%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM469+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:24:26 PM UTC 2026
% Result : Theorem 2.36s 1.04s
% Output : Refutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 108 ( 22 unt; 6 def)
% Number of atoms : 303 ( 74 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 341 ( 146 ~; 150 |; 27 &)
% ( 11 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 58 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f33,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240) ).
fof(f34,axiom,
( doDivides0(xl,xm)
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240_04) ).
fof(f35,axiom,
( xl != sz00
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1298) ).
fof(f36,conjecture,
doDivides0(xl,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f37,negated_conjecture,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(flattening,[],[f37]) ).
fof(f42,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f42]) ).
fof(f50,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f86,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f87,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f89,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f88]) ).
fof(f92,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| sz00 = xl ),
inference(ennf_transformation,[],[f35]) ).
fof(f98,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f87]) ).
fof(f99,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X3) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtasdt0(X0,sK1(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f89]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f106,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f111,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f50]) ).
fof(f116,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f149,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sdtasdt0(X0,sK1(X0,X1)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f150,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| aNaturalNumber0(sK1(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f151,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f153,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f156,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f33]) ).
fof(f157,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f33]) ).
fof(f158,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f33]) ).
fof(f159,plain,
doDivides0(xl,xn),
inference(cnf_transformation,[],[f34]) ).
fof(f160,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f34]) ).
fof(f161,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| sz00 = xl ),
inference(cnf_transformation,[],[f92]) ).
fof(f162,plain,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f40]) ).
fof(f169,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f151]) ).
fof(f171,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f153]) ).
fof(f173,definition,
sF2 = sdtpldt0(xm,xn),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f174,plain,
sdtpldt0(xm,xn) = sF2,
inference(reorient_equations,[],[f173]) ).
fof(f175,plain,
~ doDivides0(xl,sF2),
inference(definition_folding,[],[f162,f174]) ).
fof(f178,definition,
( spl3_1
<=> sz00 = xl ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f180,plain,
( sz00 = xl
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f182,definition,
( spl3_2
<=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f184,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f185,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f161,f182,f178]) ).
fof(f186,plain,
( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sF2
| ~ spl3_2 ),
inference(forward_demodulation,[],[f184,f174]) ).
fof(f200,plain,
xm = sdtpldt0(xm,sz00),
inference(resolution,[],[f111,f157]) ).
fof(f229,plain,
( aNaturalNumber0(sF2)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f106,f174]) ).
fof(f231,plain,
( aNaturalNumber0(sF2)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f229,f157]) ).
fof(f232,plain,
aNaturalNumber0(sF2),
inference(forward_subsumption_resolution,[],[f231,f156]) ).
fof(f310,definition,
( spl3_6
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f311,plain,
( sz00 != xn
| spl3_6 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f312,plain,
( sz00 = xn
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f345,plain,
( doDivides0(sz00,xn)
| ~ spl3_1 ),
inference(superposition,[],[f159,f180]) ).
fof(f346,plain,
( doDivides0(sz00,xm)
| ~ spl3_1 ),
inference(superposition,[],[f160,f180]) ).
fof(f347,plain,
( ~ doDivides0(sz00,sF2)
| ~ spl3_1 ),
inference(superposition,[],[f175,f180]) ).
fof(f363,plain,
( aNaturalNumber0(sK1(xl,xn))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f150,f159]) ).
fof(f366,plain,
( aNaturalNumber0(sK1(xl,xn))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f363,f158]) ).
fof(f368,plain,
aNaturalNumber0(sK1(xl,xn)),
inference(forward_subsumption_resolution,[],[f366,f156]) ).
fof(f403,plain,
( sF2 = sdtpldt0(xm,sz00)
| ~ spl3_6 ),
inference(superposition,[],[f174,f312]) ).
fof(f409,plain,
( xm = sF2
| ~ spl3_6 ),
inference(forward_demodulation,[],[f403,f200]) ).
fof(f489,plain,
( doDivides0(xl,sF2)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF2)
| ~ spl3_2 ),
inference(superposition,[],[f169,f186]) ).
fof(f491,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF2)
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f489,f175]) ).
fof(f493,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ aNaturalNumber0(sF2)
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f491,f158]) ).
fof(f494,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f493,f232]) ).
fof(f600,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f171,f159]) ).
fof(f601,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f171,f160]) ).
fof(f617,plain,
( ~ doDivides0(sz00,xm)
| ~ spl3_1
| ~ spl3_6 ),
inference(forward_demodulation,[],[f347,f409]) ).
