%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU340+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 02:56:58 PM UTC 2026
% Result : Theorem 3.54s 1.09s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 110 ( 28 unt; 0 def)
% Number of atoms : 370 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 449 ( 189 ~; 173 |; 58 &)
% ( 8 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 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 : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 199 ( 0 sgn 185 !; 14 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f4,axiom,
! [X0] :
( rel_str(X0)
=> ( transitive_relstr(X0)
<=> is_transitive_in(the_InternalRel(X0),the_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_orders_2) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) )
=> in(ordered_pair(X2,X4),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
fof(f7,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f18,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f19,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f37,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f39,conjecture,
! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( ( related(X0,X2,X3)
& related(X0,X1,X2) )
=> related(X0,X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_orders_2) ).
fof(f40,negated_conjecture,
~ ! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( ( related(X0,X2,X3)
& related(X0,X1,X2) )
=> related(X0,X1,X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f41,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f44,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f46,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f48,plain,
? [X0] :
( rel_str(X0)
& transitive_relstr(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,the_carrier(X0))
& ? [X3] :
( element(X3,the_carrier(X0))
& related(X0,X2,X3)
& related(X0,X1,X2)
& ~ related(X0,X1,X3) ) ) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f49,plain,
? [X0] :
( rel_str(X0)
& transitive_relstr(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,the_carrier(X0))
& ? [X3] :
( element(X3,the_carrier(X0))
& related(X0,X2,X3)
& related(X0,X1,X2)
& ~ related(X0,X1,X3) ) ) ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f54,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f53]) ).
fof(f57,plain,
! [X0] :
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f58,plain,
! [X0] :
( ~ rel_str(X0)
| ( transitive_relstr(X0)
<=> is_transitive_in(the_InternalRel(X0),the_carrier(X0)) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f59,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f60,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| in(ordered_pair(X2,X4),X0) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| in(ordered_pair(X2,X4),X0) ) ) ),
inference(flattening,[],[f63]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f68,plain,
( rel_str(sK0)
& transitive_relstr(sK0)
& element(sK1,the_carrier(sK0))
& element(sK2,the_carrier(sK0))
& element(sK3,the_carrier(sK0))
& related(sK0,sK2,sK3)
& related(sK0,sK1,sK2)
& ~ related(sK0,sK1,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f49]) ).
fof(f73,plain,
! [X0] :
( ~ rel_str(X0)
| ( ( ~ transitive_relstr(X0)
| is_transitive_in(the_InternalRel(X0),the_carrier(X0)) )
& ( ~ is_transitive_in(the_InternalRel(X0),the_carrier(X0))
| transitive_relstr(X0) ) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f74,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ related(X0,X1,X2)
| in(ordered_pair(X1,X2),the_InternalRel(X0)) )
& ( ~ in(ordered_pair(X1,X2),the_InternalRel(X0))
| related(X0,X1,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f78,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_transitive_in(X0,X1)
| ! [X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| in(ordered_pair(X2,X4),X0) ) )
& ( ? [X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1)
& ~ in(ordered_pair(X2,X4),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f79,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_transitive_in(X0,X1)
| ! [X5,X6,X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| in(ordered_pair(X5,X7),X0) ) )
& ( ? [X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1)
& ~ in(ordered_pair(X2,X4),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_transitive_in(X0,X1)
| ! [X5,X6,X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| in(ordered_pair(X5,X7),X0) ) )
& ( ( in(ordered_pair(sK12(X0,X1),sK13(X0,X1)),X0)
& in(ordered_pair(sK11(X0,X1),sK12(X0,X1)),X0)
& in(sK13(X0,X1),X1)
& in(sK12(X0,X1),X1)
& in(sK11(X0,X1),X1)
& ~ in(ordered_pair(sK11(X0,X1),sK13(X0,X1)),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X2,sK11(X0,X1)),skolemize(X3,sK12(X0,X1)),skolemize(X4,sK13(X0,X1))],[f79]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
rel_str(sK0),
inference(cnf_transformation,[],[f68]) ).
fof(f84,plain,
transitive_relstr(sK0),
inference(cnf_transformation,[],[f68]) ).
fof(f85,plain,
element(sK1,the_carrier(sK0)),
inference(cnf_transformation,[],[f68]) ).
