%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LAT328+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 : n004.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 08:48:14 AM UTC 2026
% Result : Theorem 256.46s 256.71s
% Output : Proof 256.92s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t65_filter_2,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_filter_2(u1_struct_0(A),k22_filter_2(A,B,B),k6_domain_1(u1_struct_0(A),B)) ) ),
file('theBenchmark.p',t65_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_realset1,axiom,
! [A] :
( ~ v1_realset1(A)
=> ~ v1_xboole_0(A) ),
file('theBenchmark.p',cc1_realset1) ).
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(d1_filter_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( r1_filter_2(A,B,C)
<=> ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,B)
<=> r2_hidden(D,C) ) ) ) ) ) ),
file('theBenchmark.p',d1_filter_2) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = k1_tarski(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k22_filter_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( m2_lattice4(k22_filter_2(A,B,C),A)
& ~ v1_xboole_0(k22_filter_2(A,B,C)) ) ),
file('theBenchmark.p',dt_k22_filter_2) ).
fof(dt_k6_domain_1,axiom,
! [A,B] :
( ( m1_subset_1(B,A)
& ~ v1_xboole_0(A) )
=> m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ),
file('theBenchmark.p',dt_k6_domain_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_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_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_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(fc2_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_tarski(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc3_realset1,axiom,
! [A] :
( v1_realset1(k1_tarski(A))
& v1_finset_1(k1_tarski(A))
& ~ v1_xboole_0(k1_tarski(A)) ),
file('theBenchmark.p',fc3_realset1) ).
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_realset1,axiom,
? [A] :
( v1_realset1(A)
& ~ v1_xboole_0(A) ),
file('theBenchmark.p',rc1_realset1) ).
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_realset1,axiom,
? [A] :
( ~ v1_realset1(A)
& ~ v1_xboole_0(A) ),
file('theBenchmark.p',rc2_realset1) ).
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_k6_domain_1,axiom,
! [A,B] :
( ( m1_subset_1(B,A)
& ~ v1_xboole_0(A) )
=> k6_domain_1(A,B) = k1_tarski(B) ),
file('theBenchmark.p',redefinition_k6_domain_1) ).
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(redefinition_r3_lattices,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v6_lattices(A)
& ~ v3_struct_0(A) )
=> ( r3_lattices(A,B,C)
<=> r1_lattices(A,B,C) ) ),
file('theBenchmark.p',redefinition_r3_lattices) ).
fof(reflexivity_r1_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(reflexivity_r3_lattices,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v6_lattices(A)
& ~ v3_struct_0(A) )
=> r3_lattices(A,B,B) ),
file('theBenchmark.p',reflexivity_r3_lattices) ).
fof(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(t26_lattices,axiom,
! [A] :
( ( l2_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r1_lattices(A,C,B)
& r1_lattices(A,B,C) )
=> B = C ) ) ) ),
file('theBenchmark.p',t26_lattices) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t63_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> ( r2_hidden(D,k22_filter_2(A,B,C))
<=> ( r3_lattices(A,D,C)
& r3_lattices(A,B,D) ) ) ) ) ) ) ),
file('theBenchmark.p',t63_filter_2) ).
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] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_filter_2(u1_struct_0(A),k22_filter_2(A,B,B),k6_domain_1(u1_struct_0(A),B)) ) ),
inference(negate,[status(cth)],[t65_filter_2]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ~ r1_filter_2(u1_struct_0(A),k22_filter_2(A,B,B),k6_domain_1(u1_struct_0(A),B))
& m1_subset_1(B,u1_struct_0(A)) )
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_1] :
( ? [U_0] :
( ~ r1_filter_2(u1_struct_0(U_1),k22_filter_2(U_1,U_0,U_0),k6_domain_1(u1_struct_0(U_1),U_0))
& m1_subset_1(U_0,u1_struct_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] :
( ~ r1_filter_2(u1_struct_0(sK1),k22_filter_2(sK1,U_0,U_0),k6_domain_1(u1_struct_0(sK1),U_0))
& m1_subset_1(U_0,u1_struct_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,
( ~ r1_filter_2(u1_struct_0(sK1),k22_filter_2(sK1,sK2,sK2),k6_domain_1(u1_struct_0(sK1),sK2))
& m1_subset_1(sK2,u1_struct_0(sK1))
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_0,sK2)],[f_1_4]) ).
cnf(f_1_6,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_7,negated_conjecture,
v10_lattices(sK1),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_8,negated_conjecture,
l3_lattices(sK1),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_9,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_10,negated_conjecture,
~ r1_filter_2(u1_struct_0(sK1),k22_filter_2(sK1,sK2,sK2),k6_domain_1(u1_struct_0(sK1),sK2)),
inference(clausify,[status(thm)],[f_1_5]) ).
