%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG068+1 : 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:35:22 PM UTC 2026
% Result : Theorem 7.56s 2.81s
% Output : Refutation 14.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 35
% Syntax : Number of formulae : 211 ( 68 unt; 21 def)
% Number of atoms : 633 ( 92 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 810 ( 388 ~; 379 |; 26 &)
% ( 11 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 21 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 98 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f10,axiom,
! [X0,X1] :
( ( aScalar0(X0)
& aScalar0(X1) )
=> aScalar0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X0)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
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/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( aScalar0(X0)
& aScalar0(X1)
& aScalar0(X2) )
=> ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X0)
& aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
fof(f52,axiom,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
fof(f53,axiom,
( aScalar0(xP)
& xP = sdtasdt0(xE,xH) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
fof(f54,axiom,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
fof(f55,axiom,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
fof(f57,axiom,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2004) ).
fof(f58,axiom,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2104) ).
fof(f60,axiom,
sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtasdt0(xS,xS)),xN) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtpldt0(sdtasdt0(xS,xS),xN)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2510) ).
fof(f61,conjecture,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f62,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(negated_conjecture,[status(cth)],[f61]) ).
fof(f68,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
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(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(f83,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(flattening,[],[f83]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(ennf_transformation,[],[f23]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(flattening,[],[f96]) ).
fof(f135,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
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(f147,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f82]) ).
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] :
( ~ aScalar0(X2)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f160,plain,
! [X2,X3,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(cnf_transformation,[],[f97]) ).
fof(f205,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f52]) ).
fof(f207,plain,
aScalar0(xP),
inference(cnf_transformation,[],[f53]) ).
fof(f209,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f54]) ).
fof(f210,plain,
xN = sdtasdt0(xR,xS),
inference(cnf_transformation,[],[f55]) ).
fof(f211,plain,
aScalar0(xN),
inference(cnf_transformation,[],[f55]) ).
fof(f213,plain,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(cnf_transformation,[],[f57]) ).
fof(f214,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(cnf_transformation,[],[f58]) ).
fof(f216,plain,
sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtasdt0(xS,xS)),xN) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtpldt0(sdtasdt0(xS,xS),xN)),
inference(cnf_transformation,[],[f60]) ).
fof(f217,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(cnf_transformation,[],[f68]) ).
fof(f221,definition,
sF2 = sdtasdt0(xP,xP),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f222,plain,
sdtasdt0(xP,xP) = sF2,
inference(reorient_equations,[],[f221]) ).
fof(f223,definition,
sF3 = sdtpldt0(sF2,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f224,plain,
sdtpldt0(sF2,sF2) = sF3,
inference(reorient_equations,[],[f223]) ).
fof(f225,definition,
sF4 = sdtpldt0(sF3,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f226,plain,
sdtpldt0(sF3,sF3) = sF4,
inference(reorient_equations,[],[f225]) ).
fof(f227,definition,
sF5 = sdtasdt0(xR,xR),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f228,plain,
sdtasdt0(xR,xR) = sF5,
inference(reorient_equations,[],[f227]) ).
fof(f229,definition,
sF6 = sdtasdt0(xR,xS),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f230,plain,
sdtasdt0(xR,xS) = sF6,
inference(reorient_equations,[],[f229]) ).
fof(f231,definition,
sF7 = sdtpldt0(sF5,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f232,plain,
sdtpldt0(sF5,sF6) = sF7,
inference(reorient_equations,[],[f231]) ).
fof(f233,definition,
sF8 = sdtasdt0(xS,xR),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f234,plain,
sdtasdt0(xS,xR) = sF8,
inference(reorient_equations,[],[f233]) ).
fof(f235,definition,
sF9 = sdtasdt0(xS,xS),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f236,plain,
sdtasdt0(xS,xS) = sF9,
inference(reorient_equations,[],[f235]) ).
fof(f237,definition,
sF10 = sdtpldt0(sF8,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f238,plain,
sdtpldt0(sF8,sF9) = sF10,
inference(reorient_equations,[],[f237]) ).
fof(f239,definition,
sF11 = sdtpldt0(sF7,sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f240,plain,
sdtpldt0(sF7,sF10) = sF11,
inference(reorient_equations,[],[f239]) ).
fof(f241,plain,
~ sdtlseqdt0(sF4,sF11),
inference(definition_folding,[],[f217,f240,f238,f236,f234,f232,f230,f228,f226,f224,f222,f222,f224,f222,f222]) ).
fof(f243,definition,
( spl12_1
<=> ! [X2] : ~ aScalar0(X2) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f244,plain,
( ! [X2] : ~ aScalar0(X2)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f246,definition,
( spl12_2
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f247,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X0) )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f248,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f147,f246,f243]) ).
fof(f250,definition,
( spl12_3
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f251,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X0) )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f252,plain,
( spl12_1
| spl12_3 ),
inference(avatar_split_clause,[],[f149,f250,f243]) ).
fof(f258,plain,
xN = sF6,
inference(forward_demodulation,[],[f230,f210]) ).
