%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG112+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:35:34 PM UTC 2026
% Result : Theorem 2.89s 1.33s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 8 unt; 2 def)
% Number of atoms : 461 ( 143 equ)
% Maximal formula atoms : 28 ( 8 avg)
% Number of connectives : 589 ( 180 ~; 144 |; 239 &)
% ( 13 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 10 con; 0-2 aty)
% Number of variables : 217 ( 118 !; 99 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) ) ) )
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = X0 ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xb,X1) = X0 ) )
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f44,axiom,
? [X0] :
( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
& ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& X0 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
fof(f45,axiom,
! [X0] :
( ( ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
| aElementOf0(X0,xI) )
& X0 != sz00 )
=> ? [X1] :
( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
& aElementOf0(X1,xI)
& X1 != sz00
& ! [X2] :
( ( ( ? [X3,X4] :
( aElementOf0(X3,slsdtgt0(xa))
& aElementOf0(X4,slsdtgt0(xb))
& sdtpldt0(X3,X4) = X2 )
| aElementOf0(X2,xI) )
& X2 != sz00 )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2351) ).
fof(f46,conjecture,
? [X0] :
( ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
| aElementOf0(X0,xI) )
& X0 != sz00
& ! [X1] :
( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
& aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ? [X0] :
( ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
| aElementOf0(X0,xI) )
& X0 != sz00
& ! [X1] :
( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
& aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f49,plain,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X0),xI) ) ) )
& aIdeal0(xI)
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(xa,X4) = X3 ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( aElement0(X6)
& sdtasdt0(xb,X6) = X5 ) )
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( aElementOf0(X8,slsdtgt0(xa))
& aElementOf0(X9,slsdtgt0(xb))
& sdtpldt0(X8,X9) = X7 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(rectify,[],[f42]) ).
fof(f51,plain,
? [X0] :
( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(xb,X4) = X3 ) )
& ? [X5,X6] :
( aElementOf0(X5,slsdtgt0(xa))
& aElementOf0(X6,slsdtgt0(xb))
& sdtpldt0(X5,X6) = X0 )
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& X0 != sz00 ),
inference(rectify,[],[f44]) ).
fof(f52,plain,
! [X0] :
( ( ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
| aElementOf0(X0,xI) )
& X0 != sz00 )
=> ? [X3] :
( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
& aElementOf0(X3,xI)
& sz00 != X3
& ! [X6] :
( ( ( ? [X7,X8] :
( aElementOf0(X7,slsdtgt0(xa))
& aElementOf0(X8,slsdtgt0(xb))
& sdtpldt0(X7,X8) = X6 )
| aElementOf0(X6,xI) )
& sz00 != X6 )
=> ~ iLess0(sbrdtbr0(X6),sbrdtbr0(X3)) ) ) ),
inference(rectify,[],[f45]) ).
fof(f53,plain,
~ ? [X0] :
( ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
| aElementOf0(X0,xI) )
& X0 != sz00
& ! [X3] :
( ( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
& aElementOf0(X3,xI)
& sz00 != X3 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0)) ) ),
inference(rectify,[],[f47]) ).
fof(f60,plain,
( aSet0(xI)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI) )
& ! [X2] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2) ) )
| ~ aElementOf0(X0,xI) )
& aIdeal0(xI)
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(xa,X4) = X3 ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( aElement0(X6)
& sdtasdt0(xb,X6) = X5 ) )
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( aElementOf0(X8,slsdtgt0(xa))
& aElementOf0(X9,slsdtgt0(xb))
& sdtpldt0(X8,X9) = X7 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f61,plain,
! [X0] :
( ? [X3] :
( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
& aElementOf0(X3,xI)
& sz00 != X3
& ! [X6] :
( ~ iLess0(sbrdtbr0(X6),sbrdtbr0(X3))
| ( ! [X7,X8] :
( ~ aElementOf0(X7,slsdtgt0(xa))
| ~ aElementOf0(X8,slsdtgt0(xb))
| sdtpldt0(X7,X8) != X6 )
& ~ aElementOf0(X6,xI) )
| sz00 = X6 ) )
| ( ! [X1,X2] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0 )
& ~ aElementOf0(X0,xI) )
| sz00 = X0 ),
inference(ennf_transformation,[],[f52]) ).
