%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LAT313+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 : n006.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 08:48:10 AM UTC 2026
% Result : Theorem 1.25s 1.52s
% Output : Proof 1.25s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t43_filter_2,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( ( r2_hidden(k6_lattices(A),B)
& v14_lattices(A) )
=> ( B = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) ) ) ) ),
file('theBenchmark.p',t43_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(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(d8_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k17_filter_2(A) = u1_struct_0(A) ),
file('theBenchmark.p',d8_filter_2) ).
fof(dt_k17_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> m2_filter_2(k17_filter_2(A),A) ),
file('theBenchmark.p',dt_k17_filter_2) ).
fof(dt_k19_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) )
=> m2_filter_2(k19_filter_2(A,B),A) ),
file('theBenchmark.p',dt_k19_filter_2) ).
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_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_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_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_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
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_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(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(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_subset_1,axiom,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(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_r1_filter_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(A) )
=> ( r1_filter_2(A,B,C)
<=> B = C ) ),
file('theBenchmark.p',redefinition_r1_filter_2) ).
fof(reflexivity_r1_filter_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(A) )
=> r1_filter_2(A,B,B) ),
file('theBenchmark.p',reflexivity_r1_filter_2) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(symmetry_r1_filter_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(A) )
=> ( r1_filter_2(A,B,C)
=> r1_filter_2(A,C,B) ) ),
file('theBenchmark.p',symmetry_r1_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(t38_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B) ) ),
file('theBenchmark.p',t38_filter_2) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t42_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)))
& ~ v1_xboole_0(B) )
=> ( ( r2_hidden(k6_lattices(A),B)
& v14_lattices(A) )
=> ( k19_filter_2(A,B) = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)) ) ) ) ),
file('theBenchmark.p',t42_filter_2) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& A != B
& v1_xboole_0(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( ( r2_hidden(k6_lattices(A),B)
& v14_lattices(A) )
=> ( B = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) ) ) ) ),
inference(negate,[status(cth)],[t43_filter_2]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ( B != u1_struct_0(A)
| ~ r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) )
& r2_hidden(k6_lattices(A),B)
& v14_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] :
( ( U_0 != u1_struct_0(U_1)
| ~ r1_filter_2(u1_struct_0(U_1),U_0,k17_filter_2(U_1)) )
& r2_hidden(k6_lattices(U_1),U_0)
& v14_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] :
( ( U_0 != u1_struct_0(sK1)
| ~ r1_filter_2(u1_struct_0(sK1),U_0,k17_filter_2(sK1)) )
& r2_hidden(k6_lattices(sK1),U_0)
& v14_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,
( ( sK2 != u1_struct_0(sK1)
| ~ r1_filter_2(u1_struct_0(sK1),sK2,k17_filter_2(sK1)) )
& r2_hidden(k6_lattices(sK1),sK2)
& v14_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,
( ( sK2 != u1_struct_0(sK1)
| ~ r1_filter_2(u1_struct_0(sK1),sK2,k17_filter_2(sK1)) )
& r2_hidden(k6_lattices(sK1),sK2)
& v14_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,
v14_lattices(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_12,negated_conjecture,
r2_hidden(k6_lattices(sK1),sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_13,negated_conjecture,
( sK2 != u1_struct_0(sK1)
| ~ r1_filter_2(u1_struct_0(sK1),sK2,k17_filter_2(sK1)) ),
inference(clausify,[status(thm)],[f_1_6]) ).
