%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET805+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:41:58 PM UTC 2026
% Result : Theorem 3.13s 1.49s
% Output : Refutation 4.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 100 ( 15 unt; 3 def)
% Number of atoms : 445 ( 15 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 560 ( 215 ~; 241 |; 79 &)
% ( 10 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 254 ( 0 sgn 236 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f12,axiom,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X2) )
=> X2 = X3 ) )
& ! [X2,X3,X4] :
( ( member(X2,X1)
& member(X3,X1)
& member(X4,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X4) )
=> apply(X0,X2,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f22,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2] :
( subset(X2,X1)
=> order(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV17) ).
fof(f23,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2] :
( subset(X2,X1)
=> order(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X1)
& member(X4,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X4,X3) )
=> X3 = X4 ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X1)
& member(X7,X1) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X6,X7) )
=> apply(X0,X5,X7) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f25,plain,
? [X0,X1] :
( ? [X2] :
( ~ order(X0,X2)
& subset(X2,X1) )
& order(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f27,plain,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4] :
( X3 = X4
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X3)
| ~ member(X3,X1)
| ~ member(X4,X1) )
& ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f28,plain,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4] :
( X3 = X4
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X3)
| ~ member(X3,X1)
| ~ member(X4,X1) )
& ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) ) ) ),
inference(flattening,[],[f27]) ).
fof(f29,definition,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f30,definition,
! [X0,X1] :
( sP1(X0,X1)
<=> ! [X3,X4] :
( X3 = X4
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X3)
| ~ member(X3,X1)
| ~ member(X4,X1) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f31,plain,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& sP1(X0,X1)
& sP0(X0,X1) ) ),
inference(definition_folding,[],[f28,f30,f29]) ).
fof(f32,plain,
( ~ order(sK2,sK4)
& subset(sK4,sK3)
& order(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f25]) ).
fof(f34,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f35,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X3,X4] :
( X3 != X4
& apply(X0,X3,X4)
& apply(X0,X4,X3)
& member(X3,X1)
& member(X4,X1) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X3)
| ~ member(X3,X1)
| ~ member(X4,X1) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f38,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2,X3] :
( X2 != X3
& apply(X0,X2,X3)
& apply(X0,X3,X2)
& member(X2,X1)
& member(X3,X1) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ apply(X0,X4,X5)
| ~ apply(X0,X5,X4)
| ~ member(X4,X1)
| ~ member(X5,X1) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( sK6(X0,X1) != sK7(X0,X1)
& apply(X0,sK6(X0,X1),sK7(X0,X1))
& apply(X0,sK7(X0,X1),sK6(X0,X1))
& member(sK6(X0,X1),X1)
& member(sK7(X0,X1),X1) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ apply(X0,X4,X5)
| ~ apply(X0,X5,X4)
| ~ member(X4,X1)
| ~ member(X5,X1) )
| ~ sP1(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X2,sK6(X0,X1)),skolemize(X3,sK7(X0,X1))],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X5,X6,X7] :
( ~ apply(X0,X5,X7)
& apply(X0,X5,X6)
& apply(X0,X6,X7)
& member(X5,X1)
& member(X6,X1)
& member(X7,X1) ) )
& ( ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f41,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X2,X3)
& apply(X0,X3,X4)
& member(X2,X1)
& member(X3,X1)
& member(X4,X1) ) )
& ( ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ apply(X0,sK8(X0,X1),sK10(X0,X1))
& apply(X0,sK8(X0,X1),sK9(X0,X1))
& apply(X0,sK9(X0,X1),sK10(X0,X1))
& member(sK8(X0,X1),X1)
& member(sK9(X0,X1),X1)
& member(sK10(X0,X1),X1) ) )
& ( ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1))],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( order(X0,X1)
| ? [X2] :
( ~ apply(X0,X2,X2)
& member(X2,X1) )
| ~ sP1(X0,X1)
| ~ sP0(X0,X1) )
& ( ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& sP1(X0,X1)
& sP0(X0,X1) )
| ~ order(X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f44,plain,
! [X0,X1] :
( ( order(X0,X1)
| ? [X2] :
( ~ apply(X0,X2,X2)
& member(X2,X1) )
| ~ sP1(X0,X1)
| ~ sP0(X0,X1) )
& ( ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& sP1(X0,X1)
& sP0(X0,X1) )
| ~ order(X0,X1) ) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( order(X0,X1)
| ? [X2] :
( ~ apply(X0,X2,X2)
& member(X2,X1) )
| ~ sP1(X0,X1)
| ~ sP0(X0,X1) )
& ( ( ! [X3] :
( apply(X0,X3,X3)
| ~ member(X3,X1) )
& sP1(X0,X1)
& sP0(X0,X1) )
| ~ order(X0,X1) ) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ( order(X0,X1)
| ( ~ apply(X0,sK11(X0,X1),sK11(X0,X1))
& member(sK11(X0,X1),X1) )
| ~ sP1(X0,X1)
| ~ sP0(X0,X1) )
& ( ( ! [X3] :
( apply(X0,X3,X3)
| ~ member(X3,X1) )
& sP1(X0,X1)
& sP0(X0,X1) )
| ~ order(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f45]) ).
