%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU240+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 : n001.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 3.15s 1.27s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 113 ( 17 unt; 8 def)
% Number of atoms : 491 ( 19 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 585 ( 252 ~; 269 |; 46 &)
% ( 7 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 6 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 : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 217 ( 0 sgn 197 !; 20 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f7,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(f9,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(f25,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(f26,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)],[f25]) ).
fof(f35,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(f46,plain,
! [X0] :
( ~ relation(X0)
| ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f48,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,[],[f9]) ).
fof(f49,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,[],[f48]) ).
fof(f52,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,[],[f26]) ).
fof(f53,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,[],[f52]) ).
fof(f57,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,[],[f35]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f57]) ).
fof(f62,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,[],[f46]) ).
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) ) )
& ( ? [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,[],[f49]) ).
fof(f64,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,[],[f63]) ).
fof(f65,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(sK1(X0,X1),sK2(X0,X1)),X0)
& in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& in(sK2(X0,X1),X1)
& in(sK1(X0,X1),X1)
& in(sK0(X0,X1),X1)
& ~ in(ordered_pair(sK0(X0,X1),sK2(X0,X1)),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1)),skolemize(X4,sK2(X0,X1))],[f64]) ).
fof(f67,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,[],[f53]) ).
fof(f68,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,[],[f67]) ).
fof(f69,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,[],[f68]) ).
fof(f70,plain,
( relation(sK4)
& ( transitive(sK4)
| ! [X4,X5,X6] :
( ~ in(ordered_pair(X5,X6),sK4)
| ~ in(ordered_pair(X4,X5),sK4)
| in(ordered_pair(X4,X6),sK4) ) )
& ( ~ transitive(sK4)
| ( in(ordered_pair(sK6,sK7),sK4)
& in(ordered_pair(sK5,sK6),sK4)
& ~ in(ordered_pair(sK5,sK7),sK4) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f69]) ).
fof(f80,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f82,plain,
! [X0] :
( ~ relation(X0)
| ~ transitive(X0)
| is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f83,plain,
! [X0] :
( ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f84,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f86,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,[],[f65]) ).
fof(f87,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f88,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f92,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK0(X0,X1),sK2(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f99,plain,
relation(sK4),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
! [X6,X4,X5] :
( transitive(sK4)
| ~ in(ordered_pair(X5,X6),sK4)
| ~ in(ordered_pair(X4,X5),sK4)
| in(ordered_pair(X4,X6),sK4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f101,plain,
( ~ transitive(sK4)
| in(ordered_pair(sK6,sK7),sK4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f102,plain,
( ~ transitive(sK4)
| in(ordered_pair(sK5,sK6),sK4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f103,plain,
( ~ transitive(sK4)
| ~ in(ordered_pair(sK5,sK7),sK4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f116,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_field(X2)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f121,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK2(X0,X1)),singleton(sK0(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f92,f84]) ).
fof(f122,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f88,f84]) ).
fof(f123,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK1(X0,X1),sK2(X0,X1)),singleton(sK1(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f87,f84]) ).
fof(f124,plain,
! [X0,X1,X6,X7,X5] :
( ~ relation(X0)
| ~ is_transitive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X7),singleton(X5)),X0) ),
inference(definition_unfolding,[],[f86,f84,f84,f84]) ).
fof(f126,plain,
( ~ transitive(sK4)
| ~ in(unordered_pair(unordered_pair(sK5,sK7),singleton(sK5)),sK4) ),
inference(definition_unfolding,[],[f103,f84]) ).
fof(f127,plain,
( ~ transitive(sK4)
| in(unordered_pair(unordered_pair(sK5,sK6),singleton(sK5)),sK4) ),
inference(definition_unfolding,[],[f102,f84]) ).
fof(f128,plain,
( ~ transitive(sK4)
| in(unordered_pair(unordered_pair(sK6,sK7),singleton(sK6)),sK4) ),
inference(definition_unfolding,[],[f101,f84]) ).
