%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LAT326+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:48:13 AM UTC 2026
% Result : Theorem 270.14s 270.50s
% Output : Proof 271.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t62_filter_2,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) )
=> ! [C] :
( ( m2_relset_1(C,k2_zfmisc_1(B,B),B)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& v1_funct_1(C) )
=> ! [D] :
( ( m2_relset_1(D,k2_zfmisc_1(B,B),B)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& v1_funct_1(D) )
=> ( ( D = k1_realset1(u1_lattices(A),B)
& C = k1_realset1(u2_lattices(A),B) )
=> ( r1_lattice2(B,D,C)
& r1_lattice2(B,C,D)
& v2_binop_1(D,B)
& v1_binop_1(D,B)
& v2_binop_1(C,B)
& v1_binop_1(C,B) ) ) ) ) ) ),
file('theBenchmark.p',t62_filter_2) ).
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(d3_realset1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] : k1_realset1(A,B) = k7_relat_1(A,k2_zfmisc_1(B,B)) ),
file('theBenchmark.p',d3_realset1) ).
fof(dt_k1_realset1,axiom,
$true,
file('theBenchmark.p',dt_k1_realset1) ).
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_k7_relat_1,axiom,
! [A,B] :
( v1_relat_1(A)
=> v1_relat_1(k7_relat_1(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
fof(dt_l1_lattices,axiom,
! [A] :
( l1_lattices(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_lattices) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_l2_lattices,axiom,
! [A] :
( l2_lattices(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l2_lattices) ).
fof(dt_l3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( l2_lattices(A)
& l1_lattices(A) ) ),
file('theBenchmark.p',dt_l3_lattices) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_lattice4,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_lattice4(B,A)
=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',dt_m2_lattice4) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(dt_u1_lattices,axiom,
! [A] :
( l1_lattices(A)
=> ( m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_lattices(A)) ) ),
file('theBenchmark.p',dt_u1_lattices) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(dt_u2_lattices,axiom,
! [A] :
( l2_lattices(A)
=> ( m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u2_lattices(A)) ) ),
file('theBenchmark.p',dt_u2_lattices) ).
fof(existence_l1_lattices,axiom,
? [A] : l1_lattices(A),
file('theBenchmark.p',existence_l1_lattices) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l2_lattices,axiom,
? [A] : l2_lattices(A),
file('theBenchmark.p',existence_l2_lattices) ).
fof(existence_l3_lattices,axiom,
? [A] : l3_lattices(A),
file('theBenchmark.p',existence_l3_lattices) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_lattice4,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] : m2_lattice4(B,A) ),
file('theBenchmark.p',existence_m2_lattice4) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(fc1_realset1,axiom,
! [A,B] :
( v1_relat_1(A)
=> v1_relat_1(k1_realset1(A,B)) ),
file('theBenchmark.p',fc1_realset1) ).
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(fc2_realset1,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_relat_1(A) )
=> ( v1_funct_1(k1_realset1(A,B))
& v1_relat_1(k1_realset1(A,B)) ) ),
file('theBenchmark.p',fc2_realset1) ).
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(fc4_funct_1,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_relat_1(A) )
=> ( v1_funct_1(k7_relat_1(A,B))
& v1_relat_1(k7_relat_1(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
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(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_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc5_struct_0) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_filter_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B) )
=> ! [C] :
( ( m2_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C) )
=> ! [D] :
( ( m2_relset_1(D,k2_zfmisc_1(B,B),B)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& v1_funct_1(D) )
=> ( D = k1_realset1(C,B)
=> ( ( v2_binop_1(C,A)
=> v2_binop_1(D,B) )
& ( v3_binop_1(C,A)
=> v3_binop_1(D,B) )
& ( v1_binop_1(C,A)
=> v1_binop_1(D,B) ) ) ) ) ) ) ),
file('theBenchmark.p',t1_filter_2) ).
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(t40_lattice2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> r1_lattice2(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ),
file('theBenchmark.p',t40_lattice2) ).
fof(t41_lattice2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> r1_lattice2(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ),
file('theBenchmark.p',t41_lattice2) ).
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_filter_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B) )
=> ! [C] :
( ( m2_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C) )
=> ! [D] :
( ( m2_relset_1(D,k2_zfmisc_1(A,A),A)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& v1_funct_1(D) )
=> ! [E] :
( ( m2_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(E) )
=> ! [F] :
( ( m2_relset_1(F,k2_zfmisc_1(B,B),B)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& v1_funct_1(F) )
=> ( ( r1_lattice2(A,C,D)
& F = k1_realset1(D,B)
& E = k1_realset1(C,B) )
=> r1_lattice2(B,E,F) ) ) ) ) ) ) ),
file('theBenchmark.p',t5_filter_2) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& A != B
& v1_xboole_0(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) )
=> ! [C] :
( ( m2_relset_1(C,k2_zfmisc_1(B,B),B)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& v1_funct_1(C) )
=> ! [D] :
( ( m2_relset_1(D,k2_zfmisc_1(B,B),B)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& v1_funct_1(D) )
=> ( ( D = k1_realset1(u1_lattices(A),B)
& C = k1_realset1(u2_lattices(A),B) )
=> ( r1_lattice2(B,D,C)
& r1_lattice2(B,C,D)
& v2_binop_1(D,B)
& v1_binop_1(D,B)
& v2_binop_1(C,B)
& v1_binop_1(C,B) ) ) ) ) ) ),
inference(negate,[status(cth)],[t62_filter_2]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ( ~ r1_lattice2(B,D,C)
| ~ r1_lattice2(B,C,D)
| ~ v2_binop_1(D,B)
| ~ v1_binop_1(D,B)
| ~ v2_binop_1(C,B)
| ~ v1_binop_1(C,B) )
& D = k1_realset1(u1_lattices(A),B)
& C = k1_realset1(u2_lattices(A),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& v1_funct_1(D) )
& m2_relset_1(C,k2_zfmisc_1(B,B),B)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& v1_funct_1(C) )
& m2_lattice4(B,A)
& ~ v1_xboole_0(B) )
& 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_3] :
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ( ~ r1_lattice2(U_2,U_0,U_1)
| ~ r1_lattice2(U_2,U_1,U_0)
| ~ v2_binop_1(U_0,U_2)
| ~ v1_binop_1(U_0,U_2)
| ~ v2_binop_1(U_1,U_2)
| ~ v1_binop_1(U_1,U_2) )
& U_0 = k1_realset1(u1_lattices(U_3),U_2)
& U_1 = k1_realset1(u2_lattices(U_3),U_2)
& m2_relset_1(U_0,k2_zfmisc_1(U_2,U_2),U_2)
& v1_funct_2(U_0,k2_zfmisc_1(U_2,U_2),U_2)
& v1_funct_1(U_0) )
& m2_relset_1(U_1,k2_zfmisc_1(U_2,U_2),U_2)
& v1_funct_2(U_1,k2_zfmisc_1(U_2,U_2),U_2)
& v1_funct_1(U_1) )
& m2_lattice4(U_2,U_3)
& ~ v1_xboole_0(U_2) )
& l3_lattices(U_3)
& v10_lattices(U_3)
& ~ v3_struct_0(U_3) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ( ~ r1_lattice2(U_2,U_0,U_1)
| ~ r1_lattice2(U_2,U_1,U_0)
| ~ v2_binop_1(U_0,U_2)
| ~ v1_binop_1(U_0,U_2)
| ~ v2_binop_1(U_1,U_2)
| ~ v1_binop_1(U_1,U_2) )
& U_0 = k1_realset1(u1_lattices(sK1),U_2)
& U_1 = k1_realset1(u2_lattices(sK1),U_2)
& m2_relset_1(U_0,k2_zfmisc_1(U_2,U_2),U_2)
& v1_funct_2(U_0,k2_zfmisc_1(U_2,U_2),U_2)
& v1_funct_1(U_0) )
& m2_relset_1(U_1,k2_zfmisc_1(U_2,U_2),U_2)
& v1_funct_2(U_1,k2_zfmisc_1(U_2,U_2),U_2)
& v1_funct_1(U_1) )
& m2_lattice4(U_2,sK1)
& ~ v1_xboole_0(U_2) )
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_1] :
( ? [U_0] :
( ( ~ r1_lattice2(sK2,U_0,U_1)
| ~ r1_lattice2(sK2,U_1,U_0)
| ~ v2_binop_1(U_0,sK2)
| ~ v1_binop_1(U_0,sK2)
| ~ v2_binop_1(U_1,sK2)
| ~ v1_binop_1(U_1,sK2) )
& U_0 = k1_realset1(u1_lattices(sK1),sK2)
& U_1 = k1_realset1(u2_lattices(sK1),sK2)
& m2_relset_1(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(U_0) )
& m2_relset_1(U_1,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(U_1,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(U_1) )
& m2_lattice4(sK2,sK1)
& ~ v1_xboole_0(sK2)
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_2,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ? [U_0] :
( ( ~ r1_lattice2(sK2,U_0,sK3)
| ~ r1_lattice2(sK2,sK3,U_0)
| ~ v2_binop_1(U_0,sK2)
| ~ v1_binop_1(U_0,sK2)
| ~ v2_binop_1(sK3,sK2)
| ~ v1_binop_1(sK3,sK2) )
& U_0 = k1_realset1(u1_lattices(sK1),sK2)
& sK3 = k1_realset1(u2_lattices(sK1),sK2)
& m2_relset_1(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(U_0) )