fof(f50,plain,
order(sK2,sK3),
inference(cnf_transformation,[],[f32]) ).
fof(f51,plain,
subset(sK4,sK3),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
~ order(sK2,sK4),
inference(cnf_transformation,[],[f32]) ).
fof(f55,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0,X1] :
( ~ member(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f58,plain,
! [X0,X1,X4,X5] :
( ~ apply(X0,X5,X4)
| ~ apply(X0,X4,X5)
| X4 = X5
| ~ member(X4,X1)
| ~ member(X5,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
! [X0,X1] :
( member(sK7(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
! [X0,X1] :
( member(sK6(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f61,plain,
! [X0,X1] :
( apply(X0,sK7(X0,X1),sK6(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f62,plain,
! [X0,X1] :
( apply(X0,sK6(X0,X1),sK7(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f63,plain,
! [X0,X1] :
( sK6(X0,X1) != sK7(X0,X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f64,plain,
! [X0,X1,X6,X7,X5] :
( ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f65,plain,
! [X0,X1] :
( member(sK10(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f66,plain,
! [X0,X1] :
( member(sK9(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f67,plain,
! [X0,X1] :
( member(sK8(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f68,plain,
! [X0,X1] :
( apply(X0,sK9(X0,X1),sK10(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f69,plain,
! [X0,X1] :
( apply(X0,sK8(X0,X1),sK9(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f70,plain,
! [X0,X1] :
( ~ apply(X0,sK8(X0,X1),sK10(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f71,plain,
! [X0,X1] :
( ~ order(X0,X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f72,plain,
! [X0,X1] :
( ~ order(X0,X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f73,plain,
! [X3,X0,X1] :
( ~ order(X0,X1)
| ~ member(X3,X1)
| apply(X0,X3,X3) ),
inference(cnf_transformation,[],[f46]) ).
fof(f74,plain,
! [X0,X1] :
( member(sK11(X0,X1),X1)
| order(X0,X1)
| ~ sP1(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f75,plain,
! [X0,X1] :
( ~ apply(X0,sK11(X0,X1),sK11(X0,X1))
| order(X0,X1)
| ~ sP1(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f84,plain,
sP0(sK2,sK3),
inference(resolution,[],[f71,f50]) ).
fof(f85,plain,
sP1(sK2,sK3),
inference(resolution,[],[f72,f50]) ).
fof(f90,plain,
! [X0] :
( subset(X0,X0)
| subset(X0,X0) ),
inference(resolution,[],[f57,f56]) ).
fof(f92,plain,
! [X0] : subset(X0,X0),
inference(duplicate_literal_removal,[],[f90]) ).
fof(f108,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1),X2)
| ~ subset(X1,X2)
| sP1(X0,X1) ),
inference(resolution,[],[f55,f60]) ).
fof(f109,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1),X2)
| ~ subset(X1,X2)
| sP1(X0,X1) ),
inference(resolution,[],[f55,f59]) ).
fof(f110,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1),X2)
| ~ subset(X1,X2)
| sP0(X0,X1) ),
inference(resolution,[],[f55,f67]) ).
fof(f111,plain,
! [X2,X0,X1] :
( member(sK9(X0,X1),X2)
| ~ subset(X1,X2)
| sP0(X0,X1) ),
inference(resolution,[],[f55,f66]) ).
fof(f112,plain,
! [X2,X0,X1] :
( member(sK10(X0,X1),X2)
| ~ subset(X1,X2)
| sP0(X0,X1) ),
inference(resolution,[],[f55,f65]) ).
fof(f115,plain,
! [X0] :
( apply(sK2,X0,X0)
| ~ member(X0,sK3) ),
inference(resolution,[],[f73,f50]) ).
