%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG111+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 : n010.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 12:35:33 PM UTC 2026
% Result : Theorem 3.06s 1.06s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 97 ( 16 unt; 13 def)
% Number of atoms : 478 ( 109 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 607 ( 226 ~; 177 |; 175 &)
% ( 11 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 166 ( 0 sgn 82 !; 84 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45,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))
=> ? [X2] :
( ? [X3,X4] :
( aElementOf0(X3,slsdtgt0(xa))
& aElementOf0(X4,slsdtgt0(xb))
& sdtpldt0(X3,X4) = X2 )
& aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( ( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
| aElementOf0(X3,xI) )
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) )
=> ? [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__) ).
fof(f46,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))
=> ? [X2] :
( ? [X3,X4] :
( aElementOf0(X3,slsdtgt0(xa))
& aElementOf0(X4,slsdtgt0(xb))
& sdtpldt0(X3,X4) = X2 )
& aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( ( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
| aElementOf0(X3,xI) )
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) )
=> ? [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)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f58,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))
=> ? [X6] :
( ? [X7,X8] :
( aElementOf0(X7,slsdtgt0(xa))
& aElementOf0(X8,slsdtgt0(xb))
& sdtpldt0(X7,X8) = X6 )
& aElementOf0(X6,xI)
& sz00 != X6
& ! [X9] :
( ( ( ? [X10,X11] :
( aElementOf0(X10,slsdtgt0(xa))
& aElementOf0(X11,slsdtgt0(xb))
& sdtpldt0(X10,X11) = X9 )
| aElementOf0(X9,xI) )
& sz00 != X9 )
=> ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6)) ) ) ) )
=> ? [X12] :
( ( ? [X13,X14] :
( aElementOf0(X13,slsdtgt0(xa))
& aElementOf0(X14,slsdtgt0(xb))
& sdtpldt0(X13,X14) = X12 )
| aElementOf0(X12,xI) )
& sz00 != X12
& ! [X15] :
( ( ? [X16,X17] :
( aElementOf0(X16,slsdtgt0(xa))
& aElementOf0(X17,slsdtgt0(xb))
& sdtpldt0(X16,X17) = X15 )
& aElementOf0(X15,xI)
& sz00 != X15 )
=> ~ iLess0(sbrdtbr0(X15),sbrdtbr0(X12)) ) ) ) ),
inference(rectify,[],[f46]) ).
fof(f112,plain,
? [X0] :
( ! [X12] :
( ( ! [X13,X14] :
( ~ aElementOf0(X13,slsdtgt0(xa))
| ~ aElementOf0(X14,slsdtgt0(xb))
| sdtpldt0(X13,X14) != X12 )
& ~ aElementOf0(X12,xI) )
| sz00 = X12
| ? [X15] :
( iLess0(sbrdtbr0(X15),sbrdtbr0(X12))
& ? [X16,X17] :
( aElementOf0(X16,slsdtgt0(xa))
& aElementOf0(X17,slsdtgt0(xb))
& sdtpldt0(X16,X17) = X15 )
& aElementOf0(X15,xI)
& sz00 != X15 ) )
& ! [X3] :
( ? [X6] :
( ? [X7,X8] :
( aElementOf0(X7,slsdtgt0(xa))
& aElementOf0(X8,slsdtgt0(xb))
& sdtpldt0(X7,X8) = X6 )
& aElementOf0(X6,xI)
& sz00 != X6
& ! [X9] :
( ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6))
| ( ! [X10,X11] :
( ~ aElementOf0(X10,slsdtgt0(xa))
| ~ aElementOf0(X11,slsdtgt0(xb))
| sdtpldt0(X10,X11) != X9 )
& ~ aElementOf0(X9,xI) )
| sz00 = X9 ) )
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
| ( ! [X4,X5] :
( ~ aElementOf0(X4,slsdtgt0(xa))
| ~ aElementOf0(X5,slsdtgt0(xb))
| sdtpldt0(X4,X5) != X3 )
& ~ aElementOf0(X3,xI) )
| sz00 = X3 )
& ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(ennf_transformation,[],[f58]) ).
