TSTP Solution File: NUM500+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM500+3 : 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 : n008.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 : Tue Apr 30 14:28:25 EDT 2024
% Result : Theorem 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 40
% Syntax : Number of formulae : 150 ( 17 unt; 0 def)
% Number of atoms : 611 ( 225 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 720 ( 259 ~; 220 |; 206 &)
% ( 20 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 20 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 112 ( 70 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1184,plain,
$false,
inference(avatar_sat_refutation,[],[f342,f353,f611,f620,f981,f994,f1016,f1022,f1070,f1155,f1160,f1183]) ).
fof(f1183,plain,
spl21_19,
inference(avatar_contradiction_clause,[],[f1182]) ).
fof(f1182,plain,
( $false
| spl21_19 ),
inference(subsumption_resolution,[],[f1181,f199]) ).
fof(f199,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f1181,plain,
( ~ aNaturalNumber0(xk)
| spl21_19 ),
inference(subsumption_resolution,[],[f1180,f213]) ).
fof(f213,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
( sz10 != xk
& sz00 != xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
fof(f1180,plain,
( sz00 = xk
| ~ aNaturalNumber0(xk)
| spl21_19 ),
inference(subsumption_resolution,[],[f1179,f214]) ).
fof(f214,plain,
sz10 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f1179,plain,
( sz10 = xk
| sz00 = xk
| ~ aNaturalNumber0(xk)
| spl21_19 ),
inference(resolution,[],[f1154,f272]) ).
fof(f272,plain,
! [X0] :
( isPrime0(sK18(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0] :
( ( isPrime0(sK18(X0))
& doDivides0(sK18(X0),X0)
& aNaturalNumber0(sK18(X0)) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f76,f174]) ).
fof(f174,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( isPrime0(sK18(X0))
& doDivides0(sK18(X0),X0)
& aNaturalNumber0(sK18(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ( sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) )
=> ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
fof(f1154,plain,
( ~ isPrime0(sK18(xk))
| spl21_19 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f1152,plain,
( spl21_19
<=> isPrime0(sK18(xk)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_19])]) ).
fof(f1160,plain,
spl21_18,
inference(avatar_contradiction_clause,[],[f1159]) ).
fof(f1159,plain,
( $false
| spl21_18 ),
inference(subsumption_resolution,[],[f1158,f199]) ).
fof(f1158,plain,
( ~ aNaturalNumber0(xk)
| spl21_18 ),
inference(subsumption_resolution,[],[f1157,f213]) ).
fof(f1157,plain,
( sz00 = xk
| ~ aNaturalNumber0(xk)
| spl21_18 ),
inference(subsumption_resolution,[],[f1156,f214]) ).
fof(f1156,plain,
( sz10 = xk
| sz00 = xk
| ~ aNaturalNumber0(xk)
| spl21_18 ),
inference(resolution,[],[f1150,f270]) ).
fof(f270,plain,
! [X0] :
( aNaturalNumber0(sK18(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f1150,plain,
( ~ aNaturalNumber0(sK18(xk))
| spl21_18 ),
inference(avatar_component_clause,[],[f1148]) ).
fof(f1148,plain,
( spl21_18
<=> aNaturalNumber0(sK18(xk)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_18])]) ).
fof(f1155,plain,
( ~ spl21_18
| ~ spl21_19 ),
inference(avatar_split_clause,[],[f1143,f1152,f1148]) ).
fof(f1143,plain,
( ~ isPrime0(sK18(xk))
| ~ aNaturalNumber0(sK18(xk)) ),
inference(subsumption_resolution,[],[f1142,f199]) ).
fof(f1142,plain,
( ~ aNaturalNumber0(xk)
| ~ isPrime0(sK18(xk))
| ~ aNaturalNumber0(sK18(xk)) ),
inference(subsumption_resolution,[],[f1141,f213]) ).
fof(f1141,plain,
( sz00 = xk
| ~ aNaturalNumber0(xk)
| ~ isPrime0(sK18(xk))
| ~ aNaturalNumber0(sK18(xk)) ),
inference(subsumption_resolution,[],[f1136,f214]) ).
