%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM503+3 : 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 : 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 12:15:29 PM UTC 2026
% Result : Theorem 10.42s 2.37s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 31
% Syntax : Number of formulae : 186 ( 37 unt; 14 def)
% Number of atoms : 704 ( 241 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 860 ( 342 ~; 340 |; 144 &)
% ( 17 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 15 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn 103 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| sdtasdt0(X1,X0) = sdtasdt0(X2,X0) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X0 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X0 != sz00
& X1 != X2
& sdtlseqdt0(X1,X2) )
=> ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f43,axiom,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xm )
| sdtlseqdt0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
fof(f44,axiom,
( xn != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(f45,axiom,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f46,axiom,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
fof(f50,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xk )
& sdtlseqdt0(xp,xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2389) ).
fof(f51,conjecture,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm) )
| sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) )
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xp,xm),X0) = sdtasdt0(xp,xk) )
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm) )
| sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) )
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xp,xm),X0) = sdtasdt0(xp,xk) )
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f56,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rectify,[],[f41]) ).
fof(f57,plain,
( xn != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtpldt0(xm,X1) )
& sdtlseqdt0(xm,xp) ),
inference(rectify,[],[f44]) ).
fof(f60,plain,
~ ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm) )
| sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) )
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X1) )
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ) ),
inference(rectify,[],[f52]) ).
fof(f70,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f71,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f70]) ).
fof(f75,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f80,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f81,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f80]) ).
fof(f84,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f85,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f84]) ).
fof(f93,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f94,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f96,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f95]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f99]) ).
fof(f121,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f122,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f121]) ).
fof(f127,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(ennf_transformation,[],[f56]) ).
fof(f128,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(flattening,[],[f127]) ).
fof(f130,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xm != sdtpldt0(xp,X0) )
& ~ sdtlseqdt0(xp,xm) ),
inference(ennf_transformation,[],[f43]) ).
fof(f131,plain,
( sz00 != xk
& sz10 != xk ),
inference(ennf_transformation,[],[f46]) ).
fof(f134,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xm) != sdtpldt0(sdtasdt0(xn,xm),X0) )
& ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) )
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(xp,xk) != sdtpldt0(sdtasdt0(xp,xm),X1) )
& ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ) ),
inference(ennf_transformation,[],[f60]) ).
fof(f148,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f122]) ).
fof(f149,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f148]) ).
fof(f150,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f149]) ).
fof(f151,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ( sz10 != sK4(X0)
& sK4(X0) != X0
& aNaturalNumber0(sK4(X0))
& doDivides0(sK4(X0),X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f150]) ).
fof(f161,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& aNaturalNumber0(sK10)
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK10)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10)],[f128]) ).
fof(f162,plain,
( xn != xp
& aNaturalNumber0(sK11)
& xp = sdtpldt0(xn,sK11)
& sdtlseqdt0(xn,xp)
& xm != xp
& aNaturalNumber0(sK12)
& xp = sdtpldt0(xm,sK12)
& sdtlseqdt0(xm,xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f57]) ).
fof(f165,plain,
( aNaturalNumber0(sK16)
& xk = sdtpldt0(xp,sK16)
& sdtlseqdt0(xp,xk) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f50]) ).
fof(f166,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f175,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f179,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f186,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f189,plain,
! [X0,X1] :
( sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f198,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f199,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f205,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f207,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f226,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f234,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f235,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f236,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f256,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f161]) ).
fof(f260,plain,
sz00 != xp,
inference(cnf_transformation,[],[f161]) ).
fof(f263,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f130]) ).
fof(f269,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f162]) ).
fof(f272,plain,
xn != xp,
inference(cnf_transformation,[],[f162]) ).
fof(f274,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f275,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f277,plain,
sz00 != xk,
inference(cnf_transformation,[],[f131]) ).
fof(f294,plain,
sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f165]) ).
fof(f297,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f311,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f226]) ).
