%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM422+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 : n004.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 12:15:07 PM UTC 2026
% Result : Theorem 5.00s 1.63s
% Output : Refutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 126 ( 46 unt; 5 def)
% Number of atoms : 258 ( 100 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 238 ( 106 ~; 101 |; 19 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f9,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(f11,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f12,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f13,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(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',mDistrib) ).
fof(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f16,axiom,
aInteger0(xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__446) ).
fof(f17,conjecture,
sdtasdt0(smndt0(sz10),xa) = smndt0(xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f18,negated_conjecture,
sdtasdt0(smndt0(sz10),xa) != smndt0(xa),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f20,plain,
sdtasdt0(smndt0(sz10),xa) != smndt0(xa),
inference(flattening,[],[f18]) ).
fof(f21,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f25,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f27,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(flattening,[],[f26]) ).
fof(f30,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f31,plain,
! [X0] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f32,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f33,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f35,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f37,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)) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f38,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)) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f41,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f42,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f44,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ aInteger0(X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f48,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ aInteger0(X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ aInteger0(X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f58,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f16]) ).
fof(f60,plain,
sdtasdt0(smndt0(sz10),xa) != smndt0(xa),
inference(cnf_transformation,[],[f20]) ).
fof(f61,definition,
sF0 = smndt0(sz10),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f62,plain,
smndt0(sz10) = sF0,
inference(reorient_equations,[],[f61]) ).
fof(f63,definition,
sF1 = sdtasdt0(sF0,xa),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f64,plain,
sdtasdt0(sF0,xa) = sF1,
inference(reorient_equations,[],[f63]) ).
fof(f65,definition,
sF2 = smndt0(xa),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f66,plain,
smndt0(xa) = sF2,
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
sF1 != sF2,
inference(definition_folding,[],[f60,f66,f64,f62]) ).
fof(f68,plain,
( aInteger0(sF2)
| ~ aInteger0(xa) ),
inference(superposition,[],[f42,f66]) ).
fof(f69,plain,
( aInteger0(sF0)
| ~ aInteger0(sz10) ),
inference(superposition,[],[f42,f62]) ).
fof(f70,plain,
aInteger0(sF0),
inference(forward_subsumption_resolution,[],[f69,f41]) ).
fof(f71,plain,
aInteger0(sF2),
inference(forward_subsumption_resolution,[],[f68,f59]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,sdtasdt0(X1,sF0)) = sdtasdt0(sdtasdt0(X0,X1),sF0) ),
inference(resolution,[],[f51,f70]) ).
fof(f107,plain,
sz00 = sdtpldt0(smndt0(sz10),sz10),
inference(resolution,[],[f49,f41]) ).
fof(f110,plain,
sz00 = sdtpldt0(smndt0(xa),xa),
inference(resolution,[],[f49,f59]) ).
fof(f113,plain,
sz00 = sdtpldt0(sF2,xa),
inference(forward_demodulation,[],[f110,f66]) ).
fof(f114,plain,
sz00 = sdtpldt0(sF0,sz10),
inference(forward_demodulation,[],[f107,f62]) ).
fof(f137,plain,
sF0 = sdtasdt0(sF0,sz10),
inference(resolution,[],[f54,f70]) ).
fof(f138,plain,
sF2 = sdtasdt0(sF2,sz10),
inference(resolution,[],[f54,f71]) ).
fof(f140,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,sdtpldt0(X1,sz10)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,sz10)) ),
inference(resolution,[],[f56,f41]) ).
fof(f157,plain,
sz10 = sdtpldt0(sz00,sz10),
inference(resolution,[],[f47,f41]) ).
fof(f161,plain,
xa = sdtpldt0(sz00,xa),
inference(resolution,[],[f47,f59]) ).
fof(f169,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(X0,xa) = sdtasdt0(xa,X0) ),
inference(resolution,[],[f52,f59]) ).
fof(f171,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(X0,sF2) = sdtasdt0(sF2,X0) ),
inference(resolution,[],[f52,f71]) ).
fof(f178,plain,
sz00 = sdtasdt0(sF0,sz00),
inference(resolution,[],[f58,f70]) ).
fof(f179,plain,
sz00 = sdtasdt0(sF2,sz00),
inference(resolution,[],[f58,f71]) ).