fof(f62,plain,
! [X0] :
( ? [X3] :
( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
& aElementOf0(X3,xI)
& sz00 != X3
& ! [X6] :
( ~ iLess0(sbrdtbr0(X6),sbrdtbr0(X3))
| ( ! [X7,X8] :
( ~ aElementOf0(X7,slsdtgt0(xa))
| ~ aElementOf0(X8,slsdtgt0(xb))
| sdtpldt0(X7,X8) != X6 )
& ~ aElementOf0(X6,xI) )
| sz00 = X6 ) )
| ( ! [X1,X2] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0 )
& ~ aElementOf0(X0,xI) )
| sz00 = X0 ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ( ! [X1,X2] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0 )
& ~ aElementOf0(X0,xI) )
| sz00 = X0
| ? [X3] :
( iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
& ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
& aElementOf0(X3,xI)
& sz00 != X3 ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f64,plain,
! [X0] :
( ( ! [X1,X2] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0 )
& ~ aElementOf0(X0,xI) )
| sz00 = X0
| ? [X3] :
( iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
& ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
& aElementOf0(X3,xI)
& sz00 != X3 ) ),
inference(flattening,[],[f63]) ).
fof(f103,definition,
( ? [X3] :
( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
& aElementOf0(X3,xI)
& sz00 != X3
& ! [X6] :
( ~ iLess0(sbrdtbr0(X6),sbrdtbr0(X3))
| ( ! [X7,X8] :
( ~ aElementOf0(X7,slsdtgt0(xa))
| ~ aElementOf0(X8,slsdtgt0(xb))
| sdtpldt0(X7,X8) != X6 )
& ~ aElementOf0(X6,xI) )
| sz00 = X6 ) )
| ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f104,plain,
! [X0] :
( sP2
| ( ! [X1,X2] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0 )
& ~ aElementOf0(X0,xI) )
| sz00 = X0 ),
inference(definition_folding,[],[f62,f103]) ).
fof(f105,definition,
! [X0] :
( ? [X3] :
( iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
& ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
& aElementOf0(X3,xI)
& sz00 != X3 )
| ~ sP3(X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f106,plain,
! [X0] :
( ( ! [X1,X2] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0 )
& ~ aElementOf0(X0,xI) )
| sz00 = X0
| sP3(X0) ),
inference(definition_folding,[],[f64,f105]) ).
fof(f116,plain,
( aSet0(xI)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI) )
& ! [X2] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2) ) )
| ~ aElementOf0(X0,xI) )
& aIdeal0(xI)
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xa))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xa,X4) != X3 ) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(xa,X4) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xb))
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(xb,X6) != X5 ) )
& ( ? [X6] :
( aElement0(X6)
& sdtasdt0(xb,X6) = X5 )
| ~ aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X7] :
( ( aElementOf0(X7,xI)
| ! [X8,X9] :
( ~ aElementOf0(X8,slsdtgt0(xa))
| ~ aElementOf0(X9,slsdtgt0(xb))
| sdtpldt0(X8,X9) != X7 ) )
& ( ? [X8,X9] :
( aElementOf0(X8,slsdtgt0(xa))
& aElementOf0(X9,slsdtgt0(xb))
& sdtpldt0(X8,X9) = X7 )
| ~ aElementOf0(X7,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(nnf_transformation,[],[f60]) ).
fof(f117,plain,
( aSet0(xI)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI) )
& ! [X2] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2) ) )
| ~ aElementOf0(X0,xI) )
& aIdeal0(xI)
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xa))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xa,X4) != X3 ) )
& ( ? [X5] :
( aElement0(X5)
& sdtasdt0(xa,X5) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xb))
| ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(xb,X7) != X6 ) )
& ( ? [X8] :
( aElement0(X8)
& sdtasdt0(xb,X8) = X6 )
| ~ aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X9] :
( ( aElementOf0(X9,xI)
| ! [X10,X11] :
( ~ aElementOf0(X10,slsdtgt0(xa))
| ~ aElementOf0(X11,slsdtgt0(xb))
| sdtpldt0(X10,X11) != X9 ) )
& ( ? [X12,X13] :
( aElementOf0(X12,slsdtgt0(xa))
& aElementOf0(X13,slsdtgt0(xb))
& sdtpldt0(X12,X13) = X9 )
| ~ aElementOf0(X9,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(rectify,[],[f116]) ).