fof(f315,definition,
( spl17_1
<=> sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
fof(f316,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| spl17_1 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f318,definition,
( spl17_2
<=> sdtasdt0(xp,xk) = sdtasdt0(xp,xm) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
fof(f319,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f321,definition,
( spl17_3
<=> sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f322,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| spl17_3 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f324,definition,
( spl17_4
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
fof(f325,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f326,plain,
( ~ spl17_1
| spl17_2
| ~ spl17_3
| spl17_4 ),
inference(avatar_split_clause,[],[f297,f324,f321,f318,f315]) ).
fof(f344,plain,
( ! [X0] :
( sdtasdt0(xp,X0) != sdtasdt0(xp,xm)
| xk = X0
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0)
| sz00 = xp
| ~ aNaturalNumber0(xp) )
| ~ spl17_2 ),
inference(superposition,[],[f186,f319]) ).
fof(f363,definition,
( spl17_8
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[spl17_8])],[avatar_definition]) ).
fof(f364,plain,
( ~ aNaturalNumber0(xp)
| spl17_8 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f369,definition,
( spl17_10
<=> sz00 = xp ),
introduced(definition,[new_symbols(definition,[spl17_10])],[avatar_definition]) ).
fof(f370,plain,
( sz00 = xp
| ~ spl17_10 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f372,definition,
( spl17_11
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[spl17_11])],[avatar_definition]) ).
fof(f373,plain,
( ~ aNaturalNumber0(xk)
| spl17_11 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f428,definition,
( spl17_25
<=> ! [X0] :
( sdtasdt0(xp,X0) != sdtasdt0(xp,xm)
| ~ aNaturalNumber0(X0)
| xk = X0 ) ),
introduced(definition,[new_symbols(definition,[spl17_25])],[avatar_definition]) ).
fof(f429,plain,
( ! [X0] :
( sdtasdt0(xp,X0) != sdtasdt0(xp,xm)
| ~ aNaturalNumber0(X0)
| xk = X0 )
| ~ spl17_25 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f431,plain,
( ~ spl17_8
| spl17_10
| ~ spl17_11
| spl17_25
| ~ spl17_2 ),
inference(avatar_split_clause,[],[f344,f318,f428,f372,f369,f363]) ).
fof(f459,plain,
( $false
| spl17_8 ),
inference(forward_subsumption_resolution,[],[f364,f234]) ).
fof(f460,plain,
spl17_8,
inference(avatar_contradiction_clause,[],[f459]) ).
fof(f461,plain,
( $false
| spl17_11 ),
inference(forward_subsumption_resolution,[],[f275,f373]) ).
fof(f462,plain,
spl17_11,
inference(avatar_contradiction_clause,[],[f461]) ).
fof(f475,plain,
( ! [X0] :
( sdtasdt0(xn,xm) != sdtasdt0(xp,X0)
| xm = X0
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| sz00 = xp
| ~ aNaturalNumber0(xp) )
| ~ spl17_4 ),
inference(superposition,[],[f186,f325]) ).
fof(f504,plain,
( ! [X0] :
( sdtasdt0(xn,xm) != sdtasdt0(xp,X0)
| xm = X0
| ~ aNaturalNumber0(X0)
| sz00 = xp
| ~ aNaturalNumber0(xp) )
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f475,f235]) ).
fof(f531,plain,
( ! [X0] :
( sdtasdt0(xn,xm) != sdtasdt0(xp,X0)
| xm = X0
| ~ aNaturalNumber0(X0)
| sz00 = xp )
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f504,f234]) ).
fof(f557,definition,
( spl17_35
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl17_35])],[avatar_definition]) ).
fof(f558,plain,
( sz00 = xm
| ~ spl17_35 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f600,definition,
( spl17_46
<=> ! [X0] :
( sdtasdt0(xn,xm) != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| xm = X0 ) ),
introduced(definition,[new_symbols(definition,[spl17_46])],[avatar_definition]) ).
fof(f601,plain,
( ! [X0] :
( sdtasdt0(xn,xm) != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| xm = X0 )
| ~ spl17_46 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f603,plain,
( spl17_10
| spl17_46
| ~ spl17_4 ),
inference(avatar_split_clause,[],[f531,f324,f600,f369]) ).
