%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG118+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:35:35 PM UTC 2026
% Result : Theorem 3.21s 1.06s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 13 unt; 0 def)
% Number of atoms : 381 ( 120 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 482 ( 170 ~; 158 |; 132 &)
% ( 9 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-2 aty)
% Number of variables : 150 ( 108 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f32,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1)
& X1 != sz00 )
=> ? [X2,X3] :
( aElement0(X2)
& aElement0(X3)
& X0 = sdtpldt0(sdtasdt0(X2,X1),X3)
& ( X3 != sz00
=> iLess0(sbrdtbr0(X3),sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivision) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
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/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(f45,axiom,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ( ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
| aElementOf0(X0,xI) )
& X0 != sz00 )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(f50,conjecture,
? [X0,X1] :
( aElement0(X0)
& aElement0(X1)
& xb = sdtpldt0(sdtasdt0(X0,xu),X1)
& ( X1 = sz00
| iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f51,negated_conjecture,
~ ? [X0,X1] :
( aElement0(X0)
& aElement0(X1)
& xb = sdtpldt0(sdtasdt0(X0,xu),X1)
& ( X1 = sz00
| iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f53,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(f56,plain,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X2] :
( ( ( ? [X3,X4] :
( aElementOf0(X3,slsdtgt0(xa))
& aElementOf0(X4,slsdtgt0(xb))
& sdtpldt0(X3,X4) = X2 )
| aElementOf0(X2,xI) )
& sz00 != X2 )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ) ),
inference(rectify,[],[f45]) ).
fof(f65,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,[],[f53]) ).
fof(f66,plain,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu))
| ( ! [X3,X4] :
( ~ aElementOf0(X3,slsdtgt0(xa))
| ~ aElementOf0(X4,slsdtgt0(xb))
| sdtpldt0(X3,X4) != X2 )
& ~ aElementOf0(X2,xI) )
| sz00 = X2 ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f67,plain,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu))
| ( ! [X3,X4] :
( ~ aElementOf0(X3,slsdtgt0(xa))
| ~ aElementOf0(X4,slsdtgt0(xb))
| sdtpldt0(X3,X4) != X2 )
& ~ aElementOf0(X2,xI) )
| sz00 = X2 ) ),
inference(flattening,[],[f66]) ).
fof(f70,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| ( sz00 != X1
& ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f77,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f78,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f77]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f104,plain,
! [X0,X1] :
( ? [X2,X3] :
( aElement0(X2)
& aElement0(X3)
& X0 = sdtpldt0(sdtasdt0(X2,X1),X3)
& ( iLess0(sbrdtbr0(X3),sbrdtbr0(X1))
| sz00 = X3 ) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| sz00 = X1 ),
inference(ennf_transformation,[],[f32]) ).
fof(f105,plain,
! [X0,X1] :
( ? [X2,X3] :
( aElement0(X2)
& aElement0(X3)
& X0 = sdtpldt0(sdtasdt0(X2,X1),X3)
& ( iLess0(sbrdtbr0(X3),sbrdtbr0(X1))
| sz00 = X3 ) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| sz00 = X1 ),
inference(flattening,[],[f104]) ).
fof(f120,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,[],[f65]) ).
fof(f121,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,[],[f120]) ).
fof(f122,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(sK8(X3))
& sdtasdt0(xa,sK8(X3)) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xb))
| ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(xb,X7) != X6 ) )
& ( ( aElement0(sK9(X6))
& sdtasdt0(xb,sK9(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(sK10(X9),slsdtgt0(xa))
& aElementOf0(sK11(X9),slsdtgt0(xb))
& sdtpldt0(sK10(X9),sK11(X9)) = X9 )
| ~ aElementOf0(X9,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X5,sK8(X3)),skolemize(X8,sK9(X6)),skolemize(X12,sK10(X9)),skolemize(X13,sK11(X9))],[f121]) ).