& m2_relset_1(sK3,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(sK3,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(sK3)
& m2_lattice4(sK2,sK1)
& ~ v1_xboole_0(sK2)
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_1,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ( ~ r1_lattice2(sK2,sK4,sK3)
| ~ r1_lattice2(sK2,sK3,sK4)
| ~ v2_binop_1(sK4,sK2)
| ~ v1_binop_1(sK4,sK2)
| ~ v2_binop_1(sK3,sK2)
| ~ v1_binop_1(sK3,sK2) )
& sK4 = k1_realset1(u1_lattices(sK1),sK2)
& sK3 = k1_realset1(u2_lattices(sK1),sK2)
& m2_relset_1(sK4,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(sK4,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(sK4)
& m2_relset_1(sK3,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(sK3,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(sK3)
& m2_lattice4(sK2,sK1)
& ~ v1_xboole_0(sK2)
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_0,sK4)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ( ~ r1_lattice2(sK2,sK4,sK3)
| ~ r1_lattice2(sK2,sK3,sK4)
| ~ v2_binop_1(sK4,sK2)
| ~ v1_binop_1(sK4,sK2)
| ~ v2_binop_1(sK3,sK2)
| ~ v1_binop_1(sK3,sK2) )
& sK4 = k1_realset1(u1_lattices(sK1),sK2)
& sK3 = k1_realset1(u2_lattices(sK1),sK2)
& m2_relset_1(sK4,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(sK4,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(sK4)
& m2_relset_1(sK3,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(sK3,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(sK3)
& m2_lattice4(sK2,sK1)
& ~ v1_xboole_0(sK2)
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(definitional_conversion,[status(esa)],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_10,negated_conjecture,
v10_lattices(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_11,negated_conjecture,
l3_lattices(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_12,negated_conjecture,
~ v1_xboole_0(sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_13,negated_conjecture,
m2_lattice4(sK2,sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_14,negated_conjecture,
v1_funct_1(sK3),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_15,negated_conjecture,
v1_funct_2(sK3,k2_zfmisc_1(sK2,sK2),sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_16,negated_conjecture,
m2_relset_1(sK3,k2_zfmisc_1(sK2,sK2),sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_17,negated_conjecture,
v1_funct_1(sK4),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_18,negated_conjecture,
v1_funct_2(sK4,k2_zfmisc_1(sK2,sK2),sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_19,negated_conjecture,
m2_relset_1(sK4,k2_zfmisc_1(sK2,sK2),sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_20,negated_conjecture,
sK3 = k1_realset1(u2_lattices(sK1),sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_21,negated_conjecture,
sK4 = k1_realset1(u1_lattices(sK1),sK2),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_22,negated_conjecture,
( ~ r1_lattice2(sK2,sK4,sK3)
| ~ r1_lattice2(sK2,sK3,sK4)
| ~ v2_binop_1(sK4,sK2)
| ~ v1_binop_1(sK4,sK2)
| ~ v2_binop_1(sK3,sK2)
| ~ v1_binop_1(sK3,sK2) ),
inference(clausify,[status(thm)],[f_1_8]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_2_2,plain,
! [U_5,U_4] :
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_5,U_4] :
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( v1_funct_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_3_2,plain,
! [U_6] :
( v1_funct_1(U_6)
| ~ v1_xboole_0(U_6) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_6] :
( v1_funct_1(U_6)
| ~ v1_xboole_0(U_6) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( v1_funct_1(U_6)
| ~ v1_xboole_0(U_6) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_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_4_2,plain,
! [U_7] :
( ( v9_lattices(U_7)
& v8_lattices(U_7)
& v7_lattices(U_7)
& v6_lattices(U_7)
& v5_lattices(U_7)
& v4_lattices(U_7)
& ~ v3_struct_0(U_7) )
| ~ v10_lattices(U_7)
| v3_struct_0(U_7)
| ~ l3_lattices(U_7) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_7] :
( v9_lattices(U_7)
| ~ sP0(U_7) )
& ! [U_7] :
( v8_lattices(U_7)
| ~ sP0(U_7) )
& ! [U_7] :
( v7_lattices(U_7)
| ~ sP0(U_7) )
& ! [U_7] :
( v6_lattices(U_7)
| ~ sP0(U_7) )
& ! [U_7] :
( v5_lattices(U_7)
| ~ sP0(U_7) )
& ! [U_7] :
( v4_lattices(U_7)
| ~ sP0(U_7) )
& ! [U_7] :
( ~ v3_struct_0(U_7)
| ~ sP0(U_7) )
& ! [U_7] :
( sP0(U_7)
| ~ v10_lattices(U_7)
| v3_struct_0(U_7)
| ~ l3_lattices(U_7) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_4_2]) ).
cnf(f_4_4,plain,
( sP0(U_7)
| ~ v10_lattices(U_7)
| v3_struct_0(U_7)
| ~ l3_lattices(U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ v3_struct_0(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( v4_lattices(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_7,plain,
( v5_lattices(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_8,plain,
( v6_lattices(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_9,plain,
( v7_lattices(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_10,plain,
( v8_lattices(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_11,plain,
( v9_lattices(U_7)
| ~ sP0(U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_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_5_2,plain,
! [U_10,U_9,U_8] :
( v1_relat_1(U_8)
| ~ m1_subset_1(U_8,k1_zfmisc_1(k2_zfmisc_1(U_10,U_9))) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_10,U_8,U_9] :
( v1_relat_1(U_8)
| ~ m1_subset_1(U_8,k1_zfmisc_1(k2_zfmisc_1(U_10,U_9))) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( v1_relat_1(U_8)
| ~ m1_subset_1(U_8,k1_zfmisc_1(k2_zfmisc_1(U_10,U_9))) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_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_6_2,plain,
! [U_11] :
( ( v2_funct_1(U_11)
& v1_funct_1(U_11)
& v1_relat_1(U_11) )
| ~ v1_funct_1(U_11)
| ~ v1_xboole_0(U_11)
| ~ v1_relat_1(U_11) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_11] :
( v2_funct_1(U_11)
| ~ sP1(U_11) )
& ! [U_11] :
( v1_funct_1(U_11)
| ~ sP1(U_11) )
& ! [U_11] :
( v1_relat_1(U_11)
| ~ sP1(U_11) )
& ! [U_11] :
( sP1(U_11)
| ~ v1_funct_1(U_11)
| ~ v1_xboole_0(U_11)
| ~ v1_relat_1(U_11) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP1(U_11)
| ~ v1_funct_1(U_11)
| ~ v1_xboole_0(U_11)
| ~ v1_relat_1(U_11) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( v1_relat_1(U_11)
| ~ sP1(U_11) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( v1_funct_1(U_11)
| ~ sP1(U_11) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( v2_funct_1(U_11)
| ~ sP1(U_11) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_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_7_2,plain,
! [U_12] :
( ( v10_lattices(U_12)
& ~ v3_struct_0(U_12) )
| ~ v9_lattices(U_12)
| ~ v8_lattices(U_12)
| ~ v7_lattices(U_12)
| ~ v6_lattices(U_12)
| ~ v5_lattices(U_12)
| ~ v4_lattices(U_12)
| v3_struct_0(U_12)
| ~ l3_lattices(U_12) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_12] :
( v10_lattices(U_12)
| ~ sP2(U_12) )
& ! [U_12] :
( ~ v3_struct_0(U_12)
| ~ sP2(U_12) )
& ! [U_12] :
( sP2(U_12)
| ~ v9_lattices(U_12)
| ~ v8_lattices(U_12)
| ~ v7_lattices(U_12)
| ~ v6_lattices(U_12)
| ~ v5_lattices(U_12)
| ~ v4_lattices(U_12)
| v3_struct_0(U_12)
| ~ l3_lattices(U_12) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP2(U_12)
| ~ v9_lattices(U_12)
| ~ v8_lattices(U_12)
| ~ v7_lattices(U_12)
| ~ v6_lattices(U_12)
| ~ v5_lattices(U_12)
| ~ v4_lattices(U_12)
| v3_struct_0(U_12)
| ~ l3_lattices(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( ~ v3_struct_0(U_12)
| ~ sP2(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( v10_lattices(U_12)
| ~ sP2(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] : k1_realset1(A,B) = k7_relat_1(A,k2_zfmisc_1(B,B))
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[d3_realset1]) ).
fof(f_8_2,plain,
! [U_14] :
( ! [U_13] : k1_realset1(U_14,U_13) = k7_relat_1(U_14,k2_zfmisc_1(U_13,U_13))
| ~ v1_relat_1(U_14) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_14,U_13] :
( k1_realset1(U_14,U_13) = k7_relat_1(U_14,k2_zfmisc_1(U_13,U_13))
| ~ v1_relat_1(U_14) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( k1_realset1(U_14,U_13) = k7_relat_1(U_14,k2_zfmisc_1(U_13,U_13))
| ~ v1_relat_1(U_14) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_realset1]) ).
fof(f_9_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
$true,
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_10_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
$true,
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_11_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_11_1]) ).
cnf(f_11_3,plain,
$true,
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_12_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_12_1]) ).