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_3,U_2] :
( ~ r2_hidden(U_2,U_3)
| ~ r2_hidden(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ r2_hidden(U_2,U_3)
| ~ r2_hidden(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
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_4] :
( v1_funct_1(U_4)
| ~ v1_xboole_0(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( v1_funct_1(U_4)
| ~ v1_xboole_0(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
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_5] :
( ( v9_lattices(U_5)
& v8_lattices(U_5)
& v7_lattices(U_5)
& v6_lattices(U_5)
& v5_lattices(U_5)
& v4_lattices(U_5)
& ~ v3_struct_0(U_5) )
| ~ v10_lattices(U_5)
| v3_struct_0(U_5)
| ~ l3_lattices(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( ~ v3_struct_0(U_5)
| ~ v10_lattices(U_5)
| v3_struct_0(U_5)
| ~ l3_lattices(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( v4_lattices(U_5)
| ~ v10_lattices(U_5)
| v3_struct_0(U_5)
| ~ l3_lattices(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_5,plain,
( v5_lattices(U_5)
| ~ v10_lattices(U_5)
| v3_struct_0(U_5)
| ~ l3_lattices(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_6,plain,
( v6_lattices(U_5)
| ~ v10_lattices(U_5)
| v3_struct_0(U_5)
| ~ l3_lattices(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_7,plain,
( v7_lattices(U_5)
| ~ v10_lattices(U_5)
| v3_struct_0(U_5)
| ~ l3_lattices(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_8,plain,
( v8_lattices(U_5)
| ~ v10_lattices(U_5)
| v3_struct_0(U_5)
| ~ l3_lattices(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_9,plain,
( v9_lattices(U_5)
| ~ v10_lattices(U_5)
| v3_struct_0(U_5)
| ~ l3_lattices(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_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_5_2,plain,
! [U_6] :
( ( v10_lattices(U_6)
& ~ v3_struct_0(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)
| ~ l3_lattices(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( ~ v3_struct_0(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)
| ~ l3_lattices(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( v10_lattices(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)
| ~ l3_lattices(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( k17_filter_2(A) = u1_struct_0(A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[d8_filter_2]) ).
fof(f_6_2,plain,
! [U_7] :
( k17_filter_2(U_7) = u1_struct_0(U_7)
| ~ l3_lattices(U_7)
| ~ v10_lattices(U_7)
| v3_struct_0(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( k17_filter_2(U_7) = u1_struct_0(U_7)
| ~ l3_lattices(U_7)
| ~ v10_lattices(U_7)
| v3_struct_0(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( m2_filter_2(k17_filter_2(A),A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k17_filter_2]) ).
fof(f_7_2,plain,
! [U_8] :
( m2_filter_2(k17_filter_2(U_8),U_8)
| ~ l3_lattices(U_8)
| ~ v10_lattices(U_8)
| v3_struct_0(U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( m2_filter_2(k17_filter_2(U_8),U_8)
| ~ l3_lattices(U_8)
| ~ v10_lattices(U_8)
| v3_struct_0(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A,B] :
( m2_filter_2(k19_filter_2(A,B),A)
| ~ 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)],[dt_k19_filter_2]) ).
fof(f_8_2,plain,
! [U_10,U_9] :
( m2_filter_2(k19_filter_2(U_10,U_9),U_10)
| ~ m1_subset_1(U_9,k1_zfmisc_1(u1_struct_0(U_10)))
| v1_xboole_0(U_9)
| ~ l3_lattices(U_10)
| ~ v10_lattices(U_10)
| v3_struct_0(U_10) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( m2_filter_2(k19_filter_2(U_10,U_9),U_10)
| ~ m1_subset_1(U_9,k1_zfmisc_1(u1_struct_0(U_10)))
| v1_xboole_0(U_9)
| ~ l3_lattices(U_10)
| ~ v10_lattices(U_10)
| v3_struct_0(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
! [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_11_2,plain,
! [U_11] :
( m1_subset_1(k6_lattices(U_11),u1_struct_0(U_11))
| ~ l2_lattices(U_11)
| v3_struct_0(U_11) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( m1_subset_1(k6_lattices(U_11),u1_struct_0(U_11))
| ~ l2_lattices(U_11)
| v3_struct_0(U_11) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_lattices]) ).
fof(f_12_2,plain,
! [U_12] :
( l1_struct_0(U_12)
| ~ l1_lattices(U_12) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( l1_struct_0(U_12)
| ~ l1_lattices(U_12) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_lattices]) ).
