%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG119+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 : n019.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 3.02s 1.35s
% Output : Refutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 78 ( 20 unt; 5 def)
% Number of atoms : 341 ( 84 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 404 ( 141 ~; 120 |; 117 &)
% ( 14 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-2 aty)
% Number of variables : 119 ( 0 sgn 86 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
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(f49,axiom,
~ ( ? [X0] :
( aElement0(X0)
& sdtasdt0(xu,X0) = xb )
| doDivides0(xu,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).
fof(f50,axiom,
( aElement0(xq)
& aElement0(xr)
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& ( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2666) ).
fof(f51,conjecture,
xr != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( xr != sz00 ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f61,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(f64,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(f67,plain,
sz00 = xr,
inference(flattening,[],[f52]) ).
fof(f78,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f80,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f81,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f80]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
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 ) )
& ! [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,[],[f61]) ).
fof(f121,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,[],[f64]) ).
fof(f122,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,[],[f121]) ).
fof(f124,plain,
( ! [X0] :
( ~ aElement0(X0)
| xb != sdtasdt0(xu,X0) )
& ~ doDivides0(xu,xb) ),
inference(ennf_transformation,[],[f49]) ).
fof(f172,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,[],[f120]) ).
fof(f173,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,[],[f172]) ).
fof(f174,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(sK28(X3))
& sdtasdt0(xa,sK28(X3)) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xb))
| ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(xb,X7) != X6 ) )
& ( ( aElement0(sK29(X6))
& sdtasdt0(xb,sK29(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(sK30(X9),slsdtgt0(xa))
& aElementOf0(sK31(X9),slsdtgt0(xb))
& sdtpldt0(sK30(X9),sK31(X9)) = X9 )
| ~ aElementOf0(X9,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31]),skolemize(X5,sK28(X3)),skolemize(X8,sK29(X6)),skolemize(X12,sK30(X9)),skolemize(X13,sK31(X9))],[f173]) ).
fof(f179,plain,
( aElementOf0(sK41,slsdtgt0(xa))
& aElementOf0(sK42,slsdtgt0(xb))
& xu = sdtpldt0(sK41,sK42)
& 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,[sK41,sK42]),skolemize(X0,sK41),skolemize(X1,sK42)],[f122]) ).
fof(f192,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f195,plain,
! [X0,X1] :
( ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f207,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f310,plain,
! [X2,X0] :
( ~ aElementOf0(X0,xI)
| ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) ),
inference(cnf_transformation,[],[f174]) ).
fof(f312,plain,
aSet0(xI),
inference(cnf_transformation,[],[f174]) ).
fof(f339,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f179]) ).
fof(f356,plain,
! [X0] :
( ~ aElement0(X0)
| xb != sdtasdt0(xu,X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f358,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(cnf_transformation,[],[f50]) ).
fof(f360,plain,
aElement0(xq),
inference(cnf_transformation,[],[f50]) ).
fof(f361,plain,
sz00 = xr,
inference(cnf_transformation,[],[f67]) ).
fof(f385,definition,
( spl46_2
<=> sz00 = xr ),
introduced(definition,[new_symbols(definition,[spl46_2])],[avatar_definition]) ).
fof(f387,plain,
( sz00 = xr
| ~ spl46_2 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f418,definition,
( spl46_9
<=> ! [X0] :
( ~ aElement0(X0)
| xb != sdtasdt0(xu,X0) ) ),
introduced(definition,[new_symbols(definition,[spl46_9])],[avatar_definition]) ).
fof(f419,plain,
( ! [X0] :
( xb != sdtasdt0(xu,X0)
| ~ aElement0(X0) )
| ~ spl46_9 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f430,plain,
spl46_2,
inference(avatar_split_clause,[],[f361,f385]) ).
fof(f436,plain,
spl46_9,
inference(avatar_split_clause,[],[f356,f418]) ).
fof(f437,plain,
( xb = sdtpldt0(sdtasdt0(xq,xu),sz00)
| ~ spl46_2 ),
inference(forward_demodulation,[],[f358,f387]) ).
fof(f442,plain,
( xb = sdtasdt0(xq,xu)
| ~ aElement0(sdtasdt0(xq,xu))
| ~ spl46_2 ),
inference(superposition,[],[f192,f437]) ).
fof(f445,definition,
( spl46_12
<=> aElement0(sdtasdt0(xq,xu)) ),
introduced(definition,[new_symbols(definition,[spl46_12])],[avatar_definition]) ).
