%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU197+2 : 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 : n014.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 4.43s 1.37s
% Output : CNFRefutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 71 ( 8 unt; 0 def)
% Number of atoms : 320 ( 31 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 425 ( 176 ~; 183 |; 47 &)
% ( 10 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 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 : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 216 ( 0 sgn 193 !; 23 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,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(f28,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(f30,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(f61,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f112,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(f113,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)],[f112]) ).
fof(f124,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f172,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f208,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,[],[f10]) ).
fof(f216,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f234,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f61]) ).
fof(f271,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,[],[f113]) ).
fof(f283,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ),
inference(ennf_transformation,[],[f124]) ).
fof(f284,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ),
inference(flattening,[],[f283]) ).
fof(f358,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,[],[f208]) ).
fof(f359,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,[],[f358]) ).
fof(f360,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,[],[f359]) ).
fof(f361,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(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2)
| ( in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X1)
& in(sK5(X0,X1,X2),X0) ) )
& ( ~ in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X1)
| ~ in(sK5(X0,X1,X2),X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X4,sK5(X0,X1,X2))],[f360]) ).
fof(f412,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,[],[f216]) ).
fof(f413,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,[],[f412]) ).
fof(f414,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK37(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK35(X0,X1),X1)
| in(ordered_pair(sK36(X0,X1),sK35(X0,X1)),X0) )
& ( ~ in(sK35(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK35(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35,sK36,sK37]),skolemize(X2,sK35(X0,X1)),skolemize(X4,sK36(X0,X1)),skolemize(X7,sK37(X0,X5))],[f413]) ).
fof(f442,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,[],[f271]) ).
fof(f443,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,[],[f442]) ).
fof(f444,plain,
( relation(sK55)
& ( in(sK53,relation_rng(relation_rng_restriction(sK54,sK55)))
| ( in(sK53,relation_rng(sK55))
& in(sK53,sK54) ) )
& ( ~ in(sK53,relation_rng(relation_rng_restriction(sK54,sK55)))
| ~ in(sK53,relation_rng(sK55))
| ~ in(sK53,sK54) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55)],[f443]) ).
fof(f488,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,[],[f361]) ).
fof(f489,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,[],[f361]) ).
fof(f490,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,[],[f361]) ).
fof(f572,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK37(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f414]) ).
fof(f577,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f30]) ).
fof(f607,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f234]) ).
fof(f675,plain,
relation(sK55),
inference(cnf_transformation,[],[f444]) ).
fof(f676,plain,
( in(sK53,relation_rng(relation_rng_restriction(sK54,sK55)))
| in(sK53,relation_rng(sK55)) ),
inference(cnf_transformation,[],[f444]) ).
fof(f677,plain,
( in(sK53,relation_rng(relation_rng_restriction(sK54,sK55)))
| in(sK53,sK54) ),
inference(cnf_transformation,[],[f444]) ).
fof(f678,plain,
( ~ in(sK53,relation_rng(relation_rng_restriction(sK54,sK55)))
| ~ in(sK53,relation_rng(sK55))
| ~ in(sK53,sK54) ),
inference(cnf_transformation,[],[f444]) ).
fof(f692,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f284]) ).
fof(f761,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f172]) ).
fof(f790,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f577,f761]) ).
fof(f807,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| ~ in(X6,X0)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2) ),
inference(definition_unfolding,[],[f490,f790,f790]) ).
fof(f808,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(X6,X0) ),
inference(definition_unfolding,[],[f489,f790]) ).
fof(f809,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1) ),
inference(definition_unfolding,[],[f488,f790,f790]) ).
fof(f840,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK37(X0,X5),X5),unordered_pair(sK37(X0,X5),sK37(X0,X5))),X0) ),
inference(definition_unfolding,[],[f572,f790]) ).
fof(f877,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X1,relation_rng(X2)) ),
inference(definition_unfolding,[],[f692,f790]) ).
fof(f912,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| ~ in(X6,X0)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1)) ),
inference(equality_resolution,[],[f807]) ).
fof(f913,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1))
| in(X6,X0) ),
inference(equality_resolution,[],[f808]) ).
fof(f914,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1) ),
inference(equality_resolution,[],[f809]) ).
fof(f955,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK37(X0,X5),X5),unordered_pair(sK37(X0,X5),sK37(X0,X5))),X0) ),
inference(equality_resolution,[],[f840]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ relation(relation_rng_restriction(X3,X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f912]) ).
tcf(c_74,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),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f913]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ relation(X3)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f914]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK37(X1,X0),X0),unordered_pair(sK37(X1,X0),sK37(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f955]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f607]) ).
tcf(c_256,negated_conjecture,
( ~ in(sK53,sK54)
| ~ in(sK53,relation_rng(sK55))
| ~ in(sK53,relation_rng(relation_rng_restriction(sK54,sK55))) ),
inference(cnf_transformation,[],[f678]) ).
tcf(c_257,negated_conjecture,
( in(sK53,sK54)
| in(sK53,relation_rng(relation_rng_restriction(sK54,sK55))) ),
inference(cnf_transformation,[],[f677]) ).
