TSTP Solution File: NUM476+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM476+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:30:48 EDT 2024
% Result : Theorem 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 16
% Syntax : Number of formulae : 110 ( 20 unt; 0 def)
% Number of atoms : 432 ( 163 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 515 ( 193 ~; 214 |; 82 &)
% ( 9 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 127 ( 103 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6644,plain,
$false,
inference(resolution,[],[f5921,f3185]) ).
fof(f3185,plain,
~ doDivides0(sz00,xn),
inference(backward_demodulation,[],[f121,f3182]) ).
fof(f3182,plain,
sz00 = xl,
inference(resolution,[],[f3181,f122]) ).
fof(f122,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f3181,plain,
( ~ aNaturalNumber0(xl)
| sz00 = xl ),
inference(resolution,[],[f3180,f124]) ).
fof(f124,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f3180,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| sz00 = xl ),
inference(resolution,[],[f3179,f123]) ).
fof(f123,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f3179,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| sz00 = xl ),
inference(duplicate_literal_removal,[],[f3178]) ).
fof(f3178,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sz00 = xl
| sz00 = xl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[],[f3175,f1127]) ).
fof(f1127,plain,
( aNaturalNumber0(sK2)
| sz00 = xl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[],[f1121,f125]) ).
fof(f125,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
( doDivides0(xl,sdtpldt0(xm,xn))
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
fof(f1121,plain,
( ~ doDivides0(xl,xm)
| aNaturalNumber0(sK2)
| sz00 = xl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(duplicate_literal_removal,[],[f1118]) ).
fof(f1118,plain,
( aNaturalNumber0(sK2)
| ~ doDivides0(xl,xm)
| sz00 = xl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| sz00 = xl ),
inference(superposition,[],[f188,f117]) ).
fof(f117,plain,
( sdtsldt0(xm,xl) = sK2
| sz00 = xl ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
( ~ doDivides0(xl,xn)
& ( ( sP0(sK2,sK3)
& sdtlseqdt0(sK2,sK3)
& sdtsldt0(sdtpldt0(xm,xn),xl) = sK3
& sdtsldt0(xm,xl) = sK2 )
| sz00 = xl ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f95,f100,f99]) ).
fof(f99,plain,
( ? [X0] :
( ? [X1] :
( sP0(X0,X1)
& sdtlseqdt0(X0,X1)
& sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
& sdtsldt0(xm,xl) = X0 )
=> ( ? [X1] :
( sP0(sK2,X1)
& sdtlseqdt0(sK2,X1)
& sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
& sdtsldt0(xm,xl) = sK2 ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
( ? [X1] :
( sP0(sK2,X1)
& sdtlseqdt0(sK2,X1)
& sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
=> ( sP0(sK2,sK3)
& sdtlseqdt0(sK2,sK3)
& sdtsldt0(sdtpldt0(xm,xn),xl) = sK3 ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
( ~ doDivides0(xl,xn)
& ( ? [X0] :
( ? [X1] :
( sP0(X0,X1)
& sdtlseqdt0(X0,X1)
& sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
& sdtsldt0(xm,xl) = X0 )
| sz00 = xl ) ),
inference(definition_folding,[],[f41,f94]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] :
( xn = sdtasdt0(xl,X2)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& sdtmndt0(X1,X0) = X2 )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f41,plain,
( ~ doDivides0(xl,xn)
& ( ? [X0] :
( ? [X1] :
( ? [X2] :
( xn = sdtasdt0(xl,X2)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& sdtmndt0(X1,X0) = X2 )
& sdtlseqdt0(X0,X1)
& sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
& sdtsldt0(xm,xl) = X0 )
| sz00 = xl ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,negated_conjecture,
~ ( ( sz00 != xl
=> ? [X0] :
( ? [X1] :
( ? [X2] :
( xn = sdtasdt0(xl,X2)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& sdtmndt0(X1,X0) = X2 )
& sdtlseqdt0(X0,X1)
& sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
& sdtsldt0(xm,xl) = X0 ) )
=> doDivides0(xl,xn) ),
inference(negated_conjecture,[],[f36]) ).
fof(f36,conjecture,
( ( sz00 != xl
=> ? [X0] :
( ? [X1] :
( ? [X2] :
( xn = sdtasdt0(xl,X2)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& sdtmndt0(X1,X0) = X2 )
& sdtlseqdt0(X0,X1)
& sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
& sdtsldt0(xm,xl) = X0 ) )
=> doDivides0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f188,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f158]) ).
fof(f158,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f3175,plain,
( ~ aNaturalNumber0(sK2)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sz00 = xl ),
inference(duplicate_literal_removal,[],[f3115]) ).
