%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG126+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 : n013.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 12:35:37 PM UTC 2026
% Result : Theorem 2.27s 1.19s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 10 unt; 0 def)
% Number of atoms : 408 ( 94 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 509 ( 169 ~; 146 |; 158 &)
% ( 19 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 194 ( 141 !; 53 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(f47,axiom,
? [X0] :
( aElement0(X0)
& sdtasdt0(xu,X0) = xc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2744) ).
fof(f48,conjecture,
( ! [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,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xc )
| aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ( ! [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,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xc )
| aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f51,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(f54,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(f56,plain,
~ ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = X0 ) )
=> ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xb,X3) = X2 ) )
=> ( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = xc )
| aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(rectify,[],[f49]) ).
fof(f66,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,[],[f51]) ).
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(ennf_transformation,[],[f54]) ).
fof(f68,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,[],[f67]) ).
fof(f69,plain,
( ! [X4,X5] :
( ~ aElementOf0(X4,slsdtgt0(xa))
| ~ aElementOf0(X5,slsdtgt0(xb))
| sdtpldt0(X4,X5) != xc )
& ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xb,X3) = X2 ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = X0 ) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f70,plain,
( ! [X4,X5] :
( ~ aElementOf0(X4,slsdtgt0(xa))
| ~ aElementOf0(X5,slsdtgt0(xb))
| sdtpldt0(X4,X5) != xc )
& ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xb,X3) = X2 ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = X0 ) ) ),
inference(flattening,[],[f69]) ).
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(f79,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f80,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f79]) ).
fof(f95,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f96,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f95]) ).
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 ) )
& ( ? [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,[],[f66]) ).
fof(f119,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,[],[f118]) ).
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 ) )
& ( ( aElement0(sK7(X3))
& sdtasdt0(xa,sK7(X3)) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xb))
| ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(xb,X7) != X6 ) )
& ( ( aElement0(sK8(X6))
& sdtasdt0(xb,sK8(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(sK9(X9),slsdtgt0(xa))
& aElementOf0(sK10(X9),slsdtgt0(xb))
& sdtpldt0(sK9(X9),sK10(X9)) = X9 )
| ~ aElementOf0(X9,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X5,sK7(X3)),skolemize(X8,sK8(X6)),skolemize(X12,sK9(X9)),skolemize(X13,sK10(X9))],[f119]) ).
fof(f125,plain,
( aElementOf0(sK20,slsdtgt0(xa))
& aElementOf0(sK21,slsdtgt0(xb))
& xu = sdtpldt0(sK20,sK21)
& 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,[sK20,sK21]),skolemize(X0,sK20),skolemize(X1,sK21)],[f68]) ).
fof(f127,plain,
( aElement0(sK24)
& xc = sdtasdt0(xu,sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(X0,sK24)],[f47]) ).
fof(f128,plain,
( ! [X4,X5] :
( ~ aElementOf0(X4,slsdtgt0(xa))
| ~ aElementOf0(X5,slsdtgt0(xb))
| sdtpldt0(X4,X5) != xc )
& ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X2] :
( ( aElementOf0(X2,slsdtgt0(xb))
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(xb,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(xb,X3) = X2 )
| ~ aElementOf0(X2,slsdtgt0(xb)) ) )
& ! [X0] :
( ( aElementOf0(X0,slsdtgt0(xa))
| ! [X1] :
( ~ aElement0(X1)
| sdtasdt0(xa,X1) != X0 ) )
& ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = X0 )
| ~ aElementOf0(X0,slsdtgt0(xa)) ) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f129,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) != xc )
& ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X2] :
( ( aElementOf0(X2,slsdtgt0(xb))
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(xb,X3) != X2 ) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(xb,X4) = X2 )
| ~ aElementOf0(X2,slsdtgt0(xb)) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xa))
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(xa,X6) != X5 ) )
& ( ? [X7] :
( aElement0(X7)
& sdtasdt0(xa,X7) = X5 )
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) != xc )
& ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X2] :
( ( aElementOf0(X2,slsdtgt0(xb))
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(xb,X3) != X2 ) )
& ( ( aElement0(sK25(X2))
& sdtasdt0(xb,sK25(X2)) = X2 )
| ~ aElementOf0(X2,slsdtgt0(xb)) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xa))
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(xa,X6) != X5 ) )
& ( ( aElement0(sK26(X5))
& sdtasdt0(xa,sK26(X5)) = X5 )
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26]),skolemize(X4,sK25(X2)),skolemize(X7,sK26(X5))],[f129]) ).
