%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG062+1 : 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 : n005.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 12:35:20 PM UTC 2026
% Result : Theorem 7.50s 2.04s
% Output : Refutation 8.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 106 ( 29 unt; 11 def)
% Number of atoms : 314 ( 51 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 389 ( 181 ~; 176 |; 17 &)
% ( 11 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] :
( ( aScalar0(X0)
& aScalar0(X1) )
=> aScalar0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X0)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(f12,axiom,
! [X0] :
( aScalar0(X0)
=> aScalar0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aScalar0(X0)
& aScalar0(X1)
& aScalar0(X2) )
=> ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).
fof(f52,axiom,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(f54,axiom,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(f58,axiom,
( sdtasdt0(xR,smndt0(xS)) = smndt0(xN)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2144) ).
fof(f60,axiom,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2221) ).
fof(f61,conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f62,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(negated_conjecture,[status(cth)],[f61]) ).
fof(f68,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(flattening,[],[f62]) ).
fof(f75,plain,
! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f76,plain,
! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f78,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(flattening,[],[f81]) ).
fof(f136,plain,
! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f137,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f138,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f149,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f150,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f205,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f52]) ).
fof(f209,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f54]) ).
fof(f214,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(cnf_transformation,[],[f58]) ).
fof(f216,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(cnf_transformation,[],[f58]) ).
fof(f218,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(cnf_transformation,[],[f60]) ).
fof(f219,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(cnf_transformation,[],[f68]) ).
fof(f223,plain,
! [X2] :
( ~ aScalar0(X2)
| sP2 ),
inference(cnf_transformation,[],[f223_D]) ).
fof(f223_D,definition,
( ! [X2] : ~ aScalar0(X2)
<=> ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[general_splitting_component_introduction]) ).
fof(f224,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ sP2 ),
inference(general_splitting,[],[f149,f223_D]) ).
fof(f228,definition,
( spl4_1
<=> sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f230,plain,
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN))
| spl4_1 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f231,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f219,f228]) ).
fof(f248,definition,
( spl4_2
<=> sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f250,plain,
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)))
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
spl4_2,
inference(avatar_split_clause,[],[f218,f248]) ).
fof(f298,definition,
( spl4_4
<=> sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f300,plain,
( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f301,plain,
spl4_4,
inference(avatar_split_clause,[],[f214,f298]) ).
fof(f302,plain,
( aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(smndt0(xS))
| ~ spl4_4 ),
inference(superposition,[],[f137,f300]) ).
fof(f334,plain,
( aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS))
| ~ spl4_4 ),
inference(duplicate_literal_removal,[],[f302]) ).
fof(f336,definition,
( spl4_5
<=> aScalar0(xR) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f338,plain,
( aScalar0(xR)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f339,plain,
spl4_5,
inference(avatar_split_clause,[],[f205,f336]) ).
fof(f398,plain,
( sP2
| ~ spl4_5 ),
inference(resolution,[],[f338,f223]) ).
fof(f409,plain,
( ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1) )
| ~ spl4_5 ),
inference(backward_subsumption_resolution,[],[f224,f398]) ).
fof(f411,definition,
( spl4_6
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f412,plain,
( ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f413,plain,
( spl4_6
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f409,f336,f411]) ).
fof(f455,plain,
( ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X1,sdtpldt0(X0,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X0)
| ~ aScalar0(X1) )
| ~ spl4_6 ),
inference(superposition,[],[f150,f412]) ).
fof(f483,plain,
( ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X1,sdtpldt0(X0,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2) )
| ~ spl4_6 ),
inference(duplicate_literal_removal,[],[f455]) ).
fof(f535,definition,
( spl4_8
<=> sdtasdt0(xR,smndt0(xS)) = smndt0(xN) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f537,plain,
( sdtasdt0(xR,smndt0(xS)) = smndt0(xN)
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f538,plain,
spl4_8,
inference(avatar_split_clause,[],[f216,f535]) ).
