%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU253+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.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 02:56:22 PM UTC 2026
% Result : Theorem 12.62s 2.77s
% Output : CNFRefutation 12.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 111 ( 26 unt; 1 def)
% Number of atoms : 445 ( 25 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 445 ( 182 ~; 210 |; 39 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 176 ( 0 sgn 168 !; 8 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f15,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f29,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).
fof(f35,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f36,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f37,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_field(relation_restriction(X2,X1)))
=> ( in(X0,X1)
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
fof(f40,conjecture,
! [X0,X1] :
( relation(X1)
=> ( connected(X1)
=> connected(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_wellord1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( connected(X1)
=> connected(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f57,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| ( connected(X0)
<=> ! [X1,X2] :
( in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),X0)
| X1 = X2
| ~ in(X2,relation_field(X0))
| ~ in(X1,relation_field(X0)) ) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ( in(X0,X1)
& in(X0,relation_field(X2)) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ( in(X0,X1)
& in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f62]) ).
fof(f65,plain,
? [X0,X1] :
( relation(X1)
& connected(X1)
& ~ connected(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f41]) ).
fof(f66,plain,
? [X0,X1] :
( relation(X1)
& connected(X1)
& ~ connected(relation_restriction(X1,X0)) ),
inference(flattening,[],[f65]) ).
fof(f73,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ connected(X0)
| ! [X1,X2] :
( in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),X0)
| X1 = X2
| ~ in(X2,relation_field(X0))
| ~ in(X1,relation_field(X0)) ) )
& ( ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) )
| connected(X0) ) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f74,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ connected(X0)
| ! [X3,X4] :
( in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) ) )
& ( ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) )
| connected(X0) ) ) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ connected(X0)
| ! [X3,X4] :
( in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) ) )
& ( ( ~ in(ordered_pair(sK2(X0),sK1(X0)),X0)
& ~ in(ordered_pair(sK1(X0),sK2(X0)),X0)
& sK1(X0) != sK2(X0)
& in(sK2(X0),relation_field(X0))
& in(sK1(X0),relation_field(X0)) )
| connected(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f74]) ).
fof(f81,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,[],[f35]) ).
fof(f82,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,[],[f81]) ).
fof(f83,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,[],[f61]) ).
fof(f84,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,[],[f83]) ).
fof(f85,plain,
( relation(sK9)
& connected(sK9)
& ~ connected(relation_restriction(sK9,sK8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f66]) ).
fof(f90,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f93,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f96,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f104,plain,
! [X3,X0,X4] :
( ~ relation(X0)
| ~ connected(X0)
| in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f105,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK2(X0),sK1(X0)),X0)
| connected(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f106,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK1(X0),sK2(X0)),X0)
| connected(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f107,plain,
! [X0] :
( ~ relation(X0)
| sK1(X0) != sK2(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f108,plain,
! [X0] :
( ~ relation(X0)
| in(sK2(X0),relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f109,plain,
! [X0] :
( ~ relation(X0)
| in(sK1(X0),relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f121,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f129,plain,
relation(sK9),
inference(cnf_transformation,[],[f85]) ).
fof(f130,plain,
connected(sK9),
inference(cnf_transformation,[],[f85]) ).
fof(f131,plain,
~ connected(relation_restriction(sK9,sK8)),
inference(cnf_transformation,[],[f85]) ).
fof(f138,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK1(X0),sK2(X0)),singleton(sK1(X0))),X0)
| connected(X0) ),
inference(definition_unfolding,[],[f106,f93]) ).
fof(f139,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK2(X0),sK1(X0)),singleton(sK2(X0))),X0)
| connected(X0) ),
inference(definition_unfolding,[],[f105,f93]) ).
fof(f140,plain,
! [X3,X0,X4] :
( ~ relation(X0)
| ~ connected(X0)
| in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X0)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) ),
inference(definition_unfolding,[],[f104,f93,f93]) ).