fof(f3115,plain,
( sz00 = xl
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sz00 = xl
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK2) ),
inference(resolution,[],[f3112,f925]) ).
fof(f925,plain,
( ~ aNaturalNumber0(sK3)
| sz00 = xl
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK2) ),
inference(duplicate_literal_removal,[],[f922]) ).
fof(f922,plain,
( ~ aNaturalNumber0(xl)
| sz00 = xl
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(sK2)
| sz00 = xl ),
inference(resolution,[],[f921,f119]) ).
fof(f119,plain,
( sdtlseqdt0(sK2,sK3)
| sz00 = xl ),
inference(cnf_transformation,[],[f101]) ).
fof(f921,plain,
( ~ sdtlseqdt0(sK2,sK3)
| ~ aNaturalNumber0(xl)
| sz00 = xl
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(sK2) ),
inference(resolution,[],[f920,f185]) ).
fof(f185,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f148]) ).
fof(f148,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f920,plain,
( ~ aNaturalNumber0(sdtmndt0(sK3,sK2))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| sz00 = xl ),
inference(duplicate_literal_removal,[],[f919]) ).
fof(f919,plain,
( ~ aNaturalNumber0(sdtmndt0(sK3,sK2))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| sz00 = xl
| sz00 = xl ),
inference(superposition,[],[f916,f262]) ).
fof(f262,plain,
( sdtmndt0(sK3,sK2) = sK1(sK2,sK3)
| sz00 = xl ),
inference(resolution,[],[f114,f120]) ).
fof(f120,plain,
( sP0(sK2,sK3)
| sz00 = xl ),
inference(cnf_transformation,[],[f101]) ).
fof(f114,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sdtmndt0(X1,X0) = sK1(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( xn = sdtasdt0(xl,sK1(X0,X1))
& sdtpldt0(sdtasdt0(xl,X0),xn) = sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,sK1(X0,X1)))
& sdtmndt0(X1,X0) = sK1(X0,X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f96,f97]) ).
fof(f97,plain,
! [X0,X1] :
( ? [X2] :
( xn = sdtasdt0(xl,X2)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& sdtmndt0(X1,X0) = X2 )
=> ( xn = sdtasdt0(xl,sK1(X0,X1))
& sdtpldt0(sdtasdt0(xl,X0),xn) = sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,sK1(X0,X1)))
& sdtmndt0(X1,X0) = sK1(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X2] :
( xn = sdtasdt0(xl,X2)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& sdtmndt0(X1,X0) = X2 )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f94]) ).
fof(f916,plain,
( ~ aNaturalNumber0(sK1(sK2,sK3))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| sz00 = xl ),
inference(resolution,[],[f811,f121]) ).
fof(f811,plain,
( doDivides0(xl,xn)
| ~ aNaturalNumber0(sK1(sK2,sK3))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| sz00 = xl ),
inference(superposition,[],[f189,f263]) ).
fof(f263,plain,
( xn = sdtasdt0(xl,sK1(sK2,sK3))
| sz00 = xl ),
inference(resolution,[],[f116,f120]) ).
fof(f116,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| xn = sdtasdt0(xl,sK1(X0,X1)) ),
inference(cnf_transformation,[],[f98]) ).
fof(f189,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f164]) ).
fof(f164,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtasdt0(X0,sK4(X0,X1)) = X1
& aNaturalNumber0(sK4(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f107,f108]) ).
fof(f108,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK4(X0,X1)) = X1
& aNaturalNumber0(sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f3112,plain,
( aNaturalNumber0(sK3)
| sz00 = xl
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f3092,f141]) ).
fof(f141,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f3092,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sz00 = xl
| aNaturalNumber0(sK3)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[],[f1120,f317]) ).
fof(f317,plain,
doDivides0(xl,sdtpldt0(xn,xm)),
inference(backward_demodulation,[],[f126,f315]) ).
fof(f315,plain,
sdtpldt0(xm,xn) = sdtpldt0(xn,xm),
inference(resolution,[],[f273,f124]) ).
fof(f273,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,xm) = sdtpldt0(xm,X0) ),
inference(resolution,[],[f143,f123]) ).
fof(f143,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f126,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f35]) ).
fof(f1120,plain,
( ~ doDivides0(xl,sdtpldt0(xn,xm))
| aNaturalNumber0(sK3)
| sz00 = xl
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xl) ),
inference(duplicate_literal_removal,[],[f1119]) ).