fof(f610,plain,
( isPrime0(sz00)
| ~ spl17_10 ),
inference(superposition,[],[f256,f370]) ).
fof(f612,plain,
( ~ aNaturalNumber0(sz00)
| ~ spl17_10 ),
inference(resolution,[],[f610,f311]) ).
fof(f613,plain,
( $false
| ~ spl17_10 ),
inference(forward_subsumption_resolution,[],[f612,f166]) ).
fof(f614,plain,
~ spl17_10,
inference(avatar_contradiction_clause,[],[f613]) ).
fof(f790,plain,
( sz00 = xp
| xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| spl17_1 ),
inference(resolution,[],[f316,f207]) ).
fof(f810,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f790,f260]) ).
fof(f813,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f810,f234]) ).
fof(f814,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xk)
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f813,f235]) ).
fof(f815,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f814,f275]) ).
fof(f817,definition,
( spl17_64
<=> sdtlseqdt0(xm,xk) ),
introduced(definition,[new_symbols(definition,[spl17_64])],[avatar_definition]) ).
fof(f818,plain,
( ~ sdtlseqdt0(xm,xk)
| spl17_64 ),
inference(avatar_component_clause,[],[f817]) ).
fof(f820,definition,
( spl17_65
<=> xm = xk ),
introduced(definition,[new_symbols(definition,[spl17_65])],[avatar_definition]) ).
fof(f821,plain,
( xm = xk
| ~ spl17_65 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f822,plain,
( ~ spl17_64
| spl17_65
| spl17_1 ),
inference(avatar_split_clause,[],[f815,f315,f820,f817]) ).
fof(f824,plain,
( sdtlseqdt0(xk,xm)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xm)
| spl17_64 ),
inference(resolution,[],[f818,f199]) ).
fof(f827,plain,
( sdtlseqdt0(xk,xm)
| ~ aNaturalNumber0(xm)
| spl17_64 ),
inference(forward_subsumption_resolution,[],[f824,f275]) ).
fof(f830,plain,
( sdtlseqdt0(xk,xm)
| spl17_64 ),
inference(forward_subsumption_resolution,[],[f827,f235]) ).
fof(f873,plain,
! [X0] :
( ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f263,f198]) ).
fof(f874,plain,
! [X0] :
( ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f873,f234]) ).
fof(f877,plain,
! [X0] :
( ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f874,f235]) ).
fof(f903,plain,
( sz00 = xm
| xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| spl17_3 ),
inference(resolution,[],[f322,f205]) ).
fof(f924,plain,
( sz00 = xm
| xn = xp
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f903,f269]) ).
fof(f927,plain,
( sz00 = xm
| xn = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f924,f235]) ).
fof(f928,plain,
( sz00 = xm
| xn = xp
| ~ aNaturalNumber0(xp)
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f927,f236]) ).
fof(f929,plain,
( sz00 = xm
| xn = xp
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f928,f234]) ).
fof(f1937,definition,
( spl17_118
<=> sz00 = sdtasdt0(xn,sz00) ),
introduced(definition,[new_symbols(definition,[spl17_118])],[avatar_definition]) ).
fof(f1938,plain,
( sz00 != sdtasdt0(xn,sz00)
| spl17_118 ),
inference(avatar_component_clause,[],[f1937]) ).
fof(f2007,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xn,sz00)
| ~ spl17_35 ),
inference(forward_demodulation,[],[f274,f558]) ).
fof(f2022,plain,
( sz00 != sdtasdt0(xn,sz00)
| sz00 = xk
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| ~ spl17_35 ),
inference(superposition,[],[f189,f2007]) ).
fof(f2045,plain,
( sz00 != sdtasdt0(xn,sz00)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| ~ spl17_35 ),
inference(forward_subsumption_resolution,[],[f2022,f277]) ).
fof(f2065,plain,
( sz00 != sdtasdt0(xn,sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| ~ spl17_35 ),
inference(forward_subsumption_resolution,[],[f2045,f260]) ).
