%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG126+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : 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 12:35:37 PM UTC 2026
% Result : Theorem 5.12s 1.67s
% Output : Refutation 6.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 96 ( 27 unt; 2 def)
% Number of atoms : 370 ( 29 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 449 ( 175 ~; 163 |; 84 &)
% ( 13 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 133 ( 0 sgn 116 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f34,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aElement0(X1)
& doDivides0(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDvs) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( aDivisorOf0(X2,X0)
& aDivisorOf0(X2,X1)
& ! [X3] :
( ( aDivisorOf0(X3,X0)
& aDivisorOf0(X3,X1) )
=> doDivides0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefGCD) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(f41,axiom,
aGcdOfAnd0(xc,xa,xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2129) ).
fof(f42,axiom,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(f47,axiom,
doDivides0(xu,xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2744) ).
fof(f48,conjecture,
aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f53,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(f57,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(flattening,[],[f49]) ).
fof(f69,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f70,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f69]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f87,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,[],[f53]) ).
fof(f100,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(X0,X2) = X1 ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f101,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(X0,X2) = X1 ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aElement0(X1)
& doDivides0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f103,plain,
! [X0,X1] :
( ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( aDivisorOf0(X2,X0)
& aDivisorOf0(X2,X1)
& ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X0)
| ~ aDivisorOf0(X3,X1) ) ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( aDivisorOf0(X2,X0)
& aDivisorOf0(X2,X1)
& ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X0)
| ~ aDivisorOf0(X3,X1) ) ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f103]) ).
fof(f109,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| ~ aElementOf0(X0,xI)
| sz00 = X0 ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f110,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| ~ aElementOf0(X0,xI)
| sz00 = X0 ) ),
inference(flattening,[],[f109]) ).
fof(f120,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,[],[f87]) ).
fof(f121,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,[],[f120]) ).
fof(f122,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,[],[f121]) ).
fof(f123,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ( ( ( ~ aElementOf0(sdtpldt0(sK8(X0),sK9(X0)),X0)
& aElementOf0(sK9(X0),X0) )
| ( ~ aElementOf0(sdtasdt0(sK10(X0),sK8(X0)),X0)
& aElement0(sK10(X0)) ) )
& aElementOf0(sK8(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,[sK8,sK9,sK10]),skolemize(X1,sK8(X0)),skolemize(X2,sK9(X0)),skolemize(X3,sK10(X0))],[f122]) ).
fof(f128,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,[],[f101]) ).
fof(f129,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,[],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aElement0(sK15(X0,X1))
& sdtasdt0(X0,sK15(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X3,sK15(X0,X1))],[f129]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aElement0(X1)
| ~ doDivides0(X1,X0) )
& ( ( aElement0(X1)
& doDivides0(X1,X0) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aElement0(X1)
| ~ doDivides0(X1,X0) )
& ( ( aElement0(X1)
& doDivides0(X1,X0) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( ! [X2] :
( ( aGcdOfAnd0(X2,X0,X1)
| ~ aDivisorOf0(X2,X0)
| ~ aDivisorOf0(X2,X1)
| ? [X3] :
( ~ doDivides0(X3,X2)
& aDivisorOf0(X3,X0)
& aDivisorOf0(X3,X1) ) )
& ( ( aDivisorOf0(X2,X0)
& aDivisorOf0(X2,X1)
& ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X0)
| ~ aDivisorOf0(X3,X1) ) )
| ~ aGcdOfAnd0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(nnf_transformation,[],[f104]) ).