fof(f447,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| spl46_12 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f449,definition,
( spl46_13
<=> xb = sdtasdt0(xq,xu) ),
introduced(definition,[new_symbols(definition,[spl46_13])],[avatar_definition]) ).
fof(f451,plain,
( xb = sdtasdt0(xq,xu)
| ~ spl46_13 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f453,plain,
( ~ spl46_12
| spl46_13
| ~ spl46_2 ),
inference(avatar_split_clause,[],[f442,f385,f449,f445]) ).
fof(f454,plain,
( ! [X0] :
( ~ aElementOf0(sdtasdt0(xq,xu),X0)
| ~ aSet0(X0) )
| spl46_12 ),
inference(resolution,[],[f207,f447]) ).
fof(f472,definition,
( spl46_14
<=> aElement0(xu) ),
introduced(definition,[new_symbols(definition,[spl46_14])],[avatar_definition]) ).
fof(f473,plain,
( aElement0(xu)
| ~ spl46_14 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f474,plain,
( ~ aElement0(xu)
| spl46_14 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f482,plain,
( ! [X0] :
( ~ aElementOf0(xu,X0)
| ~ aSet0(X0) )
| spl46_14 ),
inference(resolution,[],[f474,f207]) ).
fof(f507,plain,
( ~ aSet0(xI)
| spl46_14 ),
inference(resolution,[],[f482,f339]) ).
fof(f508,plain,
( $false
| spl46_14 ),
inference(forward_subsumption_resolution,[],[f507,f312]) ).
fof(f509,plain,
spl46_14,
inference(avatar_contradiction_clause,[],[f508]) ).
fof(f548,plain,
! [X0] :
( aElementOf0(sdtasdt0(X0,xu),xI)
| ~ aElement0(X0) ),
inference(resolution,[],[f310,f339]) ).
fof(f550,plain,
( ~ aElement0(xq)
| ~ aSet0(xI)
| spl46_12 ),
inference(resolution,[],[f548,f454]) ).
fof(f557,plain,
( ~ aSet0(xI)
| spl46_12 ),
inference(forward_subsumption_resolution,[],[f550,f360]) ).
fof(f560,plain,
( $false
| spl46_12 ),
inference(forward_subsumption_resolution,[],[f557,f312]) ).
fof(f561,plain,
spl46_12,
inference(avatar_contradiction_clause,[],[f560]) ).
fof(f700,plain,
! [X0] :
( sdtasdt0(xq,X0) = sdtasdt0(X0,xq)
| ~ aElement0(X0) ),
inference(resolution,[],[f195,f360]) ).
fof(f2012,plain,
( xb = sdtasdt0(xu,xq)
| ~ aElement0(xu)
| ~ spl46_13 ),
inference(superposition,[],[f451,f700]) ).
fof(f2046,plain,
( xb = sdtasdt0(xu,xq)
| ~ spl46_13
| ~ spl46_14 ),
inference(forward_subsumption_resolution,[],[f2012,f473]) ).
fof(f2572,plain,
( xb != xb
| ~ aElement0(xq)
| ~ spl46_9
| ~ spl46_13
| ~ spl46_14 ),
inference(superposition,[],[f419,f2046]) ).
fof(f2577,plain,
( ~ aElement0(xq)
| ~ spl46_9
| ~ spl46_13
| ~ spl46_14 ),
inference(trivial_inequality_removal,[],[f2572]) ).
fof(f2580,plain,
( $false
| ~ spl46_9
| ~ spl46_13
| ~ spl46_14 ),
inference(forward_subsumption_resolution,[],[f2577,f360]) ).
fof(f2581,plain,
( ~ spl46_9
| ~ spl46_13
| ~ spl46_14 ),
inference(avatar_contradiction_clause,[],[f2580]) ).
cnf(s9,plain,
spl46_2,
inference(sat_conversion,[],[f430]) ).
cnf(s12,plain,
spl46_9,
inference(sat_conversion,[],[f436]) ).
cnf(s15,plain,
( ~ spl46_2
| ~ spl46_12
| spl46_13 ),
inference(sat_conversion,[],[f453]) ).
cnf(s22,plain,
spl46_14,
inference(sat_conversion,[],[f509]) ).
cnf(s27,plain,
spl46_12,
inference(sat_conversion,[],[f561]) ).
cnf(s93,plain,
( ~ spl46_9
| ~ spl46_13
| ~ spl46_14 ),
inference(sat_conversion,[],[f2581]) ).
cnf(s117,plain,
( ~ spl46_2
| spl46_13 ),
inference(rat,[],[s15,s27]) ).
cnf(s119,plain,
~ spl46_13,
inference(rat,[],[s93,s22,s12]) ).
cnf(s123,plain,
~ spl46_2,
inference(rat,[],[s117,s119]) ).
cnf(s125,plain,
$false,
inference(rat,[],[s9,s123]) ).
fof(f2587,plain,
$false,
inference(avatar_sat_refutation,[],[s125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG119+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 23:21:18 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 3.02/1.35 % (3519524)Detected formulas, will run a generic FOF schedule.
