%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU197+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:55:51 PM UTC 2026
% Result : Theorem 2.69s 1.18s
% Output : CNFRefutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 102 ( 14 unt; 3 def)
% Number of atoms : 453 ( 36 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 506 ( 218 ~; 227 |; 44 &)
% ( 10 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 243 ( 0 sgn 220 !; 23 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_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/sandbox/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/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f12,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f35,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,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(f37,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f41,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<~> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f49,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ( in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X1)
& in(sK1(X0,X1,X2),X0) ) )
& ( ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X1)
| ~ in(sK1(X0,X1,X2),X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X4,sK1(X0,X1,X2))],[f50]) ).
fof(f52,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,[],[f36]) ).
fof(f53,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,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK4(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK2(X0,X1),X1)
| in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0) )
& ( ~ in(sK2(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK2(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X4,sK3(X0,X1)),skolemize(X7,sK4(X0,X5))],[f53]) ).
fof(f60,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f61,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1) ) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
( relation(sK12)
& ( in(sK10,relation_rng(relation_rng_restriction(sK11,sK12)))
| ( in(sK10,relation_rng(sK12))
& in(sK10,sK11) ) )
& ( ~ in(sK10,relation_rng(relation_rng_restriction(sK11,sK12)))
| ~ in(sK10,relation_rng(sK12))
| ~ in(sK10,sK11) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f61]) ).
fof(f65,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f66,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(ordered_pair(X5,X6),X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f67,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(X6,X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f68,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f72,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK4(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f73,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f76,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f77,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f94,plain,
relation(sK12),
inference(cnf_transformation,[],[f62]) ).
fof(f95,plain,
( in(sK10,relation_rng(relation_rng_restriction(sK11,sK12)))
| in(sK10,relation_rng(sK12)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f96,plain,
( in(sK10,relation_rng(relation_rng_restriction(sK11,sK12)))
| in(sK10,sK11) ),
inference(cnf_transformation,[],[f62]) ).
fof(f97,plain,
( ~ in(sK10,relation_rng(relation_rng_restriction(sK11,sK12)))
| ~ in(sK10,relation_rng(sK12))
| ~ in(sK10,sK11) ),
inference(cnf_transformation,[],[f62]) ).
fof(f106,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| ~ in(X6,X0)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2) ),
inference(definition_unfolding,[],[f68,f76,f76]) ).
fof(f107,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| in(X6,X0) ),
inference(definition_unfolding,[],[f67,f76]) ).
fof(f108,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1) ),
inference(definition_unfolding,[],[f66,f76,f76]) ).
fof(f111,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,[],[f73,f76]) ).
fof(f112,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK4(X0,X5),X5),singleton(sK4(X0,X5))),X0) ),
inference(definition_unfolding,[],[f72,f76]) ).
fof(f114,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
| ~ in(X6,X0)
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1)) ),
inference(equality_resolution,[],[f106]) ).
fof(f115,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| in(X6,X0) ),
inference(equality_resolution,[],[f107]) ).
fof(f116,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1) ),
inference(equality_resolution,[],[f108]) ).
fof(f117,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f111]) ).
fof(f118,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK4(X0,X5),X5),singleton(sK4(X0,X5))),X0) ),
inference(equality_resolution,[],[f112]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f65]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ relation(relation_rng_restriction(X3,X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ relation(X3)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X3)
| ~ relation(X3)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f116]) ).
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,[],[f117]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK4(X1,X0),X0),singleton(sK4(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_79,negated_conjecture,
( ~ in(sK10,sK11)
| ~ in(sK10,relation_rng(sK12))
| ~ in(sK10,relation_rng(relation_rng_restriction(sK11,sK12))) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_80,negated_conjecture,
( in(sK10,sK11)
| in(sK10,relation_rng(relation_rng_restriction(sK11,sK12))) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_81,negated_conjecture,
( in(sK10,relation_rng(sK12))
| in(sK10,relation_rng(relation_rng_restriction(sK11,sK12))) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_82,negated_conjecture,
relation(sK12),
inference(cnf_transformation,[],[f94]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_62]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_62]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_55,c_62]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_60,c_51]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_rng_restriction(X2,X3)) ),
inference(demodulation,[status(thm)],[c_155,c_51]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK4(X1,X0)),unordered_pair(X0,sK4(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(demodulation,[status(thm)],[c_61,c_51]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_rng_restriction(X2,X3)) ),
inference(demodulation,[status(thm)],[c_156,c_51]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_157,c_51]) ).