fof(f86,plain,
element(sK2,the_carrier(sK0)),
inference(cnf_transformation,[],[f68]) ).
fof(f87,plain,
element(sK3,the_carrier(sK0)),
inference(cnf_transformation,[],[f68]) ).
fof(f88,plain,
related(sK0,sK2,sK3),
inference(cnf_transformation,[],[f68]) ).
fof(f89,plain,
related(sK0,sK1,sK2),
inference(cnf_transformation,[],[f68]) ).
fof(f90,plain,
~ related(sK0,sK1,sK3),
inference(cnf_transformation,[],[f68]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f93,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f101,plain,
! [X0] :
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f102,plain,
! [X0] :
( ~ rel_str(X0)
| ~ transitive_relstr(X0)
| is_transitive_in(the_InternalRel(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ related(X0,X1,X2)
| in(ordered_pair(X1,X2),the_InternalRel(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0))
| related(X0,X1,X2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f106,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f113,plain,
! [X0,X1,X6,X7,X5] :
( ~ relation(X0)
| ~ is_transitive_in(X0,X1)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| in(ordered_pair(X5,X7),X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_49,negated_conjecture,
~ related(sK0,sK1,sK3),
inference(cnf_transformation,[],[f90]) ).
tcf(c_50,negated_conjecture,
related(sK0,sK1,sK2),
inference(cnf_transformation,[],[f89]) ).
tcf(c_51,negated_conjecture,
related(sK0,sK2,sK3),
inference(cnf_transformation,[],[f88]) ).
tcf(c_52,negated_conjecture,
element(sK3,the_carrier(sK0)),
inference(cnf_transformation,[],[f87]) ).
tcf(c_53,negated_conjecture,
element(sK2,the_carrier(sK0)),
inference(cnf_transformation,[],[f86]) ).
tcf(c_54,negated_conjecture,
element(sK1,the_carrier(sK0)),
inference(cnf_transformation,[],[f85]) ).
tcf(c_55,negated_conjecture,
transitive_relstr(sK0),
inference(cnf_transformation,[],[f84]) ).
tcf(c_56,negated_conjecture,
rel_str(sK0),
inference(cnf_transformation,[],[f83]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_67,plain,
! [X0: $i] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_69,plain,
! [X0: $i] :
( is_transitive_in(the_InternalRel(X0),the_carrier(X0))
| ~ rel_str(X0)
| ~ transitive_relstr(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( related(X2,X0,X1)
| ~ rel_str(X2)
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ in(ordered_pair(X0,X1),the_InternalRel(X2)) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ related(X0,X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(X0,X3),X2)
| ~ relation(X2)
| ~ is_transitive_in(X2,X4)
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(ordered_pair(X1,X3),X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_110,plain,
( is_transitive_in(the_InternalRel(sK0),the_carrier(sK0))
| ~ rel_str(sK0)
| ~ transitive_relstr(sK0) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_302,plain,
! [X0: $i] :
( element(the_InternalRel(X0),powerset(cartesian_product2(the_carrier(X0),the_carrier(X0))))
| ~ rel_str(X0) ),
inference(resolution,[status(thm)],[c_67,c_78]) ).
tcf(c_303,plain,
( element(the_InternalRel(sK0),powerset(cartesian_product2(the_carrier(sK0),the_carrier(sK0))))
| ~ rel_str(sK0) ),
inference(instantiation,[status(thm)],[c_302]) ).
tcf(c_319,plain,
( is_transitive_in(the_InternalRel(sK0),the_carrier(sK0))
| ~ rel_str(sK0) ),
inference(resolution,[status(thm)],[c_55,c_69]) ).
tcf(c_320,plain,
is_transitive_in(the_InternalRel(sK0),the_carrier(sK0)),
inference(global_subsumption_just,[status(thm)],[c_319,c_56,c_55,c_110]) ).
tcf(c_326,plain,
element(the_InternalRel(sK0),powerset(cartesian_product2(the_carrier(sK0),the_carrier(sK0)))),
inference(resolution,[status(thm)],[c_56,c_302]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,X1),the_InternalRel(sK0))
| ~ element(X1,the_carrier(sK0))
| ~ element(X0,the_carrier(sK0))
| ~ related(sK0,X0,X1) ),
inference(resolution,[status(thm)],[c_56,c_71]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i] :
( related(sK0,X0,X1)
| ~ element(X1,the_carrier(sK0))
| ~ element(X0,the_carrier(sK0))
| ~ in(ordered_pair(X0,X1),the_InternalRel(sK0)) ),
inference(resolution,[status(thm)],[c_56,c_70]) ).