fof(f_14_2,plain,
! [U_13] :
( l1_struct_0(U_13)
| ~ l2_lattices(U_13) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( l1_struct_0(U_13)
| ~ l2_lattices(U_13) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( ( l2_lattices(A)
& l1_lattices(A) )
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l3_lattices]) ).
fof(f_15_2,plain,
! [U_14] :
( ( l2_lattices(U_14)
& l1_lattices(U_14) )
| ~ l3_lattices(U_14) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( l1_lattices(U_14)
| ~ l3_lattices(U_14) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( l2_lattices(U_14)
| ~ l3_lattices(U_14) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_16_2,plain,
$true,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_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_17_2,plain,
! [U_16] :
( ! [U_15] :
( ( m2_lattice4(U_15,U_16)
& ~ v1_xboole_0(U_15) )
| ~ m2_filter_2(U_15,U_16) )
| ~ l3_lattices(U_16)
| ~ v10_lattices(U_16)
| v3_struct_0(U_16) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( ~ v1_xboole_0(U_15)
| ~ m2_filter_2(U_15,U_16)
| ~ l3_lattices(U_16)
| ~ v10_lattices(U_16)
| v3_struct_0(U_16) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( m2_lattice4(U_15,U_16)
| ~ m2_filter_2(U_15,U_16)
| ~ l3_lattices(U_16)
| ~ v10_lattices(U_16)
| v3_struct_0(U_16) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_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_18_2,plain,
! [U_18] :
( ! [U_17] :
( m1_subset_1(U_17,k1_zfmisc_1(u1_struct_0(U_18)))
| ~ m2_lattice4(U_17,U_18) )
| ~ l3_lattices(U_18)
| ~ v10_lattices(U_18)
| v3_struct_0(U_18) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( m1_subset_1(U_17,k1_zfmisc_1(u1_struct_0(U_18)))
| ~ m2_lattice4(U_17,U_18)
| ~ l3_lattices(U_18)
| ~ v10_lattices(U_18)
| v3_struct_0(U_18) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_19_2,plain,
$true,
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
? [A] : l1_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l1_lattices]) ).
fof(f_20_2,plain,
? [U_19] : l1_lattices(U_19),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
l1_lattices(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3)],[f_20_2]) ).
cnf(f_20_4,plain,
l1_lattices(sK3),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_21_2,plain,
? [U_20] : l1_struct_0(U_20),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
l1_struct_0(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_20,sK4)],[f_21_2]) ).
cnf(f_21_4,plain,
l1_struct_0(sK4),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] : l2_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l2_lattices]) ).
fof(f_22_2,plain,
? [U_21] : l2_lattices(U_21),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
l2_lattices(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_21,sK5)],[f_22_2]) ).
cnf(f_22_4,plain,
l2_lattices(sK5),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] : l3_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l3_lattices]) ).
fof(f_23_2,plain,
? [U_22] : l3_lattices(U_22),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
l3_lattices(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_22,sK6)],[f_23_2]) ).
cnf(f_23_4,plain,
l3_lattices(sK6),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_24_2,plain,
! [U_24] :
? [U_23] : m1_subset_1(U_23,U_24),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_24] : m1_subset_1(sK7(U_24),U_24),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_23,sK7(U_24))],[f_24_2]) ).
cnf(f_24_4,plain,
m1_subset_1(sK7(U_24),U_24),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_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_25_2,plain,
! [U_26] :
( ? [U_25] : m2_filter_2(U_25,U_26)
| ~ l3_lattices(U_26)
| ~ v10_lattices(U_26)
| v3_struct_0(U_26) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_26] :
( m2_filter_2(sK8(U_26),U_26)
| ~ l3_lattices(U_26)
| ~ v10_lattices(U_26)
| v3_struct_0(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_25,sK8(U_26))],[f_25_2]) ).