fof(f260,plain,
( aScalar0(sF3)
| ~ aScalar0(sF2)
| ~ aScalar0(sF2) ),
inference(superposition,[],[f136,f224]) ).
fof(f261,plain,
( aScalar0(sF3)
| ~ aScalar0(sF2) ),
inference(duplicate_literal_removal,[],[f260]) ).
fof(f264,definition,
( spl12_5
<=> aScalar0(sF2) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f265,plain,
( aScalar0(sF2)
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f266,plain,
( ~ aScalar0(sF2)
| spl12_5 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f268,definition,
( spl12_6
<=> aScalar0(sF3) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
fof(f270,plain,
( aScalar0(sF3)
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f271,plain,
( ~ spl12_5
| spl12_6 ),
inference(avatar_split_clause,[],[f261,f268,f264]) ).
fof(f283,definition,
( spl12_9
<=> aScalar0(sF7) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f284,plain,
( aScalar0(sF7)
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f291,plain,
( aScalar0(sF7)
| ~ aScalar0(sF5)
| ~ aScalar0(sF6) ),
inference(superposition,[],[f136,f232]) ).
fof(f292,plain,
( ~ aScalar0(xN)
| aScalar0(sF7)
| ~ aScalar0(sF5) ),
inference(forward_demodulation,[],[f291,f258]) ).
fof(f293,plain,
( aScalar0(sF7)
| ~ aScalar0(sF5) ),
inference(forward_subsumption_resolution,[],[f292,f211]) ).
fof(f295,definition,
( spl12_11
<=> aScalar0(sF5) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
fof(f296,plain,
( aScalar0(sF5)
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f297,plain,
( ~ aScalar0(sF5)
| spl12_11 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f298,plain,
( ~ spl12_11
| spl12_9 ),
inference(avatar_split_clause,[],[f293,f283,f295]) ).
fof(f302,definition,
( spl12_12
<=> aScalar0(sF9) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
fof(f303,plain,
( aScalar0(sF9)
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f304,plain,
( ~ aScalar0(sF9)
| spl12_12 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f306,definition,
( spl12_13
<=> aScalar0(sF8) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
fof(f307,plain,
( aScalar0(sF8)
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f310,plain,
sF7 = sdtpldt0(sF5,xN),
inference(superposition,[],[f232,f258]) ).
fof(f311,plain,
( aScalar0(sF2)
| ~ aScalar0(xP)
| ~ aScalar0(xP) ),
inference(superposition,[],[f137,f222]) ).
fof(f312,plain,
( aScalar0(sF9)
| ~ aScalar0(xS)
| ~ aScalar0(xS) ),
inference(superposition,[],[f137,f236]) ).
fof(f313,plain,
( aScalar0(sF8)
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(superposition,[],[f137,f234]) ).
fof(f314,plain,
( aScalar0(sF5)
| ~ aScalar0(xR)
| ~ aScalar0(xR) ),
inference(superposition,[],[f137,f228]) ).
fof(f315,plain,
( aScalar0(sF5)
| ~ aScalar0(xR) ),
inference(duplicate_literal_removal,[],[f314]) ).
fof(f316,plain,
( aScalar0(sF9)
| ~ aScalar0(xS) ),
inference(duplicate_literal_removal,[],[f312]) ).
fof(f317,plain,
( aScalar0(sF2)
| ~ aScalar0(xP) ),
inference(duplicate_literal_removal,[],[f311]) ).
fof(f318,plain,
( ~ aScalar0(xR)
| spl12_11 ),
inference(forward_subsumption_resolution,[],[f315,f297]) ).
fof(f319,plain,
( aScalar0(sF8)
| ~ aScalar0(xR) ),
inference(forward_subsumption_resolution,[],[f313,f209]) ).
fof(f320,plain,
( ~ aScalar0(xS)
| spl12_12 ),
inference(forward_subsumption_resolution,[],[f316,f304]) ).
fof(f321,plain,
( ~ aScalar0(xP)
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f317,f266]) ).
fof(f322,plain,
( $false
| spl12_11 ),
inference(forward_subsumption_resolution,[],[f318,f205]) ).
fof(f323,plain,
spl12_11,
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f324,plain,
aScalar0(sF8),
inference(forward_subsumption_resolution,[],[f319,f205]) ).
fof(f325,plain,
( $false
| spl12_12 ),
inference(forward_subsumption_resolution,[],[f320,f209]) ).
fof(f326,plain,
spl12_12,
inference(avatar_contradiction_clause,[],[f325]) ).
fof(f327,plain,
( $false
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f321,f207]) ).
fof(f328,plain,
spl12_5,
inference(avatar_contradiction_clause,[],[f327]) ).
fof(f329,plain,
spl12_13,
inference(avatar_split_clause,[],[f324,f306]) ).
