(U_10)
| ~ sP1(U_10) )
& ! [U_10] :
( sP1(U_10)
| ~ v1_funct_1(U_10)
| ~ v1_xboole_0(U_10)
| ~ v1_relat_1(U_10) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP1(U_10)
| ~ v1_funct_1(U_10)
| ~ v1_xboole_0(U_10)
| ~ v1_relat_1(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( v1_relat_1(U_10)
| ~ sP1(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( v1_funct_1(U_10)
| ~ sP1(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( v2_funct_1(U_10)
| ~ sP1(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
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_11] :
( ( v10_lattices(U_11)
& ~ v3_struct_0(U_11) )
| ~ v9_lattices(U_11)
| ~ v8_lattices(U_11)
| ~ v7_lattices(U_11)
| ~ v6_lattices(U_11)
| ~ v5_lattices(U_11)
| ~ v4_lattices(U_11)
| v3_struct_0(U_11)
| ~ l3_lattices(U_11) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_11] :
( v10_lattices(U_11)
| ~ sP2(U_11) )
& ! [U_11] :
( ~ v3_struct_0(U_11)
| ~ sP2(U_11) )
& ! [U_11] :
( sP2(U_11)
| ~ v9_lattices(U_11)
| ~ v8_lattices(U_11)
| ~ v7_lattices(U_11)
| ~ v6_lattices(U_11)
| ~ v5_lattices(U_11)
| ~ v4_lattices(U_11)
| v3_struct_0(U_11)
| ~ l3_lattices(U_11) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_8_2]) ).
cnf(f_8_4,plain,
( sP2(U_11)
| ~ v9_lattices(U_11)
| ~ v8_lattices(U_11)
| ~ v7_lattices(U_11)
| ~ v6_lattices(U_11)
| ~ v5_lattices(U_11)
| ~ v4_lattices(U_11)
| v3_struct_0(U_11)
| ~ l3_lattices(U_11) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( ~ v3_struct_0(U_11)
| ~ sP2(U_11) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( v10_lattices(U_11)
| ~ sP2(U_11) ),
inference(clausify,[status(thm)],[f_8_3]) ).
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_12] :
( ( v15_lattices(U_12)
& ~ v3_struct_0(U_12) )
| ~ v14_lattices(U_12)
| ~ v13_lattices(U_12)
| v3_struct_0(U_12)
| ~ l3_lattices(U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_12] :
( v15_lattices(U_12)
| ~ sP3(U_12) )
& ! [U_12] :
( ~ v3_struct_0(U_12)
| ~ sP3(U_12) )
& ! [U_12] :
( sP3(U_12)
| ~ v14_lattices(U_12)
| ~ v13_lattices(U_12)
| v3_struct_0(U_12)
| ~ l3_lattices(U_12) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP3(U_12)
| ~ v14_lattices(U_12)
| ~ v13_lattices(U_12)
| v3_struct_0(U_12)
| ~ l3_lattices(U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( ~ v3_struct_0(U_12)
| ~ sP3(U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( v15_lattices(U_12)
| ~ sP3(U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
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_13] :
( ( v14_lattices(U_13)
& v13_lattices(U_13)
& ~ v3_struct_0(U_13) )
| ~ v15_lattices(U_13)
| v3_struct_0(U_13)
| ~ l3_lattices(U_13) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_13] :
( v14_lattices(U_13)
| ~ sP4(U_13) )
& ! [U_13] :
( v13_lattices(U_13)
| ~ sP4(U_13) )
& ! [U_13] :
( ~ v3_struct_0(U_13)
| ~ sP4(U_13) )
& ! [U_13] :
( sP4(U_13)
| ~ v15_lattices(U_13)
| v3_struct_0(U_13)
| ~ l3_lattices(U_13) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_10_2]) ).
cnf(f_10_4,plain,
( sP4(U_13)
| ~ v15_lattices(U_13)
| v3_struct_0(U_13)
| ~ l3_lattices(U_13) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( ~ v3_struct_0(U_13)
| ~ sP4(U_13) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( v13_lattices(U_13)
| ~ sP4(U_13) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_7,plain,
( v14_lattices(U_13)
| ~ sP4(U_13) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] :
( k1_lattice2(A) = g3_lattices(u1_struct_0(A),u1_lattices(A),u2_lattices(A))
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[d2_lattice2]) ).
fof(f_11_2,plain,
! [U_14] :
( k1_lattice2(U_14) = g3_lattices(u1_struct_0(U_14),u1_lattices(U_14),u2_lattices(U_14))
| ~ l3_lattices(U_14) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_14] :
( k1_lattice2(U_14) = g3_lattices(u1_struct_0(U_14),u1_lattices(U_14),u2_lattices(U_14))
| ~ l3_lattices(U_14) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( k1_lattice2(U_14) = g3_lattices(u1_struct_0(U_14),u1_lattices(U_14),u2_lattices(U_14))
| ~ l3_lattices(U_14) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A] :
( ! [B] :
( k7_filter_2(A,B) = B
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[d6_filter_2]) ).
fof(f_12_2,plain,
! [U_16] :
( ! [U_15] :
( k7_filter_2(U_16,U_15) = U_15
| ~ m1_subset_1(U_15,k1_zfmisc_1(u1_struct_0(U_16))) )
| ~ l3_lattices(U_16)
| ~ v10_lattices(U_16)
| v3_struct_0(U_16) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_15,U_16] :
( k7_filter_2(U_16,U_15) = U_15
| ~ m1_subset_1(U_15,k1_zfmisc_1(u1_struct_0(U_16)))
| ~ l3_lattices(U_16)
| ~ v10_lattices(U_16)
| v3_struct_0(U_16) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( k7_filter_2(U_16,U_15) = U_15
| ~ m1_subset_1(U_15,k1_zfmisc_1(u1_struct_0(U_16)))
| ~ l3_lattices(U_16)
| ~ v10_lattices(U_16)
| v3_struct_0(U_16) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_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_13_2,plain,
! [U_19,U_18,U_17] :
( ( l3_lattices(g3_lattices(U_19,U_18,U_17))
& v3_lattices(g3_lattices(U_19,U_18,U_17)) )
| ~ m1_relset_1(U_17,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_2(U_17,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_1(U_17)
| ~ m1_relset_1(U_18,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_2(U_18,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_1(U_18) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_17,U_18,U_19] :
( l3_lattices(g3_lattices(U_19,U_18,U_17))
| ~ sP5(U_17,U_18,U_19) )
& ! [U_17,U_18,U_19] :
( v3_lattices(g3_lattices(U_19,U_18,U_17))
| ~ sP5(U_17,U_18,U_19) )
& ! [U_17,U_18,U_19] :
( sP5(U_17,U_18,U_19)
| ~ m1_relset_1(U_17,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_2(U_17,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_1(U_17)
| ~ m1_relset_1(U_18,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_2(U_18,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_1(U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_13_2]) ).
cnf(f_13_4,plain,
( sP5(U_17,U_18,U_19)
| ~ m1_relset_1(U_17,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_2(U_17,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_1(U_17)
| ~ m1_relset_1(U_18,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_2(U_18,k2_zfmisc_1(U_19,U_19),U_19)
| ~ v1_funct_1(U_18) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( v3_lattices(g3_lattices(U_19,U_18,U_17))
| ~ sP5(U_17,U_18,U_19) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( l3_lattices(g3_lattices(U_19,U_18,U_17))
| ~ sP5(U_17,U_18,U_19) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A,B] :
( m1_filter_2(k15_filter_2(A,B),k1_lattice2(A))
| ~ m2_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k15_filter_2]) ).
fof(f_14_2,plain,
! [U_21,U_20] :
( m1_filter_2(k15_filter_2(U_21,U_20),k1_lattice2(U_21))
| ~ m2_filter_2(U_20,U_21)
| ~ l3_lattices(U_21)
| ~ v10_lattices(U_21)
| v3_struct_0(U_21) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_20,U_21] :
( m1_filter_2(k15_filter_2(U_21,U_20),k1_lattice2(U_21))
| ~ m2_filter_2(U_20,U_21)
| ~ l3_lattices(U_21)
| ~ v10_lattices(U_21)
| v3_struct_0(U_21) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( m1_filter_2(k15_filter_2(U_21,U_20),k1_lattice2(U_21))
| ~ m2_filter_2(U_20,U_21)
| ~ l3_lattices(U_21)
| ~ v10_lattices(U_21)
| v3_struct_0(U_21) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A] :
( ( l3_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) )
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_lattice2]) ).
fof(f_15_2,plain,
! [U_22] :
( ( l3_lattices(k1_lattice2(U_22))
& v3_lattices(k1_lattice2(U_22)) )
| ~ l3_lattices(U_22) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_22] :
( l3_lattices(k1_lattice2(U_22))
| ~ sP6(U_22) )
& ! [U_22] :
( v3_lattices(k1_lattice2(U_22))
| ~ sP6(U_22) )
& ! [U_22] :
( sP6(U_22)
| ~ l3_lattices(U_22) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_15_2]) ).
cnf(f_15_4,plain,
( sP6(U_22)
| ~ l3_lattices(U_22) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( v3_lattices(k1_lattice2(U_22))
| ~ sP6(U_22) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_6,plain,
( l3_lattices(k1_lattice2(U_22))
| ~ sP6(U_22) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_16_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_16_1]) ).
cnf(f_16_3,plain,
$true,
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_17_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
$true,
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_18_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
$true,
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( m1_subset_1(k5_lattices(A),u1_struct_0(A))
| ~ l1_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_lattices]) ).
fof(f_19_2,plain,
! [U_23] :
( m1_subset_1(k5_lattices(U_23),u1_struct_0(U_23))
| ~ l1_lattices(U_23)
| v3_struct_0(U_23) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_23] :
( m1_subset_1(k5_lattices(U_23),u1_struct_0(U_23))
| ~ l1_lattices(U_23)
| v3_struct_0(U_23) ),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
( m1_subset_1(k5_lattices(U_23),u1_struct_0(U_23))
| ~ l1_lattices(U_23)
| v3_struct_0(U_23) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A] :
( m1_subset_1(k6_lattices(A),u1_struct_0(A))
| ~ l2_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k6_lattices]) ).