fof(f181,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(X1,sz10)) = sdtpldt0(sdtpldt0(X0,X1),sz10) ),
inference(resolution,[],[f45,f41]) ).
fof(f185,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(X1,xa)) = sdtpldt0(sdtpldt0(X0,X1),xa) ),
inference(resolution,[],[f45,f59]) ).
fof(f195,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(sF2,xa)) = sdtpldt0(sdtpldt0(X0,sF2),xa) ),
inference(resolution,[],[f185,f71]) ).
fof(f196,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sF2),xa) ),
inference(forward_demodulation,[],[f195,f113]) ).
fof(f247,plain,
sdtasdt0(sF0,xa) = sdtasdt0(xa,sF0),
inference(resolution,[],[f169,f70]) ).
fof(f250,plain,
sF1 = sdtasdt0(xa,sF0),
inference(forward_demodulation,[],[f247,f64]) ).
fof(f317,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(X0,sdtasdt0(sF0,sF0)) = sdtasdt0(sdtasdt0(X0,sF0),sF0) ),
inference(resolution,[],[f87,f70]) ).
fof(f396,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(X0,sdtpldt0(sF0,sz10)) = sdtpldt0(sdtasdt0(X0,sF0),sdtasdt0(X0,sz10)) ),
inference(resolution,[],[f140,f70]) ).
fof(f399,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(X0,sz00) = sdtpldt0(sdtasdt0(X0,sF0),sdtasdt0(X0,sz10)) ),
inference(forward_demodulation,[],[f396,f114]) ).
fof(f435,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(sF0,sz10)) = sdtpldt0(sdtpldt0(X0,sF0),sz10) ),
inference(resolution,[],[f181,f70]) ).
fof(f438,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sF0),sz10) ),
inference(forward_demodulation,[],[f435,f114]) ).
fof(f996,plain,
sdtasdt0(sF2,sF0) = sdtasdt0(sF0,sF2),
inference(resolution,[],[f171,f70]) ).
fof(f1012,plain,
sdtasdt0(sF0,sz00) = sdtpldt0(sdtasdt0(sF0,sF0),sdtasdt0(sF0,sz10)),
inference(resolution,[],[f399,f70]) ).
fof(f1014,plain,
sdtasdt0(sF2,sz00) = sdtpldt0(sdtasdt0(sF2,sF0),sdtasdt0(sF2,sz10)),
inference(resolution,[],[f399,f71]) ).
fof(f1015,plain,
sdtasdt0(sF2,sz00) = sdtpldt0(sdtasdt0(sF2,sF0),sF2),
inference(forward_demodulation,[],[f1014,f138]) ).
fof(f1017,plain,
sdtasdt0(sF0,sz00) = sdtpldt0(sdtasdt0(sF0,sF0),sF0),
inference(forward_demodulation,[],[f1012,f137]) ).
fof(f1024,plain,
sdtasdt0(sF2,sz00) = sdtpldt0(sdtasdt0(sF0,sF2),sF2),
inference(forward_demodulation,[],[f1015,f996]) ).
fof(f1026,plain,
sz00 = sdtpldt0(sdtasdt0(sF0,sF0),sF0),
inference(forward_demodulation,[],[f1017,f178]) ).
fof(f1033,plain,
sz00 = sdtpldt0(sdtasdt0(sF0,sF2),sF2),
inference(forward_demodulation,[],[f1024,f179]) ).
fof(f1098,definition,
( spl3_7
<=> aInteger0(sdtasdt0(sF0,sF2)) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f1099,plain,
( aInteger0(sdtasdt0(sF0,sF2))
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f1098]) ).
fof(f1100,plain,
( ~ aInteger0(sdtasdt0(sF0,sF2))
| spl3_7 ),
inference(avatar_component_clause,[],[f1098]) ).
fof(f1106,plain,
( ~ aInteger0(sF0)
| ~ aInteger0(sF2)
| spl3_7 ),
inference(resolution,[],[f1100,f44]) ).
fof(f1107,plain,
( ~ aInteger0(sF2)
| spl3_7 ),
inference(forward_subsumption_resolution,[],[f1106,f70]) ).
fof(f1108,plain,
( $false
| spl3_7 ),
inference(forward_subsumption_resolution,[],[f1107,f71]) ).
fof(f1109,plain,
spl3_7,
inference(avatar_contradiction_clause,[],[f1108]) ).
