%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM475+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 : n026.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 12:24:27 PM UTC 2026
% Result : Theorem 1.95s 0.83s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of formulae : 129 ( 39 unt; 7 def)
% Number of atoms : 368 ( 96 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 429 ( 190 ~; 193 |; 26 &)
% ( 12 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtpldt0(X0,X1) = sdtpldt0(X0,X2)
| sdtpldt0(X1,X0) = sdtpldt0(X2,X0) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
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(f34,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f35,axiom,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
fof(f36,axiom,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).
fof(f37,axiom,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
fof(f38,axiom,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
fof(f39,axiom,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1395) ).
fof(f40,axiom,
xr = sdtmndt0(xq,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1422) ).
fof(f41,axiom,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1459) ).
fof(f42,conjecture,
xn = sdtasdt0(xl,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f46,plain,
xn != sdtasdt0(xl,xr),
inference(flattening,[],[f43]) ).
fof(f48,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f49,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f50]) ).
fof(f65,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
& sdtpldt0(X1,X0) != sdtpldt0(X2,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f66,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
& sdtpldt0(X1,X0) != sdtpldt0(X2,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f65]) ).
fof(f75,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f76,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f75]) ).
fof(f94,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(f95,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,[],[f94]) ).
fof(f103,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f76]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f103]) ).
fof(f108,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,[],[f95]) ).
fof(f109,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,[],[f108]) ).
fof(f113,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f114,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f128,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f138,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f159,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f160,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f164,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f165,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f166,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f167,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f35]) ).
fof(f168,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f35]) ).
fof(f169,plain,
sz00 != xl,
inference(cnf_transformation,[],[f36]) ).
fof(f170,plain,
xp = sdtsldt0(xm,xl),
inference(cnf_transformation,[],[f37]) ).
fof(f171,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(cnf_transformation,[],[f38]) ).
fof(f172,plain,
sdtlseqdt0(xp,xq),
inference(cnf_transformation,[],[f39]) ).
fof(f173,plain,
xr = sdtmndt0(xq,xp),
inference(cnf_transformation,[],[f40]) ).
fof(f174,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnf_transformation,[],[f41]) ).
fof(f175,plain,
xn != sdtasdt0(xl,xr),
inference(cnf_transformation,[],[f46]) ).
fof(f178,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f138]) ).
fof(f184,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f160]) ).
fof(f185,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f159]) ).
fof(f186,definition,
sF2 = sdtasdt0(xl,xr),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f187,plain,
sdtasdt0(xl,xr) = sF2,
inference(reorient_equations,[],[f186]) ).
fof(f188,plain,
xn != sF2,
inference(definition_folding,[],[f175,f187]) ).
fof(f190,plain,
sF2 = sdtasdt0(xl,sdtmndt0(xq,xp)),
inference(forward_demodulation,[],[f187,f173]) ).
fof(f239,plain,
( aNaturalNumber0(sF2)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtmndt0(xq,xp)) ),
inference(superposition,[],[f114,f190]) ).
fof(f240,plain,
( aNaturalNumber0(sF2)
| ~ aNaturalNumber0(sdtmndt0(xq,xp)) ),
inference(forward_subsumption_resolution,[],[f239,f166]) ).
fof(f242,definition,
( spl3_1
<=> aNaturalNumber0(sdtmndt0(xq,xp)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f244,plain,
( ~ aNaturalNumber0(sdtmndt0(xq,xp))
| spl3_1 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f246,definition,
( spl3_2
<=> aNaturalNumber0(sF2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f248,plain,
( aNaturalNumber0(sF2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f249,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f240,f246,f242]) ).
fof(f277,definition,
( spl3_3
<=> aNaturalNumber0(xq) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f278,plain,
( aNaturalNumber0(xq)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f279,plain,
( ~ aNaturalNumber0(xq)
| spl3_3 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f281,definition,
( spl3_4
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f282,plain,
( aNaturalNumber0(xp)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f298,definition,
( spl3_6
<=> aNaturalNumber0(sdtpldt0(xm,xn)) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f299,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f300,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| spl3_6 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f307,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl3_6 ),
inference(resolution,[],[f300,f113]) ).
fof(f308,plain,
( ~ aNaturalNumber0(xn)
| spl3_6 ),
inference(forward_subsumption_resolution,[],[f307,f165]) ).
fof(f309,plain,
( $false
| spl3_6 ),
inference(forward_subsumption_resolution,[],[f308,f164]) ).
fof(f310,plain,
spl3_6,
inference(avatar_contradiction_clause,[],[f309]) ).
fof(f311,plain,
( aNaturalNumber0(sdtmndt0(xq,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq) ),
inference(resolution,[],[f178,f172]) ).