fof(f2084,plain,
( sz00 != sdtasdt0(xn,sz00)
| ~ aNaturalNumber0(xk)
| ~ spl17_35 ),
inference(forward_subsumption_resolution,[],[f2065,f234]) ).
fof(f2090,plain,
( sz00 != sdtasdt0(xn,sz00)
| ~ spl17_35 ),
inference(forward_subsumption_resolution,[],[f2084,f275]) ).
fof(f2091,plain,
( ~ spl17_118
| ~ spl17_35 ),
inference(avatar_split_clause,[],[f2090,f557,f1937]) ).
fof(f2373,definition,
( spl17_126
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[spl17_126])],[avatar_definition]) ).
fof(f2374,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ spl17_126 ),
inference(avatar_component_clause,[],[f2373]) ).
fof(f2400,plain,
spl17_126,
inference(avatar_split_clause,[],[f274,f2373]) ).
fof(f2612,plain,
( sz00 != sdtasdt0(sz00,xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| spl17_118 ),
inference(superposition,[],[f1938,f175]) ).
fof(f2616,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| spl17_118 ),
inference(forward_subsumption_resolution,[],[f2612,f179]) ).
fof(f2620,plain,
( ~ aNaturalNumber0(xn)
| spl17_118 ),
inference(forward_subsumption_resolution,[],[f2616,f166]) ).
fof(f2623,plain,
( $false
| spl17_118 ),
inference(forward_subsumption_resolution,[],[f2620,f236]) ).
fof(f2624,plain,
spl17_118,
inference(avatar_contradiction_clause,[],[f2623]) ).
fof(f4402,plain,
( ~ aNaturalNumber0(xm)
| xm = xk
| ~ spl17_25 ),
inference(equality_resolution,[],[f429]) ).
fof(f4405,plain,
( xm = xk
| ~ spl17_25 ),
inference(forward_subsumption_resolution,[],[f4402,f235]) ).
fof(f4413,plain,
( spl17_65
| ~ spl17_25 ),
inference(avatar_split_clause,[],[f4405,f428,f820]) ).
fof(f4424,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xk)
| xm = xk
| ~ spl17_46
| ~ spl17_126 ),
inference(superposition,[],[f601,f2374]) ).
fof(f4434,plain,
( ~ aNaturalNumber0(xk)
| xm = xk
| ~ spl17_46
| ~ spl17_126 ),
inference(trivial_inequality_removal,[],[f4424]) ).
fof(f4441,plain,
( xm = xk
| ~ spl17_46
| ~ spl17_126 ),
inference(forward_subsumption_resolution,[],[f4434,f275]) ).
fof(f4444,plain,
( spl17_65
| ~ spl17_46
| ~ spl17_126 ),
inference(avatar_split_clause,[],[f4441,f2373,f600,f820]) ).
fof(f4838,plain,
( sdtlseqdt0(xp,xm)
| ~ spl17_65 ),
inference(superposition,[],[f294,f821]) ).
fof(f4861,plain,
( $false
| ~ spl17_65 ),
inference(forward_subsumption_resolution,[],[f4838,f263]) ).
fof(f4862,plain,
~ spl17_65,
inference(avatar_contradiction_clause,[],[f4861]) ).
fof(f6713,plain,
( ~ sdtlseqdt0(xk,xm)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f877,f294]) ).
fof(f6753,plain,
( ~ aNaturalNumber0(xk)
| spl17_64 ),
inference(forward_subsumption_resolution,[],[f6713,f830]) ).
fof(f6755,plain,
( $false
| spl17_64 ),
inference(forward_subsumption_resolution,[],[f6753,f275]) ).
fof(f6756,plain,
spl17_64,
inference(avatar_contradiction_clause,[],[f6755]) ).
fof(f6759,plain,
( sz00 = xm
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f929,f272]) ).
fof(f6771,plain,
( spl17_35
| spl17_3 ),
inference(avatar_split_clause,[],[f6759,f321,f557]) ).
