%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT288+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 01:58:44 PM UTC 2026
% Result : Theorem 3.68s 1.36s
% Output : CNFRefutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 87 ( 21 unt; 0 def)
% Number of atoms : 454 ( 43 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 591 ( 224 ~; 270 |; 81 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 144 ( 0 sgn 128 !; 16 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> r1_tarski(a_2_0_lopclset(X0,X1),k7_lopclset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lopclset) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> r1_tarski(a_2_0_lopclset(X0,X1),k7_lopclset(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f30,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f31,axiom,
! [X0] :
( ( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> k7_lopclset(X0) = a_1_1_lopclset(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_lopclset) ).
fof(f52,axiom,
! [X0,X1] :
( ( l3_lattices(X1)
& ~ v3_realset2(X1)
& v17_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( r2_hidden(X0,a_1_1_lopclset(X1))
<=> ? [X2] :
( v1_filter_0(X2,X1)
& X0 = X2
& m1_filter_0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_1_lopclset) ).
fof(f53,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& ~ v3_realset2(X1)
& v17_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( r2_hidden(X0,a_2_0_lopclset(X1,X2))
<=> ? [X3] :
( r2_hidden(X2,X3)
& v1_filter_0(X3,X1)
& X0 = X3
& m1_filter_0(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lopclset) ).
fof(f72,plain,
? [X0] :
( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& ~ r1_tarski(a_2_0_lopclset(X0,X1),k7_lopclset(X0)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f73,plain,
? [X0] :
( l3_lattices(X0)
& ~ v3_realset2(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& ~ r1_tarski(a_2_0_lopclset(X0,X1),k7_lopclset(X0)) ) ),
inference(flattening,[],[f72]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( r2_hidden(X0,a_2_0_lopclset(X1,X2))
<=> ? [X3] :
( r2_hidden(X2,X3)
& v1_filter_0(X3,X1)
& X0 = X3
& m1_filter_0(X3,X1) ) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( r2_hidden(X0,a_2_0_lopclset(X1,X2))
<=> ? [X3] :
( r2_hidden(X2,X3)
& v1_filter_0(X3,X1)
& X0 = X3
& m1_filter_0(X3,X1) ) ) ),
inference(flattening,[],[f82]) ).
fof(f86,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f101,plain,
! [X0,X1] :
( ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( r2_hidden(X0,a_1_1_lopclset(X1))
<=> ? [X2] :
( v1_filter_0(X2,X1)
& X0 = X2
& m1_filter_0(X2,X1) ) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f102,plain,
! [X0,X1] :
( ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( r2_hidden(X0,a_1_1_lopclset(X1))
<=> ? [X2] :
( v1_filter_0(X2,X1)
& X0 = X2
& m1_filter_0(X2,X1) ) ) ),
inference(flattening,[],[f101]) ).
fof(f107,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k7_lopclset(X0) = a_1_1_lopclset(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f108,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k7_lopclset(X0) = a_1_1_lopclset(X0) ),
inference(flattening,[],[f107]) ).
fof(f113,plain,
( l3_lattices(sK0)
& ~ v3_realset2(sK0)
& v17_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0)
& m1_subset_1(sK1,u1_struct_0(sK0))
& ~ r1_tarski(a_2_0_lopclset(sK0,sK1),k7_lopclset(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f73]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_lopclset(X1,X2))
| ? [X3] :
( r2_hidden(X2,X3)
& v1_filter_0(X3,X1)
& X0 = X3
& m1_filter_0(X3,X1) ) )
& ( ! [X3] :
( ~ r2_hidden(X2,X3)
| ~ v1_filter_0(X3,X1)
| X0 != X3
| ~ m1_filter_0(X3,X1) )
| r2_hidden(X0,a_2_0_lopclset(X1,X2)) ) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_lopclset(X1,X2))
| ? [X4] :
( r2_hidden(X2,X4)
& v1_filter_0(X4,X1)
& X0 = X4
& m1_filter_0(X4,X1) ) )
& ( ! [X3] :
( ~ r2_hidden(X2,X3)
| ~ v1_filter_0(X3,X1)
| X0 != X3
| ~ m1_filter_0(X3,X1) )
| r2_hidden(X0,a_2_0_lopclset(X1,X2)) ) ) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_lopclset(X1,X2))
| ( r2_hidden(X2,sK3(X0,X1,X2))
& v1_filter_0(sK3(X0,X1,X2),X1)
& sK3(X0,X1,X2) = X0
& m1_filter_0(sK3(X0,X1,X2),X1) ) )
& ( ! [X3] :
( ~ r2_hidden(X2,X3)
| ~ v1_filter_0(X3,X1)
| X0 != X3
| ~ m1_filter_0(X3,X1) )
| r2_hidden(X0,a_2_0_lopclset(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X1,X2))],[f116]) ).