fof(f127,plain,
( aElementOf0(sK21,slsdtgt0(xa))
& aElementOf0(sK22,slsdtgt0(xb))
& xu = sdtpldt0(sK21,sK22)
& aElementOf0(xu,xI)
& xu != sz00
& ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu))
| ( ! [X3,X4] :
( ~ aElementOf0(X3,slsdtgt0(xa))
| ~ aElementOf0(X4,slsdtgt0(xb))
| sdtpldt0(X3,X4) != X2 )
& ~ aElementOf0(X2,xI) )
| sz00 = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X0,sK21),skolemize(X1,sK22)],[f67]) ).
fof(f156,plain,
! [X0,X1] :
( ( aElement0(sK41(X0,X1))
& aElement0(sK42(X0,X1))
& sdtpldt0(sdtasdt0(sK41(X0,X1),X1),sK42(X0,X1)) = X0
& ( iLess0(sbrdtbr0(sK42(X0,X1)),sbrdtbr0(X1))
| sz00 = sK42(X0,X1) ) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| sz00 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41,sK42]),skolemize(X2,sK41(X0,X1)),skolemize(X3,sK42(X0,X1))],[f105]) ).
fof(f157,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f194,plain,
aSet0(xI),
inference(cnf_transformation,[],[f122]) ).
fof(f220,plain,
sz00 != xu,
inference(cnf_transformation,[],[f127]) ).
fof(f221,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f127]) ).
fof(f239,plain,
! [X0,X1] :
( xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f240,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| sz00 != X1 ),
inference(cnf_transformation,[],[f70]) ).
fof(f246,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f248,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f266,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f301,plain,
! [X0,X1] :
( iLess0(sbrdtbr0(sK42(X0,X1)),sbrdtbr0(X1))
| sz00 = sK42(X0,X1)
| ~ aElement0(X0)
| ~ aElement0(X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f156]) ).
fof(f302,plain,
! [X0,X1] :
( sdtpldt0(sdtasdt0(sK41(X0,X1),X1),sK42(X0,X1)) = X0
| ~ aElement0(X0)
| ~ aElement0(X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f156]) ).
fof(f303,plain,
! [X0,X1] :
( aElement0(sK42(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f156]) ).
fof(f304,plain,
! [X0,X1] :
( aElement0(sK41(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f156]) ).
fof(f311,plain,
! [X0] :
( xb != sdtpldt0(sdtasdt0(X0,xu),sz00)
| ~ aElement0(sz00)
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f240]) ).
fof(f374,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(resolution,[],[f266,f221]) ).
fof(f381,plain,
aElement0(xu),
inference(forward_subsumption_resolution,[],[f374,f194]) ).
fof(f683,plain,
! [X0] :
( xb != sdtpldt0(sdtasdt0(xu,X0),sz00)
| ~ aElement0(sz00)
| ~ aElement0(X0)
| ~ aElement0(xu)
| ~ aElement0(X0) ),
inference(superposition,[],[f311,f248]) ).
fof(f701,plain,
! [X0] :
( xb != sdtpldt0(sdtasdt0(xu,X0),sz00)
| ~ aElement0(sz00)
| ~ aElement0(X0)
| ~ aElement0(xu) ),
inference(duplicate_literal_removal,[],[f683]) ).
fof(f739,plain,
! [X0] :
( xb != sdtpldt0(sdtasdt0(xu,X0),sz00)
| ~ aElement0(X0)
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[],[f701,f246]) ).
fof(f778,plain,
! [X0] :
( xb != sdtpldt0(sdtasdt0(xu,X0),sz00)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f739,f381]) ).
fof(f807,plain,
! [X0] :
( xb != sdtpldt0(sdtasdt0(X0,xu),sz00)
| ~ aElement0(X0)
| ~ aElement0(xu)
| ~ aElement0(X0) ),
inference(superposition,[],[f778,f248]) ).
fof(f809,plain,
! [X0] :
( xb != sdtpldt0(sdtasdt0(X0,xu),sz00)
| ~ aElement0(X0)
| ~ aElement0(xu) ),
inference(duplicate_literal_removal,[],[f807]) ).
fof(f811,plain,
! [X0] :
( xb != sdtpldt0(sdtasdt0(X0,xu),sz00)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f809,f381]) ).