cnf(f_12_3,plain,
$true,
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A,B] :
( v1_relat_1(k7_relat_1(A,B))
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_13_2,plain,
! [U_16,U_15] :
( v1_relat_1(k7_relat_1(U_16,U_15))
| ~ v1_relat_1(U_16) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_16] :
( ! [U_15] : v1_relat_1(k7_relat_1(U_16,U_15))
| ~ v1_relat_1(U_16) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
! [U_16,U_15] :
( v1_relat_1(k7_relat_1(U_16,U_15))
| ~ v1_relat_1(U_16) ),
inference(definitional_conversion,[status(esa)],[f_13_3]) ).
cnf(f_13_5,plain,
( v1_relat_1(k7_relat_1(U_16,U_15))
| ~ v1_relat_1(U_16) ),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_lattices]) ).
fof(f_14_2,plain,
! [U_17] :
( l1_struct_0(U_17)
| ~ l1_lattices(U_17) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_17] :
( l1_struct_0(U_17)
| ~ l1_lattices(U_17) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( l1_struct_0(U_17)
| ~ l1_lattices(U_17) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
fof(f_15_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_15_1]) ).
cnf(f_15_3,plain,
$true,
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_lattices]) ).
fof(f_16_2,plain,
! [U_18] :
( l1_struct_0(U_18)
| ~ l2_lattices(U_18) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_18] :
( l1_struct_0(U_18)
| ~ l2_lattices(U_18) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( l1_struct_0(U_18)
| ~ l2_lattices(U_18) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A] :
( ( l2_lattices(A)
& l1_lattices(A) )
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l3_lattices]) ).
fof(f_17_2,plain,
! [U_19] :
( ( l2_lattices(U_19)
& l1_lattices(U_19) )
| ~ l3_lattices(U_19) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_19] :
( l2_lattices(U_19)
| ~ sP3(U_19) )
& ! [U_19] :
( l1_lattices(U_19)
| ~ sP3(U_19) )
& ! [U_19] :
( sP3(U_19)
| ~ l3_lattices(U_19) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_17_2]) ).
cnf(f_17_4,plain,
( sP3(U_19)
| ~ l3_lattices(U_19) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
( l1_lattices(U_19)
| ~ sP3(U_19) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_6,plain,
( l2_lattices(U_19)
| ~ sP3(U_19) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_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,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_19_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_19_1]) ).
cnf(f_19_3,plain,
$true,
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_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_20_2,plain,
! [U_21] :
( ! [U_20] :
( m1_subset_1(U_20,k1_zfmisc_1(u1_struct_0(U_21)))
| ~ m2_lattice4(U_20,U_21) )
| ~ l3_lattices(U_21)
| ~ v10_lattices(U_21)
| v3_struct_0(U_21) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_20,U_21] :
( m1_subset_1(U_20,k1_zfmisc_1(u1_struct_0(U_21)))
| ~ m2_lattice4(U_20,U_21)
| ~ l3_lattices(U_21)
| ~ v10_lattices(U_21)
| v3_struct_0(U_21) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( m1_subset_1(U_20,k1_zfmisc_1(u1_struct_0(U_21)))
| ~ m2_lattice4(U_20,U_21)
| ~ l3_lattices(U_21)
| ~ v10_lattices(U_21)
| v3_struct_0(U_21) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_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_21_2,plain,
! [U_24,U_23,U_22] :
( m1_subset_1(U_22,k1_zfmisc_1(k2_zfmisc_1(U_24,U_23)))
| ~ m2_relset_1(U_22,U_24,U_23) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_24,U_22,U_23] :
( m1_subset_1(U_22,k1_zfmisc_1(k2_zfmisc_1(U_24,U_23)))
| ~ m2_relset_1(U_22,U_24,U_23) ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( m1_subset_1(U_22,k1_zfmisc_1(k2_zfmisc_1(U_24,U_23)))
| ~ m2_relset_1(U_22,U_24,U_23) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_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_22_2,plain,
! [U_25] :
( ( m2_relset_1(u1_lattices(U_25),k2_zfmisc_1(u1_struct_0(U_25),u1_struct_0(U_25)),u1_struct_0(U_25))
& v1_funct_2(u1_lattices(U_25),k2_zfmisc_1(u1_struct_0(U_25),u1_struct_0(U_25)),u1_struct_0(U_25))
& v1_funct_1(u1_lattices(U_25)) )
| ~ l1_lattices(U_25) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_25] :
( m2_relset_1(u1_lattices(U_25),k2_zfmisc_1(u1_struct_0(U_25),u1_struct_0(U_25)),u1_struct_0(U_25))
| ~ sP4(U_25) )
& ! [U_25] :
( v1_funct_2(u1_lattices(U_25),k2_zfmisc_1(u1_struct_0(U_25),u1_struct_0(U_25)),u1_struct_0(U_25))
| ~ sP4(U_25) )
& ! [U_25] :
( v1_funct_1(u1_lattices(U_25))
| ~ sP4(U_25) )
& ! [U_25] :
( sP4(U_25)
| ~ l1_lattices(U_25) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_22_2]) ).
cnf(f_22_4,plain,
( sP4(U_25)
| ~ l1_lattices(U_25) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( v1_funct_1(u1_lattices(U_25))
| ~ sP4(U_25) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
( v1_funct_2(u1_lattices(U_25),k2_zfmisc_1(u1_struct_0(U_25),u1_struct_0(U_25)),u1_struct_0(U_25))
| ~ sP4(U_25) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_7,plain,
( m2_relset_1(u1_lattices(U_25),k2_zfmisc_1(u1_struct_0(U_25),u1_struct_0(U_25)),u1_struct_0(U_25))
| ~ sP4(U_25) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_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] :
( ( 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_24_2,plain,
! [U_26] :
( ( m2_relset_1(u2_lattices(U_26),k2_zfmisc_1(u1_struct_0(U_26),u1_struct_0(U_26)),u1_struct_0(U_26))
& v1_funct_2(u2_lattices(U_26),k2_zfmisc_1(u1_struct_0(U_26),u1_struct_0(U_26)),u1_struct_0(U_26))
& v1_funct_1(u2_lattices(U_26)) )
| ~ l2_lattices(U_26) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_26] :
( m2_relset_1(u2_lattices(U_26),k2_zfmisc_1(u1_struct_0(U_26),u1_struct_0(U_26)),u1_struct_0(U_26))
| ~ sP5(U_26) )
& ! [U_26] :
( v1_funct_2(u2_lattices(U_26),k2_zfmisc_1(u1_struct_0(U_26),u1_struct_0(U_26)),u1_struct_0(U_26))
| ~ sP5(U_26) )
& ! [U_26] :
( v1_funct_1(u2_lattices(U_26))
| ~ sP5(U_26) )
& ! [U_26] :
( sP5(U_26)
| ~ l2_lattices(U_26) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_24_2]) ).
cnf(f_24_4,plain,
( sP5(U_26)
| ~ l2_lattices(U_26) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( v1_funct_1(u2_lattices(U_26))
| ~ sP5(U_26) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
( v1_funct_2(u2_lattices(U_26),k2_zfmisc_1(u1_struct_0(U_26),u1_struct_0(U_26)),u1_struct_0(U_26))
| ~ sP5(U_26) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_7,plain,
( m2_relset_1(u2_lattices(U_26),k2_zfmisc_1(u1_struct_0(U_26),u1_struct_0(U_26)),u1_struct_0(U_26))
| ~ sP5(U_26) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] : l1_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l1_lattices]) ).
fof(f_25_2,plain,
? [U_27] : l1_lattices(U_27),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
l1_lattices(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_27,sK5)],[f_25_2]) ).
fof(f_25_4,plain,
l1_lattices(sK5),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
l1_lattices(sK5),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_26_2,plain,
? [U_28] : l1_struct_0(U_28),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
l1_struct_0(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_28,sK6)],[f_26_2]) ).
fof(f_26_4,plain,
l1_struct_0(sK6),
inference(definitional_conversion,[status(esa)],[f_26_3]) ).
cnf(f_26_5,plain,
l1_struct_0(sK6),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_1,plain,
? [A] : l2_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l2_lattices]) ).
fof(f_27_2,plain,
? [U_29] : l2_lattices(U_29),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
l2_lattices(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_29,sK7)],[f_27_2]) ).
fof(f_27_4,plain,
l2_lattices(sK7),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
l2_lattices(sK7),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
? [A] : l3_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l3_lattices]) ).
fof(f_28_2,plain,
? [U_30] : l3_lattices(U_30),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
l3_lattices(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_30,sK8)],[f_28_2]) ).
fof(f_28_4,plain,
l3_lattices(sK8),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
l3_lattices(sK8),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_29_2,plain,
! [U_33,U_32] :
? [U_31] : m1_relset_1(U_31,U_33,U_32),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_33,U_32] : m1_relset_1(sK9(U_33,U_32),U_33,U_32),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_31,sK9(U_33,U_32))],[f_29_2]) ).
fof(f_29_4,plain,
! [U_32,U_33] : m1_relset_1(sK9(U_33,U_32),U_33,U_32),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
m1_relset_1(sK9(U_33,U_32),U_33,U_32),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_30_2,plain,
! [U_35] :
? [U_34] : m1_subset_1(U_34,U_35),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_35] : m1_subset_1(sK10(U_35),U_35),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_34,sK10(U_35))],[f_30_2]) ).
