%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM524+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:15:35 PM UTC 2026
% Result : Theorem 4.71s 2.21s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 98 ( 29 unt; 2 def)
% Number of atoms : 335 ( 112 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 426 ( 189 ~; 182 |; 39 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 72 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| sdtasdt0(X1,X0) = sdtasdt0(X2,X0) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
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(f36,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( aNaturalNumber0(X2)
=> sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
fof(f40,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(f42,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(f44,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(f45,axiom,
( aNaturalNumber0(xq)
& xn = sdtasdt0(xp,xq)
& xq = sdtsldt0(xn,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(f46,conjecture,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f48,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
& doDivides0(xp,xn) ),
inference(rectify,[],[f44]) ).
fof(f49,plain,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(flattening,[],[f47]) ).
fof(f76,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f77,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f76]) ).
fof(f83,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f84,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f83]) ).
fof(f107,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f108,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f107]) ).
fof(f116,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f117,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f116]) ).
fof(f118,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(f119,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,[],[f118]) ).
fof(f121,plain,
( aNaturalNumber0(sK2)
& sdtasdt0(xn,xn) = sdtasdt0(xp,sK2)
& doDivides0(xp,sdtasdt0(xn,xn))
& aNaturalNumber0(sK3)
& xn = sdtasdt0(xp,sK3)
& doDivides0(xp,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f48]) ).
fof(f133,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,[],[f119]) ).
fof(f134,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,[],[f133]) ).
fof(f135,plain,
sz00 != xp,
inference(cnf_transformation,[],[f40]) ).
fof(f138,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f139,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f140,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f148,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f153,plain,
doDivides0(xp,xn),
inference(cnf_transformation,[],[f121]) ).
fof(f154,plain,
xn = sdtasdt0(xp,sK3),
inference(cnf_transformation,[],[f121]) ).
fof(f155,plain,
aNaturalNumber0(sK3),
inference(cnf_transformation,[],[f121]) ).
fof(f156,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(cnf_transformation,[],[f121]) ).
fof(f157,plain,
sdtasdt0(xn,xn) = sdtasdt0(xp,sK2),
inference(cnf_transformation,[],[f121]) ).
fof(f158,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f121]) ).
fof(f159,plain,
xq = sdtsldt0(xn,xp),
inference(cnf_transformation,[],[f45]) ).
fof(f160,plain,
xn = sdtasdt0(xp,xq),
inference(cnf_transformation,[],[f45]) ).
fof(f161,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[],[f45]) ).
fof(f162,plain,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(cnf_transformation,[],[f49]) ).
fof(f186,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f193,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f219,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f225,plain,
! [X2,X0,X1] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f228,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f235,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f228]) ).
fof(f239,plain,
xn = sdtasdt0(xp,sdtsldt0(xn,xp)),
inference(forward_demodulation,[],[f160,f159]) ).
fof(f240,plain,
aNaturalNumber0(sdtsldt0(xn,xp)),
inference(forward_demodulation,[],[f161,f159]) ).
fof(f280,plain,
! [X0] :
( sdtasdt0(xp,sdtasdt0(sK3,X0)) = sdtasdt0(xn,X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f193,f154]) ).
fof(f289,plain,
! [X0] :
( sdtasdt0(xp,sdtasdt0(sK3,X0)) = sdtasdt0(xn,X0)
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f280,f138]) ).
fof(f309,plain,
! [X0] :
( sdtasdt0(xp,sdtasdt0(sK3,X0)) = sdtasdt0(xn,X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f289,f155]) ).
fof(f367,definition,
( spl8_9
<=> aNaturalNumber0(sdtasdt0(xn,xn)) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
fof(f368,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f369,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| spl8_9 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f391,plain,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))),
inference(superposition,[],[f162,f159]) ).
fof(f411,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK2) ),
inference(superposition,[],[f219,f157]) ).
fof(f418,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK2)
| spl8_9 ),
inference(forward_subsumption_resolution,[],[f411,f369]) ).
fof(f439,plain,
( ~ aNaturalNumber0(sK2)
| spl8_9 ),
inference(forward_subsumption_resolution,[],[f418,f138]) ).
fof(f458,plain,
( $false
| spl8_9 ),
inference(forward_subsumption_resolution,[],[f439,f158]) ).
fof(f459,plain,
spl8_9,
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f526,plain,
! [X0] :
( xn != sdtasdt0(xp,X0)
| sdtsldt0(xn,xp) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| sz00 = xp
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f186,f239]) ).