fof(f621,plain,
( $false
| ~ spl3_1
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f617,f346]) ).
fof(f622,plain,
( ~ spl3_1
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f621]) ).
fof(f639,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f601,f158]) ).
fof(f640,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f600,f158]) ).
fof(f641,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(forward_subsumption_resolution,[],[f639,f157]) ).
fof(f642,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xn,xl)) ),
inference(forward_subsumption_resolution,[],[f640,f156]) ).
fof(f644,definition,
( spl3_19
<=> aNaturalNumber0(sdtsldt0(xm,xl)) ),
introduced(definition,[new_symbols(definition,[spl3_19])],[avatar_definition]) ).
fof(f646,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f647,plain,
( spl3_19
| spl3_1 ),
inference(avatar_split_clause,[],[f641,f178,f644]) ).
fof(f649,definition,
( spl3_20
<=> aNaturalNumber0(sdtsldt0(xn,xl)) ),
introduced(definition,[new_symbols(definition,[spl3_20])],[avatar_definition]) ).
fof(f651,plain,
( aNaturalNumber0(sdtsldt0(xn,xl))
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f652,plain,
( spl3_20
| spl3_1 ),
inference(avatar_split_clause,[],[f642,f178,f649]) ).
fof(f654,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ spl3_2 ),
inference(resolution,[],[f494,f106]) ).
fof(f655,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ spl3_2
| ~ spl3_19 ),
inference(forward_subsumption_resolution,[],[f654,f646]) ).
fof(f656,plain,
( $false
| ~ spl3_2
| ~ spl3_19
| ~ spl3_20 ),
inference(forward_subsumption_resolution,[],[f655,f651]) ).
fof(f657,plain,
( ~ spl3_2
| ~ spl3_19
| ~ spl3_20 ),
inference(avatar_contradiction_clause,[],[f656]) ).
fof(f806,plain,
( xn = sdtasdt0(sz00,sK1(sz00,xn))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ spl3_1 ),
inference(resolution,[],[f345,f149]) ).
fof(f809,plain,
( xn = sdtasdt0(sz00,sK1(sz00,xn))
| ~ aNaturalNumber0(xn)
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f806,f103]) ).
fof(f811,plain,
( xn = sdtasdt0(sz00,sK1(sz00,xn))
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f809,f156]) ).
fof(f1464,plain,
sz00 = sdtasdt0(sz00,sK1(xl,xn)),
inference(resolution,[],[f368,f116]) ).
fof(f1480,plain,
( sz00 = sdtasdt0(sz00,sK1(sz00,xn))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1464,f180]) ).
fof(f35151,plain,
( sz00 = xn
| ~ spl3_1 ),
inference(superposition,[],[f1480,f811]) ).
fof(f35164,plain,
( $false
| ~ spl3_1
| spl3_6 ),
inference(forward_subsumption_resolution,[],[f35151,f311]) ).
fof(f35165,plain,
( ~ spl3_1
| spl3_6 ),
inference(avatar_contradiction_clause,[],[f35164]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f185]) ).
cnf(s16,plain,
( ~ spl3_1
| ~ spl3_6 ),
inference(sat_conversion,[],[f622]) ).
cnf(s19,plain,
( spl3_1
| spl3_19 ),
inference(sat_conversion,[],[f647]) ).
cnf(s20,plain,
( spl3_1
| spl3_20 ),
inference(sat_conversion,[],[f652]) ).
cnf(s21,plain,
( ~ spl3_2
| ~ spl3_19
| ~ spl3_20 ),
inference(sat_conversion,[],[f657]) ).
cnf(s1567,plain,
( ~ spl3_1
| spl3_6 ),
inference(sat_conversion,[],[f35165]) ).
cnf(s1701,plain,
spl3_1,
inference(rat,[],[s21,s1,s19,s20]) ).
cnf(s1702,plain,
spl3_6,
inference(rat,[],[s1567,s1701]) ).
cnf(s1710,plain,
$false,
inference(rat,[],[s16,s1702,s1701]) ).
fof(f35166,plain,
$false,
inference(avatar_sat_refutation,[],[s1710]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM469+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:04:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.36/1.04 % (3373560)Will run a generic schedule for satisfiability detection.
% 2.36/1.04 % (3373571)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=152635368:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.36/1.04 % (3373566)% WARNING: option uhcvi not known.