fof(f141,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,[],[f121,f93]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f90]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_64,plain,
! [X0: $i] :
( connected(X0)
| in(sK1(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_65,plain,
! [X0: $i] :
( connected(X0)
| in(sK2(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_66,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_67,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK1(X0),sK2(X0)),singleton(sK1(X0))),X0) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_68,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK2(X0),sK1(X0)),singleton(sK2(X0))),X0) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X1)
| in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),X1)
| ( X0 = X2 )
| ~ connected(X1)
| ~ relation(X1)
| ~ in(X2,relation_field(X1))
| ~ in(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_79,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,[],[f141]) ).
tcf(c_82,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,[],[f124]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X1))
| ~ relation(X1)
| ~ in(X0,relation_field(relation_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_field(relation_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_89,negated_conjecture,
~ connected(relation_restriction(sK9,sK8)),
inference(cnf_transformation,[],[f131]) ).
tcf(c_90,negated_conjecture,
connected(sK9),
inference(cnf_transformation,[],[f130]) ).
tcf(c_91,negated_conjecture,
relation(sK9),
inference(cnf_transformation,[],[f129]) ).
tcf(c_416,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK2(X0)),unordered_pair(sK1(X0),sK2(X0))),X0) ),
inference(demodulation,[status(thm)],[c_68,c_51]) ).
tcf(c_426,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK1(X0)),unordered_pair(sK1(X0),sK2(X0))),X0) ),
inference(demodulation,[status(thm)],[c_67,c_51]) ).
tcf(c_444,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_79,c_51]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X1)
| ( X0 = X2 )
| ~ connected(X1)
| ~ relation(X1)
| ~ in(X2,relation_field(X1))
| ~ in(X0,relation_field(X1)) ),
inference(demodulation,[status(thm)],[c_69,c_51]) ).
tcf(c_1284,definition,
iPr_def_10 = relation_restriction(sK9,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1285,negated_conjecture,
relation(sK9),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_1286,negated_conjecture,
connected(sK9),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_1287,negated_conjecture,
~ connected(iPr_def_10),
inference(demodulation,[status(thm)],[c_89,c_1284]) ).
tcf(c_1782,plain,
( relation(iPr_def_10)
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1284,c_56]) ).
tcf(c_1783,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1782,c_1285]) ).
tcf(c_1972,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| in(sK1(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| ~ relation(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_64,c_86]) ).
tcf(c_1973,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| in(sK2(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| ~ relation(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_86]) ).
tcf(c_2054,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| in(sK1(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0)
| ~ relation(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_64,c_85]) ).
tcf(c_2150,plain,
( connected(iPr_def_10)
| ~ relation(iPr_def_10)
| ( sK1(iPr_def_10) != sK2(iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_3632,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| in(sK1(relation_restriction(X0,X1)),X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1972,c_56,c_1972]) ).
tcf(c_3869,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| in(sK2(relation_restriction(X0,X1)),X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1973,c_56,c_1973]) ).
tcf(c_23029,plain,
( relation(iPr_def_10)
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1284,c_56]) ).
tcf(c_23030,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_23029,c_1285]) ).
tcf(c_23291,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| in(sK1(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| ~ relation(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_64,c_86]) ).
tcf(c_23292,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| in(sK2(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| ~ relation(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_86]) ).
tcf(c_23338,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| in(sK1(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0)
| ~ relation(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_64,c_85]) ).
tcf(c_23341,plain,
! [X0: $i] :
( in(X0,relation_field(sK9))
| ~ relation(sK9)
| ~ in(X0,relation_field(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1284,c_85]) ).
tcf(c_23343,plain,
! [X0: $i] :
( in(X0,relation_field(sK9))
| ~ in(X0,relation_field(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23341,c_1285]) ).
tcf(c_23384,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| in(sK1(relation_restriction(X0,X1)),X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_23291,c_3632]) ).
