%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU258+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 : n011.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 02:56:23 PM UTC 2026
% Result : Theorem 2.19s 34.63s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 20
% Syntax : Number of formulae : 162 ( 34 unt; 3 def)
% Number of atoms : 556 ( 26 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 561 ( 234 ~; 236 |; 65 &)
% ( 11 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 263 ( 0 sgn 254 !; 9 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f10,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(f19,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f26,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f33,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f40,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f41,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f44,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_wellord1) ).
fof(f46,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f47,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f48,conjecture,
! [X0,X1] :
( relation(X1)
=> ( ( subset(X0,relation_field(X1))
& well_ordering(X1) )
=> relation_field(relation_restriction(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_wellord1) ).
fof(f49,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( ( subset(X0,relation_field(X1))
& well_ordering(X1) )
=> relation_field(relation_restriction(X1,X0)) = X0 ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f50,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f51,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f54,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f65,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f66,plain,
! [X0] :
( ~ relation(X0)
| ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f69,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f72,plain,
! [X0] :
( ~ relation(X0)
| ( reflexive(X0)
<=> ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f75,plain,
! [X0,X1] :
( ~ relation(X1)
| ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f76,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f77,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
? [X0,X1] :
( relation(X1)
& subset(X0,relation_field(X1))
& well_ordering(X1)
& relation_field(relation_restriction(X1,X0)) != X0 ),
inference(ennf_transformation,[],[f49]) ).
fof(f81,plain,
? [X0,X1] :
( relation(X1)
& subset(X0,relation_field(X1))
& well_ordering(X1)
& relation_field(relation_restriction(X1,X0)) != X0 ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f51]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f82]) ).
fof(f86,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f88,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f89,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f91,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f91]) ).
fof(f93,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_ordering(X0)
| ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
& ( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f94,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_ordering(X0)
| ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
& ( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ) ) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0] : element(sK1(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f26]) ).
fof(f96,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) )
& ( ? [X1] :
( in(X1,relation_field(X0))
& ~ in(ordered_pair(X1,X1),X0) )
| reflexive(X0) ) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f97,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X2] :
( ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ) )
& ( ? [X1] :
( in(X1,relation_field(X0))
& ~ in(ordered_pair(X1,X1),X0) )
| reflexive(X0) ) ) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X2] :
( ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ) )
& ( ( in(sK2(X0),relation_field(X0))
& ~ in(ordered_pair(sK2(X0),sK2(X0)),X0) )
| reflexive(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f97]) ).
fof(f104,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
( relation(sK9)
& subset(sK8,relation_field(sK9))
& well_ordering(sK9)
& sK8 != relation_field(relation_restriction(sK9,sK8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f81]) ).
fof(f109,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f114,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f119,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f120,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f121,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f122,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f127,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f129,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f132,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f133,plain,
! [X0] : element(sK1(X0),X0),
inference(cnf_transformation,[],[f95]) ).
fof(f140,plain,
! [X2,X0] :
( ~ relation(X0)
| ~ reflexive(X0)
| ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f141,plain,
! [X0] :
( ~ relation(X0)
| in(sK2(X0),relation_field(X0))
| reflexive(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f161,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_field(relation_restriction(X1,X0)),X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f164,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f167,plain,
relation(sK9),
inference(cnf_transformation,[],[f108]) ).
fof(f168,plain,
subset(sK8,relation_field(sK9)),
inference(cnf_transformation,[],[f108]) ).
fof(f169,plain,
well_ordering(sK9),
inference(cnf_transformation,[],[f108]) ).
fof(f170,plain,
sK8 != relation_field(relation_restriction(sK9,sK8)),
inference(cnf_transformation,[],[f108]) ).
fof(f172,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f173,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f176,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f180,plain,
! [X2,X0] :
( ~ relation(X0)
| ~ reflexive(X0)
| ~ in(X2,relation_field(X0))
| in(unordered_pair(unordered_pair(X2,X2),singleton(X2)),X0) ),
inference(definition_unfolding,[],[f140,f129]) ).
fof(f181,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f155,f129]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| in(X0,relation_field(X2)) ),
inference(definition_unfolding,[],[f166,f129]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f114]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_61,plain,
! [X0: $i] :
( reflexive(X0)
| ~ relation(X0)
| ~ well_ordering(X0) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_69,plain,
! [X0: $i] : element(sK1(X0),X0),
inference(cnf_transformation,[],[f133]) ).
