%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU242+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 : n016.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 02:56:19 PM UTC 2026
% Result : Theorem 1.49s 1.43s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 11
% Syntax : Number of formulae : 111 ( 23 unt; 6 def)
% Number of atoms : 494 ( 60 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 520 ( 210 ~; 246 |; 53 &)
% ( 6 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 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 : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 144 ( 0 sgn 130 !; 14 ?; 55 :)
% 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(f6,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_2) ).
fof(f7,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(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
~ ( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_2) ).
fof(f25,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',l4_wellord1) ).
fof(f26,negated_conjecture,
~ ! [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(negated_conjecture,[status(cth)],[f25]) ).
fof(f45,plain,
! [X0] :
( ~ relation(X0)
| ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f47,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f50,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,[],[f26]) ).
fof(f57,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ connected(X0)
| is_connected_in(X0,relation_field(X0)) )
& ( ~ is_connected_in(X0,relation_field(X0))
| connected(X0) ) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f58,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_connected_in(X0,X1)
| ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
& ( ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) )
| is_connected_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f59,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_connected_in(X0,X1)
| ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) ) )
& ( ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) )
| is_connected_in(X0,X1) ) ) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_connected_in(X0,X1)
| ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) ) )
& ( ( ~ in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0)
& ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& sK0(X0,X1) != sK1(X0,X1)
& in(sK1(X0,X1),X1)
& in(sK0(X0,X1),X1) )
| is_connected_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f59]) ).
fof(f62,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)) ) )
& ( ~ 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(nnf_transformation,[],[f50]) ).
fof(f63,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)) ) )
& ( ~ 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(flattening,[],[f62]) ).
fof(f64,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)) ) )
& ( ~ 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(rectify,[],[f63]) ).
fof(f65,plain,
( relation(sK3)
& ( connected(sK3)
| ! [X3,X4] :
( in(ordered_pair(X4,X3),sK3)
| in(ordered_pair(X3,X4),sK3)
| X3 = X4
| ~ in(X4,relation_field(sK3))
| ~ in(X3,relation_field(sK3)) ) )
& ( ~ connected(sK3)
| ( ~ in(ordered_pair(sK5,sK4),sK3)
& ~ in(ordered_pair(sK4,sK5),sK3)
& sK4 != sK5
& in(sK5,relation_field(sK3))
& in(sK4,relation_field(sK3)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f64]) ).
fof(f75,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f77,plain,
! [X0] :
( ~ relation(X0)
| ~ connected(X0)
| is_connected_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f78,plain,
! [X0] :
( ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f79,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f81,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ is_connected_in(X0,X1)
| in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f82,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f83,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f84,plain,
! [X0,X1] :
( ~ relation(X0)
| sK0(X0,X1) != sK1(X0,X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f85,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK1(X0,X1),X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f86,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1),X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f93,plain,
relation(sK3),
inference(cnf_transformation,[],[f65]) ).
fof(f94,plain,
! [X3,X4] :
( connected(sK3)
| in(ordered_pair(X4,X3),sK3)
| in(ordered_pair(X3,X4),sK3)
| X3 = X4
| ~ in(X4,relation_field(sK3))
| ~ in(X3,relation_field(sK3)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f95,plain,
( ~ connected(sK3)
| ~ in(ordered_pair(sK5,sK4),sK3) ),
inference(cnf_transformation,[],[f65]) ).
fof(f96,plain,
( ~ connected(sK3)
| ~ in(ordered_pair(sK4,sK5),sK3) ),
inference(cnf_transformation,[],[f65]) ).
fof(f97,plain,
( ~ connected(sK3)
| sK4 != sK5 ),
inference(cnf_transformation,[],[f65]) ).
fof(f98,plain,
( ~ connected(sK3)
| in(sK5,relation_field(sK3)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f99,plain,
( ~ connected(sK3)
| in(sK4,relation_field(sK3)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f115,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| is_connected_in(X0,X1) ),
inference(definition_unfolding,[],[f83,f79]) ).
fof(f116,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK1(X0,X1),sK0(X0,X1)),singleton(sK1(X0,X1))),X0)
| is_connected_in(X0,X1) ),
inference(definition_unfolding,[],[f82,f79]) ).
fof(f117,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ is_connected_in(X0,X1)
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) ),
inference(definition_unfolding,[],[f81,f79,f79]) ).
fof(f119,plain,
( ~ connected(sK3)
| ~ in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK3) ),
inference(definition_unfolding,[],[f96,f79]) ).
fof(f120,plain,
( ~ connected(sK3)
| ~ in(unordered_pair(unordered_pair(sK5,sK4),singleton(sK5)),sK3) ),
inference(definition_unfolding,[],[f95,f79]) ).