fof(f331,plain,
! [X0,X1] :
( sdtlseqdt0(sF3,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sF2,X0)
| ~ sdtlseqdt0(sF2,X1)
| ~ aScalar0(sF2)
| ~ aScalar0(X0)
| ~ aScalar0(sF2)
| ~ aScalar0(X1) ),
inference(superposition,[],[f160,f224]) ).
fof(f332,plain,
! [X0,X1] :
( sdtlseqdt0(sF4,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sF3,X0)
| ~ sdtlseqdt0(sF3,X1)
| ~ aScalar0(sF3)
| ~ aScalar0(X0)
| ~ aScalar0(sF3)
| ~ aScalar0(X1) ),
inference(superposition,[],[f160,f226]) ).
fof(f345,plain,
! [X0,X1] :
( sdtlseqdt0(sF4,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sF3,X0)
| ~ sdtlseqdt0(sF3,X1)
| ~ aScalar0(sF3)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(duplicate_literal_removal,[],[f332]) ).
fof(f346,plain,
! [X0,X1] :
( sdtlseqdt0(sF3,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sF2,X0)
| ~ sdtlseqdt0(sF2,X1)
| ~ aScalar0(sF2)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(duplicate_literal_removal,[],[f331]) ).
fof(f357,plain,
( ! [X0,X1] :
( sdtlseqdt0(sF4,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sF3,X0)
| ~ sdtlseqdt0(sF3,X1)
| ~ aScalar0(X0)
| ~ aScalar0(X1) )
| ~ spl12_6 ),
inference(forward_subsumption_resolution,[],[f345,f270]) ).
fof(f358,plain,
( ! [X0,X1] :
( sdtlseqdt0(sF3,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sF2,X0)
| ~ sdtlseqdt0(sF2,X1)
| ~ aScalar0(X0)
| ~ aScalar0(X1) )
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f346,f265]) ).
fof(f460,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sF8) = sdtpldt0(sF8,X0) )
| ~ spl12_3
| ~ spl12_13 ),
inference(resolution,[],[f251,f307]) ).
fof(f461,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sF9) = sdtpldt0(sF9,X0) )
| ~ spl12_3
| ~ spl12_12 ),
inference(resolution,[],[f251,f303]) ).
fof(f464,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sF9)),
inference(superposition,[],[f214,f236]) ).
fof(f465,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sF5,sF9)),
inference(forward_demodulation,[],[f464,f228]) ).
fof(f468,plain,
sdtlseqdt0(sdtpldt0(sF2,sF2),sdtpldt0(sF5,sF9)),
inference(forward_demodulation,[],[f465,f222]) ).
fof(f471,plain,
sdtlseqdt0(sF3,sdtpldt0(sF5,sF9)),
inference(forward_demodulation,[],[f468,f224]) ).
fof(f478,plain,
sdtlseqdt0(sF2,xN),
inference(superposition,[],[f213,f222]) ).
fof(f490,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtpldt0(sdtpldt0(X0,X1),sF8) = sdtpldt0(X0,sdtpldt0(X1,sF8)) )
| ~ spl12_13 ),
inference(resolution,[],[f150,f307]) ).
fof(f782,plain,
( sdtpldt0(sF5,sF9) = sdtpldt0(sF9,sF5)
| ~ spl12_3
| ~ spl12_11
| ~ spl12_12 ),
inference(resolution,[],[f461,f296]) ).
fof(f783,plain,
( sdtpldt0(sF7,sF9) = sdtpldt0(sF9,sF7)
| ~ spl12_3
| ~ spl12_9
| ~ spl12_12 ),
inference(resolution,[],[f461,f284]) ).
fof(f877,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtpldt0(sdtpldt0(X0,X1),xN) = sdtpldt0(X0,sdtpldt0(X1,xN)) ),
inference(resolution,[],[f211,f150]) ).
fof(f881,plain,
( sdtpldt0(xN,sF9) = sdtpldt0(sF9,xN)
| ~ spl12_3
| ~ spl12_12 ),
inference(resolution,[],[f211,f461]) ).
fof(f892,plain,
sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sF9),xN) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtpldt0(sF9,xN)),
inference(superposition,[],[f216,f236]) ).
fof(f903,plain,
( sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sF9),xN) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtpldt0(xN,sF9))
| ~ spl12_3
| ~ spl12_12 ),
inference(forward_demodulation,[],[f892,f881]) ).
fof(f909,plain,
( sdtpldt0(sdtpldt0(sdtpldt0(sF5,xN),sF9),xN) = sdtpldt0(sdtpldt0(sF5,xN),sdtpldt0(xN,sF9))
| ~ spl12_3
| ~ spl12_12 ),
inference(forward_demodulation,[],[f903,f228]) ).
fof(f915,plain,
( sdtpldt0(sdtpldt0(sF7,sF9),xN) = sdtpldt0(sF7,sdtpldt0(xN,sF9))
| ~ spl12_3
| ~ spl12_12 ),
inference(forward_demodulation,[],[f909,f310]) ).
fof(f1346,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(X0,xR) = sdtasdt0(xR,X0) )
| ~ spl12_2 ),
inference(resolution,[],[f247,f205]) ).