fof(f408,definition,
( spl3_12
<=> aNaturalNumber0(sdtasdt0(xl,xp)) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f409,plain,
( aNaturalNumber0(sdtasdt0(xl,xp))
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f410,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xp))
| spl3_12 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f630,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f184,f168]) ).
fof(f631,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolution,[],[f184,f167]) ).
fof(f640,plain,
( aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f631,f169]) ).
fof(f641,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f630,f169]) ).
fof(f644,plain,
( aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f640,f166]) ).
fof(f645,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f641,f166]) ).
fof(f647,plain,
( aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f644,f299]) ).
fof(f648,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(forward_subsumption_resolution,[],[f645,f165]) ).
fof(f649,plain,
( aNaturalNumber0(xq)
| ~ spl3_6 ),
inference(forward_demodulation,[],[f647,f171]) ).
fof(f650,plain,
aNaturalNumber0(xp),
inference(forward_demodulation,[],[f648,f170]) ).
fof(f651,plain,
( $false
| spl3_3
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f649,f279]) ).
fof(f652,plain,
( spl3_3
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f651]) ).
fof(f653,plain,
spl3_4,
inference(avatar_split_clause,[],[f650,f281]) ).
fof(f656,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f311,f244]) ).
fof(f660,plain,
( ~ aNaturalNumber0(xq)
| spl3_1
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f656,f282]) ).
fof(f676,plain,
( $false
| spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f660,f278]) ).
fof(f677,plain,
( spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f676]) ).
fof(f871,plain,
! [X0] :
( sdtpldt0(sdtasdt0(xl,xp),xn) != sdtpldt0(sdtasdt0(xl,xp),X0)
| sdtasdt0(xl,xr) = X0
| ~ aNaturalNumber0(sdtasdt0(xl,xp))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xr)) ),
inference(superposition,[],[f128,f174]) ).
fof(f1018,plain,
( sz00 = xl
| xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f185,f168]) ).
fof(f1030,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f1018,f169]) ).
fof(f1035,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f1030,f166]) ).
fof(f1040,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(forward_subsumption_resolution,[],[f1035,f165]) ).
fof(f1042,plain,
xm = sdtasdt0(xl,xp),
inference(forward_demodulation,[],[f1040,f170]) ).
fof(f1590,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xp)
| spl3_12 ),
inference(resolution,[],[f410,f114]) ).
fof(f1591,plain,
( ~ aNaturalNumber0(xp)
| spl3_12 ),
inference(forward_subsumption_resolution,[],[f1590,f166]) ).
fof(f1592,plain,
( $false
| ~ spl3_4
| spl3_12 ),
inference(forward_subsumption_resolution,[],[f1591,f282]) ).
fof(f1593,plain,
( ~ spl3_4
| spl3_12 ),
inference(avatar_contradiction_clause,[],[f1592]) ).
fof(f1749,plain,
( ! [X0] :
( sdtpldt0(sdtasdt0(xl,xp),xn) != sdtpldt0(sdtasdt0(xl,xp),X0)
| sdtasdt0(xl,xr) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xr)) )
| ~ spl3_12 ),
inference(forward_subsumption_resolution,[],[f871,f409]) ).
fof(f1772,plain,
( ! [X0] :
( sdtpldt0(xm,xn) != sdtpldt0(xm,X0)
| sdtasdt0(xl,xr) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xr)) )
| ~ spl3_12 ),
inference(forward_demodulation,[],[f1749,f1042]) ).
fof(f1794,plain,
( ! [X0] :
( sdtasdt0(xl,sdtmndt0(xq,xp)) = X0
| sdtpldt0(xm,xn) != sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xr)) )
| ~ spl3_12 ),
inference(forward_demodulation,[],[f1772,f173]) ).
fof(f1816,plain,
( ! [X0] :
( sF2 = X0
| sdtpldt0(xm,xn) != sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xr)) )
| ~ spl3_12 ),
inference(forward_demodulation,[],[f1794,f190]) ).
fof(f1830,plain,
( ! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xl,sdtmndt0(xq,xp)))
| sF2 = X0
| sdtpldt0(xm,xn) != sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl3_12 ),
inference(forward_demodulation,[],[f1816,f173]) ).
fof(f1844,plain,
( ! [X0] :
( ~ aNaturalNumber0(sF2)
| sF2 = X0
| sdtpldt0(xm,xn) != sdtpldt0(xm,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl3_12 ),
inference(forward_demodulation,[],[f1830,f190]) ).