fof(f1575,plain,
! [X0] :
( xb != X0
| ~ aElement0(sK42(X0,xu))
| ~ aElement0(sK41(X0,xu))
| ~ iLess0(sbrdtbr0(sK42(X0,xu)),sbrdtbr0(xu))
| ~ aElement0(X0)
| ~ aElement0(xu)
| sz00 = xu ),
inference(superposition,[],[f239,f302]) ).
fof(f1589,plain,
! [X0] :
( xb != X0
| ~ aElement0(sK41(X0,xu))
| ~ iLess0(sbrdtbr0(sK42(X0,xu)),sbrdtbr0(xu))
| ~ aElement0(X0)
| ~ aElement0(xu)
| sz00 = xu ),
inference(forward_subsumption_resolution,[],[f1575,f303]) ).
fof(f1594,plain,
! [X0] :
( xb != X0
| ~ iLess0(sbrdtbr0(sK42(X0,xu)),sbrdtbr0(xu))
| ~ aElement0(X0)
| ~ aElement0(xu)
| sz00 = xu ),
inference(forward_subsumption_resolution,[],[f1589,f304]) ).
fof(f1595,plain,
! [X0] :
( xb != X0
| ~ iLess0(sbrdtbr0(sK42(X0,xu)),sbrdtbr0(xu))
| ~ aElement0(X0)
| sz00 = xu ),
inference(forward_subsumption_resolution,[],[f1594,f381]) ).
fof(f1596,plain,
! [X0] :
( xb != X0
| ~ iLess0(sbrdtbr0(sK42(X0,xu)),sbrdtbr0(xu))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f1595,f220]) ).
fof(f1898,plain,
( ~ iLess0(sbrdtbr0(sK42(xb,xu)),sbrdtbr0(xu))
| ~ aElement0(xb) ),
inference(equality_resolution,[],[f1596]) ).
fof(f1899,plain,
~ iLess0(sbrdtbr0(sK42(xb,xu)),sbrdtbr0(xu)),
inference(forward_subsumption_resolution,[],[f1898,f157]) ).
fof(f1900,plain,
( sz00 = sK42(xb,xu)
| ~ aElement0(xb)
| ~ aElement0(xu)
| sz00 = xu ),
inference(resolution,[],[f1899,f301]) ).
fof(f1901,plain,
( sz00 = sK42(xb,xu)
| ~ aElement0(xu)
| sz00 = xu ),
inference(forward_subsumption_resolution,[],[f1900,f157]) ).
fof(f1902,plain,
( sz00 = sK42(xb,xu)
| sz00 = xu ),
inference(forward_subsumption_resolution,[],[f1901,f381]) ).
fof(f1903,plain,
sz00 = sK42(xb,xu),
inference(forward_subsumption_resolution,[],[f1902,f220]) ).
fof(f1934,plain,
( xb = sdtpldt0(sdtasdt0(sK41(xb,xu),xu),sz00)
| ~ aElement0(xb)
| ~ aElement0(xu)
| sz00 = xu ),
inference(superposition,[],[f302,f1903]) ).
fof(f1936,plain,
( xb = sdtpldt0(sdtasdt0(sK41(xb,xu),xu),sz00)
| ~ aElement0(xu)
| sz00 = xu ),
inference(forward_subsumption_resolution,[],[f1934,f157]) ).
fof(f1937,plain,
( xb = sdtpldt0(sdtasdt0(sK41(xb,xu),xu),sz00)
| sz00 = xu ),
inference(forward_subsumption_resolution,[],[f1936,f381]) ).
fof(f1938,plain,
xb = sdtpldt0(sdtasdt0(sK41(xb,xu),xu),sz00),
inference(forward_subsumption_resolution,[],[f1937,f220]) ).
fof(f1950,plain,
( xb != xb
| ~ aElement0(sK41(xb,xu)) ),
inference(superposition,[],[f811,f1938]) ).
fof(f1973,plain,
~ aElement0(sK41(xb,xu)),
inference(trivial_inequality_removal,[],[f1950]) ).
fof(f1991,plain,
( ~ aElement0(xb)
| ~ aElement0(xu)
| sz00 = xu ),
inference(resolution,[],[f1973,f304]) ).
fof(f1992,plain,
( ~ aElement0(xu)
| sz00 = xu ),
inference(forward_subsumption_resolution,[],[f1991,f157]) ).
fof(f1993,plain,
sz00 = xu,
inference(forward_subsumption_resolution,[],[f1992,f381]) ).
fof(f1994,plain,
$false,
inference(forward_subsumption_resolution,[],[f1993,f220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG118+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n002.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 23:24:21 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.21/1.06 % (4004385)Detected formulas, will run a generic FOF schedule.