cnf(f_25_4,plain,
( m2_filter_2(sK8(U_26),U_26)
| ~ l3_lattices(U_26)
| ~ v10_lattices(U_26)
| v3_struct_0(U_26) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_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_26_2,plain,
! [U_28] :
( ? [U_27] : m2_lattice4(U_27,U_28)
| ~ l3_lattices(U_28)
| ~ v10_lattices(U_28)
| v3_struct_0(U_28) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_28] :
( m2_lattice4(sK9(U_28),U_28)
| ~ l3_lattices(U_28)
| ~ v10_lattices(U_28)
| v3_struct_0(U_28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_27,sK9(U_28))],[f_26_2]) ).
cnf(f_26_4,plain,
( m2_lattice4(sK9(U_28),U_28)
| ~ l3_lattices(U_28)
| ~ v10_lattices(U_28)
| v3_struct_0(U_28) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_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_27_2,plain,
! [U_29] :
( ~ v1_xboole_0(u1_struct_0(U_29))
| ~ l1_struct_0(U_29)
| v3_struct_0(U_29) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_29))
| ~ l1_struct_0(U_29)
| v3_struct_0(U_29) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_28_2,plain,
! [U_30] : ~ v1_xboole_0(k1_zfmisc_1(U_30)),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
~ v1_xboole_0(k1_zfmisc_1(U_30)),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_29_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_29_1]) ).
fof(f_30_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_30_2,plain,
! [U_32] :
( ? [U_31] :
( ~ v1_xboole_0(U_31)
& m2_lattice4(U_31,U_32) )
| ~ l3_lattices(U_32)
| ~ v10_lattices(U_32)
| v3_struct_0(U_32) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_32] :
( ( ~ v1_xboole_0(sK10(U_32))
& m2_lattice4(sK10(U_32),U_32) )
| ~ l3_lattices(U_32)
| ~ v10_lattices(U_32)
| v3_struct_0(U_32) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_31,sK10(U_32))],[f_30_2]) ).
cnf(f_30_4,plain,
( m2_lattice4(sK10(U_32),U_32)
| ~ l3_lattices(U_32)
| ~ v10_lattices(U_32)
| v3_struct_0(U_32) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( ~ v1_xboole_0(sK10(U_32))
| ~ l3_lattices(U_32)
| ~ v10_lattices(U_32)
| v3_struct_0(U_32) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_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_31_2,plain,
! [U_34] :
( ? [U_33] :
( ~ v1_xboole_0(U_33)
& m1_subset_1(U_33,k1_zfmisc_1(U_34)) )
| v1_xboole_0(U_34) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_34] :
( ( ~ v1_xboole_0(sK11(U_34))
& m1_subset_1(sK11(U_34),k1_zfmisc_1(U_34)) )
| v1_xboole_0(U_34) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_33,sK11(U_34))],[f_31_2]) ).
cnf(f_31_4,plain,
( m1_subset_1(sK11(U_34),k1_zfmisc_1(U_34))
| v1_xboole_0(U_34) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( ~ v1_xboole_0(sK11(U_34))
| v1_xboole_0(U_34) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_32_2,plain,
? [U_35] : v1_xboole_0(U_35),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
v1_xboole_0(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_35,sK12)],[f_32_2]) ).
cnf(f_32_4,plain,
v1_xboole_0(sK12),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_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_33_2,plain,
! [U_37] :
? [U_36] :
( v1_xboole_0(U_36)
& m1_subset_1(U_36,k1_zfmisc_1(U_37)) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_37] :
( v1_xboole_0(sK13(U_37))
& m1_subset_1(sK13(U_37),k1_zfmisc_1(U_37)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_36,sK13(U_37))],[f_33_2]) ).
cnf(f_33_4,plain,
m1_subset_1(sK13(U_37),k1_zfmisc_1(U_37)),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
v1_xboole_0(sK13(U_37)),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_34_2,plain,
? [U_38] : ~ v1_xboole_0(U_38),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
~ v1_xboole_0(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_38,sK14)],[f_34_2]) ).
cnf(f_34_4,plain,
~ v1_xboole_0(sK14),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_35_2,plain,
? [U_39] :
( ~ v3_struct_0(U_39)
& l1_struct_0(U_39) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ~ v3_struct_0(sK15)
& l1_struct_0(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_39,sK15)],[f_35_2]) ).