fof(f133,plain,
! [X2,X0,X1] :
( member(sK11(X0,X1),X2)
| ~ sP1(X0,X1)
| ~ sP0(X0,X1)
| order(X0,X1)
| ~ subset(X1,X2) ),
inference(resolution,[],[f74,f55]) ).
fof(f137,plain,
! [X0] :
( ~ member(sK11(sK2,X0),sK3)
| ~ sP1(sK2,X0)
| ~ sP0(sK2,X0)
| order(sK2,X0) ),
inference(resolution,[],[f75,f115]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ apply(X0,sK6(X0,X1),sK7(X0,X1))
| sK6(X0,X1) = sK7(X0,X1)
| ~ member(sK6(X0,X1),X2)
| ~ member(sK7(X0,X1),X2)
| ~ sP1(X0,X2)
| sP1(X0,X1) ),
inference(resolution,[],[f58,f61]) ).
fof(f147,plain,
! [X2,X0,X1] :
( sK6(X0,X1) = sK7(X0,X1)
| ~ member(sK6(X0,X1),X2)
| ~ member(sK7(X0,X1),X2)
| ~ sP1(X0,X2)
| sP1(X0,X1) ),
inference(forward_subsumption_resolution,[],[f143,f62]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ member(sK7(X0,X1),X2)
| ~ member(sK6(X0,X1),X2)
| ~ sP1(X0,X2)
| sP1(X0,X1) ),
inference(forward_subsumption_resolution,[],[f147,f63]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X1,sK9(X0,X2))
| apply(X0,X1,sK10(X0,X2))
| ~ member(X1,X3)
| ~ member(sK9(X0,X2),X3)
| ~ member(sK10(X0,X2),X3)
| ~ sP0(X0,X3)
| sP0(X0,X2) ),
inference(resolution,[],[f64,f68]) ).
fof(f228,plain,
! [X2,X3,X0,X1] :
( ~ subset(X1,X3)
| sP0(X2,X0)
| member(sK8(X2,X0),X3)
| ~ subset(X0,X1) ),
inference(resolution,[],[f110,f55]) ).
fof(f239,plain,
! [X2,X3,X0,X1] :
( ~ subset(X1,X3)
| sP0(X2,X0)
| member(sK9(X2,X0),X3)
| ~ subset(X0,X1) ),
inference(resolution,[],[f111,f55]) ).
fof(f259,plain,
! [X2,X3,X0,X1] :
( ~ subset(X1,X3)
| sP0(X2,X0)
| member(sK10(X2,X0),X3)
| ~ subset(X0,X1) ),
inference(resolution,[],[f112,f55]) ).
fof(f272,plain,
! [X2,X0,X1] :
( ~ member(sK6(X0,X1),X2)
| ~ sP1(X0,X2)
| sP1(X0,X1)
| ~ subset(X1,X2)
| sP1(X0,X1) ),
inference(resolution,[],[f149,f109]) ).
fof(f278,plain,
! [X2,X0,X1] :
( ~ member(sK6(X0,X1),X2)
| ~ sP1(X0,X2)
| sP1(X0,X1)
| ~ subset(X1,X2) ),
inference(duplicate_literal_removal,[],[f272]) ).
fof(f280,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X2)
| sP1(X0,X1)
| ~ subset(X1,X2) ),
inference(forward_subsumption_resolution,[],[f278,f108]) ).
fof(f296,plain,
! [X0] :
( ~ sP1(sK2,X0)
| ~ sP0(sK2,X0)
| order(sK2,X0)
| ~ subset(X0,sK3)
| ~ sP1(sK2,X0)
| ~ sP0(sK2,X0)
| order(sK2,X0) ),
inference(resolution,[],[f133,f137]) ).
fof(f305,plain,
! [X0] :
( ~ sP1(sK2,X0)
| ~ sP0(sK2,X0)
| order(sK2,X0)
| ~ subset(X0,sK3) ),
inference(duplicate_literal_removal,[],[f296]) ).
fof(f381,plain,
! [X2,X0,X1] :
( apply(X0,sK8(X0,X1),sK10(X0,X1))
| ~ member(sK8(X0,X1),X2)
| ~ member(sK9(X0,X1),X2)
| ~ member(sK10(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1)
| sP0(X0,X1) ),
inference(resolution,[],[f157,f69]) ).
fof(f382,plain,
! [X2,X0,X1] :
( apply(X0,sK8(X0,X1),sK10(X0,X1))
| ~ member(sK8(X0,X1),X2)
| ~ member(sK9(X0,X1),X2)
| ~ member(sK10(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1) ),
inference(duplicate_literal_removal,[],[f381]) ).
