%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU281+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 : Tue Sep 29 12:48:09 PM UTC 2026
% Result : Theorem 29.04s 4.97s
% Output : Refutation 29.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 12
% Syntax : Number of formulae : 123 ( 16 unt; 6 def)
% Number of atoms : 488 ( 162 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 558 ( 193 ~; 228 |; 121 &)
% ( 11 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-3 aty)
% Number of variables : 294 ( 0 sgn 201 !; 93 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f62,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(f204,axiom,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,cartesian_product2(X0,X1))
& X4 = X3
& ? [X9,X10] :
( ordered_pair(X9,X10) = X3
& in(X9,X0)
& X10 = singleton(X9) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
fof(f208,conjecture,
! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
fof(f209,negated_conjecture,
~ ! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) ) ),
inference(negated_conjecture,[status(cth)],[f208]) ).
fof(f215,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f340,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f376,plain,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) )
=> X3 = X4 )
=> ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) ) ),
inference(rectify,[],[f204]) ).
fof(f543,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) ) ),
inference(ennf_transformation,[],[f376]) ).
fof(f544,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) ) ),
inference(flattening,[],[f543]) ).
fof(f551,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) ) ),
inference(ennf_transformation,[],[f209]) ).
fof(f741,definition,
! [X4,X0] :
( ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) )
| ~ sP2(X4,X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f742,definition,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& sP2(X4,X0) )
| ~ sP3(X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f743,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) )
| sP3(X0) ),
inference(definition_folding,[],[f544,f742,f741]) ).
fof(f961,plain,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& sP2(X4,X0) )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f742]) ).
fof(f962,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& X1 = X2
& ? [X4,X5] :
( ordered_pair(X4,X5) = X2
& in(X4,X0)
& singleton(X4) = X5 )
& X1 = X3
& sP2(X3,X0) )
| ~ sP3(X0) ),
inference(rectify,[],[f961]) ).
fof(f963,plain,
! [X0] :
( ( sK125(X0) != sK126(X0)
& sK124(X0) = sK125(X0)
& sK125(X0) = ordered_pair(sK127(X0),sK128(X0))
& in(sK127(X0),X0)
& sK128(X0) = singleton(sK127(X0))
& sK124(X0) = sK126(X0)
& sP2(sK126(X0),X0) )
| ~ sP3(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124,sK125,sK126,sK127,sK128]),skolemize(X1,sK124(X0)),skolemize(X2,sK125(X0)),skolemize(X3,sK126(X0)),skolemize(X4,sK127(X0)),skolemize(X5,sK128(X0))],[f962]) ).
fof(f967,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( ( in(X10,X9)
| ! [X11] :
( ~ in(X11,cartesian_product2(X0,X1))
| X10 != X11
| ! [X12,X13] :
( ordered_pair(X12,X13) != X10
| ~ in(X12,X0)
| singleton(X12) != X13 ) ) )
& ( ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) )
| ~ in(X10,X9) ) )
| sP3(X0) ),
inference(nnf_transformation,[],[f743]) ).
fof(f968,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,cartesian_product2(X0,X1))
| X3 != X4
| ! [X5,X6] :
( ordered_pair(X5,X6) != X3
| ~ in(X5,X0)
| singleton(X5) != X6 ) ) )
& ( ? [X7] :
( in(X7,cartesian_product2(X0,X1))
& X3 = X7
& ? [X8,X9] :
( ordered_pair(X8,X9) = X3
& in(X8,X0)
& singleton(X8) = X9 ) )
| ~ in(X3,X2) ) )
| sP3(X0) ),
inference(rectify,[],[f967]) ).
fof(f969,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK131(X0,X1))
| ! [X4] :
( ~ in(X4,cartesian_product2(X0,X1))
| X3 != X4
| ! [X5,X6] :
( ordered_pair(X5,X6) != X3
| ~ in(X5,X0)
| singleton(X5) != X6 ) ) )
& ( ( in(sK132(X0,X1,X3),cartesian_product2(X0,X1))
& sK132(X0,X1,X3) = X3
& ordered_pair(sK133(X0,X3),sK134(X0,X3)) = X3
& in(sK133(X0,X3),X0)
& sK134(X0,X3) = singleton(sK133(X0,X3)) )
| ~ in(X3,sK131(X0,X1)) ) )
| sP3(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131,sK132,sK133,sK134]),skolemize(X2,sK131(X0,X1)),skolemize(X7,sK132(X0,X1,X3)),skolemize(X8,sK133(X0,X3)),skolemize(X9,sK134(X0,X3))],[f968]) ).
fof(f991,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ~ in(X3,cartesian_product2(X0,X1))
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X4,X0)
| singleton(X4) != X5 )
| ~ in(X3,X2) )
& ( ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) )
| in(X3,X2) ) ),
inference(nnf_transformation,[],[f551]) ).
fof(f992,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ~ in(X3,cartesian_product2(X0,X1))
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X4,X0)
| singleton(X4) != X5 )
| ~ in(X3,X2) )
& ( ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) )
| in(X3,X2) ) ),
inference(flattening,[],[f991]) ).
fof(f993,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ~ in(X3,cartesian_product2(X0,X1))
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X4,X0)
| singleton(X4) != X5 )
| ~ in(X3,X2) )
& ( ( in(X3,cartesian_product2(X0,X1))
& ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X6,X0)
& singleton(X6) = X7 ) )
| in(X3,X2) ) ),
inference(rectify,[],[f992]) ).