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] :
( ~ v1_xboole_0(A)
| v1_realset1(A) ),
inference(fof_nnf,[status(thm)],[cc1_realset1]) ).
fof(f_5_2,plain,
! [U_6] :
( ~ v1_xboole_0(U_6)
| v1_realset1(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( ~ v1_xboole_0(U_6)
| v1_realset1(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_7] :
( ( v10_lattices(U_7)
& ~ v3_struct_0(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)
| ~ l3_lattices(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( ~ v3_struct_0(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)
| ~ l3_lattices(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( v10_lattices(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)
| ~ l3_lattices(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( r1_filter_2(A,B,C)
| ? [D] :
( ( ( ~ r2_hidden(D,B)
& r2_hidden(D,C) )
| ( ~ r2_hidden(D,C)
& r2_hidden(D,B) ) )
& m1_subset_1(D,A) ) )
& ( ! [D] :
( ( ( r2_hidden(D,B)
| ~ r2_hidden(D,C) )
& ( r2_hidden(D,C)
| ~ r2_hidden(D,B) ) )
| ~ m1_subset_1(D,A) )
| ~ 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)],[d1_filter_2]) ).
fof(f_7_2,plain,
! [U_12] :
( ! [U_11] :
( ! [U_10] :
( ( ( r1_filter_2(U_12,U_11,U_10)
| ? [U_9] :
( ( ( ~ r2_hidden(U_9,U_11)
& r2_hidden(U_9,U_10) )
| ( ~ r2_hidden(U_9,U_10)
& r2_hidden(U_9,U_11) ) )
& m1_subset_1(U_9,U_12) ) )
& ( ! [U_8] :
( ( ( r2_hidden(U_8,U_11)
| ~ r2_hidden(U_8,U_10) )
& ( r2_hidden(U_8,U_10)
| ~ r2_hidden(U_8,U_11) ) )
| ~ m1_subset_1(U_8,U_12) )
| ~ r1_filter_2(U_12,U_11,U_10) ) )
| ~ m1_subset_1(U_10,k1_zfmisc_1(U_12)) )
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_12)) )
| v1_xboole_0(U_12) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_12] :
( ! [U_11] :
( ! [U_10] :
( ( ( r1_filter_2(U_12,U_11,U_10)
| ( ( ( ~ r2_hidden(sK3(U_12,U_11,U_10),U_11)
& r2_hidden(sK3(U_12,U_11,U_10),U_10) )
| ( ~ r2_hidden(sK3(U_12,U_11,U_10),U_10)
& r2_hidden(sK3(U_12,U_11,U_10),U_11) ) )
& m1_subset_1(sK3(U_12,U_11,U_10),U_12) ) )
& ( ! [U_8] :
( ( ( r2_hidden(U_8,U_11)
| ~ r2_hidden(U_8,U_10) )
& ( r2_hidden(U_8,U_10)
| ~ r2_hidden(U_8,U_11) ) )
| ~ m1_subset_1(U_8,U_12) )
| ~ r1_filter_2(U_12,U_11,U_10) ) )
| ~ m1_subset_1(U_10,k1_zfmisc_1(U_12)) )
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_12)) )
| v1_xboole_0(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_9,sK3(U_12,U_11,U_10))],[f_7_2]) ).
cnf(f_7_4,plain,
( r2_hidden(U_8,U_10)
| ~ r2_hidden(U_8,U_11)
| ~ m1_subset_1(U_8,U_12)
| ~ r1_filter_2(U_12,U_11,U_10)
| ~ m1_subset_1(U_10,k1_zfmisc_1(U_12))
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_12))
| v1_xboole_0(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( r2_hidden(U_8,U_11)
| ~ r2_hidden(U_8,U_10)
| ~ m1_subset_1(U_8,U_12)
| ~ r1_filter_2(U_12,U_11,U_10)
| ~ m1_subset_1(U_10,k1_zfmisc_1(U_12))
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_12))
| v1_xboole_0(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( m1_subset_1(sK3(U_12,U_11,U_10),U_12)
| r1_filter_2(U_12,U_11,U_10)
| ~ m1_subset_1(U_10,k1_zfmisc_1(U_12))
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_12))
| v1_xboole_0(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( r2_hidden(sK3(U_12,U_11,U_10),U_10)
| r2_hidden(sK3(U_12,U_11,U_10),U_11)
| r1_filter_2(U_12,U_11,U_10)
| ~ m1_subset_1(U_10,k1_zfmisc_1(U_12))
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_12))
| v1_xboole_0(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_8,plain,
( ~ r2_hidden(sK3(U_12,U_11,U_10),U_11)
| r2_hidden(sK3(U_12,U_11,U_10),U_11)
| r1_filter_2(U_12,U_11,U_10)
| ~ m1_subset_1(U_10,k1_zfmisc_1(U_12))
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_12))
| v1_xboole_0(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_9,plain,
( r2_hidden(sK3(U_12,U_11,U_10),U_10)
| ~ r2_hidden(sK3(U_12,U_11,U_10),U_10)
| r1_filter_2(U_12,U_11,U_10)
| ~ m1_subset_1(U_10,k1_zfmisc_1(U_12))
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_12))
| v1_xboole_0(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_10,plain,
( ~ r2_hidden(sK3(U_12,U_11,U_10),U_11)
| ~ r2_hidden(sK3(U_12,U_11,U_10),U_10)
| r1_filter_2(U_12,U_11,U_10)
| ~ m1_subset_1(U_10,k1_zfmisc_1(U_12))
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_12))