fof(f129,plain,
! [X6,X4,X5] :
( transitive(sK4)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),sK4)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),sK4)
| in(unordered_pair(unordered_pair(X4,X6),singleton(X4)),sK4) ),
inference(definition_unfolding,[],[f100,f84,f84,f84]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| in(X0,relation_field(X2)) ),
inference(definition_unfolding,[],[f117,f84]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| in(X1,relation_field(X2)) ),
inference(definition_unfolding,[],[f116,f84]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f80]) ).
tcf(c_53,plain,
! [X0: $i] :
( transitive(X0)
| ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_54,plain,
! [X0: $i] :
( is_transitive_in(X0,relation_field(X0))
| ~ relation(X0)
| ~ transitive(X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK2(X0,X1)),singleton(sK0(X0,X1))),X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK1(X0,X1),sK2(X0,X1)),singleton(sK1(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X0,X3),singleton(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),singleton(X1)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_69,negated_conjecture,
( ~ transitive(sK4)
| ~ in(unordered_pair(unordered_pair(sK5,sK7),singleton(sK5)),sK4) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_70,negated_conjecture,
( in(unordered_pair(unordered_pair(sK5,sK6),singleton(sK5)),sK4)
| ~ transitive(sK4) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_71,negated_conjecture,
( in(unordered_pair(unordered_pair(sK6,sK7),singleton(sK6)),sK4)
| ~ transitive(sK4) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_72,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( transitive(sK4)
| in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),sK4)
| ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),sK4)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK4) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_73,negated_conjecture,
relation(sK4),
inference(cnf_transformation,[],[f99]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_340,plain,
( in(unordered_pair(singleton(sK6),unordered_pair(sK6,sK7)),sK4)
| ~ transitive(sK4) ),
inference(demodulation,[status(thm)],[c_71,c_51]) ).
tcf(c_347,plain,
( in(unordered_pair(singleton(sK5),unordered_pair(sK5,sK6)),sK4)
| ~ transitive(sK4) ),
inference(demodulation,[status(thm)],[c_70,c_51]) ).
tcf(c_372,plain,
( ~ transitive(sK4)
| ~ in(unordered_pair(singleton(sK5),unordered_pair(sK5,sK7)),sK4) ),
inference(demodulation,[status(thm)],[c_69,c_51]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_87,c_51]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_86,c_51]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(singleton(sK1(X0,X1)),unordered_pair(sK1(X0,X1),sK2(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_61,c_51]) ).
tcf(c_413,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_60,c_51]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK2(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_56,c_51]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive(sK4)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),sK4)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK4) ),
inference(demodulation,[status(thm)],[c_72,c_51]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),X2)
| ~ relation(X2)
| ~ is_transitive_in(X2,X4)
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_62,c_51]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK0(X2,X1)),unordered_pair(sK0(X2,X1),sK2(X2,X1))),X2)
| ( X0 != X2 )
| ( relation_field(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_423]) ).
tcf(c_614,plain,
! [X0: $i] :
( transitive(X0)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK0(X0,relation_field(X0))),unordered_pair(sK0(X0,relation_field(X0)),sK2(X0,relation_field(X0)))),X0) ),
inference(unflattening,[status(thm)],[c_613]) ).
tcf(c_615,plain,
( transitive(sK4)
| ~ relation(sK4)
| ~ in(unordered_pair(singleton(sK0(sK4,relation_field(sK4))),unordered_pair(sK0(sK4,relation_field(sK4)),sK2(sK4,relation_field(sK4)))),sK4) ),
inference(instantiation,[status(thm)],[c_614]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive(X0)
| in(unordered_pair(singleton(sK0(X2,X1)),unordered_pair(sK0(X2,X1),sK1(X2,X1))),X2)
| ~ relation(X2)
| ~ relation(X0)
| ( X0 != X2 )
| ( relation_field(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_413]) ).