fof(f_20_2,plain,
! [U_24] :
( m1_subset_1(k6_lattices(U_24),u1_struct_0(U_24))
| ~ l2_lattices(U_24)
| v3_struct_0(U_24) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_24] :
( m1_subset_1(k6_lattices(U_24),u1_struct_0(U_24))
| ~ l2_lattices(U_24)
| v3_struct_0(U_24) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( m1_subset_1(k6_lattices(U_24),u1_struct_0(U_24))
| ~ l2_lattices(U_24)
| v3_struct_0(U_24) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] :
( m1_subset_1(k7_filter_2(A,B),k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_filter_2]) ).
fof(f_21_2,plain,
! [U_26,U_25] :
( m1_subset_1(k7_filter_2(U_26,U_25),k1_zfmisc_1(u1_struct_0(k1_lattice2(U_26))))
| ~ m1_subset_1(U_25,k1_zfmisc_1(u1_struct_0(U_26)))
| ~ l3_lattices(U_26)
| ~ v10_lattices(U_26)
| v3_struct_0(U_26) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_26,U_25] :
( m1_subset_1(k7_filter_2(U_26,U_25),k1_zfmisc_1(u1_struct_0(k1_lattice2(U_26))))
| ~ m1_subset_1(U_25,k1_zfmisc_1(u1_struct_0(U_26)))
| ~ l3_lattices(U_26)
| ~ v10_lattices(U_26)
| v3_struct_0(U_26) ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( m1_subset_1(k7_filter_2(U_26,U_25),k1_zfmisc_1(u1_struct_0(k1_lattice2(U_26))))
| ~ m1_subset_1(U_25,k1_zfmisc_1(u1_struct_0(U_26)))
| ~ l3_lattices(U_26)
| ~ v10_lattices(U_26)
| v3_struct_0(U_26) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_lattices]) ).
fof(f_22_2,plain,
! [U_27] :
( l1_struct_0(U_27)
| ~ l1_lattices(U_27) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_27] :
( l1_struct_0(U_27)
| ~ l1_lattices(U_27) ),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
( l1_struct_0(U_27)
| ~ l1_lattices(U_27) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
fof(f_23_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
$true,
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_lattices]) ).
fof(f_24_2,plain,
! [U_28] :
( l1_struct_0(U_28)
| ~ l2_lattices(U_28) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_28] :
( l1_struct_0(U_28)
| ~ l2_lattices(U_28) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( l1_struct_0(U_28)
| ~ l2_lattices(U_28) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A] :
( ( l2_lattices(A)
& l1_lattices(A) )
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l3_lattices]) ).
fof(f_25_2,plain,
! [U_29] :
( ( l2_lattices(U_29)
& l1_lattices(U_29) )
| ~ l3_lattices(U_29) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_29] :
( l2_lattices(U_29)
| ~ sP7(U_29) )
& ! [U_29] :
( l1_lattices(U_29)
| ~ sP7(U_29) )
& ! [U_29] :
( sP7(U_29)
| ~ l3_lattices(U_29) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_25_2]) ).
cnf(f_25_4,plain,
( sP7(U_29)
| ~ l3_lattices(U_29) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
( l1_lattices(U_29)
| ~ sP7(U_29) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
( l2_lattices(U_29)
| ~ sP7(U_29) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A] :
( ! [B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) )
| ~ m1_filter_0(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m1_filter_0]) ).
fof(f_26_2,plain,
! [U_31] :
( ! [U_30] :
( ( m1_subset_1(U_30,k1_zfmisc_1(u1_struct_0(U_31)))
& ~ v1_xboole_0(U_30) )
| ~ m1_filter_0(U_30,U_31) )
| ~ l3_lattices(U_31)
| ~ v10_lattices(U_31)
| v3_struct_0(U_31) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_30,U_31] :
( m1_subset_1(U_30,k1_zfmisc_1(u1_struct_0(U_31)))
| ~ sP8(U_30,U_31) )
& ! [U_30,U_31] :
( ~ v1_xboole_0(U_30)
| ~ sP8(U_30,U_31) )
& ! [U_30,U_31] :
( sP8(U_30,U_31)
| ~ m1_filter_0(U_30,U_31)
| ~ l3_lattices(U_31)
| ~ v10_lattices(U_31)
| v3_struct_0(U_31) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_26_2]) ).
cnf(f_26_4,plain,
( sP8(U_30,U_31)
| ~ m1_filter_0(U_30,U_31)
| ~ l3_lattices(U_31)
| ~ v10_lattices(U_31)
| v3_struct_0(U_31) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
( ~ v1_xboole_0(U_30)
| ~ sP8(U_30,U_31) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
( m1_subset_1(U_30,k1_zfmisc_1(u1_struct_0(U_31)))
| ~ sP8(U_30,U_31) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A] :
( ! [B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) )
| ~ m1_filter_2(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m1_filter_2]) ).
fof(f_27_2,plain,
! [U_33] :
( ! [U_32] :
( ( m2_lattice4(U_32,U_33)
& ~ v1_xboole_0(U_32) )
| ~ m1_filter_2(U_32,U_33) )
| ~ l3_lattices(U_33)
| ~ v10_lattices(U_33)
| v3_struct_0(U_33) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_32,U_33] :
( m2_lattice4(U_32,U_33)
| ~ sP9(U_32,U_33) )
& ! [U_32,U_33] :
( ~ v1_xboole_0(U_32)
| ~ sP9(U_32,U_33) )
& ! [U_32,U_33] :
( sP9(U_32,U_33)
| ~ m1_filter_2(U_32,U_33)
| ~ l3_lattices(U_33)
| ~ v10_lattices(U_33)
| v3_struct_0(U_33) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_27_2]) ).
cnf(f_27_4,plain,
( sP9(U_32,U_33)
| ~ m1_filter_2(U_32,U_33)
| ~ l3_lattices(U_33)
| ~ v10_lattices(U_33)
| v3_struct_0(U_33) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( ~ v1_xboole_0(U_32)
| ~ sP9(U_32,U_33) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
( m2_lattice4(U_32,U_33)
| ~ sP9(U_32,U_33) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
fof(f_28_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_28_1]) ).
cnf(f_28_3,plain,
$true,
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_29_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_29_1]) ).
cnf(f_29_3,plain,
$true,
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A] :
( ! [B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) )
| ~ m2_filter_2(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m2_filter_2]) ).
fof(f_30_2,plain,
! [U_35] :
( ! [U_34] :
( ( m2_lattice4(U_34,U_35)
& ~ v1_xboole_0(U_34) )
| ~ m2_filter_2(U_34,U_35) )
| ~ l3_lattices(U_35)
| ~ v10_lattices(U_35)
| v3_struct_0(U_35) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_35,U_34] :
( m2_lattice4(U_34,U_35)
| ~ sP10(U_35,U_34) )
& ! [U_35,U_34] :
( ~ v1_xboole_0(U_34)
| ~ sP10(U_35,U_34) )
& ! [U_35,U_34] :
( sP10(U_35,U_34)
| ~ m2_filter_2(U_34,U_35)
| ~ l3_lattices(U_35)
| ~ v10_lattices(U_35)
| v3_struct_0(U_35) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_30_2]) ).
cnf(f_30_4,plain,
( sP10(U_35,U_34)
| ~ m2_filter_2(U_34,U_35)
| ~ l3_lattices(U_35)
| ~ v10_lattices(U_35)
| v3_struct_0(U_35) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( ~ v1_xboole_0(U_34)
| ~ sP10(U_35,U_34) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
( m2_lattice4(U_34,U_35)
| ~ sP10(U_35,U_34) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_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_31_2,plain,
! [U_37] :
( ! [U_36] :
( m1_subset_1(U_36,k1_zfmisc_1(u1_struct_0(U_37)))
| ~ m2_lattice4(U_36,U_37) )
| ~ l3_lattices(U_37)
| ~ v10_lattices(U_37)
| v3_struct_0(U_37) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_36,U_37] :
( m1_subset_1(U_36,k1_zfmisc_1(u1_struct_0(U_37)))
| ~ m2_lattice4(U_36,U_37)
| ~ l3_lattices(U_37)
| ~ v10_lattices(U_37)
| v3_struct_0(U_37) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( m1_subset_1(U_36,k1_zfmisc_1(u1_struct_0(U_37)))
| ~ m2_lattice4(U_36,U_37)
| ~ l3_lattices(U_37)
| ~ v10_lattices(U_37)
| v3_struct_0(U_37) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m2_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_32_2,plain,
! [U_40,U_39,U_38] :
( m1_subset_1(U_38,k1_zfmisc_1(k2_zfmisc_1(U_40,U_39)))
| ~ m2_relset_1(U_38,U_40,U_39) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_39,U_38,U_40] :
( m1_subset_1(U_38,k1_zfmisc_1(k2_zfmisc_1(U_40,U_39)))
| ~ m2_relset_1(U_38,U_40,U_39) ),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
( m1_subset_1(U_38,k1_zfmisc_1(k2_zfmisc_1(U_40,U_39)))
| ~ m2_relset_1(U_38,U_40,U_39) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_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_33_2,plain,
! [U_41] :
( ( m2_relset_1(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
& v1_funct_2(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
& v1_funct_1(u1_lattices(U_41)) )
| ~ l1_lattices(U_41) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_41] :
( m2_relset_1(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
| ~ sP11(U_41) )
& ! [U_41] :
( v1_funct_2(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
| ~ sP11(U_41) )
& ! [U_41] :
( v1_funct_1(u1_lattices(U_41))
| ~ sP11(U_41) )
& ! [U_41] :
( sP11(U_41)
| ~ l1_lattices(U_41) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_33_2]) ).
cnf(f_33_4,plain,
( sP11(U_41)
| ~ l1_lattices(U_41) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
( v1_funct_1(u1_lattices(U_41))
| ~ sP11(U_41) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_6,plain,
( v1_funct_2(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
| ~ sP11(U_41) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_7,plain,
( m2_relset_1(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
| ~ sP11(U_41) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
fof(f_34_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_34_1]) ).
cnf(f_34_3,plain,
$true,
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_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_35_2,plain,
! [U_42] :
( ( m2_relset_1(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
& v1_funct_2(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
& v1_funct_1(u2_lattices(U_42)) )
| ~ l2_lattices(U_42) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_42] :
( m2_relset_1(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
| ~ sP12(U_42) )
& ! [U_42] :
( v1_funct_2(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
| ~ sP12(U_42) )
& ! [U_42] :
( v1_funct_1(u2_lattices(U_42))
| ~ sP12(U_42) )
& ! [U_42] :
( sP12(U_42)
| ~ l2_lattices(U_42) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_35_2]) ).
