%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU207+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 : n010.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 02:55:54 PM UTC 2026
% Result : Theorem 19.07s 5.46s
% Output : CNFRefutation 19.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 74 ( 9 unt; 0 def)
% Number of atoms : 384 ( 53 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 533 ( 223 ~; 240 |; 48 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 8 ( 2 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 : 18 ( 18 usr; 2 con; 0-4 aty)
% Number of variables : 237 ( 0 sgn 209 !; 28 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f6,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(f7,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(f13,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f30,conjecture,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f40,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f42,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,[],[f7]) ).
fof(f43,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f44,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f43]) ).
fof(f52,plain,
? [X0] :
( relation(X0)
& ? [X1] :
( relation(X1)
& relation_rng(relation_composition(X0,X1)) != relation_image(X1,relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f61,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK2(X0,X1,X6),X1)
& in(ordered_pair(sK2(X0,X1,X6),X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK5(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK3(X0,X1),X1)
| in(ordered_pair(sK4(X0,X1),sK3(X0,X1)),X0) )
& ( ~ in(sK3(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK3(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f64]) ).
fof(f66,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,[],[f42]) ).
fof(f67,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,[],[f66]) ).
fof(f68,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(sK9(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK9(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(sK6(X0,X1,X2),sK7(X0,X1,X2)),X2)
| ( in(ordered_pair(sK8(X0,X1,X2),sK7(X0,X1,X2)),X1)
& in(ordered_pair(sK6(X0,X1,X2),sK8(X0,X1,X2)),X0) ) )
& ( ~ in(ordered_pair(sK6(X0,X1,X2),sK7(X0,X1,X2)),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,sK7(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK6(X0,X1,X2),X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X4,sK7(X0,X1,X2)),skolemize(X6,sK8(X0,X1,X2)),skolemize(X10,sK9(X0,X1,X7,X8))],[f67]) ).
fof(f74,plain,
( relation(sK15)
& relation(sK16)
& relation_rng(relation_composition(sK15,sK16)) != relation_image(sK16,relation_rng(sK15)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X0,sK15),skolemize(X1,sK16)],[f52]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f62]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f62]) ).
fof(f85,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f62]) ).
fof(f86,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK5(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f87,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f90,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f91,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(sK9(X0,X1,X7,X8),X8),X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f92,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,sK9(X0,X1,X7,X8)),X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f93,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,[],[f68]) ).
fof(f97,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f118,plain,
relation(sK15),
inference(cnf_transformation,[],[f74]) ).
fof(f119,plain,
relation(sK16),
inference(cnf_transformation,[],[f74]) ).
fof(f120,plain,
relation_rng(relation_composition(sK15,sK16)) != relation_image(sK16,relation_rng(sK15)),
inference(cnf_transformation,[],[f74]) ).
fof(f128,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(X4,sK0(X0,X1,X2)),singleton(X4)),X0)
| relation_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f85,f90]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),singleton(sK1(X0,X1,X2))),X0)
| relation_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f84,f90]) ).
fof(f134,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f87,f90]) ).
fof(f135,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK5(X0,X5),X5),singleton(sK5(X0,X5))),X0) ),
inference(definition_unfolding,[],[f86,f90]) ).
fof(f139,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,[],[f93,f90,f90,f90]) ).
fof(f140,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,sK9(X0,X1,X7,X8)),singleton(X7)),X0) ),
inference(definition_unfolding,[],[f92,f90,f90]) ).
fof(f141,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(sK9(X0,X1,X7,X8),X8),singleton(sK9(X0,X1,X7,X8))),X1) ),
inference(definition_unfolding,[],[f91,f90,f90]) ).
fof(f146,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f134]) ).
fof(f147,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK5(X0,X5),X5),singleton(sK5(X0,X5))),X0) ),
inference(equality_resolution,[],[f135]) ).
fof(f148,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,[],[f139]) ).
fof(f149,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,sK9(X0,X1,X7,X8)),singleton(X7)),X0) ),
inference(equality_resolution,[],[f140]) ).