fof(f543,plain,
! [X0] :
( xn != sdtasdt0(xp,X0)
| sdtsldt0(xn,xp) = X0
| ~ aNaturalNumber0(X0)
| sz00 = xp
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f526,f240]) ).
fof(f556,plain,
! [X0] :
( xn != sdtasdt0(xp,X0)
| sdtsldt0(xn,xp) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f543,f135]) ).
fof(f562,plain,
! [X0] :
( sdtsldt0(xn,xp) = X0
| xn != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f556,f138]) ).
fof(f595,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(superposition,[],[f235,f148]) ).
fof(f596,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(forward_subsumption_resolution,[],[f595,f135]) ).
fof(f618,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(forward_subsumption_resolution,[],[f596,f156]) ).
fof(f640,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(forward_subsumption_resolution,[],[f618,f138]) ).
fof(f642,definition,
( spl8_20
<=> aNaturalNumber0(sdtasdt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[spl8_20])],[avatar_definition]) ).
fof(f643,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ spl8_20 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f644,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| spl8_20 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f706,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ spl8_9 ),
inference(forward_subsumption_resolution,[],[f640,f368]) ).
fof(f1125,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| spl8_20 ),
inference(resolution,[],[f644,f219]) ).
fof(f1126,plain,
( ~ aNaturalNumber0(xm)
| spl8_20 ),
inference(duplicate_literal_removal,[],[f1125]) ).
fof(f1127,plain,
( $false
| spl8_20 ),
inference(forward_subsumption_resolution,[],[f1126,f139]) ).
fof(f1128,plain,
spl8_20,
inference(avatar_contradiction_clause,[],[f1127]) ).
fof(f1149,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ spl8_9
| ~ spl8_20 ),
inference(forward_subsumption_resolution,[],[f706,f643]) ).
fof(f1206,plain,
( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ spl8_9
| ~ spl8_20 ),
inference(superposition,[],[f391,f1149]) ).
fof(f1384,plain,
( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xn,sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xn)
| sz00 = xp
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ spl8_9
| ~ spl8_20 ),
inference(superposition,[],[f1206,f225]) ).
fof(f1385,plain,
( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xn,sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xn)
| sz00 = xp
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ spl8_9
| ~ spl8_20 ),
inference(duplicate_literal_removal,[],[f1384]) ).
fof(f1386,plain,
( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xn,sdtsldt0(xn,xp))
| sz00 = xp
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ spl8_9
| ~ spl8_20 ),
inference(forward_subsumption_resolution,[],[f1385,f140]) ).
fof(f1387,plain,
( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xn,sdtsldt0(xn,xp))
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ spl8_9
| ~ spl8_20 ),
inference(forward_subsumption_resolution,[],[f1386,f135]) ).
fof(f1388,plain,
( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xn,sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ spl8_9
| ~ spl8_20 ),
inference(forward_subsumption_resolution,[],[f1387,f153]) ).
fof(f1389,plain,
( sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xn,sdtsldt0(xn,xp))
| ~ spl8_9
| ~ spl8_20 ),
inference(forward_subsumption_resolution,[],[f1388,f138]) ).
fof(f1743,plain,
( ! [X0] :
( sdtasdt0(xn,X0) != sdtasdt0(xp,sdtasdt0(X0,X0))
| xn != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl8_9
| ~ spl8_20 ),
inference(superposition,[],[f1389,f562]) ).
fof(f1756,plain,
( sdtasdt0(xn,sK3) != sdtasdt0(xn,sK3)
| xn != sdtasdt0(xp,sK3)
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(sK3)
| ~ spl8_9
| ~ spl8_20 ),
inference(superposition,[],[f1743,f309]) ).
fof(f1759,plain,
( sdtasdt0(xn,sK3) != sdtasdt0(xn,sK3)
| xn != sdtasdt0(xp,sK3)
| ~ aNaturalNumber0(sK3)
| ~ spl8_9
| ~ spl8_20 ),
inference(duplicate_literal_removal,[],[f1756]) ).
fof(f1760,plain,
( xn != sdtasdt0(xp,sK3)
| ~ aNaturalNumber0(sK3)
| ~ spl8_9
| ~ spl8_20 ),
inference(trivial_inequality_removal,[],[f1759]) ).
fof(f1768,plain,
( ~ aNaturalNumber0(sK3)
| ~ spl8_9
| ~ spl8_20 ),
inference(forward_subsumption_resolution,[],[f1760,f154]) ).
fof(f1778,plain,
( $false
| ~ spl8_9
| ~ spl8_20 ),
inference(forward_subsumption_resolution,[],[f1768,f155]) ).