| v1_xboole_0(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B] :
( ( B = k1_tarski(A)
| ? [C] :
( ( ~ r2_hidden(C,B)
& C = A )
| ( C != A
& r2_hidden(C,B) ) ) )
& ( ! [C] :
( ( r2_hidden(C,B)
| C != A )
& ( C = A
| ~ r2_hidden(C,B) ) )
| B != k1_tarski(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_8_2,plain,
! [U_16,U_15] :
( ( U_15 = k1_tarski(U_16)
| ? [U_14] :
( ( ~ r2_hidden(U_14,U_15)
& U_14 = U_16 )
| ( U_14 != U_16
& r2_hidden(U_14,U_15) ) ) )
& ( ! [U_13] :
( ( r2_hidden(U_13,U_15)
| U_13 != U_16 )
& ( U_13 = U_16
| ~ r2_hidden(U_13,U_15) ) )
| U_15 != k1_tarski(U_16) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_24,U_22] :
( U_22 = k1_tarski(U_24)
| ? [U_20] :
( ~ r2_hidden(U_20,U_22)
& U_20 = U_24 )
| ? [U_19] :
( U_19 != U_24
& r2_hidden(U_19,U_22) ) )
& ! [U_23,U_21] :
( ( ! [U_18] :
( r2_hidden(U_18,U_21)
| U_18 != U_23 )
& ! [U_17] :
( U_17 = U_23
| ~ r2_hidden(U_17,U_21) ) )
| U_21 != k1_tarski(U_23) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_24,U_22] :
( U_22 = k1_tarski(U_24)
| ? [U_20] :
( ~ r2_hidden(U_20,U_22)
& U_20 = U_24 )
| ( sK4(U_24,U_22) != U_24
& r2_hidden(sK4(U_24,U_22),U_22) ) )
& ! [U_23,U_21] :
( ( ! [U_18] :
( r2_hidden(U_18,U_21)
| U_18 != U_23 )
& ! [U_17] :
( U_17 = U_23
| ~ r2_hidden(U_17,U_21) ) )
| U_21 != k1_tarski(U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_19,sK4(U_24,U_22))],[f_8_3]) ).
fof(f_8_5,plain,
( ! [U_24,U_22] :
( U_22 = k1_tarski(U_24)
| ( ~ r2_hidden(sK5(U_24,U_22),U_22)
& sK5(U_24,U_22) = U_24 )
| ( sK4(U_24,U_22) != U_24
& r2_hidden(sK4(U_24,U_22),U_22) ) )
& ! [U_23,U_21] :
( ( ! [U_18] :
( r2_hidden(U_18,U_21)
| U_18 != U_23 )
& ! [U_17] :
( U_17 = U_23
| ~ r2_hidden(U_17,U_21) ) )
| U_21 != k1_tarski(U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_20,sK5(U_24,U_22))],[f_8_4]) ).
cnf(f_8_6,plain,
( U_17 = U_23
| ~ r2_hidden(U_17,U_21)
| U_21 != k1_tarski(U_23) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_7,plain,
( r2_hidden(U_18,U_21)
| U_18 != U_23
| U_21 != k1_tarski(U_23) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_8,plain,
( sK5(U_24,U_22) = U_24
| r2_hidden(sK4(U_24,U_22),U_22)
| U_22 = k1_tarski(U_24) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_9,plain,
( ~ r2_hidden(sK5(U_24,U_22),U_22)
| r2_hidden(sK4(U_24,U_22),U_22)
| U_22 = k1_tarski(U_24) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_10,plain,
( sK5(U_24,U_22) = U_24
| sK4(U_24,U_22) != U_24
| U_22 = k1_tarski(U_24) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_11,plain,
( ~ r2_hidden(sK5(U_24,U_22),U_22)
| sK4(U_24,U_22) != U_24
| U_22 = k1_tarski(U_24) ),
inference(clausify,[status(thm)],[f_8_5]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
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_xboole_0]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
! [A,B,C] :
( ( m2_lattice4(k22_filter_2(A,B,C),A)
& ~ v1_xboole_0(k22_filter_2(A,B,C)) )
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k22_filter_2]) ).
fof(f_12_2,plain,
! [U_27,U_26,U_25] :
( ( m2_lattice4(k22_filter_2(U_27,U_26,U_25),U_27)
& ~ v1_xboole_0(k22_filter_2(U_27,U_26,U_25)) )
| ~ m1_subset_1(U_25,u1_struct_0(U_27))
| ~ m1_subset_1(U_26,u1_struct_0(U_27))
| ~ l3_lattices(U_27)
| ~ v10_lattices(U_27)
| v3_struct_0(U_27) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( ~ v1_xboole_0(k22_filter_2(U_27,U_26,U_25))
| ~ m1_subset_1(U_25,u1_struct_0(U_27))
| ~ m1_subset_1(U_26,u1_struct_0(U_27))
| ~ l3_lattices(U_27)
| ~ v10_lattices(U_27)
| v3_struct_0(U_27) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( m2_lattice4(k22_filter_2(U_27,U_26,U_25),U_27)
| ~ m1_subset_1(U_25,u1_struct_0(U_27))
| ~ m1_subset_1(U_26,u1_struct_0(U_27))
| ~ l3_lattices(U_27)
| ~ v10_lattices(U_27)
| v3_struct_0(U_27) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A,B] :
( m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A))
| ~ m1_subset_1(B,A)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k6_domain_1]) ).
fof(f_13_2,plain,
! [U_29,U_28] :
( m1_subset_1(k6_domain_1(U_29,U_28),k1_zfmisc_1(U_29))
| ~ m1_subset_1(U_28,U_29)
| v1_xboole_0(U_29) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( m1_subset_1(k6_domain_1(U_29,U_28),k1_zfmisc_1(U_29))
| ~ m1_subset_1(U_28,U_29)
| v1_xboole_0(U_29) ),
inference(clausify,[status(thm)],[f_13_2]) ).