fof(f150,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(sK9(X0,X1,X7,X8),X8),singleton(sK9(X0,X1,X7,X8))),X1) ),
inference(equality_resolution,[],[f141]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,X2) = X3 )
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(sK0(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(X0,sK0(X1,X2,X3)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),singleton(sK1(X0,X1,X2))),X0)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK5(X1,X0),X0),singleton(sK5(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_65,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,[],[f148]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,sK9(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,[],[f149]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK9(X2,X3,X0,X1),X1),singleton(sK9(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,[],[f150]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_89,negated_conjecture,
relation_image(sK16,relation_rng(sK15)) != relation_rng(relation_composition(sK15,sK16)),
inference(cnf_transformation,[],[f120]) ).
tcf(c_90,negated_conjecture,
relation(sK16),
inference(cnf_transformation,[],[f119]) ).
tcf(c_91,negated_conjecture,
relation(sK15),
inference(cnf_transformation,[],[f118]) ).
tcf(c_295,plain,
( in(sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))),relation_rng(relation_composition(sK15,sK16)))
| in(unordered_pair(unordered_pair(sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))))),sK16)
| ( relation_image(sK16,relation_rng(sK15)) = relation_rng(relation_composition(sK15,sK16)) )
| ~ relation(sK16) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_356,plain,
( in(unordered_pair(unordered_pair(sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))))),relation_composition(sK15,sK16))
| ~ relation(relation_composition(sK15,sK16))
| ~ in(sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))),relation_rng(relation_composition(sK15,sK16))) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_770,plain,
( in(unordered_pair(unordered_pair(sK5(sK15,sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK5(sK15,sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))))),sK15)
| ~ relation(sK15)
| ~ in(sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))),relation_rng(sK15)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_779,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(X0)),relation_composition(X1,sK16))
| ~ relation(sK16)
| ~ relation(X1)
| ~ relation(relation_composition(X1,sK16))
| ~ in(unordered_pair(unordered_pair(X0,sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(X0)),X1)
| ~ in(unordered_pair(unordered_pair(sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))))),sK16) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1109,plain,
( relation(relation_composition(sK15,sK16))
| ~ relation(sK16)
| ~ relation(sK15) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_1751,plain,
! [X0: $i,X1: $i] :
( ( relation_image(sK16,relation_rng(sK15)) = X1 )
| ~ relation(sK16)
| ~ in(X0,relation_rng(sK15))
| ~ in(sK0(sK16,relation_rng(sK15),X1),X1)
| ~ in(unordered_pair(unordered_pair(X0,sK0(sK16,relation_rng(sK15),X1)),singleton(X0)),sK16) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_3836,plain,
( in(unordered_pair(unordered_pair(sK9(sK15,sK16,sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK9(sK15,sK16,sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))))),sK16)
| ~ relation(sK16)
| ~ relation(sK15)
| ~ relation(relation_composition(sK15,sK16))
| ~ in(unordered_pair(unordered_pair(sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))))),relation_composition(sK15,sK16)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_3837,plain,
( in(unordered_pair(unordered_pair(sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK9(sK15,sK16,sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))))),singleton(sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))))),sK15)
| ~ relation(sK16)
| ~ relation(sK15)
| ~ relation(relation_composition(sK15,sK16))
| ~ in(unordered_pair(unordered_pair(sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))))),relation_composition(sK15,sK16)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_4320,plain,
( in(unordered_pair(unordered_pair(sK5(sK15,sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK5(sK15,sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))))),relation_composition(sK15,sK16))
| ~ relation(sK16)
| ~ relation(sK15)
| ~ relation(relation_composition(sK15,sK16))
| ~ in(unordered_pair(unordered_pair(sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))))),sK16)
| ~ in(unordered_pair(unordered_pair(sK5(sK15,sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK5(sK15,sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))))),sK15) ),
inference(instantiation,[status(thm)],[c_779]) ).
tcf(c_5025,plain,
( in(sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))),relation_rng(sK15))
| in(sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))),relation_rng(relation_composition(sK15,sK16)))
| ~ relation(sK16) ),
inference(resolution,[status(thm)],[c_54,c_89]) ).
