%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM431+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 : n016.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 12:15:09 PM UTC 2026
% Result : Theorem 9.42s 2.21s
% Output : Refutation 10.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 120 ( 25 unt; 7 def)
% Number of atoms : 331 ( 73 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 400 ( 189 ~; 180 |; 18 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(f5,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
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/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f9,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
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/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(f22,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00
& aInteger0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(f24,axiom,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__876) ).
fof(f25,axiom,
( aInteger0(xm)
& sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__899) ).
fof(f26,conjecture,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f27,negated_conjecture,
sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f29,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)),
inference(flattening,[],[f27]) ).
fof(f30,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f31,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f32,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f31]) ).
fof(f35,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(f36,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f40,plain,
! [X0] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f46,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(f47,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,[],[f46]) ).
fof(f64,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f66,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f67,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f69,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f72,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f73,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f74,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f80,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f95,plain,
aInteger0(xc),
inference(cnf_transformation,[],[f22]) ).
fof(f97,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f22]) ).
fof(f98,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f22]) ).
fof(f99,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f22]) ).
fof(f102,plain,
sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)),
inference(cnf_transformation,[],[f24]) ).
fof(f103,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f24]) ).
fof(f104,plain,
sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)),
inference(cnf_transformation,[],[f25]) ).
fof(f105,plain,
aInteger0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f106,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)),
inference(cnf_transformation,[],[f29]) ).
fof(f111,plain,
! [X0] :
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X0)) = sdtpldt0(sdtasdt0(xq,xn),X0)
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(X0) ),
inference(superposition,[],[f69,f102]) ).
fof(f112,plain,
( aInteger0(sdtasdt0(xq,xn))
| ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb)) ),
inference(superposition,[],[f67,f102]) ).
fof(f113,plain,
( aInteger0(sdtasdt0(xq,xn))
| ~ aInteger0(smndt0(xb)) ),
inference(forward_subsumption_resolution,[],[f112,f99]) ).
fof(f114,plain,
! [X0] :
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X0)) = sdtpldt0(sdtasdt0(xq,xn),X0)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(X0) ),
inference(forward_subsumption_resolution,[],[f111,f99]) ).
fof(f118,definition,
( spl1_1
<=> aInteger0(smndt0(xb)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f119,plain,
( ~ aInteger0(smndt0(xb))
| spl1_1 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,definition,
( spl1_2
<=> aInteger0(sdtasdt0(xq,xn)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f122,plain,
( aInteger0(sdtasdt0(xq,xn))
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f113,f121,f118]) ).
fof(f125,definition,
( spl1_3
<=> ! [X0] :
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X0)) = sdtpldt0(sdtasdt0(xq,xn),X0)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f126,plain,
( ! [X0] :
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X0)) = sdtpldt0(sdtasdt0(xq,xn),X0)
| ~ aInteger0(X0) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f127,plain,
( ~ spl1_1
| spl1_3 ),
inference(avatar_split_clause,[],[f114,f125,f118]) ).
fof(f139,definition,
( spl1_4
<=> aInteger0(smndt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f140,plain,
( ~ aInteger0(smndt0(xc))
| spl1_4 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f151,plain,
( ~ aInteger0(xb)
| spl1_1 ),
inference(resolution,[],[f119,f66]) ).
fof(f152,plain,
( $false
| spl1_1 ),
inference(forward_subsumption_resolution,[],[f151,f98]) ).
fof(f153,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f152]) ).
fof(f154,plain,
( ~ aInteger0(xc)
| spl1_4 ),
inference(resolution,[],[f140,f66]) ).
fof(f155,plain,
( $false
| spl1_4 ),
inference(forward_subsumption_resolution,[],[f154,f95]) ).
fof(f156,plain,
spl1_4,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f157,plain,
( sdtpldt0(sdtasdt0(xq,xn),xb) = sdtpldt0(xa,sz00)
| ~ aInteger0(xb)
| ~ aInteger0(xb)
| ~ spl1_3 ),
inference(superposition,[],[f126,f73]) ).
fof(f162,plain,
( ! [X0,X1] :
( sdtpldt0(xa,sdtpldt0(sdtpldt0(smndt0(xb),X0),X1)) = sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),X0),X1)
| ~ aInteger0(xa)
| ~ aInteger0(sdtpldt0(smndt0(xb),X0))
| ~ aInteger0(X1)
| ~ aInteger0(X0) )
| ~ spl1_3 ),
inference(superposition,[],[f69,f126]) ).