% 3.02/1.35 % (3519530)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=3431935256:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.02/1.35 % (3519529)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=3723630529:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.02/1.35 % (3519531)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=2142320798:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.02/1.35 % (3519532)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2300779960:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.02/1.35 % (3519533)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=447990451:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.02/1.35 % (3519535)dis-21_1_sil=8000:lcm=predicate:random_seed=2952299660: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)
% 3.02/1.35 % (3519534)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3301267531:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.02/1.35 % (3519532)Instruction limit reached!
% 3.02/1.35 % (3519532)------------------------------
% 3.02/1.35 % (3519532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.35 % (3519532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.35 % (3519532)CaDiCaL version: 2.1.3
% 3.02/1.35 % (3519532)Termination reason: Instruction limit
% 3.02/1.35 % (3519532)Termination phase: Saturation
% 3.02/1.35 % (3519532)Time elapsed: 0.067 s
% 3.02/1.35 % (3519532)Peak memory usage: 89 MB
% 3.02/1.35 % (3519532)Instructions burned: 109 (million)
% 3.02/1.35 % (3519533)Instruction limit reached!
% 3.02/1.35 % (3519533)------------------------------
% 3.02/1.35 % (3519533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.35 % (3519533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.35 % (3519533)CaDiCaL version: 2.1.3
% 3.02/1.35 % (3519533)Termination reason: Instruction limit
% 3.02/1.35 % (3519533)Termination phase: Saturation
% 3.02/1.35 % (3519533)Time elapsed: 0.069 s
% 3.02/1.35 % (3519533)Peak memory usage: 88 MB
% 3.02/1.35 % (3519533)Instructions burned: 121 (million)
% 3.02/1.35 % (3519534)First to succeed.
% 3.02/1.35 % (3519534)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3519524"
% 3.02/1.35 % (3519535)Instruction limit reached!
% 3.02/1.35 % (3519535)------------------------------
% 3.02/1.35 % (3519535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.35 % (3519535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.35 % (3519535)CaDiCaL version: 2.1.3
% 3.02/1.35 % (3519535)Termination reason: Instruction limit
% 3.02/1.35 % (3519535)Termination phase: Saturation
% 3.02/1.35 % (3519535)Time elapsed: 0.074 s
% 3.02/1.35 % (3519535)Peak memory usage: 90 MB
% 3.02/1.35 % (3519535)Instructions burned: 130 (million)
% 3.02/1.35 % (3519544)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2476878330:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.02/1.35 % (3519543)lrs+10_1_sil=8000:sp=occurrence:random_seed=1762652506:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.02/1.35 % (3519544)Refutation not found, incomplete strategy
% 3.02/1.35 % (3519544)------------------------------
% 3.02/1.35 % (3519544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.35 % (3519544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.35 % (3519544)CaDiCaL version: 2.1.3
% 3.02/1.35 % (3519544)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.35 % (3519544)Time elapsed: 0.002 s
% 3.02/1.35 % (3519544)Peak memory usage: 88 MB
% 3.02/1.35 % (3519544)Instructions burned: 2 (million)
% 3.02/1.35 % (3519545)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4273845830:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.02/1.35 % (3519534)Refutation found. Thanks to Tanya!
% 3.02/1.35 % SZS status Theorem for theBenchmark
% 3.02/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.11/1.55 % (3519534)------------------------------
% 4.11/1.55 % (3519534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.55 % (3519534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.55 % (3519534)CaDiCaL version: 2.1.3
% 4.11/1.55 % (3519534)Termination reason: Refutation
% 4.11/1.55 % (3519534)Time elapsed: 0.056 s
% 4.11/1.55 % (3519534)Peak memory usage: 91 MB
% 4.11/1.55 % (3519534)Instructions burned: 83 (million)
% 4.11/1.55 % (3519534)------------------------------
% 4.11/1.55 % (3519534)------------------------------
% 4.11/1.55 % (3519524)Success in time 0.497 s
% 4.11/1.55 % Vampire exiting
%------------------------------------------------------------------------------