TSTP Solution File: NUM616+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM616+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:35:40 EDT 2024
% Result : Theorem 53.86s 8.07s
% Output : Refutation 53.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 23
% Syntax : Number of formulae : 118 ( 41 unt; 0 def)
% Number of atoms : 405 ( 79 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 426 ( 139 ~; 116 |; 137 &)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-2 aty)
% Number of variables : 138 ( 124 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f354680,plain,
$false,
inference(subsumption_resolution,[],[f343088,f1358]) ).
fof(f1358,plain,
~ aElementOf0(xp,xP),
inference(superposition,[],[f1290,f894]) ).
fof(f894,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
( xp = szmzizndt0(xQ)
& ! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) )
& aElementOf0(xp,xQ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f103,axiom,
( xp = szmzizndt0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(f1290,plain,
~ aElementOf0(szmzizndt0(xQ),xP),
inference(equality_resolution,[],[f867]) ).
fof(f867,plain,
! [X0] :
( szmzizndt0(xQ) != X0
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f475]) ).
fof(f475,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( ( aElementOf0(X0,xP)
| szmzizndt0(xQ) = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) )
& ( ( szmzizndt0(xQ) != X0
& aElementOf0(X0,xQ)
& aElement0(X0) )
| ~ aElementOf0(X0,xP) ) )
& ! [X1] :
( sdtlseqdt0(szmzizndt0(xQ),X1)
| ~ aElementOf0(X1,xQ) )
& aSet0(xP) ),
inference(flattening,[],[f474]) ).
fof(f474,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( ( aElementOf0(X0,xP)
| szmzizndt0(xQ) = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) )
& ( ( szmzizndt0(xQ) != X0
& aElementOf0(X0,xQ)
& aElement0(X0) )
| ~ aElementOf0(X0,xP) ) )
& ! [X1] :
( sdtlseqdt0(szmzizndt0(xQ),X1)
| ~ aElementOf0(X1,xQ) )
& aSet0(xP) ),
inference(nnf_transformation,[],[f147]) ).
fof(f147,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( szmzizndt0(xQ) != X0
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ! [X1] :
( sdtlseqdt0(szmzizndt0(xQ),X1)
| ~ aElementOf0(X1,xQ) )
& aSet0(xP) ),
inference(ennf_transformation,[],[f118]) ).
fof(f118,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( szmzizndt0(xQ) != X0
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X1) )
& aSet0(xP) ),
inference(rectify,[],[f104]) ).
fof(f104,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( szmzizndt0(xQ) != X0
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f343088,plain,
aElementOf0(xp,xP),
inference(superposition,[],[f748,f343035]) ).
fof(f343035,plain,
xp = sK108,
inference(unit_resulting_resolution,[],[f1563,f1583,f1550,f342992,f1272]) ).
fof(f1272,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f263]) ).
fof(f263,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(f342992,plain,
sdtlseqdt0(sK108,xp),
inference(forward_demodulation,[],[f342919,f57499]) ).
fof(f57499,plain,
sK108 = szmzizndt0(sdtlpdtrp0(xN,sK135(sK108))),
inference(forward_demodulation,[],[f57448,f20168]) ).
fof(f20168,plain,
sK108 = sdtlpdtrp0(xe,sK135(sK108)),
inference(unit_resulting_resolution,[],[f1543,f1083]) ).
fof(f1083,plain,
! [X0] :
( ~ sP69(X0)
| sdtlpdtrp0(xe,sK135(X0)) = X0 ),
inference(cnf_transformation,[],[f619]) ).
fof(f619,plain,
! [X0] :
( ( sdtlpdtrp0(xe,sK135(X0)) = X0
& aElementOf0(sK135(X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,sK135(X0))
& aElementOf0(sK135(X0),szNzAzT0) )
| ~ sP69(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK135])],[f617,f618]) ).
fof(f618,plain,
! [X0] :
( ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlpdtrp0(xe,sK135(X0)) = X0
& aElementOf0(sK135(X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,sK135(X0))
& aElementOf0(sK135(X0),szNzAzT0) ) ),
introduced(choice_axiom,[]) ).
fof(f617,plain,
! [X0] :
( ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
& aElementOf0(X1,szNzAzT0) )
| ~ sP69(X0) ),
inference(rectify,[],[f616]) ).
