TSTP Solution File: NUM498+3 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUM498+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n010.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 : Wed Aug 31 18:05:28 EDT 2022
% Result : Theorem 2.33s 0.68s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 88 ( 16 unt; 0 def)
% Number of atoms : 356 ( 155 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 411 ( 143 ~; 132 |; 115 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 85 ( 56 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1048,plain,
$false,
inference(avatar_sat_refutation,[],[f346,f824,f1043]) ).
fof(f1043,plain,
~ spl13_3,
inference(avatar_contradiction_clause,[],[f1042]) ).
fof(f1042,plain,
( $false
| ~ spl13_3 ),
inference(subsumption_resolution,[],[f1041,f297]) ).
fof(f297,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f1041,plain,
( ~ aNaturalNumber0(xn)
| ~ spl13_3 ),
inference(subsumption_resolution,[],[f1040,f494]) ).
fof(f494,plain,
sz00 != xm,
inference(subsumption_resolution,[],[f491,f292]) ).
fof(f292,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f491,plain,
( ~ aNaturalNumber0(sz00)
| sz00 != xm ),
inference(superposition,[],[f272,f390]) ).
fof(f390,plain,
sz00 = sdtasdt0(xp,sz00),
inference(resolution,[],[f274,f299]) ).
fof(f299,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f274,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,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/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f272,plain,
! [X0] :
( xm != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
( ~ doDivides0(xp,xm)
& ! [X0] :
( xm != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) )
& ( sz10 = xk
| sz00 = xk )
& ! [X1] :
( xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) )
& ~ doDivides0(xp,xn) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
( ! [X0] :
( xm != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) )
& ! [X1] :
( xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) )
& ~ doDivides0(xp,xn)
& ~ doDivides0(xp,xm)
& ( sz10 = xk
| sz00 = xk ) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
~ ( ( sz10 = xk
| sz00 = xk )
=> ( ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
| doDivides0(xp,xn)
| doDivides0(xp,xm) ) ),
inference(rectify,[],[f47]) ).
fof(f47,negated_conjecture,
~ ( ( sz10 = xk
| sz00 = xk )
=> ( doDivides0(xp,xn)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| doDivides0(xp,xm)
| ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) ) ) ),
inference(negated_conjecture,[],[f46]) ).
fof(f46,conjecture,
( ( sz10 = xk
| sz00 = xk )
=> ( doDivides0(xp,xn)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| doDivides0(xp,xm)
| ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f1040,plain,
( sz00 = xm
| ~ aNaturalNumber0(xn)
| ~ spl13_3 ),
inference(subsumption_resolution,[],[f1039,f495]) ).
fof(f495,plain,
sz00 != xn,
inference(subsumption_resolution,[],[f492,f292]) ).
fof(f492,plain,
( sz00 != xn
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[],[f270,f390]) ).
fof(f270,plain,
! [X1] :
( xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f1039,plain,
( sz00 = xn
| sz00 = xm
| ~ aNaturalNumber0(xn)
| ~ spl13_3 ),
inference(subsumption_resolution,[],[f1038,f298]) ).
fof(f298,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f1038,plain,
( ~ aNaturalNumber0(xm)
| sz00 = xn
| sz00 = xm
| ~ aNaturalNumber0(xn)
| ~ spl13_3 ),
inference(trivial_inequality_removal,[],[f1032]) ).
fof(f1032,plain,
( ~ aNaturalNumber0(xm)
| sz00 != sz00
| sz00 = xn
| sz00 = xm
| ~ aNaturalNumber0(xn)
| ~ spl13_3 ),
inference(superposition,[],[f296,f838]) ).
fof(f838,plain,
( sz00 = sdtasdt0(xn,xm)
| ~ spl13_3 ),
inference(forward_demodulation,[],[f837,f390]) ).
fof(f837,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz00)
| ~ spl13_3 ),
inference(forward_demodulation,[],[f278,f341]) ).
fof(f341,plain,
( sz00 = xk
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f339,plain,
( spl13_3
<=> sz00 = xk ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f278,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f296,plain,
! [X0,X1] :
( sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( sz00 = X0
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
! [X1,X0] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X1,X0] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(f824,plain,
~ spl13_4,
inference(avatar_contradiction_clause,[],[f823]) ).
fof(f823,plain,
( $false
| ~ spl13_4 ),
inference(subsumption_resolution,[],[f822,f253]) ).
fof(f253,plain,
xm != xp,
inference(cnf_transformation,[],[f175]) ).
fof(f175,plain,
( sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp)
& xp = sdtpldt0(xn,sK7)
& aNaturalNumber0(sK7)
& xn != xp
& xp = sdtpldt0(xm,sK8)
& aNaturalNumber0(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f172,f174,f173]) ).