fof(f994,plain,
! [X2] :
( ( ~ in(sK161(X2),cartesian_product2(sK159,sK160))
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK161(X2)
| ~ in(X4,sK159)
| singleton(X4) != X5 )
| ~ in(sK161(X2),X2) )
& ( ( in(sK161(X2),cartesian_product2(sK159,sK160))
& sK161(X2) = ordered_pair(sK162(X2),sK163(X2))
& in(sK162(X2),sK159)
& sK163(X2) = singleton(sK162(X2)) )
| in(sK161(X2),X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159,sK160,sK161,sK162,sK163]),skolemize(X0,sK159),skolemize(X1,sK160),skolemize(X3,sK161(X2)),skolemize(X6,sK162(X2)),skolemize(X7,sK163(X2))],[f993]) ).
fof(f1006,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f215]) ).
fof(f1007,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f1006]) ).
fof(f1089,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f1312,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f62]) ).
fof(f1561,plain,
! [X0] :
( sK124(X0) = sK126(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f963]) ).
fof(f1565,plain,
! [X0] :
( sK124(X0) = sK125(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f963]) ).
fof(f1566,plain,
! [X0] :
( sK125(X0) != sK126(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f963]) ).
fof(f1570,plain,
! [X3,X0,X1] :
( sK134(X0,X3) = singleton(sK133(X0,X3))
| ~ in(X3,sK131(X0,X1))
| sP3(X0) ),
inference(cnf_transformation,[],[f969]) ).
fof(f1571,plain,
! [X3,X0,X1] :
( ~ in(X3,sK131(X0,X1))
| in(sK133(X0,X3),X0)
| sP3(X0) ),
inference(cnf_transformation,[],[f969]) ).
fof(f1572,plain,
! [X3,X0,X1] :
( ordered_pair(sK133(X0,X3),sK134(X0,X3)) = X3
| ~ in(X3,sK131(X0,X1))
| sP3(X0) ),
inference(cnf_transformation,[],[f969]) ).
fof(f1573,plain,
! [X3,X0,X1] :
( sK132(X0,X1,X3) = X3
| ~ in(X3,sK131(X0,X1))
| sP3(X0) ),
inference(cnf_transformation,[],[f969]) ).
fof(f1574,plain,
! [X3,X0,X1] :
( in(sK132(X0,X1,X3),cartesian_product2(X0,X1))
| ~ in(X3,sK131(X0,X1))
| sP3(X0) ),
inference(cnf_transformation,[],[f969]) ).
fof(f1575,plain,
! [X3,X0,X1,X6,X4,X5] :
( in(X3,sK131(X0,X1))
| ~ in(X4,cartesian_product2(X0,X1))
| X3 != X4
| ordered_pair(X5,X6) != X3
| ~ in(X5,X0)
| singleton(X5) != X6
| sP3(X0) ),
inference(cnf_transformation,[],[f969]) ).
fof(f1613,plain,
! [X2] :
( sK163(X2) = singleton(sK162(X2))
| in(sK161(X2),X2) ),
inference(cnf_transformation,[],[f994]) ).
fof(f1614,plain,
! [X2] :
( in(sK162(X2),sK159)
| in(sK161(X2),X2) ),
inference(cnf_transformation,[],[f994]) ).
fof(f1615,plain,
! [X2] :
( sK161(X2) = ordered_pair(sK162(X2),sK163(X2))
| in(sK161(X2),X2) ),
inference(cnf_transformation,[],[f994]) ).
fof(f1616,plain,
! [X2] :
( in(sK161(X2),cartesian_product2(sK159,sK160))
| in(sK161(X2),X2) ),
inference(cnf_transformation,[],[f994]) ).
fof(f1617,plain,
! [X2,X4,X5] :
( ~ in(sK161(X2),cartesian_product2(sK159,sK160))
| ordered_pair(X4,X5) != sK161(X2)
| ~ in(X4,sK159)
| singleton(X4) != X5
| ~ in(sK161(X2),X2) ),
inference(cnf_transformation,[],[f994]) ).
fof(f1633,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f1007]) ).
fof(f1837,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f340]) ).
fof(f1881,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1312,f1837]) ).
fof(f2031,plain,
! [X3,X0,X1,X6,X4,X5] :
( in(X3,sK131(X0,X1))
| ~ in(X4,cartesian_product2(X0,X1))
| X3 != X4
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X3
| ~ in(X5,X0)
| unordered_pair(X5,X5) != X6
| sP3(X0) ),
inference(definition_unfolding,[],[f1575,f1881,f1837]) ).
fof(f2032,plain,
! [X3,X0,X1] :
( unordered_pair(unordered_pair(sK133(X0,X3),sK134(X0,X3)),unordered_pair(sK133(X0,X3),sK133(X0,X3))) = X3
| ~ in(X3,sK131(X0,X1))
| sP3(X0) ),
inference(definition_unfolding,[],[f1572,f1881]) ).
fof(f2033,plain,
! [X3,X0,X1] :
( sK134(X0,X3) = unordered_pair(sK133(X0,X3),sK133(X0,X3))
| ~ in(X3,sK131(X0,X1))
| sP3(X0) ),
inference(definition_unfolding,[],[f1570,f1837]) ).
fof(f2043,plain,
! [X2,X4,X5] :
( ~ in(sK161(X2),cartesian_product2(sK159,sK160))
| sK161(X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X4,sK159)
| unordered_pair(X4,X4) != X5
| ~ in(sK161(X2),X2) ),
inference(definition_unfolding,[],[f1617,f1881,f1837]) ).
fof(f2044,plain,
! [X2] :
( sK161(X2) = unordered_pair(unordered_pair(sK162(X2),sK163(X2)),unordered_pair(sK162(X2),sK162(X2)))
| in(sK161(X2),X2) ),
inference(definition_unfolding,[],[f1615,f1881]) ).
