%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX203+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 01:46:09 PM UTC 2026
% Result : Theorem 2.73s 1.11s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 26
% Syntax : Number of formulae : 151 ( 56 unt; 8 def)
% Number of atoms : 375 ( 118 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 368 ( 144 ~; 193 |; 15 &)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 195 ( 0 sgn 193 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] : proj1S(s(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
fof(f5,axiom,
! [X0] : z != s(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(f6,axiom,
! [X0] : leqNat(z,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
fof(f7,axiom,
! [X0] : ~ leqNat(s(X0),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
fof(f8,axiom,
! [X0,X1] :
( leqNat(s(X0),s(X1))
<=> leqNat(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(f10,axiom,
! [X0] : sorted(cons(X0,nil)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(f11,axiom,
! [X0,X1,X2] :
( sorted(cons(X0,cons(X1,X2)))
<=> ( leqNat(X0,X1)
& sorted(cons(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(f12,axiom,
lengthNat(nil) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(f13,axiom,
! [X0,X1] : lengthNat(cons(X0,X1)) = s(lengthNat(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
fof(f14,axiom,
! [X0] : ~ elemNat(X0,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
fof(f15,axiom,
! [X0,X1,X2] :
( elemNat(X0,cons(X1,X2))
<=> ( X0 = X1
| elemNat(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
fof(f16,axiom,
unique(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(f17,axiom,
! [X0,X1] :
( unique(cons(X0,X1))
<=> ( ~ elemNat(X0,X1)
& unique(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
fof(f18,axiom,
! [X0] : append(nil,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
fof(f19,axiom,
! [X0,X1,X2] : append(cons(X1,X2),X0) = cons(X1,append(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
fof(f20,axiom,
rev(nil) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
fof(f21,axiom,
! [X0,X1] : rev(cons(X0,X1)) = append(rev(X1),cons(X0,nil)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
fof(f22,conjecture,
? [X0] :
~ ( sorted(rev(X0))
=> ( unique(X0)
=> leqNat(lengthNat(X0),s(s(s(z)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_022) ).
fof(f23,negated_conjecture,
~ ? [X0] :
~ ( sorted(rev(X0))
=> ( unique(X0)
=> leqNat(lengthNat(X0),s(s(s(z)))) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [X0] :
( leqNat(lengthNat(X0),s(s(s(z))))
| ~ unique(X0)
| ~ sorted(rev(X0)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f25,plain,
! [X0] :
( leqNat(lengthNat(X0),s(s(s(z))))
| ~ unique(X0)
| ~ sorted(rev(X0)) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( leqNat(s(X0),s(X1))
| ~ leqNat(X0,X1) )
& ( leqNat(X0,X1)
| ~ leqNat(s(X0),s(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( sorted(cons(X0,cons(X1,X2)))
| ~ leqNat(X0,X1)
| ~ sorted(cons(X1,X2)) )
& ( ( leqNat(X0,X1)
& sorted(cons(X1,X2)) )
| ~ sorted(cons(X0,cons(X1,X2))) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( sorted(cons(X0,cons(X1,X2)))
| ~ leqNat(X0,X1)
| ~ sorted(cons(X1,X2)) )
& ( ( leqNat(X0,X1)
& sorted(cons(X1,X2)) )
| ~ sorted(cons(X0,cons(X1,X2))) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( elemNat(X0,cons(X1,X2))
| ( X0 != X1
& ~ elemNat(X0,X2) ) )
& ( X0 = X1
| elemNat(X0,X2)
| ~ elemNat(X0,cons(X1,X2)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( elemNat(X0,cons(X1,X2))
| ( X0 != X1
& ~ elemNat(X0,X2) ) )
& ( X0 = X1
| elemNat(X0,X2)
| ~ elemNat(X0,cons(X1,X2)) ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ( unique(cons(X0,X1))
| elemNat(X0,X1)
| ~ unique(X1) )
& ( ( ~ elemNat(X0,X1)
& unique(X1) )
| ~ unique(cons(X0,X1)) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0,X1] :
( ( unique(cons(X0,X1))
| elemNat(X0,X1)
| ~ unique(X1) )
& ( ( ~ elemNat(X0,X1)
& unique(X1) )
| ~ unique(cons(X0,X1)) ) ),
inference(flattening,[],[f31]) ).