fof(f113,plain,
? [X0] :
( ! [X12] :
( ( ! [X13,X14] :
( ~ aElementOf0(X13,slsdtgt0(xa))
| ~ aElementOf0(X14,slsdtgt0(xb))
| sdtpldt0(X13,X14) != X12 )
& ~ aElementOf0(X12,xI) )
| sz00 = X12
| ? [X15] :
( iLess0(sbrdtbr0(X15),sbrdtbr0(X12))
& ? [X16,X17] :
( aElementOf0(X16,slsdtgt0(xa))
& aElementOf0(X17,slsdtgt0(xb))
& sdtpldt0(X16,X17) = X15 )
& aElementOf0(X15,xI)
& sz00 != X15 ) )
& ! [X3] :
( ? [X6] :
( ? [X7,X8] :
( aElementOf0(X7,slsdtgt0(xa))
& aElementOf0(X8,slsdtgt0(xb))
& sdtpldt0(X7,X8) = X6 )
& aElementOf0(X6,xI)
& sz00 != X6
& ! [X9] :
( ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6))
| ( ! [X10,X11] :
( ~ aElementOf0(X10,slsdtgt0(xa))
| ~ aElementOf0(X11,slsdtgt0(xb))
| sdtpldt0(X10,X11) != X9 )
& ~ aElementOf0(X9,xI) )
| sz00 = X9 ) )
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
| ( ! [X4,X5] :
( ~ aElementOf0(X4,slsdtgt0(xa))
| ~ aElementOf0(X5,slsdtgt0(xb))
| sdtpldt0(X4,X5) != X3 )
& ~ aElementOf0(X3,xI) )
| sz00 = X3 )
& ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(flattening,[],[f112]) ).
fof(f120,definition,
( ? [X6] :
( ? [X7,X8] :
( aElementOf0(X7,slsdtgt0(xa))
& aElementOf0(X8,slsdtgt0(xb))
& sdtpldt0(X7,X8) = X6 )
& aElementOf0(X6,xI)
& sz00 != X6
& ! [X9] :
( ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6))
| ( ! [X10,X11] :
( ~ aElementOf0(X10,slsdtgt0(xa))
| ~ aElementOf0(X11,slsdtgt0(xb))
| sdtpldt0(X10,X11) != X9 )
& ~ aElementOf0(X9,xI) )
| sz00 = X9 ) )
| ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f121,definition,
! [X12] :
( ? [X15] :
( iLess0(sbrdtbr0(X15),sbrdtbr0(X12))
& ? [X16,X17] :
( aElementOf0(X16,slsdtgt0(xa))
& aElementOf0(X17,slsdtgt0(xb))
& sdtpldt0(X16,X17) = X15 )
& aElementOf0(X15,xI)
& sz00 != X15 )
| ~ sP5(X12) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f122,plain,
? [X0] :
( ! [X12] :
( ( ! [X13,X14] :
( ~ aElementOf0(X13,slsdtgt0(xa))
| ~ aElementOf0(X14,slsdtgt0(xb))
| sdtpldt0(X13,X14) != X12 )
& ~ aElementOf0(X12,xI) )
| sz00 = X12
| sP5(X12) )
& ! [X3] :
( sP4
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
| ( ! [X4,X5] :
( ~ aElementOf0(X4,slsdtgt0(xa))
| ~ aElementOf0(X5,slsdtgt0(xb))
| sdtpldt0(X4,X5) != X3 )
& ~ aElementOf0(X3,xI) )
| sz00 = X3 )
& ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(definition_folding,[],[f113,f121,f120]) ).
fof(f169,plain,
! [X12] :
( ? [X15] :
( iLess0(sbrdtbr0(X15),sbrdtbr0(X12))
& ? [X16,X17] :
( aElementOf0(X16,slsdtgt0(xa))
& aElementOf0(X17,slsdtgt0(xb))
& sdtpldt0(X16,X17) = X15 )
& aElementOf0(X15,xI)
& sz00 != X15 )
| ~ sP5(X12) ),
inference(nnf_transformation,[],[f121]) ).