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_30] :
( l1_struct_0(U_30)
| ~ l1_lattices(U_30) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( l1_struct_0(U_30)
| ~ l1_lattices(U_30) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
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_31] :
( l1_struct_0(U_31)
| ~ l2_lattices(U_31) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( l1_struct_0(U_31)
| ~ l2_lattices(U_31) ),
inference(clausify,[status(thm)],[f_16_2]) ).
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_32] :
( ( l2_lattices(U_32)
& l1_lattices(U_32) )
| ~ l3_lattices(U_32) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( l1_lattices(U_32)
| ~ l3_lattices(U_32) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( l2_lattices(U_32)
| ~ l3_lattices(U_32) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_18_2,plain,
$true,
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_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_19_2,plain,
! [U_34] :
( ! [U_33] :
( m1_subset_1(U_33,k1_zfmisc_1(u1_struct_0(U_34)))
| ~ m2_lattice4(U_33,U_34) )
| ~ l3_lattices(U_34)
| ~ v10_lattices(U_34)
| v3_struct_0(U_34) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( m1_subset_1(U_33,k1_zfmisc_1(u1_struct_0(U_34)))
| ~ m2_lattice4(U_33,U_34)
| ~ l3_lattices(U_34)
| ~ v10_lattices(U_34)
| v3_struct_0(U_34) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
? [A] : l1_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l1_lattices]) ).
fof(f_21_2,plain,
? [U_35] : l1_lattices(U_35),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
l1_lattices(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_35,sK6)],[f_21_2]) ).
cnf(f_21_4,plain,
l1_lattices(sK6),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_22_2,plain,
? [U_36] : l1_struct_0(U_36),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
l1_struct_0(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_36,sK7)],[f_22_2]) ).
cnf(f_22_4,plain,
l1_struct_0(sK7),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] : l2_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l2_lattices]) ).
fof(f_23_2,plain,
? [U_37] : l2_lattices(U_37),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
l2_lattices(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_37,sK8)],[f_23_2]) ).
cnf(f_23_4,plain,
l2_lattices(sK8),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] : l3_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l3_lattices]) ).
fof(f_24_2,plain,
? [U_38] : l3_lattices(U_38),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
l3_lattices(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_38,sK9)],[f_24_2]) ).
cnf(f_24_4,plain,
l3_lattices(sK9),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_25_2,plain,
! [U_40] :
? [U_39] : m1_subset_1(U_39,U_40),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_40] : m1_subset_1(sK10(U_40),U_40),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_39,sK10(U_40))],[f_25_2]) ).
cnf(f_25_4,plain,
m1_subset_1(sK10(U_40),U_40),
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_42] :
( ? [U_41] : m2_lattice4(U_41,U_42)
| ~ l3_lattices(U_42)
| ~ v10_lattices(U_42)
| v3_struct_0(U_42) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_42] :
( m2_lattice4(sK11(U_42),U_42)
| ~ l3_lattices(U_42)
| ~ v10_lattices(U_42)
| v3_struct_0(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_41,sK11(U_42))],[f_26_2]) ).
cnf(f_26_4,plain,
( m2_lattice4(sK11(U_42),U_42)
| ~ l3_lattices(U_42)
| ~ v10_lattices(U_42)
| v3_struct_0(U_42) ),
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_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_27_1]) ).
cnf(f_27_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_43))
| ~ l1_struct_0(U_43)
| v3_struct_0(U_43) ),
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_44] : ~ v1_xboole_0(k1_zfmisc_1(U_44)),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
~ v1_xboole_0(k1_zfmisc_1(U_44)),
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] : ~ v1_xboole_0(k1_tarski(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_30_2,plain,
! [U_45] : ~ v1_xboole_0(k1_tarski(U_45)),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
~ v1_xboole_0(k1_tarski(U_45)),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A] :
( v1_realset1(k1_tarski(A))
& v1_finset_1(k1_tarski(A))
& ~ v1_xboole_0(k1_tarski(A)) ),
inference(fof_nnf,[status(thm)],[fc3_realset1]) ).
fof(f_31_2,plain,
! [U_46] :
( v1_realset1(k1_tarski(U_46))
& v1_finset_1(k1_tarski(U_46))
& ~ v1_xboole_0(k1_tarski(U_46)) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_49] : v1_realset1(k1_tarski(U_49))
& ! [U_48] : v1_finset_1(k1_tarski(U_48))
& ! [U_47] : ~ v1_xboole_0(k1_tarski(U_47)) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
~ v1_xboole_0(k1_tarski(U_47)),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
v1_finset_1(k1_tarski(U_48)),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_6,plain,
v1_realset1(k1_tarski(U_49)),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_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_32_2,plain,
! [U_51] :
( ? [U_50] :
( ~ v1_xboole_0(U_50)
& m2_lattice4(U_50,U_51) )
| ~ l3_lattices(U_51)
| ~ v10_lattices(U_51)
| v3_struct_0(U_51) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_51] :
( ( ~ v1_xboole_0(sK12(U_51))
& m2_lattice4(sK12(U_51),U_51) )
| ~ l3_lattices(U_51)
| ~ v10_lattices(U_51)
| v3_struct_0(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_50,sK12(U_51))],[f_32_2]) ).
