%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU240+2 : 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 : n020.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 02:56:19 PM UTC 2026
% Result : Theorem 52.80s 20.97s
% Output : CNFRefutation 52.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 86 ( 12 unt; 0 def)
% Number of atoms : 363 ( 8 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 485 ( 208 ~; 213 |; 46 &)
% ( 7 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 186 ( 0 sgn 166 !; 20 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f21,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f49,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f56,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(f134,conjecture,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> in(ordered_pair(X1,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
fof(f135,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> in(ordered_pair(X1,X3),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f134]) ).
fof(f212,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f264,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f321,plain,
! [X0] :
( ~ relation(X0)
| ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f344,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,[],[f56]) ).
fof(f345,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,[],[f344]) ).
fof(f403,plain,
? [X0] :
( relation(X0)
& ( transitive(X0)
<~> ! [X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X1,X3),X0) ) ) ),
inference(ennf_transformation,[],[f135]) ).
fof(f404,plain,
? [X0] :
( relation(X0)
& ( transitive(X0)
<~> ! [X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X1,X3),X0) ) ) ),
inference(flattening,[],[f403]) ).
fof(f479,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(ennf_transformation,[],[f212]) ).
fof(f480,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f479]) ).
fof(f591,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ transitive(X0)
| is_transitive_in(X0,relation_field(X0)) )
& ( ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0) ) ) ),
inference(nnf_transformation,[],[f321]) ).
fof(f675,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,[],[f345]) ).
fof(f676,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,[],[f675]) ).
fof(f677,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(sK66(X0,X1),sK67(X0,X1)),X0)
& in(ordered_pair(sK65(X0,X1),sK66(X0,X1)),X0)
& in(sK67(X0,X1),X1)
& in(sK66(X0,X1),X1)
& in(sK65(X0,X1),X1)
& ~ in(ordered_pair(sK65(X0,X1),sK67(X0,X1)),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65,sK66,sK67]),skolemize(X2,sK65(X0,X1)),skolemize(X3,sK66(X0,X1)),skolemize(X4,sK67(X0,X1))],[f676]) ).
fof(f687,plain,
? [X0] :
( relation(X0)
& ( transitive(X0)
| ! [X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X1,X3),X0) ) )
& ( ~ transitive(X0)
| ? [X1,X2,X3] :
( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X1,X3),X0) ) ) ),
inference(nnf_transformation,[],[f404]) ).
fof(f688,plain,
? [X0] :
( relation(X0)
& ( transitive(X0)
| ! [X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X1,X3),X0) ) )
& ( ~ transitive(X0)
| ? [X1,X2,X3] :
( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X1,X3),X0) ) ) ),
inference(flattening,[],[f687]) ).
fof(f689,plain,
? [X0] :
( relation(X0)
& ( transitive(X0)
| ! [X4,X5,X6] :
( ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X6),X0) ) )
& ( ~ transitive(X0)
| ? [X1,X2,X3] :
( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X1,X3),X0) ) ) ),
inference(rectify,[],[f688]) ).
fof(f690,plain,
( relation(sK71)
& ( transitive(sK71)
| ! [X4,X5,X6] :
( ~ in(ordered_pair(X5,X6),sK71)
| ~ in(ordered_pair(X4,X5),sK71)
| in(ordered_pair(X4,X6),sK71) ) )
& ( ~ transitive(sK71)
| ( in(ordered_pair(sK73,sK74),sK71)
& in(ordered_pair(sK72,sK73),sK71)
& ~ in(ordered_pair(sK72,sK74),sK71) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71,sK72,sK73,sK74]),skolemize(X0,sK71),skolemize(X1,sK72),skolemize(X2,sK73),skolemize(X3,sK74)],[f689]) ).
fof(f787,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f838,plain,
! [X0] :
( ~ relation(X0)
| ~ transitive(X0)
| is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f591]) ).