fof(f1858,plain,
( ! [X0] :
( sdtpldt0(xm,xn) != sdtpldt0(xm,X0)
| sF2 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl3_2
| ~ spl3_12 ),
inference(forward_subsumption_resolution,[],[f1844,f248]) ).
fof(f6016,plain,
( xn = sF2
| ~ aNaturalNumber0(xn)
| ~ spl3_2
| ~ spl3_12 ),
inference(equality_resolution,[],[f1858]) ).
fof(f6017,plain,
( ~ aNaturalNumber0(xn)
| ~ spl3_2
| ~ spl3_12 ),
inference(forward_subsumption_resolution,[],[f6016,f188]) ).
fof(f6018,plain,
( $false
| ~ spl3_2
| ~ spl3_12 ),
inference(forward_subsumption_resolution,[],[f6017,f164]) ).
fof(f6019,plain,
( ~ spl3_2
| ~ spl3_12 ),
inference(avatar_contradiction_clause,[],[f6018]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f249]) ).
cnf(s4,plain,
spl3_6,
inference(sat_conversion,[],[f310]) ).
cnf(s11,plain,
( spl3_3
| ~ spl3_6 ),
inference(sat_conversion,[],[f652]) ).
cnf(s12,plain,
spl3_4,
inference(sat_conversion,[],[f653]) ).
cnf(s14,plain,
( spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f677]) ).
cnf(s23,plain,
( ~ spl3_4
| spl3_12 ),
inference(sat_conversion,[],[f1593]) ).
cnf(s69,plain,
( ~ spl3_2
| ~ spl3_12 ),
inference(sat_conversion,[],[f6019]) ).
cnf(s71,plain,
spl3_12,
inference(rat,[],[s23,s12]) ).
cnf(s72,plain,
~ spl3_2,
inference(rat,[],[s69,s71]) ).
cnf(s73,plain,
spl3_3,
inference(rat,[],[s11,s4]) ).
cnf(s74,plain,
spl3_1,
inference(rat,[],[s14,s12,s73]) ).
cnf(s77,plain,
$false,
inference(rat,[],[s1,s72,s74]) ).
fof(f6020,plain,
$false,
inference(avatar_sat_refutation,[],[s77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM475+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n026.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:08:11 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 1.95/0.82 % (3177277)Will run a generic schedule for satisfiability detection.
% 1.95/0.82 % (3177285)dis+10_1_sil=32000:sp=arity:random_seed=4051818368:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.95/0.82 % (3177283)% WARNING: option uhcvi not known.
% 1.95/0.82 % (3177283)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4202700073:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.95/0.82 % (3177282)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2202455025_2999 on theBenchmark for (2999ds/0Mi)
% 1.95/0.82 % (3177284)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2148948303:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.95/0.82 % (3177286)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1168001756:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.95/0.82 % (3177287)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1454237628:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.95/0.82 % (3177288)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2781795804:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.95/0.82 % TRYING [1]
% 1.95/0.82 % TRYING [2]
% 1.95/0.82 % TRYING [3]
% 1.95/0.82 % TRYING [4]
% 1.95/0.82 % (3177285)Instruction limit reached!
% 1.95/0.82 % (3177285)------------------------------
% 1.95/0.82 % (3177285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.82 % (3177285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.82 % (3177285)CaDiCaL version: 2.1.3
% 1.95/0.82 % (3177285)Termination reason: Instruction limit
% 1.95/0.82 % (3177285)Termination phase: Saturation
% 1.95/0.82 % (3177285)Time elapsed: 0.034 s
% 1.95/0.82 % (3177285)Peak memory usage: 12 MB
% 1.95/0.82 % (3177285)Instructions burned: 104 (million)
% 1.95/0.82 % (3177296)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=469713624:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.95/0.82 % TRYING [5]
% 1.95/0.82 % TRYING [1]
% 1.95/0.82 % TRYING [2]
% 1.95/0.82 % TRYING [3]
% 1.95/0.82 % TRYING [4]
% 1.95/0.82 % TRYING [5]
% 1.95/0.82 % (3177286)Instruction limit reached!
% 1.95/0.82 % (3177286)------------------------------
% 1.95/0.82 % (3177286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.83 % (3177286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.83 % (3177286)CaDiCaL version: 2.1.3
% 1.95/0.83 % (3177286)Termination reason: Instruction limit
% 1.95/0.83 % (3177286)Termination phase: Saturation
% 1.95/0.83 % (3177286)Time elapsed: 0.067 s
% 1.95/0.83 % (3177286)Peak memory usage: 12 MB
% 1.95/0.83 % (3177286)Instructions burned: 118 (million)
% 1.95/0.83 % (3177287)Instruction limit reached!