cnf(f_32_4,plain,
( m2_lattice4(sK12(U_51),U_51)
| ~ l3_lattices(U_51)
| ~ v10_lattices(U_51)
| v3_struct_0(U_51) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
( ~ v1_xboole_0(sK12(U_51))
| ~ l3_lattices(U_51)
| ~ v10_lattices(U_51)
| v3_struct_0(U_51) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] :
( v1_realset1(A)
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_realset1]) ).
fof(f_33_2,plain,
? [U_52] :
( v1_realset1(U_52)
& ~ v1_xboole_0(U_52) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( v1_realset1(sK13)
& ~ v1_xboole_0(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_52,sK13)],[f_33_2]) ).
cnf(f_33_4,plain,
~ v1_xboole_0(sK13),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
v1_realset1(sK13),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_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_34_2,plain,
! [U_54] :
( ? [U_53] :
( ~ v1_xboole_0(U_53)
& m1_subset_1(U_53,k1_zfmisc_1(U_54)) )
| v1_xboole_0(U_54) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_54] :
( ( ~ v1_xboole_0(sK14(U_54))
& m1_subset_1(sK14(U_54),k1_zfmisc_1(U_54)) )
| v1_xboole_0(U_54) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_53,sK14(U_54))],[f_34_2]) ).
cnf(f_34_4,plain,
( m1_subset_1(sK14(U_54),k1_zfmisc_1(U_54))
| v1_xboole_0(U_54) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( ~ v1_xboole_0(sK14(U_54))
| v1_xboole_0(U_54) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_35_2,plain,
? [U_55] : v1_xboole_0(U_55),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
v1_xboole_0(sK15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_55,sK15)],[f_35_2]) ).
cnf(f_35_4,plain,
v1_xboole_0(sK15),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
? [A] :
( ~ v1_realset1(A)
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc2_realset1]) ).
fof(f_36_2,plain,
? [U_56] :
( ~ v1_realset1(U_56)
& ~ v1_xboole_0(U_56) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ~ v1_realset1(sK16)
& ~ v1_xboole_0(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_56,sK16)],[f_36_2]) ).
cnf(f_36_4,plain,
~ v1_xboole_0(sK16),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
~ v1_realset1(sK16),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_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_37_2,plain,
! [U_58] :
? [U_57] :
( v1_xboole_0(U_57)
& m1_subset_1(U_57,k1_zfmisc_1(U_58)) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_58] :
( v1_xboole_0(sK17(U_58))
& m1_subset_1(sK17(U_58),k1_zfmisc_1(U_58)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_57,sK17(U_58))],[f_37_2]) ).
cnf(f_37_4,plain,
m1_subset_1(sK17(U_58),k1_zfmisc_1(U_58)),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
v1_xboole_0(sK17(U_58)),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_38_2,plain,
? [U_59] : ~ v1_xboole_0(U_59),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
~ v1_xboole_0(sK18),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_59,sK18)],[f_38_2]) ).
cnf(f_38_4,plain,
~ v1_xboole_0(sK18),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_39_2,plain,
? [U_60] :
( ~ v3_struct_0(U_60)
& l1_struct_0(U_60) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ~ v3_struct_0(sK19)
& l1_struct_0(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_60,sK19)],[f_39_2]) ).
cnf(f_39_4,plain,
l1_struct_0(sK19),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
~ v3_struct_0(sK19),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_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_40_2,plain,
! [U_62] :
( ? [U_61] :
( ~ v1_xboole_0(U_61)
& m1_subset_1(U_61,k1_zfmisc_1(u1_struct_0(U_62))) )
| ~ l1_struct_0(U_62)
| v3_struct_0(U_62) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_62] :
( ( ~ v1_xboole_0(sK20(U_62))
& m1_subset_1(sK20(U_62),k1_zfmisc_1(u1_struct_0(U_62))) )
| ~ l1_struct_0(U_62)
| v3_struct_0(U_62) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_61,sK20(U_62))],[f_40_2]) ).
cnf(f_40_4,plain,
( m1_subset_1(sK20(U_62),k1_zfmisc_1(u1_struct_0(U_62)))
| ~ l1_struct_0(U_62)
| v3_struct_0(U_62) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
( ~ v1_xboole_0(sK20(U_62))
| ~ l1_struct_0(U_62)
| v3_struct_0(U_62) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A,B] :
( k6_domain_1(A,B) = k1_tarski(B)
| ~ m1_subset_1(B,A)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k6_domain_1]) ).