cnf(s1,plain,
( ~ spl17_1
| spl17_2
| ~ spl17_3
| spl17_4 ),
inference(sat_conversion,[],[f326]) ).
cnf(s19,plain,
( ~ spl17_2
| ~ spl17_8
| spl17_10
| ~ spl17_11
| spl17_25 ),
inference(sat_conversion,[],[f431]) ).
cnf(s28,plain,
spl17_8,
inference(sat_conversion,[],[f460]) ).
cnf(s29,plain,
spl17_11,
inference(sat_conversion,[],[f462]) ).
cnf(s43,plain,
( ~ spl17_4
| spl17_10
| spl17_46 ),
inference(sat_conversion,[],[f603]) ).
cnf(s46,plain,
~ spl17_10,
inference(sat_conversion,[],[f614]) ).
cnf(s71,plain,
( spl17_1
| ~ spl17_64
| spl17_65 ),
inference(sat_conversion,[],[f822]) ).
cnf(s165,plain,
( ~ spl17_35
| ~ spl17_118 ),
inference(sat_conversion,[],[f2091]) ).
cnf(s193,plain,
spl17_126,
inference(sat_conversion,[],[f2400]) ).
cnf(s209,plain,
spl17_118,
inference(sat_conversion,[],[f2624]) ).
cnf(s360,plain,
( ~ spl17_25
| spl17_65 ),
inference(sat_conversion,[],[f4413]) ).
cnf(s361,plain,
( ~ spl17_46
| spl17_65
| ~ spl17_126 ),
inference(sat_conversion,[],[f4444]) ).
cnf(s392,plain,
~ spl17_65,
inference(sat_conversion,[],[f4862]) ).
cnf(s512,plain,
spl17_64,
inference(sat_conversion,[],[f6756]) ).
cnf(s515,plain,
( spl17_3
| spl17_35 ),
inference(sat_conversion,[],[f6771]) ).
cnf(s533,plain,
( ~ spl17_46
| ~ spl17_126 ),
inference(rat,[],[s361,s392]) ).
cnf(s534,plain,
~ spl17_25,
inference(rat,[],[s360,s392]) ).
cnf(s559,plain,
~ spl17_46,
inference(rat,[],[s533,s193]) ).
cnf(s562,plain,
~ spl17_35,
inference(rat,[],[s165,s209]) ).
cnf(s563,plain,
spl17_3,
inference(rat,[],[s515,s562]) ).
cnf(s575,plain,
spl17_1,
inference(rat,[],[s71,s392,s512]) ).
cnf(s582,plain,
~ spl17_4,
inference(rat,[],[s43,s559,s46]) ).
cnf(s591,plain,
~ spl17_2,
inference(rat,[],[s19,s534,s29,s46,s28]) ).
cnf(s601,plain,
$false,
inference(rat,[],[s1,s582,s563,s591,s575]) ).
fof(f6794,plain,
$false,
inference(avatar_sat_refutation,[],[s601]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM503+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n010.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % 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 20:14:17 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
% 10.42/2.37 % (1280012)Detected formulas, will run a generic FOF schedule.
% 10.42/2.37 % (1280116)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1599022879:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.42/2.37 % (1280116)Instruction limit reached!
% 10.42/2.37 % (1280116)------------------------------
% 10.42/2.37 % (1280116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280116)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280116)Termination reason: Instruction limit
% 10.42/2.37 % (1280116)Termination phase: Saturation
% 10.42/2.37 % (1280116)Time elapsed: 0.035 s
% 10.42/2.37 % (1280116)Peak memory usage: 88 MB
% 10.42/2.37 % (1280116)Instructions burned: 121 (million)
% 10.42/2.37 % (1280114)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=3312185717:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.42/2.37 % (1280115)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3606358310:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.42/2.37 % (1280113)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=345122791:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.42/2.37 % (1280112)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=4225496243:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.42/2.37 % (1280117)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1458010267:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.42/2.37 % (1280118)dis-21_1_sil=8000:lcm=predicate:random_seed=1905745674: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)
% 10.42/2.37 % (1280115)Instruction limit reached!