fof(f170,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 )
| ~ sP5(X0) ),
inference(rectify,[],[f169]) ).
fof(f171,plain,
! [X0] :
( ( iLess0(sbrdtbr0(sK42(X0)),sbrdtbr0(X0))
& aElementOf0(sK43(X0),slsdtgt0(xa))
& aElementOf0(sK44(X0),slsdtgt0(xb))
& sK42(X0) = sdtpldt0(sK43(X0),sK44(X0))
& aElementOf0(sK42(X0),xI)
& sz00 != sK42(X0) )
| ~ sP5(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42,sK43,sK44]),skolemize(X1,sK42(X0)),skolemize(X2,sK43(X0)),skolemize(X3,sK44(X0))],[f170]) ).
fof(f172,plain,
( ? [X6] :
( ? [X7,X8] :
( aElementOf0(X7,slsdtgt0(xa))
& aElementOf0(X8,slsdtgt0(xb))
& sdtpldt0(X7,X8) = X6 )
& aElementOf0(X6,xI)
& sz00 != X6
& ! [X9] :
( ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6))
| ( ! [X10,X11] :
( ~ aElementOf0(X10,slsdtgt0(xa))
| ~ aElementOf0(X11,slsdtgt0(xb))
| sdtpldt0(X10,X11) != X9 )
& ~ aElementOf0(X9,xI) )
| sz00 = X9 ) )
| ~ sP4 ),
inference(nnf_transformation,[],[f120]) ).
fof(f173,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 ) )
| ~ sP4 ),
inference(rectify,[],[f172]) ).
fof(f174,plain,
( ( aElementOf0(sK46,slsdtgt0(xa))
& aElementOf0(sK47,slsdtgt0(xb))
& sK45 = sdtpldt0(sK46,sK47)
& aElementOf0(sK45,xI)
& sz00 != sK45
& ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK45))
| ( ! [X4,X5] :
( ~ aElementOf0(X4,slsdtgt0(xa))
| ~ aElementOf0(X5,slsdtgt0(xb))
| sdtpldt0(X4,X5) != X3 )
& ~ aElementOf0(X3,xI) )
| sz00 = X3 ) )
| ~ sP4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45,sK46,sK47]),skolemize(X0,sK45),skolemize(X1,sK46),skolemize(X2,sK47)],[f173]) ).
fof(f175,plain,
? [X0] :
( ! [X1] :
( ( ! [X2,X3] :
( ~ aElementOf0(X2,slsdtgt0(xa))
| ~ aElementOf0(X3,slsdtgt0(xb))
| sdtpldt0(X2,X3) != X1 )
& ~ aElementOf0(X1,xI) )
| sz00 = X1
| sP5(X1) )
& ! [X4] :
( sP4
| ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X0))
| ( ! [X5,X6] :
( ~ aElementOf0(X5,slsdtgt0(xa))
| ~ aElementOf0(X6,slsdtgt0(xb))
| sdtpldt0(X5,X6) != X4 )
& ~ aElementOf0(X4,xI) )
| sz00 = X4 )
& ? [X7,X8] :
( aElementOf0(X7,slsdtgt0(xa))
& aElementOf0(X8,slsdtgt0(xb))
& sdtpldt0(X7,X8) = X0 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(rectify,[],[f122]) ).
fof(f176,plain,
( ! [X1] :
( ( ! [X2,X3] :
( ~ aElementOf0(X2,slsdtgt0(xa))
| ~ aElementOf0(X3,slsdtgt0(xb))
| sdtpldt0(X2,X3) != X1 )
& ~ aElementOf0(X1,xI) )
| sz00 = X1
| sP5(X1) )
& ! [X4] :
( sP4
| ~ iLess0(sbrdtbr0(X4),sbrdtbr0(sK48))
| ( ! [X5,X6] :
( ~ aElementOf0(X5,slsdtgt0(xa))
| ~ aElementOf0(X6,slsdtgt0(xb))
| sdtpldt0(X5,X6) != X4 )
& ~ aElementOf0(X4,xI) )
| sz00 = X4 )
& aElementOf0(sK49,slsdtgt0(xa))
& aElementOf0(sK50,slsdtgt0(xb))
& sK48 = sdtpldt0(sK49,sK50)
& aElementOf0(sK48,xI)
& sz00 != sK48 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48,sK49,sK50]),skolemize(X0,sK48),skolemize(X7,sK49),skolemize(X8,sK50)],[f175]) ).