fof(f118,plain,
( aSet0(xI)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI) )
& ! [X2] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2) ) )
| ~ aElementOf0(X0,xI) )
& aIdeal0(xI)
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xa))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xa,X4) != X3 ) )
& ( ( aElement0(sK9(X3))
& sdtasdt0(xa,sK9(X3)) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xb))
| ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(xb,X7) != X6 ) )
& ( ( aElement0(sK10(X6))
& sdtasdt0(xb,sK10(X6)) = X6 )
| ~ aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X9] :
( ( aElementOf0(X9,xI)
| ! [X10,X11] :
( ~ aElementOf0(X10,slsdtgt0(xa))
| ~ aElementOf0(X11,slsdtgt0(xb))
| sdtpldt0(X10,X11) != X9 ) )
& ( ( aElementOf0(sK11(X9),slsdtgt0(xa))
& aElementOf0(sK12(X9),slsdtgt0(xb))
& sdtpldt0(sK11(X9),sK12(X9)) = X9 )
| ~ aElementOf0(X9,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X5,sK9(X3)),skolemize(X8,sK10(X6)),skolemize(X12,sK11(X9)),skolemize(X13,sK12(X9))],[f117]) ).
fof(f120,plain,
? [X0] :
( ! [X1] :
( ( aElementOf0(X1,slsdtgt0(xa))
| ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(xa,X2) != X1 ) )
& ( ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 )
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xb,X4) != X3 ) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(xb,X4) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ? [X5,X6] :
( aElementOf0(X5,slsdtgt0(xa))
& aElementOf0(X6,slsdtgt0(xb))
& sdtpldt0(X5,X6) = X0 )
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& X0 != sz00 ),
inference(nnf_transformation,[],[f51]) ).
fof(f121,plain,
? [X0] :
( ! [X1] :
( ( aElementOf0(X1,slsdtgt0(xa))
| ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(xa,X2) != X1 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(xa,X3) = X1 )
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X4] :
( ( aElementOf0(X4,slsdtgt0(xb))
| ! [X5] :
( ~ aElement0(X5)
| sdtasdt0(xb,X5) != X4 ) )
& ( ? [X6] :
( aElement0(X6)
& sdtasdt0(xb,X6) = X4 )
| ~ aElementOf0(X4,slsdtgt0(xb)) ) )
& ? [X7,X8] :
( aElementOf0(X7,slsdtgt0(xa))
& aElementOf0(X8,slsdtgt0(xb))
& sdtpldt0(X7,X8) = X0 )
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& X0 != sz00 ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
( ! [X1] :
( ( aElementOf0(X1,slsdtgt0(xa))
| ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(xa,X2) != X1 ) )
& ( ( aElement0(sK18(X1))
& sdtasdt0(xa,sK18(X1)) = X1 )
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X4] :
( ( aElementOf0(X4,slsdtgt0(xb))
| ! [X5] :
( ~ aElement0(X5)
| sdtasdt0(xb,X5) != X4 ) )
& ( ( aElement0(sK19(X4))
& sdtasdt0(xb,sK19(X4)) = X4 )
| ~ aElementOf0(X4,slsdtgt0(xb)) ) )
& aElementOf0(sK20,slsdtgt0(xa))
& aElementOf0(sK21,slsdtgt0(xb))
& sK17 = sdtpldt0(sK20,sK21)
& aElementOf0(sK17,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& sz00 != sK17 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20,sK21]),skolemize(X0,sK17),skolemize(X3,sK18(X1)),skolemize(X6,sK19(X4)),skolemize(X7,sK20),skolemize(X8,sK21)],[f121]) ).
fof(f123,plain,
( ? [X3] :
( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
& aElementOf0(X3,xI)
& sz00 != X3
& ! [X6] :
( ~ iLess0(sbrdtbr0(X6),sbrdtbr0(X3))
| ( ! [X7,X8] :
( ~ aElementOf0(X7,slsdtgt0(xa))
| ~ aElementOf0(X8,slsdtgt0(xb))
| sdtpldt0(X7,X8) != X6 )
& ~ aElementOf0(X6,xI) )
| sz00 = X6 ) )
| ~ sP2 ),
inference(nnf_transformation,[],[f103]) ).