fof(f_41_2,plain,
! [U_64,U_63] :
( k6_domain_1(U_64,U_63) = k1_tarski(U_63)
| ~ m1_subset_1(U_63,U_64)
| v1_xboole_0(U_64) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( k6_domain_1(U_64,U_63) = k1_tarski(U_63)
| ~ m1_subset_1(U_63,U_64)
| v1_xboole_0(U_64) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_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_42_2,plain,
! [U_67,U_66,U_65] :
( ( ( r1_filter_2(U_67,U_66,U_65)
| U_66 != U_65 )
& ( U_66 = U_65
| ~ r1_filter_2(U_67,U_66,U_65) ) )
| ~ m1_subset_1(U_65,k1_zfmisc_1(U_67))
| ~ m1_subset_1(U_66,k1_zfmisc_1(U_67))
| v1_xboole_0(U_67) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( U_66 = U_65
| ~ r1_filter_2(U_67,U_66,U_65)
| ~ m1_subset_1(U_65,k1_zfmisc_1(U_67))
| ~ m1_subset_1(U_66,k1_zfmisc_1(U_67))
| v1_xboole_0(U_67) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( r1_filter_2(U_67,U_66,U_65)
| U_66 != U_65
| ~ m1_subset_1(U_65,k1_zfmisc_1(U_67))
| ~ m1_subset_1(U_66,k1_zfmisc_1(U_67))
| v1_xboole_0(U_67) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A,B,C] :
( ( ( r3_lattices(A,B,C)
| ~ r1_lattices(A,B,C) )
& ( r1_lattices(A,B,C)
| ~ r3_lattices(A,B,C) ) )
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v9_lattices(A)
| ~ v8_lattices(A)
| ~ v6_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r3_lattices]) ).
fof(f_43_2,plain,
! [U_70,U_69,U_68] :
( ( ( r3_lattices(U_70,U_69,U_68)
| ~ r1_lattices(U_70,U_69,U_68) )
& ( r1_lattices(U_70,U_69,U_68)
| ~ r3_lattices(U_70,U_69,U_68) ) )
| ~ m1_subset_1(U_68,u1_struct_0(U_70))
| ~ m1_subset_1(U_69,u1_struct_0(U_70))
| ~ l3_lattices(U_70)
| ~ v9_lattices(U_70)
| ~ v8_lattices(U_70)
| ~ v6_lattices(U_70)
| v3_struct_0(U_70) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( r1_lattices(U_70,U_69,U_68)
| ~ r3_lattices(U_70,U_69,U_68)
| ~ m1_subset_1(U_68,u1_struct_0(U_70))
| ~ m1_subset_1(U_69,u1_struct_0(U_70))
| ~ l3_lattices(U_70)
| ~ v9_lattices(U_70)
| ~ v8_lattices(U_70)
| ~ v6_lattices(U_70)
| v3_struct_0(U_70) ),
inference(clausify,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( r3_lattices(U_70,U_69,U_68)
| ~ r1_lattices(U_70,U_69,U_68)
| ~ m1_subset_1(U_68,u1_struct_0(U_70))
| ~ m1_subset_1(U_69,u1_struct_0(U_70))
| ~ l3_lattices(U_70)
| ~ v9_lattices(U_70)
| ~ v8_lattices(U_70)
| ~ v6_lattices(U_70)
| v3_struct_0(U_70) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_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_44_2,plain,
! [U_73,U_72,U_71] :
( r1_filter_2(U_73,U_72,U_72)
| ~ m1_subset_1(U_71,k1_zfmisc_1(U_73))
| ~ m1_subset_1(U_72,k1_zfmisc_1(U_73))
| v1_xboole_0(U_73) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_73,U_72] :
( ! [U_71] : ~ m1_subset_1(U_71,k1_zfmisc_1(U_73))
| ~ m1_subset_1(U_72,k1_zfmisc_1(U_73))
| v1_xboole_0(U_73)
| r1_filter_2(U_73,U_72,U_72) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
cnf(f_44_4,plain,
( ~ m1_subset_1(U_71,k1_zfmisc_1(U_73))
| ~ m1_subset_1(U_72,k1_zfmisc_1(U_73))
| v1_xboole_0(U_73)
| r1_filter_2(U_73,U_72,U_72) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_45_2,plain,
! [U_75,U_74] : r1_tarski(U_75,U_75),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_75] : r1_tarski(U_75,U_75),
inference(miniscope,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
r1_tarski(U_75,U_75),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [A,B,C] :
( r3_lattices(A,B,B)
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v9_lattices(A)
| ~ v8_lattices(A)
| ~ v6_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r3_lattices]) ).