tcf(c_821,definition,
iPr_def_10 = relation_rng_restriction(sK11,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_822,definition,
iPr_def_11 = relation_rng(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_823,definition,
iPr_def_12 = relation_rng(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_824,negated_conjecture,
relation(sK12),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_825,negated_conjecture,
( in(sK10,iPr_def_12)
| in(sK10,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_81,c_823,c_821,c_822]) ).
tcf(c_826,negated_conjecture,
( in(sK10,iPr_def_11)
| in(sK10,sK11) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_827,negated_conjecture,
( ~ in(sK10,iPr_def_12)
| ~ in(sK10,iPr_def_11)
| ~ in(sK10,sK11) ),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_1346,plain,
! [X0: $i,X1: $i] :
( in(X1,sK11)
| ~ relation(sK12)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_821,c_360]) ).
tcf(c_1347,plain,
! [X0: $i,X1: $i] :
( in(X1,sK11)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1346,c_824]) ).
tcf(c_1355,plain,
( relation(iPr_def_10)
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_821,c_62]) ).
tcf(c_1356,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1355,c_824]) ).
tcf(c_1461,plain,
! [X0: $i,X1: $i] :
( in(X1,sK11)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_51,c_1347]) ).
tcf(c_1464,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2) ),
inference(superposition,[status(thm)],[c_51,c_350]) ).
tcf(c_1508,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK12)
| ~ relation(sK12)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_821,c_380]) ).
tcf(c_1509,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK12)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1508,c_824]) ).
tcf(c_1536,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK12)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_51,c_1509]) ).
tcf(c_1548,plain,
! [X0: $i] :
( in(X0,sK11)
| ~ relation(iPr_def_10)
| ~ in(X0,relation_rng(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_370,c_1461]) ).
tcf(c_1551,plain,
! [X0: $i] :
( in(X0,sK11)
| ~ relation(iPr_def_10)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_1548,c_822]) ).
tcf(c_1552,plain,
! [X0: $i] :
( in(X0,sK11)
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1551,c_1356]) ).
tcf(c_1560,plain,
in(sK10,sK11),
inference(backward_subsumption_resolution,[status(thm)],[c_826,c_1552]) ).
tcf(c_1593,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ relation(sK12)
| ~ in(X1,sK11)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK12) ),
inference(superposition,[status(thm)],[c_821,c_403]) ).
tcf(c_1603,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ in(X1,sK11)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1593,c_824]) ).
tcf(c_1930,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ in(X1,sK11)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK12) ),
inference(superposition,[status(thm)],[c_51,c_1603]) ).
tcf(c_2320,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK4(iPr_def_10,X0)),unordered_pair(sK4(iPr_def_10,X0),X0)),sK12)
| ~ relation(iPr_def_10)
| ~ in(X0,relation_rng(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_370,c_1536]) ).
tcf(c_2324,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK4(iPr_def_10,X0)),unordered_pair(sK4(iPr_def_10,X0),X0)),sK12)
| ~ relation(iPr_def_10)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_2320,c_822]) ).
tcf(c_2325,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK4(iPr_def_10,X0)),unordered_pair(sK4(iPr_def_10,X0),X0)),sK12)
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2324,c_1356]) ).
tcf(c_2603,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK4(iPr_def_10,X0)),unordered_pair(X0,sK4(iPr_def_10,X0))),sK12)
| ~ in(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_2325,c_51]) ).
tcf(c_2700,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK4(sK12,X0)),unordered_pair(sK4(sK12,X0),X0)),iPr_def_10)
| ~ relation(sK12)
| ~ in(X0,sK11)
| ~ in(X0,relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_370,c_1930]) ).