fof(f156,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f157,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f179,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f120]) ).
fof(f180,plain,
! [X9] :
( sdtpldt0(sK9(X9),sK10(X9)) = X9
| ~ aElementOf0(X9,xI) ),
inference(cnf_transformation,[],[f120]) ).
fof(f181,plain,
! [X9] :
( aElementOf0(sK10(X9),slsdtgt0(xb))
| ~ aElementOf0(X9,xI) ),
inference(cnf_transformation,[],[f120]) ).
fof(f182,plain,
! [X9] :
( aElementOf0(sK9(X9),slsdtgt0(xa))
| ~ aElementOf0(X9,xI) ),
inference(cnf_transformation,[],[f120]) ).
fof(f191,plain,
! [X2,X0] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f120]) ).
fof(f220,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f125]) ).
fof(f232,plain,
xc = sdtasdt0(xu,sK24),
inference(cnf_transformation,[],[f127]) ).
fof(f233,plain,
aElement0(sK24),
inference(cnf_transformation,[],[f127]) ).
fof(f234,plain,
! [X5] :
( sdtasdt0(xa,sK26(X5)) = X5
| ~ aElementOf0(X5,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f235,plain,
! [X5] :
( ~ aElementOf0(X5,slsdtgt0(xa))
| aElement0(sK26(X5)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f237,plain,
! [X2] :
( sdtasdt0(xb,sK25(X2)) = X2
| ~ aElementOf0(X2,slsdtgt0(xb)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f238,plain,
! [X2] :
( ~ aElementOf0(X2,slsdtgt0(xb))
| aElement0(sK25(X2)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f240,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f130]) ).
fof(f249,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f250,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f272,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f356,plain,
~ aElementOf0(xc,xI),
inference(superposition,[],[f240,f179]) ).
fof(f456,plain,
! [X0] :
( aElement0(X0)
| ~ aElement0(xa)
| ~ aElement0(sK26(X0))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(superposition,[],[f250,f234]) ).
fof(f459,plain,
! [X0] :
( aElement0(X0)
| ~ aElement0(xb)
| ~ aElement0(sK25(X0))
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(superposition,[],[f250,f237]) ).
fof(f469,plain,
! [X0] :
( aElement0(X0)
| ~ aElement0(xb)
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(forward_subsumption_resolution,[],[f459,f238]) ).
fof(f470,plain,
! [X0] :
( aElement0(X0)
| ~ aElement0(xa)
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(forward_subsumption_resolution,[],[f456,f235]) ).
fof(f471,plain,
! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xb))
| aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f469,f156]) ).
fof(f472,plain,
! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f470,f157]) ).
fof(f476,plain,
! [X0] :
( aElement0(sK10(X0))
| ~ aElementOf0(X0,xI) ),
inference(resolution,[],[f471,f181]) ).
fof(f490,plain,
! [X0] :
( aElement0(sK9(X0))
| ~ aElementOf0(X0,xI) ),
inference(resolution,[],[f472,f182]) ).
fof(f568,plain,
! [X0] :
( aElement0(X0)
| ~ aElement0(sK9(X0))
| ~ aElement0(sK10(X0))
| ~ aElementOf0(X0,xI) ),
inference(superposition,[],[f272,f180]) ).