fof(f616,plain,
! [X0] :
( ? [X2] :
( sdtlpdtrp0(xe,X2) = X0
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
& aElementOf0(X2,szNzAzT0) )
| ~ sP69(X0) ),
inference(nnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0] :
( ? [X2] :
( sdtlpdtrp0(xe,X2) = X0
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
& aElementOf0(X2,szNzAzT0) )
| ~ sP69(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP69])]) ).
fof(f1543,plain,
sP69(sK108),
inference(unit_resulting_resolution,[],[f1538,f1085]) ).
fof(f1085,plain,
! [X0] :
( ~ aElementOf0(X0,xO)
| sP69(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( sP69(X0)
| ( ~ aElementOf0(X0,xO)
& ! [X1] :
( sdtlpdtrp0(xe,X1) != X0
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(definition_folding,[],[f171,f356]) ).
fof(f171,plain,
! [X0] :
( ? [X2] :
( sdtlpdtrp0(xe,X2) = X0
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
& aElementOf0(X2,szNzAzT0) )
| ( ~ aElementOf0(X0,xO)
& ! [X1] :
( sdtlpdtrp0(xe,X1) != X0
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(ennf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ( aElementOf0(X0,xO)
| ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
=> ? [X2] :
( sdtlpdtrp0(xe,X2) = X0
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
& aElementOf0(X2,szNzAzT0) ) ),
inference(rectify,[],[f97]) ).
fof(f97,axiom,
! [X0] :
( ( aElementOf0(X0,xO)
| ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
=> ? [X1] :
( sdtlpdtrp0(xe,X1) = X0
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
& aElementOf0(X1,szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4982) ).
fof(f1538,plain,
aElementOf0(sK108,xO),
inference(unit_resulting_resolution,[],[f1534,f888]) ).
fof(f888,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xO) ),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& xK = sbrdtbr0(xQ)
& aSubsetOf0(xQ,xO)
& ! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) )
& aSet0(xQ) ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,axiom,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& xK = sbrdtbr0(xQ)
& aSubsetOf0(xQ,xO)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xO) )
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(f1534,plain,
aElementOf0(sK108,xQ),
inference(unit_resulting_resolution,[],[f748,f866]) ).
fof(f866,plain,
! [X0] :
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f475]) ).
fof(f57448,plain,
sdtlpdtrp0(xe,sK135(sK108)) = szmzizndt0(sdtlpdtrp0(xN,sK135(sK108))),
inference(unit_resulting_resolution,[],[f1785,f760]) ).
fof(f760,plain,
! [X0] :
( ~ sP0(X0)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0) ),
inference(cnf_transformation,[],[f412]) ).
fof(f412,plain,
! [X0] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
& ! [X1] :
( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
& ! [X1] :
( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1785,plain,
sP0(sK135(sK108)),
inference(unit_resulting_resolution,[],[f1775,f763]) ).
fof(f763,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP0(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
( ! [X0] :
( sP0(X0)
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xe)
& aFunction0(xe) ),
inference(definition_folding,[],[f138,f275]) ).
fof(f138,plain,
( ! [X0] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
& ! [X1] :
( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xe)
& aFunction0(xe) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ) )
& szNzAzT0 = szDzozmdt0(xe)
& aFunction0(xe) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
fof(f1775,plain,
aElementOf0(sK135(sK108),szNzAzT0),
inference(unit_resulting_resolution,[],[f1543,f1080]) ).
fof(f1080,plain,
! [X0] :
( ~ sP69(X0)
| aElementOf0(sK135(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f619]) ).
fof(f342919,plain,
sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK135(sK108))),xp),
inference(unit_resulting_resolution,[],[f242166,f311696,f1342]) ).
fof(f1342,plain,
! [X2,X1] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2)
| sP164(X1) ),
inference(cnf_transformation,[],[f1342_D]) ).
fof(f1342_D,plain,
! [X1] :
( ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) )
<=> ~ sP164(X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP164])]) ).
fof(f311696,plain,
aElementOf0(xp,sdtlpdtrp0(xN,sK135(sK108))),
inference(unit_resulting_resolution,[],[f900,f1775,f31058,f311684,f1093]) ).