fof(f1113,plain,
( sdtasdt0(sF0,sF2) = sdtpldt0(sdtasdt0(sF0,sF2),sz00)
| ~ spl3_7 ),
inference(resolution,[],[f1099,f48]) ).
fof(f1146,plain,
( sdtpldt0(sdtasdt0(sF0,sF2),sz00) = sdtpldt0(sdtpldt0(sdtasdt0(sF0,sF2),sF2),xa)
| ~ spl3_7 ),
inference(resolution,[],[f1099,f196]) ).
fof(f1167,plain,
( sdtpldt0(sz00,xa) = sdtpldt0(sdtasdt0(sF0,sF2),sz00)
| ~ spl3_7 ),
inference(forward_demodulation,[],[f1146,f1033]) ).
fof(f1177,plain,
( sdtpldt0(sz00,xa) = sdtasdt0(sF0,sF2)
| ~ spl3_7 ),
inference(forward_demodulation,[],[f1167,f1113]) ).
fof(f1179,plain,
( xa = sdtasdt0(sF0,sF2)
| ~ spl3_7 ),
inference(forward_demodulation,[],[f1177,f161]) ).
fof(f1625,plain,
sdtasdt0(sF2,sdtasdt0(sF0,sF0)) = sdtasdt0(sdtasdt0(sF2,sF0),sF0),
inference(resolution,[],[f317,f71]) ).
fof(f1626,plain,
sdtasdt0(sdtasdt0(sF0,sF2),sF0) = sdtasdt0(sF2,sdtasdt0(sF0,sF0)),
inference(forward_demodulation,[],[f1625,f996]) ).
fof(f1635,plain,
( sdtasdt0(xa,sF0) = sdtasdt0(sF2,sdtasdt0(sF0,sF0))
| ~ spl3_7 ),
inference(forward_demodulation,[],[f1626,f1179]) ).
fof(f1641,plain,
( sF1 = sdtasdt0(sF2,sdtasdt0(sF0,sF0))
| ~ spl3_7 ),
inference(forward_demodulation,[],[f1635,f250]) ).
fof(f1648,definition,
( spl3_9
<=> aInteger0(sdtasdt0(sF0,sF0)) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f1649,plain,
( aInteger0(sdtasdt0(sF0,sF0))
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f1648]) ).
fof(f1650,plain,
( ~ aInteger0(sdtasdt0(sF0,sF0))
| spl3_9 ),
inference(avatar_component_clause,[],[f1648]) ).
fof(f1656,plain,
( ~ aInteger0(sF0)
| ~ aInteger0(sF0)
| spl3_9 ),
inference(resolution,[],[f1650,f44]) ).
fof(f1657,plain,
( ~ aInteger0(sF0)
| spl3_9 ),
inference(duplicate_literal_removal,[],[f1656]) ).
fof(f1658,plain,
( $false
| spl3_9 ),
inference(forward_subsumption_resolution,[],[f1657,f70]) ).
fof(f1659,plain,
spl3_9,
inference(avatar_contradiction_clause,[],[f1658]) ).
fof(f1754,plain,
( sdtasdt0(sF0,sF0) = sdtpldt0(sdtasdt0(sF0,sF0),sz00)
| ~ spl3_9 ),
inference(resolution,[],[f1649,f48]) ).
fof(f1800,plain,
( sdtpldt0(sdtasdt0(sF0,sF0),sz00) = sdtpldt0(sdtpldt0(sdtasdt0(sF0,sF0),sF0),sz10)
| ~ spl3_9 ),
inference(resolution,[],[f1649,f438]) ).
fof(f1814,plain,
( sdtpldt0(sz00,sz10) = sdtpldt0(sdtasdt0(sF0,sF0),sz00)
| ~ spl3_9 ),
inference(forward_demodulation,[],[f1800,f1026]) ).
fof(f1840,plain,
( sdtpldt0(sz00,sz10) = sdtasdt0(sF0,sF0)
| ~ spl3_9 ),
inference(forward_demodulation,[],[f1814,f1754]) ).
fof(f1851,plain,
( sz10 = sdtasdt0(sF0,sF0)
| ~ spl3_9 ),
inference(forward_demodulation,[],[f1840,f157]) ).
