%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU053+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 02:55:10 PM UTC 2026
% Result : Theorem 95.38s 14.05s
% Output : CNFRefutation 95.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 100 ( 36 unt; 0 def)
% Number of atoms : 278 ( 98 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 308 ( 130 ~; 135 |; 29 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 120 ( 1 sgn 114 !; 6 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f8,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f14,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f15,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f18,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f34,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
fof(f35,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ! [X1,X2] : relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(relation_image(X0,X1),relation_image(X0,X2))
=> one_to_one(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_funct_1) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ! [X1,X2] : relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(relation_image(X0,X1),relation_image(X0,X2))
=> one_to_one(X0) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,axiom,
! [X0] :
( relation(X0)
=> relation_image(X0,empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
fof(f38,axiom,
! [X0,X1] :
( X0 != X1
=> disjoint(singleton(X0),singleton(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
fof(f48,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f18]) ).
fof(f58,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(flattening,[],[f58]) ).
fof(f73,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f74,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
? [X0] :
( function(X0)
& relation(X0)
& ! [X1,X2] : relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(relation_image(X0,X1),relation_image(X0,X2))
& ~ one_to_one(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f76,plain,
? [X0] :
( function(X0)
& relation(X0)
& ! [X1,X2] : relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(relation_image(X0,X1),relation_image(X0,X2))
& ~ one_to_one(X0) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ~ relation(X0)
| relation_image(X0,empty_set) = empty_set ),
inference(ennf_transformation,[],[f37]) ).
fof(f78,plain,
! [X0,X1] :
( X0 = X1
| disjoint(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f38]) ).
fof(f92,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set )
& ( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f93,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f94,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ( apply(X0,sK1(X0)) = apply(X0,sK2(X0))
& in(sK2(X0),relation_dom(X0))
& in(sK1(X0),relation_dom(X0))
& sK1(X0) != sK2(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f94]) ).
fof(f108,plain,
( function(sK14)
& relation(sK14)
& ! [X1,X2] : relation_image(sK14,set_intersection2(X1,X2)) = set_intersection2(relation_image(sK14,X1),relation_image(sK14,X2))
& ~ one_to_one(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f76]) ).
fof(f115,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f120,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f92]) ).
fof(f123,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK1(X0)) = apply(X0,sK2(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f124,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK2(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f125,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK1(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f126,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK1(X0) != sK2(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f133,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f135,plain,
empty(empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f139,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f48]) ).
fof(f165,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f166,plain,
function(sK14),
inference(cnf_transformation,[],[f108]) ).
fof(f167,plain,
relation(sK14),
inference(cnf_transformation,[],[f108]) ).
fof(f168,plain,
! [X2,X1] : relation_image(sK14,set_intersection2(X1,X2)) = set_intersection2(relation_image(sK14,X1),relation_image(sK14,X2)),
inference(cnf_transformation,[],[f108]) ).
fof(f169,plain,
~ one_to_one(sK14),
inference(cnf_transformation,[],[f108]) ).
fof(f170,plain,
! [X0] :
( ~ relation(X0)
| empty_set = relation_image(X0,empty_set) ),
inference(cnf_transformation,[],[f77]) ).
fof(f171,plain,
! [X0,X1] :
( X0 = X1
| disjoint(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f115]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = empty_set )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_60,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_61,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK1(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_62,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK2(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_63,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK1(X0)) = apply(X0,sK2(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_71,plain,
! [X0: $i] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f133]) ).
tcf(c_72,plain,
empty(empty_set),
inference(cnf_transformation,[],[f135]) ).
tcf(c_77,plain,
! [X0: $i] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f139]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( ( singleton(apply(X1,X0)) = relation_image(X1,singleton(X0)) )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_104,negated_conjecture,
~ one_to_one(sK14),
inference(cnf_transformation,[],[f169]) ).
tcf(c_105,negated_conjecture,
! [X0: $i,X1: $i] : set_intersection2(relation_image(sK14,X0),relation_image(sK14,X1)) = relation_image(sK14,set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f168]) ).
tcf(c_106,negated_conjecture,
relation(sK14),
inference(cnf_transformation,[],[f167]) ).
tcf(c_107,negated_conjecture,
function(sK14),
inference(cnf_transformation,[],[f166]) ).
tcf(c_108,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = empty_set )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( disjoint(singleton(X0),singleton(X1))
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_840,plain,
! [X0: $i] :
( ( apply(X0,sK1(X0)) = apply(X0,sK2(X0)) )
| ~ relation(X0)
| ~ function(X0)
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_104]) ).
tcf(c_841,plain,
( ( apply(sK14,sK1(sK14)) = apply(sK14,sK2(sK14)) )
| ~ relation(sK14)
| ~ function(sK14) ),
inference(unflattening,[status(thm)],[c_840]) ).
tcf(c_847,plain,
! [X0: $i] :
( in(sK2(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0)
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_104]) ).