fof(f1093,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0,X1] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) ) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f174]) ).
fof(f174,plain,
! [X0,X1] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) ) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).
fof(f311684,plain,
sdtlseqdt0(sK135(sK108),xn),
inference(unit_resulting_resolution,[],[f900,f1775,f310997,f1270]) ).
fof(f1270,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f260,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f259]) ).
fof(f259,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
fof(f310997,plain,
~ sdtlseqdt0(szszuzczcdt0(xn),sK135(sK108)),
inference(unit_resulting_resolution,[],[f1775,f2792,f749,f31057,f1093]) ).
fof(f31057,plain,
aElementOf0(sK108,sdtlpdtrp0(xN,sK135(sK108))),
inference(forward_demodulation,[],[f31015,f20168]) ).
fof(f31015,plain,
aElementOf0(sdtlpdtrp0(xe,sK135(sK108)),sdtlpdtrp0(xN,sK135(sK108))),
inference(unit_resulting_resolution,[],[f1785,f758]) ).
fof(f758,plain,
! [X0] :
( ~ sP0(X0)
| aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f412]) ).
fof(f749,plain,
~ aElementOf0(sK108,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f411]) ).
fof(f411,plain,
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ~ aElementOf0(sK108,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aElementOf0(sK108,xP) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK108])],[f137,f410]) ).
fof(f410,plain,
( ? [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aElementOf0(X0,xP) )
=> ( ~ aElementOf0(sK108,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aElementOf0(sK108,xP) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ? [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aElementOf0(X0,xP) ) ),
inference(ennf_transformation,[],[f114]) ).
fof(f114,negated_conjecture,
~ ( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(negated_conjecture,[],[f113]) ).
fof(f113,conjecture,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f2792,plain,
aElementOf0(szszuzczcdt0(xn),szNzAzT0),
inference(unit_resulting_resolution,[],[f900,f1162]) ).
fof(f1162,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ( sz00 != szszuzczcdt0(X0)
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( sz00 != szszuzczcdt0(X0)
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(f31058,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xn)),
inference(forward_demodulation,[],[f31012,f901]) ).
fof(f901,plain,
xp = sdtlpdtrp0(xe,xn),
inference(cnf_transformation,[],[f111]) ).
fof(f111,axiom,
( xp = sdtlpdtrp0(xe,xn)
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,xn)
& aElementOf0(xn,szDzozmdt0(xd)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).
fof(f31012,plain,
aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)),
inference(unit_resulting_resolution,[],[f1379,f758]) ).
fof(f1379,plain,
sP0(xn),
inference(unit_resulting_resolution,[],[f900,f763]) ).
fof(f900,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f242166,plain,
~ sP164(sK135(sK108)),
inference(unit_resulting_resolution,[],[f179124,f1343]) ).
fof(f1343,plain,
! [X0,X1] :
( ~ sP71(X0,X1)
| ~ sP164(X1) ),
inference(general_splitting,[],[f1087,f1342_D]) ).
fof(f1087,plain,
! [X2,X0,X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ sP71(X0,X1) ),
inference(cnf_transformation,[],[f621]) ).
fof(f621,plain,
! [X0,X1] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& sP70(X1,X0)
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X1)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1)) )
| ~ sP71(X0,X1) ),
inference(rectify,[],[f620]) ).
fof(f620,plain,
! [X1,X0] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& sP70(X0,X1)
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP71(X1,X0) ),
inference(nnf_transformation,[],[f359]) ).
fof(f359,plain,
! [X1,X0] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& sP70(X0,X1)
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP71(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP71])]) ).
fof(f179124,plain,
sP71(szszuzczcdt0(sK135(sK108)),sK135(sK108)),
inference(unit_resulting_resolution,[],[f1775,f2621,f2795,f1092]) ).
fof(f1092,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| X0 = X1
| sP71(X1,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f360,plain,
! [X0,X1] :
( sP71(X1,X0)
| X0 = X1
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(definition_folding,[],[f173,f359,f358]) ).
fof(f358,plain,
! [X0,X1] :
( ? [X3] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X1)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X1))
| ~ sP70(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP70])]) ).
fof(f173,plain,
! [X0,X1] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& ( ? [X3] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X1)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X1)) )
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| X0 = X1
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f172]) ).