fof(f1445,definition,
( spl12_101
<=> aScalar0(sdtpldt0(sF5,sF9)) ),
introduced(definition,[new_symbols(definition,[spl12_101])],[avatar_definition]) ).
fof(f1446,plain,
( aScalar0(sdtpldt0(sF5,sF9))
| ~ spl12_101 ),
inference(avatar_component_clause,[],[f1445]) ).
fof(f1447,plain,
( ~ aScalar0(sdtpldt0(sF5,sF9))
| spl12_101 ),
inference(avatar_component_clause,[],[f1445]) ).
fof(f1738,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtpldt0(sdtpldt0(X0,sF8),sF8) = sdtpldt0(X0,sdtpldt0(sF8,sF8)) )
| ~ spl12_13 ),
inference(resolution,[],[f490,f307]) ).
fof(f2438,plain,
( sdtasdt0(xR,xS) = sdtasdt0(xS,xR)
| ~ spl12_2 ),
inference(resolution,[],[f1346,f209]) ).
fof(f2449,plain,
( sdtasdt0(xR,xS) = sF8
| ~ spl12_2 ),
inference(forward_demodulation,[],[f2438,f234]) ).
fof(f2450,plain,
( xN = sF8
| ~ spl12_2 ),
inference(forward_demodulation,[],[f2449,f210]) ).
fof(f2451,plain,
( sF10 = sdtpldt0(xN,sF9)
| ~ spl12_2 ),
inference(superposition,[],[f238,f2450]) ).
fof(f2461,plain,
( $false
| ~ spl12_1 ),
inference(resolution,[],[f244,f135]) ).
fof(f2510,plain,
~ spl12_1,
inference(avatar_contradiction_clause,[],[f2461]) ).
fof(f5417,plain,
( ~ aScalar0(sF5)
| ~ aScalar0(sF9)
| spl12_101 ),
inference(resolution,[],[f1447,f136]) ).
fof(f5418,plain,
( ~ aScalar0(sF9)
| ~ spl12_11
| spl12_101 ),
inference(forward_subsumption_resolution,[],[f5417,f296]) ).
fof(f5419,plain,
( $false
| ~ spl12_11
| ~ spl12_12
| spl12_101 ),
inference(forward_subsumption_resolution,[],[f5418,f303]) ).
fof(f5420,plain,
( ~ spl12_11
| ~ spl12_12
| spl12_101 ),
inference(avatar_contradiction_clause,[],[f5419]) ).
fof(f5458,plain,
( sdtpldt0(sdtpldt0(sF5,sF9),sF8) = sdtpldt0(sF8,sdtpldt0(sF5,sF9))
| ~ spl12_3
| ~ spl12_13
| ~ spl12_101 ),
inference(resolution,[],[f1446,f460]) ).
fof(f5531,plain,
( sdtpldt0(sdtpldt0(sF5,sF9),xN) = sdtpldt0(xN,sdtpldt0(sF5,sF9))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_13
| ~ spl12_101 ),
inference(forward_demodulation,[],[f5458,f2450]) ).
fof(f5953,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtpldt0(sdtpldt0(X0,sF5),xN) = sdtpldt0(X0,sdtpldt0(sF5,xN)) )
| ~ spl12_11 ),
inference(resolution,[],[f877,f296]) ).
fof(f5964,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sF7) = sdtpldt0(sdtpldt0(X0,sF5),xN) )
| ~ spl12_11 ),
inference(forward_demodulation,[],[f5953,f310]) ).
fof(f6005,plain,
( sdtpldt0(sF9,sF7) = sdtpldt0(sdtpldt0(sF9,sF5),xN)
| ~ spl12_11
| ~ spl12_12 ),
inference(resolution,[],[f5964,f303]) ).
fof(f6010,plain,
( sdtpldt0(sdtpldt0(sF5,sF9),xN) = sdtpldt0(sF9,sF7)
| ~ spl12_3
| ~ spl12_11
| ~ spl12_12 ),
inference(forward_demodulation,[],[f6005,f782]) ).
fof(f6024,plain,
( sdtpldt0(sdtpldt0(sF5,sF9),xN) = sdtpldt0(sF7,sF9)
| ~ spl12_3
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12 ),
inference(forward_demodulation,[],[f6010,f783]) ).
fof(f6034,plain,
( sdtpldt0(sF7,sF9) = sdtpldt0(xN,sdtpldt0(sF5,sF9))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101 ),
inference(forward_demodulation,[],[f6024,f5531]) ).
fof(f10822,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(X0,X1),xS) = sdtpldt0(sdtasdt0(X0,xS),sdtasdt0(X1,xS)) ),
inference(resolution,[],[f151,f209]) ).
fof(f10862,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(X0,xR),xS) = sdtpldt0(sdtasdt0(X0,xS),sdtasdt0(xR,xS)) ),
inference(resolution,[],[f10822,f205]) ).