tcf(c_626,plain,
! [X0: $i] :
( transitive(X0)
| in(unordered_pair(singleton(sK0(X0,relation_field(X0))),unordered_pair(sK0(X0,relation_field(X0)),sK1(X0,relation_field(X0)))),X0)
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_625]) ).
tcf(c_627,plain,
( transitive(sK4)
| in(unordered_pair(singleton(sK0(sK4,relation_field(sK4))),unordered_pair(sK0(sK4,relation_field(sK4)),sK1(sK4,relation_field(sK4)))),sK4)
| ~ relation(sK4) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive(X0)
| in(unordered_pair(singleton(sK1(X2,X1)),unordered_pair(sK1(X2,X1),sK2(X2,X1))),X2)
| ~ relation(X2)
| ~ relation(X0)
| ( X0 != X2 )
| ( relation_field(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_403]) ).
tcf(c_638,plain,
! [X0: $i] :
( transitive(X0)
| in(unordered_pair(singleton(sK1(X0,relation_field(X0))),unordered_pair(sK1(X0,relation_field(X0)),sK2(X0,relation_field(X0)))),X0)
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_637]) ).
tcf(c_639,plain,
( transitive(sK4)
| in(unordered_pair(singleton(sK1(sK4,relation_field(sK4))),unordered_pair(sK1(sK4,relation_field(sK4)),sK2(sK4,relation_field(sK4)))),sK4)
| ~ relation(sK4) ),
inference(instantiation,[status(thm)],[c_638]) ).
tcf(c_2768,definition,
iPr_def_10 = singleton(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2769,definition,
iPr_def_11 = unordered_pair(sK5,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2770,definition,
iPr_def_12 = unordered_pair(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2771,definition,
iPr_def_13 = unordered_pair(sK5,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2772,definition,
iPr_def_14 = unordered_pair(iPr_def_10,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2773,definition,
iPr_def_15 = singleton(sK6),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_2774,definition,
iPr_def_16 = unordered_pair(sK6,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_2775,definition,
iPr_def_17 = unordered_pair(iPr_def_15,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_2776,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive(sK4)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),sK4)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK4) ),
inference(demodulation,[status(thm)],[c_433]) ).
tcf(c_2777,plain,
( ~ transitive(sK4)
| ~ in(iPr_def_12,sK4) ),
inference(demodulation,[status(thm)],[c_372,c_2769,c_2768,c_2770]) ).
tcf(c_2778,plain,
( in(iPr_def_14,sK4)
| ~ transitive(sK4) ),
inference(demodulation,[status(thm)],[c_347,c_2771,c_2772]) ).
tcf(c_2779,plain,
( in(iPr_def_17,sK4)
| ~ transitive(sK4) ),
inference(demodulation,[status(thm)],[c_340,c_2774,c_2773,c_2775]) ).
tcf(c_3441,plain,
! [X0: $i] :
( in(sK5,relation_field(X0))
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK5),iPr_def_13),X0) ),
inference(superposition,[status(thm)],[c_2771,c_393]) ).
tcf(c_3442,plain,
! [X0: $i] :
( in(sK6,relation_field(X0))
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK5),iPr_def_13),X0) ),
inference(superposition,[status(thm)],[c_2771,c_383]) ).
tcf(c_3446,plain,
! [X0: $i] :
( in(sK6,relation_field(X0))
| ~ relation(X0)
| ~ in(iPr_def_14,X0) ),
inference(light_normalisation,[status(thm)],[c_3442,c_2768,c_2772]) ).
tcf(c_3450,plain,
! [X0: $i] :
( in(sK5,relation_field(X0))
| ~ relation(X0)
| ~ in(iPr_def_14,X0) ),
inference(light_normalisation,[status(thm)],[c_3441,c_2768,c_2772]) ).
tcf(c_3465,plain,
( in(sK5,relation_field(sK4))
| ~ relation(sK4)
| ~ in(iPr_def_14,sK4) ),
inference(instantiation,[status(thm)],[c_3450]) ).