fof(f166,plain,
( sdtpldt0(sdtasdt0(xq,xn),xb) = sdtpldt0(xa,sz00)
| ~ aInteger0(xb)
| ~ spl1_3 ),
inference(duplicate_literal_removal,[],[f157]) ).
fof(f168,plain,
( ! [X0,X1] :
( sdtpldt0(xa,sdtpldt0(sdtpldt0(smndt0(xb),X0),X1)) = sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),X0),X1)
| ~ aInteger0(sdtpldt0(smndt0(xb),X0))
| ~ aInteger0(X1)
| ~ aInteger0(X0) )
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f162,f99]) ).
fof(f176,plain,
( sdtpldt0(sdtasdt0(xq,xn),xb) = sdtpldt0(xa,sz00)
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f166,f98]) ).
fof(f192,plain,
( ! [X0] :
( sdtpldt0(sdtasdt0(xq,xn),sdtpldt0(xb,X0)) = sdtpldt0(sdtpldt0(xa,sz00),X0)
| ~ aInteger0(sdtasdt0(xq,xn))
| ~ aInteger0(xb)
| ~ aInteger0(X0) )
| ~ spl1_3 ),
inference(superposition,[],[f69,f176]) ).
fof(f195,plain,
( ! [X0] :
( sdtpldt0(sdtasdt0(xq,xn),sdtpldt0(xb,X0)) = sdtpldt0(sdtpldt0(xa,sz00),X0)
| ~ aInteger0(xb)
| ~ aInteger0(X0) )
| ~ spl1_2
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f192,f122]) ).
fof(f201,plain,
( ! [X0] :
( sdtpldt0(sdtasdt0(xq,xn),sdtpldt0(xb,X0)) = sdtpldt0(sdtpldt0(xa,sz00),X0)
| ~ aInteger0(X0) )
| ~ spl1_2
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f195,f98]) ).
fof(f449,plain,
( ! [X0] :
( sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),xb),X0) = sdtpldt0(xa,sdtpldt0(sz00,X0))
| ~ aInteger0(sz00)
| ~ aInteger0(X0)
| ~ aInteger0(xb)
| ~ aInteger0(xb) )
| ~ spl1_3 ),
inference(superposition,[],[f168,f73]) ).
fof(f458,plain,
( ! [X0] :
( sdtpldt0(xa,sz00) = sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),X0),smndt0(sdtpldt0(smndt0(xb),X0)))
| ~ aInteger0(sdtpldt0(smndt0(xb),X0))
| ~ aInteger0(smndt0(sdtpldt0(smndt0(xb),X0)))
| ~ aInteger0(X0)
| ~ aInteger0(sdtpldt0(smndt0(xb),X0)) )
| ~ spl1_3 ),
inference(superposition,[],[f168,f74]) ).
fof(f465,plain,
( ! [X0] :
( sdtpldt0(xa,sz00) = sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),X0),smndt0(sdtpldt0(smndt0(xb),X0)))
| ~ aInteger0(sdtpldt0(smndt0(xb),X0))
| ~ aInteger0(smndt0(sdtpldt0(smndt0(xb),X0)))
| ~ aInteger0(X0) )
| ~ spl1_3 ),
inference(duplicate_literal_removal,[],[f458]) ).
fof(f473,plain,
( ! [X0] :
( sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),xb),X0) = sdtpldt0(xa,sdtpldt0(sz00,X0))
| ~ aInteger0(sz00)
| ~ aInteger0(X0)
| ~ aInteger0(xb) )
| ~ spl1_3 ),
inference(duplicate_literal_removal,[],[f449]) ).
fof(f478,plain,
( ! [X0] :
( sdtpldt0(xa,sz00) = sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),X0),smndt0(sdtpldt0(smndt0(xb),X0)))
| ~ aInteger0(sdtpldt0(smndt0(xb),X0))
| ~ aInteger0(X0) )
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f465,f66]) ).
fof(f485,plain,
( ! [X0] :
( sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),xb),X0) = sdtpldt0(xa,sdtpldt0(sz00,X0))
| ~ aInteger0(X0)
| ~ aInteger0(xb) )
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f473,f64]) ).
fof(f504,plain,
( ! [X0] :
( sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),xb),X0) = sdtpldt0(xa,sdtpldt0(sz00,X0))
| ~ aInteger0(X0) )
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f485,f98]) ).