fof(f539,plain,
( aScalar0(smndt0(xN))
| ~ aScalar0(xR)
| ~ aScalar0(smndt0(xS))
| ~ spl4_8 ),
inference(superposition,[],[f137,f537]) ).
fof(f568,plain,
( aScalar0(smndt0(xN))
| ~ aScalar0(smndt0(xS))
| ~ spl4_5
| ~ spl4_8 ),
inference(forward_subsumption_resolution,[],[f539,f338]) ).
fof(f570,definition,
( spl4_9
<=> aScalar0(xS) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
fof(f572,plain,
( aScalar0(xS)
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f573,plain,
spl4_9,
inference(avatar_split_clause,[],[f209,f570]) ).
fof(f578,plain,
( aScalar0(smndt0(xS))
| ~ spl4_9 ),
inference(resolution,[],[f572,f138]) ).
fof(f649,plain,
( aScalar0(sdtasdt0(xS,xS))
| ~ spl4_4
| ~ spl4_9 ),
inference(backward_subsumption_resolution,[],[f334,f578]) ).
fof(f664,plain,
( aScalar0(smndt0(xN))
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9 ),
inference(backward_subsumption_resolution,[],[f568,f578]) ).
fof(f680,definition,
( spl4_10
<=> aScalar0(sdtasdt0(xR,xR)) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
fof(f681,plain,
( aScalar0(sdtasdt0(xR,xR))
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f682,plain,
( ~ aScalar0(sdtasdt0(xR,xR))
| spl4_10 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f688,plain,
( ~ aScalar0(xR)
| ~ aScalar0(xR)
| spl4_10 ),
inference(resolution,[],[f682,f137]) ).
fof(f689,plain,
( ~ aScalar0(xR)
| spl4_10 ),
inference(duplicate_literal_removal,[],[f688]) ).
fof(f690,plain,
( $false
| ~ spl4_5
| spl4_10 ),
inference(forward_subsumption_resolution,[],[f689,f338]) ).
fof(f691,plain,
( ~ spl4_5
| spl4_10 ),
inference(avatar_contradiction_clause,[],[f690]) ).
fof(f698,plain,
( ! [X0] :
( aScalar0(sdtpldt0(sdtasdt0(xR,xR),X0))
| ~ aScalar0(X0) )
| ~ spl4_10 ),
inference(resolution,[],[f681,f136]) ).
fof(f871,definition,
( spl4_13
<=> ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X1,sdtpldt0(X0,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2) ) ),
introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition]) ).
fof(f872,plain,
( ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X1,sdtpldt0(X0,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(X2) )
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f871]) ).
fof(f873,plain,
( spl4_13
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f483,f411,f871]) ).
fof(f900,plain,
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xS,xS),sdtpldt0(sdtasdt0(xR,xR),smndt0(xN))),smndt0(xN))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(smndt0(xN))
| spl4_1
| ~ spl4_13 ),
inference(superposition,[],[f230,f872]) ).
fof(f941,plain,
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xS,xS),sdtpldt0(sdtasdt0(xR,xR),smndt0(xN))),smndt0(xN))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(smndt0(xN))
| spl4_1
| ~ spl4_4
| ~ spl4_9
| ~ spl4_13 ),
inference(forward_subsumption_resolution,[],[f900,f649]) ).
fof(f961,plain,
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xS,xS),sdtpldt0(sdtasdt0(xR,xR),smndt0(xN))),smndt0(xN))
| ~ aScalar0(smndt0(xN))
| spl4_1
| ~ spl4_4
| ~ spl4_9
| ~ spl4_10
| ~ spl4_13 ),
inference(forward_subsumption_resolution,[],[f941,f681]) ).
fof(f972,plain,
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xS,xS),sdtpldt0(sdtasdt0(xR,xR),smndt0(xN))),smndt0(xN))
| spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9
| ~ spl4_10
| ~ spl4_13 ),
inference(forward_subsumption_resolution,[],[f961,f664]) ).
fof(f974,definition,
( spl4_14
<=> sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xS,xS),sdtpldt0(sdtasdt0(xR,xR),smndt0(xN))),smndt0(xN)) ),
introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition]) ).