fof(f839,plain,
! [X0] :
( ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0) ),
inference(cnf_transformation,[],[f591]) ).
fof(f957,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f49]) ).
fof(f978,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,[],[f677]) ).
fof(f979,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK66(X0,X1),sK67(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f677]) ).
fof(f980,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK65(X0,X1),sK66(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f677]) ).
fof(f984,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK65(X0,X1),sK67(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f677]) ).
fof(f1075,plain,
relation(sK71),
inference(cnf_transformation,[],[f690]) ).
fof(f1076,plain,
! [X6,X4,X5] :
( transitive(sK71)
| ~ in(ordered_pair(X5,X6),sK71)
| ~ in(ordered_pair(X4,X5),sK71)
| in(ordered_pair(X4,X6),sK71) ),
inference(cnf_transformation,[],[f690]) ).
fof(f1077,plain,
( ~ transitive(sK71)
| in(ordered_pair(sK73,sK74),sK71) ),
inference(cnf_transformation,[],[f690]) ).
fof(f1078,plain,
( ~ transitive(sK71)
| in(ordered_pair(sK72,sK73),sK71) ),
inference(cnf_transformation,[],[f690]) ).
fof(f1079,plain,
( ~ transitive(sK71)
| ~ in(ordered_pair(sK72,sK74),sK71) ),
inference(cnf_transformation,[],[f690]) ).
fof(f1207,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_field(X2)) ),
inference(cnf_transformation,[],[f480]) ).
fof(f1208,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f480]) ).
fof(f1305,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f264]) ).
fof(f1341,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f957,f1305]) ).
fof(f1417,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK65(X0,X1),sK67(X0,X1)),unordered_pair(sK65(X0,X1),sK65(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f984,f1341]) ).
fof(f1418,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK65(X0,X1),sK66(X0,X1)),unordered_pair(sK65(X0,X1),sK65(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f980,f1341]) ).
fof(f1419,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK66(X0,X1),sK67(X0,X1)),unordered_pair(sK66(X0,X1),sK66(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f979,f1341]) ).
fof(f1420,plain,
! [X0,X1,X6,X7,X5] :
( ~ relation(X0)
| ~ is_transitive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X7),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f978,f1341,f1341,f1341]) ).
fof(f1436,plain,
( ~ transitive(sK71)
| ~ in(unordered_pair(unordered_pair(sK72,sK74),unordered_pair(sK72,sK72)),sK71) ),
inference(definition_unfolding,[],[f1079,f1341]) ).
fof(f1437,plain,
( ~ transitive(sK71)
| in(unordered_pair(unordered_pair(sK72,sK73),unordered_pair(sK72,sK72)),sK71) ),
inference(definition_unfolding,[],[f1078,f1341]) ).
fof(f1438,plain,
( ~ transitive(sK71)
| in(unordered_pair(unordered_pair(sK73,sK74),unordered_pair(sK73,sK73)),sK71) ),
inference(definition_unfolding,[],[f1077,f1341]) ).
fof(f1439,plain,
! [X6,X4,X5] :
( transitive(sK71)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),sK71)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK71)
| in(unordered_pair(unordered_pair(X4,X6),unordered_pair(X4,X4)),sK71) ),
inference(definition_unfolding,[],[f1076,f1341,f1341,f1341]) ).
fof(f1467,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X0,relation_field(X2)) ),
inference(definition_unfolding,[],[f1208,f1341]) ).
fof(f1468,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X1,relation_field(X2)) ),
inference(definition_unfolding,[],[f1207,f1341]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f787]) ).
tcf(c_111,plain,
! [X0: $i] :
( transitive(X0)
| ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f839]) ).
tcf(c_112,plain,
! [X0: $i] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f838]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK65(X0,X1),sK67(X0,X1)),unordered_pair(sK65(X0,X1),sK65(X0,X1))),X0) ),
inference(cnf_transformation,[],[f1417]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK65(X0,X1),sK66(X0,X1)),unordered_pair(sK65(X0,X1),sK65(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1418]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK66(X0,X1),sK67(X0,X1)),unordered_pair(sK66(X0,X1),sK66(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1419]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ is_transitive_in(X2,X4)
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1420]) ).