fof(f2045,plain,
! [X2] :
( sK163(X2) = unordered_pair(sK162(X2),sK162(X2))
| in(sK161(X2),X2) ),
inference(definition_unfolding,[],[f1613,f1837]) ).
fof(f2052,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f1633,f1881]) ).
fof(f2220,plain,
! [X0,X1,X6,X4,X5] :
( in(X4,sK131(X0,X1))
| ~ in(X4,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X5,X0)
| unordered_pair(X5,X5) != X6
| sP3(X0) ),
inference(equality_resolution,[],[f2031]) ).
fof(f2221,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),sK131(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),cartesian_product2(X0,X1))
| ~ in(X5,X0)
| unordered_pair(X5,X5) != X6
| sP3(X0) ),
inference(equality_resolution,[],[f2220]) ).
fof(f2222,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)),sK131(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)),cartesian_product2(X0,X1))
| ~ in(X5,X0)
| sP3(X0) ),
inference(equality_resolution,[],[f2221]) ).
fof(f2228,plain,
! [X2,X4] :
( ~ in(sK161(X2),cartesian_product2(sK159,sK160))
| sK161(X2) != unordered_pair(unordered_pair(X4,unordered_pair(X4,X4)),unordered_pair(X4,X4))
| ~ in(X4,sK159)
| ~ in(sK161(X2),X2) ),
inference(equality_resolution,[],[f2043]) ).
fof(f2250,definition,
sF193 = cartesian_product2(sK159,sK160),
introduced(definition,[new_symbols(definition,[sF193])],[function_definition]) ).
fof(f2251,plain,
cartesian_product2(sK159,sK160) = sF193,
inference(reorient_equations,[],[f2250]) ).
fof(f2252,plain,
! [X2,X4] :
( ~ in(sK161(X2),sF193)
| sK161(X2) != unordered_pair(unordered_pair(X4,unordered_pair(X4,X4)),unordered_pair(X4,X4))
| ~ in(X4,sK159)
| ~ in(sK161(X2),X2) ),
inference(definition_folding,[],[f2228,f2251]) ).
fof(f2253,plain,
! [X2] :
( in(sK161(X2),sF193)
| in(sK161(X2),X2) ),
inference(definition_folding,[],[f1616,f2251]) ).
fof(f2305,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)),sK131(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)),cartesian_product2(X0,X1))
| sP3(X0) ),
inference(forward_subsumption_resolution,[],[f2222,f2052]) ).
fof(f2339,plain,
! [X2,X4] :
( sK161(X2) != unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(X4,X4)))
| ~ in(sK161(X2),sF193)
| ~ in(X4,sK159)
| ~ in(sK161(X2),X2) ),
inference(backward_demodulation,[],[f2252,f1089]) ).
fof(f2390,plain,
! [X3,X0,X1] :
( unordered_pair(unordered_pair(sK133(X0,X3),sK133(X0,X3)),unordered_pair(sK133(X0,X3),sK134(X0,X3))) = X3
| ~ in(X3,sK131(X0,X1))
| sP3(X0) ),
inference(backward_demodulation,[],[f2032,f1089]) ).
fof(f2394,plain,
! [X2] :
( sK161(X2) = unordered_pair(unordered_pair(sK162(X2),sK162(X2)),unordered_pair(sK162(X2),sK163(X2)))
| in(sK161(X2),X2) ),
inference(backward_demodulation,[],[f2044,f1089]) ).
fof(f2410,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,unordered_pair(X5,X5))),sK131(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)),cartesian_product2(X0,X1))
| sP3(X0) ),
inference(forward_demodulation,[],[f2305,f1089]) ).
fof(f2428,plain,
! [X0,X1,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,unordered_pair(X5,X5))),cartesian_product2(X0,X1))
| in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,unordered_pair(X5,X5))),sK131(X0,X1))
| sP3(X0) ),
inference(forward_demodulation,[],[f2410,f1089]) ).
fof(f2430,plain,
! [X0,X1] :
( sK161(X1) != unordered_pair(sK163(X0),unordered_pair(sK162(X0),sK163(X0)))
| ~ in(sK161(X1),sF193)
| ~ in(sK162(X0),sK159)
| ~ in(sK161(X1),X1)
| in(sK161(X0),X0) ),
inference(superposition,[],[f2339,f2045]) ).
fof(f2431,plain,
! [X0,X1] :
( sK161(X1) != unordered_pair(sK163(X0),unordered_pair(sK162(X0),sK163(X0)))
| ~ in(sK161(X1),sF193)
| ~ in(sK161(X1),X1)
| in(sK161(X0),X0) ),
inference(forward_subsumption_resolution,[],[f2430,f1614]) ).
fof(f2432,plain,
! [X0] :
( sK161(X0) = unordered_pair(sK163(X0),unordered_pair(sK162(X0),sK163(X0)))
| in(sK161(X0),X0)
| in(sK161(X0),X0) ),
inference(superposition,[],[f2394,f2045]) ).
fof(f2433,plain,
! [X0] :
( sK161(X0) = unordered_pair(sK163(X0),unordered_pair(sK162(X0),sK163(X0)))
| in(sK161(X0),X0) ),
inference(duplicate_literal_removal,[],[f2432]) ).
fof(f2545,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sF193)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sK131(sK159,sK160))
| sP3(sK159) ),
inference(superposition,[],[f2428,f2251]) ).
fof(f2547,definition,
( spl194_13
<=> sP3(sK159) ),
introduced(definition,[new_symbols(definition,[spl194_13])],[avatar_definition]) ).
fof(f2548,plain,
( ~ sP3(sK159)
| spl194_13 ),
inference(avatar_component_clause,[],[f2547]) ).