fof(f_46_2,plain,
! [U_78,U_77,U_76] :
( r3_lattices(U_78,U_77,U_77)
| ~ m1_subset_1(U_76,u1_struct_0(U_78))
| ~ m1_subset_1(U_77,u1_struct_0(U_78))
| ~ l3_lattices(U_78)
| ~ v9_lattices(U_78)
| ~ v8_lattices(U_78)
| ~ v6_lattices(U_78)
| v3_struct_0(U_78) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_78,U_77] :
( ! [U_76] : ~ m1_subset_1(U_76,u1_struct_0(U_78))
| ~ m1_subset_1(U_77,u1_struct_0(U_78))
| ~ l3_lattices(U_78)
| ~ v9_lattices(U_78)
| ~ v8_lattices(U_78)
| ~ v6_lattices(U_78)
| v3_struct_0(U_78)
| r3_lattices(U_78,U_77,U_77) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( ~ m1_subset_1(U_76,u1_struct_0(U_78))
| ~ m1_subset_1(U_77,u1_struct_0(U_78))
| ~ l3_lattices(U_78)
| ~ v9_lattices(U_78)
| ~ v8_lattices(U_78)
| ~ v6_lattices(U_78)
| v3_struct_0(U_78)
| r3_lattices(U_78,U_77,U_77) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_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_47_2,plain,
! [U_81,U_80,U_79] :
( r1_filter_2(U_81,U_79,U_80)
| ~ r1_filter_2(U_81,U_80,U_79)
| ~ m1_subset_1(U_79,k1_zfmisc_1(U_81))
| ~ m1_subset_1(U_80,k1_zfmisc_1(U_81))
| v1_xboole_0(U_81) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( r1_filter_2(U_81,U_79,U_80)
| ~ r1_filter_2(U_81,U_80,U_79)
| ~ m1_subset_1(U_79,k1_zfmisc_1(U_81))
| ~ m1_subset_1(U_80,k1_zfmisc_1(U_81))
| v1_xboole_0(U_81) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_48_2,plain,
! [U_83,U_82] :
( m1_subset_1(U_83,U_82)
| ~ r2_hidden(U_83,U_82) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( m1_subset_1(U_83,U_82)
| ~ r2_hidden(U_83,U_82) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( B = C
| ~ r1_lattices(A,C,B)
| ~ r1_lattices(A,B,C)
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l2_lattices(A)
| ~ v4_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t26_lattices]) ).
fof(f_49_2,plain,
! [U_86] :
( ! [U_85] :
( ! [U_84] :
( U_85 = U_84
| ~ r1_lattices(U_86,U_84,U_85)
| ~ r1_lattices(U_86,U_85,U_84)
| ~ m1_subset_1(U_84,u1_struct_0(U_86)) )
| ~ m1_subset_1(U_85,u1_struct_0(U_86)) )
| ~ l2_lattices(U_86)
| ~ v4_lattices(U_86)
| v3_struct_0(U_86) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( U_85 = U_84
| ~ r1_lattices(U_86,U_84,U_85)
| ~ r1_lattices(U_86,U_85,U_84)
| ~ m1_subset_1(U_84,u1_struct_0(U_86))
| ~ m1_subset_1(U_85,u1_struct_0(U_86))
| ~ l2_lattices(U_86)
| ~ v4_lattices(U_86)
| v3_struct_0(U_86) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_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_50_2,plain,
! [U_88,U_87] :
( r2_hidden(U_88,U_87)
| v1_xboole_0(U_87)
| ~ m1_subset_1(U_88,U_87) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( r2_hidden(U_88,U_87)
| v1_xboole_0(U_87)
| ~ m1_subset_1(U_88,U_87) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_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_51_2,plain,
! [U_90,U_89] :
( ( m1_subset_1(U_90,k1_zfmisc_1(U_89))
| ~ r1_tarski(U_90,U_89) )
& ( r1_tarski(U_90,U_89)
| ~ m1_subset_1(U_90,k1_zfmisc_1(U_89)) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_94,U_92] :
( m1_subset_1(U_94,k1_zfmisc_1(U_92))
| ~ r1_tarski(U_94,U_92) )
& ! [U_93,U_91] :
( r1_tarski(U_93,U_91)
| ~ m1_subset_1(U_93,k1_zfmisc_1(U_91)) ) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
( r1_tarski(U_93,U_91)
| ~ m1_subset_1(U_93,k1_zfmisc_1(U_91)) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
( m1_subset_1(U_94,k1_zfmisc_1(U_92))
| ~ r1_tarski(U_94,U_92) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_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_52_2,plain,
! [U_97,U_96,U_95] :
( m1_subset_1(U_97,U_95)
| ~ m1_subset_1(U_96,k1_zfmisc_1(U_95))
| ~ r2_hidden(U_97,U_96) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( m1_subset_1(U_97,U_95)
| ~ m1_subset_1(U_96,k1_zfmisc_1(U_95))
| ~ r2_hidden(U_97,U_96) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_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_53_2,plain,
! [U_100,U_99,U_98] :
( ~ v1_xboole_0(U_98)
| ~ m1_subset_1(U_99,k1_zfmisc_1(U_98))
| ~ r2_hidden(U_100,U_99) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_100,U_99] :
( ! [U_98] :
( ~ v1_xboole_0(U_98)
| ~ m1_subset_1(U_99,k1_zfmisc_1(U_98)) )
| ~ r2_hidden(U_100,U_99) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
cnf(f_53_4,plain,
( ~ v1_xboole_0(U_98)
| ~ m1_subset_1(U_99,k1_zfmisc_1(U_98))
| ~ r2_hidden(U_100,U_99) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ( ( r2_hidden(D,k22_filter_2(A,B,C))
| ~ r3_lattices(A,D,C)
| ~ r3_lattices(A,B,D) )
& ( ( r3_lattices(A,D,C)
& r3_lattices(A,B,D) )
| ~ r2_hidden(D,k22_filter_2(A,B,C)) ) )
| ~ r3_lattices(A,B,C)
| ~ m1_subset_1(D,u1_struct_0(A)) )
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t63_filter_2]) ).