cnf(f_35_4,plain,
l1_struct_0(sK15),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
~ v3_struct_0(sK15),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_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_36_2,plain,
! [U_41] :
( ? [U_40] :
( ~ v1_xboole_0(U_40)
& m1_subset_1(U_40,k1_zfmisc_1(u1_struct_0(U_41))) )
| ~ l1_struct_0(U_41)
| v3_struct_0(U_41) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_41] :
( ( ~ v1_xboole_0(sK16(U_41))
& m1_subset_1(sK16(U_41),k1_zfmisc_1(u1_struct_0(U_41))) )
| ~ l1_struct_0(U_41)
| v3_struct_0(U_41) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_40,sK16(U_41))],[f_36_2]) ).
cnf(f_36_4,plain,
( m1_subset_1(sK16(U_41),k1_zfmisc_1(u1_struct_0(U_41)))
| ~ l1_struct_0(U_41)
| v3_struct_0(U_41) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
( ~ v1_xboole_0(sK16(U_41))
| ~ l1_struct_0(U_41)
| v3_struct_0(U_41) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B,C] :
( ( ( r1_filter_2(A,B,C)
| B != C )
& ( B = C
| ~ r1_filter_2(A,B,C) ) )
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r1_filter_2]) ).
fof(f_37_2,plain,
! [U_44,U_43,U_42] :
( ( ( r1_filter_2(U_44,U_43,U_42)
| U_43 != U_42 )
& ( U_43 = U_42
| ~ r1_filter_2(U_44,U_43,U_42) ) )
| ~ m1_subset_1(U_42,k1_zfmisc_1(U_44))
| ~ m1_subset_1(U_43,k1_zfmisc_1(U_44))
| v1_xboole_0(U_44) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( U_43 = U_42
| ~ r1_filter_2(U_44,U_43,U_42)
| ~ m1_subset_1(U_42,k1_zfmisc_1(U_44))
| ~ m1_subset_1(U_43,k1_zfmisc_1(U_44))
| v1_xboole_0(U_44) ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( r1_filter_2(U_44,U_43,U_42)
| U_43 != U_42
| ~ m1_subset_1(U_42,k1_zfmisc_1(U_44))
| ~ m1_subset_1(U_43,k1_zfmisc_1(U_44))
| v1_xboole_0(U_44) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A,B,C] :
( r1_filter_2(A,B,B)
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_filter_2]) ).
fof(f_38_2,plain,
! [U_47,U_46,U_45] :
( r1_filter_2(U_47,U_46,U_46)
| ~ m1_subset_1(U_45,k1_zfmisc_1(U_47))
| ~ m1_subset_1(U_46,k1_zfmisc_1(U_47))
| v1_xboole_0(U_47) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_47,U_46] :
( ! [U_45] : ~ m1_subset_1(U_45,k1_zfmisc_1(U_47))
| ~ m1_subset_1(U_46,k1_zfmisc_1(U_47))
| v1_xboole_0(U_47)
| r1_filter_2(U_47,U_46,U_46) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( ~ m1_subset_1(U_45,k1_zfmisc_1(U_47))
| ~ m1_subset_1(U_46,k1_zfmisc_1(U_47))
| v1_xboole_0(U_47)
| r1_filter_2(U_47,U_46,U_46) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_39_2,plain,
! [U_49,U_48] : r1_tarski(U_49,U_49),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_49] : r1_tarski(U_49,U_49),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
r1_tarski(U_49,U_49),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B,C] :
( r1_filter_2(A,C,B)
| ~ r1_filter_2(A,B,C)
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_filter_2]) ).
