%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU239+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : 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 02:56:18 PM UTC 2026
% Result : Theorem 39.89s 6.40s
% Output : CNFRefutation 39.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 8 unt; 0 def)
% Number of atoms : 169 ( 5 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 201 ( 82 ~; 85 |; 20 &)
% ( 6 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 62 !; 9 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(X2,X1)
=> in(ordered_pair(X2,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
fof(f48,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(f58,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f127,conjecture,
! [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(f128,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f127]) ).
fof(f261,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f320,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( ~ in(X2,X1)
| in(ordered_pair(X2,X2),X0) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f345,plain,
! [X0] :
( ~ relation(X0)
| ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f393,plain,
? [X0] :
( relation(X0)
& ( reflexive(X0)
<~> ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) ) ),
inference(ennf_transformation,[],[f128]) ).
fof(f590,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_reflexive_in(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| in(ordered_pair(X2,X2),X0) ) )
& ( ? [X2] :
( in(X2,X1)
& ~ in(ordered_pair(X2,X2),X0) )
| is_reflexive_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f320]) ).
fof(f591,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_reflexive_in(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| in(ordered_pair(X3,X3),X0) ) )
& ( ? [X2] :
( in(X2,X1)
& ~ in(ordered_pair(X2,X2),X0) )
| is_reflexive_in(X0,X1) ) ) ),
inference(rectify,[],[f590]) ).
fof(f592,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_reflexive_in(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| in(ordered_pair(X3,X3),X0) ) )
& ( ( in(sK21(X0,X1),X1)
& ~ in(ordered_pair(sK21(X0,X1),sK21(X0,X1)),X0) )
| is_reflexive_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X2,sK21(X0,X1))],[f591]) ).
fof(f670,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) )
& ( ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0) ) ) ),
inference(nnf_transformation,[],[f345]) ).
fof(f672,plain,
? [X0] :
( relation(X0)
& ( reflexive(X0)
| ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) )
& ( ~ reflexive(X0)
| ? [X1] :
( in(X1,relation_field(X0))
& ~ in(ordered_pair(X1,X1),X0) ) ) ),
inference(nnf_transformation,[],[f393]) ).
fof(f673,plain,
? [X0] :
( relation(X0)
& ( reflexive(X0)
| ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) )
& ( ~ reflexive(X0)
| ? [X1] :
( in(X1,relation_field(X0))
& ~ in(ordered_pair(X1,X1),X0) ) ) ),
inference(flattening,[],[f672]) ).
fof(f674,plain,
? [X0] :
( relation(X0)
& ( reflexive(X0)
| ! [X2] :
( ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ) )
& ( ~ reflexive(X0)
| ? [X1] :
( in(X1,relation_field(X0))
& ~ in(ordered_pair(X1,X1),X0) ) ) ),
inference(rectify,[],[f673]) ).
fof(f675,plain,
( relation(sK67)
& ( reflexive(sK67)
| ! [X2] :
( ~ in(X2,relation_field(sK67))
| in(ordered_pair(X2,X2),sK67) ) )
& ( ~ reflexive(sK67)
| ( in(sK68,relation_field(sK67))
& ~ in(ordered_pair(sK68,sK68),sK67) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67,sK68]),skolemize(X0,sK67),skolemize(X1,sK68)],[f674]) ).
fof(f835,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ is_reflexive_in(X0,X1)
| ~ in(X3,X1)
| in(ordered_pair(X3,X3),X0) ),
inference(cnf_transformation,[],[f592]) ).
fof(f836,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK21(X0,X1),X1)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f592]) ).
fof(f837,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK21(X0,X1),sK21(X0,X1)),X0)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f592]) ).
fof(f940,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f968,plain,
! [X0] :
( ~ relation(X0)
| ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f670]) ).
fof(f969,plain,
! [X0] :
( ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0) ),
inference(cnf_transformation,[],[f670]) ).
fof(f1044,plain,
relation(sK67),
inference(cnf_transformation,[],[f675]) ).
fof(f1045,plain,
! [X2] :
( reflexive(sK67)
| ~ in(X2,relation_field(sK67))
| in(ordered_pair(X2,X2),sK67) ),
inference(cnf_transformation,[],[f675]) ).
fof(f1046,plain,
( ~ reflexive(sK67)
| in(sK68,relation_field(sK67)) ),
inference(cnf_transformation,[],[f675]) ).
fof(f1047,plain,
( ~ reflexive(sK67)
| ~ in(ordered_pair(sK68,sK68),sK67) ),
inference(cnf_transformation,[],[f675]) ).
fof(f1277,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f261]) ).
fof(f1313,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f940,f1277]) ).
fof(f1344,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK21(X0,X1),sK21(X0,X1)),unordered_pair(sK21(X0,X1),sK21(X0,X1))),X0)
| is_reflexive_in(X0,X1) ),
inference(definition_unfolding,[],[f837,f1313]) ).
fof(f1345,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ is_reflexive_in(X0,X1)
| ~ in(X3,X1)
| in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X3)),X0) ),
inference(definition_unfolding,[],[f835,f1313]) ).
fof(f1398,plain,
( ~ reflexive(sK67)
| ~ in(unordered_pair(unordered_pair(sK68,sK68),unordered_pair(sK68,sK68)),sK67) ),
inference(definition_unfolding,[],[f1047,f1313]) ).
fof(f1399,plain,
! [X2] :
( reflexive(sK67)
| ~ in(X2,relation_field(sK67))
| in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X2)),sK67) ),
inference(definition_unfolding,[],[f1045,f1313]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK21(X0,X1),sK21(X0,X1)),unordered_pair(sK21(X0,X1),sK21(X0,X1))),X0) ),
inference(cnf_transformation,[],[f1344]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( is_reflexive_in(X0,X1)
| in(sK21(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f836]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ is_reflexive_in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1345]) ).