% 1.95/0.83 % (3177287)------------------------------
% 1.95/0.83 % (3177287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.83 % (3177287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.83 % (3177287)CaDiCaL version: 2.1.3
% 1.95/0.83 % (3177287)Termination reason: Instruction limit
% 1.95/0.83 % (3177287)Termination phase: Saturation
% 1.95/0.83 % (3177287)Time elapsed: 0.076 s
% 1.95/0.83 % (3177287)Peak memory usage: 14 MB
% 1.95/0.83 % (3177287)Instructions burned: 131 (million)
% 1.95/0.83 % (3177298)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2252401164:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.95/0.83 % TRYING [6]
% 1.95/0.83 % (3177299)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=924094725:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.95/0.83 % (3177288)Instruction limit reached!
% 1.95/0.83 % (3177288)------------------------------
% 1.95/0.83 % (3177288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.83 % (3177288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.83 % (3177288)CaDiCaL version: 2.1.3
% 1.95/0.83 % (3177288)Termination reason: Instruction limit
% 1.95/0.83 % (3177288)Termination phase: Saturation
% 1.95/0.83 % (3177288)Time elapsed: 0.097 s
% 1.95/0.83 % (3177288)Peak memory usage: 15 MB
% 1.95/0.83 % (3177288)Instructions burned: 159 (million)
% 1.95/0.83 % TRYING [6]
% 1.95/0.83 % (3177302)ott-21_1_sil=16000:fs=off:random_seed=413679860:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.95/0.83 % (3177298)Instruction limit reached!
% 1.95/0.83 % (3177298)------------------------------
% 1.95/0.83 % (3177298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.83 % (3177298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.83 % (3177298)CaDiCaL version: 2.1.3
% 1.95/0.83 % (3177298)Termination reason: Instruction limit
% 1.95/0.83 % (3177298)Termination phase: Saturation
% 1.95/0.83 % (3177298)Time elapsed: 0.066 s
% 1.95/0.83 % (3177298)Peak memory usage: 12 MB
% 1.95/0.83 % (3177298)Instructions burned: 131 (million)
% 1.95/0.83 % (3177304)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3657165166:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.95/0.83 % (3177296)Instruction limit reached!
% 1.95/0.83 % (3177296)------------------------------
% 1.95/0.83 % (3177296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.83 % (3177296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.83 % (3177296)CaDiCaL version: 2.1.3
% 1.95/0.83 % (3177296)Termination reason: Instruction limit
% 1.95/0.83 % (3177296)Termination phase: Finite model building SAT solving
% 1.95/0.83 % (3177296)Time elapsed: 0.149 s
% 1.95/0.83 % (3177296)Peak memory usage: 34 MB
% 1.95/0.83 % (3177296)Instructions burned: 717 (million)
% 1.95/0.83 % (3177306)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1076412532:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.95/0.83 % TRYING [1]
% 1.95/0.83 % TRYING [2]
% 1.95/0.83 % TRYING [3]
% 1.95/0.83 % TRYING [4]
% 1.95/0.83 % (3177302)Instruction limit reached!
% 1.95/0.83 % (3177302)------------------------------
% 1.95/0.83 % (3177302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.83 % (3177302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.83 % (3177302)CaDiCaL version: 2.1.3
% 1.95/0.83 % (3177302)Termination reason: Instruction limit
% 1.95/0.83 % (3177302)Termination phase: Saturation
% 1.95/0.83 % (3177302)Time elapsed: 0.095 s
% 1.95/0.83 % (3177302)Peak memory usage: 13 MB
% 1.95/0.83 % (3177302)Instructions burned: 182 (million)
% 1.95/0.83 % (3177308)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=556910020:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.95/0.83 % TRYING [5]
% 1.95/0.83 % TRYING [7]
% 1.95/0.83 % (3177308) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3177277-3177308"...
% 1.95/0.83 % (3177308)...printing done.
% 1.95/0.83 % (3177308)Refutation found. Thanks to Tanya!
% 1.95/0.83 % SZS status Theorem for theBenchmark
% 1.95/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 1.95/0.83 % (3177308)------------------------------
% 1.95/0.83 % (3177308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.83 % (3177308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.83 % (3177308)CaDiCaL version: 2.1.3
% 1.95/0.83 % (3177308)Termination reason: Refutation
% 1.95/0.83 % (3177308)Time elapsed: 0.119 s
% 1.95/0.83 % (3177308)Peak memory usage: 15 MB
% 1.95/0.83 % (3177308)Instructions burned: 210 (million)
% 1.95/0.83 % (3177277)Success in time 0.395 s
% 1.95/0.83 % Vampire exiting
%------------------------------------------------------------------------------