fof(f134,plain,
! [X0,X1] :
( ! [X2] :
( ( aGcdOfAnd0(X2,X0,X1)
| ~ aDivisorOf0(X2,X0)
| ~ aDivisorOf0(X2,X1)
| ? [X3] :
( ~ doDivides0(X3,X2)
& aDivisorOf0(X3,X0)
& aDivisorOf0(X3,X1) ) )
& ( ( aDivisorOf0(X2,X0)
& aDivisorOf0(X2,X1)
& ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X0)
| ~ aDivisorOf0(X3,X1) ) )
| ~ aGcdOfAnd0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
! [X0,X1] :
( ! [X2] :
( ( aGcdOfAnd0(X2,X0,X1)
| ~ aDivisorOf0(X2,X0)
| ~ aDivisorOf0(X2,X1)
| ? [X3] :
( ~ doDivides0(X3,X2)
& aDivisorOf0(X3,X0)
& aDivisorOf0(X3,X1) ) )
& ( ( aDivisorOf0(X2,X0)
& aDivisorOf0(X2,X1)
& ! [X4] :
( doDivides0(X4,X2)
| ~ aDivisorOf0(X4,X0)
| ~ aDivisorOf0(X4,X1) ) )
| ~ aGcdOfAnd0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(rectify,[],[f134]) ).
fof(f136,plain,
! [X0,X1] :
( ! [X2] :
( ( aGcdOfAnd0(X2,X0,X1)
| ~ aDivisorOf0(X2,X0)
| ~ aDivisorOf0(X2,X1)
| ( ~ doDivides0(sK16(X0,X1,X2),X2)
& aDivisorOf0(sK16(X0,X1,X2),X0)
& aDivisorOf0(sK16(X0,X1,X2),X1) ) )
& ( ( aDivisorOf0(X2,X0)
& aDivisorOf0(X2,X1)
& ! [X4] :
( doDivides0(X4,X2)
| ~ aDivisorOf0(X4,X0)
| ~ aDivisorOf0(X4,X1) ) )
| ~ aGcdOfAnd0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X3,sK16(X0,X1,X2))],[f135]) ).
fof(f154,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f166,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f187,plain,
! [X0,X6,X4] :
( ~ aIdeal0(X0)
| ~ aElement0(X6)
| ~ aElementOf0(X4,X0)
| aElementOf0(sdtasdt0(X6,X4),X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f189,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f210,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sdtasdt0(X0,sK15(X0,X1)) = X1
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f211,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| aElement0(sK15(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f214,plain,
! [X0,X1] :
( ~ aDivisorOf0(X1,X0)
| aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f217,plain,
! [X2,X0,X1] :
( ~ aGcdOfAnd0(X2,X0,X1)
| aDivisorOf0(X2,X1)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ aGcdOfAnd0(X2,X0,X1)
| aDivisorOf0(X2,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f232,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f233,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f235,plain,
aGcdOfAnd0(xc,xa,xb),
inference(cnf_transformation,[],[f41]) ).
fof(f236,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f42]) ).
fof(f237,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f246,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f110]) ).
fof(f249,plain,
doDivides0(xu,xc),
inference(cnf_transformation,[],[f47]) ).
fof(f250,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f57]) ).
fof(f274,plain,
~ aElementOf0(xc,xI),
inference(superposition,[],[f250,f236]) ).
fof(f278,plain,
aSet0(xI),
inference(resolution,[],[f237,f189]) ).
fof(f283,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| aElement0(X0) ),
inference(resolution,[],[f166,f278]) ).
fof(f310,plain,
aElement0(xu),
inference(resolution,[],[f283,f246]) ).
fof(f313,plain,
( xc = sdtasdt0(xu,sK15(xu,xc))
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(resolution,[],[f210,f249]) ).
fof(f314,plain,
( xc = sdtasdt0(xu,sK15(xu,xc))
| ~ aElement0(xc) ),
inference(forward_subsumption_resolution,[],[f313,f310]) ).
fof(f316,definition,
( spl21_5
<=> aElement0(xc) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
fof(f317,plain,
( ~ aElement0(xc)
| spl21_5 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f319,definition,
( spl21_6
<=> xc = sdtasdt0(xu,sK15(xu,xc)) ),
introduced(definition,[new_symbols(definition,[spl21_6])],[avatar_definition]) ).
fof(f320,plain,
( xc = sdtasdt0(xu,sK15(xu,xc))
| ~ spl21_6 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f321,plain,
( ~ spl21_5
| spl21_6 ),
inference(avatar_split_clause,[],[f314,f319,f316]) ).