fof(f173,plain,
( ? [X0] :
( xp = sdtpldt0(xn,X0)
& aNaturalNumber0(X0) )
=> ( xp = sdtpldt0(xn,sK7)
& aNaturalNumber0(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f174,plain,
( ? [X1] :
( xp = sdtpldt0(xm,X1)
& aNaturalNumber0(X1) )
=> ( xp = sdtpldt0(xm,sK8)
& aNaturalNumber0(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f172,plain,
( sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp)
& ? [X0] :
( xp = sdtpldt0(xn,X0)
& aNaturalNumber0(X0) )
& xn != xp
& ? [X1] :
( xp = sdtpldt0(xm,X1)
& aNaturalNumber0(X1) ) ),
inference(rectify,[],[f61]) ).
fof(f61,plain,
( sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp)
& ? [X1] :
( xp = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& xn != xp
& ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) ) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
( ? [X0] :
( xp = sdtpldt0(xm,X0)
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xp)
& sdtlseqdt0(xn,xp)
& xn != xp
& ? [X0] :
( xp = sdtpldt0(xn,X0)
& aNaturalNumber0(X0) )
& xm != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(f822,plain,
( xm = xp
| ~ spl13_4 ),
inference(forward_demodulation,[],[f805,f405]) ).
fof(f405,plain,
xm = sdtasdt0(sz10,xm),
inference(resolution,[],[f294,f298]) ).
fof(f294,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,sz10) = X0
& sdtasdt0(sz10,X0) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& sdtasdt0(sz10,X0) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f805,plain,
( xp = sdtasdt0(sz10,xm)
| ~ spl13_4 ),
inference(backward_demodulation,[],[f418,f781]) ).
fof(f781,plain,
( sz10 = xn
| ~ spl13_4 ),
inference(subsumption_resolution,[],[f780,f249]) ).
fof(f249,plain,
xn != xp,
inference(cnf_transformation,[],[f175]) ).
fof(f780,plain,
( sz10 = xn
| xn = xp
| ~ spl13_4 ),
inference(subsumption_resolution,[],[f779,f297]) ).
fof(f779,plain,
( ~ aNaturalNumber0(xn)
| xn = xp
| sz10 = xn
| ~ spl13_4 ),
inference(resolution,[],[f776,f309]) ).
fof(f309,plain,
! [X1] :
( ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1)
| sz10 = X1
| xp = X1 ),
inference(cnf_transformation,[],[f200]) ).
fof(f200,plain,
( isPrime0(xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK12)
& aNaturalNumber0(sK12)
& sz10 != xp
& sz00 != xp
& ! [X1] :
( sz10 = X1
| xp = X1
| ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != xp )
& ~ doDivides0(X1,xp) ) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f198,f199]) ).
fof(f199,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK12)
& aNaturalNumber0(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f198,plain,
( isPrime0(xp)
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& sz10 != xp
& sz00 != xp
& ! [X1] :
( sz10 = X1
| xp = X1
| ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != xp )
& ~ doDivides0(X1,xp) ) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rectify,[],[f134]) ).
fof(f134,plain,
( isPrime0(xp)
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& sz10 != xp
& sz00 != xp
& ! [X0] :
( sz10 = X0
| xp = X0
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(flattening,[],[f133]) ).
fof(f133,plain,
( sz10 != xp
& sz00 != xp
& ! [X0] :
( xp = X0
| sz10 = X0
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
( sz10 != xp
& sz00 != xp
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( doDivides0(X0,xp)
| ? [X1] :
( sdtasdt0(X0,X1) = xp
& aNaturalNumber0(X1) ) ) )
=> ( xp = X0
| sz10 = X0 ) )
& isPrime0(xp)
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
( ! [X0] :
( ( aNaturalNumber0(X0)
& ( doDivides0(X0,xp)
| ? [X1] :
( sdtasdt0(X0,X1) = xp
& aNaturalNumber0(X1) ) ) )
=> ( xp = X0
| sz10 = X0 ) )
& sz00 != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X0) )
& sz10 != xp
& isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f776,plain,
( doDivides0(xn,xp)
| ~ spl13_4 ),
inference(subsumption_resolution,[],[f775,f299]) ).
fof(f775,plain,
( doDivides0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ spl13_4 ),
inference(subsumption_resolution,[],[f774,f298]) ).
fof(f774,plain,
( doDivides0(xn,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl13_4 ),
inference(subsumption_resolution,[],[f750,f297]) ).
fof(f750,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| doDivides0(xn,xp)
| ~ aNaturalNumber0(xm)
| ~ spl13_4 ),
inference(superposition,[],[f322,f418]) ).
fof(f322,plain,
! [X2,X1] :
( ~ aNaturalNumber0(sdtasdt0(X1,X2))
| doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f258]) ).
fof(f258,plain,
! [X2,X0,X1] :
( doDivides0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0,X1] :
( ( ( doDivides0(X1,X0)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aNaturalNumber0(sK9(X0,X1))
& sdtasdt0(X1,sK9(X0,X1)) = X0 )
| ~ doDivides0(X1,X0) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f178,f179]) ).
fof(f179,plain,
! [X0,X1] :
( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X1,X3) = X0 )
=> ( aNaturalNumber0(sK9(X0,X1))
& sdtasdt0(X1,sK9(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f178,plain,
! [X0,X1] :
( ( ( doDivides0(X1,X0)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X1,X3) = X0 )
| ~ doDivides0(X1,X0) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f177]) ).
