%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM463+2 : 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 : n006.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 12:15:18 PM UTC 2026
% Result : Theorem 4.03s 1.23s
% Output : Refutation 4.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 100 ( 18 unt; 6 def)
% Number of atoms : 328 ( 69 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 410 ( 182 ~; 174 |; 36 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 64 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
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(f26,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sz00
| X0 = sz10
| ( sz10 != X0
& sdtlseqdt0(sz10,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
fof(f27,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).
fof(f28,conjecture,
( xm != sz00
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = sdtasdt0(xn,xm) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f29,negated_conjecture,
~ ( xm != sz00
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = sdtasdt0(xn,xm) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f31,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) != sdtasdt0(xn,xm) )
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& xm != sz00 ),
inference(ennf_transformation,[],[f29]) ).
fof(f32,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) != sdtasdt0(xn,xm) )
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& xm != sz00 ),
inference(flattening,[],[f31]) ).
fof(f33,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(f34,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,[],[f33]) ).
fof(f37,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f38,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f40,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f39]) ).
fof(f43,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f56,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f66,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f67,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f66]) ).
fof(f70,plain,
! [X0] :
( X0 = sz00
| X0 = sz10
| ( sz10 != X0
& sdtlseqdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f71,plain,
! [X0] :
( X0 = sz00
| X0 = sz10
| ( sz10 != X0
& sdtlseqdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f76,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f27]) ).
fof(f77,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f27]) ).
fof(f78,plain,
sz00 != xm,
inference(cnf_transformation,[],[f32]) ).
fof(f79,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f32]) ).
fof(f83,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,[],[f34]) ).
fof(f89,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f91,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f93,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f106,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f114,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f116,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f117,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f120,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f122,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f127,plain,
! [X0] :
( ~ sdtlseqdt0(xn,X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f79,f91]) ).
fof(f130,plain,
! [X0] :
( ~ sdtlseqdt0(xn,X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f127,f76]) ).
fof(f132,definition,
( spl1_1
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f134,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl1_1 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f141,definition,
( spl1_3
<=> ! [X0] :
( ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f142,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f143,plain,
( ~ spl1_1
| spl1_3 ),
inference(avatar_split_clause,[],[f130,f141,f132]) ).
fof(f144,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl1_1 ),
inference(resolution,[],[f134,f114]) ).
fof(f145,plain,
( ~ aNaturalNumber0(xm)
| spl1_1 ),
inference(forward_subsumption_resolution,[],[f144,f76]) ).
fof(f146,plain,
( $false
| spl1_1 ),
inference(forward_subsumption_resolution,[],[f145,f77]) ).
fof(f147,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f146]) ).
fof(f164,plain,
( ! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xn,X0))
| ~ sdtlseqdt0(xn,sdtasdt0(xn,X0))
| sz00 = xn
| xm = X0
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) )
| ~ spl1_3 ),
inference(resolution,[],[f142,f83]) ).
fof(f179,plain,
( ! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xn,X0))
| ~ sdtlseqdt0(xn,sdtasdt0(xn,X0))
| sz00 = xn
| xm = X0
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) )
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f164,f76]) ).
fof(f182,plain,
( ! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xn,X0))
| ~ sdtlseqdt0(xn,sdtasdt0(xn,X0))
| sz00 = xn
| xm = X0
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) )
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f179,f77]) ).
fof(f198,definition,
( spl1_7
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f200,plain,
( sz00 = xn
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f202,definition,
( spl1_8
<=> ! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm)
| xm = X0
| ~ sdtlseqdt0(xn,sdtasdt0(xn,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f203,plain,
( ! [X0] :
( ~ sdtlseqdt0(xn,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm)
| xm = X0
| ~ aNaturalNumber0(sdtasdt0(xn,X0)) )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f204,plain,
( spl1_7
| spl1_8
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f182,f141,f202,f198]) ).
fof(f215,plain,
( ~ sdtlseqdt0(sz00,sdtasdt0(sz00,xm))
| ~ spl1_7 ),
inference(superposition,[],[f79,f200]) ).