cnf(f_35_4,plain,
( sP12(U_42)
| ~ l2_lattices(U_42) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( v1_funct_1(u2_lattices(U_42))
| ~ sP12(U_42) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_6,plain,
( v1_funct_2(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
| ~ sP12(U_42) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_7,plain,
( m2_relset_1(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
| ~ sP12(U_42) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
? [A] : l1_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l1_lattices]) ).
fof(f_36_2,plain,
? [U_43] : l1_lattices(U_43),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
l1_lattices(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_43,sK3)],[f_36_2]) ).
fof(f_36_4,plain,
l1_lattices(sK3),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
l1_lattices(sK3),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_37_2,plain,
? [U_44] : l1_struct_0(U_44),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
l1_struct_0(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_44,sK4)],[f_37_2]) ).
fof(f_37_4,plain,
l1_struct_0(sK4),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
l1_struct_0(sK4),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,plain,
? [A] : l2_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l2_lattices]) ).
fof(f_38_2,plain,
? [U_45] : l2_lattices(U_45),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
l2_lattices(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_45,sK5)],[f_38_2]) ).
fof(f_38_4,plain,
l2_lattices(sK5),
inference(definitional_conversion,[status(esa)],[f_38_3]) ).
cnf(f_38_5,plain,
l2_lattices(sK5),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_1,plain,
? [A] : l3_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l3_lattices]) ).
fof(f_39_2,plain,
? [U_46] : l3_lattices(U_46),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
l3_lattices(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_46,sK6)],[f_39_2]) ).
fof(f_39_4,plain,
l3_lattices(sK6),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
l3_lattices(sK6),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
! [A] :
( ? [B] : m1_filter_0(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m1_filter_0]) ).
fof(f_40_2,plain,
! [U_48] :
( ? [U_47] : m1_filter_0(U_47,U_48)
| ~ l3_lattices(U_48)
| ~ v10_lattices(U_48)
| v3_struct_0(U_48) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_48] :
( m1_filter_0(sK7(U_48),U_48)
| ~ l3_lattices(U_48)
| ~ v10_lattices(U_48)
| v3_struct_0(U_48) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_47,sK7(U_48))],[f_40_2]) ).
fof(f_40_4,plain,
! [U_48] :
( m1_filter_0(sK7(U_48),U_48)
| ~ l3_lattices(U_48)
| ~ v10_lattices(U_48)
| v3_struct_0(U_48) ),
inference(definitional_conversion,[status(esa)],[f_40_3]) ).
cnf(f_40_5,plain,
( m1_filter_0(sK7(U_48),U_48)
| ~ l3_lattices(U_48)
| ~ v10_lattices(U_48)
| v3_struct_0(U_48) ),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_1,plain,
! [A] :
( ? [B] : m1_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m1_filter_2]) ).
fof(f_41_2,plain,
! [U_50] :
( ? [U_49] : m1_filter_2(U_49,U_50)
| ~ l3_lattices(U_50)
| ~ v10_lattices(U_50)
| v3_struct_0(U_50) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_50] :
( m1_filter_2(sK8(U_50),U_50)
| ~ l3_lattices(U_50)
| ~ v10_lattices(U_50)
| v3_struct_0(U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_49,sK8(U_50))],[f_41_2]) ).
fof(f_41_4,plain,
! [U_50] :
( m1_filter_2(sK8(U_50),U_50)
| ~ l3_lattices(U_50)
| ~ v10_lattices(U_50)
| v3_struct_0(U_50) ),
inference(definitional_conversion,[status(esa)],[f_41_3]) ).
cnf(f_41_5,plain,
( m1_filter_2(sK8(U_50),U_50)
| ~ l3_lattices(U_50)
| ~ v10_lattices(U_50)
| v3_struct_0(U_50) ),
inference(clausify,[status(thm)],[f_41_4]) ).
fof(f_42_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_42_2,plain,
! [U_53,U_52] :
? [U_51] : m1_relset_1(U_51,U_53,U_52),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_53,U_52] : m1_relset_1(sK9(U_53,U_52),U_53,U_52),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_51,sK9(U_53,U_52))],[f_42_2]) ).
fof(f_42_4,plain,
! [U_52,U_53] : m1_relset_1(sK9(U_53,U_52),U_53,U_52),
inference(definitional_conversion,[status(esa)],[f_42_3]) ).
cnf(f_42_5,plain,
m1_relset_1(sK9(U_53,U_52),U_53,U_52),
inference(clausify,[status(thm)],[f_42_4]) ).
fof(f_43_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_43_2,plain,
! [U_55] :
? [U_54] : m1_subset_1(U_54,U_55),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_55] : m1_subset_1(sK10(U_55),U_55),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_54,sK10(U_55))],[f_43_2]) ).
fof(f_43_4,plain,
! [U_55] : m1_subset_1(sK10(U_55),U_55),
inference(definitional_conversion,[status(esa)],[f_43_3]) ).
cnf(f_43_5,plain,
m1_subset_1(sK10(U_55),U_55),
inference(clausify,[status(thm)],[f_43_4]) ).
fof(f_44_1,plain,
! [A] :
( ? [B] : m2_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m2_filter_2]) ).
fof(f_44_2,plain,
! [U_57] :
( ? [U_56] : m2_filter_2(U_56,U_57)
| ~ l3_lattices(U_57)
| ~ v10_lattices(U_57)
| v3_struct_0(U_57) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_57] :
( m2_filter_2(sK11(U_57),U_57)
| ~ l3_lattices(U_57)
| ~ v10_lattices(U_57)
| v3_struct_0(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_56,sK11(U_57))],[f_44_2]) ).
fof(f_44_4,plain,
! [U_57] :
( m2_filter_2(sK11(U_57),U_57)
| ~ l3_lattices(U_57)
| ~ v10_lattices(U_57)
| v3_struct_0(U_57) ),
inference(definitional_conversion,[status(esa)],[f_44_3]) ).
cnf(f_44_5,plain,
( m2_filter_2(sK11(U_57),U_57)
| ~ l3_lattices(U_57)
| ~ v10_lattices(U_57)
| v3_struct_0(U_57) ),
inference(clausify,[status(thm)],[f_44_4]) ).
fof(f_45_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_45_2,plain,
! [U_59] :
( ? [U_58] : m2_lattice4(U_58,U_59)
| ~ l3_lattices(U_59)
| ~ v10_lattices(U_59)
| v3_struct_0(U_59) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_59] :
( m2_lattice4(sK12(U_59),U_59)
| ~ l3_lattices(U_59)
| ~ v10_lattices(U_59)
| v3_struct_0(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_58,sK12(U_59))],[f_45_2]) ).
fof(f_45_4,plain,
! [U_59] :
( m2_lattice4(sK12(U_59),U_59)
| ~ l3_lattices(U_59)
| ~ v10_lattices(U_59)
| v3_struct_0(U_59) ),
inference(definitional_conversion,[status(esa)],[f_45_3]) ).
cnf(f_45_5,plain,
( m2_lattice4(sK12(U_59),U_59)
| ~ l3_lattices(U_59)
| ~ v10_lattices(U_59)
| v3_struct_0(U_59) ),
inference(clausify,[status(thm)],[f_45_4]) ).
fof(f_46_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_46_2,plain,
! [U_62,U_61] :
? [U_60] : m2_relset_1(U_60,U_62,U_61),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_62,U_61] : m2_relset_1(sK13(U_62,U_61),U_62,U_61),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_60,sK13(U_62,U_61))],[f_46_2]) ).
fof(f_46_4,plain,
! [U_61,U_62] : m2_relset_1(sK13(U_62,U_61),U_62,U_61),
inference(definitional_conversion,[status(esa)],[f_46_3]) ).
cnf(f_46_5,plain,
m2_relset_1(sK13(U_62,U_61),U_62,U_61),
inference(clausify,[status(thm)],[f_46_4]) ).
fof(f_47_1,plain,
! [A,B] :
( ~ v1_xboole_0(k7_filter_2(A,B))
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc1_filter_2]) ).
fof(f_47_2,plain,
! [U_64,U_63] :
( ~ v1_xboole_0(k7_filter_2(U_64,U_63))
| ~ m1_subset_1(U_63,k1_zfmisc_1(u1_struct_0(U_64)))
| v1_xboole_0(U_63)
| ~ l3_lattices(U_64)
| ~ v10_lattices(U_64)
| v3_struct_0(U_64) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_63,U_64] :
( ~ v1_xboole_0(k7_filter_2(U_64,U_63))
| ~ m1_subset_1(U_63,k1_zfmisc_1(u1_struct_0(U_64)))
| v1_xboole_0(U_63)
| ~ l3_lattices(U_64)
| ~ v10_lattices(U_64)
| v3_struct_0(U_64) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( ~ v1_xboole_0(k7_filter_2(U_64,U_63))
| ~ m1_subset_1(U_63,k1_zfmisc_1(u1_struct_0(U_64)))
| v1_xboole_0(U_63)
| ~ l3_lattices(U_64)
| ~ v10_lattices(U_64)
| v3_struct_0(U_64) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A] :
( ( v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) )
| ~ l3_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc1_lattice2]) ).
fof(f_48_2,plain,
! [U_65] :
( ( v3_lattices(k1_lattice2(U_65))
& ~ v3_struct_0(k1_lattice2(U_65)) )
| ~ l3_lattices(U_65)
| v3_struct_0(U_65) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
( ! [U_65] :
( v3_lattices(k1_lattice2(U_65))
| ~ sP13(U_65) )
& ! [U_65] :
( ~ v3_struct_0(k1_lattice2(U_65))
| ~ sP13(U_65) )
& ! [U_65] :
( sP13(U_65)
| ~ l3_lattices(U_65)
| v3_struct_0(U_65) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_48_2]) ).
cnf(f_48_4,plain,
( sP13(U_65)
| ~ l3_lattices(U_65)
| v3_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_5,plain,
( ~ v3_struct_0(k1_lattice2(U_65))
| ~ sP13(U_65) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_6,plain,
( v3_lattices(k1_lattice2(U_65))
| ~ sP13(U_65) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_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_49_2,plain,
! [U_66] :
( ~ v1_xboole_0(u1_struct_0(U_66))
| ~ l1_struct_0(U_66)
| v3_struct_0(U_66) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_66] :
( ~ v1_xboole_0(u1_struct_0(U_66))
| ~ l1_struct_0(U_66)
| v3_struct_0(U_66) ),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
( ~ v1_xboole_0(u1_struct_0(U_66))
| ~ l1_struct_0(U_66)
| v3_struct_0(U_66) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_50_2,plain,
! [U_67] : ~ v1_xboole_0(k1_zfmisc_1(U_67)),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_67] : ~ v1_xboole_0(k1_zfmisc_1(U_67)),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
~ v1_xboole_0(k1_zfmisc_1(U_67)),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_51_2,plain,
v1_xboole_0(k1_xboole_0),
inference(definitional_conversion,[status(esa)],[f_51_1]) ).