fof(f976,plain,
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xS,xS),sdtpldt0(sdtasdt0(xR,xR),smndt0(xN))),smndt0(xN))
| spl4_14 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f977,plain,
( ~ spl4_14
| spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9
| ~ spl4_10
| ~ spl4_13 ),
inference(avatar_split_clause,[],[f972,f871,f680,f570,f535,f336,f298,f228,f974]) ).
fof(f1004,plain,
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xN))
| ~ spl4_13
| spl4_14 ),
inference(superposition,[],[f976,f872]) ).
fof(f1011,plain,
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xN))
| ~ spl4_10
| ~ spl4_13
| spl4_14 ),
inference(forward_subsumption_resolution,[],[f1004,f698]) ).
fof(f1015,plain,
( ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xN))
| ~ spl4_2
| ~ spl4_10
| ~ spl4_13
| spl4_14 ),
inference(forward_subsumption_resolution,[],[f1011,f250]) ).
fof(f1019,plain,
( ~ aScalar0(smndt0(xN))
| ~ spl4_2
| ~ spl4_4
| ~ spl4_9
| ~ spl4_10
| ~ spl4_13
| spl4_14 ),
inference(forward_subsumption_resolution,[],[f1015,f649]) ).
fof(f1020,plain,
( $false
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9
| ~ spl4_10
| ~ spl4_13
| spl4_14 ),
inference(forward_subsumption_resolution,[],[f1019,f664]) ).
fof(f1021,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9
| ~ spl4_10
| ~ spl4_13
| spl4_14 ),
inference(avatar_contradiction_clause,[],[f1020]) ).
cnf(s1,plain,
~ spl4_1,
inference(sat_conversion,[],[f231]) ).
cnf(s2,plain,
spl4_2,
inference(sat_conversion,[],[f251]) ).
cnf(s4,plain,
spl4_4,
inference(sat_conversion,[],[f301]) ).
cnf(s5,plain,
spl4_5,
inference(sat_conversion,[],[f339]) ).
cnf(s6,plain,
( ~ spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f413]) ).
cnf(s8,plain,
spl4_8,
inference(sat_conversion,[],[f538]) ).
cnf(s9,plain,
spl4_9,
inference(sat_conversion,[],[f573]) ).
cnf(s11,plain,
( ~ spl4_5
| spl4_10 ),
inference(sat_conversion,[],[f691]) ).
cnf(s13,plain,
( ~ spl4_6
| spl4_13 ),
inference(sat_conversion,[],[f873]) ).
cnf(s14,plain,
( spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9
| ~ spl4_10
| ~ spl4_13
| ~ spl4_14 ),
inference(sat_conversion,[],[f977]) ).
cnf(s17,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9
| ~ spl4_10
| ~ spl4_13
| spl4_14 ),
inference(sat_conversion,[],[f1021]) ).
cnf(s20,plain,
spl4_10,
inference(rat,[],[s11,s5]) ).
cnf(s22,plain,
spl4_6,
inference(rat,[],[s6,s5]) ).
cnf(s24,plain,
spl4_13,
inference(rat,[],[s13,s22]) ).
cnf(s25,plain,
spl4_14,
inference(rat,[],[s17,s4,s24,s20,s9,s8,s5,s2]) ).
cnf(s26,plain,
spl4_1,
inference(rat,[],[s14,s4,s24,s20,s9,s8,s5,s25]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s1,s26]) ).
fof(f1022,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG062+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 23:03:47 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 7.50/2.04 % (283674)Detected formulas, will run a generic FOF schedule.
% 7.50/2.04 % (283679)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=1281243335:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.50/2.04 % (283683)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2496264116:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.50/2.04 % (283682)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=106270471:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.50/2.04 % (283684)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1625058006:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.50/2.04 % (283685)dis-21_1_sil=8000:lcm=predicate:random_seed=3362782780: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)
% 7.50/2.04 % (283680)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=100573365:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.50/2.04 % (283681)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=4153636906:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.50/2.04 % (283682)Instruction limit reached!