fof(f10879,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(X0,xR),xS) = sdtpldt0(sdtasdt0(X0,xS),xN) ),
inference(forward_demodulation,[],[f10862,f210]) ).
fof(f11014,plain,
sdtasdt0(sdtpldt0(xR,xR),xS) = sdtpldt0(sdtasdt0(xR,xS),xN),
inference(resolution,[],[f10879,f205]) ).
fof(f11031,plain,
sdtpldt0(xN,xN) = sdtasdt0(sdtpldt0(xR,xR),xS),
inference(forward_demodulation,[],[f11014,f210]) ).
fof(f12687,definition,
( spl12_410
<=> aScalar0(sdtpldt0(xR,xR)) ),
introduced(definition,[new_symbols(definition,[spl12_410])],[avatar_definition]) ).
fof(f12688,plain,
( aScalar0(sdtpldt0(xR,xR))
| ~ spl12_410 ),
inference(avatar_component_clause,[],[f12687]) ).
fof(f12689,plain,
( ~ aScalar0(sdtpldt0(xR,xR))
| spl12_410 ),
inference(avatar_component_clause,[],[f12687]) ).
fof(f12699,plain,
( ~ aScalar0(xR)
| ~ aScalar0(xR)
| spl12_410 ),
inference(resolution,[],[f12689,f136]) ).
fof(f12700,plain,
( ~ aScalar0(xR)
| spl12_410 ),
inference(duplicate_literal_removal,[],[f12699]) ).
fof(f12701,plain,
( $false
| spl12_410 ),
inference(forward_subsumption_resolution,[],[f12700,f205]) ).
fof(f12702,plain,
spl12_410,
inference(avatar_contradiction_clause,[],[f12701]) ).
fof(f14301,plain,
( aScalar0(sdtpldt0(xN,xN))
| ~ aScalar0(sdtpldt0(xR,xR))
| ~ aScalar0(xS) ),
inference(superposition,[],[f137,f11031]) ).
fof(f14302,plain,
( aScalar0(sdtpldt0(xN,xN))
| ~ aScalar0(xS)
| ~ spl12_410 ),
inference(forward_subsumption_resolution,[],[f14301,f12688]) ).
fof(f14304,plain,
( aScalar0(sdtpldt0(xN,xN))
| ~ spl12_410 ),
inference(forward_subsumption_resolution,[],[f14302,f209]) ).
fof(f22365,plain,
( sdtpldt0(sdtpldt0(sdtpldt0(sF5,sF9),sF8),sF8) = sdtpldt0(sdtpldt0(sF5,sF9),sdtpldt0(sF8,sF8))
| ~ spl12_13
| ~ spl12_101 ),
inference(resolution,[],[f1738,f1446]) ).
fof(f22432,plain,
( sdtpldt0(sdtpldt0(sdtpldt0(sF5,sF9),xN),xN) = sdtpldt0(sdtpldt0(sF5,sF9),sdtpldt0(xN,xN))
| ~ spl12_2
| ~ spl12_13
| ~ spl12_101 ),
inference(forward_demodulation,[],[f22365,f2450]) ).
fof(f22481,plain,
( sdtpldt0(sdtpldt0(sF5,sF9),sdtpldt0(xN,xN)) = sdtpldt0(sdtpldt0(xN,sdtpldt0(sF5,sF9)),xN)
| ~ spl12_2
| ~ spl12_3
| ~ spl12_13
| ~ spl12_101 ),
inference(forward_demodulation,[],[f22432,f5531]) ).
fof(f22505,plain,
( sdtpldt0(sdtpldt0(sF7,sF9),xN) = sdtpldt0(sdtpldt0(sF5,sF9),sdtpldt0(xN,xN))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101 ),
inference(forward_demodulation,[],[f22481,f6034]) ).
fof(f22509,plain,
( sdtpldt0(sF7,sdtpldt0(xN,sF9)) = sdtpldt0(sdtpldt0(sF5,sF9),sdtpldt0(xN,xN))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101 ),
inference(forward_demodulation,[],[f22505,f915]) ).
fof(f22510,plain,
( sdtpldt0(sF7,sF10) = sdtpldt0(sdtpldt0(sF5,sF9),sdtpldt0(xN,xN))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101 ),
inference(forward_demodulation,[],[f22509,f2451]) ).
fof(f22511,plain,
( sF11 = sdtpldt0(sdtpldt0(sF5,sF9),sdtpldt0(xN,xN))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101 ),
inference(forward_demodulation,[],[f22510,f240]) ).
fof(f22517,plain,
( sdtlseqdt0(sF4,sF11)
| ~ sdtlseqdt0(sF3,sdtpldt0(sF5,sF9))
| ~ sdtlseqdt0(sF3,sdtpldt0(xN,xN))
| ~ aScalar0(sdtpldt0(sF5,sF9))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_6
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101 ),
inference(superposition,[],[f357,f22511]) ).