tcf(c_3466,plain,
( in(sK6,relation_field(sK4))
| ~ relation(sK4)
| ~ in(iPr_def_14,sK4) ),
inference(instantiation,[status(thm)],[c_3446]) ).
tcf(c_3485,plain,
! [X0: $i] :
( in(sK7,relation_field(X0))
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK6),iPr_def_16),X0) ),
inference(superposition,[status(thm)],[c_2774,c_383]) ).
tcf(c_3488,plain,
! [X0: $i] :
( in(sK7,relation_field(X0))
| ~ relation(X0)
| ~ in(iPr_def_17,X0) ),
inference(light_normalisation,[status(thm)],[c_3485,c_2773,c_2775]) ).
tcf(c_3507,plain,
( in(sK7,relation_field(sK4))
| ~ relation(sK4)
| ~ in(iPr_def_17,sK4) ),
inference(instantiation,[status(thm)],[c_3488]) ).
tcf(c_4472,plain,
! [X0: $i] :
( transitive(sK4)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK2(sK4,relation_field(sK4)))),sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK1(sK4,relation_field(sK4)))),sK4)
| ~ in(unordered_pair(singleton(sK1(sK4,relation_field(sK4))),unordered_pair(sK1(sK4,relation_field(sK4)),sK2(sK4,relation_field(sK4)))),sK4) ),
inference(instantiation,[status(thm)],[c_2776]) ).
tcf(c_4813,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(singleton(sK5),unordered_pair(sK5,X0)),X1)
| ~ relation(X1)
| ~ in(sK6,X2)
| ~ in(sK5,X2)
| ~ is_transitive_in(X1,X2)
| ~ in(X0,X2)
| ~ in(unordered_pair(singleton(sK5),iPr_def_13),X1)
| ~ in(unordered_pair(singleton(sK6),unordered_pair(sK6,X0)),X1) ),
inference(superposition,[status(thm)],[c_2771,c_446]) ).
tcf(c_4851,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(iPr_def_10,unordered_pair(sK5,X0)),X1)
| ~ relation(X1)
| ~ in(iPr_def_14,X1)
| ~ in(sK6,X2)
| ~ in(sK5,X2)
| ~ is_transitive_in(X1,X2)
| ~ in(X0,X2)
| ~ in(unordered_pair(iPr_def_15,unordered_pair(sK6,X0)),X1) ),
inference(light_normalisation,[status(thm)],[c_4813,c_2768,c_2772,c_2773]) ).
tcf(c_4996,plain,
! [X0: $i] :
( transitive(sK4)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK7)),sK4)
| ~ in(unordered_pair(singleton(sK5),iPr_def_11),sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK5)),sK4) ),
inference(superposition,[status(thm)],[c_2769,c_2776]) ).
tcf(c_5007,plain,
! [X0: $i] :
( transitive(sK4)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK7)),sK4)
| ~ in(iPr_def_12,sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK5)),sK4) ),
inference(light_normalisation,[status(thm)],[c_4996,c_2768,c_2770]) ).
tcf(c_5087,plain,
( transitive(sK4)
| in(unordered_pair(singleton(sK0(sK4,relation_field(sK4))),unordered_pair(sK0(sK4,relation_field(sK4)),sK2(sK4,relation_field(sK4)))),sK4)
| ~ in(unordered_pair(singleton(sK1(sK4,relation_field(sK4))),unordered_pair(sK1(sK4,relation_field(sK4)),sK2(sK4,relation_field(sK4)))),sK4)
| ~ in(unordered_pair(singleton(sK0(sK4,relation_field(sK4))),unordered_pair(sK0(sK4,relation_field(sK4)),sK1(sK4,relation_field(sK4)))),sK4) ),
inference(instantiation,[status(thm)],[c_4472]) ).
tcf(c_5091,plain,
transitive(sK4),
inference(global_subsumption_just,[status(thm)],[c_5007,c_73,c_615,c_627,c_639,c_5087]) ).