fof(f1864,plain,
( sF1 = sdtasdt0(sF2,sz10)
| ~ spl3_7
| ~ spl3_9 ),
inference(superposition,[],[f1641,f1851]) ).
fof(f1867,plain,
( sF1 = sF2
| ~ spl3_7
| ~ spl3_9 ),
inference(forward_demodulation,[],[f1864,f138]) ).
fof(f1869,plain,
( $false
| ~ spl3_7
| ~ spl3_9 ),
inference(forward_subsumption_resolution,[],[f1867,f67]) ).
fof(f1870,plain,
( ~ spl3_7
| ~ spl3_9 ),
inference(avatar_contradiction_clause,[],[f1869]) ).
cnf(s8,plain,
spl3_7,
inference(sat_conversion,[],[f1109]) ).
cnf(s11,plain,
spl3_9,
inference(sat_conversion,[],[f1659]) ).
cnf(s12,plain,
( ~ spl3_7
| ~ spl3_9 ),
inference(sat_conversion,[],[f1870]) ).
cnf(s13,plain,
~ spl3_7,
inference(rat,[],[s12,s11]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s8,s13]) ).
fof(f1871,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM422+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n004.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 19:50:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 5.00/1.63 % (3835884)Detected formulas, will run a generic FOF schedule.
% 5.00/1.63 % (3835889)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=400633993:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.00/1.63 % (3835891)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=1217770469:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.00/1.63 % (3835894)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=122680520:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.00/1.63 % (3835890)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=3543122247:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.00/1.63 % (3835893)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4145917547:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.00/1.63 % (3835892)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=522527638:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.00/1.63 % (3835892)Refutation not found, incomplete strategy
% 5.00/1.63 % (3835892)------------------------------
% 5.00/1.63 % (3835892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.63 % (3835892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.63 % (3835892)CaDiCaL version: 2.1.3
% 5.00/1.63 % (3835892)Termination reason: Refutation not found, incomplete strategy
% 5.00/1.63 % (3835892)Time elapsed: 0.001 s
% 5.00/1.63 % (3835892)Peak memory usage: 88 MB
% 5.00/1.63 % (3835895)dis-21_1_sil=8000:lcm=predicate:random_seed=372695564: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)
% 5.00/1.63 % (3835895)Refutation not found, incomplete strategy
% 5.00/1.63 % (3835895)------------------------------
% 5.00/1.63 % (3835895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.63 % (3835895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.63 % (3835895)CaDiCaL version: 2.1.3
% 5.00/1.63 % (3835895)Termination reason: Refutation not found, incomplete strategy
% 5.00/1.63 % (3835895)Time elapsed: 0.001 s
% 5.00/1.63 % (3835895)Peak memory usage: 88 MB
% 5.00/1.63 % (3835895)Instructions burned: 1 (million)
% 5.00/1.63 % (3835893)Instruction limit reached!
% 5.00/1.63 % (3835893)------------------------------
% 5.00/1.63 % (3835893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.63 % (3835893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.63 % (3835893)CaDiCaL version: 2.1.3
% 5.00/1.63 % (3835893)Termination reason: Instruction limit
% 5.00/1.63 % (3835893)Termination phase: Saturation
% 5.00/1.63 % (3835893)Time elapsed: 0.067 s
% 5.00/1.63 % (3835893)Peak memory usage: 88 MB
% 5.00/1.63 % (3835893)Instructions burned: 119 (million)
% 5.00/1.63 % (3835894)Instruction limit reached!
% 5.00/1.63 % (3835894)------------------------------
% 5.00/1.63 % (3835894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.63 % (3835894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.63 % (3835894)CaDiCaL version: 2.1.3
% 5.00/1.63 % (3835894)Termination reason: Instruction limit
% 5.00/1.63 % (3835894)Termination phase: Saturation
% 5.00/1.63 % (3835894)Time elapsed: 0.086 s
% 5.00/1.63 % (3835894)Peak memory usage: 90 MB
% 5.00/1.63 % (3835894)Instructions burned: 140 (million)
% 5.00/1.63 % (3835903)lrs+10_1_sil=8000:sp=occurrence:random_seed=876007902:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.00/1.63 % (3835904)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1644341859:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.00/1.63 % (3835892)------------------------------
% 5.00/1.63 % (3835892)------------------------------
% 5.00/1.63 % (3835895)------------------------------
% 5.00/1.63 % (3835895)------------------------------
% 5.00/1.63 % (3835904)Instruction limit reached!
