%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU191+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 : n017.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 02:55:49 PM UTC 2026
% Result : Theorem 3.52s 1.18s
% Output : CNFRefutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 99 ( 17 unt; 0 def)
% Number of atoms : 421 ( 65 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 563 ( 241 ~; 251 |; 53 &)
% ( 10 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 267 ( 0 sgn 239 !; 28 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f5,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(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f12,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f29,conjecture,
! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f35,plain,
! [X0,X1] :
( ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f38,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f37]) ).
fof(f47,plain,
? [X0,X1,X2,X3] :
( relation(X3)
& ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<~> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f50,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( X2 != X3
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f51,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( X2 != X3
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| ( X4 = X5
& in(X4,X0) ) )
& ( X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| ( X4 = X5
& in(X4,X0) ) )
& ( X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ( ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ( sK0(X0,X1) = sK1(X0,X1)
& in(sK0(X0,X1),X0) ) )
& ( ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f52]) ).
fof(f54,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X6] :
( in(ordered_pair(X6,X4),X1)
& in(ordered_pair(X3,X6),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(rectify,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ( in(ordered_pair(sK5(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK5(X0,X1,X7,X8)),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ( ( in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2)
| ( in(ordered_pair(sK4(X0,X1,X2),sK3(X0,X1,X2)),X1)
& in(ordered_pair(sK2(X0,X1,X2),sK4(X0,X1,X2)),X0) ) )
& ( ~ in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,sK3(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK2(X0,X1,X2),X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X4,sK3(X0,X1,X2)),skolemize(X6,sK4(X0,X1,X2)),skolemize(X10,sK5(X0,X1,X7,X8))],[f55]) ).
fof(f62,plain,
? [X0,X1,X2,X3] :
( relation(X3)
& ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f63,plain,
? [X0,X1,X2,X3] :
( relation(X3)
& ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2) ) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
( relation(sK14)
& ( in(ordered_pair(sK11,sK12),relation_composition(identity_relation(sK13),sK14))
| ( in(ordered_pair(sK11,sK12),sK14)
& in(sK11,sK13) ) )
& ( ~ in(ordered_pair(sK11,sK12),relation_composition(identity_relation(sK13),sK14))
| ~ in(ordered_pair(sK11,sK12),sK14)
| ~ in(sK11,sK13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14)],[f63]) ).
fof(f67,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f68,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| X4 = X5 ),
inference(cnf_transformation,[],[f53]) ).
fof(f69,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f70,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f74,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f75,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X7,X8),X2)
| in(ordered_pair(sK5(X0,X1,X7,X8),X8),X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f76,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X7,X8),X2)
| in(ordered_pair(X7,sK5(X0,X1,X7,X8)),X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f77,plain,
! [X2,X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0)
| in(ordered_pair(X7,X8),X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f81,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f82,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f103,plain,
relation(sK14),
inference(cnf_transformation,[],[f64]) ).
fof(f104,plain,
( in(ordered_pair(sK11,sK12),relation_composition(identity_relation(sK13),sK14))
| in(ordered_pair(sK11,sK12),sK14) ),
inference(cnf_transformation,[],[f64]) ).
fof(f105,plain,
( in(ordered_pair(sK11,sK12),relation_composition(identity_relation(sK13),sK14))
| in(sK11,sK13) ),
inference(cnf_transformation,[],[f64]) ).
fof(f106,plain,
( ~ in(ordered_pair(sK11,sK12),relation_composition(identity_relation(sK13),sK14))
| ~ in(ordered_pair(sK11,sK12),sK14)
| ~ in(sK11,sK13) ),
inference(cnf_transformation,[],[f64]) ).
fof(f112,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| X4 != X5
| ~ in(X4,X0)
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1) ),
inference(definition_unfolding,[],[f70,f74]) ).
fof(f113,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| in(X4,X0) ),
inference(definition_unfolding,[],[f69,f74]) ).
fof(f114,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| X4 = X5 ),
inference(definition_unfolding,[],[f68,f74]) ).
fof(f118,plain,
! [X2,X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2) ),
inference(definition_unfolding,[],[f77,f74,f74,f74]) ).
fof(f119,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
| in(unordered_pair(unordered_pair(X7,sK5(X0,X1,X7,X8)),singleton(X7)),X0) ),
inference(definition_unfolding,[],[f76,f74,f74]) ).
fof(f120,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
| in(unordered_pair(unordered_pair(sK5(X0,X1,X7,X8),X8),singleton(sK5(X0,X1,X7,X8))),X1) ),
inference(definition_unfolding,[],[f75,f74,f74]) ).