cnf(f_51_3,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_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_52_2,plain,
! [U_68] :
( ( v1_partfun1(u2_lattices(U_68),k2_zfmisc_1(u1_struct_0(U_68),u1_struct_0(U_68)),u1_struct_0(U_68))
& v1_binop_1(u2_lattices(U_68),u1_struct_0(U_68))
& v1_funct_2(u2_lattices(U_68),k2_zfmisc_1(u1_struct_0(U_68),u1_struct_0(U_68)),u1_struct_0(U_68))
& v1_funct_1(u2_lattices(U_68))
& v1_relat_1(u2_lattices(U_68)) )
| ~ l2_lattices(U_68)
| ~ v4_lattices(U_68)
| v3_struct_0(U_68) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ! [U_68] :
( v1_partfun1(u2_lattices(U_68),k2_zfmisc_1(u1_struct_0(U_68),u1_struct_0(U_68)),u1_struct_0(U_68))
| ~ sP14(U_68) )
& ! [U_68] :
( v1_binop_1(u2_lattices(U_68),u1_struct_0(U_68))
| ~ sP14(U_68) )
& ! [U_68] :
( v1_funct_2(u2_lattices(U_68),k2_zfmisc_1(u1_struct_0(U_68),u1_struct_0(U_68)),u1_struct_0(U_68))
| ~ sP14(U_68) )
& ! [U_68] :
( v1_funct_1(u2_lattices(U_68))
| ~ sP14(U_68) )
& ! [U_68] :
( v1_relat_1(u2_lattices(U_68))
| ~ sP14(U_68) )
& ! [U_68] :
( sP14(U_68)
| ~ l2_lattices(U_68)
| ~ v4_lattices(U_68)
| v3_struct_0(U_68) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_52_2]) ).
cnf(f_52_4,plain,
( sP14(U_68)
| ~ l2_lattices(U_68)
| ~ v4_lattices(U_68)
| v3_struct_0(U_68) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
( v1_relat_1(u2_lattices(U_68))
| ~ sP14(U_68) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_6,plain,
( v1_funct_1(u2_lattices(U_68))
| ~ sP14(U_68) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_7,plain,
( v1_funct_2(u2_lattices(U_68),k2_zfmisc_1(u1_struct_0(U_68),u1_struct_0(U_68)),u1_struct_0(U_68))
| ~ sP14(U_68) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_8,plain,
( v1_binop_1(u2_lattices(U_68),u1_struct_0(U_68))
| ~ sP14(U_68) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_9,plain,
( v1_partfun1(u2_lattices(U_68),k2_zfmisc_1(u1_struct_0(U_68),u1_struct_0(U_68)),u1_struct_0(U_68))
| ~ sP14(U_68) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_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_53_2,plain,
! [U_69] :
( ( v1_partfun1(u2_lattices(U_69),k2_zfmisc_1(u1_struct_0(U_69),u1_struct_0(U_69)),u1_struct_0(U_69))
& v2_binop_1(u2_lattices(U_69),u1_struct_0(U_69))
& v1_funct_2(u2_lattices(U_69),k2_zfmisc_1(u1_struct_0(U_69),u1_struct_0(U_69)),u1_struct_0(U_69))
& v1_funct_1(u2_lattices(U_69))
& v1_relat_1(u2_lattices(U_69)) )
| ~ l2_lattices(U_69)
| ~ v5_lattices(U_69)
| v3_struct_0(U_69) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( ! [U_69] :
( v1_partfun1(u2_lattices(U_69),k2_zfmisc_1(u1_struct_0(U_69),u1_struct_0(U_69)),u1_struct_0(U_69))
| ~ sP15(U_69) )
& ! [U_69] :
( v2_binop_1(u2_lattices(U_69),u1_struct_0(U_69))
| ~ sP15(U_69) )
& ! [U_69] :
( v1_funct_2(u2_lattices(U_69),k2_zfmisc_1(u1_struct_0(U_69),u1_struct_0(U_69)),u1_struct_0(U_69))
| ~ sP15(U_69) )
& ! [U_69] :
( v1_funct_1(u2_lattices(U_69))
| ~ sP15(U_69) )
& ! [U_69] :
( v1_relat_1(u2_lattices(U_69))
| ~ sP15(U_69) )
& ! [U_69] :
( sP15(U_69)
| ~ l2_lattices(U_69)
| ~ v5_lattices(U_69)
| v3_struct_0(U_69) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_53_2]) ).
cnf(f_53_4,plain,
( sP15(U_69)
| ~ l2_lattices(U_69)
| ~ v5_lattices(U_69)
| v3_struct_0(U_69) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_5,plain,
( v1_relat_1(u2_lattices(U_69))
| ~ sP15(U_69) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_6,plain,
( v1_funct_1(u2_lattices(U_69))
| ~ sP15(U_69) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_7,plain,
( v1_funct_2(u2_lattices(U_69),k2_zfmisc_1(u1_struct_0(U_69),u1_struct_0(U_69)),u1_struct_0(U_69))
| ~ sP15(U_69) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_8,plain,
( v2_binop_1(u2_lattices(U_69),u1_struct_0(U_69))
| ~ sP15(U_69) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_9,plain,
( v1_partfun1(u2_lattices(U_69),k2_zfmisc_1(u1_struct_0(U_69),u1_struct_0(U_69)),u1_struct_0(U_69))
| ~ sP15(U_69) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_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_54_2,plain,
! [U_72,U_71,U_70] :
( ( v3_lattices(g3_lattices(U_72,U_71,U_70))
& ~ v3_struct_0(g3_lattices(U_72,U_71,U_70)) )
| ~ 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)
| v1_xboole_0(U_72) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ! [U_72,U_71,U_70] :
( v3_lattices(g3_lattices(U_72,U_71,U_70))
| ~ sP16(U_72,U_71,U_70) )
& ! [U_72,U_71,U_70] :
( ~ v3_struct_0(g3_lattices(U_72,U_71,U_70))
| ~ sP16(U_72,U_71,U_70) )
& ! [U_72,U_71,U_70] :
( sP16(U_72,U_71,U_70)
| ~ 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)
| v1_xboole_0(U_72) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_54_2]) ).
cnf(f_54_4,plain,
( sP16(U_72,U_71,U_70)
| ~ 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)
| v1_xboole_0(U_72) ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_5,plain,
( ~ v3_struct_0(g3_lattices(U_72,U_71,U_70))
| ~ sP16(U_72,U_71,U_70) ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_6,plain,
( v3_lattices(g3_lattices(U_72,U_71,U_70))
| ~ sP16(U_72,U_71,U_70) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_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_55_2,plain,
! [U_73] :
( ( v1_partfun1(u1_lattices(U_73),k2_zfmisc_1(u1_struct_0(U_73),u1_struct_0(U_73)),u1_struct_0(U_73))
& v1_binop_1(u1_lattices(U_73),u1_struct_0(U_73))
& v1_funct_2(u1_lattices(U_73),k2_zfmisc_1(u1_struct_0(U_73),u1_struct_0(U_73)),u1_struct_0(U_73))
& v1_funct_1(u1_lattices(U_73))
& v1_relat_1(u1_lattices(U_73)) )
| ~ l1_lattices(U_73)
| ~ v6_lattices(U_73)
| v3_struct_0(U_73) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( ! [U_73] :
( v1_partfun1(u1_lattices(U_73),k2_zfmisc_1(u1_struct_0(U_73),u1_struct_0(U_73)),u1_struct_0(U_73))
| ~ sP17(U_73) )
& ! [U_73] :
( v1_binop_1(u1_lattices(U_73),u1_struct_0(U_73))
| ~ sP17(U_73) )
& ! [U_73] :
( v1_funct_2(u1_lattices(U_73),k2_zfmisc_1(u1_struct_0(U_73),u1_struct_0(U_73)),u1_struct_0(U_73))
| ~ sP17(U_73) )
& ! [U_73] :
( v1_funct_1(u1_lattices(U_73))
| ~ sP17(U_73) )
& ! [U_73] :
( v1_relat_1(u1_lattices(U_73))
| ~ sP17(U_73) )
& ! [U_73] :
( sP17(U_73)
| ~ l1_lattices(U_73)
| ~ v6_lattices(U_73)
| v3_struct_0(U_73) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_55_2]) ).
cnf(f_55_4,plain,
( sP17(U_73)
| ~ l1_lattices(U_73)
| ~ v6_lattices(U_73)
| v3_struct_0(U_73) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_5,plain,
( v1_relat_1(u1_lattices(U_73))
| ~ sP17(U_73) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_6,plain,
( v1_funct_1(u1_lattices(U_73))
| ~ sP17(U_73) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_7,plain,
( v1_funct_2(u1_lattices(U_73),k2_zfmisc_1(u1_struct_0(U_73),u1_struct_0(U_73)),u1_struct_0(U_73))
| ~ sP17(U_73) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_8,plain,
( v1_binop_1(u1_lattices(U_73),u1_struct_0(U_73))
| ~ sP17(U_73) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_9,plain,
( v1_partfun1(u1_lattices(U_73),k2_zfmisc_1(u1_struct_0(U_73),u1_struct_0(U_73)),u1_struct_0(U_73))
| ~ sP17(U_73) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_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_56_2,plain,
! [U_75,U_74] :
( ~ v1_xboole_0(k2_zfmisc_1(U_75,U_74))
| v1_xboole_0(U_74)
| v1_xboole_0(U_75) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_74,U_75] :
( ~ v1_xboole_0(k2_zfmisc_1(U_75,U_74))
| v1_xboole_0(U_74)
| v1_xboole_0(U_75) ),
inference(definitional_conversion,[status(esa)],[f_56_2]) ).