fof(f2549,plain,
( sP3(sK159)
| ~ spl194_13 ),
inference(avatar_component_clause,[],[f2547]) ).
fof(f2551,definition,
( spl194_14
<=> ! [X0] :
( ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sF193)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sK131(sK159,sK160)) ) ),
introduced(definition,[new_symbols(definition,[spl194_14])],[avatar_definition]) ).
fof(f2552,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sK131(sK159,sK160))
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sF193) )
| ~ spl194_14 ),
inference(avatar_component_clause,[],[f2551]) ).
fof(f2553,plain,
( spl194_13
| spl194_14 ),
inference(avatar_split_clause,[],[f2545,f2551,f2547]) ).
fof(f3086,plain,
( ! [X0] :
( in(unordered_pair(sK163(X0),unordered_pair(sK162(X0),sK163(X0))),sK131(sK159,sK160))
| ~ in(unordered_pair(sK163(X0),unordered_pair(sK162(X0),sK163(X0))),sF193)
| in(sK161(X0),X0) )
| ~ spl194_14 ),
inference(superposition,[],[f2552,f2045]) ).
fof(f3087,plain,
( ! [X0] :
( in(sK161(X0),sK131(sK159,sK160))
| ~ in(sK161(X0),sF193)
| in(sK161(X0),X0)
| in(sK161(X0),X0) )
| ~ spl194_14 ),
inference(superposition,[],[f3086,f2433]) ).
fof(f3088,plain,
( ! [X0] :
( in(sK161(X0),sK131(sK159,sK160))
| ~ in(sK161(X0),sF193)
| in(sK161(X0),X0) )
| ~ spl194_14 ),
inference(duplicate_literal_removal,[],[f3087]) ).
fof(f3089,plain,
( ! [X0] :
( in(sK161(X0),sK131(sK159,sK160))
| in(sK161(X0),X0) )
| ~ spl194_14 ),
inference(forward_subsumption_resolution,[],[f3088,f2253]) ).
fof(f3091,plain,
( in(sK161(sK131(sK159,sK160)),sK131(sK159,sK160))
| ~ spl194_14 ),
inference(factoring,[],[f3089]) ).
fof(f3158,plain,
( sK134(sK159,sK161(sK131(sK159,sK160))) = unordered_pair(sK133(sK159,sK161(sK131(sK159,sK160))),sK133(sK159,sK161(sK131(sK159,sK160))))
| spl194_13
| ~ spl194_14 ),
inference(unit_resulting_resolution,[],[f2033,f2548,f3091]) ).
fof(f3263,definition,
( spl194_33
<=> in(sK133(sK159,sK161(sK131(sK159,sK160))),sK159) ),
introduced(definition,[new_symbols(definition,[spl194_33])],[avatar_definition]) ).
fof(f3264,plain,
( in(sK133(sK159,sK161(sK131(sK159,sK160))),sK159)
| ~ spl194_33 ),
inference(avatar_component_clause,[],[f3263]) ).
fof(f3265,plain,
( ~ in(sK133(sK159,sK161(sK131(sK159,sK160))),sK159)
| spl194_33 ),
inference(avatar_component_clause,[],[f3263]) ).
fof(f3666,plain,
! [X2,X0,X1] :
( in(X0,cartesian_product2(X1,X2))
| ~ in(X0,sK131(X1,X2))
| sP3(X1)
| ~ in(X0,sK131(X1,X2))
| sP3(X1) ),
inference(superposition,[],[f1574,f1573]) ).
fof(f3667,plain,
! [X2,X0,X1] :
( ~ in(X0,sK131(X1,X2))
| in(X0,cartesian_product2(X1,X2))
| sP3(X1) ),
inference(duplicate_literal_removal,[],[f3666]) ).
fof(f3677,plain,
( in(sK161(sK131(sK159,sK160)),cartesian_product2(sK159,sK160))
| sP3(sK159)
| ~ spl194_14 ),
inference(resolution,[],[f3667,f3091]) ).
fof(f4304,plain,
( sK124(sK159) = sK126(sK159)
| ~ spl194_13 ),
inference(unit_resulting_resolution,[],[f1561,f2549]) ).
fof(f5129,plain,
( in(sK133(sK159,sK161(sK131(sK159,sK160))),sK159)
| sP3(sK159)
| ~ spl194_14 ),
inference(resolution,[],[f1571,f3091]) ).
fof(f5253,plain,
( sK124(sK159) = sK125(sK159)
| ~ spl194_13 ),
inference(unit_resulting_resolution,[],[f1565,f2549]) ).
fof(f5914,plain,
( sK126(sK159) != sK125(sK159)
| ~ spl194_13 ),
inference(unit_resulting_resolution,[],[f1566,f2549]) ).
fof(f5915,plain,
! [X0] :
( sK124(X0) != sK125(X0)
| ~ sP3(X0)
| ~ sP3(X0) ),
inference(superposition,[],[f1566,f1561]) ).
fof(f5917,plain,
! [X0] :
( sK124(X0) != sK125(X0)
| ~ sP3(X0) ),
inference(duplicate_literal_removal,[],[f5915]) ).
fof(f5919,plain,
! [X0] : ~ sP3(X0),
inference(forward_subsumption_resolution,[],[f5917,f1565]) ).
fof(f5920,plain,
( sK124(sK159) != sK126(sK159)
| ~ spl194_13 ),
inference(forward_demodulation,[],[f5914,f5253]) ).
fof(f5923,plain,
( $false
| ~ spl194_13 ),
inference(forward_subsumption_resolution,[],[f5920,f4304]) ).
fof(f5924,plain,
~ spl194_13,
inference(avatar_contradiction_clause,[],[f5923]) ).