fof(f_30_4,plain,
! [U_35] : m1_subset_1(sK10(U_35),U_35),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
m1_subset_1(sK10(U_35),U_35),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_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_31_2,plain,
! [U_37] :
( ? [U_36] : 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_37] :
( m2_lattice4(sK11(U_37),U_37)
| ~ l3_lattices(U_37)
| ~ v10_lattices(U_37)
| v3_struct_0(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_36,sK11(U_37))],[f_31_2]) ).
fof(f_31_4,plain,
! [U_37] :
( m2_lattice4(sK11(U_37),U_37)
| ~ l3_lattices(U_37)
| ~ v10_lattices(U_37)
| v3_struct_0(U_37) ),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
( m2_lattice4(sK11(U_37),U_37)
| ~ l3_lattices(U_37)
| ~ v10_lattices(U_37)
| v3_struct_0(U_37) ),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_32_2,plain,
! [U_40,U_39] :
? [U_38] : m2_relset_1(U_38,U_40,U_39),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_40,U_39] : m2_relset_1(sK12(U_40,U_39),U_40,U_39),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_38,sK12(U_40,U_39))],[f_32_2]) ).
fof(f_32_4,plain,
! [U_39,U_40] : m2_relset_1(sK12(U_40,U_39),U_40,U_39),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
m2_relset_1(sK12(U_40,U_39),U_40,U_39),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
! [A,B] :
( v1_relat_1(k1_realset1(A,B))
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[fc1_realset1]) ).
fof(f_33_2,plain,
! [U_42,U_41] :
( v1_relat_1(k1_realset1(U_42,U_41))
| ~ v1_relat_1(U_42) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_42] :
( ! [U_41] : v1_relat_1(k1_realset1(U_42,U_41))
| ~ v1_relat_1(U_42) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_41,U_42] :
( v1_relat_1(k1_realset1(U_42,U_41))
| ~ v1_relat_1(U_42) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
( v1_relat_1(k1_realset1(U_42,U_41))
| ~ v1_relat_1(U_42) ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_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_34_2,plain,
! [U_43] :
( ~ v1_xboole_0(u1_struct_0(U_43))
| ~ l1_struct_0(U_43)
| v3_struct_0(U_43) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_43] :
( ~ v1_xboole_0(u1_struct_0(U_43))
| ~ l1_struct_0(U_43)
| v3_struct_0(U_43) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( ~ v1_xboole_0(u1_struct_0(U_43))
| ~ l1_struct_0(U_43)
| v3_struct_0(U_43) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_35_2,plain,
! [U_44] : ~ v1_xboole_0(k1_zfmisc_1(U_44)),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_44] : ~ v1_xboole_0(k1_zfmisc_1(U_44)),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
~ v1_xboole_0(k1_zfmisc_1(U_44)),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_36_2,plain,
v1_xboole_0(k1_xboole_0),
inference(definitional_conversion,[status(esa)],[f_36_1]) ).
cnf(f_36_3,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_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_37_2,plain,
! [U_45] :
( ( v1_partfun1(u2_lattices(U_45),k2_zfmisc_1(u1_struct_0(U_45),u1_struct_0(U_45)),u1_struct_0(U_45))
& v1_binop_1(u2_lattices(U_45),u1_struct_0(U_45))
& v1_funct_2(u2_lattices(U_45),k2_zfmisc_1(u1_struct_0(U_45),u1_struct_0(U_45)),u1_struct_0(U_45))
& v1_funct_1(u2_lattices(U_45))
& v1_relat_1(u2_lattices(U_45)) )
| ~ l2_lattices(U_45)
| ~ v4_lattices(U_45)
| v3_struct_0(U_45) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_45] :
( v1_partfun1(u2_lattices(U_45),k2_zfmisc_1(u1_struct_0(U_45),u1_struct_0(U_45)),u1_struct_0(U_45))
| ~ sP6(U_45) )
& ! [U_45] :
( v1_binop_1(u2_lattices(U_45),u1_struct_0(U_45))
| ~ sP6(U_45) )
& ! [U_45] :
( v1_funct_2(u2_lattices(U_45),k2_zfmisc_1(u1_struct_0(U_45),u1_struct_0(U_45)),u1_struct_0(U_45))
| ~ sP6(U_45) )
& ! [U_45] :
( v1_funct_1(u2_lattices(U_45))
| ~ sP6(U_45) )
& ! [U_45] :
( v1_relat_1(u2_lattices(U_45))
| ~ sP6(U_45) )
& ! [U_45] :
( sP6(U_45)
| ~ l2_lattices(U_45)
| ~ v4_lattices(U_45)
| v3_struct_0(U_45) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_37_2]) ).
cnf(f_37_4,plain,
( sP6(U_45)
| ~ l2_lattices(U_45)
| ~ v4_lattices(U_45)
| v3_struct_0(U_45) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( v1_relat_1(u2_lattices(U_45))
| ~ sP6(U_45) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
( v1_funct_1(u2_lattices(U_45))
| ~ sP6(U_45) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_7,plain,
( v1_funct_2(u2_lattices(U_45),k2_zfmisc_1(u1_struct_0(U_45),u1_struct_0(U_45)),u1_struct_0(U_45))
| ~ sP6(U_45) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_8,plain,
( v1_binop_1(u2_lattices(U_45),u1_struct_0(U_45))
| ~ sP6(U_45) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_9,plain,
( v1_partfun1(u2_lattices(U_45),k2_zfmisc_1(u1_struct_0(U_45),u1_struct_0(U_45)),u1_struct_0(U_45))
| ~ sP6(U_45) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A,B] :
( ( v1_funct_1(k1_realset1(A,B))
& v1_relat_1(k1_realset1(A,B)) )
| ~ v1_funct_1(A)
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[fc2_realset1]) ).
fof(f_38_2,plain,
! [U_47,U_46] :
( ( v1_funct_1(k1_realset1(U_47,U_46))
& v1_relat_1(k1_realset1(U_47,U_46)) )
| ~ v1_funct_1(U_47)
| ~ v1_relat_1(U_47) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_47] :
( ( ! [U_49] : v1_funct_1(k1_realset1(U_47,U_49))
& ! [U_48] : v1_relat_1(k1_realset1(U_47,U_48)) )
| ~ v1_funct_1(U_47)
| ~ v1_relat_1(U_47) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
( ! [U_49,U_47,U_48] :
( v1_funct_1(k1_realset1(U_47,U_49))
| ~ sP7(U_49,U_47,U_48) )
& ! [U_49,U_47,U_48] :
( v1_relat_1(k1_realset1(U_47,U_48))
| ~ sP7(U_49,U_47,U_48) )
& ! [U_49,U_47,U_48] :
( sP7(U_49,U_47,U_48)
| ~ v1_funct_1(U_47)
| ~ v1_relat_1(U_47) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_38_3]) ).
cnf(f_38_5,plain,
( sP7(U_49,U_47,U_48)
| ~ v1_funct_1(U_47)
| ~ v1_relat_1(U_47) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
( v1_relat_1(k1_realset1(U_47,U_48))
| ~ sP7(U_49,U_47,U_48) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_7,plain,
( v1_funct_1(k1_realset1(U_47,U_49))
| ~ sP7(U_49,U_47,U_48) ),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_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_39_2,plain,
! [U_50] :
( ( v1_partfun1(u2_lattices(U_50),k2_zfmisc_1(u1_struct_0(U_50),u1_struct_0(U_50)),u1_struct_0(U_50))
& v2_binop_1(u2_lattices(U_50),u1_struct_0(U_50))
& v1_funct_2(u2_lattices(U_50),k2_zfmisc_1(u1_struct_0(U_50),u1_struct_0(U_50)),u1_struct_0(U_50))
& v1_funct_1(u2_lattices(U_50))
& v1_relat_1(u2_lattices(U_50)) )
| ~ l2_lattices(U_50)
| ~ v5_lattices(U_50)
| v3_struct_0(U_50) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_50] :
( v1_partfun1(u2_lattices(U_50),k2_zfmisc_1(u1_struct_0(U_50),u1_struct_0(U_50)),u1_struct_0(U_50))
| ~ sP8(U_50) )
& ! [U_50] :
( v2_binop_1(u2_lattices(U_50),u1_struct_0(U_50))
| ~ sP8(U_50) )
& ! [U_50] :
( v1_funct_2(u2_lattices(U_50),k2_zfmisc_1(u1_struct_0(U_50),u1_struct_0(U_50)),u1_struct_0(U_50))
| ~ sP8(U_50) )
& ! [U_50] :
( v1_funct_1(u2_lattices(U_50))
| ~ sP8(U_50) )
& ! [U_50] :
( v1_relat_1(u2_lattices(U_50))
| ~ sP8(U_50) )
& ! [U_50] :
( sP8(U_50)
| ~ l2_lattices(U_50)
| ~ v5_lattices(U_50)
| v3_struct_0(U_50) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_39_2]) ).