% 2.36/1.04 % (3373565)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4053869566_2999 on theBenchmark for (2999ds/0Mi)
% 2.36/1.04 % (3373567)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3170617930:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.36/1.04 % (3373568)dis+10_1_sil=32000:sp=arity:random_seed=2787592319:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.36/1.04 % (3373569)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1513886:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.36/1.04 % (3373570)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1052471508:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.36/1.04 % (3373566)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=103443027:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.36/1.04 % TRYING [1]
% 2.36/1.04 % TRYING [2]
% 2.36/1.04 % TRYING [3]
% 2.36/1.04 % TRYING [4]
% 2.36/1.04 % TRYING [5]
% 2.36/1.04 % (3373571)Instruction limit reached!
% 2.36/1.04 % (3373571)------------------------------
% 2.36/1.04 % (3373571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/1.04 % (3373571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.04 % (3373571)CaDiCaL version: 2.1.3
% 2.36/1.04 % (3373571)Termination reason: Instruction limit
% 2.36/1.04 % (3373571)Termination phase: Saturation
% 2.36/1.04 % (3373571)Time elapsed: 0.057 s
% 2.36/1.04 % (3373571)Peak memory usage: 15 MB
% 2.36/1.04 % (3373571)Instructions burned: 160 (million)
% 2.36/1.04 % (3373568)Instruction limit reached!
% 2.36/1.04 % (3373568)------------------------------
% 2.36/1.04 % (3373568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/1.04 % (3373568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.04 % (3373568)CaDiCaL version: 2.1.3
% 2.36/1.04 % (3373568)Termination reason: Instruction limit
% 2.36/1.04 % (3373568)Termination phase: Saturation
% 2.36/1.04 % (3373568)Time elapsed: 0.060 s
% 2.36/1.04 % (3373568)Peak memory usage: 12 MB
% 2.36/1.04 % (3373568)Instructions burned: 103 (million)
% 2.36/1.04 % (3373579)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3644328497:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.36/1.04 % TRYING [1]
% 2.36/1.04 % TRYING [2]
% 2.36/1.04 % TRYING [3]
% 2.36/1.04 % (3373569)Instruction limit reached!
% 2.36/1.04 % (3373569)------------------------------
% 2.36/1.04 % (3373569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/1.04 % (3373569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.04 % (3373569)CaDiCaL version: 2.1.3
% 2.36/1.04 % (3373569)Termination reason: Instruction limit
% 2.36/1.04 % (3373569)Termination phase: Saturation
% 2.36/1.04 % (3373569)Time elapsed: 0.069 s
% 2.36/1.04 % (3373569)Peak memory usage: 13 MB
% 2.36/1.04 % (3373569)Instructions burned: 117 (million)
% 2.36/1.04 % TRYING [4]
% 2.36/1.04 % (3373570)Instruction limit reached!
% 2.36/1.04 % (3373570)------------------------------
% 2.36/1.04 % (3373570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/1.04 % (3373570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.04 % (3373570)CaDiCaL version: 2.1.3
% 2.36/1.04 % (3373570)Termination reason: Instruction limit
% 2.36/1.04 % (3373570)Termination phase: Saturation
% 2.36/1.04 % (3373570)Time elapsed: 0.078 s
% 2.36/1.04 % (3373570)Peak memory usage: 14 MB
% 2.36/1.04 % (3373570)Instructions burned: 131 (million)
% 2.36/1.04 % TRYING [5]
% 2.36/1.04 % (3373582)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=672661927:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.36/1.04 % (3373580)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3516373302:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.36/1.04 % (3373583)ott-21_1_sil=16000:fs=off:random_seed=2477911084:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.36/1.04 % TRYING [6]
% 2.36/1.04 % TRYING [6]
% 2.36/1.04 % (3373580)Instruction limit reached!
% 2.36/1.04 % (3373580)------------------------------
% 2.36/1.04 % (3373580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/1.04 % (3373580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.04 % (3373580)CaDiCaL version: 2.1.3
% 2.36/1.04 % (3373580)Termination reason: Instruction limit
% 2.36/1.04 % (3373580)Termination phase: Saturation
% 2.36/1.04 % (3373580)Time elapsed: 0.067 s
% 2.36/1.04 % (3373580)Peak memory usage: 12 MB
% 2.36/1.04 % (3373580)Instructions burned: 131 (million)
% 2.36/1.04 % (3373587)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4129541117:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.36/1.04 % (3373583)Instruction limit reached!