fof(f1136,plain,
( sz10 = xk
| sz00 = xk
| ~ aNaturalNumber0(xk)
| ~ isPrime0(sK18(xk))
| ~ aNaturalNumber0(sK18(xk)) ),
inference(resolution,[],[f271,f198]) ).
fof(f198,plain,
! [X0] :
( ~ doDivides0(X0,xk)
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( sP1(X0)
| sz10 = X0
| sz00 = X0 ) )
| ( ~ doDivides0(X0,xk)
& ! [X1] :
( sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( sP1(X0)
| sz10 = X0
| sz00 = X0 ) )
| ( ~ doDivides0(X0,xk)
& ! [X3] :
( xk != sdtasdt0(X0,X3)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f57,f130,f129]) ).
fof(f129,plain,
! [X0,X1] :
( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f130,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& sP0(X0,X1)
& aNaturalNumber0(X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f57,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 ) )
| ( ~ doDivides0(X0,xk)
& ! [X3] :
( xk != sdtasdt0(X0,X3)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 ) )
| ( ~ doDivides0(X0,xk)
& ! [X3] :
( xk != sdtasdt0(X0,X3)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,plain,
~ ? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) )
& ( doDivides0(X0,xk)
| ? [X3] :
( xk = sdtasdt0(X0,X3)
& aNaturalNumber0(X3) ) )
& aNaturalNumber0(X0) ),
inference(rectify,[],[f49]) ).
fof(f49,negated_conjecture,
~ ? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) )
& ( doDivides0(X0,xk)
| ? [X1] :
( sdtasdt0(X0,X1) = xk
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) )
& ( doDivides0(X0,xk)
| ? [X1] :
( sdtasdt0(X0,X1) = xk
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f271,plain,
! [X0] :
( doDivides0(sK18(X0),X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f1070,plain,
( ~ spl21_16
| ~ spl21_17 ),
inference(avatar_split_clause,[],[f1061,f1067,f1063]) ).
fof(f1063,plain,
( spl21_16
<=> isPrime0(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_16])]) ).
fof(f1067,plain,
( spl21_17
<=> xk = sdtasdt0(xn,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_17])]) ).
fof(f1061,plain,
( xk != sdtasdt0(xn,sK12)
| ~ isPrime0(sK12) ),
inference(subsumption_resolution,[],[f1060,f220]) ).
fof(f220,plain,
aNaturalNumber0(sK12),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK12)
& aNaturalNumber0(sK12)
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f59,f150]) ).
fof(f150,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK12)
& aNaturalNumber0(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( sdtasdt0(X1,X2) = xp
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( xp = X1
| sz10 = X1 ) )
& sz10 != xp
& sz00 != xp ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( sdtasdt0(X0,X1) = xp
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xp = X0
| sz10 = X0 ) )
& sz10 != xp
& sz00 != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f1060,plain,
( xk != sdtasdt0(xn,sK12)
| ~ isPrime0(sK12)
| ~ aNaturalNumber0(sK12) ),
inference(subsumption_resolution,[],[f1058,f202]) ).
fof(f202,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f1058,plain,
( xk != sdtasdt0(xn,sK12)
| ~ isPrime0(sK12)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK12) ),
inference(superposition,[],[f197,f933]) ).
fof(f933,plain,
sdtasdt0(sK12,xn) = sdtasdt0(xn,sK12),
inference(resolution,[],[f716,f220]) ).
fof(f716,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xn) = sdtasdt0(xn,X0) ),
inference(resolution,[],[f276,f202]) ).
fof(f276,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f197,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) != xk
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f1022,plain,
( spl21_13
| spl21_15 ),
inference(avatar_contradiction_clause,[],[f1021]) ).
fof(f1021,plain,
( $false
| spl21_13
| spl21_15 ),
inference(subsumption_resolution,[],[f1020,f213]) ).
fof(f1020,plain,
( sz00 = xk
| spl21_13
| spl21_15 ),
inference(subsumption_resolution,[],[f1019,f214]) ).
fof(f1019,plain,
( sz10 = xk
| sz00 = xk
| spl21_13
| spl21_15 ),
inference(subsumption_resolution,[],[f1018,f1014]) ).
fof(f1014,plain,
( ~ sP6(xk)
| spl21_15 ),
inference(avatar_component_clause,[],[f1013]) ).