cnf(f_39_4,plain,
( sP8(U_50)
| ~ l2_lattices(U_50)
| ~ v5_lattices(U_50)
| v3_struct_0(U_50) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
( v1_relat_1(u2_lattices(U_50))
| ~ sP8(U_50) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_6,plain,
( v1_funct_1(u2_lattices(U_50))
| ~ sP8(U_50) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_7,plain,
( v1_funct_2(u2_lattices(U_50),k2_zfmisc_1(u1_struct_0(U_50),u1_struct_0(U_50)),u1_struct_0(U_50))
| ~ sP8(U_50) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_8,plain,
( v2_binop_1(u2_lattices(U_50),u1_struct_0(U_50))
| ~ sP8(U_50) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_9,plain,
( v1_partfun1(u2_lattices(U_50),k2_zfmisc_1(u1_struct_0(U_50),u1_struct_0(U_50)),u1_struct_0(U_50))
| ~ sP8(U_50) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B] :
( ( v1_funct_1(k7_relat_1(A,B))
& v1_relat_1(k7_relat_1(A,B)) )
| ~ v1_funct_1(A)
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[fc4_funct_1]) ).
fof(f_40_2,plain,
! [U_52,U_51] :
( ( v1_funct_1(k7_relat_1(U_52,U_51))
& v1_relat_1(k7_relat_1(U_52,U_51)) )
| ~ v1_funct_1(U_52)
| ~ v1_relat_1(U_52) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_52] :
( ( ! [U_54] : v1_funct_1(k7_relat_1(U_52,U_54))
& ! [U_53] : v1_relat_1(k7_relat_1(U_52,U_53)) )
| ~ v1_funct_1(U_52)
| ~ v1_relat_1(U_52) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
( ! [U_54,U_52,U_53] :
( v1_funct_1(k7_relat_1(U_52,U_54))
| ~ sP9(U_54,U_52,U_53) )
& ! [U_54,U_52,U_53] :
( v1_relat_1(k7_relat_1(U_52,U_53))
| ~ sP9(U_54,U_52,U_53) )
& ! [U_54,U_52,U_53] :
( sP9(U_54,U_52,U_53)
| ~ v1_funct_1(U_52)
| ~ v1_relat_1(U_52) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_40_3]) ).
cnf(f_40_5,plain,
( sP9(U_54,U_52,U_53)
| ~ v1_funct_1(U_52)
| ~ v1_relat_1(U_52) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_6,plain,
( v1_relat_1(k7_relat_1(U_52,U_53))
| ~ sP9(U_54,U_52,U_53) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_7,plain,
( v1_funct_1(k7_relat_1(U_52,U_54))
| ~ sP9(U_54,U_52,U_53) ),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_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_41_2,plain,
! [U_55] :
( ( v1_partfun1(u1_lattices(U_55),k2_zfmisc_1(u1_struct_0(U_55),u1_struct_0(U_55)),u1_struct_0(U_55))
& v1_binop_1(u1_lattices(U_55),u1_struct_0(U_55))
& v1_funct_2(u1_lattices(U_55),k2_zfmisc_1(u1_struct_0(U_55),u1_struct_0(U_55)),u1_struct_0(U_55))
& v1_funct_1(u1_lattices(U_55))
& v1_relat_1(u1_lattices(U_55)) )
| ~ l1_lattices(U_55)
| ~ v6_lattices(U_55)
| v3_struct_0(U_55) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_55] :
( v1_partfun1(u1_lattices(U_55),k2_zfmisc_1(u1_struct_0(U_55),u1_struct_0(U_55)),u1_struct_0(U_55))
| ~ sP10(U_55) )
& ! [U_55] :
( v1_binop_1(u1_lattices(U_55),u1_struct_0(U_55))
| ~ sP10(U_55) )
& ! [U_55] :
( v1_funct_2(u1_lattices(U_55),k2_zfmisc_1(u1_struct_0(U_55),u1_struct_0(U_55)),u1_struct_0(U_55))
| ~ sP10(U_55) )
& ! [U_55] :
( v1_funct_1(u1_lattices(U_55))
| ~ sP10(U_55) )
& ! [U_55] :
( v1_relat_1(u1_lattices(U_55))
| ~ sP10(U_55) )
& ! [U_55] :
( sP10(U_55)
| ~ l1_lattices(U_55)
| ~ v6_lattices(U_55)
| v3_struct_0(U_55) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_41_2]) ).
cnf(f_41_4,plain,
( sP10(U_55)
| ~ l1_lattices(U_55)
| ~ v6_lattices(U_55)
| v3_struct_0(U_55) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
( v1_relat_1(u1_lattices(U_55))
| ~ sP10(U_55) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_6,plain,
( v1_funct_1(u1_lattices(U_55))
| ~ sP10(U_55) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_7,plain,
( v1_funct_2(u1_lattices(U_55),k2_zfmisc_1(u1_struct_0(U_55),u1_struct_0(U_55)),u1_struct_0(U_55))
| ~ sP10(U_55) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_8,plain,
( v1_binop_1(u1_lattices(U_55),u1_struct_0(U_55))
| ~ sP10(U_55) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_9,plain,
( v1_partfun1(u1_lattices(U_55),k2_zfmisc_1(u1_struct_0(U_55),u1_struct_0(U_55)),u1_struct_0(U_55))
| ~ sP10(U_55) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_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_42_2,plain,
! [U_57,U_56] :
( ~ v1_xboole_0(k2_zfmisc_1(U_57,U_56))
| v1_xboole_0(U_56)
| v1_xboole_0(U_57) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_57,U_56] :
( ~ v1_xboole_0(k2_zfmisc_1(U_57,U_56))
| v1_xboole_0(U_56)
| v1_xboole_0(U_57) ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
( ~ v1_xboole_0(k2_zfmisc_1(U_57,U_56))
| v1_xboole_0(U_56)
| v1_xboole_0(U_57) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_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_43_2,plain,
! [U_58] :
( ( v1_partfun1(u1_lattices(U_58),k2_zfmisc_1(u1_struct_0(U_58),u1_struct_0(U_58)),u1_struct_0(U_58))
& v2_binop_1(u1_lattices(U_58),u1_struct_0(U_58))
& v1_funct_2(u1_lattices(U_58),k2_zfmisc_1(u1_struct_0(U_58),u1_struct_0(U_58)),u1_struct_0(U_58))
& v1_funct_1(u1_lattices(U_58))
& v1_relat_1(u1_lattices(U_58)) )
| ~ l1_lattices(U_58)
| ~ v7_lattices(U_58)
| v3_struct_0(U_58) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( ! [U_58] :
( v1_partfun1(u1_lattices(U_58),k2_zfmisc_1(u1_struct_0(U_58),u1_struct_0(U_58)),u1_struct_0(U_58))
| ~ sP11(U_58) )
& ! [U_58] :
( v2_binop_1(u1_lattices(U_58),u1_struct_0(U_58))
| ~ sP11(U_58) )
& ! [U_58] :
( v1_funct_2(u1_lattices(U_58),k2_zfmisc_1(u1_struct_0(U_58),u1_struct_0(U_58)),u1_struct_0(U_58))
| ~ sP11(U_58) )
& ! [U_58] :
( v1_funct_1(u1_lattices(U_58))
| ~ sP11(U_58) )
& ! [U_58] :
( v1_relat_1(u1_lattices(U_58))
| ~ sP11(U_58) )
& ! [U_58] :
( sP11(U_58)
| ~ l1_lattices(U_58)
| ~ v7_lattices(U_58)
| v3_struct_0(U_58) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_43_2]) ).
cnf(f_43_4,plain,
( sP11(U_58)
| ~ l1_lattices(U_58)
| ~ v7_lattices(U_58)
| v3_struct_0(U_58) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
( v1_relat_1(u1_lattices(U_58))
| ~ sP11(U_58) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_6,plain,
( v1_funct_1(u1_lattices(U_58))
| ~ sP11(U_58) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_7,plain,
( v1_funct_2(u1_lattices(U_58),k2_zfmisc_1(u1_struct_0(U_58),u1_struct_0(U_58)),u1_struct_0(U_58))
| ~ sP11(U_58) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_8,plain,
( v2_binop_1(u1_lattices(U_58),u1_struct_0(U_58))
| ~ sP11(U_58) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_9,plain,
( v1_partfun1(u1_lattices(U_58),k2_zfmisc_1(u1_struct_0(U_58),u1_struct_0(U_58)),u1_struct_0(U_58))
| ~ sP11(U_58) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_44_2,plain,
? [U_59] :
( v1_funct_1(U_59)
& v1_relat_1(U_59) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( v1_funct_1(sK13)
& v1_relat_1(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_59,sK13)],[f_44_2]) ).
fof(f_44_4,plain,
( v1_funct_1(sK13)
& v1_relat_1(sK13) ),
inference(definitional_conversion,[status(esa)],[f_44_3]) ).
cnf(f_44_5,plain,
v1_relat_1(sK13),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_6,plain,
v1_funct_1(sK13),
inference(clausify,[status(thm)],[f_44_4]) ).
fof(f_45_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_45_2,plain,
! [U_61] :
( ? [U_60] :
( ~ v1_xboole_0(U_60)
& m2_lattice4(U_60,U_61) )
| ~ l3_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_61] :
( ( ~ v1_xboole_0(sK14(U_61))
& m2_lattice4(sK14(U_61),U_61) )
| ~ l3_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_60,sK14(U_61))],[f_45_2]) ).