tcf(c_5937,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(iPr_def_10,unordered_pair(sK5,sK7)),X0)
| ~ relation(X0)
| ~ in(iPr_def_14,X0)
| ~ in(sK6,X1)
| ~ in(sK7,X1)
| ~ in(sK5,X1)
| ~ is_transitive_in(X0,X1)
| ~ in(unordered_pair(iPr_def_15,iPr_def_16),X0) ),
inference(superposition,[status(thm)],[c_2774,c_4851]) ).
tcf(c_5938,plain,
! [X0: $i,X1: $i] :
( in(iPr_def_12,X0)
| ~ relation(X0)
| ~ in(iPr_def_17,X0)
| ~ in(iPr_def_14,X0)
| ~ in(sK6,X1)
| ~ in(sK7,X1)
| ~ in(sK5,X1)
| ~ is_transitive_in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_5937,c_2769,c_2770,c_2775]) ).
tcf(c_5972,plain,
! [X0: $i] :
( in(iPr_def_12,X0)
| ~ relation(X0)
| ~ transitive(X0)
| ~ in(iPr_def_17,X0)
| ~ in(iPr_def_14,X0)
| ~ in(sK6,relation_field(X0))
| ~ in(sK7,relation_field(X0))
| ~ in(sK5,relation_field(X0)) ),
inference(superposition,[status(thm)],[c_54,c_5938]) ).
tcf(c_5999,plain,
( in(iPr_def_12,sK4)
| ~ relation(sK4)
| ~ transitive(sK4)
| ~ in(iPr_def_17,sK4)
| ~ in(iPr_def_14,sK4)
| ~ in(sK6,relation_field(sK4))
| ~ in(sK7,relation_field(sK4))
| ~ in(sK5,relation_field(sK4)) ),
inference(instantiation,[status(thm)],[c_5972]) ).
tcf(c_6000,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5999,c_5091,c_3507,c_3466,c_3465,c_2779,c_2778,c_2777,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU240+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 13:27:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 3.15/1.27 % SZS status Started for theBenchmark.p
% 3.15/1.27 % SZS status Theorem for theBenchmark.p
% 3.15/1.27
% 3.15/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.15/1.27
% 3.15/1.27 % ------ iProver source info
% 3.15/1.27
% 3.15/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.15/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.15/1.27 % git: non_committed_changes: false
% 3.15/1.27
% 3.15/1.27 % ------ Parsing...
% 3.15/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.15/1.27
% 3.15/1.27 % ------ Preprocessing... sup_sim: 11 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 3.15/1.27
% 3.15/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.15/1.27
% 3.15/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.15/1.27 % ------ Proving...
% 3.15/1.27 % ------ Problem Properties
% 3.15/1.27
% 3.15/1.27 %
% 3.15/1.27 % clauses 44
% 3.15/1.27 % conjectures 1
% 3.15/1.27 % EPR 15
% 3.15/1.27 % Horn 37
% 3.15/1.27 % unary 21
% 3.15/1.27 % binary 10
% 3.15/1.27 % lits 86
% 3.15/1.27 % lits eq 15
% 3.15/1.27 % fd_pure 0
% 3.15/1.27 % fd_pseudo 0
% 3.15/1.27 % fd_cond 1
% 3.15/1.27 % fd_pseudo_cond 1
% 3.15/1.27 % AC symbols 0
% 3.15/1.27
% 3.15/1.27 % ------ Schedule dynamic 5 is on
% 3.15/1.27
% 3.15/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.15/1.27
% 3.15/1.27
% 3.15/1.27 % ------
% 3.15/1.27 % Current options:
% 3.15/1.27 % ------
% 3.15/1.27
% 3.15/1.27
% 3.15/1.27 %
% 3.15/1.27
% 3.15/1.27 % ------ Proving...
% 3.15/1.27 %
% 3.15/1.27
% 3.15/1.27 % SZS status Theorem for theBenchmark.p
% 3.15/1.27
% 3.15/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.15/1.27
% 3.15/1.27
%------------------------------------------------------------------------------