fof(f121,plain,
! [X3,X4] :
( connected(sK3)
| in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),sK3)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK3)
| X3 = X4
| ~ in(X4,relation_field(sK3))
| ~ in(X3,relation_field(sK3)) ),
inference(definition_unfolding,[],[f94,f79,f79]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f75]) ).
tcf(c_53,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_54,plain,
! [X0: $i] :
( is_connected_in(X0,relation_field(X0))
| ~ relation(X0)
| ~ connected(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| in(sK0(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| in(sK1(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ( sK0(X0,X1) != sK1(X0,X1) ) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK1(X0,X1),sK0(X0,X1)),singleton(sK1(X0,X1))),X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),X3)
| in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),X3)
| ( X0 = X2 )
| ~ relation(X3)
| ~ is_connected_in(X3,X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_68,negated_conjecture,
( in(sK4,relation_field(sK3))
| ~ connected(sK3) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_69,negated_conjecture,
( in(sK5,relation_field(sK3))
| ~ connected(sK3) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_70,negated_conjecture,
( ~ connected(sK3)
| ( sK4 != sK5 ) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_71,negated_conjecture,
( ~ connected(sK3)
| ~ in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK3) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_72,negated_conjecture,
( ~ connected(sK3)
| ~ in(unordered_pair(unordered_pair(sK5,sK4),singleton(sK5)),sK3) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_73,negated_conjecture,
! [X0: $i,X1: $i] :
( connected(sK3)
| in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK3)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK3)
| ( X0 = X1 )
| ~ in(X1,relation_field(sK3))
| ~ in(X0,relation_field(sK3)) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_74,negated_conjecture,
relation(sK3),
inference(cnf_transformation,[],[f93]) ).
tcf(c_354,plain,
( ~ connected(sK3)
| ~ in(unordered_pair(singleton(sK5),unordered_pair(sK4,sK5)),sK3) ),
inference(demodulation,[status(thm)],[c_72,c_51]) ).
tcf(c_361,plain,
( ~ connected(sK3)
| ~ in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK5)),sK3) ),
inference(demodulation,[status(thm)],[c_71,c_51]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK1(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_60,c_51]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_59,c_51]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i] :
( connected(sK3)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK3)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3)
| ( X0 = X1 )
| ~ in(X1,relation_field(sK3))
| ~ in(X0,relation_field(sK3)) ),
inference(demodulation,[status(thm)],[c_73,c_51]) ).
tcf(c_417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X3)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),X3)
| ( X0 = X2 )
| ~ relation(X3)
| ~ is_connected_in(X3,X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_61,c_51]) ).
tcf(c_950,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_388,c_74]) ).
tcf(c_951,plain,
! [X0: $i] :
( is_connected_in(sK3,X0)
| ~ in(unordered_pair(singleton(sK0(sK3,X0)),unordered_pair(sK0(sK3,X0),sK1(sK3,X0))),sK3) ),
inference(unflattening,[status(thm)],[c_950]) ).
tcf(c_968,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ( X0 != sK3 )
| ( sK0(X0,X1) != sK1(X0,X1) ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_74]) ).
tcf(c_969,plain,
! [X0: $i] :
( is_connected_in(sK3,X0)
| ( sK0(sK3,X0) != sK1(sK3,X0) ) ),
inference(unflattening,[status(thm)],[c_968]) ).
tcf(c_2533,definition,
iPr_def_10 = relation_field(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2534,definition,
iPr_def_11 = singleton(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2535,definition,
iPr_def_12 = unordered_pair(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2536,definition,
iPr_def_13 = unordered_pair(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2537,definition,
iPr_def_14 = singleton(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2538,definition,
iPr_def_15 = unordered_pair(iPr_def_14,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_2539,plain,
! [X0: $i,X1: $i] :
( connected(sK3)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK3)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3)
| ( X0 = X1 )
| ~ in(X1,iPr_def_10)
| ~ in(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_398,c_2533]) ).
tcf(c_2540,plain,
( ~ connected(sK3)
| ~ in(iPr_def_13,sK3) ),
inference(demodulation,[status(thm)],[c_361,c_2535,c_2534,c_2536]) ).
tcf(c_2541,plain,
( ~ connected(sK3)
| ~ in(iPr_def_15,sK3) ),
inference(demodulation,[status(thm)],[c_354,c_2537,c_2538]) ).
tcf(c_2542,negated_conjecture,
relation(sK3),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_2543,negated_conjecture,
( ~ connected(sK3)
| ( sK4 != sK5 ) ),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_2544,negated_conjecture,
( in(sK5,iPr_def_10)
| ~ connected(sK3) ),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_2545,negated_conjecture,
( in(sK4,iPr_def_10)
| ~ connected(sK3) ),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_3126,plain,
unordered_pair(iPr_def_12,iPr_def_14) = iPr_def_15,
inference(demodulation,[status(thm)],[c_2538,c_51]) ).