tcf(c_346,negated_conjecture,
( ~ transitive(sK71)
| ~ in(unordered_pair(unordered_pair(sK72,sK74),unordered_pair(sK72,sK72)),sK71) ),
inference(cnf_transformation,[],[f1436]) ).
tcf(c_347,negated_conjecture,
( in(unordered_pair(unordered_pair(sK72,sK73),unordered_pair(sK72,sK72)),sK71)
| ~ transitive(sK71) ),
inference(cnf_transformation,[],[f1437]) ).
tcf(c_348,negated_conjecture,
( in(unordered_pair(unordered_pair(sK73,sK74),unordered_pair(sK73,sK73)),sK71)
| ~ transitive(sK71) ),
inference(cnf_transformation,[],[f1438]) ).
tcf(c_349,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( transitive(sK71)
| in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),sK71)
| ~ in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),sK71)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK71) ),
inference(cnf_transformation,[],[f1439]) ).
tcf(c_350,negated_conjecture,
relation(sK71),
inference(cnf_transformation,[],[f1075]) ).
tcf(c_478,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1467]) ).
tcf(c_479,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1468]) ).
tcf(c_1186,plain,
( in(unordered_pair(unordered_pair(sK72,sK72),unordered_pair(sK72,sK73)),sK71)
| ~ transitive(sK71) ),
inference(demodulation,[status(thm)],[c_347,c_60]) ).
tcf(c_1223,plain,
( in(unordered_pair(unordered_pair(sK74,sK73),unordered_pair(sK73,sK73)),sK71)
| ~ transitive(sK71) ),
inference(demodulation,[status(thm)],[c_348,c_60]) ).
tcf(c_3093,plain,
( transitive(sK71)
| ~ relation(sK71)
| ~ is_transitive_in(sK71,relation_field(sK71)) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_3966,plain,
( is_transitive_in(sK71,relation_field(sK71))
| in(unordered_pair(unordered_pair(sK66(sK71,relation_field(sK71)),sK67(sK71,relation_field(sK71))),unordered_pair(sK66(sK71,relation_field(sK71)),sK66(sK71,relation_field(sK71)))),sK71)
| ~ relation(sK71) ),
inference(instantiation,[status(thm)],[c_254]) ).
tcf(c_3967,plain,
( is_transitive_in(sK71,relation_field(sK71))
| in(unordered_pair(unordered_pair(sK65(sK71,relation_field(sK71)),sK66(sK71,relation_field(sK71))),unordered_pair(sK65(sK71,relation_field(sK71)),sK65(sK71,relation_field(sK71)))),sK71)
| ~ relation(sK71) ),
inference(instantiation,[status(thm)],[c_253]) ).
tcf(c_3968,plain,
( is_transitive_in(sK71,relation_field(sK71))
| ~ relation(sK71)
| ~ in(unordered_pair(unordered_pair(sK65(sK71,relation_field(sK71)),sK67(sK71,relation_field(sK71))),unordered_pair(sK65(sK71,relation_field(sK71)),sK65(sK71,relation_field(sK71)))),sK71) ),
inference(instantiation,[status(thm)],[c_249]) ).
tcf(c_4360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ is_transitive_in(X2,X4)
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_60,c_255]) ).
tcf(c_6205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X3,X0),unordered_pair(X3,X3)),X2)
| ~ relation(X2)
| ~ is_transitive_in(X2,X4)
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X1)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2) ),
inference(superposition,[status(thm)],[c_60,c_4360]) ).
tcf(c_7441,plain,
( in(sK72,relation_field(sK71))
| ~ relation(sK71)
| ~ in(unordered_pair(unordered_pair(sK72,sK73),unordered_pair(sK72,sK72)),sK71) ),
inference(instantiation,[status(thm)],[c_478]) ).