fof(f177,plain,
! [X0,X1] :
( ( ( doDivides0(X1,X0)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
| ~ doDivides0(X1,X0) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ( doDivides0(X1,X0)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ( doDivides0(X1,X0)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X0)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 ) ) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X1,X0] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f418,plain,
( xp = sdtasdt0(xn,xm)
| ~ spl13_4 ),
inference(backward_demodulation,[],[f353,f414]) ).
fof(f414,plain,
xp = sdtasdt0(xp,sz10),
inference(resolution,[],[f295,f299]) ).
fof(f295,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f91]) ).
fof(f353,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz10)
| ~ spl13_4 ),
inference(backward_demodulation,[],[f278,f345]) ).
fof(f345,plain,
( sz10 = xk
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f343,plain,
( spl13_4
<=> sz10 = xk ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f346,plain,
( spl13_3
| spl13_4 ),
inference(avatar_split_clause,[],[f271,f343,f339]) ).
fof(f271,plain,
( sz10 = xk
| sz00 = xk ),
inference(cnf_transformation,[],[f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM498+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 06:38:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.51 % (4281)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.52 TRYING [3]
% 0.19/0.52 % (4303)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 1.37/0.55 % (4292)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.62/0.56 % (4293)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.62/0.57 TRYING [4]
% 1.62/0.57 % (4302)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.62/0.57 % (4286)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.62/0.57 % (4285)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.62/0.59 % (4291)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.62/0.59 % (4289)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.62/0.59 % (4307)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.62/0.60 % (4304)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.62/0.60 % (4299)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.62/0.60 % (4284)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.62/0.60 % (4296)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.62/0.61 % (4282)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.62/0.61 % (4289)Instruction limit reached!
% 1.62/0.61 % (4289)------------------------------
% 1.62/0.61 % (4289)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.62/0.61 % (4289)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.62/0.61 % (4289)Termination reason: Unknown
% 1.62/0.61 % (4289)Termination phase: Preprocessing 1
% 1.62/0.61
% 1.62/0.61 % (4289)Memory used [KB]: 895
% 1.62/0.61 % (4289)Time elapsed: 0.003 s
% 1.62/0.61 % (4289)Instructions burned: 2 (million)
% 1.62/0.61 % (4289)------------------------------
% 1.62/0.61 % (4289)------------------------------
% 1.62/0.61 % (4288)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.62/0.61 % (4287)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.62/0.62 % (4288)Instruction limit reached!
% 1.62/0.62 % (4288)------------------------------
% 1.62/0.62 % (4288)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.62/0.62 % (4288)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.62/0.62 % (4288)Termination reason: Unknown
% 1.62/0.62 % (4288)Termination phase: Saturation
% 1.62/0.62
% 1.62/0.62 % (4288)Memory used [KB]: 5628
% 1.62/0.62 % (4288)Time elapsed: 0.007 s
% 1.62/0.62 % (4288)Instructions burned: 7 (million)
% 1.62/0.62 % (4288)------------------------------
% 1.62/0.62 % (4288)------------------------------
% 1.62/0.62 % (4290)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.62/0.62 % (4306)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.62/0.62 % (4310)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.62/0.63 % (4305)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.62/0.63 % (4297)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.62/0.64 % (4298)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.62/0.64 % (4283)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 2.33/0.65 % (4309)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 2.33/0.66 % (4286)Instruction limit reached!
% 2.33/0.66 % (4286)------------------------------
% 2.33/0.66 % (4286)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.33/0.66 % (4286)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.33/0.66 % (4286)Termination reason: Unknown
% 2.33/0.66 % (4286)Termination phase: Saturation
% 2.33/0.66
% 2.33/0.66 % (4286)Memory used [KB]: 6140
% 2.33/0.66 % (4286)Time elapsed: 0.226 s
% 2.33/0.66 % (4286)Instructions burned: 48 (million)
% 2.33/0.66 % (4286)------------------------------
% 2.33/0.66 % (4286)------------------------------
% 2.33/0.66 % (4301)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 2.33/0.67 % (4302)First to succeed.
% 2.33/0.67 TRYING [3]
% 2.33/0.68 % (4300)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 2.33/0.68 % (4302)Refutation found. Thanks to Tanya!
% 2.33/0.68 % SZS status Theorem for theBenchmark
% 2.33/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 2.33/0.68 % (4302)------------------------------
% 2.33/0.68 % (4302)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.33/0.68 % (4302)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.33/0.68 % (4302)Termination reason: Refutation
% 2.33/0.68
% 2.33/0.68 % (4302)Memory used [KB]: 6140
% 2.33/0.68 % (4302)Time elapsed: 0.259 s
% 2.33/0.68 % (4302)Instructions burned: 45 (million)
% 2.33/0.68 % (4302)------------------------------
% 2.33/0.68 % (4302)------------------------------
% 2.33/0.68 % (4280)Success in time 0.333 s
%------------------------------------------------------------------------------