fof(f1013,plain,
( spl21_15
<=> sP6(xk) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_15])]) ).
fof(f1018,plain,
( sP6(xk)
| sz10 = xk
| sz00 = xk
| spl21_13 ),
inference(resolution,[],[f1007,f265]) ).
fof(f265,plain,
! [X0] :
( aNaturalNumber0(sK17(X0))
| sP6(X0)
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f173]) ).
fof(f173,plain,
! [X0] :
( ( sP6(X0)
| ( sK17(X0) != X0
& sz10 != sK17(X0)
& doDivides0(sK17(X0),X0)
& aNaturalNumber0(sK17(X0)) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ sP6(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f171,f172]) ).
fof(f172,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK17(X0) != X0
& sz10 != sK17(X0)
& doDivides0(sK17(X0),X0)
& aNaturalNumber0(sK17(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f171,plain,
! [X0] :
( ( sP6(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ sP6(X0) ) ),
inference(rectify,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ( sP6(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ sP6(X0) ) ),
inference(flattening,[],[f169]) ).
fof(f169,plain,
! [X0] :
( ( sP6(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ sP6(X0) ) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0] :
( sP6(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f1007,plain,
( ~ aNaturalNumber0(sK17(xk))
| spl21_13 ),
inference(avatar_component_clause,[],[f1005]) ).
fof(f1005,plain,
( spl21_13
<=> aNaturalNumber0(sK17(xk)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_13])]) ).
fof(f1016,plain,
( ~ spl21_13
| ~ spl21_14
| spl21_15 ),
inference(avatar_split_clause,[],[f1001,f1013,f1009,f1005]) ).
fof(f1009,plain,
( spl21_14
<=> isPrime0(sK17(xk)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_14])]) ).
fof(f1001,plain,
( sP6(xk)
| ~ isPrime0(sK17(xk))
| ~ aNaturalNumber0(sK17(xk)) ),
inference(subsumption_resolution,[],[f1000,f213]) ).
fof(f1000,plain,
( sP6(xk)
| sz00 = xk
| ~ isPrime0(sK17(xk))
| ~ aNaturalNumber0(sK17(xk)) ),
inference(subsumption_resolution,[],[f996,f214]) ).
fof(f996,plain,
( sP6(xk)
| sz10 = xk
| sz00 = xk
| ~ isPrime0(sK17(xk))
| ~ aNaturalNumber0(sK17(xk)) ),
inference(resolution,[],[f266,f198]) ).
fof(f266,plain,
! [X0] :
( doDivides0(sK17(X0),X0)
| sP6(X0)
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f173]) ).
fof(f994,plain,
( ~ spl21_11
| ~ spl21_12 ),
inference(avatar_split_clause,[],[f985,f991,f987]) ).
fof(f987,plain,
( spl21_11
<=> isPrime0(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_11])]) ).
fof(f991,plain,
( spl21_12
<=> xk = sdtasdt0(xn,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_12])]) ).
fof(f985,plain,
( xk != sdtasdt0(xn,sK11)
| ~ isPrime0(sK11) ),
inference(subsumption_resolution,[],[f984,f206]) ).
fof(f206,plain,
aNaturalNumber0(sK11),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
( sdtlseqdt0(xm,xp)
& xp = sdtpldt0(xm,sK10)
& aNaturalNumber0(sK10)
& xm != xp
& sdtlseqdt0(xn,xp)
& xp = sdtpldt0(xn,sK11)
& aNaturalNumber0(sK11)
& xn != xp ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f51,f148,f147]) ).
fof(f147,plain,
( ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
=> ( xp = sdtpldt0(xm,sK10)
& aNaturalNumber0(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f148,plain,
( ? [X1] :
( xp = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
=> ( xp = sdtpldt0(xn,sK11)
& aNaturalNumber0(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
( sdtlseqdt0(xm,xp)
& ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X1] :
( xp = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& xn != xp ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
( sdtlseqdt0(xm,xp)
& ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X0] :
( xp = sdtpldt0(xn,X0)
& aNaturalNumber0(X0) )
& xn != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(f984,plain,
( xk != sdtasdt0(xn,sK11)
| ~ isPrime0(sK11)
| ~ aNaturalNumber0(sK11) ),
inference(subsumption_resolution,[],[f982,f202]) ).