fof(f506,plain,
( ! [X0] :
( sdtpldt0(sdtpldt0(xa,sz00),X0) = sdtpldt0(xa,sdtpldt0(sz00,X0))
| ~ aInteger0(X0) )
| ~ spl1_3 ),
inference(forward_demodulation,[],[f504,f176]) ).
fof(f508,definition,
( spl1_28
<=> ! [X0] :
( sdtpldt0(sdtpldt0(xa,sz00),X0) = sdtpldt0(xa,sdtpldt0(sz00,X0))
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_28])],[avatar_definition]) ).
fof(f509,plain,
( ! [X0] :
( sdtpldt0(sdtpldt0(xa,sz00),X0) = sdtpldt0(xa,sdtpldt0(sz00,X0))
| ~ aInteger0(X0) )
| ~ spl1_28 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f511,plain,
( spl1_28
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f506,f125,f508]) ).
fof(f677,plain,
( ! [X0] :
( sdtpldt0(xa,sdtpldt0(sz00,X0)) = sdtpldt0(xa,X0)
| ~ aInteger0(X0)
| ~ aInteger0(xa) )
| ~ spl1_28 ),
inference(superposition,[],[f509,f72]) ).
fof(f716,plain,
( ! [X0] :
( sdtpldt0(xa,sdtpldt0(sz00,X0)) = sdtpldt0(xa,X0)
| ~ aInteger0(X0) )
| ~ spl1_28 ),
inference(forward_subsumption_resolution,[],[f677,f99]) ).
fof(f817,plain,
( sdtpldt0(sdtpldt0(xa,sz00),smndt0(xc)) = sdtpldt0(sdtasdt0(xq,xn),sdtasdt0(xq,xm))
| ~ aInteger0(smndt0(xc))
| ~ spl1_2
| ~ spl1_3 ),
inference(superposition,[],[f201,f104]) ).
fof(f849,definition,
( spl1_47
<=> sdtpldt0(sdtpldt0(xa,sz00),smndt0(xc)) = sdtpldt0(sdtasdt0(xq,xn),sdtasdt0(xq,xm)) ),
introduced(definition,[new_symbols(definition,[spl1_47])],[avatar_definition]) ).
fof(f850,plain,
( sdtpldt0(sdtpldt0(xa,sz00),smndt0(xc)) = sdtpldt0(sdtasdt0(xq,xn),sdtasdt0(xq,xm))
| ~ spl1_47 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f851,plain,
( ~ spl1_4
| spl1_47
| ~ spl1_2
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f817,f125,f121,f849,f139]) ).
fof(f2735,plain,
( sdtpldt0(xa,sz00) = sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),xb),smndt0(sz00))
| ~ aInteger0(sz00)
| ~ aInteger0(xb)
| ~ aInteger0(xb)
| ~ spl1_3 ),
inference(superposition,[],[f478,f73]) ).
fof(f2763,plain,
( sdtpldt0(xa,sz00) = sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),xb),smndt0(sz00))
| ~ aInteger0(sz00)
| ~ aInteger0(xb)
| ~ spl1_3 ),
inference(duplicate_literal_removal,[],[f2735]) ).
fof(f2783,plain,
( sdtpldt0(xa,sz00) = sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),xb),smndt0(sz00))
| ~ aInteger0(xb)
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f2763,f64]) ).
fof(f2816,plain,
( sdtpldt0(xa,sz00) = sdtpldt0(sdtpldt0(sdtasdt0(xq,xn),xb),smndt0(sz00))
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f2783,f98]) ).
fof(f2842,plain,
( sdtpldt0(xa,sz00) = sdtpldt0(sdtpldt0(xa,sz00),smndt0(sz00))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f2816,f176]) ).
fof(f2849,definition,
( spl1_197
<=> sdtpldt0(xa,sz00) = sdtpldt0(sdtpldt0(xa,sz00),smndt0(sz00)) ),
introduced(definition,[new_symbols(definition,[spl1_197])],[avatar_definition]) ).
fof(f2850,plain,
( sdtpldt0(xa,sz00) = sdtpldt0(sdtpldt0(xa,sz00),smndt0(sz00))
| ~ spl1_197 ),
inference(avatar_component_clause,[],[f2849]) ).
fof(f2852,plain,
( spl1_197
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f2842,f125,f2849]) ).