fof(f121,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) )
& ( ? [X2] :
( r2_hidden(X2,X0)
& ~ r2_hidden(X2,X1) )
| r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f86]) ).
fof(f122,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ? [X2] :
( r2_hidden(X2,X0)
& ~ r2_hidden(X2,X1) )
| r1_tarski(X0,X1) ) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ( r2_hidden(sK6(X0,X1),X0)
& ~ r2_hidden(sK6(X0,X1),X1) )
| r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f122]) ).
fof(f129,plain,
! [X0,X1] :
( ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_1_1_lopclset(X1))
| ? [X2] :
( v1_filter_0(X2,X1)
& X0 = X2
& m1_filter_0(X2,X1) ) )
& ( ! [X2] :
( ~ v1_filter_0(X2,X1)
| X0 != X2
| ~ m1_filter_0(X2,X1) )
| r2_hidden(X0,a_1_1_lopclset(X1)) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f130,plain,
! [X0,X1] :
( ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_1_1_lopclset(X1))
| ? [X3] :
( v1_filter_0(X3,X1)
& X0 = X3
& m1_filter_0(X3,X1) ) )
& ( ! [X2] :
( ~ v1_filter_0(X2,X1)
| X0 != X2
| ~ m1_filter_0(X2,X1) )
| r2_hidden(X0,a_1_1_lopclset(X1)) ) ) ),
inference(rectify,[],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_1_1_lopclset(X1))
| ( v1_filter_0(sK11(X0,X1),X1)
& sK11(X0,X1) = X0
& m1_filter_0(sK11(X0,X1),X1) ) )
& ( ! [X2] :
( ~ v1_filter_0(X2,X1)
| X0 != X2
| ~ m1_filter_0(X2,X1) )
| r2_hidden(X0,a_1_1_lopclset(X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f130]) ).
fof(f133,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f113]) ).
fof(f134,plain,
~ v3_realset2(sK0),
inference(cnf_transformation,[],[f113]) ).
fof(f135,plain,
v17_lattices(sK0),
inference(cnf_transformation,[],[f113]) ).
fof(f136,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f113]) ).
fof(f137,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f113]) ).
fof(f138,plain,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f113]) ).
fof(f139,plain,
~ r1_tarski(a_2_0_lopclset(sK0,sK1),k7_lopclset(sK0)),
inference(cnf_transformation,[],[f113]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ r2_hidden(X0,a_2_0_lopclset(X1,X2))
| v1_filter_0(sK3(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ r2_hidden(X0,a_2_0_lopclset(X1,X2))
| sK3(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f117]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ r2_hidden(X0,a_2_0_lopclset(X1,X2))
| m1_filter_0(sK3(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f158,plain,
! [X0,X1] :
( r2_hidden(sK6(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f159,plain,
! [X0,X1] :
( ~ r2_hidden(sK6(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f179,plain,
! [X2,X0,X1] :
( ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ v1_filter_0(X2,X1)
| X0 != X2
| ~ m1_filter_0(X2,X1)
| r2_hidden(X0,a_1_1_lopclset(X1)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f189,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k7_lopclset(X0) = a_1_1_lopclset(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f209,plain,
! [X2,X1] :
( ~ l3_lattices(X1)
| v3_realset2(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ v1_filter_0(X2,X1)
| ~ m1_filter_0(X2,X1)
| r2_hidden(X2,a_1_1_lopclset(X1)) ),
inference(equality_resolution,[],[f179]) ).
tcf(c_49,negated_conjecture,
~ r1_tarski(a_2_0_lopclset(sK0,sK1),k7_lopclset(sK0)),
inference(cnf_transformation,[],[f139]) ).
tcf(c_50,negated_conjecture,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f138]) ).
tcf(c_51,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f137]) ).
tcf(c_52,negated_conjecture,
v10_lattices(sK0),
inference(cnf_transformation,[],[f136]) ).
tcf(c_53,negated_conjecture,
v17_lattices(sK0),
inference(cnf_transformation,[],[f135]) ).
tcf(c_54,negated_conjecture,
~ v3_realset2(sK0),
inference(cnf_transformation,[],[f134]) ).