fof(f982,plain,
( xk != sdtasdt0(xn,sK11)
| ~ isPrime0(sK11)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK11) ),
inference(superposition,[],[f197,f932]) ).
fof(f932,plain,
sdtasdt0(sK11,xn) = sdtasdt0(xn,sK11),
inference(resolution,[],[f716,f206]) ).
fof(f981,plain,
( ~ spl21_9
| ~ spl21_10 ),
inference(avatar_split_clause,[],[f972,f978,f974]) ).
fof(f974,plain,
( spl21_9
<=> isPrime0(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_9])]) ).
fof(f978,plain,
( spl21_10
<=> xk = sdtasdt0(xn,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_10])]) ).
fof(f972,plain,
( xk != sdtasdt0(xn,sK10)
| ~ isPrime0(sK10) ),
inference(subsumption_resolution,[],[f971,f210]) ).
fof(f210,plain,
aNaturalNumber0(sK10),
inference(cnf_transformation,[],[f149]) ).
fof(f971,plain,
( xk != sdtasdt0(xn,sK10)
| ~ isPrime0(sK10)
| ~ aNaturalNumber0(sK10) ),
inference(subsumption_resolution,[],[f969,f202]) ).
fof(f969,plain,
( xk != sdtasdt0(xn,sK10)
| ~ isPrime0(sK10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK10) ),
inference(superposition,[],[f197,f931]) ).
fof(f931,plain,
sdtasdt0(sK10,xn) = sdtasdt0(xn,sK10),
inference(resolution,[],[f716,f210]) ).
fof(f620,plain,
( ~ spl21_7
| ~ spl21_8 ),
inference(avatar_split_clause,[],[f577,f617,f613]) ).
fof(f613,plain,
( spl21_7
<=> isPrime0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_7])]) ).
fof(f617,plain,
( spl21_8
<=> xm = xk ),
introduced(avatar_definition,[new_symbols(naming,[spl21_8])]) ).
fof(f577,plain,
( xm != xk
| ~ isPrime0(xm) ),
inference(subsumption_resolution,[],[f576,f203]) ).
fof(f203,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f576,plain,
( xm != xk
| ~ isPrime0(xm)
| ~ aNaturalNumber0(xm) ),
inference(subsumption_resolution,[],[f557,f247]) ).
fof(f247,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f557,plain,
( xm != xk
| ~ isPrime0(xm)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f197,f427]) ).
fof(f427,plain,
xm = sdtasdt0(xm,sz10),
inference(resolution,[],[f254,f203]) ).
fof(f254,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f611,plain,
( ~ spl21_5
| ~ spl21_6 ),
inference(avatar_split_clause,[],[f575,f608,f604]) ).
fof(f604,plain,
( spl21_5
<=> isPrime0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_5])]) ).
fof(f608,plain,
( spl21_6
<=> xn = xk ),
introduced(avatar_definition,[new_symbols(naming,[spl21_6])]) ).
fof(f575,plain,
( xn != xk
| ~ isPrime0(xn) ),
inference(subsumption_resolution,[],[f574,f202]) ).
fof(f574,plain,
( xn != xk
| ~ isPrime0(xn)
| ~ aNaturalNumber0(xn) ),
inference(subsumption_resolution,[],[f555,f247]) ).
fof(f555,plain,
( xn != xk
| ~ isPrime0(xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f197,f426]) ).
fof(f426,plain,
xn = sdtasdt0(xn,sz10),
inference(resolution,[],[f254,f202]) ).
fof(f353,plain,
( ~ spl21_3
| ~ spl21_4 ),
inference(avatar_split_clause,[],[f344,f350,f346]) ).
fof(f346,plain,
( spl21_3
<=> isPrime0(sK15(xk)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_3])]) ).
fof(f350,plain,
( spl21_4
<=> sP3(xk) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_4])]) ).
fof(f344,plain,
( ~ sP3(xk)
| ~ isPrime0(sK15(xk)) ),
inference(subsumption_resolution,[],[f343,f235]) ).
fof(f235,plain,
! [X0] :
( aNaturalNumber0(sK15(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f163]) ).
