%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG119+1 : 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 : n011.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 1.50s 1.89s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 101 ( 22 unt; 5 def)
% Number of atoms : 393 ( 74 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 480 ( 188 ~; 181 |; 83 &)
% ( 15 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-2 aty)
% Number of variables : 135 ( 0 sgn 110 !; 25 ?)
% 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(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f33,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f42,axiom,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f45,axiom,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ( aElementOf0(X0,xI)
& X0 != sz00 )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(f49,axiom,
~ 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(f56,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f60,plain,
sz00 = xr,
inference(flattening,[],[f52]) ).
fof(f71,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f73,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f74,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f73]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f91,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f102,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(X0,X2) = X1 ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f103,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(X0,X2) = X1 ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f102]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f111,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| ~ aElementOf0(X0,xI)
| sz00 = X0 ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f112,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| ~ aElementOf0(X0,xI)
| sz00 = X0 ) ),
inference(flattening,[],[f111]) ).
fof(f128,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f129,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6) ) )
| ~ aElementOf0(X4,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f129]) ).
fof(f131,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ( ( ( ~ aElementOf0(sdtpldt0(sK10(X0),sK11(X0)),X0)
& aElementOf0(sK11(X0),X0) )
| ( ~ aElementOf0(sdtasdt0(sK12(X0),sK10(X0)),X0)
& aElement0(sK12(X0)) ) )
& aElementOf0(sK10(X0),X0) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6) ) )
| ~ aElementOf0(X4,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0)),skolemize(X3,sK12(X0))],[f130]) ).
fof(f136,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aElement0(X2)
& sdtasdt0(X0,X2) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(nnf_transformation,[],[f103]) ).
fof(f137,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(rectify,[],[f136]) ).
fof(f138,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aElement0(sK17(X0,X1))
& sdtasdt0(X0,sK17(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X3,sK17(X0,X1))],[f137]) ).
fof(f146,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f109]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f146]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(X0,X4) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ? [X7] :
( aElement0(X7)
& sdtasdt0(X0,X7) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(rectify,[],[f147]) ).
fof(f149,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != sK19(X0,X1) )
| ~ aElementOf0(sK19(X0,X1),X1) )
& ( ( aElement0(sK20(X0,X1))
& sK19(X0,X1) = sdtasdt0(X0,sK20(X0,X1)) )
| aElementOf0(sK19(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ( aElement0(sK21(X0,X5))
& sdtasdt0(X0,sK21(X0,X5)) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X2,sK19(X0,X1)),skolemize(X4,sK20(X0,X1)),skolemize(X7,sK21(X0,X5))],[f148]) ).
fof(f160,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f163,plain,
! [X0,X1] :
( ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f175,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f201,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f223,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aElement0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f237,plain,
! [X0,X1,X6,X5] :
( aElementOf0(X5,X1)
| ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f238,plain,
! [X0,X1] :
( aSet0(X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f243,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f248,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f257,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f112]) ).
fof(f263,plain,
~ doDivides0(xu,xb),
inference(cnf_transformation,[],[f49]) ).
fof(f265,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(cnf_transformation,[],[f50]) ).
fof(f267,plain,
aElement0(xq),
inference(cnf_transformation,[],[f50]) ).
fof(f268,plain,
sz00 = xr,
inference(cnf_transformation,[],[f60]) ).
fof(f275,plain,
! [X2,X0] :
( ~ aElement0(sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(X0)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f223]) ).
fof(f276,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f238]) ).
fof(f277,plain,
! [X0,X1,X6] :
( aElementOf0(sdtasdt0(X0,X6),X1)
| ~ aElement0(X6)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f237]) ).
fof(f278,plain,
! [X0,X6] :
( aElementOf0(sdtasdt0(X0,X6),slsdtgt0(X0))
| ~ aElement0(X6)
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f277]) ).
fof(f286,definition,
( spl25_2
<=> sz00 = xr ),
introduced(definition,[new_symbols(definition,[spl25_2])],[avatar_definition]) ).
fof(f288,plain,
( sz00 = xr
| ~ spl25_2 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f308,plain,
spl25_2,
inference(avatar_split_clause,[],[f268,f286]) ).
fof(f311,plain,
( xb = sdtpldt0(sdtasdt0(xq,xu),sz00)
| ~ spl25_2 ),
inference(forward_demodulation,[],[f265,f288]) ).
fof(f312,plain,
( xb = sdtasdt0(xq,xu)
| ~ aElement0(sdtasdt0(xq,xu))
| ~ spl25_2 ),
inference(superposition,[],[f160,f311]) ).
fof(f315,definition,
( spl25_7
<=> aElement0(sdtasdt0(xq,xu)) ),
introduced(definition,[new_symbols(definition,[spl25_7])],[avatar_definition]) ).