fof(f5933,plain,
( in(sK161(sK131(sK159,sK160)),cartesian_product2(sK159,sK160))
| ~ spl194_14 ),
inference(forward_subsumption_resolution,[],[f3677,f5919]) ).
fof(f5945,plain,
( in(sK161(sK131(sK159,sK160)),sF193)
| ~ spl194_14 ),
inference(forward_demodulation,[],[f5933,f2251]) ).
fof(f6163,plain,
( sK161(sK131(sK159,sK160)) != unordered_pair(unordered_pair(sK133(sK159,sK161(sK131(sK159,sK160))),sK133(sK159,sK161(sK131(sK159,sK160)))),unordered_pair(sK133(sK159,sK161(sK131(sK159,sK160))),unordered_pair(sK133(sK159,sK161(sK131(sK159,sK160))),sK133(sK159,sK161(sK131(sK159,sK160))))))
| ~ spl194_14
| ~ spl194_33 ),
inference(unit_resulting_resolution,[],[f2339,f3264,f3091,f5945]) ).
fof(f6270,plain,
( sK161(sK131(sK159,sK160)) != unordered_pair(sK134(sK159,sK161(sK131(sK159,sK160))),unordered_pair(sK133(sK159,sK161(sK131(sK159,sK160))),sK134(sK159,sK161(sK131(sK159,sK160)))))
| spl194_13
| ~ spl194_14
| ~ spl194_33 ),
inference(forward_demodulation,[],[f6163,f3158]) ).
fof(f6336,plain,
( ! [X0] :
( sK161(sK131(sK159,sK160)) = unordered_pair(sK134(sK159,sK161(sK131(sK159,sK160))),unordered_pair(sK133(sK159,sK161(sK131(sK159,sK160))),sK134(sK159,sK161(sK131(sK159,sK160)))))
| ~ in(sK161(sK131(sK159,sK160)),sK131(sK159,X0))
| sP3(sK159) )
| spl194_13
| ~ spl194_14 ),
inference(superposition,[],[f2390,f3158]) ).
fof(f6453,plain,
( ! [X0] :
( ~ in(sK161(sK131(sK159,sK160)),sK131(sK159,X0))
| sP3(sK159) )
| spl194_13
| ~ spl194_14
| ~ spl194_33 ),
inference(forward_subsumption_resolution,[],[f6336,f6270]) ).
fof(f6461,plain,
( ! [X0] : ~ in(sK161(sK131(sK159,sK160)),sK131(sK159,X0))
| spl194_13
| ~ spl194_14
| ~ spl194_33 ),
inference(forward_subsumption_resolution,[],[f6453,f5919]) ).
fof(f6475,plain,
( sK163(sK131(sK159,sK160)) = unordered_pair(sK162(sK131(sK159,sK160)),sK162(sK131(sK159,sK160)))
| spl194_13
| ~ spl194_14
| ~ spl194_33 ),
inference(unit_resulting_resolution,[],[f2045,f6461]) ).
fof(f6477,plain,
( sK161(sK131(sK159,sK160)) = unordered_pair(unordered_pair(sK162(sK131(sK159,sK160)),sK162(sK131(sK159,sK160))),unordered_pair(sK162(sK131(sK159,sK160)),sK163(sK131(sK159,sK160))))
| spl194_13
| ~ spl194_14
| ~ spl194_33 ),
inference(unit_resulting_resolution,[],[f2394,f6461]) ).
fof(f6479,plain,
( sK161(sK131(sK159,sK160)) != unordered_pair(sK163(sK131(sK159,sK160)),unordered_pair(sK162(sK131(sK159,sK160)),sK163(sK131(sK159,sK160))))
| spl194_13
| ~ spl194_14
| ~ spl194_33 ),
inference(unit_resulting_resolution,[],[f2431,f5945,f3091,f6461]) ).
fof(f6538,plain,
( sK161(sK131(sK159,sK160)) = unordered_pair(sK163(sK131(sK159,sK160)),unordered_pair(sK162(sK131(sK159,sK160)),sK163(sK131(sK159,sK160))))
| spl194_13
| ~ spl194_14
| ~ spl194_33 ),
inference(forward_demodulation,[],[f6477,f6475]) ).
fof(f6550,plain,
( $false
| spl194_13
| ~ spl194_14
| ~ spl194_33 ),
inference(forward_subsumption_resolution,[],[f6538,f6479]) ).
fof(f6551,plain,
( spl194_13
| ~ spl194_14
| ~ spl194_33 ),
inference(avatar_contradiction_clause,[],[f6550]) ).
fof(f6552,plain,
( sP3(sK159)
| ~ spl194_14
| spl194_33 ),
inference(forward_subsumption_resolution,[],[f5129,f3265]) ).
fof(f6556,plain,
( $false
| ~ spl194_14
| spl194_33 ),
inference(forward_subsumption_resolution,[],[f6552,f5919]) ).
fof(f6557,plain,
( ~ spl194_14
| spl194_33 ),
inference(avatar_contradiction_clause,[],[f6556]) ).
cnf(s11,plain,
( spl194_13
| spl194_14 ),
inference(sat_conversion,[],[f2553]) ).
cnf(s98,plain,
~ spl194_13,
inference(sat_conversion,[],[f5924]) ).
cnf(s115,plain,
( spl194_13
| ~ spl194_14
| ~ spl194_33 ),
inference(sat_conversion,[],[f6551]) ).
cnf(s116,plain,
( ~ spl194_14
| spl194_33 ),
inference(sat_conversion,[],[f6557]) ).
cnf(s135,plain,
spl194_14,
inference(rat,[],[s11,s98]) ).
cnf(s136,plain,
spl194_33,
inference(rat,[],[s116,s135]) ).
cnf(s137,plain,
$false,
inference(rat,[],[s115,s98,s136,s135]) ).
fof(f6561,plain,
$false,
inference(avatar_sat_refutation,[],[s137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU281+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:34:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.65/2.59 % (19582)Detected formulas, will run a generic FOF schedule.