fof(f172,plain,
! [X0,X1] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& ( ? [X3] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X1)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X1)) )
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| X0 = X1
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( ( X0 != X1
& aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ~ ( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) = szmzizndt0(sdtlpdtrp0(xN,X1))
| ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X1)) ) ) ) ),
inference(rectify,[],[f84]) ).
fof(f84,axiom,
! [X0,X1] :
( ( X0 != X1
& aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ~ ( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) = szmzizndt0(sdtlpdtrp0(xN,X1))
| ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3821) ).
fof(f2795,plain,
aElementOf0(szszuzczcdt0(sK135(sK108)),szNzAzT0),
inference(unit_resulting_resolution,[],[f1775,f1162]) ).
fof(f2621,plain,
sK135(sK108) != szszuzczcdt0(sK135(sK108)),
inference(unit_resulting_resolution,[],[f1775,f1157]) ).
fof(f1157,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != X0 ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( szszuzczcdt0(X0) != X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> szszuzczcdt0(X0) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatNSucc) ).
fof(f1550,plain,
sdtlseqdt0(xp,sK108),
inference(unit_resulting_resolution,[],[f1534,f893]) ).
fof(f893,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(xp,X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f1583,plain,
aElementOf0(xp,szNzAzT0),
inference(unit_resulting_resolution,[],[f1557,f884]) ).
fof(f884,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f1557,plain,
aElementOf0(xp,xS),
inference(unit_resulting_resolution,[],[f1537,f917]) ).
fof(f917,plain,
! [X0] :
( ~ aElementOf0(X0,xO)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
( aSubsetOf0(xO,xS)
& ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xO) ) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,axiom,
( aSubsetOf0(xO,xS)
& ! [X0] :
( aElementOf0(X0,xO)
=> aElementOf0(X0,xS) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4998) ).
fof(f1537,plain,
aElementOf0(xp,xO),
inference(unit_resulting_resolution,[],[f753,f888]) ).
fof(f753,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5173) ).
fof(f1563,plain,
aElementOf0(sK108,szNzAzT0),
inference(unit_resulting_resolution,[],[f1558,f884]) ).
fof(f1558,plain,
aElementOf0(sK108,xS),
inference(unit_resulting_resolution,[],[f1538,f917]) ).
fof(f748,plain,
aElementOf0(sK108,xP),
inference(cnf_transformation,[],[f411]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : NUM616+3 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n010.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 23:07:50 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.32 % (26138)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.34 % (26141)WARNING: value z3 for option sas not known
% 0.10/0.34 % (26140)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.34 % (26145)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.10/0.34 % (26141)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.34 % (26139)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.34 % (26142)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.34 % (26144)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.10/0.34 % (26143)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.39 TRYING [1]
% 0.16/0.40 TRYING [2]
% 0.16/0.46 TRYING [3]
% 2.26/0.66 TRYING [4]
% 6.43/1.25 TRYING [5]
% 16.98/2.78 TRYING [6]
% 18.30/3.02 TRYING [1]
% 20.39/3.26 TRYING [2]
% 24.07/3.86 TRYING [1]
% 26.59/4.14 TRYING [2]
% 32.25/5.00 TRYING [3]
% 38.81/5.90 TRYING [3]
% 42.99/6.51 TRYING [7]
% 53.31/8.03 % (26145)First to succeed.
% 53.86/8.07 % (26145)Refutation found. Thanks to Tanya!
% 53.86/8.07 % SZS status Theorem for theBenchmark
% 53.86/8.07 % SZS output start Proof for theBenchmark
% See solution above
% 53.86/8.07 % (26145)------------------------------
% 53.86/8.07 % (26145)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 53.86/8.07 % (26145)Termination reason: Refutation
% 53.86/8.07
% 53.86/8.07 % (26145)Memory used [KB]: 162505
% 53.86/8.07 % (26145)Time elapsed: 7.697 s
% 53.86/8.07 % (26145)Instructions burned: 14426 (million)
% 53.86/8.07 % (26145)------------------------------
% 53.86/8.07 % (26145)------------------------------
% 53.86/8.07 % (26138)Success in time 7.751 s
%------------------------------------------------------------------------------