fof(f387,plain,
! [X2,X0,X1] :
( ~ member(sK10(X0,X1),X2)
| ~ member(sK9(X0,X1),X2)
| ~ member(sK8(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f382,f70]) ).
fof(f404,plain,
! [X0] :
( ~ subset(X0,sK3)
| sP1(sK2,X0) ),
inference(resolution,[],[f280,f85]) ).
fof(f412,plain,
sP1(sK2,sK4),
inference(resolution,[],[f404,f51]) ).
fof(f423,plain,
( ~ sP0(sK2,sK4)
| order(sK2,sK4)
| ~ subset(sK4,sK3) ),
inference(resolution,[],[f412,f305]) ).
fof(f427,plain,
( ~ sP0(sK2,sK4)
| ~ subset(sK4,sK3) ),
inference(forward_subsumption_resolution,[],[f423,f52]) ).
fof(f433,definition,
( spl12_2
<=> sP0(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f435,plain,
( ~ sP0(sK2,sK4)
| spl12_2 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f437,plain,
~ sP0(sK2,sK4),
inference(forward_subsumption_resolution,[],[f427,f51]) ).
fof(f438,plain,
~ spl12_2,
inference(avatar_split_clause,[],[f437,f433]) ).
fof(f655,plain,
! [X0,X1] :
( member(sK8(X0,X1),sK3)
| sP0(X0,X1)
| ~ subset(X1,sK4) ),
inference(resolution,[],[f228,f51]) ).
fof(f675,plain,
! [X0,X1] :
( member(sK9(X0,X1),sK3)
| sP0(X0,X1)
| ~ subset(X1,sK4) ),
inference(resolution,[],[f239,f51]) ).
fof(f695,plain,
! [X0,X1] :
( member(sK10(X0,X1),sK3)
| sP0(X0,X1)
| ~ subset(X1,sK4) ),
inference(resolution,[],[f259,f51]) ).
fof(f1091,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ subset(X1,sK4)
| ~ member(sK9(X0,X1),sK3)
| ~ member(sK8(X0,X1),sK3)
| ~ sP0(X0,sK3)
| sP0(X0,X1) ),
inference(resolution,[],[f695,f387]) ).
fof(f1093,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ subset(X1,sK4)
| ~ member(sK9(X0,X1),sK3)
| ~ member(sK8(X0,X1),sK3)
| ~ sP0(X0,sK3) ),
inference(duplicate_literal_removal,[],[f1091]) ).
fof(f1094,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ subset(X1,sK4)
| ~ member(sK8(X0,X1),sK3)
| ~ sP0(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f1093,f675]) ).
fof(f1095,plain,
! [X0,X1] :
( ~ sP0(X0,sK3)
| ~ subset(X1,sK4)
| sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f1094,f655]) ).
fof(f1114,plain,
! [X0] :
( ~ subset(X0,sK4)
| sP0(sK2,X0) ),
inference(resolution,[],[f1095,f84]) ).
fof(f1118,plain,
sP0(sK2,sK4),
inference(resolution,[],[f1114,f92]) ).
fof(f1135,plain,
( $false
| spl12_2 ),
inference(forward_subsumption_resolution,[],[f1118,f435]) ).
fof(f1136,plain,
spl12_2,
inference(avatar_contradiction_clause,[],[f1135]) ).
cnf(s2,plain,
~ spl12_2,
inference(sat_conversion,[],[f438]) ).
cnf(s3,plain,
spl12_2,
inference(sat_conversion,[],[f1136]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f1137,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET805+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n014.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 : Mon Sep 28 02:50:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.13/1.49 % (1391879)Detected formulas, will run a generic FOF schedule.
% 3.13/1.49 % (1391885)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=2667050699:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.13/1.49 % (1391884)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=1091941472:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.13/1.49 % (1391890)dis-21_1_sil=8000:lcm=predicate:random_seed=2873382044: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)
% 3.13/1.49 % (1391889)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2527493371:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.13/1.49 % (1391888)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=66841784:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.13/1.49 % (1391887)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=201818264:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.13/1.49 % (1391886)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=3674572081:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.13/1.49 % (1391887)Refutation not found, incomplete strategy
% 3.13/1.49 % (1391887)------------------------------
% 3.13/1.49 % (1391887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.49 % (1391887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.49 % (1391887)CaDiCaL version: 2.1.3
% 3.13/1.49 % (1391887)Termination reason: Refutation not found, incomplete strategy
% 3.13/1.49 % (1391887)Time elapsed: 0.002 s
% 3.13/1.49 % (1391887)Peak memory usage: 88 MB
% 3.13/1.49 % (1391887)Instructions burned: 1 (million)
% 3.13/1.49 % (1391888)Instruction limit reached!