% 11.65/2.59 % (19590)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1089951439:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.65/2.59 % (19587)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3166264928:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.65/2.59 % (19588)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1199080761:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.65/2.59 % (19589)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1837946101:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.65/2.59 % (19590)Instruction limit reached!
% 11.65/2.59 % (19590)------------------------------
% 11.65/2.59 % (19590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.65/2.59 % (19590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.65/2.59 % (19590)CaDiCaL version: 2.1.3
% 11.65/2.59 % (19590)Termination reason: Instruction limit
% 11.65/2.59 % (19590)Termination phase: Saturation
% 11.65/2.59 % (19590)Time elapsed: 0.039 s
% 11.65/2.59 % (19590)Peak memory usage: 91 MB
% 11.65/2.59 % (19590)Instructions burned: 112 (million)
% 11.65/2.59 % (19592)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2050480153:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.65/2.59 % (19593)dis-21_1_sil=8000:lcm=predicate:random_seed=3809051606:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 11.65/2.59 % (19591)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2089348441:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.65/2.59 % (19591)Instruction limit reached!
% 11.65/2.59 % (19591)------------------------------
% 11.65/2.59 % (19591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.65/2.59 % (19591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.65/2.59 % (19591)CaDiCaL version: 2.1.3
% 11.65/2.59 % (19591)Termination reason: Instruction limit
% 11.65/2.59 % (19591)Termination phase: Saturation
% 11.65/2.59 % (19591)Time elapsed: 0.043 s
% 11.65/2.59 % (19591)Peak memory usage: 90 MB
% 11.65/2.59 % (19591)Instructions burned: 120 (million)
% 11.65/2.59 % (19593)Instruction limit reached!
% 11.65/2.59 % (19593)------------------------------
% 11.65/2.59 % (19593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.65/2.59 % (19593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.65/2.59 % (19593)CaDiCaL version: 2.1.3
% 11.65/2.59 % (19593)Termination reason: Instruction limit
% 11.65/2.59 % (19593)Termination phase: Saturation
% 11.65/2.59 % (19593)Time elapsed: 0.066 s
% 11.65/2.59 % (19593)Peak memory usage: 90 MB
% 11.65/2.59 % (19593)Instructions burned: 129 (million)
% 11.65/2.59 % (19592)Instruction limit reached!
% 11.65/2.59 % (19592)------------------------------
% 11.65/2.59 % (19592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.65/2.59 % (19592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.65/2.59 % (19592)CaDiCaL version: 2.1.3
% 11.65/2.59 % (19592)Termination reason: Instruction limit
% 11.65/2.59 % (19592)Termination phase: Saturation
% 11.65/2.59 % (19592)Time elapsed: 0.092 s
% 11.65/2.59 % (19592)Peak memory usage: 91 MB
% 11.65/2.59 % (19592)Instructions burned: 139 (million)
% 11.65/2.59 % (19600)lrs+10_1_sil=8000:sp=occurrence:random_seed=3826102257:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 11.65/2.59 % (19602)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2535645999:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.65/2.59 % (19603)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2235805907:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 11.65/2.59 % (19602)Instruction limit reached!
% 11.65/2.59 % (19602)------------------------------
% 11.65/2.59 % (19602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.65/2.59 % (19602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.65/2.59 % (19602)CaDiCaL version: 2.1.3
% 11.65/2.59 % (19602)Termination reason: Instruction limit
% 28.30/4.88 % (19602)Termination phase: Saturation
% 28.30/4.88 % (19602)Time elapsed: 0.049 s
% 28.30/4.88 % (19602)Peak memory usage: 91 MB
% 28.30/4.88 % (19602)Instructions burned: 158 (million)
% 28.30/4.88 % (19604)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3859239400:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 28.30/4.88 % (19608)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=361096573:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 28.30/4.88 % (19600)Instruction limit reached!
% 28.30/4.88 % (19600)------------------------------
% 28.30/4.88 % (19600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.30/4.88 % (19600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.30/4.88 % (19600)CaDiCaL version: 2.1.3
% 28.30/4.88 % (19600)Termination reason: Instruction limit
% 28.30/4.88 % (19600)Termination phase: Saturation
% 28.30/4.88 % (19600)Time elapsed: 0.190 s
% 28.30/4.88 % (19600)Peak memory usage: 94 MB
% 28.30/4.88 % (19600)Instructions burned: 285 (million)
% 28.30/4.88 % (19604)Instruction limit reached!
% 28.30/4.88 % (19604)------------------------------
% 28.30/4.88 % (19604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.30/4.88 % (19604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.30/4.88 % (19604)CaDiCaL version: 2.1.3
% 28.30/4.88 % (19604)Termination reason: Instruction limit
% 28.30/4.88 % (19604)Termination phase: Saturation
% 28.30/4.88 % (19604)Time elapsed: 0.150 s
% 28.30/4.88 % (19604)Peak memory usage: 93 MB
% 28.30/4.88 % (19604)Instructions burned: 248 (million)
% 28.30/4.88 % (19608)Instruction limit reached!