fof(f122,plain,
( ~ in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14))
| ~ in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK14)
| ~ in(sK11,sK13) ),
inference(definition_unfolding,[],[f106,f74,f74]) ).
fof(f123,plain,
( in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14))
| in(sK11,sK13) ),
inference(definition_unfolding,[],[f105,f74]) ).
fof(f124,plain,
( in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14))
| in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK14) ),
inference(definition_unfolding,[],[f104,f74,f74]) ).
fof(f125,plain,
! [X0,X1,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X5,X0)
| in(unordered_pair(unordered_pair(X5,X5),singleton(X5)),X1) ),
inference(equality_resolution,[],[f112]) ).
fof(f126,plain,
! [X0,X5] :
( ~ relation(identity_relation(X0))
| ~ in(X5,X0)
| in(unordered_pair(unordered_pair(X5,X5),singleton(X5)),identity_relation(X0)) ),
inference(equality_resolution,[],[f125]) ).
fof(f127,plain,
! [X0,X4,X5] :
( ~ relation(identity_relation(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),identity_relation(X0))
| in(X4,X0) ),
inference(equality_resolution,[],[f113]) ).
fof(f128,plain,
! [X0,X4,X5] :
( ~ relation(identity_relation(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),identity_relation(X0))
| X4 = X5 ),
inference(equality_resolution,[],[f114]) ).
fof(f129,plain,
! [X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f118]) ).
fof(f130,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(X7,sK5(X0,X1,X7,X8)),singleton(X7)),X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f131,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(sK5(X0,X1,X7,X8),X8),singleton(sK5(X0,X1,X7,X8))),X1) ),
inference(equality_resolution,[],[f120]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f67]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(identity_relation(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2)) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ relation(identity_relation(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2)) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,sK5(X2,X3,X0,X1)),singleton(X0)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK5(X2,X3,X0,X1),X1),singleton(sK5(X2,X3,X0,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_65,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f82]) ).
tcf(c_86,negated_conjecture,
( ~ in(sK11,sK13)
| ~ in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK14)
| ~ in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14)) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_87,negated_conjecture,
( in(sK11,sK13)
| in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14)) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_88,negated_conjecture,
( in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK14)
| in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),relation_composition(identity_relation(sK13),sK14)) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_89,negated_conjecture,
relation(sK14),
inference(cnf_transformation,[],[f103]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_55,c_65]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_65]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_65]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,sK5(X2,X3,X0,X1)),singleton(X0)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_62,c_64]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK5(X2,X3,X0,X1),X1),singleton(sK5(X2,X3,X0,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_64]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_61,c_64]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),identity_relation(X2)) ),
inference(demodulation,[status(thm)],[c_136,c_51]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_135,c_51]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),identity_relation(X2)) ),
inference(demodulation,[status(thm)],[c_137,c_51]) ).
tcf(c_339,plain,
( in(sK11,sK13)
| in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14)) ),
inference(demodulation,[status(thm)],[c_87,c_51]) ).
tcf(c_340,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK14)
| in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14)) ),
inference(demodulation,[status(thm)],[c_88,c_51]) ).
tcf(c_341,plain,
( ~ in(sK11,sK13)
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK14)
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14)) ),
inference(demodulation,[status(thm)],[c_86,c_51]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3,X0,X1))),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(X2,X3)) ),
inference(demodulation,[status(thm)],[c_204,c_51]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(sK5(X2,X3,X0,X1)),unordered_pair(X1,sK5(X2,X3,X0,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(X2,X3)) ),
inference(demodulation,[status(thm)],[c_205,c_51]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_206,c_51]) ).
tcf(c_1110,plain,
! [X0: $i] :
( in(sK11,sK13)
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),identity_relation(sK13)) ),
inference(instantiation,[status(thm)],[c_336]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i] :
( in(sK11,sK13)
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK5(identity_relation(sK13),X0,sK11,X1))),identity_relation(sK13)) ),
inference(instantiation,[status(thm)],[c_1110]) ).
tcf(c_1142,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK11)),identity_relation(sK13))
| ~ in(sK11,sK13) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_1195,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14))
| ~ relation(sK14)
| ~ relation(identity_relation(sK13))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK12)),sK14)
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),identity_relation(sK13)) ),
inference(instantiation,[status(thm)],[c_346]) ).
tcf(c_1196,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14))
| ~ relation(sK14)
| ~ relation(identity_relation(sK13))
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK14)
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK11)),identity_relation(sK13)) ),
inference(instantiation,[status(thm)],[c_1195]) ).