fof(f263,plain,
( ~ sdtlseqdt0(sz00,sz00)
| ~ aNaturalNumber0(xm)
| ~ spl1_7 ),
inference(superposition,[],[f215,f106]) ).
fof(f264,plain,
( ~ sdtlseqdt0(sz00,sz00)
| ~ spl1_7 ),
inference(forward_subsumption_resolution,[],[f263,f77]) ).
fof(f296,plain,
( ~ aNaturalNumber0(sz00)
| ~ spl1_7 ),
inference(resolution,[],[f264,f93]) ).
fof(f305,plain,
( $false
| ~ spl1_7 ),
inference(forward_subsumption_resolution,[],[f296,f116]) ).
fof(f306,plain,
~ spl1_7,
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f358,plain,
( ~ sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(sz10)
| ~ sdtlseqdt0(sz10,xm)
| sz10 = xm
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ spl1_8 ),
inference(superposition,[],[f203,f122]) ).
fof(f359,plain,
( ~ sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(sz10)
| ~ sdtlseqdt0(sz10,xm)
| sz10 = xm
| ~ aNaturalNumber0(xn)
| ~ spl1_8 ),
inference(duplicate_literal_removal,[],[f358]) ).
fof(f365,plain,
( ~ aNaturalNumber0(sz10)
| ~ sdtlseqdt0(sz10,xm)
| sz10 = xm
| ~ aNaturalNumber0(xn)
| ~ spl1_8 ),
inference(forward_subsumption_resolution,[],[f359,f89]) ).
fof(f369,plain,
( ~ sdtlseqdt0(sz10,xm)
| sz10 = xm
| ~ aNaturalNumber0(xn)
| ~ spl1_8 ),
inference(forward_subsumption_resolution,[],[f365,f120]) ).
fof(f370,plain,
( ~ sdtlseqdt0(sz10,xm)
| sz10 = xm
| ~ spl1_8 ),
inference(forward_subsumption_resolution,[],[f369,f76]) ).
fof(f372,definition,
( spl1_13
<=> sz10 = xm ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f373,plain,
( sz10 != xm
| spl1_13 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f374,plain,
( sz10 = xm
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f376,definition,
( spl1_14
<=> sdtlseqdt0(sz10,xm) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f378,plain,
( ~ sdtlseqdt0(sz10,xm)
| spl1_14 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f379,plain,
( spl1_13
| ~ spl1_14
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f370,f202,f376,f372]) ).
fof(f399,plain,
( sz10 = xm
| sz00 = xm
| ~ aNaturalNumber0(xm)
| spl1_14 ),
inference(resolution,[],[f378,f117]) ).
fof(f404,plain,
( sz00 = xm
| ~ aNaturalNumber0(xm)
| spl1_13
| spl1_14 ),
inference(forward_subsumption_resolution,[],[f399,f373]) ).
fof(f407,plain,
( ~ aNaturalNumber0(xm)
| spl1_13
| spl1_14 ),
inference(forward_subsumption_resolution,[],[f404,f78]) ).
fof(f408,plain,
( $false
| spl1_13
| spl1_14 ),
inference(forward_subsumption_resolution,[],[f407,f77]) ).
fof(f409,plain,
( spl1_13
| spl1_14 ),
inference(avatar_contradiction_clause,[],[f408]) ).
fof(f412,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,sz10))
| ~ spl1_13 ),
inference(superposition,[],[f79,f374]) ).
fof(f480,plain,
( ~ sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl1_13 ),
inference(superposition,[],[f412,f122]) ).
fof(f485,plain,
( ~ aNaturalNumber0(xn)
| ~ spl1_13 ),
inference(forward_subsumption_resolution,[],[f480,f89]) ).
fof(f488,plain,
( $false
| ~ spl1_13 ),
inference(forward_subsumption_resolution,[],[f485,f76]) ).
fof(f489,plain,
~ spl1_13,
inference(avatar_contradiction_clause,[],[f488]) ).