tcf(c_77,plain,
! [X0: $i] :
( reflexive(X0)
| in(sK2(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),X1)
| ~ relation(X1)
| ~ reflexive(X1)
| ~ in(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_restriction(X2,X1))
| ~ relation(X2)
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( subset(relation_field(relation_restriction(X0,X1)),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_103,negated_conjecture,
relation_field(relation_restriction(sK9,sK8)) != sK8,
inference(cnf_transformation,[],[f170]) ).
tcf(c_104,negated_conjecture,
well_ordering(sK9),
inference(cnf_transformation,[],[f169]) ).
tcf(c_105,negated_conjecture,
subset(sK8,relation_field(sK9)),
inference(cnf_transformation,[],[f168]) ).
tcf(c_106,negated_conjecture,
relation(sK9),
inference(cnf_transformation,[],[f167]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_107]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_109,c_149]) ).
tcf(c_733,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_101,c_51]) ).
tcf(c_761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_89,c_51]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ reflexive(X1)
| ~ in(X0,relation_field(X1)) ),
inference(demodulation,[status(thm)],[c_78,c_51]) ).
tcf(c_821,plain,
! [X0: $i] :
( reflexive(X0)
| ~ relation(X0)
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_104]) ).
tcf(c_822,plain,
( reflexive(sK9)
| ~ relation(sK9) ),
inference(unflattening,[status(thm)],[c_821]) ).
tcf(c_823,plain,
reflexive(sK9),
inference(global_subsumption_just,[status(thm)],[c_822,c_106,c_822]) ).
tcf(c_1590,definition,
iPr_def_10 = relation_field(sK9),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1591,definition,
iPr_def_11 = relation_restriction(sK9,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1592,definition,
iPr_def_12 = relation_field(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1593,plain,
reflexive(sK9),
inference(demodulation,[status(thm)],[c_823]) ).
tcf(c_1594,negated_conjecture,
relation(sK9),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_1595,negated_conjecture,
subset(sK8,iPr_def_10),
inference(demodulation,[status(thm)],[c_105,c_1590]) ).
tcf(c_1596,negated_conjecture,
iPr_def_12 != sK8,
inference(demodulation,[status(thm)],[c_103,c_1591,c_1592]) ).
tcf(c_2536,plain,
( relation(iPr_def_11)
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1591,c_68]) ).
tcf(c_2537,plain,
relation(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_2536,c_1594]) ).
tcf(c_2646,plain,
( subset(relation_field(iPr_def_11),sK8)
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1591,c_98]) ).
tcf(c_2647,plain,
( subset(iPr_def_12,sK8)
| ~ relation(sK9) ),
inference(light_normalisation,[status(thm)],[c_2646,c_1592]) ).
tcf(c_2648,plain,
subset(iPr_def_12,sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_2647,c_1594]) ).
tcf(c_2655,plain,
! [X0: $i] :
( empty(X0)
| in(sK1(X0),X0) ),
inference(superposition,[status(thm)],[c_69,c_100]) ).
tcf(c_2669,plain,
( reflexive(iPr_def_11)
| in(sK2(iPr_def_11),iPr_def_12)
| ~ relation(iPr_def_11) ),
inference(superposition,[status(thm)],[c_1592,c_77]) ).
tcf(c_2676,plain,
( reflexive(iPr_def_11)
| in(sK2(iPr_def_11),iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2669,c_2537]) ).
tcf(c_2794,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK1(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_2655,c_59]) ).
tcf(c_2795,plain,
! [X0: $i] :
( reflexive(iPr_def_11)
| in(sK2(iPr_def_11),X0)
| ~ subset(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_2676,c_59]) ).
tcf(c_2911,plain,
! [X0: $i] :
( reflexive(iPr_def_11)
| ~ empty(X0)
| ~ subset(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_2795,c_112]) ).
tcf(c_3018,plain,
( ( iPr_def_12 = sK8 )
| ~ subset(iPr_def_12,sK8)
| ~ subset(sK8,iPr_def_12) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_3179,plain,
( subset(sK8,iPr_def_12)
| in(sK0(sK8,iPr_def_12),sK8) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_3983,plain,
( ~ empty(sK8)
| ~ in(sK0(sK8,iPr_def_12),sK8) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_4313,plain,
( reflexive(iPr_def_11)
| ~ empty(sK8) ),
inference(superposition,[status(thm)],[c_2648,c_2911]) ).