tcf(c_23392,plain,
( connected(relation_restriction(sK9,sK8))
| in(sK1(iPr_def_10),sK8)
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1284,c_23384]) ).
tcf(c_23405,plain,
( connected(iPr_def_10)
| in(sK1(iPr_def_10),sK8)
| ~ relation(sK9) ),
inference(light_normalisation,[status(thm)],[c_23392,c_1284]) ).
tcf(c_23406,plain,
in(sK1(iPr_def_10),sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_23405,c_1287,c_1285]) ).
tcf(c_23429,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| in(sK2(relation_restriction(X0,X1)),X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_23292,c_3869]) ).
tcf(c_23437,plain,
( connected(relation_restriction(sK9,sK8))
| in(sK2(iPr_def_10),sK8)
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1284,c_23429]) ).
tcf(c_23447,plain,
( connected(iPr_def_10)
| in(sK2(iPr_def_10),sK8)
| ~ relation(sK9) ),
inference(light_normalisation,[status(thm)],[c_23437,c_1284]) ).
tcf(c_23448,plain,
in(sK2(iPr_def_10),sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_23447,c_1287,c_1285]) ).
tcf(c_23471,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| in(sK1(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_23338,c_56,c_2054]) ).
tcf(c_23479,plain,
( connected(relation_restriction(sK9,sK8))
| in(sK1(iPr_def_10),relation_field(sK9))
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1284,c_23471]) ).
tcf(c_23490,plain,
( connected(iPr_def_10)
| in(sK1(iPr_def_10),relation_field(sK9))
| ~ relation(sK9) ),
inference(light_normalisation,[status(thm)],[c_23479,c_1284]) ).
tcf(c_23491,plain,
in(sK1(iPr_def_10),relation_field(sK9)),
inference(forward_subsumption_resolution,[status(thm)],[c_23490,c_1287,c_1285]) ).
tcf(c_23554,plain,
( connected(iPr_def_10)
| in(sK2(iPr_def_10),relation_field(sK9))
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_65,c_23343]) ).
tcf(c_23560,plain,
in(sK2(iPr_def_10),relation_field(sK9)),
inference(forward_subsumption_resolution,[status(thm)],[c_23554,c_1287,c_23030]) ).
tcf(c_23646,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_444,c_82]) ).
tcf(c_26285,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ relation(sK9)
| ~ in(X1,sK8)
| ~ in(X0,sK8)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9) ),
inference(superposition,[status(thm)],[c_1284,c_23646]) ).
tcf(c_26297,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ in(X1,sK8)
| ~ in(X0,sK8)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26285,c_1285]) ).
tcf(c_26729,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),iPr_def_10)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9)
| ( X0 = X1 )
| ~ connected(sK9)
| ~ relation(sK9)
| ~ in(X1,sK8)
| ~ in(X0,sK8)
| ~ in(X1,relation_field(sK9))
| ~ in(X0,relation_field(sK9)) ),
inference(superposition,[status(thm)],[c_454,c_26297]) ).
tcf(c_26730,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ in(X1,sK8)
| ~ in(X0,sK8)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK9) ),
inference(superposition,[status(thm)],[c_51,c_26297]) ).
tcf(c_26736,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),iPr_def_10)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9)
| ( X0 = X1 )
| ~ in(X1,sK8)
| ~ in(X0,sK8)
| ~ in(X1,relation_field(sK9))
| ~ in(X0,relation_field(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26729,c_1286,c_1285]) ).
tcf(c_26780,plain,
( connected(iPr_def_10)
| in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK2(iPr_def_10),sK1(iPr_def_10))),sK9)
| ( sK1(iPr_def_10) = sK2(iPr_def_10) )
| ~ relation(iPr_def_10)
| ~ in(sK2(iPr_def_10),sK8)
| ~ in(sK1(iPr_def_10),sK8)
| ~ in(sK2(iPr_def_10),relation_field(sK9))
| ~ in(sK1(iPr_def_10),relation_field(sK9)) ),
inference(superposition,[status(thm)],[c_26736,c_426]) ).