% 10.42/2.37 % (1280115)------------------------------
% 10.42/2.37 % (1280115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280115)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280115)Termination reason: Instruction limit
% 10.42/2.37 % (1280115)Termination phase: Saturation
% 10.42/2.37 % (1280115)Time elapsed: 0.063 s
% 10.42/2.37 % (1280115)Peak memory usage: 89 MB
% 10.42/2.37 % (1280115)Instructions burned: 110 (million)
% 10.42/2.37 % (1280117)Instruction limit reached!
% 10.42/2.37 % (1280117)------------------------------
% 10.42/2.37 % (1280117)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280117)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280117)Termination reason: Instruction limit
% 10.42/2.37 % (1280117)Termination phase: Saturation
% 10.42/2.37 % (1280117)Time elapsed: 0.090 s
% 10.42/2.37 % (1280117)Peak memory usage: 90 MB
% 10.42/2.37 % (1280117)Instructions burned: 140 (million)
% 10.42/2.37 % (1280118)Instruction limit reached!
% 10.42/2.37 % (1280118)------------------------------
% 10.42/2.37 % (1280118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280118)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280118)Termination reason: Instruction limit
% 10.42/2.37 % (1280118)Termination phase: Saturation
% 10.42/2.37 % (1280118)Time elapsed: 0.080 s
% 10.42/2.37 % (1280118)Peak memory usage: 91 MB
% 10.42/2.37 % (1280118)Instructions burned: 131 (million)
% 10.42/2.37 % (1280131)lrs+10_1_sil=8000:sp=occurrence:random_seed=2461380506:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 10.42/2.37 % (1280131)Instruction limit reached!
% 10.42/2.37 % (1280131)------------------------------
% 10.42/2.37 % (1280131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280131)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280131)Termination reason: Instruction limit
% 10.42/2.37 % (1280131)Termination phase: Saturation
% 10.42/2.37 % (1280131)Time elapsed: 0.082 s
% 10.42/2.37 % (1280131)Peak memory usage: 91 MB
% 10.42/2.37 % (1280131)Instructions burned: 286 (million)
% 10.42/2.37 % (1280133)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2790771398:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.42/2.37 % (1280134)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3036814184:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.42/2.37 % (1280140)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=55259225:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 10.42/2.37 % (1280150)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3384389071:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 10.42/2.37 % (1280133)Instruction limit reached!
% 10.42/2.37 % (1280133)------------------------------
% 10.42/2.37 % (1280133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280133)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280133)Termination reason: Instruction limit
% 10.42/2.37 % (1280133)Termination phase: Saturation
% 10.42/2.37 % (1280133)Time elapsed: 0.135 s
% 10.42/2.37 % (1280133)Peak memory usage: 91 MB
% 10.42/2.37 % (1280133)Instructions burned: 157 (million)
% 10.42/2.37 % (1280140)Instruction limit reached!
% 10.42/2.37 % (1280140)------------------------------
% 10.42/2.37 % (1280140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280140)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280140)Termination reason: Instruction limit
% 10.42/2.37 % (1280140)Termination phase: Saturation
% 10.42/2.37 % (1280140)Time elapsed: 0.114 s
% 10.42/2.37 % (1280140)Peak memory usage: 94 MB
% 10.42/2.37 % (1280140)Instructions burned: 248 (million)
% 10.42/2.37 % (1280150)Instruction limit reached!
% 10.42/2.37 % (1280150)------------------------------
% 10.42/2.37 % (1280150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280150)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280150)Termination reason: Instruction limit
% 10.42/2.37 % (1280150)Termination phase: Saturation
% 10.42/2.37 % (1280150)Time elapsed: 0.086 s
% 10.42/2.37 % (1280150)Peak memory usage: 89 MB
% 10.42/2.37 % (1280150)Instructions burned: 296 (million)
% 10.42/2.37 % (1280134)Instruction limit reached!