fof(f36,plain,
! [X0] : proj1S(s(X0)) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0] : s(X0) != z,
inference(cnf_transformation,[],[f5]) ).
fof(f38,plain,
! [X0] : leqNat(z,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f39,plain,
! [X0] : ~ leqNat(s(X0),z),
inference(cnf_transformation,[],[f7]) ).
fof(f40,plain,
! [X0,X1] :
( ~ leqNat(s(X0),s(X1))
| leqNat(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X0,X1] :
( leqNat(s(X0),s(X1))
| ~ leqNat(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X0] : sorted(cons(X0,nil)),
inference(cnf_transformation,[],[f10]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ sorted(cons(X1,X2))
| ~ leqNat(X0,X1)
| sorted(cons(X0,cons(X1,X2))) ),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
z = lengthNat(nil),
inference(cnf_transformation,[],[f12]) ).
fof(f48,plain,
! [X0,X1] : lengthNat(cons(X0,X1)) = s(lengthNat(X1)),
inference(cnf_transformation,[],[f13]) ).
fof(f49,plain,
! [X0] : ~ elemNat(X0,nil),
inference(cnf_transformation,[],[f14]) ).
fof(f50,plain,
! [X2,X0,X1] :
( elemNat(X0,X2)
| X0 = X1
| ~ elemNat(X0,cons(X1,X2)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
unique(nil),
inference(cnf_transformation,[],[f16]) ).
fof(f56,plain,
! [X0,X1] :
( ~ unique(X1)
| elemNat(X0,X1)
| unique(cons(X0,X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f57,plain,
! [X0] : append(nil,X0) = X0,
inference(cnf_transformation,[],[f18]) ).
fof(f58,plain,
! [X2,X0,X1] : append(cons(X1,X2),X0) = cons(X1,append(X2,X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f59,plain,
nil = rev(nil),
inference(cnf_transformation,[],[f20]) ).
fof(f60,plain,
! [X0,X1] : rev(cons(X0,X1)) = append(rev(X1),cons(X0,nil)),
inference(cnf_transformation,[],[f21]) ).
fof(f61,plain,
! [X0] :
( ~ sorted(rev(X0))
| ~ unique(X0)
| leqNat(lengthNat(X0),s(s(s(z)))) ),
inference(cnf_transformation,[],[f25]) ).
fof(f68,plain,
! [X0] :
( elemNat(X0,nil)
| unique(cons(X0,nil)) ),
inference(resolution,[],[f56,f53]) ).
fof(f69,plain,
! [X0] : unique(cons(X0,nil)),
inference(forward_subsumption_resolution,[],[f68,f49]) ).
fof(f72,plain,
! [X0,X1] :
( elemNat(X0,cons(X1,nil))
| unique(cons(X0,cons(X1,nil))) ),
inference(resolution,[],[f69,f56]) ).
fof(f73,plain,
! [X0] : rev(cons(X0,nil)) = append(nil,cons(X0,nil)),
inference(superposition,[],[f60,f59]) ).
fof(f74,plain,
! [X0] : cons(X0,nil) = rev(cons(X0,nil)),
inference(forward_demodulation,[],[f73,f57]) ).
fof(f75,plain,
! [X0,X1] :
( ~ leqNat(X0,X1)
| sorted(cons(X0,cons(X1,nil))) ),
inference(resolution,[],[f46,f43]) ).
fof(f76,plain,
! [X0,X1] : rev(cons(X1,cons(X0,nil))) = append(cons(X0,nil),cons(X1,nil)),
inference(superposition,[],[f60,f74]) ).