cnf(f_56_4,plain,
( ~ v1_xboole_0(k2_zfmisc_1(U_75,U_74))
| v1_xboole_0(U_74)
| v1_xboole_0(U_75) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_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_57_2,plain,
! [U_76] :
( ( v1_partfun1(u1_lattices(U_76),k2_zfmisc_1(u1_struct_0(U_76),u1_struct_0(U_76)),u1_struct_0(U_76))
& v2_binop_1(u1_lattices(U_76),u1_struct_0(U_76))
& v1_funct_2(u1_lattices(U_76),k2_zfmisc_1(u1_struct_0(U_76),u1_struct_0(U_76)),u1_struct_0(U_76))
& v1_funct_1(u1_lattices(U_76))
& v1_relat_1(u1_lattices(U_76)) )
| ~ l1_lattices(U_76)
| ~ v7_lattices(U_76)
| v3_struct_0(U_76) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ! [U_76] :
( v1_partfun1(u1_lattices(U_76),k2_zfmisc_1(u1_struct_0(U_76),u1_struct_0(U_76)),u1_struct_0(U_76))
| ~ sP18(U_76) )
& ! [U_76] :
( v2_binop_1(u1_lattices(U_76),u1_struct_0(U_76))
| ~ sP18(U_76) )
& ! [U_76] :
( v1_funct_2(u1_lattices(U_76),k2_zfmisc_1(u1_struct_0(U_76),u1_struct_0(U_76)),u1_struct_0(U_76))
| ~ sP18(U_76) )
& ! [U_76] :
( v1_funct_1(u1_lattices(U_76))
| ~ sP18(U_76) )
& ! [U_76] :
( v1_relat_1(u1_lattices(U_76))
| ~ sP18(U_76) )
& ! [U_76] :
( sP18(U_76)
| ~ l1_lattices(U_76)
| ~ v7_lattices(U_76)
| v3_struct_0(U_76) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_57_2]) ).
cnf(f_57_4,plain,
( sP18(U_76)
| ~ l1_lattices(U_76)
| ~ v7_lattices(U_76)
| v3_struct_0(U_76) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
( v1_relat_1(u1_lattices(U_76))
| ~ sP18(U_76) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_6,plain,
( v1_funct_1(u1_lattices(U_76))
| ~ sP18(U_76) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_7,plain,
( v1_funct_2(u1_lattices(U_76),k2_zfmisc_1(u1_struct_0(U_76),u1_struct_0(U_76)),u1_struct_0(U_76))
| ~ sP18(U_76) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_8,plain,
( v2_binop_1(u1_lattices(U_76),u1_struct_0(U_76))
| ~ sP18(U_76) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_9,plain,
( v1_partfun1(u1_lattices(U_76),k2_zfmisc_1(u1_struct_0(U_76),u1_struct_0(U_76)),u1_struct_0(U_76))
| ~ sP18(U_76) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A] :
( ( v10_lattices(k1_lattice2(A))
& v9_lattices(k1_lattice2(A))
& v8_lattices(k1_lattice2(A))
& v7_lattices(k1_lattice2(A))
& v6_lattices(k1_lattice2(A))
& v5_lattices(k1_lattice2(A))
& v4_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc6_lattice2]) ).
fof(f_58_2,plain,
! [U_77] :
( ( v10_lattices(k1_lattice2(U_77))
& v9_lattices(k1_lattice2(U_77))
& v8_lattices(k1_lattice2(U_77))
& v7_lattices(k1_lattice2(U_77))
& v6_lattices(k1_lattice2(U_77))
& v5_lattices(k1_lattice2(U_77))
& v4_lattices(k1_lattice2(U_77))
& v3_lattices(k1_lattice2(U_77))
& ~ v3_struct_0(k1_lattice2(U_77)) )
| ~ l3_lattices(U_77)
| ~ v10_lattices(U_77)
| v3_struct_0(U_77) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ! [U_77] :
( v10_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) )
& ! [U_77] :
( v9_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) )
& ! [U_77] :
( v8_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) )
& ! [U_77] :
( v7_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) )
& ! [U_77] :
( v6_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) )
& ! [U_77] :
( v5_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) )
& ! [U_77] :
( v4_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) )
& ! [U_77] :
( v3_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) )
& ! [U_77] :
( ~ v3_struct_0(k1_lattice2(U_77))
| ~ sP19(U_77) )
& ! [U_77] :
( sP19(U_77)
| ~ l3_lattices(U_77)
| ~ v10_lattices(U_77)
| v3_struct_0(U_77) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_58_2]) ).
cnf(f_58_4,plain,
( sP19(U_77)
| ~ l3_lattices(U_77)
| ~ v10_lattices(U_77)
| v3_struct_0(U_77) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
( ~ v3_struct_0(k1_lattice2(U_77))
| ~ sP19(U_77) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_6,plain,
( v3_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_7,plain,
( v4_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_8,plain,
( v5_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_9,plain,
( v6_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_10,plain,
( v7_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_11,plain,
( v8_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_12,plain,
( v9_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_13,plain,
( v10_lattices(k1_lattice2(U_77))
| ~ sP19(U_77) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_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_59_2,plain,
! [U_83,U_82,U_81] :
( ! [U_80,U_79,U_78] :
( ( U_81 = U_78
& U_82 = U_79
& U_83 = U_80 )
| g3_lattices(U_83,U_82,U_81) != g3_lattices(U_80,U_79,U_78) )
| ~ m1_relset_1(U_81,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_2(U_81,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_1(U_81)
| ~ m1_relset_1(U_82,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_2(U_82,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_1(U_82) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( ! [U_83,U_79,U_80,U_81,U_78,U_82] :
( U_81 = U_78
| ~ sP20(U_83,U_79,U_80,U_81,U_78,U_82) )
& ! [U_83,U_79,U_80,U_81,U_78,U_82] :
( U_82 = U_79
| ~ sP20(U_83,U_79,U_80,U_81,U_78,U_82) )
& ! [U_83,U_79,U_80,U_81,U_78,U_82] :
( U_83 = U_80
| ~ sP20(U_83,U_79,U_80,U_81,U_78,U_82) )
& ! [U_83,U_79,U_80,U_81,U_78,U_82] :
( sP20(U_83,U_79,U_80,U_81,U_78,U_82)
| g3_lattices(U_83,U_82,U_81) != g3_lattices(U_80,U_79,U_78)
| ~ m1_relset_1(U_81,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_2(U_81,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_1(U_81)
| ~ m1_relset_1(U_82,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_2(U_82,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_1(U_82) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_59_2]) ).
cnf(f_59_4,plain,
( sP20(U_83,U_79,U_80,U_81,U_78,U_82)
| g3_lattices(U_83,U_82,U_81) != g3_lattices(U_80,U_79,U_78)
| ~ m1_relset_1(U_81,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_2(U_81,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_1(U_81)
| ~ m1_relset_1(U_82,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_2(U_82,k2_zfmisc_1(U_83,U_83),U_83)
| ~ v1_funct_1(U_82) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_5,plain,
( U_83 = U_80
| ~ sP20(U_83,U_79,U_80,U_81,U_78,U_82) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_6,plain,
( U_82 = U_79
| ~ sP20(U_83,U_79,U_80,U_81,U_78,U_82) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_7,plain,
( U_81 = U_78
| ~ sP20(U_83,U_79,U_80,U_81,U_78,U_82) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_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_60_2,plain,
? [U_84] :
( v15_lattices(U_84)
& v14_lattices(U_84)
& v13_lattices(U_84)
& v10_lattices(U_84)
& v9_lattices(U_84)
& v8_lattices(U_84)
& v7_lattices(U_84)
& v6_lattices(U_84)
& v5_lattices(U_84)
& v4_lattices(U_84)
& v3_lattices(U_84)
& ~ v3_struct_0(U_84)
& l3_lattices(U_84) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_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_84,sK14)],[f_60_2]) ).
fof(f_60_4,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(definitional_conversion,[status(esa)],[f_60_3]) ).
cnf(f_60_5,plain,
l3_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_6,plain,
~ v3_struct_0(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_7,plain,
v3_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_8,plain,
v4_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_9,plain,
v5_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_10,plain,
v6_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_11,plain,
v7_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_12,plain,
v8_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_13,plain,
v9_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_14,plain,
v10_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_15,plain,
v13_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_16,plain,
v14_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_17,plain,
v15_lattices(sK14),
inference(clausify,[status(thm)],[f_60_4]) ).
fof(f_61_1,plain,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_61_2,plain,
? [U_85] :
( v1_funct_1(U_85)
& v1_relat_1(U_85) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( v1_funct_1(sK15)
& v1_relat_1(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_85,sK15)],[f_61_2]) ).
fof(f_61_4,plain,
( v1_funct_1(sK15)
& v1_relat_1(sK15) ),
inference(definitional_conversion,[status(esa)],[f_61_3]) ).
cnf(f_61_5,plain,
v1_relat_1(sK15),
inference(clausify,[status(thm)],[f_61_4]) ).
cnf(f_61_6,plain,
v1_funct_1(sK15),
inference(clausify,[status(thm)],[f_61_4]) ).
fof(f_62_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_62_2,plain,
! [U_87] :
( ? [U_86] :
( ~ v1_xboole_0(U_86)
& m2_lattice4(U_86,U_87) )
| ~ l3_lattices(U_87)
| ~ v10_lattices(U_87)
| v3_struct_0(U_87) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_87] :
( ( ~ v1_xboole_0(sK16(U_87))
& m2_lattice4(sK16(U_87),U_87) )
| ~ l3_lattices(U_87)
| ~ v10_lattices(U_87)
| v3_struct_0(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_86,sK16(U_87))],[f_62_2]) ).
fof(f_62_4,plain,
( ! [U_87] :
( ~ v1_xboole_0(sK16(U_87))
| ~ sP21(U_87) )
& ! [U_87] :
( m2_lattice4(sK16(U_87),U_87)
| ~ sP21(U_87) )
& ! [U_87] :
( sP21(U_87)
| ~ l3_lattices(U_87)
| ~ v10_lattices(U_87)
| v3_struct_0(U_87) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_62_3]) ).
cnf(f_62_5,plain,
( sP21(U_87)
| ~ l3_lattices(U_87)
| ~ v10_lattices(U_87)
| v3_struct_0(U_87) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_6,plain,
( m2_lattice4(sK16(U_87),U_87)
| ~ sP21(U_87) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_7,plain,
( ~ v1_xboole_0(sK16(U_87))
| ~ sP21(U_87) ),
inference(clausify,[status(thm)],[f_62_4]) ).
