%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU298+1 : 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 : 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 : Tue Sep 29 12:48:13 PM UTC 2026
% Result : Theorem 1.76s 1.15s
% Output : Refutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 66 ( 6 unt; 1 def)
% Number of atoms : 366 ( 92 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 476 ( 176 ~; 174 |; 109 &)
% ( 7 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-3 aty)
% Number of variables : 215 ( 141 !; 74 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(X0))
& ? [X4] :
( in(X4,X1)
& X3 = set_difference(X4,singleton(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_27_3_1__finset_1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(X0))
& ? [X4] :
( in(X4,X1)
& X3 = set_difference(X4,singleton(X0)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f43,axiom,
! [X0,X1] :
( ( ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) )
=> ( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5] :
( in(X5,X1)
& X3 = set_difference(X5,singleton(X0)) )
& X2 = X4
& ? [X6] :
( in(X6,X1)
& X4 = set_difference(X6,singleton(X0)) ) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,powerset(X0))
& X4 = X3
& ? [X7] :
( in(X7,X1)
& X3 = set_difference(X7,singleton(X0)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_27_3_1__finset_1__1) ).
fof(f44,plain,
! [X0,X1] :
( ( ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) )
=> ( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5] :
( in(X5,X1)
& X3 = set_difference(X5,singleton(X0)) )
& X2 = X4
& ? [X6] :
( in(X6,X1)
& X4 = set_difference(X6,singleton(X0)) ) )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(X0))
& X8 = X9
& ? [X10] :
( in(X10,X1)
& set_difference(X10,singleton(X0)) = X8 ) ) ) ) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(X3,powerset(X0))
& ? [X4] :
( in(X4,X1)
& X3 = set_difference(X4,singleton(X0)) ) ) )
& ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f46,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(X3,powerset(X0))
& ? [X4] :
( in(X4,X1)
& X3 = set_difference(X4,singleton(X0)) ) ) )
& ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(X0))
& X8 = X9
& ? [X10] :
( in(X10,X1)
& set_difference(X10,singleton(X0)) = X8 ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( in(X5,X1)
& X3 = set_difference(X5,singleton(X0)) )
& X2 = X4
& ? [X6] :
( in(X6,X1)
& X4 = set_difference(X6,singleton(X0)) ) )
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(ennf_transformation,[],[f44]) ).
fof(f48,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(X0))
& X8 = X9
& ? [X10] :
( in(X10,X1)
& set_difference(X10,singleton(X0)) = X8 ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( in(X5,X1)
& X3 = set_difference(X5,singleton(X0)) )
& X2 = X4
& ? [X6] :
( in(X6,X1)
& X4 = set_difference(X6,singleton(X0)) ) )
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(flattening,[],[f47]) ).
fof(f64,definition,
! [X1,X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( in(X5,X1)
& X3 = set_difference(X5,singleton(X0)) )
& X2 = X4
& ? [X6] :
( in(X6,X1)
& X4 = set_difference(X6,singleton(X0)) ) )
| ~ sP0(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(X0))
& X8 = X9
& ? [X10] :
( in(X10,X1)
& set_difference(X10,singleton(X0)) = X8 ) ) )
| sP0(X1,X0)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(definition_folding,[],[f48,f64]) ).
fof(f66,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,powerset(X0))
| ! [X4] :
( ~ in(X4,X1)
| set_difference(X4,singleton(X0)) != X3 )
| ~ in(X3,X2) )
& ( ( in(X3,powerset(X0))
& ? [X4] :
( in(X4,X1)
& X3 = set_difference(X4,singleton(X0)) ) )
| in(X3,X2) ) )
& ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) ),
inference(nnf_transformation,[],[f46]) ).
fof(f67,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,powerset(X0))
| ! [X4] :
( ~ in(X4,X1)
| set_difference(X4,singleton(X0)) != X3 )
| ~ in(X3,X2) )
& ( ( in(X3,powerset(X0))
& ? [X4] :
( in(X4,X1)
& X3 = set_difference(X4,singleton(X0)) ) )
| in(X3,X2) ) )
& ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,powerset(X0))
| ! [X4] :
( ~ in(X4,X1)
| set_difference(X4,singleton(X0)) != X3 )
| ~ in(X3,X2) )
& ( ( in(X3,powerset(X0))
& ? [X5] :
( in(X5,X1)
& set_difference(X5,singleton(X0)) = X3 ) )
| in(X3,X2) ) )
& ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
( ! [X2] :
( ( ~ in(sK3(X2),powerset(sK1))
| ! [X4] :
( ~ in(X4,sK2)
| sK3(X2) != set_difference(X4,singleton(sK1)) )
| ~ in(sK3(X2),X2) )
& ( ( in(sK3(X2),powerset(sK1))
& in(sK4(X2),sK2)
& sK3(X2) = set_difference(sK4(X2),singleton(sK1)) )
| in(sK3(X2),X2) ) )
& ordinal(sK1)
& element(sK2,powerset(powerset(succ(sK1)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X3,sK3(X2)),skolemize(X5,sK4(X2))],[f68]) ).