cnf(s2,plain,
( ~ spl1_1
| spl1_3 ),
inference(sat_conversion,[],[f143]) ).
cnf(s3,plain,
spl1_1,
inference(sat_conversion,[],[f147]) ).
cnf(s5,plain,
( ~ spl1_3
| spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f204]) ).
cnf(s7,plain,
~ spl1_7,
inference(sat_conversion,[],[f306]) ).
cnf(s10,plain,
( ~ spl1_8
| spl1_13
| ~ spl1_14 ),
inference(sat_conversion,[],[f379]) ).
cnf(s12,plain,
( spl1_13
| spl1_14 ),
inference(sat_conversion,[],[f409]) ).
cnf(s14,plain,
~ spl1_13,
inference(sat_conversion,[],[f489]) ).
cnf(s15,plain,
spl1_14,
inference(rat,[],[s12,s14]) ).
cnf(s16,plain,
~ spl1_8,
inference(rat,[],[s10,s15,s14]) ).
cnf(s17,plain,
~ spl1_3,
inference(rat,[],[s5,s16,s7]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s2,s17,s3]) ).
fof(f490,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM463+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:01:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 4.03/1.23 % (3279630)Detected formulas, will run a generic FOF schedule.
% 4.03/1.23 % (3279640)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1524087479:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.03/1.23 % (3279638)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1334832026:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.03/1.23 % (3279641)dis-21_1_sil=8000:lcm=predicate:random_seed=4065515628: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)
% 4.03/1.23 % (3279639)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=922262717:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.03/1.23 % (3279635)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=1653377173:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.03/1.23 % (3279636)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=2679835569:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.03/1.23 % (3279637)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=1752689476:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.03/1.23 % (3279638)Instruction limit reached!
% 4.03/1.23 % (3279638)------------------------------
% 4.03/1.23 % (3279638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.23 % (3279638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.23 % (3279638)CaDiCaL version: 2.1.3
% 4.03/1.23 % (3279638)Termination reason: Instruction limit
% 4.03/1.23 % (3279638)Termination phase: Saturation
% 4.03/1.23 % (3279638)Time elapsed: 0.067 s
% 4.03/1.23 % (3279638)Peak memory usage: 89 MB
% 4.03/1.23 % (3279638)Instructions burned: 110 (million)
% 4.03/1.23 % (3279639)Instruction limit reached!
% 4.03/1.23 % (3279639)------------------------------
% 4.03/1.23 % (3279639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.23 % (3279639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.23 % (3279639)CaDiCaL version: 2.1.3
% 4.03/1.23 % (3279639)Termination reason: Instruction limit
% 4.03/1.23 % (3279639)Termination phase: Saturation
% 4.03/1.23 % (3279639)Time elapsed: 0.069 s
% 4.03/1.23 % (3279639)Peak memory usage: 88 MB
% 4.03/1.23 % (3279639)Instructions burned: 120 (million)
% 4.03/1.23 % (3279641)Instruction limit reached!
% 4.03/1.23 % (3279641)------------------------------
% 4.03/1.23 % (3279641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.23 % (3279641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.23 % (3279641)CaDiCaL version: 2.1.3
% 4.03/1.23 % (3279641)Termination reason: Instruction limit
% 4.03/1.23 % (3279641)Termination phase: Saturation
% 4.03/1.23 % (3279641)Time elapsed: 0.078 s
% 4.03/1.23 % (3279641)Peak memory usage: 90 MB
% 4.03/1.23 % (3279641)Instructions burned: 131 (million)
% 4.03/1.23 % (3279640)Instruction limit reached!
% 4.03/1.23 % (3279640)------------------------------
% 4.03/1.23 % (3279640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.23 % (3279640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.23 % (3279640)CaDiCaL version: 2.1.3
% 4.03/1.23 % (3279640)Termination reason: Instruction limit
% 4.03/1.23 % (3279640)Termination phase: Saturation
% 4.03/1.23 % (3279640)Time elapsed: 0.085 s
% 4.03/1.23 % (3279640)Peak memory usage: 89 MB
% 4.03/1.23 % (3279640)Instructions burned: 140 (million)
% 4.03/1.23 % (3279649)lrs+10_1_sil=8000:sp=occurrence:random_seed=1556769200:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.03/1.23 % (3279651)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1027073371:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.03/1.23 % (3279650)lrs+10_1_sil=32000:urr=on:br=off:random_seed=255883839:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.03/1.23 % (3279652)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=562260206:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.03/1.23 % (3279649)Instruction limit reached!
