%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT289+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 : Sun Sep 27 07:50:02 AM UTC 2026
% Result : Theorem 1.79s 0.65s
% Output : CNFRefutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 75 ( 18 unt; 0 def)
% Number of atoms : 310 ( 20 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 387 ( 152 ~; 167 |; 51 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 68 ( 0 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_l2_lattices,axiom,
! [A] :
( l2_lattices(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l2_lattices) ).
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(redefinition_k8_funct_2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(D,A)
& m1_relset_1(C,A,B)
& v1_funct_2(C,A,B)
& v1_funct_1(C)
& ~ v1_xboole_0(A) )
=> k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ),
file('theBenchmark.p',redefinition_k8_funct_2) ).
fof(redefinition_k9_lopclset,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k9_lopclset(A) = k8_lopclset(A) ),
file('theBenchmark.p',redefinition_k9_lopclset) ).
fof(dt_k9_lopclset,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( m2_relset_1(k9_lopclset(A),u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)))
& v1_funct_2(k9_lopclset(A),u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)))
& v1_funct_1(k9_lopclset(A)) ) ),
file('theBenchmark.p',dt_k9_lopclset) ).
fof(dt_l3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( l2_lattices(A)
& l1_lattices(A) ) ),
file('theBenchmark.p',dt_l3_lattices) ).
fof(t21_lopclset,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_filter_0(C,A)
=> ( r2_hidden(C,k1_funct_1(k8_lopclset(A),B))
<=> ( r2_hidden(B,C)
& v1_filter_0(C,A) ) ) ) ) ),
file('theBenchmark.p',t21_lopclset) ).
fof(t27_lopclset,conjecture,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_filter_0(C,A)
=> ~ ( r2_hidden(B,C)
& ~ r2_hidden(C,k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),B))
& v1_filter_0(C,A) ) ) ) ),
file('theBenchmark.p',t27_lopclset) ).
fof(t27_lopclset_neg,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_filter_0(C,A)
=> ~ ( r2_hidden(B,C)
& ~ r2_hidden(C,k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),B))
& v1_filter_0(C,A) ) ) ) ),
inference(assume_negation,[status(cth)],[t27_lopclset]) ).
cnf(c_102,plain,
( k8_lopclset(A) = k9_lopclset(A)
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[redefinition_k9_lopclset]) ).
cnf(c_106,plain,
( v1_funct_1(k9_lopclset(A))
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k9_lopclset]) ).
cnf(c_107,plain,
( v1_funct_2(k9_lopclset(A),u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)))
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k9_lopclset]) ).
cnf(c_108,plain,
( m2_relset_1(k9_lopclset(A),u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)))
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k9_lopclset]) ).
cnf(c_121,plain,
( ~ r2_hidden(B,C)
| ~ v1_filter_0(C,A)
| r2_hidden(C,k1_funct_1(k8_lopclset(A),B))
| ~ m1_filter_0(C,A)
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t21_lopclset]) ).
fof(nnf_87,plain,
? [A] :
( ? [B] :
( ? [C] :
( r2_hidden(B,C)
& ~ r2_hidden(C,k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),B))
& v1_filter_0(C,A)
& m1_filter_0(C,A) )
& m1_subset_1(B,u1_struct_0(A)) )
& l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t27_lopclset_neg]) ).
fof(sk_t27_lopclset_neg,plain,
( r2_hidden(sK1,sK2)
& ~ r2_hidden(sK2,k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),sK1))
& v1_filter_0(sK2,sK0)
& m1_filter_0(sK2,sK0)
& m1_subset_1(sK1,u1_struct_0(sK0))
& l3_lattices(sK0)
& ~ v3_realset2(sK0)
& v17_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_87]) ).
cnf(c_122,negated_conjecture,
v10_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t27_lopclset_neg]) ).
cnf(c_125,plain,
( m1_relset_1(A,B,C)
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_132,plain,
( k1_funct_1(B,D) = k8_funct_2(A,C,B,D)
| ~ m1_subset_1(D,A)
| ~ m1_relset_1(B,A,C)
| ~ v1_funct_2(B,A,C)
| ~ v1_funct_1(B)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[redefinition_k8_funct_2]) ).
cnf(c_177,plain,
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc1_struct_0]) ).
cnf(c_178,plain,
( l1_struct_0(A)
| ~ l2_lattices(A) ),
inference(clausify,[status(thm)],[dt_l2_lattices]) ).
cnf(c_181,plain,
( ~ v1_xboole_0(u1_struct_0(A))
| v3_struct_0(A)
| ~ l2_lattices(A) ),
inference(resolve,[status(thm)],[c_178,c_177]) ).
cnf(c_184,plain,
( l2_lattices(A)
| ~ l3_lattices(A) ),
inference(clausify,[status(thm)],[dt_l3_lattices]) ).