fof(f4322,plain,
( xa = sdtpldt0(xa,smndt0(sz00))
| ~ aInteger0(xa)
| ~ spl1_197 ),
inference(superposition,[],[f2850,f72]) ).
fof(f4358,plain,
( xa = sdtpldt0(xa,smndt0(sz00))
| ~ spl1_197 ),
inference(forward_subsumption_resolution,[],[f4322,f99]) ).
fof(f4510,plain,
( sdtpldt0(xa,sz00) = sdtpldt0(xa,smndt0(sz00))
| ~ aInteger0(smndt0(sz00))
| ~ aInteger0(sz00)
| ~ spl1_28 ),
inference(superposition,[],[f716,f74]) ).
fof(f4545,plain,
( sdtpldt0(xa,sz00) = sdtpldt0(xa,smndt0(sz00))
| ~ aInteger0(sz00)
| ~ spl1_28 ),
inference(forward_subsumption_resolution,[],[f4510,f66]) ).
fof(f4555,plain,
( sdtpldt0(xa,sz00) = sdtpldt0(xa,smndt0(sz00))
| ~ spl1_28 ),
inference(forward_subsumption_resolution,[],[f4545,f64]) ).
fof(f4562,plain,
( xa = sdtpldt0(xa,sz00)
| ~ spl1_28
| ~ spl1_197 ),
inference(forward_demodulation,[],[f4555,f4358]) ).
fof(f5886,plain,
( sdtpldt0(xa,smndt0(xc)) = sdtpldt0(sdtasdt0(xq,xn),sdtasdt0(xq,xm))
| ~ spl1_28
| ~ spl1_47
| ~ spl1_197 ),
inference(forward_demodulation,[],[f850,f4562]) ).
fof(f5906,plain,
( sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc))
| ~ aInteger0(xq)
| ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ spl1_28
| ~ spl1_47
| ~ spl1_197 ),
inference(superposition,[],[f5886,f80]) ).
fof(f5931,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ spl1_28
| ~ spl1_47
| ~ spl1_197 ),
inference(forward_subsumption_resolution,[],[f5906,f106]) ).
fof(f5957,plain,
( ~ aInteger0(xn)
| ~ aInteger0(xm)
| ~ spl1_28
| ~ spl1_47
| ~ spl1_197 ),
inference(forward_subsumption_resolution,[],[f5931,f97]) ).
fof(f5964,plain,
( ~ aInteger0(xm)
| ~ spl1_28
| ~ spl1_47
| ~ spl1_197 ),
inference(forward_subsumption_resolution,[],[f5957,f103]) ).
fof(f5967,plain,
( $false
| ~ spl1_28
| ~ spl1_47
| ~ spl1_197 ),
inference(forward_subsumption_resolution,[],[f5964,f105]) ).
fof(f5968,plain,
( ~ spl1_28
| ~ spl1_47
| ~ spl1_197 ),
inference(avatar_contradiction_clause,[],[f5967]) ).
cnf(s1,plain,
( ~ spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f123]) ).
cnf(s2,plain,
( ~ spl1_1
| spl1_3 ),
inference(sat_conversion,[],[f127]) ).
cnf(s5,plain,
spl1_1,
inference(sat_conversion,[],[f153]) ).
cnf(s6,plain,
spl1_4,
inference(sat_conversion,[],[f156]) ).
cnf(s39,plain,
( ~ spl1_3
| spl1_28 ),
inference(sat_conversion,[],[f511]) ).
cnf(s67,plain,
( ~ spl1_2
| ~ spl1_3
| ~ spl1_4
| spl1_47 ),
inference(sat_conversion,[],[f851]) ).
cnf(s267,plain,
( ~ spl1_3
| spl1_197 ),
inference(sat_conversion,[],[f2852]) ).
cnf(s576,plain,
( ~ spl1_28
| ~ spl1_47
| ~ spl1_197 ),
inference(sat_conversion,[],[f5968]) ).
cnf(s774,plain,
spl1_3,
inference(rat,[],[s2,s5]) ).
cnf(s786,plain,
spl1_197,
inference(rat,[],[s267,s774]) ).
cnf(s801,plain,
spl1_28,
inference(rat,[],[s39,s774]) ).
cnf(s810,plain,
~ spl1_47,
inference(rat,[],[s576,s786,s801]) ).
cnf(s854,plain,
~ spl1_2,
inference(rat,[],[s67,s774,s6,s810]) ).
cnf(s885,plain,
$false,
inference(rat,[],[s1,s854,s5]) ).
fof(f5969,plain,
$false,
inference(avatar_sat_refutation,[],[s885]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM431+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 : n016.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 19:58:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 9.42/2.21 % (2954197)Detected formulas, will run a generic FOF schedule.