fof(f22545,plain,
( ~ sdtlseqdt0(sF3,sdtpldt0(sF5,sF9))
| ~ sdtlseqdt0(sF3,sdtpldt0(xN,xN))
| ~ aScalar0(sdtpldt0(sF5,sF9))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_6
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101 ),
inference(forward_subsumption_resolution,[],[f22517,f241]) ).
fof(f22556,plain,
( ~ sdtlseqdt0(sF3,sdtpldt0(xN,xN))
| ~ aScalar0(sdtpldt0(sF5,sF9))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_6
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101 ),
inference(forward_subsumption_resolution,[],[f22545,f471]) ).
fof(f22595,plain,
( ~ sdtlseqdt0(sF3,sdtpldt0(xN,xN))
| ~ aScalar0(sdtpldt0(xN,xN))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_6
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101 ),
inference(forward_subsumption_resolution,[],[f22556,f1446]) ).
fof(f22608,plain,
( ~ sdtlseqdt0(sF3,sdtpldt0(xN,xN))
| ~ spl12_2
| ~ spl12_3
| ~ spl12_6
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101
| ~ spl12_410 ),
inference(forward_subsumption_resolution,[],[f22595,f14304]) ).
fof(f22609,plain,
( ~ sdtlseqdt0(sF2,xN)
| ~ sdtlseqdt0(sF2,xN)
| ~ aScalar0(xN)
| ~ aScalar0(xN)
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101
| ~ spl12_410 ),
inference(resolution,[],[f22608,f358]) ).
fof(f22610,plain,
( ~ sdtlseqdt0(sF2,xN)
| ~ aScalar0(xN)
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101
| ~ spl12_410 ),
inference(duplicate_literal_removal,[],[f22609]) ).
fof(f22611,plain,
( ~ aScalar0(xN)
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101
| ~ spl12_410 ),
inference(forward_subsumption_resolution,[],[f22610,f478]) ).
fof(f22612,plain,
( $false
| ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101
| ~ spl12_410 ),
inference(forward_subsumption_resolution,[],[f22611,f211]) ).
fof(f22613,plain,
( ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101
| ~ spl12_410 ),
inference(avatar_contradiction_clause,[],[f22612]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f248]) ).
cnf(s2,plain,
( spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f252]) ).
cnf(s4,plain,
( ~ spl12_5
| spl12_6 ),
inference(sat_conversion,[],[f271]) ).
cnf(s7,plain,
( spl12_9
| ~ spl12_11 ),
inference(sat_conversion,[],[f298]) ).
cnf(s9,plain,
spl12_11,
inference(sat_conversion,[],[f323]) ).
cnf(s10,plain,
spl12_12,
inference(sat_conversion,[],[f326]) ).
cnf(s11,plain,
spl12_5,
inference(sat_conversion,[],[f328]) ).
cnf(s12,plain,
spl12_13,
inference(sat_conversion,[],[f329]) ).
cnf(s105,plain,
~ spl12_1,
inference(sat_conversion,[],[f2510]) ).
cnf(s215,plain,
( ~ spl12_11
| ~ spl12_12
| spl12_101 ),
inference(sat_conversion,[],[f5420]) ).
cnf(s403,plain,
spl12_410,
inference(sat_conversion,[],[f12702]) ).
cnf(s676,plain,
( ~ spl12_2
| ~ spl12_3
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13
| ~ spl12_101
| ~ spl12_410 ),
inference(sat_conversion,[],[f22613]) ).
cnf(s723,plain,
spl12_101,
inference(rat,[],[s215,s10,s9]) ).
cnf(s726,plain,
spl12_9,
inference(rat,[],[s7,s9]) ).
cnf(s734,plain,
spl12_6,
inference(rat,[],[s4,s11]) ).
cnf(s745,plain,
spl12_3,
inference(rat,[],[s2,s105]) ).
cnf(s746,plain,
~ spl12_2,
inference(rat,[],[s676,s403,s723,s12,s10,s9,s726,s734,s11,s745]) ).
cnf(s776,plain,
$false,
inference(rat,[],[s1,s746,s105]) ).
fof(f22614,plain,
$false,
inference(avatar_sat_refutation,[],[s776]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG068+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n006.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 23:07:56 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 7.56/2.81 % (3435466)Detected formulas, will run a generic FOF schedule.
% 7.56/2.81 % (3435471)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=638084148:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.56/2.81 % (3435475)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=976702051:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.56/2.81 % (3435477)dis-21_1_sil=8000:lcm=predicate:random_seed=2437129536: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)
% 7.56/2.81 % (3435473)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=1563080595:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.56/2.81 % (3435474)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1855331063:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.56/2.81 % (3435472)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=794843145:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.56/2.81 % (3435476)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3867068598:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.56/2.81 % (3435474)Instruction limit reached!
% 7.56/2.81 % (3435474)------------------------------
% 7.56/2.81 % (3435474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435474)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435474)Termination reason: Instruction limit
% 7.56/2.81 % (3435474)Termination phase: Saturation
% 7.56/2.81 % (3435474)Time elapsed: 0.055 s
% 7.56/2.81 % (3435474)Peak memory usage: 89 MB
% 7.56/2.81 % (3435474)Instructions burned: 111 (million)
% 7.56/2.81 % (3435477)Instruction limit reached!