tcf(c_527,plain,
( ~ element(sK3,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| ~ in(ordered_pair(sK1,sK3),the_InternalRel(sK0)) ),
inference(resolution,[status(thm)],[c_49,c_344]) ).
tcf(c_528,plain,
~ in(ordered_pair(sK1,sK3),the_InternalRel(sK0)),
inference(global_subsumption_just,[status(thm)],[c_527,c_54,c_52,c_527]) ).
tcf(c_533,plain,
( in(ordered_pair(sK1,sK2),the_InternalRel(sK0))
| ~ element(sK2,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0)) ),
inference(resolution,[status(thm)],[c_50,c_330]) ).
tcf(c_534,plain,
in(ordered_pair(sK1,sK2),the_InternalRel(sK0)),
inference(global_subsumption_just,[status(thm)],[c_533,c_54,c_53,c_533]) ).
tcf(c_539,plain,
( in(ordered_pair(sK2,sK3),the_InternalRel(sK0))
| ~ element(sK2,the_carrier(sK0))
| ~ element(sK3,the_carrier(sK0)) ),
inference(resolution,[status(thm)],[c_51,c_330]) ).
tcf(c_540,plain,
in(ordered_pair(sK2,sK3),the_InternalRel(sK0)),
inference(global_subsumption_just,[status(thm)],[c_539,c_53,c_52,c_539]) ).
tcf(c_1273,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ element(the_InternalRel(sK0),powerset(X0))
| ~ in(ordered_pair(sK1,sK2),the_InternalRel(sK0)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1324,plain,
( ~ empty(cartesian_product2(the_carrier(sK0),the_carrier(sK0)))
| ~ in(ordered_pair(sK1,sK2),the_InternalRel(sK0))
| ~ element(the_InternalRel(sK0),powerset(cartesian_product2(the_carrier(sK0),the_carrier(sK0)))) ),
inference(instantiation,[status(thm)],[c_1273]) ).
tcf(c_1596,plain,
( empty(the_carrier(sK0))
| in(sK1,the_carrier(sK0)) ),
inference(superposition,[status(thm)],[c_54,c_59]) ).
tcf(c_1755,plain,
relation(the_InternalRel(sK0)),
inference(superposition,[status(thm)],[c_326,c_90]) ).
tcf(c_2021,plain,
! [X0: $i] :
( ~ in(X0,the_InternalRel(sK0))
| ~ empty(cartesian_product2(the_carrier(sK0),the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_326,c_57]) ).
tcf(c_2258,plain,
~ empty(cartesian_product2(the_carrier(sK0),the_carrier(sK0))),
inference(global_subsumption_just,[status(thm)],[c_2021,c_56,c_54,c_53,c_303,c_533,c_1324]) ).
tcf(c_2398,plain,
! [X0: $i] :
( element(X0,cartesian_product2(the_carrier(sK0),the_carrier(sK0)))
| ~ in(X0,the_InternalRel(sK0)) ),
inference(superposition,[status(thm)],[c_326,c_58]) ).
tcf(c_2933,plain,
! [X0: $i] :
( empty(cartesian_product2(the_carrier(sK0),the_carrier(sK0)))
| in(X0,cartesian_product2(the_carrier(sK0),the_carrier(sK0)))
| ~ in(X0,the_InternalRel(sK0)) ),
inference(superposition,[status(thm)],[c_2398,c_59]) ).
tcf(c_2934,plain,
! [X0: $i] :
( in(X0,cartesian_product2(the_carrier(sK0),the_carrier(sK0)))
| ~ in(X0,the_InternalRel(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2933,c_2258]) ).
tcf(c_2954,plain,
! [X0: $i,X1: $i] :
( in(X1,the_carrier(sK0))
| ~ in(ordered_pair(X0,X1),the_InternalRel(sK0)) ),
inference(superposition,[status(thm)],[c_2934,c_88]) ).
tcf(c_3026,plain,
in(sK2,the_carrier(sK0)),
inference(superposition,[status(thm)],[c_534,c_2954]) ).