% 9.42/2.21 % (2954206)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1499832429:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.42/2.21 % (2954205)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2609634003:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.42/2.21 % (2954202)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=3953109887:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.42/2.21 % (2954207)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1648367881:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.42/2.21 % (2954208)dis-21_1_sil=8000:lcm=predicate:random_seed=7428956: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)
% 9.42/2.21 % (2954204)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=1239527776:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.42/2.21 % (2954203)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=2597701149:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.42/2.21 % (2954206)Instruction limit reached!
% 9.42/2.21 % (2954206)------------------------------
% 9.42/2.21 % (2954206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954206)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954206)Termination reason: Instruction limit
% 9.42/2.21 % (2954206)Termination phase: Saturation
% 9.42/2.21 % (2954206)Time elapsed: 0.036 s
% 9.42/2.21 % (2954206)Peak memory usage: 88 MB
% 9.42/2.21 % (2954206)Instructions burned: 121 (million)
% 9.42/2.21 % (2954208)Refutation not found, incomplete strategy
% 9.42/2.21 % (2954208)------------------------------
% 9.42/2.21 % (2954208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954208)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954208)Termination reason: Refutation not found, incomplete strategy
% 9.42/2.21 % (2954208)Time elapsed: 0.005 s
% 9.42/2.21 % (2954208)Peak memory usage: 88 MB
% 9.42/2.21 % (2954208)Instructions burned: 5 (million)
% 9.42/2.21 % (2954205)Instruction limit reached!
% 9.42/2.21 % (2954205)------------------------------
% 9.42/2.21 % (2954205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954205)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954205)Termination reason: Instruction limit
% 9.42/2.21 % (2954205)Termination phase: Saturation
% 9.42/2.21 % (2954205)Time elapsed: 0.068 s
% 9.42/2.21 % (2954205)Peak memory usage: 89 MB
% 9.42/2.21 % (2954205)Instructions burned: 110 (million)
% 9.42/2.21 % (2954207)Instruction limit reached!
% 9.42/2.21 % (2954207)------------------------------
% 9.42/2.21 % (2954207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954207)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954207)Termination reason: Instruction limit
% 9.42/2.21 % (2954207)Termination phase: Saturation
% 9.42/2.21 % (2954207)Time elapsed: 0.086 s
% 9.42/2.21 % (2954207)Peak memory usage: 90 MB
% 9.42/2.21 % (2954207)Instructions burned: 140 (million)
% 9.42/2.21 % (2954216)lrs+10_1_sil=8000:sp=occurrence:random_seed=242445835:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 9.42/2.21 % (2954216)Instruction limit reached!
% 9.42/2.21 % (2954216)------------------------------
% 9.42/2.21 % (2954216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954216)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954216)Termination reason: Instruction limit
% 9.42/2.21 % (2954216)Termination phase: Saturation
% 9.42/2.21 % (2954216)Time elapsed: 0.088 s
% 9.42/2.21 % (2954216)Peak memory usage: 93 MB
% 9.42/2.21 % (2954216)Instructions burned: 286 (million)
% 9.42/2.21 % (2954217)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2358301823:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.42/2.21 % (2954218)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2275853977:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.42/2.21 % (2954208)------------------------------
% 9.42/2.21 % (2954208)------------------------------
% 9.42/2.21 % (2954217)Instruction limit reached!
% 9.42/2.21 % (2954217)------------------------------
% 9.42/2.21 % (2954217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954217)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954217)Termination reason: Instruction limit
% 9.42/2.21 % (2954217)Termination phase: Saturation
% 9.42/2.21 % (2954217)Time elapsed: 0.078 s
% 9.42/2.21 % (2954217)Peak memory usage: 93 MB
% 9.42/2.21 % (2954217)Instructions burned: 159 (million)
% 9.42/2.21 % (2954220)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=3601916386:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 9.42/2.21 % (2954220)Instruction limit reached!