fof(f329,plain,
! [X0] :
( sz00 != sK42(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f171]) ).
fof(f330,plain,
! [X0] :
( ~ sP5(X0)
| aElementOf0(sK42(X0),xI) ),
inference(cnf_transformation,[],[f171]) ).
fof(f334,plain,
! [X0] :
( iLess0(sbrdtbr0(sK42(X0)),sbrdtbr0(X0))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f171]) ).
fof(f335,plain,
! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK45))
| ~ aElementOf0(X3,xI)
| sz00 = X3
| ~ sP4 ),
inference(cnf_transformation,[],[f174]) ).
fof(f337,plain,
( sz00 != sK45
| ~ sP4 ),
inference(cnf_transformation,[],[f174]) ).
fof(f338,plain,
( aElementOf0(sK45,xI)
| ~ sP4 ),
inference(cnf_transformation,[],[f174]) ).
fof(f342,plain,
sz00 != sK48,
inference(cnf_transformation,[],[f176]) ).
fof(f343,plain,
aElementOf0(sK48,xI),
inference(cnf_transformation,[],[f176]) ).
fof(f347,plain,
! [X4] :
( sP4
| ~ iLess0(sbrdtbr0(X4),sbrdtbr0(sK48))
| ~ aElementOf0(X4,xI)
| sz00 = X4 ),
inference(cnf_transformation,[],[f176]) ).
fof(f349,plain,
! [X1] :
( ~ aElementOf0(X1,xI)
| sz00 = X1
| sP5(X1) ),
inference(cnf_transformation,[],[f176]) ).
fof(f371,definition,
! [X0,X1] :
( sQ51_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ51_eqProxy])],[equality_proxy_definition]) ).
fof(f429,plain,
! [X0] :
( ~ sQ51_eqProxy(sz00,sK42(X0))
| ~ sP5(X0) ),
inference(equality_proxy_replacement,[],[f329,f371]) ).
fof(f431,plain,
( ~ sQ51_eqProxy(sz00,sK45)
| ~ sP4 ),
inference(equality_proxy_replacement,[],[f337,f371]) ).
fof(f433,plain,
! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK45))
| ~ aElementOf0(X3,xI)
| sQ51_eqProxy(sz00,X3)
| ~ sP4 ),
inference(equality_proxy_replacement,[],[f335,f371]) ).
fof(f435,plain,
! [X1] :
( sQ51_eqProxy(sz00,X1)
| ~ aElementOf0(X1,xI)
| sP5(X1) ),
inference(equality_proxy_replacement,[],[f349,f371]) ).
fof(f437,plain,
! [X4] :
( sP4
| ~ iLess0(sbrdtbr0(X4),sbrdtbr0(sK48))
| ~ aElementOf0(X4,xI)
| sQ51_eqProxy(sz00,X4) ),
inference(equality_proxy_replacement,[],[f347,f371]) ).
fof(f439,plain,
~ sQ51_eqProxy(sz00,sK48),
inference(equality_proxy_replacement,[],[f342,f371]) ).
fof(f443,definition,
( spl52_1
<=> ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(sK48))
| sQ51_eqProxy(sz00,X4)
| ~ aElementOf0(X4,xI) ) ),
introduced(definition,[new_symbols(definition,[spl52_1])],[avatar_definition]) ).
fof(f444,plain,
( ! [X4] :
( sQ51_eqProxy(sz00,X4)
| ~ iLess0(sbrdtbr0(X4),sbrdtbr0(sK48))
| ~ aElementOf0(X4,xI) )
| ~ spl52_1 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f446,definition,
( spl52_2
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl52_2])],[avatar_definition]) ).