tcf(c_848,plain,
( in(sK2(sK14),relation_dom(sK14))
| ~ relation(sK14)
| ~ function(sK14) ),
inference(unflattening,[status(thm)],[c_847]) ).
tcf(c_854,plain,
! [X0: $i] :
( in(sK1(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0)
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_104]) ).
tcf(c_855,plain,
( in(sK1(sK14),relation_dom(sK14))
| ~ relation(sK14)
| ~ function(sK14) ),
inference(unflattening,[status(thm)],[c_854]) ).
tcf(c_861,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ function(X0)
| ( X0 != sK14 )
| ( sK1(X0) != sK2(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_104]) ).
tcf(c_862,plain,
( ~ relation(sK14)
| ~ function(sK14)
| ( sK1(sK14) != sK2(sK14) ) ),
inference(unflattening,[status(thm)],[c_861]) ).
tcf(c_1007,plain,
! [X0: $i,X1: $i] :
( ( singleton(apply(X0,X1)) = relation_image(X0,singleton(X1)) )
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_103,c_107]) ).
tcf(c_1008,plain,
! [X0: $i] :
( ( singleton(apply(sK14,X0)) = relation_image(sK14,singleton(X0)) )
| ~ relation(sK14)
| ~ in(X0,relation_dom(sK14)) ),
inference(unflattening,[status(thm)],[c_1007]) ).
tcf(c_1010,plain,
! [X0: $i] :
( ( singleton(apply(sK14,X0)) = relation_image(sK14,singleton(X0)) )
| ~ in(X0,relation_dom(sK14)) ),
inference(global_subsumption_just,[status(thm)],[c_1008,c_106,c_1008]) ).
tcf(c_1167,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK1(X0)) = apply(X0,sK2(X0)) )
| ~ relation(X0)
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_107]) ).
tcf(c_1168,plain,
( one_to_one(sK14)
| ( apply(sK14,sK1(sK14)) = apply(sK14,sK2(sK14)) )
| ~ relation(sK14) ),
inference(unflattening,[status(thm)],[c_1167]) ).
tcf(c_1169,plain,
apply(sK14,sK1(sK14)) = apply(sK14,sK2(sK14)),
inference(global_subsumption_just,[status(thm)],[c_1168,c_107,c_106,c_841]) ).
tcf(c_1174,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK2(X0),relation_dom(X0))
| ~ relation(X0)
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_107]) ).
tcf(c_1175,plain,
( one_to_one(sK14)
| in(sK2(sK14),relation_dom(sK14))
| ~ relation(sK14) ),
inference(unflattening,[status(thm)],[c_1174]) ).
tcf(c_1176,plain,
in(sK2(sK14),relation_dom(sK14)),
inference(global_subsumption_just,[status(thm)],[c_1175,c_107,c_106,c_848]) ).
tcf(c_1181,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK1(X0),relation_dom(X0))
| ~ relation(X0)
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_107]) ).
tcf(c_1182,plain,
( one_to_one(sK14)
| in(sK1(sK14),relation_dom(sK14))
| ~ relation(sK14) ),
inference(unflattening,[status(thm)],[c_1181]) ).
tcf(c_1183,plain,
in(sK1(sK14),relation_dom(sK14)),
inference(global_subsumption_just,[status(thm)],[c_1182,c_107,c_106,c_855]) ).
tcf(c_1188,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ relation(X0)
| ( X0 != sK14 )
| ( sK1(X0) != sK2(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_107]) ).
tcf(c_1189,plain,
( one_to_one(sK14)
| ~ relation(sK14)
| ( sK1(sK14) != sK2(sK14) ) ),
inference(unflattening,[status(thm)],[c_1188]) ).
tcf(c_1190,plain,
sK1(sK14) != sK2(sK14),
inference(global_subsumption_just,[status(thm)],[c_1189,c_107,c_106,c_862]) ).
tcf(c_1951,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3329,plain,
relation_image(sK14,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_106,c_108]) ).
tcf(c_3347,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( set_intersection2(singleton(X0),singleton(X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_109,c_59]) ).
tcf(c_3375,plain,
! [X0: $i,X1: $i] : set_intersection2(relation_image(sK14,X0),relation_image(sK14,X1)) = relation_image(sK14,set_intersection2(X1,X0)),
inference(superposition,[status(thm)],[c_105,c_53]) ).
tcf(c_3379,plain,
singleton(apply(sK14,sK2(sK14))) = relation_image(sK14,singleton(sK2(sK14))),
inference(superposition,[status(thm)],[c_1176,c_1010]) ).
tcf(c_3380,plain,
singleton(apply(sK14,sK1(sK14))) = relation_image(sK14,singleton(sK1(sK14))),
inference(superposition,[status(thm)],[c_1183,c_1010]) ).
tcf(c_3381,plain,
singleton(apply(sK14,sK1(sK14))) = relation_image(sK14,singleton(sK2(sK14))),
inference(light_normalisation,[status(thm)],[c_3379,c_1169]) ).