fof(f_63_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_63_2,plain,
! [U_89] :
( ? [U_88] :
( ~ v1_xboole_0(U_88)
& m1_subset_1(U_88,k1_zfmisc_1(U_89)) )
| v1_xboole_0(U_89) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_89] :
( ( ~ v1_xboole_0(sK17(U_89))
& m1_subset_1(sK17(U_89),k1_zfmisc_1(U_89)) )
| v1_xboole_0(U_89) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_88,sK17(U_89))],[f_63_2]) ).
fof(f_63_4,plain,
( ! [U_89] :
( ~ v1_xboole_0(sK17(U_89))
| ~ sP22(U_89) )
& ! [U_89] :
( m1_subset_1(sK17(U_89),k1_zfmisc_1(U_89))
| ~ sP22(U_89) )
& ! [U_89] :
( sP22(U_89)
| v1_xboole_0(U_89) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_63_3]) ).
cnf(f_63_5,plain,
( sP22(U_89)
| v1_xboole_0(U_89) ),
inference(clausify,[status(thm)],[f_63_4]) ).
cnf(f_63_6,plain,
( m1_subset_1(sK17(U_89),k1_zfmisc_1(U_89))
| ~ sP22(U_89) ),
inference(clausify,[status(thm)],[f_63_4]) ).
cnf(f_63_7,plain,
( ~ v1_xboole_0(sK17(U_89))
| ~ sP22(U_89) ),
inference(clausify,[status(thm)],[f_63_4]) ).
fof(f_64_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_64_2,plain,
? [U_90] : v1_xboole_0(U_90),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
v1_xboole_0(sK18),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_90,sK18)],[f_64_2]) ).
fof(f_64_4,plain,
v1_xboole_0(sK18),
inference(definitional_conversion,[status(esa)],[f_64_3]) ).
cnf(f_64_5,plain,
v1_xboole_0(sK18),
inference(clausify,[status(thm)],[f_64_4]) ).
fof(f_65_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_65_2,plain,
? [U_91] :
( v1_funct_1(U_91)
& v1_xboole_0(U_91)
& v1_relat_1(U_91) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
( v1_funct_1(sK19)
& v1_xboole_0(sK19)
& v1_relat_1(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_91,sK19)],[f_65_2]) ).
fof(f_65_4,plain,
( v1_funct_1(sK19)
& v1_xboole_0(sK19)
& v1_relat_1(sK19) ),
inference(definitional_conversion,[status(esa)],[f_65_3]) ).
cnf(f_65_5,plain,
v1_relat_1(sK19),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_6,plain,
v1_xboole_0(sK19),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_7,plain,
v1_funct_1(sK19),
inference(clausify,[status(thm)],[f_65_4]) ).
fof(f_66_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_66_2,plain,
! [U_93] :
? [U_92] :
( v1_xboole_0(U_92)
& m1_subset_1(U_92,k1_zfmisc_1(U_93)) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_93] :
( v1_xboole_0(sK20(U_93))
& m1_subset_1(sK20(U_93),k1_zfmisc_1(U_93)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_92,sK20(U_93))],[f_66_2]) ).
fof(f_66_4,plain,
( ! [U_93] : v1_xboole_0(sK20(U_93))
& ! [U_93] : m1_subset_1(sK20(U_93),k1_zfmisc_1(U_93)) ),
inference(definitional_conversion,[status(esa)],[f_66_3]) ).
cnf(f_66_5,plain,
m1_subset_1(sK20(U_93),k1_zfmisc_1(U_93)),
inference(clausify,[status(thm)],[f_66_4]) ).
cnf(f_66_6,plain,
v1_xboole_0(sK20(U_93)),
inference(clausify,[status(thm)],[f_66_4]) ).
fof(f_67_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_67_2,plain,
? [U_94] : ~ v1_xboole_0(U_94),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
~ v1_xboole_0(sK21),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_94,sK21)],[f_67_2]) ).
fof(f_67_4,plain,
~ v1_xboole_0(sK21),
inference(definitional_conversion,[status(esa)],[f_67_3]) ).
cnf(f_67_5,plain,
~ v1_xboole_0(sK21),
inference(clausify,[status(thm)],[f_67_4]) ).
fof(f_68_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_68_2,plain,
? [U_95] :
( v2_funct_1(U_95)
& v1_funct_1(U_95)
& v1_relat_1(U_95) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
( v2_funct_1(sK22)
& v1_funct_1(sK22)
& v1_relat_1(sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_95,sK22)],[f_68_2]) ).
fof(f_68_4,plain,
( v2_funct_1(sK22)
& v1_funct_1(sK22)
& v1_relat_1(sK22) ),
inference(definitional_conversion,[status(esa)],[f_68_3]) ).
cnf(f_68_5,plain,
v1_relat_1(sK22),
inference(clausify,[status(thm)],[f_68_4]) ).
cnf(f_68_6,plain,
v1_funct_1(sK22),
inference(clausify,[status(thm)],[f_68_4]) ).
cnf(f_68_7,plain,
v2_funct_1(sK22),
inference(clausify,[status(thm)],[f_68_4]) ).
fof(f_69_1,plain,
? [A] :
( v3_lattices(A)
& l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[rc3_lattices]) ).
fof(f_69_2,plain,
? [U_96] :
( v3_lattices(U_96)
& l3_lattices(U_96) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
( v3_lattices(sK23)
& l3_lattices(sK23) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_96,sK23)],[f_69_2]) ).
fof(f_69_4,plain,
( v3_lattices(sK23)
& l3_lattices(sK23) ),
inference(definitional_conversion,[status(esa)],[f_69_3]) ).
cnf(f_69_5,plain,
l3_lattices(sK23),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_6,plain,
v3_lattices(sK23),
inference(clausify,[status(thm)],[f_69_4]) ).
fof(f_70_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_70_2,plain,
? [U_97] :
( ~ v3_struct_0(U_97)
& l1_struct_0(U_97) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
( ~ v3_struct_0(sK24)
& l1_struct_0(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_97,sK24)],[f_70_2]) ).
fof(f_70_4,plain,
( ~ v3_struct_0(sK24)
& l1_struct_0(sK24) ),
inference(definitional_conversion,[status(esa)],[f_70_3]) ).
cnf(f_70_5,plain,
l1_struct_0(sK24),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_6,plain,
~ v3_struct_0(sK24),
inference(clausify,[status(thm)],[f_70_4]) ).
fof(f_71_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_71_2,plain,
! [U_99] :
( ? [U_98] :
( ~ v1_xboole_0(U_98)
& m1_subset_1(U_98,k1_zfmisc_1(u1_struct_0(U_99))) )
| ~ l1_struct_0(U_99)
| v3_struct_0(U_99) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_99] :
( ( ~ v1_xboole_0(sK25(U_99))
& m1_subset_1(sK25(U_99),k1_zfmisc_1(u1_struct_0(U_99))) )
| ~ l1_struct_0(U_99)
| v3_struct_0(U_99) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_98,sK25(U_99))],[f_71_2]) ).
fof(f_71_4,plain,
( ! [U_99] :
( ~ v1_xboole_0(sK25(U_99))
| ~ sP23(U_99) )
& ! [U_99] :
( m1_subset_1(sK25(U_99),k1_zfmisc_1(u1_struct_0(U_99)))
| ~ sP23(U_99) )
& ! [U_99] :
( sP23(U_99)
| ~ l1_struct_0(U_99)
| v3_struct_0(U_99) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_71_3]) ).
cnf(f_71_5,plain,
( sP23(U_99)
| ~ l1_struct_0(U_99)
| v3_struct_0(U_99) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_6,plain,
( m1_subset_1(sK25(U_99),k1_zfmisc_1(u1_struct_0(U_99)))
| ~ sP23(U_99) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_7,plain,
( ~ v1_xboole_0(sK25(U_99))
| ~ sP23(U_99) ),
inference(clausify,[status(thm)],[f_71_4]) ).
fof(f_72_1,plain,
? [A] :
( v3_lattices(A)
& ~ v3_struct_0(A)
& l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[rc6_lattices]) ).
fof(f_72_2,plain,
? [U_100] :
( v3_lattices(U_100)
& ~ v3_struct_0(U_100)
& l3_lattices(U_100) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
( v3_lattices(sK26)
& ~ v3_struct_0(sK26)
& l3_lattices(sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_100,sK26)],[f_72_2]) ).
fof(f_72_4,plain,
( v3_lattices(sK26)
& ~ v3_struct_0(sK26)
& l3_lattices(sK26) ),
inference(definitional_conversion,[status(esa)],[f_72_3]) ).
cnf(f_72_5,plain,
l3_lattices(sK26),
inference(clausify,[status(thm)],[f_72_4]) ).
cnf(f_72_6,plain,
~ v3_struct_0(sK26),
inference(clausify,[status(thm)],[f_72_4]) ).
cnf(f_72_7,plain,
v3_lattices(sK26),
inference(clausify,[status(thm)],[f_72_4]) ).
fof(f_73_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_73_2,plain,
? [U_101] :
( v10_lattices(U_101)
& v9_lattices(U_101)
& v8_lattices(U_101)
& v7_lattices(U_101)
& v6_lattices(U_101)
& v5_lattices(U_101)
& v4_lattices(U_101)
& v3_lattices(U_101)
& ~ v3_struct_0(U_101)
& l3_lattices(U_101) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
( v10_lattices(sK27)
& v9_lattices(sK27)
& v8_lattices(sK27)
& v7_lattices(sK27)
& v6_lattices(sK27)
& v5_lattices(sK27)
& v4_lattices(sK27)
& v3_lattices(sK27)
& ~ v3_struct_0(sK27)
& l3_lattices(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_101,sK27)],[f_73_2]) ).
fof(f_73_4,plain,
( v10_lattices(sK27)
& v9_lattices(sK27)
& v8_lattices(sK27)
& v7_lattices(sK27)
& v6_lattices(sK27)
& v5_lattices(sK27)
& v4_lattices(sK27)
& v3_lattices(sK27)
& ~ v3_struct_0(sK27)
& l3_lattices(sK27) ),
inference(definitional_conversion,[status(esa)],[f_73_3]) ).
cnf(f_73_5,plain,
l3_lattices(sK27),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_6,plain,
~ v3_struct_0(sK27),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_7,plain,
v3_lattices(sK27),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_8,plain,
v4_lattices(sK27),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_9,plain,
v5_lattices(sK27),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_10,plain,
v6_lattices(sK27),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_11,plain,
v7_lattices(sK27),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_12,plain,
v8_lattices(sK27),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_13,plain,
v9_lattices(sK27),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_14,plain,
v10_lattices(sK27),
inference(clausify,[status(thm)],[f_73_4]) ).