tcf(c_7526,plain,
( in(sK74,relation_field(sK71))
| ~ relation(sK71)
| ~ in(unordered_pair(unordered_pair(sK73,sK74),unordered_pair(sK73,sK73)),sK71) ),
inference(instantiation,[status(thm)],[c_479]) ).
tcf(c_7527,plain,
( in(sK73,relation_field(sK71))
| ~ relation(sK71)
| ~ in(unordered_pair(unordered_pair(sK73,sK74),unordered_pair(sK73,sK73)),sK71) ),
inference(instantiation,[status(thm)],[c_478]) ).
tcf(c_13006,plain,
! [X0: $i] :
( transitive(sK71)
| in(unordered_pair(unordered_pair(sK65(sK71,relation_field(sK71)),X0),unordered_pair(sK65(sK71,relation_field(sK71)),sK65(sK71,relation_field(sK71)))),sK71)
| ~ in(unordered_pair(unordered_pair(sK66(sK71,relation_field(sK71)),X0),unordered_pair(sK66(sK71,relation_field(sK71)),sK66(sK71,relation_field(sK71)))),sK71)
| ~ in(unordered_pair(unordered_pair(sK65(sK71,relation_field(sK71)),sK66(sK71,relation_field(sK71))),unordered_pair(sK65(sK71,relation_field(sK71)),sK65(sK71,relation_field(sK71)))),sK71) ),
inference(instantiation,[status(thm)],[c_349]) ).
tcf(c_14034,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK74),unordered_pair(X0,X0)),sK71)
| ~ transitive(sK71)
| ~ relation(sK71)
| ~ is_transitive_in(sK71,X1)
| ~ in(sK73,X1)
| ~ in(sK74,X1)
| ~ in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK73)),sK71) ),
inference(superposition,[status(thm)],[c_1223,c_6205]) ).
tcf(c_14039,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK74),unordered_pair(X0,X0)),sK71)
| ~ transitive(sK71)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK73)),sK71)
| ~ in(X0,X1)
| ~ in(sK74,X1)
| ~ in(sK73,X1)
| ~ is_transitive_in(sK71,X1) ),
inference(global_subsumption_just,[status(thm)],[c_14034,c_350,c_14034]) ).
tcf(c_14040,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK74),unordered_pair(X0,X0)),sK71)
| ~ transitive(sK71)
| ~ is_transitive_in(sK71,X1)
| ~ in(sK73,X1)
| ~ in(sK74,X1)
| ~ in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK73)),sK71) ),
inference(renaming,[status(thm)],[c_14039]) ).
tcf(c_14232,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK72,sK74),unordered_pair(sK72,sK72)),sK71)
| ~ transitive(sK71)
| ~ is_transitive_in(sK71,X0)
| ~ in(sK73,X0)
| ~ in(sK74,X0)
| ~ in(sK72,X0) ),
inference(superposition,[status(thm)],[c_1186,c_14040]) ).
tcf(c_14238,plain,
! [X0: $i] :
( ~ in(sK72,X0)
| ~ in(sK74,X0)
| ~ in(sK73,X0)
| ~ is_transitive_in(sK71,X0)
| ~ transitive(sK71) ),
inference(global_subsumption_just,[status(thm)],[c_14232,c_346,c_14232]) ).
tcf(c_14239,plain,
! [X0: $i] :
( ~ transitive(sK71)
| ~ is_transitive_in(sK71,X0)
| ~ in(sK73,X0)
| ~ in(sK74,X0)
| ~ in(sK72,X0) ),
inference(renaming,[status(thm)],[c_14238]) ).
tcf(c_14458,plain,
( ~ transitive(sK71)
| ~ relation(sK71)
| ~ in(sK73,relation_field(sK71))
| ~ in(sK74,relation_field(sK71))
| ~ in(sK72,relation_field(sK71)) ),
inference(superposition,[status(thm)],[c_112,c_14239]) ).