tcf(c_55,negated_conjecture,
l3_lattices(sK0),
inference(cnf_transformation,[],[f133]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_realset2(X1)
| v3_struct_0(X1)
| m1_filter_0(sK3(X0,X1,X2),X1)
| ~ l3_lattices(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(X0,a_2_0_lopclset(X1,X2)) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_realset2(X1)
| v3_struct_0(X1)
| ( sK3(X0,X1,X2) = X0 )
| ~ l3_lattices(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(X0,a_2_0_lopclset(X1,X2)) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_realset2(X1)
| v3_struct_0(X1)
| v1_filter_0(sK3(X0,X1,X2),X1)
| ~ l3_lattices(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(X0,a_2_0_lopclset(X1,X2)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| r2_hidden(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( v3_realset2(X1)
| v3_struct_0(X1)
| r2_hidden(X0,a_1_1_lopclset(X1))
| ~ l3_lattices(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| ~ v1_filter_0(X0,X1)
| ~ m1_filter_0(X0,X1) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_105,plain,
! [X0: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| ( k7_lopclset(X0) = a_1_1_lopclset(X0) )
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_156,plain,
( v3_realset2(sK0)
| v3_struct_0(sK0)
| ( k7_lopclset(sK0) = a_1_1_lopclset(sK0) )
| ~ l3_lattices(sK0)
| ~ v17_lattices(sK0)
| ~ v10_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_1632,plain,
! [X0: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| ( k7_lopclset(X0) = a_1_1_lopclset(X0) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_105]) ).
tcf(c_1633,plain,
( v3_realset2(sK0)
| v3_struct_0(sK0)
| ( k7_lopclset(sK0) = a_1_1_lopclset(sK0) )
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0) ),
inference(unflattening,[status(thm)],[c_1632]) ).
tcf(c_1634,plain,
k7_lopclset(sK0) = a_1_1_lopclset(sK0),
inference(global_subsumption_just,[status(thm)],[c_1633,c_55,c_53,c_52,c_54,c_51,c_156]) ).
tcf(c_1689,plain,
! [X0: $i,X1: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| r2_hidden(X1,a_1_1_lopclset(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ v1_filter_0(X1,X0)
| ~ m1_filter_0(X1,X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_92]) ).
tcf(c_1690,plain,
! [X0: $i] :
( v3_realset2(sK0)
| v3_struct_0(sK0)
| r2_hidden(X0,a_1_1_lopclset(sK0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ v1_filter_0(X0,sK0)
| ~ m1_filter_0(X0,sK0) ),
inference(unflattening,[status(thm)],[c_1689]) ).
tcf(c_1692,plain,
! [X0: $i] :
( r2_hidden(X0,a_1_1_lopclset(sK0))
| ~ v1_filter_0(X0,sK0)
| ~ m1_filter_0(X0,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_1690,c_55,c_52,c_54,c_51,c_1690]) ).
tcf(c_1719,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| v1_filter_0(sK3(X1,X0,X2),X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r2_hidden(X1,a_2_0_lopclset(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_65]) ).
tcf(c_1720,plain,
! [X0: $i,X1: $i] :
( v3_realset2(sK0)
| v3_struct_0(sK0)
| v1_filter_0(sK3(X0,sK0,X1),sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_lopclset(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_1719]) ).
tcf(c_1722,plain,
! [X0: $i,X1: $i] :
( v1_filter_0(sK3(X0,sK0,X1),sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_lopclset(sK0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_1720,c_55,c_52,c_54,c_51,c_1720]) ).
tcf(c_1734,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| ( sK3(X1,X0,X2) = X1 )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r2_hidden(X1,a_2_0_lopclset(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_64]) ).
tcf(c_1735,plain,
! [X0: $i,X1: $i] :
( v3_realset2(sK0)
| v3_struct_0(sK0)
| ( sK3(X0,sK0,X1) = X0 )
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_lopclset(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_1734]) ).
tcf(c_1737,plain,
! [X0: $i,X1: $i] :
( ( sK3(X0,sK0,X1) = X0 )
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_lopclset(sK0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_1735,c_55,c_52,c_54,c_51,c_1735]) ).
tcf(c_1749,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_realset2(X0)
| v3_struct_0(X0)
| m1_filter_0(sK3(X1,X0,X2),X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r2_hidden(X1,a_2_0_lopclset(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_63]) ).
tcf(c_1750,plain,
! [X0: $i,X1: $i] :
( v3_realset2(sK0)
| v3_struct_0(sK0)
| m1_filter_0(sK3(X0,sK0,X1),sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_lopclset(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_1749]) ).
tcf(c_1752,plain,
! [X0: $i,X1: $i] :
( m1_filter_0(sK3(X0,sK0,X1),sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,a_2_0_lopclset(sK0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_1750,c_55,c_52,c_54,c_51,c_1750]) ).
tcf(c_3138,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK6(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_74]) ).
tcf(c_3139,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| r2_hidden(sK6(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_3138]) ).
tcf(c_3434,plain,
~ r1_tarski(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),
inference(light_normalisation,[status(thm)],[c_49,c_1634]) ).
tcf(c_3981,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK6(X0,X1),X0)
| ( a_1_1_lopclset(sK0) != X1 )
| ( a_2_0_lopclset(sK0,sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_3139,c_3434]) ).
tcf(c_3982,plain,
r2_hidden(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),a_2_0_lopclset(sK0,sK1)),
inference(unflattening,[status(thm)],[c_3981]) ).