fof(f_54_2,plain,
! [U_104] :
( ! [U_103] :
( ! [U_102] :
( ! [U_101] :
( ( ( r2_hidden(U_101,k22_filter_2(U_104,U_103,U_102))
| ~ r3_lattices(U_104,U_101,U_102)
| ~ r3_lattices(U_104,U_103,U_101) )
& ( ( r3_lattices(U_104,U_101,U_102)
& r3_lattices(U_104,U_103,U_101) )
| ~ r2_hidden(U_101,k22_filter_2(U_104,U_103,U_102)) ) )
| ~ r3_lattices(U_104,U_103,U_102)
| ~ m1_subset_1(U_101,u1_struct_0(U_104)) )
| ~ m1_subset_1(U_102,u1_struct_0(U_104)) )
| ~ m1_subset_1(U_103,u1_struct_0(U_104)) )
| ~ l3_lattices(U_104)
| ~ v10_lattices(U_104)
| v3_struct_0(U_104) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( r3_lattices(U_104,U_103,U_101)
| ~ r2_hidden(U_101,k22_filter_2(U_104,U_103,U_102))
| ~ r3_lattices(U_104,U_103,U_102)
| ~ m1_subset_1(U_101,u1_struct_0(U_104))
| ~ m1_subset_1(U_102,u1_struct_0(U_104))
| ~ m1_subset_1(U_103,u1_struct_0(U_104))
| ~ l3_lattices(U_104)
| ~ v10_lattices(U_104)
| v3_struct_0(U_104) ),
inference(clausify,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
( r3_lattices(U_104,U_101,U_102)
| ~ r2_hidden(U_101,k22_filter_2(U_104,U_103,U_102))
| ~ r3_lattices(U_104,U_103,U_102)
| ~ m1_subset_1(U_101,u1_struct_0(U_104))
| ~ m1_subset_1(U_102,u1_struct_0(U_104))
| ~ m1_subset_1(U_103,u1_struct_0(U_104))
| ~ l3_lattices(U_104)
| ~ v10_lattices(U_104)
| v3_struct_0(U_104) ),
inference(clausify,[status(thm)],[f_54_2]) ).
cnf(f_54_5,plain,
( r2_hidden(U_101,k22_filter_2(U_104,U_103,U_102))
| ~ r3_lattices(U_104,U_101,U_102)
| ~ r3_lattices(U_104,U_103,U_101)
| ~ r3_lattices(U_104,U_103,U_102)
| ~ m1_subset_1(U_101,u1_struct_0(U_104))
| ~ m1_subset_1(U_102,u1_struct_0(U_104))
| ~ m1_subset_1(U_103,u1_struct_0(U_104))
| ~ l3_lattices(U_104)
| ~ v10_lattices(U_104)
| v3_struct_0(U_104) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_55_2,plain,
! [U_105] :
( U_105 = k1_xboole_0
| ~ v1_xboole_0(U_105) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( U_105 = k1_xboole_0
| ~ v1_xboole_0(U_105) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_56_2,plain,
! [U_107,U_106] :
( ~ v1_xboole_0(U_106)
| ~ r2_hidden(U_107,U_106) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( ~ v1_xboole_0(U_106)
| ~ r2_hidden(U_107,U_106) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_57_2,plain,
! [U_109,U_108] :
( ~ v1_xboole_0(U_108)
| U_109 = U_108
| ~ v1_xboole_0(U_109) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_109] :
( ! [U_108] :
( ~ v1_xboole_0(U_108)
| U_109 = U_108 )
| ~ v1_xboole_0(U_109) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
cnf(f_57_4,plain,
( ~ v1_xboole_0(U_108)
| U_109 = U_108
| ~ v1_xboole_0(U_109) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_7_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_8]) ).
cnf(f_7_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_9]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_15_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_2]) ).
cnf(f_18_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( u1_struct_0(Eq_x_0) = u1_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k22_filter_2(Eq_x_0,Eq_x_1,Eq_x_2) = k22_filter_2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( k6_domain_1(Eq_x_0,Eq_x_1) = k6_domain_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_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,
( k1_tarski(Eq_x_0) = k1_tarski(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(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) = sK12(Eq_y_0)
| 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,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK20(Eq_x_0) = sK20(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,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_19,axiom,
( v10_lattices(Eq_y_0)
| ~ v10_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( l3_lattices(Eq_y_0)
| ~ l3_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,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_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,
( 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_24,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_25,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_26,axiom,
( v4_lattices(Eq_y_0)
| ~ v4_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( v5_lattices(Eq_y_0)
| ~ v5_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( v6_lattices(Eq_y_0)
| ~ v6_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( v7_lattices(Eq_y_0)
| ~ v7_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( v8_lattices(Eq_y_0)
| ~ v8_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( v9_lattices(Eq_y_0)
| ~ v9_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( v1_realset1(Eq_y_0)
| ~ v1_realset1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,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_34,axiom,
( l1_lattices(Eq_y_0)
| ~ l1_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,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_36,axiom,
( l2_lattices(Eq_y_0)
| ~ l2_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( v1_finset_1(Eq_y_0)
| ~ v1_finset_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( r3_lattices(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r3_lattices(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( r1_lattices(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r1_lattices(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( r1_tarski(Eq_y_0,Eq_y_1)
| ~ r1_tarski(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT328+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 13:24:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 256.46/256.71 % SZS status Theorem for theBenchmark
% 256.46/256.71 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------