fof(f_74_1,plain,
! [A,B] :
( k15_filter_2(A,B) = k7_filter_2(A,B)
| ~ m2_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k15_filter_2]) ).
fof(f_74_2,plain,
! [U_103,U_102] :
( k15_filter_2(U_103,U_102) = k7_filter_2(U_103,U_102)
| ~ m2_filter_2(U_102,U_103)
| ~ l3_lattices(U_103)
| ~ v10_lattices(U_103)
| v3_struct_0(U_103) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_103,U_102] :
( k15_filter_2(U_103,U_102) = k7_filter_2(U_103,U_102)
| ~ m2_filter_2(U_102,U_103)
| ~ l3_lattices(U_103)
| ~ v10_lattices(U_103)
| v3_struct_0(U_103) ),
inference(definitional_conversion,[status(esa)],[f_74_2]) ).
cnf(f_74_4,plain,
( k15_filter_2(U_103,U_102) = k7_filter_2(U_103,U_102)
| ~ m2_filter_2(U_102,U_103)
| ~ l3_lattices(U_103)
| ~ v10_lattices(U_103)
| v3_struct_0(U_103) ),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [A] :
( ! [B] :
( ( m1_filter_2(B,A)
| ~ m1_filter_0(B,A) )
& ( m1_filter_0(B,A)
| ~ m1_filter_2(B,A) ) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[redefinition_m1_filter_2]) ).
fof(f_75_2,plain,
! [U_105] :
( ! [U_104] :
( ( m1_filter_2(U_104,U_105)
| ~ m1_filter_0(U_104,U_105) )
& ( m1_filter_0(U_104,U_105)
| ~ m1_filter_2(U_104,U_105) ) )
| ~ l3_lattices(U_105)
| ~ v10_lattices(U_105)
| v3_struct_0(U_105) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_105] :
( ( ! [U_107] :
( m1_filter_2(U_107,U_105)
| ~ m1_filter_0(U_107,U_105) )
& ! [U_106] :
( m1_filter_0(U_106,U_105)
| ~ m1_filter_2(U_106,U_105) ) )
| ~ l3_lattices(U_105)
| ~ v10_lattices(U_105)
| v3_struct_0(U_105) ),
inference(miniscope,[status(thm)],[f_75_2]) ).
fof(f_75_4,plain,
( ! [U_106,U_107,U_105] :
( m1_filter_2(U_107,U_105)
| ~ m1_filter_0(U_107,U_105)
| ~ sP24(U_106,U_107,U_105) )
& ! [U_106,U_107,U_105] :
( m1_filter_0(U_106,U_105)
| ~ m1_filter_2(U_106,U_105)
| ~ sP24(U_106,U_107,U_105) )
& ! [U_106,U_107,U_105] :
( sP24(U_106,U_107,U_105)
| ~ l3_lattices(U_105)
| ~ v10_lattices(U_105)
| v3_struct_0(U_105) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_75_3]) ).
cnf(f_75_5,plain,
( sP24(U_106,U_107,U_105)
| ~ l3_lattices(U_105)
| ~ v10_lattices(U_105)
| v3_struct_0(U_105) ),
inference(clausify,[status(thm)],[f_75_4]) ).
cnf(f_75_6,plain,
( m1_filter_0(U_106,U_105)
| ~ m1_filter_2(U_106,U_105)
| ~ sP24(U_106,U_107,U_105) ),
inference(clausify,[status(thm)],[f_75_4]) ).
cnf(f_75_7,plain,
( m1_filter_2(U_107,U_105)
| ~ m1_filter_0(U_107,U_105)
| ~ sP24(U_106,U_107,U_105) ),
inference(clausify,[status(thm)],[f_75_4]) ).
fof(f_76_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_76_2,plain,
! [U_110,U_109,U_108] :
( ( m2_relset_1(U_108,U_110,U_109)
| ~ m1_relset_1(U_108,U_110,U_109) )
& ( m1_relset_1(U_108,U_110,U_109)
| ~ m2_relset_1(U_108,U_110,U_109) ) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
( ! [U_116,U_114,U_112] :
( m2_relset_1(U_112,U_116,U_114)
| ~ m1_relset_1(U_112,U_116,U_114) )
& ! [U_115,U_113,U_111] :
( m1_relset_1(U_111,U_115,U_113)
| ~ m2_relset_1(U_111,U_115,U_113) ) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
fof(f_76_4,plain,
( ! [U_114,U_116,U_112] :
( m2_relset_1(U_112,U_116,U_114)
| ~ m1_relset_1(U_112,U_116,U_114) )
& ! [U_111,U_113,U_115] :
( m1_relset_1(U_111,U_115,U_113)
| ~ m2_relset_1(U_111,U_115,U_113) ) ),
inference(definitional_conversion,[status(esa)],[f_76_3]) ).
cnf(f_76_5,plain,
( m1_relset_1(U_111,U_115,U_113)
| ~ m2_relset_1(U_111,U_115,U_113) ),
inference(clausify,[status(thm)],[f_76_4]) ).
cnf(f_76_6,plain,
( m2_relset_1(U_112,U_116,U_114)
| ~ m1_relset_1(U_112,U_116,U_114) ),
inference(clausify,[status(thm)],[f_76_4]) ).
fof(f_77_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_77_2,plain,
! [U_118,U_117] : r1_tarski(U_118,U_118),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_118] : r1_tarski(U_118,U_118),
inference(miniscope,[status(thm)],[f_77_2]) ).
fof(f_77_4,plain,
! [U_118] : r1_tarski(U_118,U_118),
inference(definitional_conversion,[status(esa)],[f_77_3]) ).
cnf(f_77_5,plain,
r1_tarski(U_118,U_118),
inference(clausify,[status(thm)],[f_77_4]) ).
fof(f_78_1,plain,
! [A] :
( ! [B] :
( r2_hidden(k6_lattices(A),B)
| ~ l3_lattices(A)
| ~ v14_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A)
| ~ m1_filter_0(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t12_filter_0]) ).
fof(f_78_2,plain,
! [U_120] :
( ! [U_119] :
( r2_hidden(k6_lattices(U_120),U_119)
| ~ l3_lattices(U_120)
| ~ v14_lattices(U_120)
| ~ v10_lattices(U_120)
| v3_struct_0(U_120)
| ~ m1_filter_0(U_119,U_120) )
| ~ l3_lattices(U_120)
| ~ v10_lattices(U_120)
| v3_struct_0(U_120) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_120,U_119] :
( r2_hidden(k6_lattices(U_120),U_119)
| ~ l3_lattices(U_120)
| ~ v14_lattices(U_120)
| ~ v10_lattices(U_120)
| v3_struct_0(U_120)
| ~ m1_filter_0(U_119,U_120)
| ~ l3_lattices(U_120)
| ~ v10_lattices(U_120)
| v3_struct_0(U_120) ),
inference(definitional_conversion,[status(esa)],[f_78_2]) ).
cnf(f_78_4,plain,
( r2_hidden(k6_lattices(U_120),U_119)
| ~ l3_lattices(U_120)
| ~ v14_lattices(U_120)
| ~ v10_lattices(U_120)
| v3_struct_0(U_120)
| ~ m1_filter_0(U_119,U_120)
| ~ l3_lattices(U_120)
| ~ v10_lattices(U_120)
| v3_struct_0(U_120) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_79_2,plain,
! [U_122,U_121] :
( m1_subset_1(U_122,U_121)
| ~ r2_hidden(U_122,U_121) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_121,U_122] :
( m1_subset_1(U_122,U_121)
| ~ r2_hidden(U_122,U_121) ),
inference(definitional_conversion,[status(esa)],[f_79_2]) ).
cnf(f_79_4,plain,
( m1_subset_1(U_122,U_121)
| ~ r2_hidden(U_122,U_121) ),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_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_80_2,plain,
! [U_124,U_123] :
( r2_hidden(U_124,U_123)
| v1_xboole_0(U_123)
| ~ m1_subset_1(U_124,U_123) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_123,U_124] :
( r2_hidden(U_124,U_123)
| v1_xboole_0(U_123)
| ~ m1_subset_1(U_124,U_123) ),
inference(definitional_conversion,[status(esa)],[f_80_2]) ).
cnf(f_80_4,plain,
( r2_hidden(U_124,U_123)
| v1_xboole_0(U_123)
| ~ m1_subset_1(U_124,U_123) ),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_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_81_2,plain,
! [U_126,U_125] :
( ( m1_subset_1(U_126,k1_zfmisc_1(U_125))
| ~ r1_tarski(U_126,U_125) )
& ( r1_tarski(U_126,U_125)
| ~ m1_subset_1(U_126,k1_zfmisc_1(U_125)) ) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
( ! [U_130,U_128] :
( m1_subset_1(U_130,k1_zfmisc_1(U_128))
| ~ r1_tarski(U_130,U_128) )
& ! [U_129,U_127] :
( r1_tarski(U_129,U_127)
| ~ m1_subset_1(U_129,k1_zfmisc_1(U_127)) ) ),
inference(miniscope,[status(thm)],[f_81_2]) ).
fof(f_81_4,plain,
( ! [U_130,U_128] :
( m1_subset_1(U_130,k1_zfmisc_1(U_128))
| ~ r1_tarski(U_130,U_128) )
& ! [U_127,U_129] :
( r1_tarski(U_129,U_127)
| ~ m1_subset_1(U_129,k1_zfmisc_1(U_127)) ) ),
inference(definitional_conversion,[status(esa)],[f_81_3]) ).
cnf(f_81_5,plain,
( r1_tarski(U_129,U_127)
| ~ m1_subset_1(U_129,k1_zfmisc_1(U_127)) ),
inference(clausify,[status(thm)],[f_81_4]) ).
cnf(f_81_6,plain,
( m1_subset_1(U_130,k1_zfmisc_1(U_128))
| ~ r1_tarski(U_130,U_128) ),
inference(clausify,[status(thm)],[f_81_4]) ).