tcf(c_4333,plain,
~ empty(sK8),
inference(global_subsumption_just,[status(thm)],[c_4313,c_1596,c_2648,c_3018,c_3179,c_3983]) ).
tcf(c_5491,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_2794,c_112]) ).
tcf(c_5590,plain,
( empty(sK8)
| ~ empty(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1595,c_5491]) ).
tcf(c_5603,plain,
~ empty(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_5590,c_4333]) ).
tcf(c_28543,plain,
! [X0: $i] :
( empty(iPr_def_10)
| in(X0,iPr_def_10)
| ~ element(X0,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_37063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_761,c_92]) ).
tcf(c_39818,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_11)
| ~ relation(sK9)
| ~ in(X1,sK8)
| ~ in(X0,sK8)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9) ),
inference(superposition,[status(thm)],[c_1591,c_37063]) ).
tcf(c_39841,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_11)
| ~ in(X1,sK8)
| ~ in(X0,sK8)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39818,c_1594]) ).
tcf(c_40381,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),iPr_def_11)
| ~ relation(sK9)
| ~ reflexive(sK9)
| ~ in(X0,sK8)
| ~ in(X0,relation_field(sK9)) ),
inference(superposition,[status(thm)],[c_771,c_39841]) ).
tcf(c_40389,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),iPr_def_11)
| ~ relation(sK9)
| ~ reflexive(sK9)
| ~ in(X0,iPr_def_10)
| ~ in(X0,sK8) ),
inference(light_normalisation,[status(thm)],[c_40381,c_1590]) ).
tcf(c_40390,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),iPr_def_11)
| ~ in(X0,iPr_def_10)
| ~ in(X0,sK8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40389,c_1594,c_1593]) ).
tcf(c_74714,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ subset(sK8,X1)
| ~ in(X0,sK8) ),
inference(instantiation,[status(thm)],[c_302]) ).
tcf(c_90559,plain,
! [X0: $i] :
( element(X0,iPr_def_10)
| ~ subset(sK8,iPr_def_10)
| ~ in(X0,sK8) ),
inference(instantiation,[status(thm)],[c_74714]) ).
tcf(c_191426,plain,
( relation(iPr_def_11)
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1591,c_68]) ).
tcf(c_191427,plain,
relation(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_191426,c_1594]) ).
tcf(c_191516,plain,
( subset(relation_field(iPr_def_11),sK8)
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1591,c_98]) ).
tcf(c_191517,plain,
( subset(iPr_def_12,sK8)
| ~ relation(sK9) ),
inference(light_normalisation,[status(thm)],[c_191516,c_1592]) ).
tcf(c_191518,plain,
subset(iPr_def_12,sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_191517,c_1594]) ).
tcf(c_191766,plain,
( ( sK8 = iPr_def_12 )
| ~ subset(sK8,iPr_def_12) ),
inference(superposition,[status(thm)],[c_191518,c_54]) ).
tcf(c_191839,plain,
~ subset(sK8,iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_191766,c_1596,c_2648,c_3018]) ).
tcf(c_191929,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2) ),
inference(superposition,[status(thm)],[c_51,c_733]) ).
tcf(c_192111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_761,c_92]) ).
tcf(c_263515,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_11)
| ~ relation(sK9)
| ~ in(X1,sK8)
| ~ in(X0,sK8)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9) ),
inference(superposition,[status(thm)],[c_1591,c_192111]) ).
tcf(c_263543,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_11)
| ~ in(X1,sK8)
| ~ in(X0,sK8)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9) ),
inference(forward_subsumption_resolution,[status(thm)],[c_263515,c_1594]) ).
tcf(c_264298,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),iPr_def_11)
| ~ relation(sK9)
| ~ reflexive(sK9)
| ~ in(X0,sK8)
| ~ in(X0,relation_field(sK9)) ),
inference(superposition,[status(thm)],[c_771,c_263543]) ).
tcf(c_264305,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),iPr_def_11)
| ~ relation(sK9)
| ~ reflexive(sK9)
| ~ in(X0,iPr_def_10)
| ~ in(X0,sK8) ),
inference(light_normalisation,[status(thm)],[c_264298,c_1590]) ).
tcf(c_264306,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),iPr_def_11)
| ~ in(X0,iPr_def_10)
| ~ in(X0,sK8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_264305,c_1594,c_1593]) ).