% 7.56/2.81 % (3435477)------------------------------
% 7.56/2.81 % (3435477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435477)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435477)Termination reason: Instruction limit
% 7.56/2.81 % (3435477)Termination phase: Saturation
% 7.56/2.81 % (3435477)Time elapsed: 0.058 s
% 7.56/2.81 % (3435477)Peak memory usage: 88 MB
% 7.56/2.81 % (3435477)Instructions burned: 130 (million)
% 7.56/2.81 % (3435475)Instruction limit reached!
% 7.56/2.81 % (3435475)------------------------------
% 7.56/2.81 % (3435475)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435475)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435475)Termination reason: Instruction limit
% 7.56/2.81 % (3435475)Termination phase: Saturation
% 7.56/2.81 % (3435475)Time elapsed: 0.069 s
% 7.56/2.81 % (3435475)Peak memory usage: 88 MB
% 7.56/2.81 % (3435475)Instructions burned: 120 (million)
% 7.56/2.81 % (3435476)Instruction limit reached!
% 7.56/2.81 % (3435476)------------------------------
% 7.56/2.81 % (3435476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435476)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435476)Termination reason: Instruction limit
% 7.56/2.81 % (3435476)Termination phase: Saturation
% 7.56/2.81 % (3435476)Time elapsed: 0.089 s
% 7.56/2.81 % (3435476)Peak memory usage: 90 MB
% 7.56/2.81 % (3435476)Instructions burned: 140 (million)
% 7.56/2.81 % (3435485)lrs+10_1_sil=8000:sp=occurrence:random_seed=2465273535:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 7.56/2.81 % (3435486)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1461675130:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.56/2.81 % (3435487)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1384774947:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.56/2.81 % (3435488)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=602139684:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 7.56/2.81 % (3435486)Instruction limit reached!
% 7.56/2.81 % (3435486)------------------------------
% 7.56/2.81 % (3435486)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435486)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435486)Termination reason: Instruction limit
% 7.56/2.81 % (3435486)Termination phase: Saturation
% 7.56/2.81 % (3435486)Time elapsed: 0.071 s
% 7.56/2.81 % (3435486)Peak memory usage: 91 MB
% 7.56/2.81 % (3435486)Instructions burned: 158 (million)
% 7.56/2.81 % (3435488)Instruction limit reached!
% 7.56/2.81 % (3435488)------------------------------
% 7.56/2.81 % (3435488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435488)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435488)Termination reason: Instruction limit
% 7.56/2.81 % (3435488)Termination phase: Saturation
% 7.56/2.81 % (3435488)Time elapsed: 0.110 s
% 7.56/2.81 % (3435488)Peak memory usage: 94 MB
% 7.56/2.81 % (3435488)Instructions burned: 250 (million)
% 7.56/2.81 % (3435485)Instruction limit reached!
% 7.56/2.81 % (3435485)------------------------------
% 7.56/2.81 % (3435485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435485)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435485)Termination reason: Instruction limit
% 7.56/2.81 % (3435485)Termination phase: Saturation
% 7.56/2.81 % (3435485)Time elapsed: 0.168 s
% 7.56/2.81 % (3435485)Peak memory usage: 93 MB
% 7.56/2.81 % (3435485)Instructions burned: 286 (million)
% 7.56/2.81 % (3435487)Instruction limit reached!
% 7.56/2.81 % (3435487)------------------------------
% 7.56/2.81 % (3435487)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435487)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435487)Termination reason: Instruction limit
% 7.56/2.81 % (3435487)Termination phase: Saturation
% 7.56/2.81 % (3435487)Time elapsed: 0.194 s
% 7.56/2.81 % (3435487)Peak memory usage: 93 MB
% 7.56/2.81 % (3435487)Instructions burned: 326 (million)
% 7.56/2.81 % (3435493)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1785558:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 7.56/2.81 % (3435494)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1334346414:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 7.56/2.81 % (3435495)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3256870307:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 7.56/2.81 % (3435496)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2590877719:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 7.56/2.81 % (3435493)Instruction limit reached!
% 7.56/2.81 % (3435493)------------------------------
% 7.56/2.81 % (3435493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435493)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435493)Termination reason: Instruction limit
% 7.56/2.81 % (3435493)Termination phase: Saturation
% 7.56/2.81 % (3435493)Time elapsed: 0.171 s
% 7.56/2.81 % (3435493)Peak memory usage: 90 MB
% 7.56/2.81 % (3435493)Instructions burned: 295 (million)
% 7.56/2.81 % (3435495)Instruction limit reached!