fof(f1779,plain,
( ~ spl8_9
| ~ spl8_20 ),
inference(avatar_contradiction_clause,[],[f1778]) ).
cnf(s10,plain,
spl8_9,
inference(sat_conversion,[],[f459]) ).
cnf(s47,plain,
spl8_20,
inference(sat_conversion,[],[f1128]) ).
cnf(s68,plain,
( ~ spl8_9
| ~ spl8_20 ),
inference(sat_conversion,[],[f1779]) ).
cnf(s71,plain,
~ spl8_9,
inference(rat,[],[s68,s47]) ).
cnf(s94,plain,
$false,
inference(rat,[],[s10,s71]) ).
fof(f1799,plain,
$false,
inference(avatar_sat_refutation,[],[s94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM524+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n010.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 20:20:47 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.71/2.20 % (1283964)Detected formulas, will run a generic FOF schedule.
% 4.71/2.20 % (1283978)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4141113184:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.71/2.20 % (1283980)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=857936698:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.71/2.20 % (1283978)Instruction limit reached!
% 4.71/2.20 % (1283978)------------------------------
% 4.71/2.20 % (1283978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/2.20 % (1283978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/2.20 % (1283978)CaDiCaL version: 2.1.3
% 4.71/2.20 % (1283978)Termination reason: Instruction limit
% 4.71/2.20 % (1283978)Termination phase: Saturation
% 4.71/2.20 % (1283978)Time elapsed: 0.065 s
% 4.71/2.20 % (1283978)Peak memory usage: 89 MB
% 4.71/2.20 % (1283978)Instructions burned: 109 (million)
% 4.71/2.20 % (1283977)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=422111724:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.71/2.20 % (1283979)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3211740648:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.71/2.20 % (1283975)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=1527208468:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.71/2.20 % (1283976)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=2575249229:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.71/2.20 % (1283980)Instruction limit reached!
% 4.71/2.20 % (1283980)------------------------------
% 4.71/2.20 % (1283980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/2.20 % (1283980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/2.20 % (1283980)CaDiCaL version: 2.1.3
% 4.71/2.20 % (1283980)Termination reason: Instruction limit
% 4.71/2.20 % (1283980)Termination phase: Saturation
% 4.71/2.20 % (1283980)Time elapsed: 0.077 s
% 4.71/2.20 % (1283980)Peak memory usage: 90 MB
% 4.71/2.20 % (1283980)Instructions burned: 139 (million)
% 4.71/2.20 % (1283981)dis-21_1_sil=8000:lcm=predicate:random_seed=3010842830: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)
% 4.71/2.20 % (1283979)Instruction limit reached!
% 4.71/2.20 % (1283979)------------------------------
% 4.71/2.20 % (1283979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/2.20 % (1283979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/2.20 % (1283979)CaDiCaL version: 2.1.3
% 4.71/2.20 % (1283979)Termination reason: Instruction limit
% 4.71/2.20 % (1283979)Termination phase: Saturation
% 4.71/2.20 % (1283979)Time elapsed: 0.109 s
% 4.71/2.20 % (1283979)Peak memory usage: 88 MB
% 4.71/2.20 % (1283979)Instructions burned: 120 (million)
% 4.71/2.20 % (1283981)Instruction limit reached!
% 4.71/2.20 % (1283981)------------------------------
% 4.71/2.20 % (1283981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/2.20 % (1283981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/2.20 % (1283981)CaDiCaL version: 2.1.3
% 4.71/2.20 % (1283981)Termination reason: Instruction limit
% 4.71/2.20 % (1283981)Termination phase: Saturation
% 4.71/2.20 % (1283981)Time elapsed: 0.133 s
% 4.71/2.20 % (1283981)Peak memory usage: 91 MB
% 4.71/2.20 % (1283981)Instructions burned: 130 (million)
% 4.71/2.20 % (1283990)lrs+10_1_sil=8000:sp=occurrence:random_seed=450182476:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.71/2.20 % (1283991)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3402102503:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.71/2.20 % (1283991)Instruction limit reached!
% 4.71/2.20 % (1283991)------------------------------
% 4.71/2.20 % (1283991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/2.20 % (1283991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/2.20 % (1283991)CaDiCaL version: 2.1.3
% 4.71/2.20 % (1283991)Termination reason: Instruction limit
% 4.71/2.20 % (1283991)Termination phase: Saturation
% 4.71/2.20 % (1283991)Time elapsed: 0.078 s
% 4.71/2.20 % (1283991)Peak memory usage: 91 MB
% 4.71/2.20 % (1283991)Instructions burned: 157 (million)
% 4.71/2.20 % (1283990)Instruction limit reached!