% 28.30/4.88 % (19608)------------------------------
% 28.30/4.88 % (19608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.30/4.88 % (19608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.30/4.88 % (19608)CaDiCaL version: 2.1.3
% 28.30/4.88 % (19608)Termination reason: Instruction limit
% 28.30/4.88 % (19608)Termination phase: Saturation
% 28.30/4.88 % (19608)Time elapsed: 0.101 s
% 28.30/4.88 % (19608)Peak memory usage: 91 MB
% 28.30/4.88 % (19608)Instructions burned: 296 (million)
% 28.30/4.88 % (19603)Instruction limit reached!
% 28.30/4.88 % (19603)------------------------------
% 28.30/4.88 % (19603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.30/4.88 % (19603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.30/4.88 % (19603)CaDiCaL version: 2.1.3
% 28.30/4.88 % (19603)Termination reason: Instruction limit
% 28.30/4.88 % (19603)Termination phase: Saturation
% 28.30/4.88 % (19603)Time elapsed: 0.226 s
% 28.30/4.88 % (19603)Peak memory usage: 94 MB
% 28.30/4.88 % (19603)Instructions burned: 325 (million)
% 28.30/4.88 % (19611)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2128219354:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 28.30/4.88 % (19612)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=988549921:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 28.30/4.88 % (19612)Instruction limit reached!
% 28.30/4.88 % (19612)------------------------------
% 28.30/4.88 % (19612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.30/4.88 % (19612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.30/4.88 % (19612)CaDiCaL version: 2.1.3
% 28.30/4.88 % (19612)Termination reason: Instruction limit
% 28.30/4.88 % (19612)Termination phase: Saturation
% 28.30/4.88 % (19612)Time elapsed: 0.038 s
% 28.30/4.88 % (19612)Peak memory usage: 90 MB
% 28.30/4.88 % (19612)Instructions burned: 113 (million)
% 28.30/4.88 % (19613)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2827552978:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 28.30/4.88 % (19614)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=928759201:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 28.30/4.88 % (19613)Instruction limit reached!
% 28.30/4.88 % (19613)------------------------------
% 28.30/4.88 % (19613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.30/4.88 % (19613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.30/4.88 % (19613)CaDiCaL version: 2.1.3
% 28.30/4.88 % (19613)Termination reason: Instruction limit
% 28.30/4.88 % (19613)Termination phase: Saturation
% 28.30/4.88 % (19613)Time elapsed: 0.070 s
% 28.30/4.88 % (19613)Peak memory usage: 90 MB
% 29.04/4.97 % (19613)Instructions burned: 127 (million)
% 29.04/4.97 % (19618)lrs+10_1_sil=8000:sp=occurrence:random_seed=4132473345:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 29.04/4.97 % (19614)Instruction limit reached!
% 29.04/4.97 % (19614)------------------------------
% 29.04/4.97 % (19614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19614)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19614)Termination reason: Instruction limit
% 29.04/4.97 % (19614)Termination phase: Saturation
% 29.04/4.97 % (19614)Time elapsed: 0.061 s
% 29.04/4.97 % (19614)Peak memory usage: 89 MB
% 29.04/4.97 % (19614)Instructions burned: 114 (million)
% 29.04/4.97 % (19620)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2826460152:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 29.04/4.97 % (19622)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4026123109:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 29.04/4.97 % (19618)Instruction limit reached!
% 29.04/4.97 % (19618)------------------------------
% 29.04/4.97 % (19618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19618)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19618)Termination reason: Instruction limit
% 29.04/4.97 % (19618)Termination phase: Saturation
% 29.04/4.97 % (19618)Time elapsed: 0.307 s
% 29.04/4.97 % (19618)Peak memory usage: 102 MB
% 29.04/4.97 % (19618)Instructions burned: 907 (million)
% 29.04/4.97 % (19620)Instruction limit reached!
% 29.04/4.97 % (19620)------------------------------
% 29.04/4.97 % (19620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19620)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19620)Termination reason: Instruction limit
% 29.04/4.97 % (19620)Termination phase: Saturation
% 29.04/4.97 % (19620)Time elapsed: 0.268 s
% 29.04/4.97 % (19620)Peak memory usage: 93 MB
% 29.04/4.97 % (19620)Instructions burned: 438 (million)
% 29.04/4.97 % (19625)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=4133168558:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 29.04/4.97 % (19625)Instruction limit reached!
% 29.04/4.97 % (19625)------------------------------
% 29.04/4.97 % (19625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19625)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19625)Termination reason: Instruction limit
% 29.04/4.97 % (19625)Termination phase: Saturation
% 29.04/4.97 % (19625)Time elapsed: 0.081 s
% 29.04/4.97 % (19625)Peak memory usage: 92 MB
% 29.04/4.97 % (19625)Instructions burned: 134 (million)
% 29.04/4.97 % (19626)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3493437224:st=8:i=592:sd=3:ep=RST:ss=axioms_2988 on theBenchmark for (2988ds/592Mi)
% 29.04/4.97 % (19629)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=4161608616:st=3:i=13193:sd=3:ss=axioms_2987 on theBenchmark for (2987ds/13193Mi)
% 29.04/4.97 % (19626)Instruction limit reached!
% 29.04/4.97 % (19626)------------------------------
% 29.04/4.97 % (19626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19626)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19626)Termination reason: Instruction limit
% 29.04/4.97 % (19626)Termination phase: Saturation
% 29.04/4.97 % (19626)Time elapsed: 0.344 s
% 29.04/4.97 % (19626)Peak memory usage: 100 MB
% 29.04/4.97 % (19626)Instructions burned: 594 (million)
% 29.04/4.97 % (19611)Instruction limit reached!