fof(f_45_4,plain,
( ! [U_61] :
( ~ v1_xboole_0(sK14(U_61))
| ~ sP12(U_61) )
& ! [U_61] :
( m2_lattice4(sK14(U_61),U_61)
| ~ sP12(U_61) )
& ! [U_61] :
( sP12(U_61)
| ~ l3_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_45_3]) ).
cnf(f_45_5,plain,
( sP12(U_61)
| ~ l3_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_6,plain,
( m2_lattice4(sK14(U_61),U_61)
| ~ sP12(U_61) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_7,plain,
( ~ v1_xboole_0(sK14(U_61))
| ~ sP12(U_61) ),
inference(clausify,[status(thm)],[f_45_4]) ).
fof(f_46_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_46_2,plain,
! [U_63] :
( ? [U_62] :
( ~ v1_xboole_0(U_62)
& m1_subset_1(U_62,k1_zfmisc_1(U_63)) )
| v1_xboole_0(U_63) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_63] :
( ( ~ v1_xboole_0(sK15(U_63))
& m1_subset_1(sK15(U_63),k1_zfmisc_1(U_63)) )
| v1_xboole_0(U_63) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_62,sK15(U_63))],[f_46_2]) ).
fof(f_46_4,plain,
( ! [U_63] :
( ~ v1_xboole_0(sK15(U_63))
| ~ sP13(U_63) )
& ! [U_63] :
( m1_subset_1(sK15(U_63),k1_zfmisc_1(U_63))
| ~ sP13(U_63) )
& ! [U_63] :
( sP13(U_63)
| v1_xboole_0(U_63) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_46_3]) ).
cnf(f_46_5,plain,
( sP13(U_63)
| v1_xboole_0(U_63) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_6,plain,
( m1_subset_1(sK15(U_63),k1_zfmisc_1(U_63))
| ~ sP13(U_63) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_7,plain,
( ~ v1_xboole_0(sK15(U_63))
| ~ sP13(U_63) ),
inference(clausify,[status(thm)],[f_46_4]) ).
fof(f_47_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_47_2,plain,
? [U_64] : v1_xboole_0(U_64),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
v1_xboole_0(sK16),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_64,sK16)],[f_47_2]) ).
fof(f_47_4,plain,
v1_xboole_0(sK16),
inference(definitional_conversion,[status(esa)],[f_47_3]) ).
cnf(f_47_5,plain,
v1_xboole_0(sK16),
inference(clausify,[status(thm)],[f_47_4]) ).
fof(f_48_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_48_2,plain,
? [U_65] :
( v1_funct_1(U_65)
& v1_xboole_0(U_65)
& v1_relat_1(U_65) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
( v1_funct_1(sK17)
& v1_xboole_0(sK17)
& v1_relat_1(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_65,sK17)],[f_48_2]) ).
fof(f_48_4,plain,
( v1_funct_1(sK17)
& v1_xboole_0(sK17)
& v1_relat_1(sK17) ),
inference(definitional_conversion,[status(esa)],[f_48_3]) ).
cnf(f_48_5,plain,
v1_relat_1(sK17),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_6,plain,
v1_xboole_0(sK17),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_7,plain,
v1_funct_1(sK17),
inference(clausify,[status(thm)],[f_48_4]) ).
fof(f_49_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_49_2,plain,
! [U_67] :
? [U_66] :
( v1_xboole_0(U_66)
& m1_subset_1(U_66,k1_zfmisc_1(U_67)) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_67] :
( v1_xboole_0(sK18(U_67))
& m1_subset_1(sK18(U_67),k1_zfmisc_1(U_67)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_66,sK18(U_67))],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_67] : v1_xboole_0(sK18(U_67))
& ! [U_67] : m1_subset_1(sK18(U_67),k1_zfmisc_1(U_67)) ),
inference(definitional_conversion,[status(esa)],[f_49_3]) ).
cnf(f_49_5,plain,
m1_subset_1(sK18(U_67),k1_zfmisc_1(U_67)),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_6,plain,
v1_xboole_0(sK18(U_67)),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_50_2,plain,
? [U_68] : ~ v1_xboole_0(U_68),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
~ v1_xboole_0(sK19),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_68,sK19)],[f_50_2]) ).
fof(f_50_4,plain,
~ v1_xboole_0(sK19),
inference(definitional_conversion,[status(esa)],[f_50_3]) ).
cnf(f_50_5,plain,
~ v1_xboole_0(sK19),
inference(clausify,[status(thm)],[f_50_4]) ).
fof(f_51_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_51_2,plain,
? [U_69] :
( v2_funct_1(U_69)
& v1_funct_1(U_69)
& v1_relat_1(U_69) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( v2_funct_1(sK20)
& v1_funct_1(sK20)
& v1_relat_1(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_69,sK20)],[f_51_2]) ).
fof(f_51_4,plain,
( v2_funct_1(sK20)
& v1_funct_1(sK20)
& v1_relat_1(sK20) ),
inference(definitional_conversion,[status(esa)],[f_51_3]) ).
cnf(f_51_5,plain,
v1_relat_1(sK20),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_6,plain,
v1_funct_1(sK20),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_7,plain,
v2_funct_1(sK20),
inference(clausify,[status(thm)],[f_51_4]) ).
fof(f_52_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_52_2,plain,
? [U_70] :
( ~ v3_struct_0(U_70)
& l1_struct_0(U_70) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ~ v3_struct_0(sK21)
& l1_struct_0(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_70,sK21)],[f_52_2]) ).
fof(f_52_4,plain,
( ~ v3_struct_0(sK21)
& l1_struct_0(sK21) ),
inference(definitional_conversion,[status(esa)],[f_52_3]) ).
cnf(f_52_5,plain,
l1_struct_0(sK21),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_6,plain,
~ v3_struct_0(sK21),
inference(clausify,[status(thm)],[f_52_4]) ).
fof(f_53_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_53_2,plain,
! [U_72] :
( ? [U_71] :
( ~ v1_xboole_0(U_71)
& m1_subset_1(U_71,k1_zfmisc_1(u1_struct_0(U_72))) )
| ~ l1_struct_0(U_72)
| v3_struct_0(U_72) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_72] :
( ( ~ v1_xboole_0(sK22(U_72))
& m1_subset_1(sK22(U_72),k1_zfmisc_1(u1_struct_0(U_72))) )
| ~ l1_struct_0(U_72)
| v3_struct_0(U_72) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_71,sK22(U_72))],[f_53_2]) ).
fof(f_53_4,plain,
( ! [U_72] :
( ~ v1_xboole_0(sK22(U_72))
| ~ sP14(U_72) )
& ! [U_72] :
( m1_subset_1(sK22(U_72),k1_zfmisc_1(u1_struct_0(U_72)))
| ~ sP14(U_72) )
& ! [U_72] :
( sP14(U_72)
| ~ l1_struct_0(U_72)
| v3_struct_0(U_72) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_53_3]) ).
cnf(f_53_5,plain,
( sP14(U_72)
| ~ l1_struct_0(U_72)
| v3_struct_0(U_72) ),
inference(clausify,[status(thm)],[f_53_4]) ).
cnf(f_53_6,plain,
( m1_subset_1(sK22(U_72),k1_zfmisc_1(u1_struct_0(U_72)))
| ~ sP14(U_72) ),
inference(clausify,[status(thm)],[f_53_4]) ).
cnf(f_53_7,plain,
( ~ v1_xboole_0(sK22(U_72))
| ~ sP14(U_72) ),
inference(clausify,[status(thm)],[f_53_4]) ).
fof(f_54_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_54_2,plain,
! [U_75,U_74,U_73] :
( ( m2_relset_1(U_73,U_75,U_74)
| ~ m1_relset_1(U_73,U_75,U_74) )
& ( m1_relset_1(U_73,U_75,U_74)
| ~ m2_relset_1(U_73,U_75,U_74) ) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ! [U_81,U_79,U_77] :
( m2_relset_1(U_77,U_81,U_79)
| ~ m1_relset_1(U_77,U_81,U_79) )
& ! [U_80,U_78,U_76] :
( m1_relset_1(U_76,U_80,U_78)
| ~ m2_relset_1(U_76,U_80,U_78) ) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
( ! [U_79,U_81,U_77] :
( m2_relset_1(U_77,U_81,U_79)
| ~ m1_relset_1(U_77,U_81,U_79) )
& ! [U_76,U_78,U_80] :
( m1_relset_1(U_76,U_80,U_78)
| ~ m2_relset_1(U_76,U_80,U_78) ) ),
inference(definitional_conversion,[status(esa)],[f_54_3]) ).
cnf(f_54_5,plain,
( m1_relset_1(U_76,U_80,U_78)
| ~ m2_relset_1(U_76,U_80,U_78) ),
inference(clausify,[status(thm)],[f_54_4]) ).
cnf(f_54_6,plain,
( m2_relset_1(U_77,U_81,U_79)
| ~ m1_relset_1(U_77,U_81,U_79) ),
inference(clausify,[status(thm)],[f_54_4]) ).
fof(f_55_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_55_2,plain,
! [U_83,U_82] : r1_tarski(U_83,U_83),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_83] : r1_tarski(U_83,U_83),
inference(miniscope,[status(thm)],[f_55_2]) ).