fof(f367,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(X0) ),
inference(resolution,[],[f187,f237]) ).
fof(f440,plain,
( aDivisorOf0(xc,xa)
| ~ aElement0(xa)
| ~ aElement0(xb) ),
inference(resolution,[],[f218,f235]) ).
fof(f441,plain,
( aDivisorOf0(xc,xa)
| ~ aElement0(xb) ),
inference(forward_subsumption_resolution,[],[f440,f233]) ).
fof(f442,plain,
aDivisorOf0(xc,xa),
inference(forward_subsumption_resolution,[],[f441,f232]) ).
fof(f476,plain,
( aDivisorOf0(xc,xb)
| ~ aElement0(xa)
| ~ aElement0(xb) ),
inference(resolution,[],[f217,f235]) ).
fof(f477,plain,
( aDivisorOf0(xc,xb)
| ~ aElement0(xb) ),
inference(forward_subsumption_resolution,[],[f476,f233]) ).
fof(f478,plain,
aDivisorOf0(xc,xb),
inference(forward_subsumption_resolution,[],[f477,f232]) ).
fof(f571,plain,
( aElement0(xc)
| ~ aElement0(xa) ),
inference(resolution,[],[f214,f442]) ).
fof(f572,plain,
( aElement0(xc)
| ~ aElement0(xb) ),
inference(resolution,[],[f214,f478]) ).
fof(f576,plain,
( ~ aElement0(xa)
| spl21_5 ),
inference(forward_subsumption_resolution,[],[f571,f317]) ).
fof(f579,plain,
( $false
| spl21_5 ),
inference(forward_subsumption_resolution,[],[f576,f233]) ).
fof(f580,plain,
spl21_5,
inference(avatar_contradiction_clause,[],[f579]) ).
fof(f582,plain,
aElement0(xc),
inference(forward_subsumption_resolution,[],[f572,f232]) ).
fof(f747,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(xu,X0) = sdtasdt0(X0,xu) ),
inference(resolution,[],[f154,f310]) ).
fof(f1781,plain,
( aElement0(sK15(xu,xc))
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(resolution,[],[f211,f249]) ).
fof(f1790,plain,
( aElement0(sK15(xu,xc))
| ~ aElement0(xc) ),
inference(forward_subsumption_resolution,[],[f1781,f310]) ).
fof(f1791,plain,
aElement0(sK15(xu,xc)),
inference(forward_subsumption_resolution,[],[f1790,f582]) ).
fof(f1833,plain,
sdtasdt0(xu,sK15(xu,xc)) = sdtasdt0(sK15(xu,xc),xu),
inference(resolution,[],[f1791,f747]) ).
fof(f1841,plain,
( xc = sdtasdt0(sK15(xu,xc),xu)
| ~ spl21_6 ),
inference(forward_demodulation,[],[f1833,f320]) ).
fof(f1866,plain,
( aElementOf0(xc,xI)
| ~ aElementOf0(xu,xI)
| ~ aElement0(sK15(xu,xc))
| ~ spl21_6 ),
inference(superposition,[],[f367,f1841]) ).
fof(f1869,plain,
( ~ aElementOf0(xu,xI)
| ~ aElement0(sK15(xu,xc))
| ~ spl21_6 ),
inference(forward_subsumption_resolution,[],[f1866,f274]) ).
fof(f1871,plain,
( ~ aElement0(sK15(xu,xc))
| ~ spl21_6 ),
inference(forward_subsumption_resolution,[],[f1869,f246]) ).
fof(f1872,plain,
( $false
| ~ spl21_6 ),
inference(forward_subsumption_resolution,[],[f1871,f1791]) ).
fof(f1873,plain,
~ spl21_6,
inference(avatar_contradiction_clause,[],[f1872]) ).
cnf(s5,plain,
( ~ spl21_5
| spl21_6 ),
inference(sat_conversion,[],[f321]) ).
cnf(s30,plain,
spl21_5,
inference(sat_conversion,[],[f580]) ).
cnf(s101,plain,
~ spl21_6,
inference(sat_conversion,[],[f1873]) ).
cnf(s136,plain,
$false,
inference(rat,[],[s5,s101,s30]) ).
fof(f1874,plain,
$false,
inference(avatar_sat_refutation,[],[s136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG126+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 23:23:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.12/1.67 % (3520740)Detected formulas, will run a generic FOF schedule.