% 29.04/4.97 % (19611)------------------------------
% 29.04/4.97 % (19611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19611)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19611)Termination reason: Instruction limit
% 29.04/4.97 % (19611)Termination phase: Saturation
% 29.04/4.97 % (19611)Time elapsed: 1.039 s
% 29.04/4.97 % (19611)Peak memory usage: 144 MB
% 29.04/4.97 % (19611)Instructions burned: 2352 (million)
% 29.04/4.97 % (19632)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=4189037209:i=134:gtgl=5:slsql=off:gtg=exists_sym_2983 on theBenchmark for (2983ds/134Mi)
% 29.04/4.97 % (19631)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=3727401813:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/125Mi)
% 29.04/4.97 % (19632)Instruction limit reached!
% 29.04/4.97 % (19632)------------------------------
% 29.04/4.97 % (19632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19632)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19632)Termination reason: Instruction limit
% 29.04/4.97 % (19632)Termination phase: Saturation
% 29.04/4.97 % (19632)Time elapsed: 0.045 s
% 29.04/4.97 % (19632)Peak memory usage: 91 MB
% 29.04/4.97 % (19632)Instructions burned: 136 (million)
% 29.04/4.97 % (19631)Instruction limit reached!
% 29.04/4.97 % (19631)------------------------------
% 29.04/4.97 % (19631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19631)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19631)Termination reason: Instruction limit
% 29.04/4.97 % (19631)Termination phase: Saturation
% 29.04/4.97 % (19631)Time elapsed: 0.083 s
% 29.04/4.97 % (19631)Peak memory usage: 91 MB
% 29.04/4.97 % (19631)Instructions burned: 126 (million)
% 29.04/4.97 % (19635)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=925235279:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2982 on theBenchmark for (2982ds/141Mi)
% 29.04/4.97 % (19635)Instruction limit reached!
% 29.04/4.97 % (19635)------------------------------
% 29.04/4.97 % (19635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19635)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19635)Termination reason: Instruction limit
% 29.04/4.97 % (19635)Termination phase: Saturation
% 29.04/4.97 % (19635)Time elapsed: 0.046 s
% 29.04/4.97 % (19635)Peak memory usage: 91 MB
% 29.04/4.97 % (19635)Instructions burned: 143 (million)
% 29.04/4.97 % (19636)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=678270618:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2981 on theBenchmark for (2981ds/431Mi)
% 29.04/4.97 % (19638)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=683947346:i=6060:aac=none:ins=25_2980 on theBenchmark for (2980ds/6060Mi)
% 29.04/4.97 % (19636)Instruction limit reached!
% 29.04/4.97 % (19636)------------------------------
% 29.04/4.97 % (19636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19636)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19636)Termination reason: Instruction limit
% 29.04/4.97 % (19636)Termination phase: Saturation
% 29.04/4.97 % (19636)Time elapsed: 0.258 s
% 29.04/4.97 % (19636)Peak memory usage: 94 MB
% 29.04/4.97 % (19636)Instructions burned: 431 (million)
% 29.04/4.97 % (19641)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=9775976:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2977 on theBenchmark for (2977ds/150Mi)
% 29.04/4.97 % (19641)Instruction limit reached!
% 29.04/4.97 % (19641)------------------------------
% 29.04/4.97 % (19641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19641)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19641)Termination reason: Instruction limit
% 29.04/4.97 % (19641)Termination phase: Saturation
% 29.04/4.97 % (19641)Time elapsed: 0.090 s
% 29.04/4.97 % (19641)Peak memory usage: 91 MB
% 29.04/4.97 % (19641)Instructions burned: 151 (million)
% 29.04/4.97 % (19643)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=512370388:i=14155:bd=all_2975 on theBenchmark for (2975ds/14155Mi)
% 29.04/4.97 % (19643)First to succeed.
% 29.04/4.97 % (19643)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19582"
% 29.04/4.97 % (19622)Instruction limit reached!
% 29.04/4.97 % (19622)------------------------------
% 29.04/4.97 % (19622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19622)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19622)Termination reason: Instruction limit
% 29.04/4.97 % (19622)Termination phase: Saturation
% 29.04/4.97 % (19622)Time elapsed: 3.112 s
% 29.04/4.97 % (19622)Peak memory usage: 156 MB
% 29.04/4.97 % (19622)Instructions burned: 5203 (million)
% 29.04/4.97 % (19638)Instruction limit reached!
% 29.04/4.97 % (19638)------------------------------
% 29.04/4.97 % (19638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.04/4.97 % (19638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.04/4.97 % (19638)CaDiCaL version: 2.1.3
% 29.04/4.97 % (19638)Termination reason: Instruction limit
% 29.04/4.97 % (19638)Termination phase: Saturation
% 29.04/4.97 % (19638)Time elapsed: 2.025 s
% 29.04/4.97 % (19638)Peak memory usage: 166 MB
% 29.04/4.97 % (19638)Instructions burned: 6062 (million)
% 29.04/4.97 % (19643)Refutation found. Thanks to Tanya!
% 29.04/4.97 % SZS status Theorem for theBenchmark
% 29.04/4.97 % SZS output start Proof for theBenchmark
% See solution above
% 29.67/5.17 % (19643)------------------------------
% 29.67/5.17 % (19643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.67/5.17 % (19643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.67/5.17 % (19643)CaDiCaL version: 2.1.3
% 29.67/5.17 % (19643)Termination reason: Refutation
% 29.67/5.17 % (19643)Time elapsed: 1.250 s
% 29.67/5.17 % (19643)Peak memory usage: 142 MB
% 29.67/5.17 % (19643)Instructions burned: 1981 (million)
% 29.67/5.17 % (19643)------------------------------
% 29.67/5.17 % (19643)------------------------------
% 29.67/5.17 % (19582)Success in time 4.119 s
% 29.67/5.17 % Vampire exiting
%------------------------------------------------------------------------------