fof(f1119,plain,
( aNaturalNumber0(sK3)
| ~ doDivides0(xl,sdtpldt0(xn,xm))
| sz00 = xl
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xl)
| sz00 = xl ),
inference(superposition,[],[f188,f318]) ).
fof(f318,plain,
( sK3 = sdtsldt0(sdtpldt0(xn,xm),xl)
| sz00 = xl ),
inference(backward_demodulation,[],[f118,f315]) ).
fof(f118,plain,
( sdtsldt0(sdtpldt0(xm,xn),xl) = sK3
| sz00 = xl ),
inference(cnf_transformation,[],[f101]) ).
fof(f121,plain,
~ doDivides0(xl,xn),
inference(cnf_transformation,[],[f101]) ).
fof(f5921,plain,
doDivides0(sz00,xn),
inference(forward_demodulation,[],[f5372,f206]) ).
fof(f206,plain,
xn = sdtpldt0(xn,sz00),
inference(resolution,[],[f133,f124]) ).
fof(f133,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f5372,plain,
doDivides0(sz00,sdtpldt0(xn,sz00)),
inference(backward_demodulation,[],[f3201,f5220]) ).
fof(f5220,plain,
sz00 = xm,
inference(resolution,[],[f5219,f127]) ).
fof(f127,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f5219,plain,
( ~ aNaturalNumber0(sz00)
| sz00 = xm ),
inference(resolution,[],[f5217,f123]) ).
fof(f5217,plain,
( ~ aNaturalNumber0(xm)
| sz00 = xm
| ~ aNaturalNumber0(sz00) ),
inference(forward_demodulation,[],[f5193,f3728]) ).
fof(f3728,plain,
xm = sdtasdt0(sz00,sK4(sz00,xm)),
inference(resolution,[],[f3727,f127]) ).
fof(f3727,plain,
( ~ aNaturalNumber0(sz00)
| xm = sdtasdt0(sz00,sK4(sz00,xm)) ),
inference(resolution,[],[f3443,f123]) ).
fof(f3443,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| xm = sdtasdt0(sz00,sK4(sz00,xm)) ),
inference(forward_demodulation,[],[f3253,f3182]) ).
fof(f3253,plain,
( ~ aNaturalNumber0(sz00)
| xm = sdtasdt0(xl,sK4(xl,xm))
| ~ aNaturalNumber0(xm) ),
inference(backward_demodulation,[],[f886,f3182]) ).
fof(f886,plain,
( xm = sdtasdt0(xl,sK4(xl,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[],[f163,f125]) ).
fof(f163,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sdtasdt0(X0,sK4(X0,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f5193,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| sz00 = sdtasdt0(sz00,sK4(sz00,xm)) ),
inference(resolution,[],[f321,f3187]) ).
fof(f3187,plain,
doDivides0(sz00,xm),
inference(backward_demodulation,[],[f125,f3182]) ).
fof(f321,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,sK4(X0,X1)) ),
inference(resolution,[],[f162,f132]) ).
fof(f132,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f162,plain,
! [X0,X1] :
( aNaturalNumber0(sK4(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f3201,plain,
doDivides0(sz00,sdtpldt0(xn,xm)),
inference(backward_demodulation,[],[f317,f3182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM476+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri May 3 14:11:53 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (9050)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (9051)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (9055)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (9057)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 % (9056)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 TRYING [3]
% 0.14/0.38 % (9054)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (9053)WARNING: value z3 for option sas not known
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (9053)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 TRYING [3]
% 0.14/0.38 % (9052)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40 TRYING [4]
% 0.20/0.40 TRYING [4]
% 0.20/0.47 TRYING [5]
% 0.20/0.47 TRYING [1]
% 0.20/0.47 TRYING [2]
% 0.20/0.47 TRYING [3]
% 0.20/0.47 TRYING [5]
% 0.20/0.47 TRYING [4]
% 0.20/0.52 TRYING [5]
% 0.20/0.54 % (9056)First to succeed.
% 0.20/0.55 % (9056)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9050"
% 0.20/0.55 % (9056)Refutation found. Thanks to Tanya!
% 0.20/0.55 % SZS status Theorem for theBenchmark
% 0.20/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55 % (9056)------------------------------
% 0.20/0.55 % (9056)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.55 % (9056)Termination reason: Refutation
% 0.20/0.55
% 0.20/0.55 % (9056)Memory used [KB]: 3660
% 0.20/0.55 % (9056)Time elapsed: 0.178 s
% 0.20/0.55 % (9056)Instructions burned: 469 (million)
% 0.20/0.55 % (9050)Success in time 0.201 s
%------------------------------------------------------------------------------