fof(f124,plain,
( ? [X0] :
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
& aElementOf0(X0,xI)
& sz00 != X0
& ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
| ( ! [X4,X5] :
( ~ aElementOf0(X4,slsdtgt0(xa))
| ~ aElementOf0(X5,slsdtgt0(xb))
| sdtpldt0(X4,X5) != X3 )
& ~ aElementOf0(X3,xI) )
| sz00 = X3 ) )
| ~ sP2 ),
inference(rectify,[],[f123]) ).
fof(f125,plain,
( ( aElementOf0(sK23,slsdtgt0(xa))
& aElementOf0(sK24,slsdtgt0(xb))
& sK22 = sdtpldt0(sK23,sK24)
& aElementOf0(sK22,xI)
& sz00 != sK22
& ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK22))
| ( ! [X4,X5] :
( ~ aElementOf0(X4,slsdtgt0(xa))
| ~ aElementOf0(X5,slsdtgt0(xb))
| sdtpldt0(X4,X5) != X3 )
& ~ aElementOf0(X3,xI) )
| sz00 = X3 ) )
| ~ sP2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23,sK24]),skolemize(X0,sK22),skolemize(X1,sK23),skolemize(X2,sK24)],[f124]) ).
fof(f126,plain,
! [X0] :
( ? [X3] :
( iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
& ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
& aElementOf0(X3,xI)
& sz00 != X3 )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f105]) ).
fof(f127,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
& aElementOf0(X1,xI)
& sz00 != X1 )
| ~ sP3(X0) ),
inference(rectify,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ( iLess0(sbrdtbr0(sK25(X0)),sbrdtbr0(X0))
& aElementOf0(sK26(X0),slsdtgt0(xa))
& aElementOf0(sK27(X0),slsdtgt0(xb))
& sK25(X0) = sdtpldt0(sK26(X0),sK27(X0))
& aElementOf0(sK25(X0),xI)
& sz00 != sK25(X0) )
| ~ sP3(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X1,sK25(X0)),skolemize(X2,sK26(X0)),skolemize(X3,sK27(X0))],[f127]) ).
fof(f177,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f118]) ).
fof(f204,plain,
sz00 != sK17,
inference(cnf_transformation,[],[f122]) ).
fof(f205,plain,
aElementOf0(sK17,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f122]) ).
fof(f215,plain,
! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK22))
| ~ aElementOf0(X3,xI)
| sz00 = X3
| ~ sP2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f217,plain,
( sz00 != sK22
| ~ sP2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f218,plain,
( aElementOf0(sK22,xI)
| ~ sP2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f222,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| sP2
| sz00 = X0 ),
inference(cnf_transformation,[],[f104]) ).
fof(f224,plain,
! [X0] :
( sz00 != sK25(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f225,plain,
! [X0] :
( aElementOf0(sK25(X0),xI)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f229,plain,
! [X0] :
( iLess0(sbrdtbr0(sK25(X0)),sbrdtbr0(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f230,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0
| sP3(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f312,plain,
( ~ sP2
| sz00 = sK22
| sP3(sK22) ),
inference(resolution,[],[f218,f230]) ).
fof(f313,plain,
( sP3(sK22)
| ~ sP2 ),
inference(forward_subsumption_resolution,[],[f312,f217]) ).
fof(f344,plain,
aElementOf0(sK17,xI),
inference(forward_demodulation,[],[f205,f177]) ).
fof(f356,plain,
( sP2
| sz00 = sK17 ),
inference(resolution,[],[f222,f344]) ).
fof(f357,plain,
sP2,
inference(forward_subsumption_resolution,[],[f356,f204]) ).
fof(f1029,plain,
! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK22))
| ~ aElementOf0(X3,xI)
| sz00 = X3 ),
inference(forward_subsumption_resolution,[],[f215,f222]) ).
fof(f1042,plain,
( ~ aElementOf0(sK25(sK22),xI)
| sz00 = sK25(sK22)
| ~ sP3(sK22) ),
inference(resolution,[],[f1029,f229]) ).
fof(f1043,plain,
( sz00 = sK25(sK22)
| ~ sP3(sK22) ),
inference(forward_subsumption_resolution,[],[f1042,f225]) ).
fof(f1044,plain,
~ sP3(sK22),
inference(forward_subsumption_resolution,[],[f1043,f224]) ).
fof(f2876,plain,
~ sP2,
inference(resolution,[],[f1044,f313]) ).
fof(f2877,plain,
$false,
inference(forward_subsumption_resolution,[],[f2876,f357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG112+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 23:19:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.89/1.33 % (288365)Detected formulas, will run a generic FOF schedule.