fof(f_55_4,plain,
! [U_83] : r1_tarski(U_83,U_83),
inference(definitional_conversion,[status(esa)],[f_55_3]) ).
cnf(f_55_5,plain,
r1_tarski(U_83,U_83),
inference(clausify,[status(thm)],[f_55_4]) ).
fof(f_56_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ( ( v2_binop_1(D,B)
| ~ v2_binop_1(C,A) )
& ( v3_binop_1(D,B)
| ~ v3_binop_1(C,A) )
& ( v1_binop_1(D,B)
| ~ v1_binop_1(C,A) ) )
| D != k1_realset1(C,B)
| ~ m2_relset_1(D,k2_zfmisc_1(B,B),B)
| ~ v1_funct_2(D,k2_zfmisc_1(B,B),B)
| ~ v1_funct_1(D) )
| ~ m2_relset_1(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(C) )
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(B) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t1_filter_2]) ).
fof(f_56_2,plain,
! [U_87] :
( ! [U_86] :
( ! [U_85] :
( ! [U_84] :
( ( ( v2_binop_1(U_84,U_86)
| ~ v2_binop_1(U_85,U_87) )
& ( v3_binop_1(U_84,U_86)
| ~ v3_binop_1(U_85,U_87) )
& ( v1_binop_1(U_84,U_86)
| ~ v1_binop_1(U_85,U_87) ) )
| U_84 != k1_realset1(U_85,U_86)
| ~ m2_relset_1(U_84,k2_zfmisc_1(U_86,U_86),U_86)
| ~ v1_funct_2(U_84,k2_zfmisc_1(U_86,U_86),U_86)
| ~ v1_funct_1(U_84) )
| ~ m2_relset_1(U_85,k2_zfmisc_1(U_87,U_87),U_87)
| ~ v1_funct_2(U_85,k2_zfmisc_1(U_87,U_87),U_87)
| ~ v1_funct_1(U_85) )
| ~ m1_subset_1(U_86,k1_zfmisc_1(U_87))
| v1_xboole_0(U_86) )
| v1_xboole_0(U_87) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( ! [U_85,U_84,U_86,U_87] :
( v2_binop_1(U_84,U_86)
| ~ v2_binop_1(U_85,U_87)
| ~ sP15(U_85,U_84,U_86,U_87) )
& ! [U_85,U_84,U_86,U_87] :
( v3_binop_1(U_84,U_86)
| ~ v3_binop_1(U_85,U_87)
| ~ sP15(U_85,U_84,U_86,U_87) )
& ! [U_85,U_84,U_86,U_87] :
( v1_binop_1(U_84,U_86)
| ~ v1_binop_1(U_85,U_87)
| ~ sP15(U_85,U_84,U_86,U_87) )
& ! [U_85,U_84,U_86,U_87] :
( sP15(U_85,U_84,U_86,U_87)
| U_84 != k1_realset1(U_85,U_86)
| ~ m2_relset_1(U_84,k2_zfmisc_1(U_86,U_86),U_86)
| ~ v1_funct_2(U_84,k2_zfmisc_1(U_86,U_86),U_86)
| ~ v1_funct_1(U_84)
| ~ m2_relset_1(U_85,k2_zfmisc_1(U_87,U_87),U_87)
| ~ v1_funct_2(U_85,k2_zfmisc_1(U_87,U_87),U_87)
| ~ v1_funct_1(U_85)
| ~ m1_subset_1(U_86,k1_zfmisc_1(U_87))
| v1_xboole_0(U_86)
| v1_xboole_0(U_87) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_56_2]) ).
cnf(f_56_4,plain,
( sP15(U_85,U_84,U_86,U_87)
| U_84 != k1_realset1(U_85,U_86)
| ~ m2_relset_1(U_84,k2_zfmisc_1(U_86,U_86),U_86)
| ~ v1_funct_2(U_84,k2_zfmisc_1(U_86,U_86),U_86)
| ~ v1_funct_1(U_84)
| ~ m2_relset_1(U_85,k2_zfmisc_1(U_87,U_87),U_87)
| ~ v1_funct_2(U_85,k2_zfmisc_1(U_87,U_87),U_87)
| ~ v1_funct_1(U_85)
| ~ m1_subset_1(U_86,k1_zfmisc_1(U_87))
| v1_xboole_0(U_86)
| v1_xboole_0(U_87) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
( v1_binop_1(U_84,U_86)
| ~ v1_binop_1(U_85,U_87)
| ~ sP15(U_85,U_84,U_86,U_87) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_6,plain,
( v3_binop_1(U_84,U_86)
| ~ v3_binop_1(U_85,U_87)
| ~ sP15(U_85,U_84,U_86,U_87) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_7,plain,
( v2_binop_1(U_84,U_86)
| ~ v2_binop_1(U_85,U_87)
| ~ sP15(U_85,U_84,U_86,U_87) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_57_2,plain,
! [U_89,U_88] :
( m1_subset_1(U_89,U_88)
| ~ r2_hidden(U_89,U_88) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_89,U_88] :
( m1_subset_1(U_89,U_88)
| ~ r2_hidden(U_89,U_88) ),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
( m1_subset_1(U_89,U_88)
| ~ r2_hidden(U_89,U_88) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_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_58_2,plain,
! [U_91,U_90] :
( r2_hidden(U_91,U_90)
| v1_xboole_0(U_90)
| ~ m1_subset_1(U_91,U_90) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_91,U_90] :
( r2_hidden(U_91,U_90)
| v1_xboole_0(U_90)
| ~ m1_subset_1(U_91,U_90) ),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
( r2_hidden(U_91,U_90)
| v1_xboole_0(U_90)
| ~ m1_subset_1(U_91,U_90) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_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_59_2,plain,
! [U_93,U_92] :
( ( m1_subset_1(U_93,k1_zfmisc_1(U_92))
| ~ r1_tarski(U_93,U_92) )
& ( r1_tarski(U_93,U_92)
| ~ m1_subset_1(U_93,k1_zfmisc_1(U_92)) ) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( ! [U_97,U_95] :
( m1_subset_1(U_97,k1_zfmisc_1(U_95))
| ~ r1_tarski(U_97,U_95) )
& ! [U_96,U_94] :
( r1_tarski(U_96,U_94)
| ~ m1_subset_1(U_96,k1_zfmisc_1(U_94)) ) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
fof(f_59_4,plain,
( ! [U_95,U_97] :
( m1_subset_1(U_97,k1_zfmisc_1(U_95))
| ~ r1_tarski(U_97,U_95) )
& ! [U_94,U_96] :
( r1_tarski(U_96,U_94)
| ~ m1_subset_1(U_96,k1_zfmisc_1(U_94)) ) ),
inference(definitional_conversion,[status(esa)],[f_59_3]) ).
cnf(f_59_5,plain,
( r1_tarski(U_96,U_94)
| ~ m1_subset_1(U_96,k1_zfmisc_1(U_94)) ),
inference(clausify,[status(thm)],[f_59_4]) ).
cnf(f_59_6,plain,
( m1_subset_1(U_97,k1_zfmisc_1(U_95))
| ~ r1_tarski(U_97,U_95) ),
inference(clausify,[status(thm)],[f_59_4]) ).
fof(f_60_1,plain,
! [A] :
( r1_lattice2(u1_struct_0(A),u2_lattices(A),u1_lattices(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t40_lattice2]) ).
fof(f_60_2,plain,
! [U_98] :
( r1_lattice2(u1_struct_0(U_98),u2_lattices(U_98),u1_lattices(U_98))
| ~ l3_lattices(U_98)
| ~ v10_lattices(U_98)
| v3_struct_0(U_98) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_98] :
( r1_lattice2(u1_struct_0(U_98),u2_lattices(U_98),u1_lattices(U_98))
| ~ l3_lattices(U_98)
| ~ v10_lattices(U_98)
| v3_struct_0(U_98) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( r1_lattice2(u1_struct_0(U_98),u2_lattices(U_98),u1_lattices(U_98))
| ~ l3_lattices(U_98)
| ~ v10_lattices(U_98)
| v3_struct_0(U_98) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [A] :
( r1_lattice2(u1_struct_0(A),u1_lattices(A),u2_lattices(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t41_lattice2]) ).
fof(f_61_2,plain,
! [U_99] :
( r1_lattice2(u1_struct_0(U_99),u1_lattices(U_99),u2_lattices(U_99))
| ~ l3_lattices(U_99)
| ~ v10_lattices(U_99)
| v3_struct_0(U_99) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_99] :
( r1_lattice2(u1_struct_0(U_99),u1_lattices(U_99),u2_lattices(U_99))
| ~ l3_lattices(U_99)
| ~ v10_lattices(U_99)
| v3_struct_0(U_99) ),
inference(definitional_conversion,[status(esa)],[f_61_2]) ).