tcf(c_6158,plain,
! [X0: $i,X1: $i] :
( r1_tarski(a_2_0_lopclset(sK0,X0),X1)
| ( sK3(sK6(a_2_0_lopclset(sK0,X0),X1),sK0,X0) = sK6(a_2_0_lopclset(sK0,X0),X1) )
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_74,c_1737]) ).
tcf(c_6203,plain,
! [X0: $i] :
( r1_tarski(X0,a_1_1_lopclset(sK0))
| ~ v1_filter_0(sK6(X0,a_1_1_lopclset(sK0)),sK0)
| ~ m1_filter_0(sK6(X0,a_1_1_lopclset(sK0)),sK0) ),
inference(superposition,[status(thm)],[c_1692,c_73]) ).
tcf(c_6736,plain,
( ( sK3(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),sK0,sK1) = sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)) )
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_6158,c_3434]) ).
tcf(c_6737,plain,
sK3(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),sK0,sK1) = sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_6736,c_50]) ).
tcf(c_6749,plain,
( m1_filter_0(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ r2_hidden(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),a_2_0_lopclset(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_6737,c_1752]) ).
tcf(c_6750,plain,
( v1_filter_0(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ r2_hidden(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),a_2_0_lopclset(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_6737,c_1722]) ).
tcf(c_6755,plain,
( v1_filter_0(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),sK0)
| ~ r2_hidden(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),a_2_0_lopclset(sK0,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6750,c_50]) ).
tcf(c_6758,plain,
( m1_filter_0(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),sK0)
| ~ r2_hidden(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),a_2_0_lopclset(sK0,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6749,c_50]) ).
tcf(c_6799,plain,
v1_filter_0(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),sK0),
inference(global_subsumption_just,[status(thm)],[c_6755,c_3982,c_6755]) ).
tcf(c_6807,plain,
m1_filter_0(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),sK0),
inference(global_subsumption_just,[status(thm)],[c_6758,c_3982,c_6758]) ).
tcf(c_6810,plain,
( r1_tarski(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0))
| ~ v1_filter_0(sK6(a_2_0_lopclset(sK0,sK1),a_1_1_lopclset(sK0)),sK0) ),
inference(superposition,[status(thm)],[c_6807,c_6203]) ).
tcf(c_6811,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6810,c_3434,c_6799]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT288+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n013.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.40 % DateTime : Wed Sep 23 20:50:21 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.45
% 0.13/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.46
% 0.13/0.46 % Detected problem language: tptp
% 0.13/0.48 % Proving...
% 3.68/1.36 % SZS status Started for theBenchmark.p
% 3.68/1.36 % SZS status Theorem for theBenchmark.p
% 3.68/1.36
% 3.68/1.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.68/1.36
% 3.68/1.36 % ------ iProver source info
% 3.68/1.36
% 3.68/1.36 % git: date: 2026-07-19 20:42:38 +0200
% 3.68/1.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.68/1.36 % git: non_committed_changes: false
% 3.68/1.36
% 3.68/1.36 % ------ Parsing...
% 3.68/1.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.68/1.36
% 3.68/1.36 % ------ Preprocessing... sup_sim: 0 sf_s rm: 35 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 3 sf_s rm: 11 0s sf_e pe_s pe_e %
% 3.68/1.36
% 3.68/1.36 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.68/1.36
% 3.68/1.36 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.68/1.36 % ------ Proving...
% 3.68/1.36 % ------ Problem Properties
% 3.68/1.36
% 3.68/1.36 %
% 3.68/1.36 % clauses 42
% 3.68/1.36 % conjectures 2
% 3.68/1.36 % EPR 13
% 3.68/1.36 % Horn 38
% 3.68/1.36 % unary 14
% 3.68/1.36 % binary 15
% 3.68/1.36 % lits 85
% 3.68/1.36 % lits eq 6
% 3.68/1.36 % fd_pure 0
% 3.68/1.36 % fd_pseudo 0
% 3.68/1.36 % fd_cond 0
% 3.68/1.36 % fd_pseudo_cond 3
% 3.68/1.36 % AC symbols 0
% 3.68/1.36
% 3.68/1.36 % ------ Schedule dynamic 5 is on
% 3.68/1.36
% 3.68/1.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.68/1.36
% 3.68/1.36
% 3.68/1.36 % ------
% 3.68/1.36 % Current options:
% 3.68/1.36 % ------
% 3.68/1.36
% 3.68/1.36
% 3.68/1.36 %
% 3.68/1.36
% 3.68/1.36 % ------ Proving...
% 3.68/1.36 %
% 3.68/1.36
% 3.68/1.36 % SZS status Theorem for theBenchmark.p
% 3.68/1.36
% 3.68/1.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.68/1.36
% 3.68/1.36
%------------------------------------------------------------------------------