% 4.71/2.20 % (1283990)------------------------------
% 4.71/2.20 % (1283990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/2.20 % (1283990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/2.20 % (1283990)CaDiCaL version: 2.1.3
% 4.71/2.20 % (1283990)Termination reason: Instruction limit
% 4.71/2.20 % (1283990)Termination phase: Saturation
% 4.71/2.20 % (1283990)Time elapsed: 0.140 s
% 4.71/2.20 % (1283990)Peak memory usage: 91 MB
% 4.71/2.20 % (1283990)Instructions burned: 286 (million)
% 4.71/2.20 % (1283993)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1912233278:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 4.71/2.20 % (1283995)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=1346735516:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.71/2.20 % (1283998)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1678701717:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.71/2.20 % (1283997)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2292475061:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.71/2.20 % (1283997)First to succeed.
% 4.71/2.20 % (1283997)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1283964"
% 4.71/2.20 % (1283995)Instruction limit reached!
% 4.71/2.20 % (1283995)------------------------------
% 4.71/2.20 % (1283995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/2.20 % (1283995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/2.20 % (1283995)CaDiCaL version: 2.1.3
% 4.71/2.20 % (1283995)Termination reason: Instruction limit
% 4.71/2.20 % (1283995)Termination phase: Saturation
% 4.71/2.20 % (1283995)Time elapsed: 0.203 s
% 4.71/2.20 % (1283995)Peak memory usage: 94 MB
% 4.71/2.20 % (1283995)Instructions burned: 249 (million)
% 4.71/2.20 % (1283993)Instruction limit reached!
% 4.71/2.20 % (1283993)------------------------------
% 4.71/2.20 % (1283993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/2.21 % (1283993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/2.21 % (1283993)CaDiCaL version: 2.1.3
% 4.71/2.21 % (1283993)Termination reason: Instruction limit
% 4.71/2.21 % (1283993)Termination phase: Saturation
% 4.71/2.21 % (1283993)Time elapsed: 0.301 s
% 4.71/2.21 % (1283993)Peak memory usage: 91 MB
% 4.71/2.21 % (1283993)Instructions burned: 325 (million)
% 4.71/2.21 % (1284003)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=897255771:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 4.71/2.21 % (1284004)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3061697767:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 4.71/2.21 % (1284003)Instruction limit reached!
% 4.71/2.21 % (1284003)------------------------------
% 4.71/2.21 % (1284003)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/2.21 % (1284003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/2.21 % (1284003)CaDiCaL version: 2.1.3
% 4.71/2.21 % (1284003)Termination reason: Instruction limit
% 4.71/2.21 % (1284003)Termination phase: Saturation
% 4.71/2.21 % (1284003)Time elapsed: 0.116 s
% 4.71/2.21 % (1284003)Peak memory usage: 91 MB
% 4.71/2.21 % (1284003)Instructions burned: 113 (million)
% 4.71/2.21 % (1284004)Instruction limit reached!
% 4.71/2.21 % (1284004)------------------------------
% 4.71/2.21 % (1284004)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/2.21 % (1284004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/2.21 % (1284004)CaDiCaL version: 2.1.3
% 4.71/2.21 % (1284004)Termination reason: Instruction limit
% 4.71/2.21 % (1284004)Termination phase: Saturation
% 4.71/2.21 % (1284004)Time elapsed: 0.105 s
% 4.71/2.21 % (1284004)Peak memory usage: 89 MB
% 4.71/2.21 % (1284004)Instructions burned: 127 (million)
% 4.71/2.21 % (1283997)Refutation found. Thanks to Tanya!
% 4.71/2.21 % SZS status Theorem for theBenchmark
% 4.71/2.21 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/2.50 % (1283997)------------------------------
% 0.22/2.50 % (1283997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/2.50 % (1283997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/2.50 % (1283997)CaDiCaL version: 2.1.3
% 0.22/2.50 % (1283997)Termination reason: Refutation
% 0.22/2.50 % (1283997)Time elapsed: 0.080 s
% 0.22/2.50 % (1283997)Peak memory usage: 90 MB
% 0.22/2.50 % (1283997)Instructions burned: 85 (million)
% 0.22/2.50 % (1283997)------------------------------
% 0.22/2.50 % (1283997)------------------------------
% 0.22/2.50 % (1283964)Success in time 1.213 s
% 0.22/2.50 % Vampire exiting
%------------------------------------------------------------------------------