cnf(c_187,plain,
( ~ m2_relset_1(B,A,C)
| k1_funct_1(B,D) = k8_funct_2(A,C,B,D)
| ~ m1_subset_1(D,A)
| ~ v1_funct_2(B,A,C)
| ~ v1_funct_1(B)
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_132,c_125]) ).
cnf(c_194,negated_conjecture,
( m2_relset_1(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_122,c_108]) ).
cnf(c_204,plain,
( ~ v1_xboole_0(u1_struct_0(A))
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(resolve,[status(thm)],[c_184,c_181]) ).
cnf(c_264,negated_conjecture,
( k8_lopclset(sK0) = k9_lopclset(sK0)
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_122,c_102]) ).
cnf(c_267,negated_conjecture,
( v1_funct_1(k9_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_122,c_106]) ).
cnf(c_268,negated_conjecture,
( v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_122,c_107]) ).
cnf(c_280,negated_conjecture,
( ~ r2_hidden(A,B)
| ~ v1_filter_0(B,sK0)
| r2_hidden(B,k1_funct_1(k8_lopclset(sK0),A))
| ~ m1_filter_0(B,sK0)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_122,c_121]) ).
cnf(c_303,negated_conjecture,
r2_hidden(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t27_lopclset_neg]) ).
cnf(c_304,negated_conjecture,
~ r2_hidden(sK2,k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),sK1)),
inference(split_conjunct,[status(thm)],[sk_t27_lopclset_neg]) ).
cnf(c_305,negated_conjecture,
v1_filter_0(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t27_lopclset_neg]) ).
cnf(c_306,negated_conjecture,
m1_filter_0(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t27_lopclset_neg]) ).
cnf(c_307,negated_conjecture,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(split_conjunct,[status(thm)],[sk_t27_lopclset_neg]) ).
cnf(c_308,negated_conjecture,
l3_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t27_lopclset_neg]) ).
cnf(c_309,negated_conjecture,
~ v3_realset2(sK0),
inference(split_conjunct,[status(thm)],[sk_t27_lopclset_neg]) ).
cnf(c_310,negated_conjecture,
v17_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t27_lopclset_neg]) ).
cnf(c_311,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t27_lopclset_neg]) ).
cnf(c_436,negated_conjecture,
( k1_funct_1(k9_lopclset(sK0),A) = k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),A)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| ~ v1_funct_1(k9_lopclset(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_194,c_187]) ).
cnf(c_1107,negated_conjecture,
( k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),A) = k1_funct_1(k9_lopclset(sK0),A)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| ~ v1_funct_1(k9_lopclset(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(copy,[status(thm)],[c_436]) ).
cnf(c_1108,negated_conjecture,
( k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),A) = k1_funct_1(k9_lopclset(sK0),A)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| ~ v1_funct_1(k9_lopclset(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_311,c_1107]) ).
cnf(c_1109,negated_conjecture,
( k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),A) = k1_funct_1(k9_lopclset(sK0),A)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| ~ v1_funct_1(k9_lopclset(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0) ),
inference(resolve,[status(thm)],[c_310,c_1108]) ).
cnf(c_1110,negated_conjecture,
( k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),A) = k1_funct_1(k9_lopclset(sK0),A)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| ~ v1_funct_1(k9_lopclset(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_309,c_1109]) ).
cnf(c_437,negated_conjecture,
( k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),A) = k1_funct_1(k9_lopclset(sK0),A)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| ~ v1_funct_1(k9_lopclset(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_308,c_1110]) ).
cnf(c_1111,negated_conjecture,
( ~ r2_hidden(A,B)
| ~ v1_filter_0(B,sK0)
| r2_hidden(B,k1_funct_1(k8_lopclset(sK0),A))
| ~ m1_filter_0(B,sK0)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_311,c_280]) ).
cnf(c_1112,negated_conjecture,
( ~ r2_hidden(A,B)
| ~ v1_filter_0(B,sK0)
| r2_hidden(B,k1_funct_1(k8_lopclset(sK0),A))
| ~ m1_filter_0(B,sK0)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0) ),
inference(resolve,[status(thm)],[c_310,c_1111]) ).
cnf(c_1113,negated_conjecture,
( ~ r2_hidden(A,B)
| ~ v1_filter_0(B,sK0)
| r2_hidden(B,k1_funct_1(k8_lopclset(sK0),A))
| ~ m1_filter_0(B,sK0)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_309,c_1112]) ).
cnf(c_461,negated_conjecture,
( ~ r2_hidden(A,B)
| ~ v1_filter_0(B,sK0)
| r2_hidden(B,k1_funct_1(k8_lopclset(sK0),A))
| ~ m1_filter_0(B,sK0)
| ~ m1_subset_1(A,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_308,c_1113]) ).
cnf(c_1114,negated_conjecture,
( v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_311,c_268]) ).
cnf(c_1115,negated_conjecture,
( v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| ~ l3_lattices(sK0)
| v3_realset2(sK0) ),
inference(resolve,[status(thm)],[c_310,c_1114]) ).