fof(f163,plain,
! [X0] :
( ( sK15(X0) != X0
& sz10 != sK15(X0)
& doDivides0(sK15(X0),X0)
& sP2(X0,sK15(X0))
& aNaturalNumber0(sK15(X0)) )
| ~ sP3(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f161,f162]) ).
fof(f162,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& sP2(X0,X1)
& aNaturalNumber0(X1) )
=> ( sK15(X0) != X0
& sz10 != sK15(X0)
& doDivides0(sK15(X0),X0)
& sP2(X0,sK15(X0))
& aNaturalNumber0(sK15(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& sP2(X0,X1)
& aNaturalNumber0(X1) )
| ~ sP3(X0) ),
inference(rectify,[],[f160]) ).
fof(f160,plain,
! [X2] :
( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& sP2(X2,X4)
& aNaturalNumber0(X4) )
| ~ sP3(X2) ),
inference(nnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X2] :
( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& sP2(X2,X4)
& aNaturalNumber0(X4) )
| ~ sP3(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f343,plain,
( ~ sP3(xk)
| ~ isPrime0(sK15(xk))
| ~ aNaturalNumber0(sK15(xk)) ),
inference(resolution,[],[f237,f198]) ).
fof(f237,plain,
! [X0] :
( doDivides0(sK15(X0),X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f163]) ).
fof(f342,plain,
( ~ spl21_1
| ~ spl21_2 ),
inference(avatar_split_clause,[],[f333,f339,f335]) ).
fof(f335,plain,
( spl21_1
<=> isPrime0(sK8(xk)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_1])]) ).
fof(f339,plain,
( spl21_2
<=> sP1(xk) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_2])]) ).
fof(f333,plain,
( ~ sP1(xk)
| ~ isPrime0(sK8(xk)) ),
inference(subsumption_resolution,[],[f332,f188]) ).
fof(f188,plain,
! [X0] :
( aNaturalNumber0(sK8(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( ( sK8(X0) != X0
& sz10 != sK8(X0)
& doDivides0(sK8(X0),X0)
& sP0(X0,sK8(X0))
& aNaturalNumber0(sK8(X0)) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f140,f141]) ).
fof(f141,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& sP0(X0,X1)
& aNaturalNumber0(X1) )
=> ( sK8(X0) != X0
& sz10 != sK8(X0)
& doDivides0(sK8(X0),X0)
& sP0(X0,sK8(X0))
& aNaturalNumber0(sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f140,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& sP0(X0,X1)
& aNaturalNumber0(X1) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f130]) ).
fof(f332,plain,
( ~ sP1(xk)
| ~ isPrime0(sK8(xk))
| ~ aNaturalNumber0(sK8(xk)) ),
inference(resolution,[],[f190,f198]) ).
fof(f190,plain,
! [X0] :
( doDivides0(sK8(X0),X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.16 % Problem : NUM500+3 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.18 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.39 % Computer : n008.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8042.1875MB
% 0.14/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Mon Apr 29 23:49:58 EDT 2024
% 0.14/0.39 % CPUTime :
% 0.14/0.40 % (18707)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (18710)WARNING: value z3 for option sas not known
% 0.20/0.41 % (18709)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.41 % (18711)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.41 % (18708)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.41 % (18710)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)
% 0.20/0.41 % (18713)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)
% 0.20/0.42 % (18712)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)
% 0.20/0.42 % (18714)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)
% 0.20/0.43 Detected minimum model sizes of [3]
% 0.20/0.43 Detected maximum model sizes of [max]
% 0.20/0.43 TRYING [3]
% 0.20/0.45 % (18710)First to succeed.
% 0.20/0.45 % (18710)Refutation found. Thanks to Tanya!
% 0.20/0.45 % SZS status Theorem for theBenchmark
% 0.20/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.45 % (18710)------------------------------
% 0.20/0.45 % (18710)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.45 % (18710)Termination reason: Refutation
% 0.20/0.45
% 0.20/0.45 % (18710)Memory used [KB]: 1413
% 0.20/0.45 % (18710)Time elapsed: 0.038 s
% 0.20/0.45 % (18710)Instructions burned: 67 (million)
% 0.20/0.45 % (18710)------------------------------
% 0.20/0.45 % (18710)------------------------------
% 0.20/0.45 % (18707)Success in time 0.044 s
%------------------------------------------------------------------------------