% 5.00/1.63 % (3835904)------------------------------
% 5.00/1.63 % (3835904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.63 % (3835904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.63 % (3835904)CaDiCaL version: 2.1.3
% 5.00/1.63 % (3835904)Termination reason: Instruction limit
% 5.00/1.63 % (3835904)Termination phase: Saturation
% 5.00/1.63 % (3835904)Time elapsed: 0.073 s
% 5.00/1.63 % (3835904)Peak memory usage: 90 MB
% 5.00/1.63 % (3835904)Instructions burned: 157 (million)
% 5.00/1.63 % (3835903)Instruction limit reached!
% 5.00/1.63 % (3835903)------------------------------
% 5.00/1.63 % (3835903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.63 % (3835903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.63 % (3835903)CaDiCaL version: 2.1.3
% 5.00/1.63 % (3835903)Termination reason: Instruction limit
% 5.00/1.63 % (3835903)Termination phase: Saturation
% 5.00/1.63 % (3835903)Time elapsed: 0.162 s
% 5.00/1.63 % (3835903)Peak memory usage: 92 MB
% 5.00/1.63 % (3835903)Instructions burned: 286 (million)
% 5.00/1.63 % (3835907)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2508720587:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 5.00/1.63 % (3835908)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=2905289570:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.00/1.63 % (3835909)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1890517672:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.00/1.63 % (3835909)Refutation not found, incomplete strategy
% 5.00/1.63 % (3835909)------------------------------
% 5.00/1.63 % (3835909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.63 % (3835909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.63 % (3835909)CaDiCaL version: 2.1.3
% 5.00/1.63 % (3835909)Termination reason: Refutation not found, incomplete strategy
% 5.00/1.63 % (3835909)Time elapsed: 0.001 s
% 5.00/1.63 % (3835909)Peak memory usage: 88 MB
% 5.00/1.63 % (3835909)Instructions burned: 1 (million)
% 5.00/1.63 % (3835889)First to succeed.
% 5.00/1.63 % (3835889)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3835884"
% 5.00/1.63 % (3835911)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1873617745:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.00/1.63 % (3835908)Instruction limit reached!
% 5.00/1.63 % (3835908)------------------------------
% 5.00/1.63 % (3835908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.63 % (3835908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.63 % (3835908)CaDiCaL version: 2.1.3
% 5.00/1.63 % (3835908)Termination reason: Instruction limit
% 5.00/1.63 % (3835908)Termination phase: Saturation
% 5.00/1.63 % (3835908)Time elapsed: 0.118 s
% 5.00/1.63 % (3835908)Peak memory usage: 94 MB
% 5.00/1.63 % (3835908)Instructions burned: 250 (million)
% 5.00/1.63 % (3835907)Instruction limit reached!
% 5.00/1.63 % (3835907)------------------------------
% 5.00/1.63 % (3835907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.63 % (3835907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.63 % (3835907)CaDiCaL version: 2.1.3
% 5.00/1.63 % (3835907)Termination reason: Instruction limit
% 5.00/1.63 % (3835907)Termination phase: Saturation
% 5.00/1.63 % (3835907)Time elapsed: 0.198 s
% 5.00/1.63 % (3835907)Peak memory usage: 93 MB
% 5.00/1.63 % (3835907)Instructions burned: 325 (million)
% 5.00/1.63 % (3835889)Refutation found. Thanks to Tanya!
% 5.00/1.63 % SZS status Theorem for theBenchmark
% 5.00/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 6.05/1.83 % (3835889)------------------------------
% 6.05/1.83 % (3835889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.05/1.83 % (3835889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.83 % (3835889)CaDiCaL version: 2.1.3
% 6.05/1.83 % (3835889)Termination reason: Refutation
% 6.05/1.83 % (3835889)Time elapsed: 0.515 s
% 6.05/1.83 % (3835889)Peak memory usage: 133 MB
% 6.05/1.83 % (3835889)Instructions burned: 1361 (million)
% 6.05/1.83 % (3835889)------------------------------
% 6.05/1.83 % (3835889)------------------------------
% 6.05/1.83 % (3835884)Success in time 0.779 s
% 6.05/1.83 % Vampire exiting
%------------------------------------------------------------------------------