%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU255+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 : 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 02:56:22 PM UTC 2026
% Result : Theorem 23.66s 16.82s
% Output : CNFRefutation 23.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 12 unt; 0 def)
% Number of atoms : 174 ( 22 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 205 ( 84 ~; 86 |; 22 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 78 !; 8 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f56,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(f85,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f152,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f204,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(f230,conjecture,
! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord1) ).
fof(f231,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f230]) ).
fof(f291,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f393,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f85]) ).
fof(f449,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f152]) ).
fof(f450,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) ) ),
inference(flattening,[],[f449]) ).
fof(f494,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f204]) ).
fof(f533,plain,
? [X0,X1] :
( relation(X1)
& antisymmetric(X1)
& ~ antisymmetric(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f231]) ).
fof(f534,plain,
? [X0,X1] :
( relation(X1)
& antisymmetric(X1)
& ~ antisymmetric(relation_restriction(X1,X0)) ),
inference(flattening,[],[f533]) ).
fof(f777,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) )
& ( ? [X1,X2] :
( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0)
& X1 != X2 )
| antisymmetric(X0) ) ) ),
inference(nnf_transformation,[],[f450]) ).
fof(f778,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| ! [X3,X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| X3 = X4 ) )
& ( ? [X1,X2] :
( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0)
& X1 != X2 )
| antisymmetric(X0) ) ) ),
inference(rectify,[],[f777]) ).
fof(f779,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| ! [X3,X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| X3 = X4 ) )
& ( ( in(ordered_pair(sK84(X0),sK83(X0)),X0)
& in(ordered_pair(sK83(X0),sK84(X0)),X0)
& sK83(X0) != sK84(X0) )
| antisymmetric(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83,sK84]),skolemize(X1,sK83(X0)),skolemize(X2,sK84(X0))],[f778]) ).
fof(f816,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,[],[f494]) ).
fof(f817,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,[],[f816]) ).
fof(f820,plain,
( relation(sK106)
& antisymmetric(sK106)
& ~ antisymmetric(relation_restriction(sK106,sK105)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105,sK106]),skolemize(X0,sK105),skolemize(X1,sK106)],[f534]) ).
fof(f1084,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f56]) ).
fof(f1137,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f393]) ).
fof(f1228,plain,
! [X3,X0,X4] :
( ~ relation(X0)
| ~ antisymmetric(X0)
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| X3 = X4 ),
inference(cnf_transformation,[],[f779]) ).
fof(f1229,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK84(X0),sK83(X0)),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f779]) ).
fof(f1230,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK83(X0),sK84(X0)),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f779]) ).
fof(f1231,plain,
! [X0] :
( ~ relation(X0)
| sK83(X0) != sK84(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f779]) ).
fof(f1333,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,X2) ),
inference(cnf_transformation,[],[f817]) ).
fof(f1366,plain,
relation(sK106),
inference(cnf_transformation,[],[f820]) ).
fof(f1367,plain,
antisymmetric(sK106),
inference(cnf_transformation,[],[f820]) ).
fof(f1368,plain,
~ antisymmetric(relation_restriction(sK106,sK105)),
inference(cnf_transformation,[],[f820]) ).
fof(f1476,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f291]) ).
fof(f1514,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1084,f1476]) ).
fof(f1626,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK83(X0),sK84(X0)),unordered_pair(sK83(X0),sK83(X0))),X0)
| antisymmetric(X0) ),
inference(definition_unfolding,[],[f1230,f1514]) ).
fof(f1627,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK84(X0),sK83(X0)),unordered_pair(sK84(X0),sK84(X0))),X0)
| antisymmetric(X0) ),
inference(definition_unfolding,[],[f1229,f1514]) ).
fof(f1628,plain,
! [X3,X0,X4] :
( ~ relation(X0)
| ~ antisymmetric(X0)
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X0)
| X3 = X4 ),
inference(definition_unfolding,[],[f1228,f1514,f1514]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1137]) ).
tcf(c_404,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ relation(X0)
| ( sK83(X0) != sK84(X0) ) ),
inference(cnf_transformation,[],[f1231]) ).
tcf(c_405,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK83(X0),sK84(X0)),unordered_pair(sK83(X0),sK83(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1626]) ).
tcf(c_406,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK84(X0),sK83(X0)),unordered_pair(sK84(X0),sK84(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1627]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ antisymmetric(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1628]) ).
tcf(c_509,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(X1)
| ~ in(X0,relation_restriction(X1,X2)) ),
inference(cnf_transformation,[],[f1333]) ).
tcf(c_542,negated_conjecture,
~ antisymmetric(relation_restriction(sK106,sK105)),
inference(cnf_transformation,[],[f1368]) ).
tcf(c_543,negated_conjecture,
antisymmetric(sK106),
inference(cnf_transformation,[],[f1367]) ).
tcf(c_544,negated_conjecture,
relation(sK106),
inference(cnf_transformation,[],[f1366]) ).
tcf(c_12825,plain,
( antisymmetric(relation_restriction(sK106,sK105))
| ~ relation(relation_restriction(sK106,sK105))
| ( sK83(relation_restriction(sK106,sK105)) != sK84(relation_restriction(sK106,sK105)) ) ),
inference(instantiation,[status(thm)],[c_404]) ).