fof(f448,plain,
( spl52_1
| spl52_2 ),
inference(avatar_split_clause,[],[f437,f446,f443]) ).
fof(f455,definition,
( spl52_4
<=> ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK45))
| sQ51_eqProxy(sz00,X3)
| ~ aElementOf0(X3,xI) ) ),
introduced(definition,[new_symbols(definition,[spl52_4])],[avatar_definition]) ).
fof(f456,plain,
( ! [X3] :
( sQ51_eqProxy(sz00,X3)
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK45))
| ~ aElementOf0(X3,xI) )
| ~ spl52_4 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f457,plain,
( ~ spl52_2
| spl52_4 ),
inference(avatar_split_clause,[],[f433,f455,f446]) ).
fof(f463,definition,
( spl52_6
<=> sQ51_eqProxy(sz00,sK45) ),
introduced(definition,[new_symbols(definition,[spl52_6])],[avatar_definition]) ).
fof(f464,plain,
( ~ sQ51_eqProxy(sz00,sK45)
| spl52_6 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f465,plain,
( ~ spl52_2
| ~ spl52_6 ),
inference(avatar_split_clause,[],[f431,f463,f446]) ).
fof(f467,definition,
( spl52_7
<=> aElementOf0(sK45,xI) ),
introduced(definition,[new_symbols(definition,[spl52_7])],[avatar_definition]) ).
fof(f469,plain,
( ~ spl52_2
| spl52_7 ),
inference(avatar_split_clause,[],[f338,f467,f446]) ).
fof(f505,definition,
( spl52_16
<=> aElementOf0(sK48,xI) ),
introduced(definition,[new_symbols(definition,[spl52_16])],[avatar_definition]) ).
fof(f506,plain,
( ~ aElementOf0(sK48,xI)
| spl52_16 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f511,plain,
( $false
| spl52_16 ),
inference(resolution,[],[f506,f343]) ).
fof(f512,plain,
spl52_16,
inference(avatar_contradiction_clause,[],[f511]) ).
fof(f514,plain,
( ~ aElementOf0(sK45,xI)
| sP5(sK45)
| spl52_6 ),
inference(resolution,[],[f435,f464]) ).
fof(f515,plain,
( ~ aElementOf0(sK48,xI)
| sP5(sK48) ),
inference(resolution,[],[f435,f439]) ).
fof(f517,definition,
( spl52_18
<=> sP5(sK48) ),
introduced(definition,[new_symbols(definition,[spl52_18])],[avatar_definition]) ).
fof(f518,plain,
( sP5(sK48)
| ~ spl52_18 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f519,plain,
( spl52_18
| ~ spl52_16 ),
inference(avatar_split_clause,[],[f515,f505,f517]) ).
fof(f521,definition,
( spl52_19
<=> sP5(sK45) ),
introduced(definition,[new_symbols(definition,[spl52_19])],[avatar_definition]) ).
fof(f522,plain,
( sP5(sK45)
| ~ spl52_19 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f523,plain,
( spl52_19
| ~ spl52_7
| spl52_6 ),
inference(avatar_split_clause,[],[f514,f463,f467,f521]) ).
fof(f556,plain,
( aElementOf0(sK42(sK48),xI)
| ~ spl52_18 ),
inference(resolution,[],[f330,f518]) ).
fof(f557,plain,
( aElementOf0(sK42(sK45),xI)
| ~ spl52_19 ),
inference(resolution,[],[f330,f522]) ).
fof(f559,plain,
( ! [X0] :
( ~ iLess0(sbrdtbr0(sK42(X0)),sbrdtbr0(sK45))
| ~ sP5(X0)
| ~ aElementOf0(sK42(X0),xI) )
| ~ spl52_4 ),
inference(resolution,[],[f429,f456]) ).
fof(f579,definition,
( spl52_28
<=> aElementOf0(sK42(sK45),xI) ),
introduced(definition,[new_symbols(definition,[spl52_28])],[avatar_definition]) ).