tcf(c_9499,plain,
( in(sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))),relation_rng(relation_composition(sK15,sK16)))
| ~ relation(relation_composition(sK15,sK16))
| ~ in(unordered_pair(unordered_pair(sK5(sK15,sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK5(sK15,sK1(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))))),relation_composition(sK15,sK16)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_22171,plain,
( ( relation_image(sK16,relation_rng(sK15)) = relation_rng(relation_composition(sK15,sK16)) )
| ~ relation(sK16)
| ~ in(sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))),relation_rng(relation_composition(sK15,sK16)))
| ~ in(sK9(sK15,sK16,sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),relation_rng(sK15))
| ~ in(unordered_pair(unordered_pair(sK9(sK15,sK16,sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),singleton(sK9(sK15,sK16,sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))))),sK16) ),
inference(instantiation,[status(thm)],[c_1751]) ).
tcf(c_22175,plain,
( in(sK9(sK15,sK16,sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),relation_rng(sK15))
| ~ relation(sK15)
| ~ in(unordered_pair(unordered_pair(sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK9(sK15,sK16,sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16))))),singleton(sK5(relation_composition(sK15,sK16),sK0(sK16,relation_rng(sK15),relation_rng(relation_composition(sK15,sK16)))))),sK15) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_28096,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_22175,c_22171,c_9499,c_5025,c_4320,c_3836,c_3837,c_1109,c_770,c_356,c_295,c_89,c_90,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU207+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/1.07 % Computer : n010.cluster.edu
% 0.18/1.07 % Model : x86_64 x86_64
% 0.18/1.07 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/1.07 % Memory : 8046.5625MB
% 0.18/1.07 % OS : Linux 6.8.0-71-generic
% 0.18/1.07 % CPULimit : 300
% 0.18/1.07 % WCLimit : 300
% 0.18/1.07 % DateTime : Thu Sep 24 13:10:45 UTC 2026
% 0.18/1.08 % CPUTime :
% 0.18/1.08 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/1.13 Running first-order theorem proving
% 0.18/1.13 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
% 0.21/1.14
% 0.21/1.14 % ======== iProver multi-core TPTP/SMT =========
% 0.21/1.14
% 0.21/1.15 % Detected problem language: tptp
% 0.21/1.16 % Proving...
% 19.07/5.46 % SZS status Started for theBenchmark.p
% 19.07/5.46 % SZS status Theorem for theBenchmark.p
% 19.07/5.46
% 19.07/5.46 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 19.07/5.46
% 19.07/5.46 % ------ iProver source info
% 19.07/5.46
% 19.07/5.46 % git: date: 2026-07-19 20:42:38 +0200
% 19.07/5.46 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 19.07/5.46 % git: non_committed_changes: false
% 19.07/5.46
% 19.07/5.46 % ------ Parsing...
% 19.07/5.46 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 19.07/5.46
% 19.07/5.46 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 19.07/5.46
% 19.07/5.46 % ------ Preprocessing...%
% 19.07/5.46
% 19.07/5.46 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 19.07/5.46 % ------ Proving...
% 19.07/5.46 % ------ Problem Properties
% 19.07/5.46
% 19.07/5.46 %
% 19.07/5.46 % clauses 49
% 19.07/5.46 % conjectures 10
% 19.07/5.46 % EPR 17
% 19.07/5.46 % Horn 42
% 19.07/5.46 % unary 16
% 19.07/5.46 % binary 7
% 19.07/5.46 % lits 132
% 19.07/5.46 % lits eq 14
% 19.07/5.46 % fd_pure 0
% 19.07/5.46 % fd_pseudo 0
% 19.07/5.46 % fd_cond 1
% 19.07/5.46 % fd_pseudo_cond 11
% 19.07/5.46 % AC symbols 0
% 19.07/5.46
% 19.07/5.46 % ------ Input Options Time Limit: Unbounded
% 19.07/5.46
% 19.07/5.46
% 19.07/5.46 % ------
% 19.07/5.46 % Current options:
% 19.07/5.46 % ------
% 19.07/5.46
% 19.07/5.46
% 19.07/5.46 %
% 19.07/5.46
% 19.07/5.46 % ------ Proving...
% 19.07/5.46 %
% 19.07/5.46
% 19.07/5.46 % SZS status Theorem for theBenchmark.p
% 19.07/5.46
% 19.07/5.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 19.07/5.47
% 19.07/5.47
%------------------------------------------------------------------------------