% 10.42/2.37 % (1280134)------------------------------
% 10.42/2.37 % (1280134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280134)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280134)Termination reason: Instruction limit
% 10.42/2.37 % (1280134)Termination phase: Saturation
% 10.42/2.37 % (1280134)Time elapsed: 0.201 s
% 10.42/2.37 % (1280134)Peak memory usage: 92 MB
% 10.42/2.37 % (1280134)Instructions burned: 326 (million)
% 10.42/2.37 % (1280155)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2819937712:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 10.42/2.37 % (1280157)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3446412074:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 10.42/2.37 % (1280156)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2079681679:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 10.42/2.37 % (1280157)Instruction limit reached!
% 10.42/2.37 % (1280157)------------------------------
% 10.42/2.37 % (1280157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280157)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280157)Termination reason: Instruction limit
% 10.42/2.37 % (1280157)Termination phase: Saturation
% 10.42/2.37 % (1280157)Time elapsed: 0.033 s
% 10.42/2.37 % (1280157)Peak memory usage: 89 MB
% 10.42/2.37 % (1280157)Instructions burned: 130 (million)
% 10.42/2.37 % (1280158)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3393532615:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 10.42/2.37 % (1280156)Instruction limit reached!
% 10.42/2.37 % (1280156)------------------------------
% 10.42/2.37 % (1280156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280156)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280156)Termination reason: Instruction limit
% 10.42/2.37 % (1280156)Termination phase: Saturation
% 10.42/2.37 % (1280156)Time elapsed: 0.068 s
% 10.42/2.37 % (1280156)Peak memory usage: 90 MB
% 10.42/2.37 % (1280156)Instructions burned: 113 (million)
% 10.42/2.37 % (1280158)Instruction limit reached!
% 10.42/2.37 % (1280158)------------------------------
% 10.42/2.37 % (1280158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280158)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280158)Termination reason: Instruction limit
% 10.42/2.37 % (1280158)Termination phase: Saturation
% 10.42/2.37 % (1280158)Time elapsed: 0.057 s
% 10.42/2.37 % (1280158)Peak memory usage: 89 MB
% 10.42/2.37 % (1280158)Instructions burned: 116 (million)
% 10.42/2.37 % (1280162)lrs+10_1_sil=8000:sp=occurrence:random_seed=3571312146:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 10.42/2.37 % (1280164)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3624240427:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 10.42/2.37 % (1280165)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3070020601:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 10.42/2.37 % (1280164)First to succeed.
% 10.42/2.37 % (1280164)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1280012"
% 10.42/2.37 % (1280162)Instruction limit reached!
% 10.42/2.37 % (1280162)------------------------------
% 10.42/2.37 % (1280162)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.42/2.37 % (1280162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.42/2.37 % (1280162)CaDiCaL version: 2.1.3
% 10.42/2.37 % (1280162)Termination reason: Instruction limit
% 10.42/2.37 % (1280162)Termination phase: Saturation
% 10.42/2.37 % (1280162)Time elapsed: 0.410 s
% 10.42/2.37 % (1280162)Peak memory usage: 98 MB
% 10.42/2.37 % (1280162)Instructions burned: 907 (million)
% 10.42/2.37 % (1280112)Also succeeded, but the first one will report.
% 10.42/2.37 % (1280187)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1981135314:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 10.42/2.37 % (1280164)Refutation found. Thanks to Tanya!
% 10.42/2.37 % SZS status Theorem for theBenchmark
% 10.42/2.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/2.61 % (1280164)------------------------------
% 0.15/2.61 % (1280164)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/2.61 % (1280164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/2.61 % (1280164)CaDiCaL version: 2.1.3
% 0.15/2.61 % (1280164)Termination reason: Refutation
% 0.15/2.61 % (1280164)Time elapsed: 0.180 s
% 0.15/2.61 % (1280164)Peak memory usage: 91 MB
% 0.15/2.61 % (1280164)Instructions burned: 200 (million)
% 0.15/2.61 % (1280164)------------------------------
% 0.15/2.61 % (1280164)------------------------------
% 0.15/2.61 % (1280012)Success in time 1.506 s
% 0.15/2.61 % Vampire exiting
%------------------------------------------------------------------------------