fof(f580,plain,
( ~ aElementOf0(sK42(sK45),xI)
| spl52_28 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f586,definition,
( spl52_30
<=> aElementOf0(sK42(sK48),xI) ),
introduced(definition,[new_symbols(definition,[spl52_30])],[avatar_definition]) ).
fof(f587,plain,
( ~ aElementOf0(sK42(sK48),xI)
| spl52_30 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f589,plain,
( $false
| ~ spl52_19
| spl52_28 ),
inference(resolution,[],[f580,f557]) ).
fof(f590,plain,
( ~ spl52_19
| spl52_28 ),
inference(avatar_contradiction_clause,[],[f589]) ).
fof(f594,plain,
( ! [X0] :
( ~ iLess0(sbrdtbr0(sK42(X0)),sbrdtbr0(sK48))
| ~ aElementOf0(sK42(X0),xI)
| ~ sP5(X0) )
| ~ spl52_1 ),
inference(resolution,[],[f444,f429]) ).
fof(f605,plain,
( $false
| ~ spl52_18
| spl52_30 ),
inference(resolution,[],[f587,f556]) ).
fof(f606,plain,
( ~ spl52_18
| spl52_30 ),
inference(avatar_contradiction_clause,[],[f605]) ).
fof(f741,plain,
( ~ sP5(sK45)
| ~ sP5(sK45)
| ~ aElementOf0(sK42(sK45),xI)
| ~ spl52_4 ),
inference(resolution,[],[f334,f559]) ).
fof(f742,plain,
( ~ sP5(sK48)
| ~ aElementOf0(sK42(sK48),xI)
| ~ sP5(sK48)
| ~ spl52_1 ),
inference(resolution,[],[f334,f594]) ).
fof(f743,plain,
( ~ sP5(sK48)
| ~ aElementOf0(sK42(sK48),xI)
| ~ spl52_1 ),
inference(duplicate_literal_removal,[],[f742]) ).
fof(f744,plain,
( ~ sP5(sK45)
| ~ aElementOf0(sK42(sK45),xI)
| ~ spl52_4 ),
inference(duplicate_literal_removal,[],[f741]) ).
fof(f746,plain,
( ~ spl52_30
| ~ spl52_18
| ~ spl52_1 ),
inference(avatar_split_clause,[],[f743,f443,f517,f586]) ).
fof(f748,plain,
( ~ spl52_28
| ~ spl52_19
| ~ spl52_4 ),
inference(avatar_split_clause,[],[f744,f455,f521,f579]) ).
cnf(s1,plain,
( spl52_1
| spl52_2 ),
inference(sat_conversion,[],[f448]) ).
cnf(s3,plain,
( ~ spl52_2
| spl52_4 ),
inference(sat_conversion,[],[f457]) ).
cnf(s5,plain,
( ~ spl52_2
| ~ spl52_6 ),
inference(sat_conversion,[],[f465]) ).
cnf(s6,plain,
( ~ spl52_2
| spl52_7 ),
inference(sat_conversion,[],[f469]) ).
cnf(s14,plain,
spl52_16,
inference(sat_conversion,[],[f512]) ).
cnf(s15,plain,
( ~ spl52_16
| spl52_18 ),
inference(sat_conversion,[],[f519]) ).
cnf(s16,plain,
( spl52_6
| ~ spl52_7
| spl52_19 ),
inference(sat_conversion,[],[f523]) ).
cnf(s24,plain,
( ~ spl52_19
| spl52_28 ),
inference(sat_conversion,[],[f590]) ).
cnf(s26,plain,
( ~ spl52_18
| spl52_30 ),
inference(sat_conversion,[],[f606]) ).
cnf(s39,plain,
( ~ spl52_1
| ~ spl52_18
| ~ spl52_30 ),
inference(sat_conversion,[],[f746]) ).
cnf(s40,plain,
( ~ spl52_4
| ~ spl52_19
| ~ spl52_28 ),
inference(sat_conversion,[],[f748]) ).
cnf(s41,plain,
spl52_18,
inference(rat,[],[s15,s14]) ).