% 5.12/1.67 % (3520746)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=3931522655:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.12/1.67 % (3520748)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1710816000:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.12/1.67 % (3520745)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=2000650655:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.12/1.67 % (3520747)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=972737548:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.12/1.67 % (3520749)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1223512087:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.12/1.67 % (3520748)Refutation not found, incomplete strategy
% 5.12/1.67 % (3520748)------------------------------
% 5.12/1.67 % (3520748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.67 % (3520748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.67 % (3520748)CaDiCaL version: 2.1.3
% 5.12/1.67 % (3520748)Termination reason: Refutation not found, incomplete strategy
% 5.12/1.67 % (3520748)Time elapsed: 0.007 s
% 5.12/1.67 % (3520748)Peak memory usage: 88 MB
% 5.12/1.67 % (3520748)Instructions burned: 9 (million)
% 5.12/1.67 % (3520751)dis-21_1_sil=8000:lcm=predicate:random_seed=3424003071: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)
% 5.12/1.67 % (3520750)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2800412121:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.12/1.67 % (3520749)Instruction limit reached!
% 5.12/1.67 % (3520749)------------------------------
% 5.12/1.67 % (3520749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.67 % (3520749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.67 % (3520749)CaDiCaL version: 2.1.3
% 5.12/1.67 % (3520749)Termination reason: Instruction limit
% 5.12/1.67 % (3520749)Termination phase: Saturation
% 5.12/1.67 % (3520749)Time elapsed: 0.073 s
% 5.12/1.67 % (3520749)Peak memory usage: 89 MB
% 5.12/1.67 % (3520749)Instructions burned: 119 (million)
% 5.12/1.67 % (3520751)Instruction limit reached!
% 5.12/1.67 % (3520751)------------------------------
% 5.12/1.67 % (3520751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.67 % (3520751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.67 % (3520751)CaDiCaL version: 2.1.3
% 5.12/1.67 % (3520751)Termination reason: Instruction limit
% 5.12/1.67 % (3520751)Termination phase: Saturation
% 5.12/1.67 % (3520751)Time elapsed: 0.074 s
% 5.12/1.67 % (3520751)Peak memory usage: 90 MB
% 5.12/1.67 % (3520751)Instructions burned: 131 (million)
% 5.12/1.67 % (3520750)Instruction limit reached!
% 5.12/1.67 % (3520750)------------------------------
% 5.12/1.67 % (3520750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.67 % (3520750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.67 % (3520750)CaDiCaL version: 2.1.3
% 5.12/1.67 % (3520750)Termination reason: Instruction limit
% 5.12/1.67 % (3520750)Termination phase: Saturation
% 5.12/1.67 % (3520750)Time elapsed: 0.095 s
% 5.12/1.67 % (3520750)Peak memory usage: 90 MB
% 5.12/1.67 % (3520750)Instructions burned: 140 (million)
% 5.12/1.67 % (3520760)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1322759644:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.12/1.67 % (3520759)lrs+10_1_sil=8000:sp=occurrence:random_seed=1089432736:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.12/1.67 % (3520748)------------------------------
% 5.12/1.67 % (3520748)------------------------------
% 5.12/1.67 % (3520761)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2011675691:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.12/1.67 % (3520760)Instruction limit reached!