tcf(c_254,plain,
! [X0: $i] :
( reflexive(X0)
| ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f969]) ).
tcf(c_255,plain,
! [X0: $i] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f968]) ).
tcf(c_330,negated_conjecture,
( ~ reflexive(sK67)
| ~ in(unordered_pair(unordered_pair(sK68,sK68),unordered_pair(sK68,sK68)),sK67) ),
inference(cnf_transformation,[],[f1398]) ).
tcf(c_331,negated_conjecture,
( in(sK68,relation_field(sK67))
| ~ reflexive(sK67) ),
inference(cnf_transformation,[],[f1046]) ).
tcf(c_332,negated_conjecture,
! [X0: $i] :
( reflexive(sK67)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),sK67)
| ~ in(X0,relation_field(sK67)) ),
inference(cnf_transformation,[],[f1399]) ).
tcf(c_333,negated_conjecture,
relation(sK67),
inference(cnf_transformation,[],[f1044]) ).
tcf(c_10127,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK68,sK68),unordered_pair(sK68,sK68)),X0)
| ~ relation(X0)
| ~ in(sK68,relation_field(sK67))
| ~ is_reflexive_in(X0,relation_field(sK67)) ),
inference(instantiation,[status(thm)],[c_124]) ).
tcf(c_10321,plain,
( reflexive(sK67)
| ~ relation(sK67)
| ~ is_reflexive_in(sK67,relation_field(sK67)) ),
inference(instantiation,[status(thm)],[c_254]) ).
tcf(c_11540,plain,
( is_reflexive_in(sK67,relation_field(sK67))
| in(sK21(sK67,relation_field(sK67)),relation_field(sK67))
| ~ relation(sK67) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_11541,plain,
( is_reflexive_in(sK67,relation_field(sK67))
| ~ relation(sK67)
| ~ in(unordered_pair(unordered_pair(sK21(sK67,relation_field(sK67)),sK21(sK67,relation_field(sK67))),unordered_pair(sK21(sK67,relation_field(sK67)),sK21(sK67,relation_field(sK67)))),sK67) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_11542,plain,
( is_reflexive_in(sK67,relation_field(sK67))
| ~ reflexive(sK67)
| ~ relation(sK67) ),
inference(instantiation,[status(thm)],[c_255]) ).
tcf(c_14897,plain,
( reflexive(sK67)
| in(unordered_pair(unordered_pair(sK21(sK67,relation_field(sK67)),sK21(sK67,relation_field(sK67))),unordered_pair(sK21(sK67,relation_field(sK67)),sK21(sK67,relation_field(sK67)))),sK67)
| ~ in(sK21(sK67,relation_field(sK67)),relation_field(sK67)) ),
inference(instantiation,[status(thm)],[c_332]) ).
tcf(c_15673,plain,
( in(unordered_pair(unordered_pair(sK68,sK68),unordered_pair(sK68,sK68)),sK67)
| ~ relation(sK67)
| ~ is_reflexive_in(sK67,relation_field(sK67))
| ~ in(sK68,relation_field(sK67)) ),
inference(instantiation,[status(thm)],[c_10127]) ).
tcf(c_16688,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_15673,c_14897,c_11542,c_11540,c_11541,c_10321,c_330,c_331,c_333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU239+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 13:21:59 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 39.89/6.40 % SZS status Started for theBenchmark.p
% 39.89/6.40 % SZS status Theorem for theBenchmark.p
% 39.89/6.40
% 39.89/6.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 39.89/6.40
% 39.89/6.40 % ------ iProver source info
% 39.89/6.40
% 39.89/6.40 % git: date: 2026-07-19 20:42:38 +0200
% 39.89/6.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 39.89/6.40 % git: non_committed_changes: false
% 39.89/6.40
% 39.89/6.40 % ------ Parsing...
% 39.89/6.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 39.89/6.40
% 39.89/6.40 % ------ Preprocessing...%
% 39.89/6.40
% 39.89/6.40 % ------ Preprocessing...%
% 39.89/6.40
% 39.89/6.40 % ------ Preprocessing...
% 39.89/6.40 % ------ Proving...
% 39.89/6.40 % ------ Problem Properties
% 39.89/6.40
% 39.89/6.40 %
% 39.89/6.40 % clauses 487
% 39.89/6.40 % conjectures 4
% 39.89/6.40 % EPR 83
% 39.89/6.40 % Horn 389
% 39.89/6.40 % unary 85
% 39.89/6.40 % binary 140
% 39.89/6.40 % lits 1369
% 39.89/6.40 % lits eq 242
% 39.89/6.40 % fd_pure 0
% 39.89/6.40 % fd_pseudo 0
% 39.89/6.40 % fd_cond 17
% 39.89/6.40 % fd_pseudo_cond 92
% 39.89/6.40 % AC symbols 0
% 39.89/6.40
% 39.89/6.40 % ------ Input Options Time Limit: Unbounded
% 39.89/6.40
% 39.89/6.40
% 39.89/6.40 % ------
% 39.89/6.40 % Current options:
% 39.89/6.40 % ------
% 39.89/6.40
% 39.89/6.40
% 39.89/6.40 %
% 39.89/6.40
% 39.89/6.40 % ------ Proving...
% 39.89/6.40 %
% 39.89/6.40
% 39.89/6.40 % SZS status Theorem for theBenchmark.p
% 39.89/6.40
% 39.89/6.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 39.89/6.40
% 39.89/6.40
%------------------------------------------------------------------------------