% 4.03/1.23 % (3279649)------------------------------
% 4.03/1.23 % (3279649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.23 % (3279649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.23 % (3279649)CaDiCaL version: 2.1.3
% 4.03/1.23 % (3279649)Termination reason: Instruction limit
% 4.03/1.23 % (3279649)Termination phase: Saturation
% 4.03/1.23 % (3279649)Time elapsed: 0.091 s
% 4.03/1.23 % (3279649)Peak memory usage: 91 MB
% 4.03/1.23 % (3279649)Instructions burned: 288 (million)
% 4.03/1.23 % (3279650)Instruction limit reached!
% 4.03/1.23 % (3279650)------------------------------
% 4.03/1.23 % (3279650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.23 % (3279650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.23 % (3279650)CaDiCaL version: 2.1.3
% 4.03/1.23 % (3279650)Termination reason: Instruction limit
% 4.03/1.23 % (3279650)Termination phase: Saturation
% 4.03/1.23 % (3279650)Time elapsed: 0.075 s
% 4.03/1.23 % (3279650)Peak memory usage: 90 MB
% 4.03/1.23 % (3279650)Instructions burned: 159 (million)
% 4.03/1.23 % (3279657)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1010136138:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.03/1.23 % (3279657)First to succeed.
% 4.03/1.23 % (3279657)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3279630"
% 4.03/1.23 % (3279652)Instruction limit reached!
% 4.03/1.23 % (3279652)------------------------------
% 4.03/1.23 % (3279652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.23 % (3279652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.23 % (3279652)CaDiCaL version: 2.1.3
% 4.03/1.23 % (3279652)Termination reason: Instruction limit
% 4.03/1.23 % (3279652)Termination phase: Saturation
% 4.03/1.23 % (3279652)Time elapsed: 0.125 s
% 4.03/1.23 % (3279652)Peak memory usage: 93 MB
% 4.03/1.23 % (3279652)Instructions burned: 249 (million)
% 4.03/1.23 % (3279651)Instruction limit reached!
% 4.03/1.23 % (3279651)------------------------------
% 4.03/1.23 % (3279651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.23 % (3279651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.23 % (3279651)CaDiCaL version: 2.1.3
% 4.03/1.23 % (3279651)Termination reason: Instruction limit
% 4.03/1.23 % (3279651)Termination phase: Saturation
% 4.03/1.23 % (3279651)Time elapsed: 0.195 s
% 4.03/1.23 % (3279651)Peak memory usage: 92 MB
% 4.03/1.23 % (3279651)Instructions burned: 325 (million)
% 4.03/1.23 % (3279658)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1341497321:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.03/1.23 % (3279660)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3635281227:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 4.03/1.23 % (3279657)Refutation found. Thanks to Tanya!
% 4.03/1.23 % SZS status Theorem for theBenchmark
% 4.03/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 4.81/1.42 % (3279657)------------------------------
% 4.81/1.42 % (3279657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/1.42 % (3279657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/1.42 % (3279657)CaDiCaL version: 2.1.3
% 4.81/1.42 % (3279657)Termination reason: Refutation
% 4.81/1.42 % (3279657)Time elapsed: 0.007 s
% 4.81/1.42 % (3279657)Peak memory usage: 89 MB
% 4.81/1.42 % (3279657)Instructions burned: 18 (million)
% 4.81/1.42 % (3279657)------------------------------
% 4.81/1.42 % (3279657)------------------------------
% 4.81/1.42 % (3279630)Success in time 0.626 s
% 4.81/1.42 % Vampire exiting
%------------------------------------------------------------------------------