% 3.21/1.06 % (4004395)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3665312768:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.21/1.06 % (4004391)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=2935075159:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.21/1.06 % (4004393)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1330836883:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.21/1.06 % (4004390)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=2772226253:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.21/1.06 % (4004394)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=249918267:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.21/1.06 % (4004392)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=4116953939:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.21/1.06 % (4004396)dis-21_1_sil=8000:lcm=predicate:random_seed=3297824225: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)
% 3.21/1.06 % (4004394)First to succeed.
% 3.21/1.06 % (4004394)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4004385"
% 3.21/1.06 % (4004396)Instruction limit reached!
% 3.21/1.06 % (4004396)------------------------------
% 3.21/1.06 % (4004396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.06 % (4004396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.06 % (4004396)CaDiCaL version: 2.1.3
% 3.21/1.06 % (4004396)Termination reason: Instruction limit
% 3.21/1.06 % (4004396)Termination phase: Saturation
% 3.21/1.06 % (4004396)Time elapsed: 0.060 s
% 3.21/1.06 % (4004396)Peak memory usage: 90 MB
% 3.21/1.06 % (4004396)Instructions burned: 131 (million)
% 3.21/1.06 % (4004393)Instruction limit reached!
% 3.21/1.06 % (4004393)------------------------------
% 3.21/1.06 % (4004393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.06 % (4004393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.06 % (4004393)CaDiCaL version: 2.1.3
% 3.21/1.06 % (4004393)Termination reason: Instruction limit
% 3.21/1.06 % (4004393)Termination phase: Saturation
% 3.21/1.06 % (4004393)Time elapsed: 0.068 s
% 3.21/1.06 % (4004393)Peak memory usage: 89 MB
% 3.21/1.06 % (4004393)Instructions burned: 109 (million)
% 3.21/1.06 % (4004395)Instruction limit reached!
% 3.21/1.06 % (4004395)------------------------------
% 3.21/1.06 % (4004395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.06 % (4004395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.06 % (4004395)CaDiCaL version: 2.1.3
% 3.21/1.06 % (4004395)Termination reason: Instruction limit
% 3.21/1.06 % (4004395)Termination phase: Saturation
% 3.21/1.06 % (4004395)Time elapsed: 0.095 s
% 3.21/1.06 % (4004395)Peak memory usage: 90 MB
% 3.21/1.06 % (4004395)Instructions burned: 140 (million)
% 3.21/1.06 % (4004404)lrs+10_1_sil=8000:sp=occurrence:random_seed=260218378:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.21/1.06 % (4004405)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1182406404:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.21/1.06 % (4004406)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1805540969:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.21/1.06 % (4004394)Refutation found. Thanks to Tanya!
% 3.21/1.06 % SZS status Theorem for theBenchmark
% 3.21/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.19 % (4004394)------------------------------
% 3.55/1.19 % (4004394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.19 % (4004394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.19 % (4004394)CaDiCaL version: 2.1.3
% 3.55/1.19 % (4004394)Termination reason: Refutation
% 3.55/1.19 % (4004394)Time elapsed: 0.035 s
% 3.55/1.19 % (4004394)Peak memory usage: 89 MB
% 3.55/1.19 % (4004394)Instructions burned: 55 (million)
% 3.55/1.19 % (4004394)------------------------------
% 3.55/1.19 % (4004394)------------------------------
% 3.55/1.19 % (4004385)Success in time 0.457 s
% 3.55/1.19 % Vampire exiting
%------------------------------------------------------------------------------