tcf(c_26833,plain,
( in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK2(iPr_def_10),sK1(iPr_def_10))),sK9)
| ( sK1(iPr_def_10) = sK2(iPr_def_10) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26780,c_1287,c_23030,c_23448,c_23406,c_23560,c_23491]) ).
tcf(c_26844,plain,
in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK2(iPr_def_10),sK1(iPr_def_10))),sK9),
inference(global_subsumption_just,[status(thm)],[c_26833,c_1287,c_1783,c_2150,c_26833]) ).
tcf(c_26846,plain,
in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK1(iPr_def_10),sK2(iPr_def_10))),sK9),
inference(demodulation,[status(thm)],[c_26844,c_51]) ).
tcf(c_27865,plain,
( in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK2(iPr_def_10),sK1(iPr_def_10))),iPr_def_10)
| ~ in(sK2(iPr_def_10),sK8)
| ~ in(sK1(iPr_def_10),sK8) ),
inference(superposition,[status(thm)],[c_26846,c_26730]) ).
tcf(c_27868,plain,
in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK2(iPr_def_10),sK1(iPr_def_10))),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_27865,c_23448,c_23406]) ).
tcf(c_27869,plain,
in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK1(iPr_def_10),sK2(iPr_def_10))),iPr_def_10),
inference(demodulation,[status(thm)],[c_27868,c_51]) ).
tcf(c_27872,plain,
( connected(iPr_def_10)
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_27869,c_416]) ).
tcf(c_27876,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_27872,c_1287,c_23030]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU253+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 13:24:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 12.62/2.77 % SZS status Started for theBenchmark.p
% 12.62/2.77 % SZS status Theorem for theBenchmark.p
% 12.62/2.77
% 12.62/2.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.62/2.77
% 12.62/2.77 % ------ iProver source info
% 12.62/2.77
% 12.62/2.77 % git: date: 2026-07-19 20:42:38 +0200
% 12.62/2.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.62/2.77 % git: non_committed_changes: false
% 12.62/2.77
% 12.62/2.77 % ------ Parsing...
% 12.62/2.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 12.62/2.77
% 12.62/2.77 % ------ Preprocessing... sup_sim: 7 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 12.62/2.77
% 12.62/2.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 12.62/2.77
% 12.62/2.77 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 12.62/2.77 % ------ Proving...
% 12.62/2.77 % ------ Problem Properties
% 12.62/2.77
% 12.62/2.77 %
% 12.62/2.77 % clauses 43
% 12.62/2.77 % conjectures 3
% 12.62/2.77 % EPR 14
% 12.62/2.77 % Horn 39
% 12.62/2.77 % unary 19
% 12.62/2.77 % binary 11
% 12.62/2.77 % lits 85
% 12.62/2.77 % lits eq 14
% 12.62/2.77 % fd_pure 0
% 12.62/2.77 % fd_pseudo 0
% 12.62/2.77 % fd_cond 1
% 12.62/2.77 % fd_pseudo_cond 2
% 12.62/2.77 % AC symbols 0
% 12.62/2.77
% 12.62/2.77 % ------ Schedule dynamic 5 is on
% 12.62/2.77
% 12.62/2.77 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 12.62/2.77
% 12.62/2.77
% 12.62/2.77 % ------
% 12.62/2.77 % Current options:
% 12.62/2.77 % ------
% 12.62/2.77
% 12.62/2.77
% 12.62/2.77 %
% 12.62/2.77
% 12.62/2.77 % ------ Proving...
% 12.62/2.77 %
% 12.62/2.77
% 12.62/2.77 % SZS status Theorem for theBenchmark.p
% 12.62/2.77
% 12.62/2.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.62/2.77
%------------------------------------------------------------------------------