fof(f70,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( in(X5,X1)
& X3 = set_difference(X5,singleton(X0)) )
& X2 = X4
& ? [X6] :
( in(X6,X1)
& X4 = set_difference(X6,singleton(X0)) ) )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f64]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( in(X5,X0)
& set_difference(X5,singleton(X1)) = X3 )
& X2 = X4
& ? [X6] :
( in(X6,X0)
& set_difference(X6,singleton(X1)) = X4 ) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ( sK6(X0,X1) != sK7(X0,X1)
& sK5(X0,X1) = sK6(X0,X1)
& in(sK8(X0,X1),X0)
& sK6(X0,X1) = set_difference(sK8(X0,X1),singleton(X1))
& sK5(X0,X1) = sK7(X0,X1)
& in(sK9(X0,X1),X0)
& sK7(X0,X1) = set_difference(sK9(X0,X1),singleton(X1)) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1)),skolemize(X4,sK7(X0,X1)),skolemize(X5,sK8(X0,X1)),skolemize(X6,sK9(X0,X1))],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( ( in(X8,X7)
| ! [X9] :
( ~ in(X9,powerset(X0))
| X8 != X9
| ! [X10] :
( ~ in(X10,X1)
| set_difference(X10,singleton(X0)) != X8 ) ) )
& ( ? [X9] :
( in(X9,powerset(X0))
& X8 = X9
& ? [X10] :
( in(X10,X1)
& set_difference(X10,singleton(X0)) = X8 ) )
| ~ in(X8,X7) ) )
| sP0(X1,X0)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(nnf_transformation,[],[f65]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,powerset(X0))
| X3 != X4
| ! [X5] :
( ~ in(X5,X1)
| set_difference(X5,singleton(X0)) != X3 ) ) )
& ( ? [X6] :
( in(X6,powerset(X0))
& X3 = X6
& ? [X7] :
( in(X7,X1)
& set_difference(X7,singleton(X0)) = X3 ) )
| ~ in(X3,X2) ) )
| sP0(X1,X0)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK10(X0,X1))
| ! [X4] :
( ~ in(X4,powerset(X0))
| X3 != X4
| ! [X5] :
( ~ in(X5,X1)
| set_difference(X5,singleton(X0)) != X3 ) ) )
& ( ( in(sK11(X0,X1,X3),powerset(X0))
& sK11(X0,X1,X3) = X3
& in(sK12(X0,X1,X3),X1)
& set_difference(sK12(X0,X1,X3),singleton(X0)) = X3 )
| ~ in(X3,sK10(X0,X1)) ) )
| sP0(X1,X0)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X2,sK10(X0,X1)),skolemize(X6,sK11(X0,X1,X3)),skolemize(X7,sK12(X0,X1,X3))],[f74]) ).
fof(f86,plain,
element(sK2,powerset(powerset(succ(sK1)))),
inference(cnf_transformation,[],[f69]) ).
fof(f87,plain,
ordinal(sK1),
inference(cnf_transformation,[],[f69]) ).
fof(f88,plain,
! [X2] :
( sK3(X2) = set_difference(sK4(X2),singleton(sK1))
| in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f89,plain,
! [X2] :
( in(sK4(X2),sK2)
| in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f90,plain,
! [X2] :
( in(sK3(X2),powerset(sK1))
| in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f91,plain,
! [X2,X4] :
( sK3(X2) != set_difference(X4,singleton(sK1))
| ~ in(X4,sK2)
| ~ in(sK3(X2),powerset(sK1))
| ~ in(sK3(X2),X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f94,plain,
! [X0,X1] :
( sK5(X0,X1) = sK7(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f97,plain,
! [X0,X1] :
( sK5(X0,X1) = sK6(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f98,plain,
! [X0,X1] :
( sK6(X0,X1) != sK7(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f99,plain,
! [X3,X0,X1] :
( set_difference(sK12(X0,X1,X3),singleton(X0)) = X3
| ~ in(X3,sK10(X0,X1))
| sP0(X1,X0)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(cnf_transformation,[],[f75]) ).