fof(f_40_2,plain,
! [U_52,U_51,U_50] :
( r1_filter_2(U_52,U_50,U_51)
| ~ r1_filter_2(U_52,U_51,U_50)
| ~ m1_subset_1(U_50,k1_zfmisc_1(U_52))
| ~ m1_subset_1(U_51,k1_zfmisc_1(U_52))
| v1_xboole_0(U_52) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( r1_filter_2(U_52,U_50,U_51)
| ~ r1_filter_2(U_52,U_51,U_50)
| ~ m1_subset_1(U_50,k1_zfmisc_1(U_52))
| ~ m1_subset_1(U_51,k1_zfmisc_1(U_52))
| v1_xboole_0(U_52) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_41_2,plain,
! [U_54,U_53] :
( m1_subset_1(U_54,U_53)
| ~ r2_hidden(U_54,U_53) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( m1_subset_1(U_54,U_53)
| ~ r2_hidden(U_54,U_53) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_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_42_2,plain,
! [U_56,U_55] :
( r2_hidden(U_56,U_55)
| v1_xboole_0(U_55)
| ~ m1_subset_1(U_56,U_55) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( r2_hidden(U_56,U_55)
| v1_xboole_0(U_55)
| ~ m1_subset_1(U_56,U_55) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A] :
( ! [B] :
( r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B)
| ~ m2_filter_2(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t38_filter_2]) ).
fof(f_43_2,plain,
! [U_58] :
( ! [U_57] :
( r1_filter_2(u1_struct_0(U_58),k19_filter_2(U_58,U_57),U_57)
| ~ m2_filter_2(U_57,U_58) )
| ~ l3_lattices(U_58)
| ~ v10_lattices(U_58)
| v3_struct_0(U_58) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( r1_filter_2(u1_struct_0(U_58),k19_filter_2(U_58,U_57),U_57)
| ~ m2_filter_2(U_57,U_58)
| ~ l3_lattices(U_58)
| ~ v10_lattices(U_58)
| v3_struct_0(U_58) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_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_44_2,plain,
! [U_60,U_59] :
( ( m1_subset_1(U_60,k1_zfmisc_1(U_59))
| ~ r1_tarski(U_60,U_59) )
& ( r1_tarski(U_60,U_59)
| ~ m1_subset_1(U_60,k1_zfmisc_1(U_59)) ) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ! [U_64,U_62] :
( m1_subset_1(U_64,k1_zfmisc_1(U_62))
| ~ r1_tarski(U_64,U_62) )
& ! [U_63,U_61] :
( r1_tarski(U_63,U_61)
| ~ m1_subset_1(U_63,k1_zfmisc_1(U_61)) ) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
cnf(f_44_4,plain,
( r1_tarski(U_63,U_61)
| ~ m1_subset_1(U_63,k1_zfmisc_1(U_61)) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_5,plain,
( m1_subset_1(U_64,k1_zfmisc_1(U_62))
| ~ r1_tarski(U_64,U_62) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A] :
( ! [B] :
( ( k19_filter_2(A,B) = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)) )
| ~ r2_hidden(k6_lattices(A),B)
| ~ v14_lattices(A)
| ~ 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)],[t42_filter_2]) ).