fof(f_82_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_82_2,plain,
! [U_133,U_132,U_131] :
( m1_subset_1(U_133,U_131)
| ~ m1_subset_1(U_132,k1_zfmisc_1(U_131))
| ~ r2_hidden(U_133,U_132) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_133,U_132,U_131] :
( m1_subset_1(U_133,U_131)
| ~ m1_subset_1(U_132,k1_zfmisc_1(U_131))
| ~ r2_hidden(U_133,U_132) ),
inference(definitional_conversion,[status(esa)],[f_82_2]) ).
cnf(f_82_4,plain,
( m1_subset_1(U_133,U_131)
| ~ m1_subset_1(U_132,k1_zfmisc_1(U_131))
| ~ r2_hidden(U_133,U_132) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_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_83_2,plain,
! [U_136,U_135,U_134] :
( ~ v1_xboole_0(U_134)
| ~ m1_subset_1(U_135,k1_zfmisc_1(U_134))
| ~ r2_hidden(U_136,U_135) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_136,U_135] :
( ! [U_134] :
( ~ v1_xboole_0(U_134)
| ~ m1_subset_1(U_135,k1_zfmisc_1(U_134)) )
| ~ r2_hidden(U_136,U_135) ),
inference(miniscope,[status(thm)],[f_83_2]) ).
fof(f_83_4,plain,
! [U_136,U_134,U_135] :
( ~ v1_xboole_0(U_134)
| ~ m1_subset_1(U_135,k1_zfmisc_1(U_134))
| ~ r2_hidden(U_136,U_135) ),
inference(definitional_conversion,[status(esa)],[f_83_3]) ).
cnf(f_83_5,plain,
( ~ v1_xboole_0(U_134)
| ~ m1_subset_1(U_135,k1_zfmisc_1(U_134))
| ~ r2_hidden(U_136,U_135) ),
inference(clausify,[status(thm)],[f_83_4]) ).
fof(f_84_1,plain,
! [A] :
( ( ( v13_lattices(A)
| ~ v14_lattices(k1_lattice2(A)) )
& ( v14_lattices(k1_lattice2(A))
| ~ v13_lattices(A) ) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t63_lattice2]) ).
fof(f_84_2,plain,
! [U_137] :
( ( ( v13_lattices(U_137)
| ~ v14_lattices(k1_lattice2(U_137)) )
& ( v14_lattices(k1_lattice2(U_137))
| ~ v13_lattices(U_137) ) )
| ~ l3_lattices(U_137)
| ~ v10_lattices(U_137)
| v3_struct_0(U_137) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
( ! [U_137] :
( v13_lattices(U_137)
| ~ v14_lattices(k1_lattice2(U_137))
| ~ sP25(U_137) )
& ! [U_137] :
( v14_lattices(k1_lattice2(U_137))
| ~ v13_lattices(U_137)
| ~ sP25(U_137) )
& ! [U_137] :
( sP25(U_137)
| ~ l3_lattices(U_137)
| ~ v10_lattices(U_137)
| v3_struct_0(U_137) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_84_2]) ).
cnf(f_84_4,plain,
( sP25(U_137)
| ~ l3_lattices(U_137)
| ~ v10_lattices(U_137)
| v3_struct_0(U_137) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_5,plain,
( v14_lattices(k1_lattice2(U_137))
| ~ v13_lattices(U_137)
| ~ sP25(U_137) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_6,plain,
( v13_lattices(U_137)
| ~ v14_lattices(k1_lattice2(U_137))
| ~ sP25(U_137) ),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_85_2,plain,
! [U_138] :
( U_138 = k1_xboole_0
| ~ v1_xboole_0(U_138) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_138] :
( U_138 = k1_xboole_0
| ~ v1_xboole_0(U_138) ),
inference(definitional_conversion,[status(esa)],[f_85_2]) ).
cnf(f_85_4,plain,
( U_138 = k1_xboole_0
| ~ v1_xboole_0(U_138) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [A] :
( k5_lattices(A) = k6_lattices(k1_lattice2(A))
| ~ l3_lattices(A)
| ~ v13_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t78_lattice2]) ).
fof(f_86_2,plain,
! [U_139] :
( k5_lattices(U_139) = k6_lattices(k1_lattice2(U_139))
| ~ l3_lattices(U_139)
| ~ v13_lattices(U_139)
| ~ v10_lattices(U_139)
| v3_struct_0(U_139) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_139] :
( k5_lattices(U_139) = k6_lattices(k1_lattice2(U_139))
| ~ l3_lattices(U_139)
| ~ v13_lattices(U_139)
| ~ v10_lattices(U_139)
| v3_struct_0(U_139) ),
inference(definitional_conversion,[status(esa)],[f_86_2]) ).
cnf(f_86_4,plain,
( k5_lattices(U_139) = k6_lattices(k1_lattice2(U_139))
| ~ l3_lattices(U_139)
| ~ v13_lattices(U_139)
| ~ v10_lattices(U_139)
| v3_struct_0(U_139) ),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_87_2,plain,
! [U_141,U_140] :
( ~ v1_xboole_0(U_140)
| ~ r2_hidden(U_141,U_140) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_140,U_141] :
( ~ v1_xboole_0(U_140)
| ~ r2_hidden(U_141,U_140) ),
inference(definitional_conversion,[status(esa)],[f_87_2]) ).
cnf(f_87_4,plain,
( ~ v1_xboole_0(U_140)
| ~ r2_hidden(U_141,U_140) ),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_88_2,plain,
! [U_143,U_142] :
( ~ v1_xboole_0(U_142)
| U_143 = U_142
| ~ v1_xboole_0(U_143) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_143] :
( ! [U_142] :
( ~ v1_xboole_0(U_142)
| U_143 = U_142 )
| ~ v1_xboole_0(U_143) ),
inference(miniscope,[status(thm)],[f_88_2]) ).
fof(f_88_4,plain,
! [U_142,U_143] :
( ~ v1_xboole_0(U_142)
| U_143 = U_142
| ~ v1_xboole_0(U_143) ),
inference(definitional_conversion,[status(esa)],[f_88_3]) ).
cnf(f_88_5,plain,
( ~ v1_xboole_0(U_142)
| U_143 = U_142
| ~ v1_xboole_0(U_143) ),
inference(clausify,[status(thm)],[f_88_4]) ).
cnf(f_16_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_3]) ).
cnf(f_17_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_3]) ).
cnf(f_18_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_3]) ).
cnf(f_23_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_23_3]) ).
cnf(f_28_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_3]) ).
cnf(f_29_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_3]) ).
cnf(f_34_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_34_3]) ).
cnf(f_78_4_simplified,plain,
( r2_hidden(k6_lattices(U_120),U_119)
| ~ l3_lattices(U_120)
| ~ v14_lattices(U_120)
| ~ v10_lattices(U_120)
| v3_struct_0(U_120)
| ~ m1_filter_0(U_119,U_120) ),
inference(simplify_clause,[status(thm)],[f_78_4]) ).
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,
( k5_lattices(Eq_x_0) = k5_lattices(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,axiom,
( u2_lattices(Eq_x_0) = u2_lattices(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( u1_lattices(Eq_x_0) = u1_lattices(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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_9,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_10,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_11,axiom,
( k1_lattice2(Eq_x_0) = k1_lattice2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( k7_filter_2(Eq_x_0,Eq_x_1) = k7_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_13,axiom,
( k15_filter_2(Eq_x_0,Eq_x_1) = k15_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_14,axiom,
( k6_lattices(Eq_x_0) = k6_lattices(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( sK20(Eq_x_0) = sK20(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( sK25(Eq_x_0) = sK25(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,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_27,axiom,
( v10_lattices(Eq_y_0)
| ~ v10_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( l3_lattices(Eq_y_0)
| ~ l3_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( m2_filter_2(Eq_y_0,Eq_y_1)
| ~ m2_filter_2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( v13_lattices(Eq_y_0)
| ~ v13_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,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_32,axiom,
( v3_lattices(Eq_y_0)
| ~ v3_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( v1_xboole_0(Eq_y_0)
| ~ v1_xboole_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( v1_funct_1(Eq_y_0)
| ~ v1_funct_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( v4_lattices(Eq_y_0)
| ~ v4_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( v5_lattices(Eq_y_0)
| ~ v5_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( v6_lattices(Eq_y_0)
| ~ v6_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( v7_lattices(Eq_y_0)
| ~ v7_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( v8_lattices(Eq_y_0)
| ~ v8_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( v9_lattices(Eq_y_0)
| ~ v9_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( m1_subset_1(Eq_y_0,Eq_y_1)
| ~ m1_subset_1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( v1_relat_1(Eq_y_0)
| ~ v1_relat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,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_44,axiom,
( v14_lattices(Eq_y_0)
| ~ v14_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( v15_lattices(Eq_y_0)
| ~ v15_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,
( m1_filter_2(Eq_y_0,Eq_y_1)
| ~ m1_filter_2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( l1_lattices(Eq_y_0)
| ~ l1_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( l2_lattices(Eq_y_0)
| ~ l2_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,
( m1_filter_0(Eq_y_0,Eq_y_1)
| ~ m1_filter_0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,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_54,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_55,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_56,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_57,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_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(equality_59,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_60,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_61,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( sP3(Eq_y_0)
| ~ sP3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_64,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(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_65,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_66,axiom,
( sP7(Eq_y_0)
| ~ sP7(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_67,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_68,axiom,
( sP9(Eq_y_0,Eq_y_1)
| ~ sP9(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_69,axiom,
( sP10(Eq_y_0,Eq_y_1)
| ~ sP10(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_70,axiom,
( sP11(Eq_y_0)
| ~ sP11(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_71,axiom,
( sP12(Eq_y_0)
| ~ sP12(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_72,axiom,
( sP13(Eq_y_0)
| ~ sP13(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_73,axiom,
( sP14(Eq_y_0)
| ~ sP14(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_74,axiom,
( sP15(Eq_y_0)
| ~ sP15(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_75,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP16(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_76,axiom,
( sP17(Eq_y_0)
| ~ sP17(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_77,axiom,
( sP18(Eq_y_0)
| ~ sP18(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_78,axiom,
( sP19(Eq_y_0)
| ~ sP19(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_79,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_80,axiom,
( sP21(Eq_y_0)
| ~ sP21(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_81,axiom,
( sP22(Eq_y_0)
| ~ sP22(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_82,axiom,
( sP23(Eq_y_0)
| ~ sP23(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_83,axiom,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP24(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_84,axiom,
( sP25(Eq_y_0)
| ~ sP25(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT301+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 19 13:10:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 285.15/285.42 % SZS status Theorem for theBenchmark
% 285.15/285.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------