% 3.13/1.49 % (1391888)------------------------------
% 3.13/1.49 % (1391888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.49 % (1391888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.49 % (1391888)CaDiCaL version: 2.1.3
% 3.13/1.49 % (1391888)Termination reason: Instruction limit
% 3.13/1.49 % (1391888)Termination phase: Saturation
% 3.13/1.49 % (1391888)Time elapsed: 0.049 s
% 3.13/1.49 % (1391888)Peak memory usage: 88 MB
% 3.13/1.49 % (1391888)Instructions burned: 121 (million)
% 3.13/1.49 % (1391889)Instruction limit reached!
% 3.13/1.49 % (1391889)------------------------------
% 3.13/1.49 % (1391889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.49 % (1391889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.49 % (1391889)CaDiCaL version: 2.1.3
% 3.13/1.49 % (1391889)Termination reason: Instruction limit
% 3.13/1.49 % (1391889)Termination phase: Saturation
% 3.13/1.49 % (1391889)Time elapsed: 0.065 s
% 3.13/1.49 % (1391889)Peak memory usage: 88 MB
% 3.13/1.49 % (1391889)Instructions burned: 139 (million)
% 3.13/1.49 % (1391890)Instruction limit reached!
% 3.13/1.49 % (1391890)------------------------------
% 3.13/1.49 % (1391890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.49 % (1391890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.49 % (1391890)CaDiCaL version: 2.1.3
% 3.13/1.49 % (1391890)Termination reason: Instruction limit
% 3.13/1.49 % (1391890)Termination phase: Saturation
% 3.13/1.49 % (1391890)Time elapsed: 0.081 s
% 3.13/1.49 % (1391890)Peak memory usage: 90 MB
% 3.13/1.49 % (1391890)Instructions burned: 129 (million)
% 3.13/1.49 % (1391898)lrs+10_1_sil=8000:sp=occurrence:random_seed=1642423439:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.13/1.49 % (1391899)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3254950127:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.13/1.49 % (1391899)Refutation not found, incomplete strategy
% 3.13/1.49 % (1391899)------------------------------
% 3.13/1.49 % (1391899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.49 % (1391899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.49 % (1391899)CaDiCaL version: 2.1.3
% 3.13/1.49 % (1391899)Termination reason: Refutation not found, incomplete strategy
% 3.13/1.49 % (1391899)Time elapsed: 0.002 s
% 3.13/1.49 % (1391899)Peak memory usage: 88 MB
% 3.13/1.49 % (1391899)Instructions burned: 2 (million)
% 3.13/1.49 % (1391900)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3502222197:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.13/1.49 % (1391898)First to succeed.
% 3.13/1.49 % (1391898)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1391879"
% 3.13/1.49 % (1391900)Also succeeded, but the first one will report.
% 3.13/1.49 % (1391887)------------------------------
% 3.13/1.49 % (1391887)------------------------------
% 3.13/1.49 % (1391885)Also succeeded, but the first one will report.
% 3.13/1.49 % (1391904)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=2144603739:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 3.13/1.49 % (1391899)------------------------------
% 3.13/1.49 % (1391899)------------------------------
% 3.13/1.49 % (1391898)Refutation found. Thanks to Tanya!
% 3.13/1.49 % SZS status Theorem for theBenchmark
% 3.13/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 4.98/1.69 % (1391898)------------------------------
% 4.98/1.69 % (1391898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.98/1.69 % (1391898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.98/1.69 % (1391898)CaDiCaL version: 2.1.3
% 4.98/1.69 % (1391898)Termination reason: Refutation
% 4.98/1.69 % (1391898)Time elapsed: 0.048 s
% 4.98/1.69 % (1391898)Peak memory usage: 90 MB
% 4.98/1.69 % (1391898)Instructions burned: 80 (million)
% 4.98/1.69 % (1391898)------------------------------
% 4.98/1.69 % (1391898)------------------------------
% 4.98/1.69 % (1391879)Success in time 0.628 s
% 4.98/1.69 % Vampire exiting
%------------------------------------------------------------------------------