fof(f86,plain,
! [X0,X1] :
( ~ elemNat(X0,cons(X1,nil))
| X0 = X1 ),
inference(resolution,[],[f50,f49]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ elemNat(X0,cons(X2,cons(X1,nil)))
| X0 = X2
| X0 = X1 ),
inference(resolution,[],[f86,f50]) ).
fof(f102,plain,
! [X0,X1] :
( unique(cons(X0,cons(X1,nil)))
| X0 = X1 ),
inference(resolution,[],[f72,f86]) ).
fof(f112,plain,
! [X0,X1] : rev(cons(X1,cons(X0,nil))) = cons(X0,append(nil,cons(X1,nil))),
inference(forward_demodulation,[],[f76,f58]) ).
fof(f113,plain,
! [X0,X1] : cons(X0,cons(X1,nil)) = rev(cons(X1,cons(X0,nil))),
inference(forward_demodulation,[],[f112,f57]) ).
fof(f117,plain,
! [X2,X0,X1] : rev(cons(X2,cons(X1,cons(X0,nil)))) = append(cons(X0,cons(X1,nil)),cons(X2,nil)),
inference(superposition,[],[f60,f113]) ).
fof(f120,plain,
! [X2,X0,X1] : rev(cons(X2,cons(X1,cons(X0,nil)))) = cons(X0,append(cons(X1,nil),cons(X2,nil))),
inference(forward_demodulation,[],[f117,f58]) ).
fof(f122,plain,
! [X2,X0,X1] : rev(cons(X2,cons(X1,cons(X0,nil)))) = cons(X0,cons(X1,append(nil,cons(X2,nil)))),
inference(forward_demodulation,[],[f120,f58]) ).
fof(f124,plain,
! [X2,X0,X1] : rev(cons(X2,cons(X1,cons(X0,nil)))) = cons(X0,cons(X1,cons(X2,nil))),
inference(forward_demodulation,[],[f122,f57]) ).
fof(f129,definition,
( spl0_2
<=> leqNat(s(s(z)),s(s(s(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f130,plain,
( ~ leqNat(s(s(z)),s(s(s(z))))
| spl0_2 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f131,plain,
( leqNat(s(s(z)),s(s(s(z))))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f133,plain,
( leqNat(s(z),s(s(z)))
| ~ spl0_2 ),
inference(resolution,[],[f131,f40]) ).
fof(f137,plain,
! [X2,X0,X1] :
( elemNat(X2,cons(X0,cons(X1,nil)))
| X0 = X1
| unique(cons(X2,cons(X0,cons(X1,nil)))) ),
inference(resolution,[],[f102,f56]) ).
fof(f146,plain,
! [X2,X3,X0,X1] :
( ~ elemNat(X0,cons(X3,cons(X1,cons(X2,nil))))
| X0 = X2
| X0 = X3
| X0 = X1 ),
inference(resolution,[],[f100,f50]) ).
fof(f150,plain,
! [X2,X3,X0,X1] : rev(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) = append(cons(X0,cons(X1,cons(X2,nil))),cons(X3,nil)),
inference(superposition,[],[f60,f124]) ).
fof(f153,plain,
! [X2,X3,X0,X1] : rev(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) = cons(X0,append(cons(X1,cons(X2,nil)),cons(X3,nil))),
inference(forward_demodulation,[],[f150,f58]) ).
fof(f155,plain,
! [X2,X3,X0,X1] : rev(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) = cons(X0,cons(X1,append(cons(X2,nil),cons(X3,nil)))),
inference(forward_demodulation,[],[f153,f58]) ).
fof(f157,plain,
! [X2,X3,X0,X1] : rev(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) = cons(X0,cons(X1,cons(X2,append(nil,cons(X3,nil))))),
inference(forward_demodulation,[],[f155,f58]) ).
fof(f159,plain,
! [X2,X3,X0,X1] : rev(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) = cons(X0,cons(X1,cons(X2,cons(X3,nil)))),
inference(forward_demodulation,[],[f157,f57]) ).