fof(f317,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| spl25_7 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f319,definition,
( spl25_8
<=> xb = sdtasdt0(xq,xu) ),
introduced(definition,[new_symbols(definition,[spl25_8])],[avatar_definition]) ).
fof(f321,plain,
( xb = sdtasdt0(xq,xu)
| ~ spl25_8 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f323,plain,
( ~ spl25_7
| spl25_8
| ~ spl25_2 ),
inference(avatar_split_clause,[],[f312,f286,f319,f315]) ).
fof(f344,plain,
( ! [X0] :
( ~ aElementOf0(sdtasdt0(xq,xu),X0)
| ~ aSet0(X0) )
| spl25_7 ),
inference(resolution,[],[f175,f317]) ).
fof(f366,definition,
( spl25_13
<=> aElement0(xu) ),
introduced(definition,[new_symbols(definition,[spl25_13])],[avatar_definition]) ).
fof(f367,plain,
( ~ aElement0(xu)
| spl25_13 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f368,plain,
( aElement0(xu)
| ~ spl25_13 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f373,plain,
( ~ aElement0(xu)
| ~ aElement0(xq)
| ~ aSet0(slsdtgt0(xq))
| spl25_7 ),
inference(resolution,[],[f278,f344]) ).
fof(f402,plain,
( ~ aElement0(xu)
| ~ aSet0(slsdtgt0(xq))
| spl25_7 ),
inference(forward_subsumption_resolution,[],[f373,f267]) ).
fof(f412,definition,
( spl25_19
<=> aSet0(slsdtgt0(xq)) ),
introduced(definition,[new_symbols(definition,[spl25_19])],[avatar_definition]) ).
fof(f414,plain,
( ~ aSet0(slsdtgt0(xq))
| spl25_19 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f415,plain,
( ~ spl25_19
| ~ spl25_13
| spl25_7 ),
inference(avatar_split_clause,[],[f402,f315,f366,f412]) ).
fof(f454,plain,
( ~ aElement0(xq)
| spl25_19 ),
inference(resolution,[],[f414,f276]) ).
fof(f457,plain,
( $false
| spl25_19 ),
inference(forward_subsumption_resolution,[],[f454,f267]) ).
fof(f458,plain,
spl25_19,
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f467,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(xq,X0) = sdtasdt0(X0,xq) ),
inference(resolution,[],[f163,f267]) ).
fof(f474,plain,
( ! [X0] :
( ~ aElementOf0(xu,X0)
| ~ aSet0(X0) )
| spl25_13 ),
inference(resolution,[],[f367,f175]) ).
fof(f480,plain,
( ~ aSet0(xI)
| spl25_13 ),
inference(resolution,[],[f474,f257]) ).
fof(f482,plain,
( ~ aIdeal0(xI)
| spl25_13 ),
inference(resolution,[],[f480,f201]) ).
fof(f483,plain,
( $false
| spl25_13 ),
inference(forward_subsumption_resolution,[],[f482,f248]) ).
fof(f484,plain,
spl25_13,
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f1525,plain,
( sdtasdt0(xq,xu) = sdtasdt0(xu,xq)
| ~ spl25_13 ),
inference(resolution,[],[f467,f368]) ).
fof(f1544,plain,
( xb = sdtasdt0(xu,xq)
| ~ spl25_8
| ~ spl25_13 ),
inference(forward_demodulation,[],[f1525,f321]) ).
fof(f1663,plain,
( ~ aElement0(xb)
| ~ aElement0(xq)
| ~ aElement0(xu)
| doDivides0(xu,xb)
| ~ spl25_8
| ~ spl25_13 ),
inference(superposition,[],[f275,f1544]) ).
fof(f1666,plain,
( ~ aElement0(xq)
| ~ aElement0(xu)
| doDivides0(xu,xb)
| ~ spl25_8
| ~ spl25_13 ),
inference(forward_subsumption_resolution,[],[f1663,f243]) ).
fof(f1673,plain,
( ~ aElement0(xu)
| doDivides0(xu,xb)
| ~ spl25_8
| ~ spl25_13 ),
inference(forward_subsumption_resolution,[],[f1666,f267]) ).
fof(f1679,plain,
( doDivides0(xu,xb)
| ~ spl25_8
| ~ spl25_13 ),
inference(forward_subsumption_resolution,[],[f1673,f368]) ).
fof(f1680,plain,
( $false
| ~ spl25_8
| ~ spl25_13 ),
inference(forward_subsumption_resolution,[],[f1679,f263]) ).
fof(f1681,plain,
( ~ spl25_8
| ~ spl25_13 ),
inference(avatar_contradiction_clause,[],[f1680]) ).
cnf(s4,plain,
spl25_2,
inference(sat_conversion,[],[f308]) ).