cnf(s42,plain,
spl52_30,
inference(rat,[],[s26,s41]) ).
cnf(s46,plain,
~ spl52_1,
inference(rat,[],[s39,s41,s42]) ).
cnf(s58,plain,
spl52_2,
inference(rat,[],[s1,s46]) ).
cnf(s62,plain,
spl52_7,
inference(rat,[],[s6,s58]) ).
cnf(s63,plain,
~ spl52_6,
inference(rat,[],[s5,s58]) ).
cnf(s65,plain,
spl52_4,
inference(rat,[],[s3,s58]) ).
cnf(s66,plain,
spl52_19,
inference(rat,[],[s16,s62,s63]) ).
cnf(s69,plain,
~ spl52_28,
inference(rat,[],[s40,s65,s66]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s24,s69,s66]) ).
fof(f749,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG111+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 23:19:32 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.06/1.06 % (1415759)Detected formulas, will run a generic FOF schedule.
% 3.06/1.06 % (1415764)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=2769587448:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.06/1.06 % (1415770)dis-21_1_sil=8000:lcm=predicate:random_seed=2328665482: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)
% 3.06/1.06 % (1415766)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=887481792:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.06/1.06 % (1415769)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1587512844:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.06/1.06 % (1415765)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=2729445009:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.06/1.06 % (1415767)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=16324593:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.06/1.06 % (1415768)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=441576193:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.06/1.06 % (1415770)First to succeed.
% 3.06/1.06 % (1415770)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1415759"
% 3.06/1.06 % (1415768)Also succeeded, but the first one will report.
% 3.06/1.06 % (1415767)Instruction limit reached!
% 3.06/1.06 % (1415767)------------------------------
% 3.06/1.06 % (1415767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.06 % (1415767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.06 % (1415767)CaDiCaL version: 2.1.3
% 3.06/1.06 % (1415767)Termination reason: Instruction limit
% 3.06/1.06 % (1415767)Termination phase: Saturation
% 3.06/1.06 % (1415767)Time elapsed: 0.065 s
% 3.06/1.06 % (1415767)Peak memory usage: 89 MB
% 3.06/1.06 % (1415767)Instructions burned: 109 (million)
% 3.06/1.06 % (1415769)Instruction limit reached!
% 3.06/1.06 % (1415769)------------------------------
% 3.06/1.06 % (1415769)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.06 % (1415769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.06 % (1415769)CaDiCaL version: 2.1.3
% 3.06/1.06 % (1415769)Termination reason: Instruction limit
% 3.06/1.06 % (1415769)Termination phase: Saturation
% 3.06/1.06 % (1415769)Time elapsed: 0.093 s
% 3.06/1.06 % (1415769)Peak memory usage: 90 MB
% 3.06/1.06 % (1415769)Instructions burned: 139 (million)
% 3.06/1.06 % (1415778)lrs+10_1_sil=8000:sp=occurrence:random_seed=1573796156:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.06/1.06 % (1415779)lrs+10_1_sil=32000:urr=on:br=off:random_seed=444202228:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.06/1.06 % (1415778)Also succeeded, but the first one will report.
% 3.06/1.06 % (1415770)Refutation found. Thanks to Tanya!
% 3.06/1.06 % SZS status Theorem for theBenchmark
% 3.06/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.15 % (1415770)------------------------------
% 3.41/1.15 % (1415770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.15 % (1415770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.15 % (1415770)CaDiCaL version: 2.1.3
% 3.41/1.15 % (1415770)Termination reason: Refutation
% 3.41/1.15 % (1415770)Time elapsed: 0.012 s
% 3.41/1.15 % (1415770)Peak memory usage: 90 MB
% 3.41/1.15 % (1415770)Instructions burned: 17 (million)
% 3.41/1.15 % (1415770)------------------------------
% 3.41/1.15 % (1415770)------------------------------
% 3.41/1.15 % (1415759)Success in time 0.434 s
% 3.41/1.15 % Vampire exiting
%------------------------------------------------------------------------------