fof(f100,plain,
! [X3,X0,X1] :
( in(sK12(X0,X1,X3),X1)
| ~ in(X3,sK10(X0,X1))
| sP0(X1,X0)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(cnf_transformation,[],[f75]) ).
fof(f101,plain,
! [X3,X0,X1] :
( sK11(X0,X1,X3) = X3
| ~ in(X3,sK10(X0,X1))
| sP0(X1,X0)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(cnf_transformation,[],[f75]) ).
fof(f102,plain,
! [X3,X0,X1] :
( in(sK11(X0,X1,X3),powerset(X0))
| ~ in(X3,sK10(X0,X1))
| sP0(X1,X0)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(cnf_transformation,[],[f75]) ).
fof(f103,plain,
! [X3,X0,X1,X4,X5] :
( in(X3,sK10(X0,X1))
| ~ in(X4,powerset(X0))
| X3 != X4
| ~ in(X5,X1)
| set_difference(X5,singleton(X0)) != X3
| sP0(X1,X0)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(cnf_transformation,[],[f75]) ).
fof(f150,plain,
! [X0,X1,X4,X5] :
( in(X4,sK10(X0,X1))
| ~ in(X4,powerset(X0))
| ~ in(X5,X1)
| set_difference(X5,singleton(X0)) != X4
| sP0(X1,X0)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(equality_resolution,[],[f103]) ).
fof(f151,plain,
! [X0,X1,X5] :
( in(set_difference(X5,singleton(X0)),sK10(X0,X1))
| ~ in(set_difference(X5,singleton(X0)),powerset(X0))
| ~ in(X5,X1)
| sP0(X1,X0)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(equality_resolution,[],[f150]) ).
fof(f196,plain,
! [X0,X1] :
( sK5(X0,X1) != sK6(X0,X1)
| ~ sP0(X0,X1)
| ~ sP0(X0,X1) ),
inference(superposition,[],[f98,f94]) ).
fof(f197,plain,
! [X0,X1] :
( sK5(X0,X1) != sK6(X0,X1)
| ~ sP0(X0,X1) ),
inference(duplicate_literal_removal,[],[f196]) ).
fof(f198,plain,
! [X0,X1] : ~ sP0(X0,X1),
inference(forward_subsumption_resolution,[],[f197,f97]) ).
fof(f199,plain,
! [X3,X0,X1] :
( in(sK12(X0,X1,X3),X1)
| ~ in(X3,sK10(X0,X1))
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(forward_subsumption_resolution,[],[f100,f198]) ).
fof(f201,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ in(X3,sK10(X0,X1))
| ~ ordinal(X0)
| sK11(X0,X1,X3) = X3 ),
inference(forward_subsumption_resolution,[],[f101,f198]) ).
fof(f202,plain,
! [X0] :
( ~ in(X0,sK10(sK1,sK2))
| ~ ordinal(sK1)
| sK11(sK1,sK2,X0) = X0 ),
inference(resolution,[],[f201,f86]) ).
fof(f208,plain,
! [X0] :
( sK11(sK1,sK2,X0) = X0
| ~ in(X0,sK10(sK1,sK2)) ),
inference(forward_subsumption_resolution,[],[f202,f87]) ).
fof(f209,plain,
! [X3,X0,X1] :
( in(sK11(X0,X1,X3),powerset(X0))
| ~ in(X3,sK10(X0,X1))
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(forward_subsumption_resolution,[],[f102,f198]) ).
fof(f211,plain,
! [X0] :
( in(X0,powerset(sK1))
| ~ in(X0,sK10(sK1,sK2))
| ~ ordinal(sK1)
| ~ element(sK2,powerset(powerset(succ(sK1))))
| ~ in(X0,sK10(sK1,sK2)) ),
inference(superposition,[],[f209,f208]) ).
fof(f212,plain,
! [X0] :
( in(X0,powerset(sK1))
| ~ in(X0,sK10(sK1,sK2))
| ~ ordinal(sK1)
| ~ element(sK2,powerset(powerset(succ(sK1)))) ),
inference(duplicate_literal_removal,[],[f211]) ).
fof(f213,plain,
! [X0] :
( in(X0,powerset(sK1))
| ~ in(X0,sK10(sK1,sK2))
| ~ element(sK2,powerset(powerset(succ(sK1)))) ),
inference(forward_subsumption_resolution,[],[f212,f87]) ).