fof(f_45_2,plain,
! [U_66] :
( ! [U_65] :
( ( k19_filter_2(U_66,U_65) = u1_struct_0(U_66)
& r1_filter_2(u1_struct_0(U_66),k19_filter_2(U_66,U_65),k17_filter_2(U_66)) )
| ~ r2_hidden(k6_lattices(U_66),U_65)
| ~ v14_lattices(U_66)
| ~ m1_subset_1(U_65,k1_zfmisc_1(u1_struct_0(U_66)))
| v1_xboole_0(U_65) )
| ~ l3_lattices(U_66)
| ~ v10_lattices(U_66)
| v3_struct_0(U_66) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( r1_filter_2(u1_struct_0(U_66),k19_filter_2(U_66,U_65),k17_filter_2(U_66))
| ~ r2_hidden(k6_lattices(U_66),U_65)
| ~ v14_lattices(U_66)
| ~ m1_subset_1(U_65,k1_zfmisc_1(u1_struct_0(U_66)))
| v1_xboole_0(U_65)
| ~ l3_lattices(U_66)
| ~ v10_lattices(U_66)
| v3_struct_0(U_66) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
( k19_filter_2(U_66,U_65) = u1_struct_0(U_66)
| ~ r2_hidden(k6_lattices(U_66),U_65)
| ~ v14_lattices(U_66)
| ~ m1_subset_1(U_65,k1_zfmisc_1(u1_struct_0(U_66)))
| v1_xboole_0(U_65)
| ~ l3_lattices(U_66)
| ~ v10_lattices(U_66)
| v3_struct_0(U_66) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_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_46_2,plain,
! [U_69,U_68,U_67] :
( m1_subset_1(U_69,U_67)
| ~ m1_subset_1(U_68,k1_zfmisc_1(U_67))
| ~ r2_hidden(U_69,U_68) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( m1_subset_1(U_69,U_67)
| ~ m1_subset_1(U_68,k1_zfmisc_1(U_67))
| ~ r2_hidden(U_69,U_68) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_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_47_2,plain,
! [U_72,U_71,U_70] :
( ~ v1_xboole_0(U_70)
| ~ m1_subset_1(U_71,k1_zfmisc_1(U_70))
| ~ r2_hidden(U_72,U_71) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_72,U_71] :
( ! [U_70] :
( ~ v1_xboole_0(U_70)
| ~ m1_subset_1(U_71,k1_zfmisc_1(U_70)) )
| ~ r2_hidden(U_72,U_71) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
cnf(f_47_4,plain,
( ~ v1_xboole_0(U_70)
| ~ m1_subset_1(U_71,k1_zfmisc_1(U_70))
| ~ r2_hidden(U_72,U_71) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_48_2,plain,
! [U_73] :
( U_73 = k1_xboole_0
| ~ v1_xboole_0(U_73) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( U_73 = k1_xboole_0
| ~ v1_xboole_0(U_73) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_49_2,plain,
! [U_75,U_74] :
( ~ v1_xboole_0(U_74)
| ~ r2_hidden(U_75,U_74) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( ~ v1_xboole_0(U_74)
| ~ r2_hidden(U_75,U_74) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_50_2,plain,
! [U_77,U_76] :
( ~ v1_xboole_0(U_76)
| U_77 = U_76
| ~ v1_xboole_0(U_77) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_77] :
( ! [U_76] :
( ~ v1_xboole_0(U_76)
| U_77 = U_76 )
| ~ v1_xboole_0(U_77) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
cnf(f_50_4,plain,
( ~ v1_xboole_0(U_76)
| U_77 = U_76
| ~ v1_xboole_0(U_77) ),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(f_16_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_2]) ).
cnf(f_19_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_2]) ).
cnf(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,
( k6_lattices(Eq_x_0) = k6_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,
( k17_filter_2(Eq_x_0) = k17_filter_2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,axiom,
( k19_filter_2(Eq_x_0,Eq_x_1) = k19_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_9,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| 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,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( v10_lattices(Eq_y_0)
| ~ v10_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( l3_lattices(Eq_y_0)
| ~ l3_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,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_20,axiom,
( v14_lattices(Eq_y_0)
| ~ v14_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,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_22,axiom,
( r1_filter_2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r1_filter_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_23,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_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,
( v4_lattices(Eq_y_0)
| ~ v4_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( v5_lattices(Eq_y_0)
| ~ v5_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( v6_lattices(Eq_y_0)
| ~ v6_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( v7_lattices(Eq_y_0)
| ~ v7_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( v8_lattices(Eq_y_0)
| ~ v8_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( v9_lattices(Eq_y_0)
| ~ v9_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,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_32,axiom,
( l2_lattices(Eq_y_0)
| ~ l2_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( l1_lattices(Eq_y_0)
| ~ l1_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,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_35,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_36,axiom,
( r1_tarski(Eq_y_0,Eq_y_1)
| ~ r1_tarski(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT313+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n006.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 19 13:16:27 UTC 2026
% 0.08/0.34 % CPUTime :
% 1.25/1.52 % SZS status Theorem for theBenchmark
% 1.25/1.52 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------