cnf(f_61_4,plain,
( r1_lattice2(u1_struct_0(U_99),u1_lattices(U_99),u2_lattices(U_99))
| ~ l3_lattices(U_99)
| ~ v10_lattices(U_99)
| v3_struct_0(U_99) ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_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_62_2,plain,
! [U_102,U_101,U_100] :
( m1_subset_1(U_102,U_100)
| ~ m1_subset_1(U_101,k1_zfmisc_1(U_100))
| ~ r2_hidden(U_102,U_101) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_101,U_102,U_100] :
( m1_subset_1(U_102,U_100)
| ~ m1_subset_1(U_101,k1_zfmisc_1(U_100))
| ~ r2_hidden(U_102,U_101) ),
inference(definitional_conversion,[status(esa)],[f_62_2]) ).
cnf(f_62_4,plain,
( m1_subset_1(U_102,U_100)
| ~ m1_subset_1(U_101,k1_zfmisc_1(U_100))
| ~ r2_hidden(U_102,U_101) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ! [F] :
( r1_lattice2(B,E,F)
| ~ r1_lattice2(A,C,D)
| F != k1_realset1(D,B)
| E != k1_realset1(C,B)
| ~ m2_relset_1(F,k2_zfmisc_1(B,B),B)
| ~ v1_funct_2(F,k2_zfmisc_1(B,B),B)
| ~ v1_funct_1(F) )
| ~ m2_relset_1(E,k2_zfmisc_1(B,B),B)
| ~ v1_funct_2(E,k2_zfmisc_1(B,B),B)
| ~ v1_funct_1(E) )
| ~ m2_relset_1(D,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(D,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(D) )
| ~ m2_relset_1(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(C) )
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(B) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t5_filter_2]) ).
fof(f_63_2,plain,
! [U_108] :
( ! [U_107] :
( ! [U_106] :
( ! [U_105] :
( ! [U_104] :
( ! [U_103] :
( r1_lattice2(U_107,U_104,U_103)
| ~ r1_lattice2(U_108,U_106,U_105)
| U_103 != k1_realset1(U_105,U_107)
| U_104 != k1_realset1(U_106,U_107)
| ~ m2_relset_1(U_103,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_2(U_103,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_1(U_103) )
| ~ m2_relset_1(U_104,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_2(U_104,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_1(U_104) )
| ~ m2_relset_1(U_105,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_2(U_105,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_1(U_105) )
| ~ m2_relset_1(U_106,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_2(U_106,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_1(U_106) )
| ~ m1_subset_1(U_107,k1_zfmisc_1(U_108))
| v1_xboole_0(U_107) )
| v1_xboole_0(U_108) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_107,U_106,U_108,U_105,U_104,U_103] :
( r1_lattice2(U_107,U_104,U_103)
| ~ r1_lattice2(U_108,U_106,U_105)
| U_103 != k1_realset1(U_105,U_107)
| U_104 != k1_realset1(U_106,U_107)
| ~ m2_relset_1(U_103,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_2(U_103,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_1(U_103)
| ~ m2_relset_1(U_104,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_2(U_104,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_1(U_104)
| ~ m2_relset_1(U_105,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_2(U_105,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_1(U_105)
| ~ m2_relset_1(U_106,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_2(U_106,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_1(U_106)
| ~ m1_subset_1(U_107,k1_zfmisc_1(U_108))
| v1_xboole_0(U_107)
| v1_xboole_0(U_108) ),
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
( r1_lattice2(U_107,U_104,U_103)
| ~ r1_lattice2(U_108,U_106,U_105)
| U_103 != k1_realset1(U_105,U_107)
| U_104 != k1_realset1(U_106,U_107)
| ~ m2_relset_1(U_103,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_2(U_103,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_1(U_103)
| ~ m2_relset_1(U_104,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_2(U_104,k2_zfmisc_1(U_107,U_107),U_107)
| ~ v1_funct_1(U_104)
| ~ m2_relset_1(U_105,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_2(U_105,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_1(U_105)
| ~ m2_relset_1(U_106,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_2(U_106,k2_zfmisc_1(U_108,U_108),U_108)
| ~ v1_funct_1(U_106)
| ~ m1_subset_1(U_107,k1_zfmisc_1(U_108))
| v1_xboole_0(U_107)
| v1_xboole_0(U_108) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_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_64_2,plain,
! [U_111,U_110,U_109] :
( ~ v1_xboole_0(U_109)
| ~ m1_subset_1(U_110,k1_zfmisc_1(U_109))
| ~ r2_hidden(U_111,U_110) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_111,U_110] :
( ! [U_109] :
( ~ v1_xboole_0(U_109)
| ~ m1_subset_1(U_110,k1_zfmisc_1(U_109)) )
| ~ r2_hidden(U_111,U_110) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
fof(f_64_4,plain,
! [U_111,U_110,U_109] :
( ~ v1_xboole_0(U_109)
| ~ m1_subset_1(U_110,k1_zfmisc_1(U_109))
| ~ r2_hidden(U_111,U_110) ),
inference(definitional_conversion,[status(esa)],[f_64_3]) ).
cnf(f_64_5,plain,
( ~ v1_xboole_0(U_109)
| ~ m1_subset_1(U_110,k1_zfmisc_1(U_109))
| ~ r2_hidden(U_111,U_110) ),
inference(clausify,[status(thm)],[f_64_4]) ).
fof(f_65_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_65_2,plain,
! [U_112] :
( U_112 = k1_xboole_0
| ~ v1_xboole_0(U_112) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_112] :
( U_112 = k1_xboole_0
| ~ v1_xboole_0(U_112) ),
inference(definitional_conversion,[status(esa)],[f_65_2]) ).
cnf(f_65_4,plain,
( U_112 = k1_xboole_0
| ~ v1_xboole_0(U_112) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_66_2,plain,
! [U_114,U_113] :
( ~ v1_xboole_0(U_113)
| ~ r2_hidden(U_114,U_113) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_113,U_114] :
( ~ v1_xboole_0(U_113)
| ~ r2_hidden(U_114,U_113) ),
inference(definitional_conversion,[status(esa)],[f_66_2]) ).
cnf(f_66_4,plain,
( ~ v1_xboole_0(U_113)
| ~ r2_hidden(U_114,U_113) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_67_2,plain,
! [U_116,U_115] :
( ~ v1_xboole_0(U_115)
| U_116 = U_115
| ~ v1_xboole_0(U_116) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_116] :
( ! [U_115] :
( ~ v1_xboole_0(U_115)
| U_116 = U_115 )
| ~ v1_xboole_0(U_116) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
fof(f_67_4,plain,
! [U_115,U_116] :
( ~ v1_xboole_0(U_115)
| U_116 = U_115
| ~ v1_xboole_0(U_116) ),
inference(definitional_conversion,[status(esa)],[f_67_3]) ).
cnf(f_67_5,plain,
( ~ v1_xboole_0(U_115)
| U_116 = U_115
| ~ v1_xboole_0(U_116) ),
inference(clausify,[status(thm)],[f_67_4]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_3]) ).
cnf(f_10_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_3]) ).
cnf(f_11_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_3]) ).
cnf(f_12_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_3]) ).
cnf(f_15_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_3]) ).
cnf(f_18_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_3]) ).
cnf(f_19_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_3]) ).
cnf(f_23_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_23_3]) ).
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,
( 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_5,axiom,
( u2_lattices(Eq_x_0) = u2_lattices(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( k1_realset1(Eq_x_0,Eq_x_1) = k1_realset1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( u1_lattices(Eq_x_0) = u1_lattices(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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_9,axiom,
( k7_relat_1(Eq_x_0,Eq_x_1) = k7_relat_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,
( u1_struct_0(Eq_x_0) = u1_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK22(Eq_x_0) = sK22(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,axiom,
( v10_lattices(Eq_y_0)
| ~ v10_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( l3_lattices(Eq_y_0)
| ~ l3_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,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_23,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_24,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_25,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_26,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_27,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_28,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_29,axiom,
( r1_lattice2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r1_lattice2(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_30,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_31,axiom,
( v4_lattices(Eq_y_0)
| ~ v4_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( v5_lattices(Eq_y_0)
| ~ v5_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( v6_lattices(Eq_y_0)
| ~ v6_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( v7_lattices(Eq_y_0)
| ~ v7_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( v8_lattices(Eq_y_0)
| ~ v8_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( v9_lattices(Eq_y_0)
| ~ v9_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,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_38,axiom,
( v1_relat_1(Eq_y_0)
| ~ v1_relat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( v2_funct_1(Eq_y_0)
| ~ v2_funct_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( l1_lattices(Eq_y_0)
| ~ l1_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,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_42,axiom,
( l2_lattices(Eq_y_0)
| ~ l2_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,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_44,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_45,axiom,
( r1_tarski(Eq_y_0,Eq_y_1)
| ~ r1_tarski(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( v3_binop_1(Eq_y_0,Eq_y_1)
| ~ v3_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_47,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( sP3(Eq_y_0)
| ~ sP3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(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,
( sP8(Eq_y_0)
| ~ sP8(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(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,
( sP10(Eq_y_0)
| ~ sP10(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( sP11(Eq_y_0)
| ~ sP11(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_59,axiom,
( sP12(Eq_y_0)
| ~ sP12(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_60,axiom,
( sP13(Eq_y_0)
| ~ sP13(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_61,axiom,
( sP14(Eq_y_0)
| ~ sP14(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT326+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n008.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 13:23:39 UTC 2026
% 0.07/0.35 % CPUTime :
% 270.14/270.50 % SZS status Theorem for theBenchmark
% 270.14/270.50 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------