tcf(c_3027,plain,
in(sK3,the_carrier(sK0)),
inference(superposition,[status(thm)],[c_540,c_2954]) ).
tcf(c_3064,plain,
~ empty(the_carrier(sK0)),
inference(superposition,[status(thm)],[c_3026,c_72]) ).
tcf(c_3068,plain,
in(sK1,the_carrier(sK0)),
inference(backward_subsumption_resolution,[status(thm)],[c_1596,c_3064]) ).
tcf(c_3187,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK1,X0),the_InternalRel(sK0))
| ~ relation(the_InternalRel(sK0))
| ~ in(sK2,X1)
| ~ in(sK1,X1)
| ~ in(X0,X1)
| ~ is_transitive_in(the_InternalRel(sK0),X1)
| ~ in(ordered_pair(sK2,X0),the_InternalRel(sK0)) ),
inference(superposition,[status(thm)],[c_534,c_85]) ).
tcf(c_3197,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK1,X0),the_InternalRel(sK0))
| ~ in(sK2,X1)
| ~ in(sK1,X1)
| ~ in(X0,X1)
| ~ is_transitive_in(the_InternalRel(sK0),X1)
| ~ in(ordered_pair(sK2,X0),the_InternalRel(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3187,c_1755]) ).
tcf(c_3586,plain,
! [X0: $i] :
( in(ordered_pair(sK1,sK3),the_InternalRel(sK0))
| ~ in(sK2,X0)
| ~ in(sK3,X0)
| ~ in(sK1,X0)
| ~ is_transitive_in(the_InternalRel(sK0),X0) ),
inference(superposition,[status(thm)],[c_540,c_3197]) ).
tcf(c_3587,plain,
! [X0: $i] :
( ~ in(sK2,X0)
| ~ in(sK3,X0)
| ~ in(sK1,X0)
| ~ is_transitive_in(the_InternalRel(sK0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3586,c_528]) ).
tcf(c_3646,plain,
( ~ in(sK2,the_carrier(sK0))
| ~ in(sK3,the_carrier(sK0))
| ~ in(sK1,the_carrier(sK0)) ),
inference(superposition,[status(thm)],[c_320,c_3587]) ).
tcf(c_3649,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3646,c_3026,c_3027,c_3068]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU340+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n019.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 13:46:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 3.54/1.09 % SZS status Started for theBenchmark.p
% 3.54/1.09 % SZS status Theorem for theBenchmark.p
% 3.54/1.09
% 3.54/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.54/1.09
% 3.54/1.09 % ------ iProver source info
% 3.54/1.09
% 3.54/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 3.54/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.54/1.09 % git: non_committed_changes: false
% 3.54/1.09
% 3.54/1.09 % ------ Parsing...
% 3.54/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.54/1.09
% 3.54/1.09 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.54/1.09
% 3.54/1.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.54/1.09 % ------ Proving...
% 3.54/1.09 % ------ Problem Properties
% 3.54/1.09
% 3.54/1.09 %
% 3.54/1.09 % clauses 36
% 3.54/1.09 % conjectures 3
% 3.54/1.09 % EPR 6
% 3.54/1.09 % Horn 28
% 3.54/1.09 % unary 16
% 3.54/1.09 % binary 8
% 3.54/1.09 % lits 73
% 3.54/1.09 % lits eq 0
% 3.54/1.09 % fd_pure 0
% 3.54/1.09 % fd_pseudo 0
% 3.54/1.09 % fd_cond 0
% 3.54/1.09 % fd_pseudo_cond 0
% 3.54/1.09 % AC symbols 0
% 3.54/1.09
% 3.54/1.09 % ------ Schedule dynamic 5 is on
% 3.54/1.09
% 3.54/1.09 % ------ no equalities: superposition off
% 3.54/1.09
% 3.54/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.54/1.09
% 3.54/1.09
% 3.54/1.09 % ------
% 3.54/1.09 % Current options:
% 3.54/1.09 % ------
% 3.54/1.09
% 3.54/1.09
% 3.54/1.09 %
% 3.54/1.09
% 3.54/1.09 % ------ Proving...
% 3.54/1.09 %
% 3.54/1.09
% 3.54/1.09 % SZS status Theorem for theBenchmark.p
% 3.54/1.09
% 3.54/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.54/1.09
% 3.54/1.09
%------------------------------------------------------------------------------