% 9.42/2.21 % (2954220)------------------------------
% 9.42/2.21 % (2954220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954220)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954220)Termination reason: Instruction limit
% 9.42/2.21 % (2954220)Termination phase: Saturation
% 9.42/2.21 % (2954220)Time elapsed: 0.063 s
% 9.42/2.21 % (2954220)Peak memory usage: 95 MB
% 9.42/2.21 % (2954220)Instructions burned: 252 (million)
% 9.42/2.21 % (2954223)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3745574996:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.42/2.21 % (2954218)Instruction limit reached!
% 9.42/2.21 % (2954218)------------------------------
% 9.42/2.21 % (2954218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954218)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954218)Termination reason: Instruction limit
% 9.42/2.21 % (2954218)Termination phase: Saturation
% 9.42/2.21 % (2954218)Time elapsed: 0.205 s
% 9.42/2.21 % (2954218)Peak memory usage: 93 MB
% 9.42/2.21 % (2954218)Instructions burned: 326 (million)
% 9.42/2.21 % (2954224)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3312805298:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 9.42/2.21 % (2954226)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2440019527:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.42/2.21 % (2954226)Instruction limit reached!
% 9.42/2.21 % (2954226)------------------------------
% 9.42/2.21 % (2954226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954226)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954226)Termination reason: Instruction limit
% 9.42/2.21 % (2954226)Termination phase: Saturation
% 9.42/2.21 % (2954226)Time elapsed: 0.042 s
% 9.42/2.21 % (2954226)Peak memory usage: 91 MB
% 9.42/2.21 % (2954226)Instructions burned: 114 (million)
% 9.42/2.21 % (2954223)Instruction limit reached!
% 9.42/2.21 % (2954223)------------------------------
% 9.42/2.21 % (2954223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954223)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954223)Termination reason: Instruction limit
% 9.42/2.21 % (2954223)Termination phase: Saturation
% 9.42/2.21 % (2954223)Time elapsed: 0.168 s
% 9.42/2.21 % (2954223)Peak memory usage: 90 MB
% 9.42/2.21 % (2954223)Instructions burned: 294 (million)
% 9.42/2.21 % (2954229)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3908654958:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 9.42/2.21 % (2954229)Instruction limit reached!
% 9.42/2.21 % (2954229)------------------------------
% 9.42/2.21 % (2954229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954229)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954229)Termination reason: Instruction limit
% 9.42/2.21 % (2954229)Termination phase: Saturation
% 9.42/2.21 % (2954229)Time elapsed: 0.065 s
% 9.42/2.21 % (2954229)Peak memory usage: 89 MB
% 9.42/2.21 % (2954229)Instructions burned: 128 (million)
% 9.42/2.21 % (2954231)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=952966858:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 9.42/2.21 % (2954232)lrs+10_1_sil=8000:sp=occurrence:random_seed=3195700443:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 9.42/2.21 % (2954231)Instruction limit reached!
% 9.42/2.21 % (2954231)------------------------------
% 9.42/2.21 % (2954231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.21 % (2954231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.21 % (2954231)CaDiCaL version: 2.1.3
% 9.42/2.21 % (2954231)Termination reason: Instruction limit
% 9.42/2.21 % (2954231)Termination phase: Saturation
% 9.42/2.21 % (2954231)Time elapsed: 0.035 s
% 9.42/2.21 % (2954231)Peak memory usage: 89 MB
% 9.42/2.21 % (2954231)Instructions burned: 115 (million)
% 9.42/2.21 % (2954234)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2473035614:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 9.42/2.21 % (2954237)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2928974020:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 9.42/2.21 % (2954234)First to succeed.
% 9.42/2.21 % (2954234)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2954197"
% 9.42/2.21 % (2954234)Refutation found. Thanks to Tanya!
% 9.42/2.21 % SZS status Theorem for theBenchmark
% 9.42/2.21 % SZS output start Proof for theBenchmark
% See solution above
% 10.11/2.32 % (2954234)------------------------------
% 10.11/2.32 % (2954234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.32 % (2954234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.32 % (2954234)CaDiCaL version: 2.1.3
% 10.11/2.32 % (2954234)Termination reason: Refutation
% 10.11/2.32 % (2954234)Time elapsed: 0.105 s
% 10.11/2.32 % (2954234)Peak memory usage: 92 MB
% 10.11/2.32 % (2954234)Instructions burned: 170 (million)
% 10.11/2.32 % (2954234)------------------------------
% 10.11/2.32 % (2954234)------------------------------
% 10.11/2.32 % (2954197)Success in time 1.355 s
% 10.11/2.32 % Vampire exiting
%------------------------------------------------------------------------------