% 2.89/1.33 % (288370)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=3633758183:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.89/1.33 % (288371)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=1810352029:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.89/1.33 % (288376)dis-21_1_sil=8000:lcm=predicate:random_seed=2071114651: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)
% 2.89/1.33 % (288374)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2730505972:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.89/1.33 % (288373)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=286765814:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.89/1.33 % (288372)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=693406873:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.89/1.33 % (288375)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=879379916:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.89/1.33 % (288374)First to succeed.
% 2.89/1.33 % (288374)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-288365"
% 2.89/1.33 % (288376)Instruction limit reached!
% 2.89/1.33 % (288376)------------------------------
% 2.89/1.33 % (288376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.33 % (288376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.33 % (288376)CaDiCaL version: 2.1.3
% 2.89/1.33 % (288376)Termination reason: Instruction limit
% 2.89/1.33 % (288376)Termination phase: Saturation
% 2.89/1.33 % (288376)Time elapsed: 0.061 s
% 2.89/1.33 % (288376)Peak memory usage: 90 MB
% 2.89/1.33 % (288376)Instructions burned: 129 (million)
% 2.89/1.33 % (288373)Instruction limit reached!
% 2.89/1.33 % (288373)------------------------------
% 2.89/1.33 % (288373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.33 % (288373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.33 % (288373)CaDiCaL version: 2.1.3
% 2.89/1.33 % (288373)Termination reason: Instruction limit
% 2.89/1.33 % (288373)Termination phase: Saturation
% 2.89/1.33 % (288373)Time elapsed: 0.067 s
% 2.89/1.33 % (288373)Peak memory usage: 90 MB
% 2.89/1.33 % (288373)Instructions burned: 110 (million)
% 2.89/1.33 % (288375)Instruction limit reached!
% 2.89/1.33 % (288375)------------------------------
% 2.89/1.33 % (288375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.33 % (288375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.33 % (288375)CaDiCaL version: 2.1.3
% 2.89/1.33 % (288375)Termination reason: Instruction limit
% 2.89/1.33 % (288375)Termination phase: Saturation
% 2.89/1.33 % (288375)Time elapsed: 0.095 s
% 2.89/1.33 % (288375)Peak memory usage: 90 MB
% 2.89/1.33 % (288375)Instructions burned: 139 (million)
% 2.89/1.33 % (288384)lrs+10_1_sil=8000:sp=occurrence:random_seed=500466275:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.89/1.33 % (288385)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4155577803:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.89/1.33 % (288384)Also succeeded, but the first one will report.
% 2.89/1.33 % (288385)Also succeeded, but the first one will report.
% 2.89/1.33 % (288386)lrs+1011_1_sil=32000:sp=occurrence:random_seed=404376707:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.89/1.33 % (288386)Also succeeded, but the first one will report.
% 2.89/1.33 % (288374)Refutation found. Thanks to Tanya!
% 2.89/1.33 % SZS status Theorem for theBenchmark
% 2.89/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.89/1.53 % (288374)------------------------------
% 3.89/1.53 % (288374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.53 % (288374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.53 % (288374)CaDiCaL version: 2.1.3
% 3.89/1.53 % (288374)Termination reason: Refutation
% 3.89/1.53 % (288374)Time elapsed: 0.054 s
% 3.89/1.53 % (288374)Peak memory usage: 89 MB
% 3.89/1.53 % (288374)Instructions burned: 87 (million)
% 3.89/1.53 % (288374)------------------------------
% 3.89/1.53 % (288374)------------------------------
% 3.89/1.53 % (288365)Success in time 0.462 s
% 3.89/1.53 % Vampire exiting
%------------------------------------------------------------------------------