% 5.12/1.67 % (3520760)------------------------------
% 5.12/1.67 % (3520760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.67 % (3520760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.67 % (3520760)CaDiCaL version: 2.1.3
% 5.12/1.67 % (3520760)Termination reason: Instruction limit
% 5.12/1.67 % (3520760)Termination phase: Saturation
% 5.12/1.67 % (3520760)Time elapsed: 0.080 s
% 5.12/1.67 % (3520760)Peak memory usage: 91 MB
% 5.12/1.67 % (3520760)Instructions burned: 157 (million)
% 5.12/1.67 % (3520759)Instruction limit reached!
% 5.12/1.67 % (3520759)------------------------------
% 5.12/1.67 % (3520759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.67 % (3520759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.67 % (3520759)CaDiCaL version: 2.1.3
% 5.12/1.67 % (3520759)Termination reason: Instruction limit
% 5.12/1.67 % (3520759)Termination phase: Saturation
% 5.12/1.67 % (3520759)Time elapsed: 0.165 s
% 5.12/1.67 % (3520759)Peak memory usage: 93 MB
% 5.12/1.67 % (3520759)Instructions burned: 285 (million)
% 5.12/1.67 % (3520764)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1085352129:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.12/1.67 % (3520761)Instruction limit reached!
% 5.12/1.67 % (3520761)------------------------------
% 5.12/1.67 % (3520761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.67 % (3520761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.67 % (3520761)CaDiCaL version: 2.1.3
% 5.12/1.67 % (3520761)Termination reason: Instruction limit
% 5.12/1.67 % (3520761)Termination phase: Saturation
% 5.12/1.67 % (3520761)Time elapsed: 0.205 s
% 5.12/1.67 % (3520761)Peak memory usage: 93 MB
% 5.12/1.67 % (3520761)Instructions burned: 325 (million)
% 5.12/1.67 % (3520746)First to succeed.
% 5.12/1.67 % (3520746)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3520740"
% 5.12/1.67 % (3520766)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3907106723:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.12/1.67 % (3520766)Refutation not found, incomplete strategy
% 5.12/1.67 % (3520766)------------------------------
% 5.12/1.67 % (3520766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.67 % (3520766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.67 % (3520766)CaDiCaL version: 2.1.3
% 5.12/1.67 % (3520766)Termination reason: Refutation not found, incomplete strategy
% 5.12/1.67 % (3520766)Time elapsed: 0.009 s
% 5.12/1.67 % (3520766)Peak memory usage: 89 MB
% 5.12/1.67 % (3520766)Instructions burned: 11 (million)
% 5.12/1.67 % (3520764)Instruction limit reached!
% 5.12/1.67 % (3520764)------------------------------
% 5.12/1.67 % (3520764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.67 % (3520764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.67 % (3520764)CaDiCaL version: 2.1.3
% 5.12/1.67 % (3520764)Termination reason: Instruction limit
% 5.12/1.67 % (3520764)Termination phase: Saturation
% 5.12/1.67 % (3520764)Time elapsed: 0.119 s
% 5.12/1.67 % (3520764)Peak memory usage: 94 MB
% 5.12/1.67 % (3520764)Instructions burned: 249 (million)
% 5.12/1.67 % (3520767)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2409560430:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.12/1.67 % (3520769)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=454997664:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.12/1.67 % (3520746)Refutation found. Thanks to Tanya!
% 5.12/1.67 % SZS status Theorem for theBenchmark
% 5.12/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 6.32/1.87 % (3520746)------------------------------
% 6.32/1.87 % (3520746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.87 % (3520746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.87 % (3520746)CaDiCaL version: 2.1.3
% 6.32/1.87 % (3520746)Termination reason: Refutation
% 6.32/1.87 % (3520746)Time elapsed: 0.509 s
% 6.32/1.87 % (3520746)Peak memory usage: 134 MB
% 6.32/1.87 % (3520746)Instructions burned: 1331 (million)
% 6.32/1.87 % (3520746)------------------------------
% 6.32/1.87 % (3520746)------------------------------
% 6.32/1.87 % (3520740)Success in time 0.813 s
% 6.32/1.87 % Vampire exiting
%------------------------------------------------------------------------------