tcf(c_1200,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK5(identity_relation(sK13),X1,sK11,X0))),identity_relation(sK13))
| ~ relation(X1)
| ~ relation(identity_relation(sK13))
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),relation_composition(identity_relation(sK13),X1)) ),
inference(instantiation,[status(thm)],[c_343]) ).
tcf(c_1399,plain,
relation(identity_relation(sK13)),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1503,plain,
in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14)),
inference(global_subsumption_just,[status(thm)],[c_339,c_89,c_339,c_340,c_1142,c_1196,c_1399]) ).
tcf(c_1545,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK5(identity_relation(sK13),sK14,sK11,sK12))),identity_relation(sK13))
| ~ relation(sK14)
| ~ relation(identity_relation(sK13))
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14)) ),
inference(instantiation,[status(thm)],[c_1200]) ).
tcf(c_1859,plain,
( in(sK11,sK13)
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK5(identity_relation(sK13),sK14,sK11,sK12))),identity_relation(sK13)) ),
inference(instantiation,[status(thm)],[c_1124]) ).
tcf(c_6805,plain,
in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14)),
inference(global_subsumption_just,[status(thm)],[c_340,c_1503]) ).
tcf(c_7026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(identity_relation(X2),X3,X0,X1) = X0 )
| ~ relation(X3)
| ~ relation(identity_relation(X2))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(identity_relation(X2),X3)) ),
inference(superposition,[status(thm)],[c_343,c_338]) ).
tcf(c_7603,plain,
( ( sK5(identity_relation(sK13),sK14,sK11,sK12) = sK11 )
| ~ relation(sK14)
| ~ relation(identity_relation(sK13)) ),
inference(superposition,[status(thm)],[c_6805,c_7026]) ).
tcf(c_7714,plain,
sK5(identity_relation(sK13),sK14,sK11,sK12) = sK11,
inference(global_subsumption_just,[status(thm)],[c_7603,c_89,c_1399,c_7603]) ).
tcf(c_7717,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK12,sK11)),sK14)
| ~ relation(sK14)
| ~ relation(identity_relation(sK13))
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),relation_composition(identity_relation(sK13),sK14)) ),
inference(superposition,[status(thm)],[c_7714,c_345]) ).
tcf(c_7895,plain,
in(unordered_pair(singleton(sK11),unordered_pair(sK12,sK11)),sK14),
inference(global_subsumption_just,[status(thm)],[c_7717,c_89,c_1399,c_1503,c_7717]) ).
tcf(c_7897,plain,
in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK14),
inference(superposition,[status(thm)],[c_51,c_7895]) ).
tcf(c_7902,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7897,c_1859,c_1545,c_1503,c_1399,c_341,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU191+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.36 % Computer : n017.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Thu Sep 24 13:02:01 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.52/1.18 % SZS status Started for theBenchmark.p
% 3.52/1.18 % SZS status Theorem for theBenchmark.p
% 3.52/1.18
% 3.52/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.52/1.18
% 3.52/1.18 % ------ iProver source info
% 3.52/1.18
% 3.52/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.52/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.52/1.18 % git: non_committed_changes: false
% 3.52/1.18
% 3.52/1.18 % ------ Parsing...
% 3.52/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.52/1.18
% 3.52/1.18 % ------ Preprocessing... sup_sim: 15 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.52/1.18
% 3.52/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.52/1.18
% 3.52/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.52/1.18 % ------ Proving...
% 3.52/1.18 % ------ Problem Properties
% 3.52/1.18
% 3.52/1.18 %
% 3.52/1.18 % clauses 39
% 3.52/1.18 % conjectures 1
% 3.52/1.18 % EPR 14
% 3.52/1.18 % Horn 32
% 3.52/1.18 % unary 13
% 3.52/1.18 % binary 10
% 3.52/1.18 % lits 99
% 3.52/1.18 % lits eq 12
% 3.52/1.18 % fd_pure 0
% 3.52/1.18 % fd_pseudo 0
% 3.52/1.18 % fd_cond 1
% 3.52/1.18 % fd_pseudo_cond 8
% 3.52/1.18 % AC symbols 0
% 3.52/1.18
% 3.52/1.18 % ------ Input Options Time Limit: Unbounded
% 3.52/1.18
% 3.52/1.18
% 3.52/1.18 % ------
% 3.52/1.18 % Current options:
% 3.52/1.18 % ------
% 3.52/1.18
% 3.52/1.18
% 3.52/1.18 %
% 3.52/1.18
% 3.52/1.18 % ------ Proving...
% 3.52/1.18 %
% 3.52/1.18
% 3.52/1.18 % SZS status Theorem for theBenchmark.p
% 3.52/1.18
% 3.52/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.52/1.19
%------------------------------------------------------------------------------