% 7.50/2.04 % (283682)------------------------------
% 7.50/2.04 % (283682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283682)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283682)Termination reason: Instruction limit
% 7.50/2.04 % (283682)Termination phase: Saturation
% 7.50/2.04 % (283682)Time elapsed: 0.055 s
% 7.50/2.04 % (283682)Peak memory usage: 89 MB
% 7.50/2.04 % (283682)Instructions burned: 111 (million)
% 7.50/2.04 % (283683)Instruction limit reached!
% 7.50/2.04 % (283683)------------------------------
% 7.50/2.04 % (283683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283683)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283683)Termination reason: Instruction limit
% 7.50/2.04 % (283683)Termination phase: Saturation
% 7.50/2.04 % (283683)Time elapsed: 0.069 s
% 7.50/2.04 % (283683)Peak memory usage: 88 MB
% 7.50/2.04 % (283683)Instructions burned: 120 (million)
% 7.50/2.04 % (283685)Instruction limit reached!
% 7.50/2.04 % (283685)------------------------------
% 7.50/2.04 % (283685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283685)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283685)Termination reason: Instruction limit
% 7.50/2.04 % (283685)Termination phase: Saturation
% 7.50/2.04 % (283685)Time elapsed: 0.069 s
% 7.50/2.04 % (283685)Peak memory usage: 89 MB
% 7.50/2.04 % (283685)Instructions burned: 129 (million)
% 7.50/2.04 % (283684)Instruction limit reached!
% 7.50/2.04 % (283684)------------------------------
% 7.50/2.04 % (283684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283684)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283684)Termination reason: Instruction limit
% 7.50/2.04 % (283684)Termination phase: Saturation
% 7.50/2.04 % (283684)Time elapsed: 0.088 s
% 7.50/2.04 % (283684)Peak memory usage: 90 MB
% 7.50/2.04 % (283684)Instructions burned: 139 (million)
% 7.50/2.04 % (283693)lrs+10_1_sil=8000:sp=occurrence:random_seed=619832916:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 7.50/2.04 % (283695)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3214447033:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.50/2.04 % (283694)lrs+10_1_sil=32000:urr=on:br=off:random_seed=563235660:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.50/2.04 % (283696)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=3458658980:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 7.50/2.04 % (283694)Instruction limit reached!
% 7.50/2.04 % (283694)------------------------------
% 7.50/2.04 % (283694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283694)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283694)Termination reason: Instruction limit
% 7.50/2.04 % (283694)Termination phase: Saturation
% 7.50/2.04 % (283694)Time elapsed: 0.076 s
% 7.50/2.04 % (283694)Peak memory usage: 92 MB
% 7.50/2.04 % (283694)Instructions burned: 158 (million)
% 7.50/2.04 % (283696)Instruction limit reached!
% 7.50/2.04 % (283696)------------------------------
% 7.50/2.04 % (283696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283696)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283696)Termination reason: Instruction limit
% 7.50/2.04 % (283696)Termination phase: Saturation
% 7.50/2.04 % (283696)Time elapsed: 0.110 s
% 7.50/2.04 % (283696)Peak memory usage: 95 MB
% 7.50/2.04 % (283696)Instructions burned: 249 (million)
% 7.50/2.04 % (283693)Instruction limit reached!
% 7.50/2.04 % (283693)------------------------------
% 7.50/2.04 % (283693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283693)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283693)Termination reason: Instruction limit
% 7.50/2.04 % (283693)Termination phase: Saturation
% 7.50/2.04 % (283693)Time elapsed: 0.167 s
% 7.50/2.04 % (283693)Peak memory usage: 93 MB
% 7.50/2.04 % (283693)Instructions burned: 285 (million)
% 7.50/2.04 % (283695)Instruction limit reached!