cnf(c_1116,negated_conjecture,
( v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_309,c_1115]) ).
cnf(c_473,negated_conjecture,
v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0))),
inference(resolve,[status(thm)],[c_308,c_1116]) ).
cnf(c_1117,negated_conjecture,
( v1_funct_1(k9_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_311,c_267]) ).
cnf(c_1118,negated_conjecture,
( v1_funct_1(k9_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0) ),
inference(resolve,[status(thm)],[c_310,c_1117]) ).
cnf(c_1119,negated_conjecture,
( v1_funct_1(k9_lopclset(sK0))
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_309,c_1118]) ).
cnf(c_474,negated_conjecture,
v1_funct_1(k9_lopclset(sK0)),
inference(resolve,[status(thm)],[c_308,c_1119]) ).
cnf(c_1120,negated_conjecture,
( k8_lopclset(sK0) = k9_lopclset(sK0)
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_311,c_264]) ).
cnf(c_1121,negated_conjecture,
( k8_lopclset(sK0) = k9_lopclset(sK0)
| ~ l3_lattices(sK0)
| v3_realset2(sK0) ),
inference(resolve,[status(thm)],[c_310,c_1120]) ).
cnf(c_1122,negated_conjecture,
( k8_lopclset(sK0) = k9_lopclset(sK0)
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_309,c_1121]) ).
cnf(c_477,negated_conjecture,
k8_lopclset(sK0) = k9_lopclset(sK0),
inference(resolve,[status(thm)],[c_308,c_1122]) ).
cnf(c_1123,negated_conjecture,
( k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),A) = k1_funct_1(k9_lopclset(sK0),A)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ v1_funct_2(k9_lopclset(sK0),u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_474,c_437]) ).
cnf(c_503,negated_conjecture,
( k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),A) = k1_funct_1(k9_lopclset(sK0),A)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_473,c_1123]) ).
cnf(c_508,negated_conjecture,
( ~ r2_hidden(A,B)
| ~ v1_filter_0(B,sK0)
| r2_hidden(B,k1_funct_1(k9_lopclset(sK0),A))
| ~ m1_filter_0(B,sK0)
| ~ m1_subset_1(A,u1_struct_0(sK0)) ),
inference(paramod,[status(thm)],[c_477,c_461]) ).
cnf(c_1124,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_308,c_204]) ).
cnf(c_521,negated_conjecture,
~ v1_xboole_0(u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_311,c_1124]) ).
cnf(c_527,negated_conjecture,
( k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),A) = k1_funct_1(k9_lopclset(sK0),A)
| ~ m1_subset_1(A,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_521,c_503]) ).
cnf(c_1125,negated_conjecture,
( ~ v1_filter_0(sK2,sK0)
| r2_hidden(sK2,k1_funct_1(k9_lopclset(sK0),sK1))
| ~ m1_filter_0(sK2,sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_508,c_303]) ).
cnf(c_1126,negated_conjecture,
( ~ v1_filter_0(sK2,sK0)
| r2_hidden(sK2,k1_funct_1(k9_lopclset(sK0),sK1))
| ~ m1_filter_0(sK2,sK0) ),
inference(resolve,[status(thm)],[c_307,c_1125]) ).
cnf(c_1127,negated_conjecture,
( ~ v1_filter_0(sK2,sK0)
| r2_hidden(sK2,k1_funct_1(k9_lopclset(sK0),sK1)) ),
inference(resolve,[status(thm)],[c_306,c_1126]) ).
cnf(c_1049,negated_conjecture,
r2_hidden(sK2,k1_funct_1(k9_lopclset(sK0),sK1)),
inference(resolve,[status(thm)],[c_305,c_1127]) ).
cnf(c_1105,plain,
k8_funct_2(u1_struct_0(sK0),k1_zfmisc_1(k7_lopclset(sK0)),k9_lopclset(sK0),sK1) = k1_funct_1(k9_lopclset(sK0),sK1),
inference(resolve,[status(thm)],[c_527,c_307]) ).
cnf(c_1128,negated_conjecture,
~ r2_hidden(sK2,k1_funct_1(k9_lopclset(sK0),sK1)),
inference(paramod,[status(thm)],[c_1105,c_304]) ).
cnf(c_1106,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1049,c_1128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT289+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Fri Sep 25 20:28:38 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1130161 was started by sandbox on n013,
% 0.09/0.38 % Fri Sep 25 20:28:38 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.40
% 0.09/0.40 % From the command line: assign(max_seconds, 300).
% 1.79/0.65
% 1.79/0.65 % SZS status Theorem for theBenchmark
% 1.79/0.65
% 1.79/0.65 % Proof 1 at 0.21 (+ 0.03) seconds.
% 1.79/0.65 % Length of proof is 50.
% 1.79/0.65 % Level of proof is 8.
% 1.79/0.65 % Maximum clause weight is 52.000.
% 1.79/0.65 % Given clauses 200.
% 1.79/0.65
% 1.79/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------