tcf(c_2708,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK4(sK12,X0)),unordered_pair(sK4(sK12,X0),X0)),iPr_def_10)
| ~ relation(sK12)
| ~ in(X0,iPr_def_12)
| ~ in(X0,sK11) ),
inference(light_normalisation,[status(thm)],[c_2700,c_823]) ).
tcf(c_2709,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK4(sK12,X0)),unordered_pair(sK4(sK12,X0),X0)),iPr_def_10)
| ~ in(X0,iPr_def_12)
| ~ in(X0,sK11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2708,c_824]) ).
tcf(c_2767,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK4(sK12,X0)),unordered_pair(X0,sK4(sK12,X0))),iPr_def_10)
| ~ in(X0,iPr_def_12)
| ~ in(X0,sK11) ),
inference(demodulation,[status(thm)],[c_2709,c_51]) ).
tcf(c_3071,plain,
! [X0: $i] :
( in(X0,relation_rng(sK12))
| ~ relation(sK12)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2603,c_1464]) ).
tcf(c_3072,plain,
! [X0: $i] :
( in(X0,relation_rng(iPr_def_10))
| ~ relation(iPr_def_10)
| ~ in(X0,iPr_def_12)
| ~ in(X0,sK11) ),
inference(superposition,[status(thm)],[c_2767,c_1464]) ).
tcf(c_3077,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ relation(sK12)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_3071,c_823]) ).
tcf(c_3078,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3077,c_824]) ).
tcf(c_3081,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ relation(iPr_def_10)
| ~ in(X0,iPr_def_12)
| ~ in(X0,sK11) ),
inference(light_normalisation,[status(thm)],[c_3072,c_822]) ).
tcf(c_3082,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_12)
| ~ in(X0,sK11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3081,c_1356]) ).
tcf(c_3106,plain,
( in(sK10,iPr_def_12)
| ~ in(sK10,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_3078]) ).
tcf(c_3107,plain,
( in(sK10,iPr_def_11)
| ~ in(sK10,iPr_def_12)
| ~ in(sK10,sK11) ),
inference(instantiation,[status(thm)],[c_3082]) ).
tcf(c_3113,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3107,c_3106,c_1560,c_827,c_825]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU197+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 13:03:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 2.69/1.18 % SZS status Started for theBenchmark.p
% 2.69/1.18 % SZS status Theorem for theBenchmark.p
% 2.69/1.18
% 2.69/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.69/1.18
% 2.69/1.18 % ------ iProver source info
% 2.69/1.18
% 2.69/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.69/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.69/1.18 % git: non_committed_changes: false
% 2.69/1.18
% 2.69/1.18 % ------ Parsing...
% 2.69/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.69/1.18
% 2.69/1.18 % ------ Preprocessing... sup_sim: 10 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 %
% 2.69/1.18
% 2.69/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.69/1.18
% 2.69/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.69/1.18 % ------ Proving...
% 2.69/1.18 % ------ Problem Properties
% 2.69/1.18
% 2.69/1.18 %
% 2.69/1.18 % clauses 38
% 2.69/1.18 % conjectures 4
% 2.69/1.18 % EPR 17
% 2.69/1.18 % Horn 32
% 2.69/1.18 % unary 15
% 2.69/1.18 % binary 10
% 2.69/1.18 % lits 84
% 2.69/1.18 % lits eq 11
% 2.69/1.18 % fd_pure 0
% 2.69/1.18 % fd_pseudo 0
% 2.69/1.18 % fd_cond 1
% 2.69/1.18 % fd_pseudo_cond 6
% 2.69/1.18 % AC symbols 0
% 2.69/1.18
% 2.69/1.18 % ------ Schedule dynamic 5 is on
% 2.69/1.18
% 2.69/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.69/1.18
% 2.69/1.18
% 2.69/1.18 % ------
% 2.69/1.18 % Current options:
% 2.69/1.18 % ------
% 2.69/1.18
% 2.69/1.18
% 2.69/1.18 %
% 2.69/1.18
% 2.69/1.18 % ------ Proving...
% 2.69/1.18 %
% 2.69/1.18
% 2.69/1.18 % SZS status Theorem for theBenchmark.p
% 2.69/1.18
% 2.69/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.69/1.18
% 2.69/1.18
%------------------------------------------------------------------------------