tcf(c_264314,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),iPr_def_11)
| ~ in(X0,sK8) ),
inference(global_subsumption_just,[status(thm)],[c_264306,c_1595,c_5603,c_28543,c_40390,c_90559]) ).
tcf(c_264335,plain,
! [X0: $i] :
( in(X0,relation_field(iPr_def_11))
| ~ relation(iPr_def_11)
| ~ in(X0,sK8) ),
inference(superposition,[status(thm)],[c_264314,c_191929]) ).
tcf(c_264341,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ relation(iPr_def_11)
| ~ in(X0,sK8) ),
inference(light_normalisation,[status(thm)],[c_264335,c_1592]) ).
tcf(c_264342,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ in(X0,sK8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_264341,c_191427]) ).
tcf(c_264951,plain,
! [X0: $i] :
( subset(sK8,X0)
| in(sK0(sK8,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_58,c_264342]) ).
tcf(c_269022,plain,
subset(sK8,iPr_def_12),
inference(superposition,[status(thm)],[c_264951,c_57]) ).
tcf(c_269026,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_269022,c_191839]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU258+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.42/17.28 % CPULimit : 300
% 0.42/17.28 % WCLimit : 300
% 0.42/17.28 % DateTime : Thu Sep 24 13:25:27 UTC 2026
% 0.42/17.28 % CPUTime :
% 0.42/17.28 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.51/17.34 Running first-order theorem proving
% 0.51/17.34 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
% 0.51/17.35
% 0.51/17.35 % ======== iProver multi-core TPTP/SMT =========
% 0.51/17.35
% 0.51/17.36 % Detected problem language: tptp
% 0.51/17.37 % Proving...
% 2.19/34.63 % SZS status Started for theBenchmark.p
% 2.19/34.63 % SZS status Theorem for theBenchmark.p
% 2.19/34.63
% 2.19/34.63 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.19/34.63
% 2.19/34.63 % ------ iProver source info
% 2.19/34.63
% 2.19/34.63 % git: date: 2026-07-19 20:42:38 +0200
% 2.19/34.63 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.19/34.63 % git: non_committed_changes: false
% 2.19/34.63
% 2.19/34.63 % ------ Parsing...
% 2.19/34.63 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.19/34.63
% 2.19/34.63 % ------ Preprocessing... sup_sim: 8 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 2.19/34.63
% 2.19/34.63 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.19/34.63
% 2.19/34.63 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.19/34.63 % ------ Proving...
% 2.19/34.63 % ------ Problem Properties
% 2.19/34.63
% 2.19/34.63 %
% 2.19/34.63 % clauses 56
% 2.19/34.63 % conjectures 3
% 2.19/34.63 % EPR 22
% 2.19/34.63 % Horn 53
% 2.19/34.63 % unary 24
% 2.19/34.63 % binary 17
% 2.19/34.63 % lits 105
% 2.19/34.63 % lits eq 16
% 2.19/34.63 % fd_pure 0
% 2.19/34.63 % fd_pseudo 0
% 2.19/34.63 % fd_cond 1
% 2.19/34.63 % fd_pseudo_cond 2
% 2.19/34.63 % AC symbols 0
% 2.19/34.63
% 2.19/34.63 % ------ Schedule dynamic 5 is on
% 2.19/34.63
% 2.19/34.63 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.19/34.63
% 2.19/34.63
% 2.19/34.63 % ------
% 2.19/34.63 % Current options:
% 2.19/34.63 % ------
% 2.19/34.63
% 2.19/34.63
% 2.19/34.63 %
% 2.19/34.63
% 2.19/34.63 % ------ Proving...
% 2.19/34.63 % Proof_search_loop: time out after: 4162 full_loop iterations
% 2.19/34.63
% 2.19/34.63 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 2.19/34.63
% 2.19/34.63
% 2.19/34.63 % ------
% 2.19/34.63 % Current options:
% 2.19/34.63 % ------
% 2.19/34.63
% 2.19/34.63
% 2.19/34.63 %
% 2.19/34.63
% 2.19/34.63 % ------ Proving...
% 2.19/34.63 %
% 2.19/34.63
% 2.19/34.63 % SZS status Theorem for theBenchmark.p
% 2.19/34.63
% 2.19/34.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.19/34.63
% 2.19/34.63
%------------------------------------------------------------------------------