tcf(c_3308,plain,
! [X0: $i,X1: $i] :
( connected(sK3)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK3)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK3)
| ( X0 = X1 )
| ~ in(X1,iPr_def_10)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_51,c_2539]) ).
tcf(c_3409,plain,
( connected(sK3)
| ~ relation(sK3)
| ~ is_connected_in(sK3,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2533,c_53]) ).
tcf(c_3410,plain,
( connected(sK3)
| ~ is_connected_in(sK3,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3409,c_2542]) ).
tcf(c_3447,plain,
! [X0: $i,X1: $i] :
( connected(sK3)
| in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK3)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK3)
| ( X0 = X1 )
| ~ in(X1,iPr_def_10)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_51,c_3308]) ).
tcf(c_3667,plain,
( is_connected_in(sK3,iPr_def_10)
| ~ relation(sK3)
| ~ connected(sK3) ),
inference(superposition,[status(thm)],[c_2533,c_54]) ).
tcf(c_3669,plain,
( is_connected_in(sK3,iPr_def_10)
| ~ connected(sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3667,c_2542]) ).
tcf(c_4112,plain,
! [X0: $i] :
( connected(sK3)
| is_connected_in(sK3,X0)
| in(unordered_pair(singleton(sK0(sK3,X0)),unordered_pair(sK0(sK3,X0),sK1(sK3,X0))),sK3)
| ( sK0(sK3,X0) = sK1(sK3,X0) )
| ~ relation(sK3)
| ~ in(sK1(sK3,X0),iPr_def_10)
| ~ in(sK0(sK3,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3308,c_378]) ).
tcf(c_4113,plain,
! [X0: $i] :
( connected(sK3)
| is_connected_in(sK3,X0)
| in(unordered_pair(singleton(sK0(sK3,X0)),unordered_pair(sK1(sK3,X0),sK0(sK3,X0))),sK3)
| ( sK0(sK3,X0) = sK1(sK3,X0) )
| ~ relation(sK3)
| ~ in(sK1(sK3,X0),iPr_def_10)
| ~ in(sK0(sK3,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3447,c_378]) ).
tcf(c_4114,plain,
! [X0: $i] :
( connected(sK3)
| is_connected_in(sK3,X0)
| in(unordered_pair(singleton(sK0(sK3,X0)),unordered_pair(sK1(sK3,X0),sK0(sK3,X0))),sK3)
| ( sK0(sK3,X0) = sK1(sK3,X0) )
| ~ in(sK1(sK3,X0),iPr_def_10)
| ~ in(sK0(sK3,X0),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4113,c_2542]) ).
tcf(c_4121,plain,
! [X0: $i] :
( connected(sK3)
| is_connected_in(sK3,X0)
| in(unordered_pair(singleton(sK0(sK3,X0)),unordered_pair(sK0(sK3,X0),sK1(sK3,X0))),sK3)
| ( sK0(sK3,X0) = sK1(sK3,X0) )
| ~ in(sK1(sK3,X0),iPr_def_10)
| ~ in(sK0(sK3,X0),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4112,c_2542]) ).
tcf(c_4184,plain,
! [X0: $i] :
( connected(sK3)
| is_connected_in(sK3,X0)
| ~ in(sK1(sK3,X0),iPr_def_10)
| ~ in(sK0(sK3,X0),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_4114,c_951,c_969,c_4121]) ).
tcf(c_4195,plain,
( connected(sK3)
| is_connected_in(sK3,iPr_def_10)
| ~ relation(sK3)
| ~ in(sK0(sK3,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_57,c_4184]) ).
tcf(c_4196,plain,
( connected(sK3)
| is_connected_in(sK3,iPr_def_10)
| ~ in(sK0(sK3,iPr_def_10),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4195,c_2542]) ).
tcf(c_4200,plain,
( connected(sK3)
| ~ in(sK0(sK3,iPr_def_10),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_4196,c_3410,c_4196]) ).
tcf(c_4206,plain,
( connected(sK3)
| is_connected_in(sK3,iPr_def_10)
| ~ relation(sK3) ),
inference(superposition,[status(thm)],[c_56,c_4200]) ).
tcf(c_4207,plain,
( connected(sK3)
| is_connected_in(sK3,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4206,c_2542]) ).
tcf(c_4210,plain,
connected(sK3),
inference(global_subsumption_just,[status(thm)],[c_4207,c_3410,c_4207]) ).
tcf(c_4212,plain,
is_connected_in(sK3,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_3669,c_4210]) ).
tcf(c_4216,plain,
in(sK4,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_2545,c_4210]) ).
tcf(c_4217,plain,
in(sK5,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_2544,c_4210]) ).
tcf(c_4218,plain,
~ in(iPr_def_15,sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_2541,c_4210]) ).