fof(f214,plain,
! [X0] :
( ~ in(X0,sK10(sK1,sK2))
| in(X0,powerset(sK1)) ),
inference(forward_subsumption_resolution,[],[f213,f86]) ).
fof(f221,plain,
! [X3,X0,X1] :
( set_difference(sK12(X0,X1,X3),singleton(X0)) = X3
| ~ in(X3,sK10(X0,X1))
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(forward_subsumption_resolution,[],[f99,f198]) ).
fof(f223,plain,
! [X2,X0,X1] :
( sK3(X1) != X0
| ~ in(sK12(sK1,X2,X0),sK2)
| ~ in(sK3(X1),powerset(sK1))
| ~ in(sK3(X1),X1)
| ~ in(X0,sK10(sK1,X2))
| ~ ordinal(sK1)
| ~ element(X2,powerset(powerset(succ(sK1)))) ),
inference(superposition,[],[f91,f221]) ).
fof(f226,plain,
! [X2,X0,X1] :
( sK3(X1) != X0
| ~ in(sK12(sK1,X2,X0),sK2)
| ~ in(sK3(X1),powerset(sK1))
| ~ in(sK3(X1),X1)
| ~ in(X0,sK10(sK1,X2))
| ~ element(X2,powerset(powerset(succ(sK1)))) ),
inference(forward_subsumption_resolution,[],[f223,f87]) ).
fof(f228,plain,
! [X0,X1,X5] :
( in(set_difference(X5,singleton(X0)),sK10(X0,X1))
| ~ in(set_difference(X5,singleton(X0)),powerset(X0))
| ~ in(X5,X1)
| ~ ordinal(X0)
| ~ element(X1,powerset(powerset(succ(X0)))) ),
inference(forward_subsumption_resolution,[],[f151,f198]) ).
fof(f232,plain,
! [X0,X1] :
( in(sK3(X0),sK10(sK1,X1))
| ~ in(sK3(X0),powerset(sK1))
| ~ in(sK4(X0),X1)
| ~ ordinal(sK1)
| ~ element(X1,powerset(powerset(succ(sK1))))
| in(sK3(X0),X0) ),
inference(superposition,[],[f228,f88]) ).
fof(f235,plain,
! [X0,X1] :
( in(sK3(X0),sK10(sK1,X1))
| ~ in(sK3(X0),powerset(sK1))
| ~ in(sK4(X0),X1)
| ~ element(X1,powerset(powerset(succ(sK1))))
| in(sK3(X0),X0) ),
inference(forward_subsumption_resolution,[],[f232,f87]) ).
fof(f236,plain,
! [X0,X1] :
( in(sK3(X0),sK10(sK1,X1))
| ~ in(sK4(X0),X1)
| ~ element(X1,powerset(powerset(succ(sK1))))
| in(sK3(X0),X0) ),
inference(forward_subsumption_resolution,[],[f235,f90]) ).
fof(f239,plain,
! [X0,X1] :
( ~ in(sK12(sK1,X0,sK3(X1)),sK2)
| ~ in(sK3(X1),powerset(sK1))
| ~ in(sK3(X1),X1)
| ~ in(sK3(X1),sK10(sK1,X0))
| ~ element(X0,powerset(powerset(succ(sK1)))) ),
inference(equality_resolution,[],[f226]) ).
fof(f246,plain,
! [X0] :
( ~ in(sK3(X0),powerset(sK1))
| ~ in(sK3(X0),X0)
| ~ in(sK3(X0),sK10(sK1,sK2))
| ~ element(sK2,powerset(powerset(succ(sK1))))
| ~ in(sK3(X0),sK10(sK1,sK2))
| ~ ordinal(sK1)
| ~ element(sK2,powerset(powerset(succ(sK1)))) ),
inference(resolution,[],[f239,f199]) ).
fof(f247,plain,
! [X0] :
( ~ in(sK3(X0),powerset(sK1))
| ~ in(sK3(X0),X0)
| ~ in(sK3(X0),sK10(sK1,sK2))
| ~ element(sK2,powerset(powerset(succ(sK1))))
| ~ ordinal(sK1) ),
inference(duplicate_literal_removal,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ~ in(sK3(X0),X0)
| ~ in(sK3(X0),sK10(sK1,sK2))
| ~ element(sK2,powerset(powerset(succ(sK1))))
| ~ ordinal(sK1) ),
inference(forward_subsumption_resolution,[],[f247,f214]) ).