tcf(c_14459,plain,
~ transitive(sK71),
inference(global_subsumption_just,[status(thm)],[c_14458,c_350,c_348,c_347,c_7441,c_7527,c_7526,c_14458]) ).
tcf(c_16006,plain,
( transitive(sK71)
| in(unordered_pair(unordered_pair(sK65(sK71,relation_field(sK71)),sK67(sK71,relation_field(sK71))),unordered_pair(sK65(sK71,relation_field(sK71)),sK65(sK71,relation_field(sK71)))),sK71)
| ~ in(unordered_pair(unordered_pair(sK66(sK71,relation_field(sK71)),sK67(sK71,relation_field(sK71))),unordered_pair(sK66(sK71,relation_field(sK71)),sK66(sK71,relation_field(sK71)))),sK71)
| ~ in(unordered_pair(unordered_pair(sK65(sK71,relation_field(sK71)),sK66(sK71,relation_field(sK71))),unordered_pair(sK65(sK71,relation_field(sK71)),sK65(sK71,relation_field(sK71)))),sK71) ),
inference(instantiation,[status(thm)],[c_13006]) ).
tcf(c_16007,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16006,c_14459,c_3966,c_3967,c_3968,c_3093,c_350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU240+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.39 % Computer : n020.cluster.edu
% 0.09/5.39 % Model : x86_64 x86_64
% 0.09/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.39 % Memory : 8046.5625MB
% 0.09/5.39 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Thu Sep 24 13:23:08 UTC 2026
% 0.09/5.40 % CPUTime :
% 0.09/5.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 52.80/20.97 % SZS status Started for theBenchmark.p
% 52.80/20.97 % SZS status Theorem for theBenchmark.p
% 52.80/20.97
% 52.80/20.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 52.80/20.97
% 52.80/20.97 % ------ iProver source info
% 52.80/20.97
% 52.80/20.97 % git: date: 2026-07-19 20:42:38 +0200
% 52.80/20.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 52.80/20.97 % git: non_committed_changes: false
% 52.80/20.97
% 52.80/20.97 % ------ Parsing...
% 52.80/20.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 52.80/20.97
% 52.80/20.97 % ------ Preprocessing... sf_s rm: 6 0s sf_e sf_s rm: 2 0s sf_e %
% 52.80/20.97
% 52.80/20.97 % ------ Preprocessing...%
% 52.80/20.97
% 52.80/20.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 52.80/20.97 % ------ Proving...
% 52.80/20.97 % ------ Problem Properties
% 52.80/20.97
% 52.80/20.97 %
% 52.80/20.97 % clauses 506
% 52.80/20.97 % conjectures 5
% 52.80/20.97 % EPR 80
% 52.80/20.97 % Horn 402
% 52.80/20.97 % unary 88
% 52.80/20.97 % binary 140
% 52.80/20.97 % lits 1444
% 52.80/20.97 % lits eq 242
% 52.80/20.97 % fd_pure 0
% 52.80/20.97 % fd_pseudo 0
% 52.80/20.97 % fd_cond 17
% 52.80/20.97 % fd_pseudo_cond 92
% 52.80/20.97 % AC symbols 0
% 52.80/20.97
% 52.80/20.97 % ------ Input Options Time Limit: Unbounded
% 52.80/20.97
% 52.80/20.97
% 52.80/20.97 % ------
% 52.80/20.97 % Current options:
% 52.80/20.97 % ------
% 52.80/20.97
% 52.80/20.97
% 52.80/20.97 %
% 52.80/20.97
% 52.80/20.97 % ------ Proving...
% 52.80/20.97 %
% 52.80/20.97
% 52.80/20.97 % SZS status Theorem for theBenchmark.p
% 52.80/20.97
% 52.80/20.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 52.80/20.97
% 52.80/20.97
%------------------------------------------------------------------------------