cnf(s6,plain,
( ~ spl25_2
| ~ spl25_7
| spl25_8 ),
inference(sat_conversion,[],[f323]) ).
cnf(s13,plain,
( spl25_7
| ~ spl25_13
| ~ spl25_19 ),
inference(sat_conversion,[],[f415]) ).
cnf(s23,plain,
spl25_19,
inference(sat_conversion,[],[f458]) ).
cnf(s24,plain,
spl25_13,
inference(sat_conversion,[],[f484]) ).
cnf(s73,plain,
( ~ spl25_8
| ~ spl25_13 ),
inference(sat_conversion,[],[f1681]) ).
cnf(s105,plain,
~ spl25_8,
inference(rat,[],[s73,s24]) ).
cnf(s112,plain,
spl25_7,
inference(rat,[],[s13,s23,s24]) ).
cnf(s116,plain,
~ spl25_2,
inference(rat,[],[s6,s105,s112]) ).
cnf(s117,plain,
$false,
inference(rat,[],[s4,s116]) ).
fof(f1682,plain,
$false,
inference(avatar_sat_refutation,[],[s117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG119+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.44 % Computer : n011.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 27 23:21:30 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.50 Running first-order theorem proving
% 0.20/0.50 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
% 1.50/1.89 % (2874781)Detected formulas, will run a generic FOF schedule.
% 1.50/1.89 % (2874787)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=3220680836:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.50/1.89 % (2874792)dis-21_1_sil=8000:lcm=predicate:random_seed=568591038: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)
% 1.50/1.89 % (2874792)Instruction limit reached!
% 1.50/1.89 % (2874792)------------------------------
% 1.50/1.89 % (2874792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.50/1.89 % (2874792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.50/1.89 % (2874792)CaDiCaL version: 2.1.3
% 1.50/1.89 % (2874792)Termination reason: Instruction limit
% 1.50/1.89 % (2874792)Termination phase: Saturation
% 1.50/1.89 % (2874792)Time elapsed: 0.080 s
% 1.50/1.89 % (2874792)Peak memory usage: 91 MB
% 1.50/1.89 % (2874792)Instructions burned: 129 (million)
% 1.50/1.89 % (2874788)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=983560795:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.50/1.89 % (2874786)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=3859749988:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.50/1.89 % (2874789)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1329821431:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.50/1.89 % (2874790)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=372725310:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.50/1.89 % (2874791)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4064279524:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.50/1.89 % (2874791)First to succeed.
% 1.50/1.89 % (2874791)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2874781"
% 1.50/1.89 % (2874790)Also succeeded, but the first one will report.
% 1.50/1.89 % (2874789)Instruction limit reached!
% 1.50/1.89 % (2874789)------------------------------
% 1.50/1.89 % (2874789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.50/1.89 % (2874789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.50/1.89 % (2874789)CaDiCaL version: 2.1.3
% 1.50/1.89 % (2874789)Termination reason: Instruction limit
% 1.50/1.89 % (2874789)Termination phase: Saturation
% 1.50/1.89 % (2874789)Time elapsed: 0.110 s
% 1.50/1.89 % (2874789)Peak memory usage: 90 MB
% 1.50/1.89 % (2874789)Instructions burned: 109 (million)
% 1.50/1.89 % (2874796)lrs+10_1_sil=8000:sp=occurrence:random_seed=1240830879:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 1.50/1.89 % (2874802)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3083654663:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 1.50/1.89 % (2874802)Refutation not found, incomplete strategy
% 1.50/1.89 % (2874802)------------------------------
% 1.50/1.89 % (2874802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.50/1.89 % (2874802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.50/1.89 % (2874802)CaDiCaL version: 2.1.3
% 1.50/1.89 % (2874802)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.89 % (2874802)Time elapsed: 0.003 s
% 1.50/1.89 % (2874802)Peak memory usage: 88 MB
% 1.50/1.89 % (2874802)Instructions burned: 1 (million)
% 1.50/1.89 % (2874791)Refutation found. Thanks to Tanya!
% 1.50/1.89 % SZS status Theorem for theBenchmark
% 1.50/1.89 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/2.16 % (2874791)------------------------------
% 0.24/2.16 % (2874791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/2.16 % (2874791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/2.16 % (2874791)CaDiCaL version: 2.1.3
% 0.24/2.16 % (2874791)Termination reason: Refutation
% 0.24/2.16 % (2874791)Time elapsed: 0.058 s
% 0.24/2.16 % (2874791)Peak memory usage: 90 MB
% 0.24/2.16 % (2874791)Instructions burned: 50 (million)
% 0.24/2.16 % (2874791)------------------------------
% 0.24/2.16 % (2874791)------------------------------
% 0.24/2.16 % (2874781)Success in time 0.749 s
% 0.24/2.16 % Vampire exiting
%------------------------------------------------------------------------------