fof(f249,plain,
! [X0] :
( ~ in(sK3(X0),X0)
| ~ in(sK3(X0),sK10(sK1,sK2))
| ~ ordinal(sK1) ),
inference(forward_subsumption_resolution,[],[f248,f86]) ).
fof(f250,plain,
! [X0] :
( ~ in(sK3(X0),sK10(sK1,sK2))
| ~ in(sK3(X0),X0) ),
inference(forward_subsumption_resolution,[],[f249,f87]) ).
fof(f257,plain,
~ in(sK3(sK10(sK1,sK2)),sK10(sK1,sK2)),
inference(factoring,[],[f250]) ).
fof(f272,plain,
( ~ in(sK4(sK10(sK1,sK2)),sK2)
| ~ element(sK2,powerset(powerset(succ(sK1))))
| in(sK3(sK10(sK1,sK2)),sK10(sK1,sK2)) ),
inference(resolution,[],[f257,f236]) ).
fof(f276,plain,
( ~ element(sK2,powerset(powerset(succ(sK1))))
| in(sK3(sK10(sK1,sK2)),sK10(sK1,sK2)) ),
inference(forward_subsumption_resolution,[],[f272,f89]) ).
fof(f277,plain,
in(sK3(sK10(sK1,sK2)),sK10(sK1,sK2)),
inference(forward_subsumption_resolution,[],[f276,f86]) ).
fof(f278,plain,
$false,
inference(forward_subsumption_resolution,[],[f277,f257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU298+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n009.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 04:34:31 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 1.76/1.15 % (2661354)Detected formulas, will run a generic FOF schedule.
% 1.76/1.15 % (2661363)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2080130316:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.76/1.15 % (2661363)First to succeed.
% 1.76/1.15 % (2661363)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2661354"
% 1.76/1.15 % (2661362)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3350563555:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.76/1.15 % (2661359)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=3458500795:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.76/1.15 % (2661360)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=2096170293:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.76/1.15 % (2661361)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=3488624701:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.76/1.15 % (2661364)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=34266443:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.76/1.15 % (2661362)Refutation not found, incomplete strategy
% 1.76/1.15 % (2661362)------------------------------
% 1.76/1.15 % (2661362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.76/1.15 % (2661362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.76/1.15 % (2661362)CaDiCaL version: 2.1.3
% 1.76/1.15 % (2661362)Termination reason: Refutation not found, incomplete strategy
% 1.76/1.15 % (2661362)Time elapsed: 0.004 s
% 1.76/1.15 % (2661362)Peak memory usage: 88 MB
% 1.76/1.15 % (2661362)Instructions burned: 4 (million)
% 1.76/1.15 % (2661365)dis-21_1_sil=8000:lcm=predicate:random_seed=3281161206: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)
% 1.76/1.15 % (2661364)Also succeeded, but the first one will report.
% 1.76/1.15 % (2661365)Refutation not found, incomplete strategy
% 1.76/1.15 % (2661365)------------------------------
% 1.76/1.15 % (2661365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.76/1.15 % (2661365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.76/1.15 % (2661365)CaDiCaL version: 2.1.3
% 1.76/1.15 % (2661365)Termination reason: Refutation not found, incomplete strategy
% 1.76/1.15 % (2661365)Time elapsed: 0.011 s
% 1.76/1.15 % (2661365)Peak memory usage: 88 MB
% 1.76/1.15 % (2661365)Instructions burned: 16 (million)
% 1.76/1.15 % (2661363)Refutation found. Thanks to Tanya!
% 1.76/1.15 % SZS status Theorem for theBenchmark
% 1.76/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.61/1.35 % (2661363)------------------------------
% 2.61/1.35 % (2661363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.35 % (2661363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.35 % (2661363)CaDiCaL version: 2.1.3
% 2.61/1.35 % (2661363)Termination reason: Refutation
% 2.61/1.35 % (2661363)Time elapsed: 0.005 s
% 2.61/1.35 % (2661363)Peak memory usage: 88 MB
% 2.61/1.35 % (2661363)Instructions burned: 12 (million)
% 2.61/1.35 % (2661363)------------------------------
% 2.61/1.35 % (2661363)------------------------------
% 2.61/1.35 % (2661354)Success in time 0.285 s
% 2.61/1.35 % Vampire exiting
%------------------------------------------------------------------------------