tcf(c_4219,plain,
~ in(iPr_def_13,sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_2540,c_4210]) ).
tcf(c_4220,plain,
sK4 != sK5,
inference(backward_subsumption_resolution,[status(thm)],[c_2543,c_4210]) ).
tcf(c_4253,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK4),unordered_pair(sK4,X0)),X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK4)),X1)
| ( X0 = sK4 )
| ~ relation(X1)
| ~ is_connected_in(X1,iPr_def_10)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4216,c_417]) ).
tcf(c_4254,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(iPr_def_11,unordered_pair(sK4,X0)),X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK4)),X1)
| ( X0 = sK4 )
| ~ relation(X1)
| ~ is_connected_in(X1,iPr_def_10)
| ~ in(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_4253,c_2534]) ).
tcf(c_4311,plain,
! [X0: $i] :
( in(unordered_pair(iPr_def_14,unordered_pair(sK5,sK4)),X0)
| in(unordered_pair(iPr_def_11,unordered_pair(sK4,sK5)),X0)
| ( sK4 = sK5 )
| ~ relation(X0)
| ~ in(sK5,iPr_def_10)
| ~ is_connected_in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2537,c_4254]) ).
tcf(c_4324,plain,
! [X0: $i] :
( in(iPr_def_13,X0)
| in(unordered_pair(iPr_def_14,unordered_pair(sK5,sK4)),X0)
| ( sK4 = sK5 )
| ~ relation(X0)
| ~ in(sK5,iPr_def_10)
| ~ is_connected_in(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_4311,c_2535,c_2536]) ).
tcf(c_4325,plain,
! [X0: $i] :
( in(iPr_def_13,X0)
| in(unordered_pair(iPr_def_14,unordered_pair(sK5,sK4)),X0)
| ~ relation(X0)
| ~ is_connected_in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4324,c_4220,c_4217]) ).
tcf(c_4364,plain,
! [X0: $i] :
( in(iPr_def_15,X0)
| in(iPr_def_13,X0)
| ~ relation(X0)
| ~ is_connected_in(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_4325,c_51,c_2535,c_3126]) ).
tcf(c_4377,plain,
( in(iPr_def_15,sK3)
| in(iPr_def_13,sK3)
| ~ relation(sK3) ),
inference(superposition,[status(thm)],[c_4212,c_4364]) ).
tcf(c_4378,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4377,c_4218,c_4219,c_2542]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU242+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.44 % Computer : n016.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Thu Sep 24 13:26:58 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.24/0.50 Running first-order theorem proving
% 0.24/0.50 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
% 0.24/0.52
% 0.24/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.52
% 0.24/0.52 % Detected problem language: tptp
% 0.24/0.54 % Proving...
% 1.49/1.43 % SZS status Started for theBenchmark.p
% 1.49/1.43 % SZS status Theorem for theBenchmark.p
% 1.49/1.43
% 1.49/1.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.49/1.43
% 1.49/1.43 % ------ iProver source info
% 1.49/1.43
% 1.49/1.43 % git: date: 2026-07-19 20:42:38 +0200
% 1.49/1.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.49/1.43 % git: non_committed_changes: false
% 1.49/1.43
% 1.49/1.43 % ------ Parsing...
% 1.49/1.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.49/1.43
% 1.49/1.43 % ------ 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 %
% 1.49/1.43
% 1.49/1.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.49/1.43
% 1.49/1.43 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.49/1.43 % ------ Proving...
% 1.49/1.43 % ------ Problem Properties
% 1.49/1.43
% 1.49/1.43 %
% 1.49/1.43 % clauses 41
% 1.49/1.43 % conjectures 4
% 1.49/1.43 % EPR 17
% 1.49/1.43 % Horn 36
% 1.49/1.43 % unary 19
% 1.49/1.43 % binary 12
% 1.49/1.43 % lits 80
% 1.49/1.43 % lits eq 17
% 1.49/1.43 % fd_pure 0
% 1.49/1.43 % fd_pseudo 0
% 1.49/1.43 % fd_cond 1
% 1.49/1.43 % fd_pseudo_cond 3
% 1.49/1.43 % AC symbols 0
% 1.49/1.43
% 1.49/1.43 % ------ Schedule dynamic 5 is on
% 1.49/1.43
% 1.49/1.43 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.49/1.43
% 1.49/1.43
% 1.49/1.43 % ------
% 1.49/1.43 % Current options:
% 1.49/1.43 % ------
% 1.49/1.43
% 1.49/1.43
% 1.49/1.43 %
% 1.49/1.43
% 1.49/1.43 % ------ Proving...
% 1.49/1.43 %
% 1.49/1.43
% 1.49/1.43 % SZS status Theorem for theBenchmark.p
% 1.49/1.43
% 1.49/1.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.49/1.43
% 1.49/1.43
%------------------------------------------------------------------------------