fof(f571,plain,
! [X0] :
( aElement0(X0)
| ~ aElement0(sK10(X0))
| ~ aElementOf0(X0,xI) ),
inference(forward_subsumption_resolution,[],[f568,f490]) ).
fof(f573,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f571,f476]) ).
fof(f846,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X0,X1),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(superposition,[],[f191,f249]) ).
fof(f864,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X0,X1),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI)
| ~ aElement0(X0) ),
inference(duplicate_literal_removal,[],[f846]) ).
fof(f913,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X0,X1),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI) ),
inference(forward_subsumption_resolution,[],[f864,f573]) ).
fof(f2853,plain,
( aElementOf0(xc,xI)
| ~ aElement0(sK24)
| ~ aElementOf0(xu,xI) ),
inference(superposition,[],[f913,f232]) ).
fof(f2860,plain,
( ~ aElement0(sK24)
| ~ aElementOf0(xu,xI) ),
inference(forward_subsumption_resolution,[],[f2853,f356]) ).
fof(f2866,plain,
~ aElementOf0(xu,xI),
inference(forward_subsumption_resolution,[],[f2860,f233]) ).
fof(f2868,plain,
$false,
inference(forward_subsumption_resolution,[],[f2866,f220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG126+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 23:22:36 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.27/1.19 % (658376)Detected formulas, will run a generic FOF schedule.
% 2.27/1.19 % (658385)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3440259144:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.27/1.19 % (658385)First to succeed.
% 2.27/1.19 % (658385)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-658376"
% 2.27/1.19 % (658384)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1704512090:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.27/1.19 % (658387)dis-21_1_sil=8000:lcm=predicate:random_seed=679242316: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)
% 2.27/1.19 % (658381)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=543326423:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.27/1.19 % (658382)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=3298549405:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.27/1.19 % (658383)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=2186130177:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.27/1.19 % (658386)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3318858009:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.27/1.19 % (658387)Instruction limit reached!
% 2.27/1.19 % (658387)------------------------------
% 2.27/1.19 % (658387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.27/1.19 % (658387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/1.19 % (658387)CaDiCaL version: 2.1.3
% 2.27/1.19 % (658387)Termination reason: Instruction limit
% 2.27/1.19 % (658387)Termination phase: Saturation
% 2.27/1.19 % (658387)Time elapsed: 0.062 s
% 2.27/1.19 % (658387)Peak memory usage: 90 MB
% 2.27/1.19 % (658387)Instructions burned: 130 (million)
% 2.27/1.19 % (658384)Instruction limit reached!
% 2.27/1.19 % (658384)------------------------------
% 2.27/1.19 % (658384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.27/1.19 % (658384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/1.19 % (658384)CaDiCaL version: 2.1.3
% 2.27/1.19 % (658384)Termination reason: Instruction limit
% 2.27/1.19 % (658384)Termination phase: Saturation
% 2.27/1.19 % (658384)Time elapsed: 0.068 s
% 2.27/1.19 % (658384)Peak memory usage: 89 MB
% 2.27/1.19 % (658384)Instructions burned: 109 (million)
% 2.27/1.19 % (658386)Also succeeded, but the first one will report.
% 2.27/1.19 % (658385)Refutation found. Thanks to Tanya!
% 2.27/1.19 % SZS status Theorem for theBenchmark
% 2.27/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.86/1.39 % (658385)------------------------------
% 2.86/1.39 % (658385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.39 % (658385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.39 % (658385)CaDiCaL version: 2.1.3
% 2.86/1.39 % (658385)Termination reason: Refutation
% 2.86/1.39 % (658385)Time elapsed: 0.026 s
% 2.86/1.39 % (658385)Peak memory usage: 89 MB
% 2.86/1.39 % (658385)Instructions burned: 77 (million)
% 2.86/1.39 % (658385)------------------------------
% 2.86/1.39 % (658385)------------------------------
% 2.86/1.39 % (658376)Success in time 0.326 s
% 2.86/1.39 % Vampire exiting
%------------------------------------------------------------------------------