% 2.36/1.04 % (3373583)------------------------------
% 2.36/1.04 % (3373583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/1.04 % (3373583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.04 % (3373583)CaDiCaL version: 2.1.3
% 2.36/1.04 % (3373583)Termination reason: Instruction limit
% 2.36/1.04 % (3373583)Termination phase: Saturation
% 2.36/1.04 % (3373583)Time elapsed: 0.093 s
% 2.36/1.04 % (3373583)Peak memory usage: 13 MB
% 2.36/1.04 % (3373583)Instructions burned: 180 (million)
% 2.36/1.04 % (3373589)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=30618537:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.36/1.04 % (3373579)Instruction limit reached!
% 2.36/1.04 % (3373579)------------------------------
% 2.36/1.04 % (3373579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/1.04 % (3373579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.04 % (3373579)CaDiCaL version: 2.1.3
% 2.36/1.04 % (3373579)Termination reason: Instruction limit
% 2.36/1.04 % (3373579)Termination phase: Finite model building SAT solving
% 2.36/1.04 % (3373579)Time elapsed: 0.151 s
% 2.36/1.04 % (3373579)Peak memory usage: 33 MB
% 2.36/1.04 % (3373579)Instructions burned: 716 (million)
% 2.36/1.04 % TRYING [1]
% 2.36/1.04 % TRYING [2]
% 2.36/1.04 % TRYING [3]
% 2.36/1.04 % TRYING [4]
% 2.36/1.04 % (3373591)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=915075386:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.36/1.04 % TRYING [7]
% 2.36/1.04 % TRYING [5]
% 2.36/1.04 % (3373582)Instruction limit reached!
% 2.36/1.04 % (3373582)------------------------------
% 2.36/1.04 % (3373582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/1.04 % (3373582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.04 % (3373582)CaDiCaL version: 2.1.3
% 2.36/1.04 % (3373582)Termination reason: Instruction limit
% 2.36/1.04 % (3373582)Termination phase: Saturation
% 2.36/1.04 % (3373582)Time elapsed: 0.379 s
% 2.36/1.04 % (3373582)Peak memory usage: 19 MB
% 2.36/1.04 % (3373582)Instructions burned: 685 (million)
% 2.36/1.04 % (3373587)Instruction limit reached!
% 2.36/1.04 % (3373587)------------------------------
% 2.36/1.04 % (3373587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/1.04 % (3373587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.04 % (3373587)CaDiCaL version: 2.1.3
% 2.36/1.04 % (3373587)Termination reason: Instruction limit
% 2.36/1.04 % (3373587)Termination phase: Saturation
% 2.36/1.04 % (3373587)Time elapsed: 0.308 s
% 2.36/1.04 % (3373587)Peak memory usage: 14 MB
% 2.36/1.04 % (3373587)Instructions burned: 477 (million)
% 2.36/1.04 % (3373593)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3306776183:i=889:ins=1_2994 on theBenchmark for (2994ds/889Mi)
% 2.36/1.04 % TRYING [6]
% 2.36/1.04 % (3373594)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2097960828:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 2.36/1.04 % (3373589)Instruction limit reached!
% 2.36/1.04 % (3373589)------------------------------
% 2.36/1.04 % (3373589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/1.04 % (3373589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.04 % (3373589)CaDiCaL version: 2.1.3
% 2.36/1.04 % (3373589)Termination reason: Instruction limit
% 2.36/1.04 % (3373589)Termination phase: Finite model building constraint generation
% 2.36/1.04 % (3373589)Time elapsed: 0.337 s
% 2.36/1.04 % (3373589)Peak memory usage: 22 MB
% 2.36/1.04 % (3373589)Instructions burned: 867 (million)
% 2.36/1.04 % (3373597)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1663987651:i=879:kws=inv_precedence:fsr=off_2994 on theBenchmark for (2994ds/879Mi)
% 2.36/1.04 % (3373591) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3373560-3373591"...
% 2.36/1.04 % (3373591)...printing done.
% 2.36/1.04 % (3373591)Refutation found. Thanks to Tanya!
% 2.36/1.04 % SZS status Theorem for theBenchmark
% 2.36/1.04 % SZS output start Proof for theBenchmark
% See solution above
% 2.36/1.04 % (3373591)------------------------------
% 2.36/1.04 % (3373591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/1.04 % (3373591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.04 % (3373591)CaDiCaL version: 2.1.3
% 2.36/1.04 % (3373591)Termination reason: Refutation
% 2.36/1.04 % (3373591)Time elapsed: 0.346 s
% 2.36/1.04 % (3373591)Peak memory usage: 26 MB
% 2.36/1.04 % (3373591)Instructions burned: 1119 (million)
% 2.36/1.04 % (3373560)Success in time 0.624 s
% 2.36/1.04 % Vampire exiting
%------------------------------------------------------------------------------