% 7.50/2.04 % (283695)------------------------------
% 7.50/2.04 % (283695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283695)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283695)Termination reason: Instruction limit
% 7.50/2.04 % (283695)Termination phase: Saturation
% 7.50/2.04 % (283695)Time elapsed: 0.192 s
% 7.50/2.04 % (283695)Peak memory usage: 94 MB
% 7.50/2.04 % (283695)Instructions burned: 326 (million)
% 7.50/2.04 % (283701)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=165217409:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 7.50/2.04 % (283702)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1592999262:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 7.50/2.04 % (283703)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3336110139:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 7.50/2.04 % (283704)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1051358619:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 7.50/2.04 % (283703)Instruction limit reached!
% 7.50/2.04 % (283703)------------------------------
% 7.50/2.04 % (283703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283703)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283703)Termination reason: Instruction limit
% 7.50/2.04 % (283703)Termination phase: Saturation
% 7.50/2.04 % (283703)Time elapsed: 0.072 s
% 7.50/2.04 % (283703)Peak memory usage: 91 MB
% 7.50/2.04 % (283703)Instructions burned: 114 (million)
% 7.50/2.04 % (283701)Instruction limit reached!
% 7.50/2.04 % (283701)------------------------------
% 7.50/2.04 % (283701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283701)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283701)Termination reason: Instruction limit
% 7.50/2.04 % (283701)Termination phase: Saturation
% 7.50/2.04 % (283701)Time elapsed: 0.168 s
% 7.50/2.04 % (283701)Peak memory usage: 90 MB
% 7.50/2.04 % (283701)Instructions burned: 295 (million)
% 7.50/2.04 % (283704)Instruction limit reached!
% 7.50/2.04 % (283704)------------------------------
% 7.50/2.04 % (283704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283704)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283704)Termination reason: Instruction limit
% 7.50/2.04 % (283704)Termination phase: Saturation
% 7.50/2.04 % (283704)Time elapsed: 0.066 s
% 7.50/2.04 % (283704)Peak memory usage: 89 MB
% 7.50/2.04 % (283704)Instructions burned: 128 (million)
% 7.50/2.04 % (283681)First to succeed.
% 7.50/2.04 % (283681)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-283674"
% 7.50/2.04 % (283709)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4208746598:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 7.50/2.04 % (283710)lrs+10_1_sil=8000:sp=occurrence:random_seed=3947362753:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 7.50/2.04 % (283711)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2243051561:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 7.50/2.04 % (283711)Also succeeded, but the first one will report.
% 7.50/2.04 % (283709)Instruction limit reached!
% 7.50/2.04 % (283709)------------------------------
% 7.50/2.04 % (283709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.50/2.04 % (283709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.50/2.04 % (283709)CaDiCaL version: 2.1.3
% 7.50/2.04 % (283709)Termination reason: Instruction limit
% 7.50/2.04 % (283709)Termination phase: Saturation
% 7.50/2.04 % (283709)Time elapsed: 0.062 s
% 7.50/2.04 % (283709)Peak memory usage: 89 MB
% 7.50/2.04 % (283709)Instructions burned: 114 (million)
% 7.50/2.04 % (283715)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=703891698:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 7.50/2.04 % (283681)Refutation found. Thanks to Tanya!
% 7.50/2.04 % SZS status Theorem for theBenchmark
% 7.50/2.04 % SZS output start Proof for theBenchmark
% See solution above
% 8.94/2.23 % (283681)------------------------------
% 8.94/2.23 % (283681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.94/2.23 % (283681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.94/2.23 % (283681)CaDiCaL version: 2.1.3
% 8.94/2.23 % (283681)Termination reason: Refutation
% 8.94/2.23 % (283681)Time elapsed: 0.739 s
% 8.94/2.23 % (283681)Peak memory usage: 130 MB
% 8.94/2.23 % (283681)Instructions burned: 1087 (million)
% 8.94/2.23 % (283681)------------------------------
% 8.94/2.23 % (283681)------------------------------
% 8.94/2.23 % (283674)Success in time 1.179 s
% 8.94/2.23 % Vampire exiting
%------------------------------------------------------------------------------