tcf(c_12826,plain,
( antisymmetric(relation_restriction(sK106,sK105))
| in(unordered_pair(unordered_pair(sK83(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105))),unordered_pair(sK83(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105)))),relation_restriction(sK106,sK105))
| ~ relation(relation_restriction(sK106,sK105)) ),
inference(instantiation,[status(thm)],[c_405]) ).
tcf(c_12827,plain,
( antisymmetric(relation_restriction(sK106,sK105))
| in(unordered_pair(unordered_pair(sK84(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105))),unordered_pair(sK84(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105)))),relation_restriction(sK106,sK105))
| ~ relation(relation_restriction(sK106,sK105)) ),
inference(instantiation,[status(thm)],[c_406]) ).
tcf(c_13697,plain,
( relation(relation_restriction(sK106,sK105))
| ~ relation(sK106) ),
inference(instantiation,[status(thm)],[c_313]) ).
tcf(c_14564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_restriction(X2,X3)) ),
inference(instantiation,[status(thm)],[c_509]) ).
tcf(c_15184,plain,
! [X0: $i] :
( ( sK83(relation_restriction(sK106,sK105)) = sK84(relation_restriction(sK106,sK105)) )
| ~ antisymmetric(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK84(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105))),unordered_pair(sK84(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105)))),X0)
| ~ in(unordered_pair(unordered_pair(sK83(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105))),unordered_pair(sK83(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105)))),X0) ),
inference(instantiation,[status(thm)],[c_407]) ).
tcf(c_16335,plain,
( in(unordered_pair(unordered_pair(sK83(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105))),unordered_pair(sK83(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105)))),sK106)
| ~ relation(sK106)
| ~ in(unordered_pair(unordered_pair(sK83(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105))),unordered_pair(sK83(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105)))),relation_restriction(sK106,sK105)) ),
inference(instantiation,[status(thm)],[c_14564]) ).
tcf(c_16336,plain,
( in(unordered_pair(unordered_pair(sK84(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105))),unordered_pair(sK84(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105)))),sK106)
| ~ relation(sK106)
| ~ in(unordered_pair(unordered_pair(sK84(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105))),unordered_pair(sK84(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105)))),relation_restriction(sK106,sK105)) ),
inference(instantiation,[status(thm)],[c_14564]) ).
tcf(c_16337,plain,
( ( sK83(relation_restriction(sK106,sK105)) = sK84(relation_restriction(sK106,sK105)) )
| ~ antisymmetric(sK106)
| ~ relation(sK106)
| ~ in(unordered_pair(unordered_pair(sK84(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105))),unordered_pair(sK84(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105)))),sK106)
| ~ in(unordered_pair(unordered_pair(sK83(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105))),unordered_pair(sK83(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105)))),sK106) ),
inference(instantiation,[status(thm)],[c_15184]) ).
tcf(c_16338,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16337,c_16336,c_16335,c_13697,c_12827,c_12826,c_12825,c_542,c_543,c_544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU255+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.37 % Computer : n011.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Thu Sep 24 13:25:23 UTC 2026
% 0.10/10.37 % CPUTime :
% 0.10/10.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/10.41 Running first-order theorem proving
% 0.13/10.41 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
% 0.13/10.42
% 0.13/10.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/10.42
% 0.13/10.43 % Detected problem language: tptp
% 0.13/10.44 % Proving...
% 23.66/16.82 % SZS status Started for theBenchmark.p
% 23.66/16.82 % SZS status Theorem for theBenchmark.p
% 23.66/16.82
% 23.66/16.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 23.66/16.82
% 23.66/16.82 % ------ iProver source info
% 23.66/16.82
% 23.66/16.82 % git: date: 2026-07-19 20:42:38 +0200
% 23.66/16.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 23.66/16.82 % git: non_committed_changes: false
% 23.66/16.82
% 23.66/16.82 % ------ Parsing...
% 23.66/16.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 23.66/16.82
% 23.66/16.82 % ------ Preprocessing...%
% 23.66/16.82
% 23.66/16.82 % ------ Preprocessing...%
% 23.66/16.82
% 23.66/16.82 % ------ Preprocessing...
% 23.66/16.82 % ------ Proving...
% 23.66/16.82 % ------ Problem Properties
% 23.66/16.82
% 23.66/16.82 %
% 23.66/16.82 % clauses 577
% 23.66/16.82 % conjectures 3
% 23.66/16.82 % EPR 96
% 23.66/16.82 % Horn 450
% 23.66/16.82 % unary 87
% 23.66/16.82 % binary 147
% 23.66/16.82 % lits 1674
% 23.66/16.82 % lits eq 265
% 23.66/16.82 % fd_pure 0
% 23.66/16.82 % fd_pseudo 0
% 23.66/16.82 % fd_cond 21
% 23.66/16.82 % fd_pseudo_cond 99
% 23.66/16.82 % AC symbols 0
% 23.66/16.82
% 23.66/16.82 % ------ Input Options Time Limit: Unbounded
% 23.66/16.82
% 23.66/16.82
% 23.66/16.82 % ------
% 23.66/16.82 % Current options:
% 23.66/16.82 % ------
% 23.66/16.82
% 23.66/16.82
% 23.66/16.82 %
% 23.66/16.82
% 23.66/16.82 % ------ Proving...
% 23.66/16.82 %
% 23.66/16.82
% 23.66/16.82 % SZS status Theorem for theBenchmark.p
% 23.66/16.82
% 23.66/16.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 23.66/16.82
% 23.66/16.82
%------------------------------------------------------------------------------