% 7.56/2.81 % (3435495)------------------------------
% 7.56/2.81 % (3435495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435495)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435495)Termination reason: Instruction limit
% 7.56/2.81 % (3435495)Termination phase: Saturation
% 7.56/2.81 % (3435495)Time elapsed: 0.072 s
% 7.56/2.81 % (3435495)Peak memory usage: 91 MB
% 7.56/2.81 % (3435495)Instructions burned: 113 (million)
% 7.56/2.81 % (3435496)Instruction limit reached!
% 7.56/2.81 % (3435496)------------------------------
% 7.56/2.81 % (3435496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435496)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435496)Termination reason: Instruction limit
% 7.56/2.81 % (3435496)Termination phase: Saturation
% 7.56/2.81 % (3435496)Time elapsed: 0.065 s
% 7.56/2.81 % (3435496)Peak memory usage: 89 MB
% 7.56/2.81 % (3435496)Instructions burned: 129 (million)
% 7.56/2.81 % (3435501)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1007349365:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 7.56/2.81 % (3435502)lrs+10_1_sil=8000:sp=occurrence:random_seed=180677984:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 7.56/2.81 % (3435501)Refutation not found, incomplete strategy
% 7.56/2.81 % (3435501)------------------------------
% 7.56/2.81 % (3435501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435501)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435501)Termination reason: Refutation not found, incomplete strategy
% 7.56/2.81 % (3435501)Time elapsed: 0.004 s
% 7.56/2.81 % (3435501)Peak memory usage: 88 MB
% 7.56/2.81 % (3435501)Instructions burned: 4 (million)
% 7.56/2.81 % (3435503)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1494846082:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 7.56/2.81 % (3435501)------------------------------
% 7.56/2.81 % (3435501)------------------------------
% 7.56/2.81 % (3435503)Instruction limit reached!
% 7.56/2.81 % (3435503)------------------------------
% 7.56/2.81 % (3435503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435503)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435503)Termination reason: Instruction limit
% 7.56/2.81 % (3435503)Termination phase: Saturation
% 7.56/2.81 % (3435503)Time elapsed: 0.247 s
% 7.56/2.81 % (3435503)Peak memory usage: 94 MB
% 7.56/2.81 % (3435503)Instructions burned: 439 (million)
% 7.56/2.81 % (3435507)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2469112129:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 7.56/2.81 % (3435508)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=666192982:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 7.56/2.81 % (3435502)Instruction limit reached!
% 7.56/2.81 % (3435502)------------------------------
% 7.56/2.81 % (3435502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435502)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435502)Termination reason: Instruction limit
% 7.56/2.81 % (3435502)Termination phase: Saturation
% 7.56/2.81 % (3435502)Time elapsed: 0.495 s
% 7.56/2.81 % (3435502)Peak memory usage: 104 MB
% 7.56/2.81 % (3435502)Instructions burned: 908 (million)
% 7.56/2.81 % (3435508)Instruction limit reached!
% 7.56/2.81 % (3435508)------------------------------
% 7.56/2.81 % (3435508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435508)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435508)Termination reason: Instruction limit
% 7.56/2.81 % (3435508)Termination phase: Saturation
% 7.56/2.81 % (3435508)Time elapsed: 0.059 s
% 7.56/2.81 % (3435508)Peak memory usage: 91 MB
% 7.56/2.81 % (3435508)Instructions burned: 134 (million)
% 7.56/2.81 % (3435511)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=500863505:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 7.56/2.81 % (3435512)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1447390965:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 7.56/2.81 % (3435471)First to succeed.
% 7.56/2.81 % (3435471)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3435466"
% 7.56/2.81 % (3435511)Instruction limit reached!
% 7.56/2.81 % (3435511)------------------------------
% 7.56/2.81 % (3435511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.56/2.81 % (3435511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/2.81 % (3435511)CaDiCaL version: 2.1.3
% 7.56/2.81 % (3435511)Termination reason: Instruction limit
% 7.56/2.81 % (3435511)Termination phase: Saturation
% 7.56/2.81 % (3435511)Time elapsed: 0.300 s
% 7.56/2.81 % (3435511)Peak memory usage: 93 MB
% 7.56/2.81 % (3435511)Instructions burned: 592 (million)
% 7.56/2.81 % (3435471)Refutation found. Thanks to Tanya!
% 7.56/2.81 % SZS status Theorem for theBenchmark
% 7.56/2.81 % SZS output start Proof for theBenchmark
% See solution above
% 14.21/3.01 % (3435471)------------------------------
% 14.21/3.01 % (3435471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.21/3.01 % (3435471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.21/3.01 % (3435471)CaDiCaL version: 2.1.3
% 14.21/3.01 % (3435471)Termination reason: Refutation
% 14.21/3.01 % (3435471)Time elapsed: 1.646 s
% 14.21/3.01 % (3435471)Peak memory usage: 172 MB
% 14.21/3.01 % (3435471)Instructions burned: 4875 (million)
% 14.21/3.01 % (3435471)------------------------------
% 14.21/3.01 % (3435471)------------------------------
% 14.21/3.01 % (3435466)Success in time 1.934 s
% 14.21/3.01 % Vampire exiting
%------------------------------------------------------------------------------