tcf(c_3635,plain,
! [X0: $i,X1: $i] : relation_image(sK14,set_intersection2(X0,X1)) = relation_image(sK14,set_intersection2(X1,X0)),
inference(superposition,[status(thm)],[c_3375,c_105]) ).
tcf(c_3672,plain,
! [X0: $i] : set_intersection2(relation_image(sK14,X0),singleton(apply(sK14,sK1(sK14)))) = relation_image(sK14,set_intersection2(X0,singleton(sK2(sK14)))),
inference(superposition,[status(thm)],[c_3381,c_105]) ).
tcf(c_3884,plain,
! [X0: $i,X1: $i] :
( empty(singleton(X0))
| ~ empty(X1)
| ( singleton(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_1951]) ).
tcf(c_4305,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( relation_image(sK14,set_intersection2(singleton(X0),singleton(X1))) = relation_image(sK14,empty_set) ) ),
inference(superposition,[status(thm)],[c_3347,c_3635]) ).
tcf(c_4321,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( relation_image(sK14,set_intersection2(singleton(X0),singleton(X1))) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_4305,c_3329]) ).
tcf(c_4602,plain,
set_intersection2(singleton(apply(sK14,sK1(sK14))),singleton(apply(sK14,sK1(sK14)))) = relation_image(sK14,set_intersection2(singleton(sK1(sK14)),singleton(sK2(sK14)))),
inference(superposition,[status(thm)],[c_3380,c_3672]) ).
tcf(c_4621,plain,
relation_image(sK14,set_intersection2(singleton(sK1(sK14)),singleton(sK2(sK14)))) = singleton(apply(sK14,sK1(sK14))),
inference(demodulation,[status(thm)],[c_4602,c_77]) ).
tcf(c_6945,plain,
~ empty(singleton(apply(sK14,sK1(sK14)))),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_13385,plain,
( ( sK1(sK14) = sK2(sK14) )
| ( singleton(apply(sK14,sK1(sK14))) = empty_set ) ),
inference(superposition,[status(thm)],[c_4621,c_4321]) ).
tcf(c_13386,plain,
singleton(apply(sK14,sK1(sK14))) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_13385,c_1190]) ).
tcf(c_20199,plain,
! [X0: $i] :
( empty(singleton(apply(sK14,sK1(sK14))))
| ~ empty(X0)
| ( singleton(apply(sK14,sK1(sK14))) != X0 ) ),
inference(instantiation,[status(thm)],[c_3884]) ).
tcf(c_20200,plain,
( empty(singleton(apply(sK14,sK1(sK14))))
| ~ empty(empty_set)
| ( singleton(apply(sK14,sK1(sK14))) != empty_set ) ),
inference(instantiation,[status(thm)],[c_20199]) ).
tcf(c_20201,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_20200,c_13386,c_6945,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU053+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:41:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 0.15/0.45
% 0.15/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.45
% 0.15/0.45 % Detected problem language: tptp
% 0.15/0.46 % Proving...
% 95.38/14.05 % SZS status Started for theBenchmark.p
% 95.38/14.05 % SZS status Theorem for theBenchmark.p
% 95.38/14.05
% 95.38/14.05 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 95.38/14.05
% 95.38/14.05 % ------ iProver source info
% 95.38/14.05
% 95.38/14.05 % git: date: 2026-07-19 20:42:38 +0200
% 95.38/14.05 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 95.38/14.05 % git: non_committed_changes: false
% 95.38/14.05
% 95.38/14.05 % ------ Parsing...
% 95.38/14.05 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 95.38/14.05
% 95.38/14.05 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 95.38/14.05
% 95.38/14.05 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 95.38/14.05
% 95.38/14.05 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 95.38/14.05 % ------ Proving...
% 95.38/14.05 % ------ Problem Properties
% 95.38/14.05
% 95.38/14.05 %
% 95.38/14.05 % clauses 78
% 95.38/14.05 % conjectures 3
% 95.38/14.05 % EPR 31
% 95.38/14.05 % Horn 64
% 95.38/14.05 % unary 31
% 95.38/14.05 % binary 30
% 95.38/14.05 % lits 151
% 95.38/14.05 % lits eq 34
% 95.38/14.05 % fd_pure 0
% 95.38/14.05 % fd_pseudo 0
% 95.38/14.05 % fd_cond 1
% 95.38/14.05 % fd_pseudo_cond 8
% 95.38/14.05 % AC symbols 0
% 95.38/14.05
% 95.38/14.05 % ------ Input Options Time Limit: Unbounded
% 95.38/14.05
% 95.38/14.05
% 95.38/14.05 % ------
% 95.38/14.05 % Current options:
% 95.38/14.05 % ------
% 95.38/14.05
% 95.38/14.05
% 95.38/14.05 %
% 95.38/14.05
% 95.38/14.05 % ------ Proving...
% 95.38/14.05 %
% 95.38/14.05
% 95.38/14.05 % SZS status Theorem for theBenchmark.p
% 95.38/14.05
% 95.38/14.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 95.38/14.05
% 95.38/14.05
%------------------------------------------------------------------------------