tcf(c_258,negated_conjecture,
( in(sK53,relation_rng(sK55))
| in(sK53,relation_rng(relation_rng_restriction(sK54,sK55))) ),
inference(cnf_transformation,[],[f676]) ).
tcf(c_259,negated_conjecture,
relation(sK55),
inference(cnf_transformation,[],[f675]) ).
tcf(c_274,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f877]) ).
tcf(c_516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_74,c_188]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(superposition,[status(thm)],[c_157,c_516]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75,c_188]) ).
tcf(c_542,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK37(relation_rng_restriction(X1,X2),X0),X0),unordered_pair(sK37(relation_rng_restriction(X1,X2),X0),sK37(relation_rng_restriction(X1,X2),X0))),X2)
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(superposition,[status(thm)],[c_157,c_532]) ).
tcf(c_549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_73,c_188]) ).
tcf(c_564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_rng(relation_rng_restriction(X3,X2)))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ relation(relation_rng_restriction(X3,X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(superposition,[status(thm)],[c_549,c_274]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_526,c_188]) ).
tcf(c_651,plain,
( in(sK53,sK54)
| ~ relation(sK55) ),
inference(superposition,[status(thm)],[c_257,c_639]) ).
tcf(c_673,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK37(relation_rng_restriction(X1,X2),X0),X0),unordered_pair(sK37(relation_rng_restriction(X1,X2),X0),sK37(relation_rng_restriction(X1,X2),X0))),X2)
| ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_542,c_188]) ).
tcf(c_685,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(superposition,[status(thm)],[c_673,c_274]) ).
tcf(c_745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_rng(relation_rng_restriction(X3,X2)))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_564,c_188]) ).
tcf(c_759,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_rng(relation_rng_restriction(X2,X1)))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_157,c_745]) ).
tcf(c_992,plain,
( in(sK53,relation_rng(sK55))
| ~ relation(sK55) ),
inference(superposition,[status(thm)],[c_258,c_685]) ).
tcf(c_1279,plain,
( ~ relation(sK55)
| ~ in(sK53,sK54)
| ~ in(sK53,relation_rng(sK55)) ),
inference(superposition,[status(thm)],[c_759,c_256]) ).
tcf(c_1285,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1279,c_992,c_651,c_259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU197+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.43 % Computer : n014.cluster.edu
% 0.10/0.43 % Model : x86_64 x86_64
% 0.10/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.43 % Memory : 8046.5625MB
% 0.10/0.43 % OS : Linux 6.8.0-71-generic
% 0.10/0.44 % CPULimit : 300
% 0.10/0.44 % WCLimit : 300
% 0.10/0.44 % DateTime : Thu Sep 24 13:08:32 UTC 2026
% 0.10/0.44 % CPUTime :
% 0.10/0.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.47 Running first-order theorem proving
% 0.15/0.47 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
% 0.15/0.48
% 0.15/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.48
% 0.15/0.48 % Detected problem language: tptp
% 0.15/0.50 % Proving...
% 4.43/1.37 % SZS status Started for theBenchmark.p
% 4.43/1.37 % SZS status Theorem for theBenchmark.p
% 4.43/1.37
% 4.43/1.37 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.43/1.37
% 4.43/1.37 % ------ iProver source info
% 4.43/1.37
% 4.43/1.37 % git: date: 2026-07-19 20:42:38 +0200
% 4.43/1.37 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.43/1.37 % git: non_committed_changes: false
% 4.43/1.37
% 4.43/1.37 % ------ Parsing...
% 4.43/1.37 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.43/1.37 % ------ Proving...
% 4.43/1.37 % ------ Problem Properties
% 4.43/1.37
% 4.43/1.37 %
% 4.43/1.37 % clauses 320
% 4.43/1.37 % conjectures 4
% 4.43/1.37 % EPR 37
% 4.43/1.37 % Horn 256
% 4.43/1.37 % unary 58
% 4.43/1.37 % binary 107
% 4.43/1.37 % lits 829
% 4.43/1.37 % lits eq 162
% 4.43/1.37 % fd_pure 0
% 4.43/1.37 % fd_pseudo 0
% 4.43/1.37 % fd_cond 13
% 4.43/1.37 % fd_pseudo_cond 63
% 4.43/1.37 % AC symbols 0
% 4.43/1.37
% 4.43/1.37 % ------ Input Options Time Limit: Unbounded
% 4.43/1.37
% 4.43/1.37
% 4.43/1.37 % ------
% 4.43/1.37 % Current options:
% 4.43/1.37 % ------
% 4.43/1.37
% 4.43/1.37
% 4.43/1.37 %
% 4.43/1.37
% 4.43/1.37 % ------ Proving...
% 4.43/1.37 %
% 4.43/1.37
% 4.43/1.37 % SZS status Theorem for theBenchmark.p
% 4.43/1.37
% 4.43/1.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.43/1.37
% 4.43/1.37
%------------------------------------------------------------------------------