fof(f184,plain,
! [X2,X0,X1] :
( unique(cons(X2,cons(X0,cons(X1,nil))))
| X0 = X1
| X0 = X2
| X1 = X2 ),
inference(resolution,[],[f137,f100]) ).
fof(f195,plain,
! [X2,X3,X0,X1] :
( ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil)))))
| leqNat(lengthNat(cons(X3,cons(X2,cons(X1,cons(X0,nil))))),s(s(s(z)))) ),
inference(superposition,[],[f61,f159]) ).
fof(f196,plain,
! [X2,X3,X0,X1] :
( leqNat(s(lengthNat(cons(X2,cons(X1,cons(X0,nil))))),s(s(s(z))))
| ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) ),
inference(forward_demodulation,[],[f195,f48]) ).
fof(f198,plain,
! [X2,X3,X0,X1] :
( leqNat(s(s(lengthNat(cons(X1,cons(X0,nil))))),s(s(s(z))))
| ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) ),
inference(forward_demodulation,[],[f196,f48]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( leqNat(s(s(s(lengthNat(cons(X0,nil))))),s(s(s(z))))
| ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) ),
inference(forward_demodulation,[],[f198,f48]) ).
fof(f202,plain,
! [X2,X3,X0,X1] :
( leqNat(s(s(s(s(lengthNat(nil))))),s(s(s(z))))
| ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) ),
inference(forward_demodulation,[],[f200,f48]) ).
fof(f204,plain,
! [X2,X3,X0,X1] :
( leqNat(s(s(s(s(z)))),s(s(s(z))))
| ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) ),
inference(forward_demodulation,[],[f202,f47]) ).
fof(f207,definition,
( spl0_5
<=> ! [X0,X3,X2,X1] :
( ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil))))) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f208,plain,
( ! [X2,X3,X0,X1] :
( ~ unique(cons(X3,cons(X2,cons(X1,cons(X0,nil)))))
| ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil))))) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f210,definition,
( spl0_6
<=> leqNat(s(s(s(s(z)))),s(s(s(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f212,plain,
( leqNat(s(s(s(s(z)))),s(s(s(z))))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f213,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f204,f210,f207]) ).
fof(f231,plain,
! [X2,X3,X0,X1] :
( elemNat(X3,cons(X2,cons(X0,cons(X1,nil))))
| X0 = X2
| X1 = X2
| X0 = X1
| unique(cons(X3,cons(X2,cons(X0,cons(X1,nil))))) ),
inference(resolution,[],[f184,f56]) ).
fof(f247,definition,
( spl0_8
<=> s(s(z)) = s(s(s(z))) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f248,plain,
( s(s(z)) != s(s(s(z)))
| spl0_8 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f249,plain,
( s(s(z)) = s(s(s(z)))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f255,definition,
( spl0_10
<=> s(z) = s(s(z)) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f256,plain,
( s(z) != s(s(z))
| spl0_10 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( s(z) = s(s(z))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f260,plain,
( ~ leqNat(s(z),s(s(z)))
| spl0_2 ),
inference(resolution,[],[f130,f41]) ).
fof(f261,plain,
( ~ leqNat(z,s(z))
| spl0_2 ),
inference(resolution,[],[f260,f41]) ).
fof(f262,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f261,f38]) ).
fof(f263,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f262]) ).
fof(f265,plain,
( sorted(cons(s(s(z)),cons(s(s(s(z))),nil)))
| ~ spl0_2 ),
inference(resolution,[],[f131,f75]) ).
fof(f720,plain,
( ! [X0] :
( sorted(cons(X0,cons(s(s(z)),cons(s(s(s(z))),nil))))
| ~ leqNat(X0,s(s(z))) )
| ~ spl0_2 ),
inference(resolution,[],[f265,f46]) ).
fof(f732,plain,
( ! [X0,X1] :
( sorted(cons(X1,cons(X0,cons(s(s(z)),cons(s(s(s(z))),nil)))))
| ~ leqNat(X1,X0)
| ~ leqNat(X0,s(s(z))) )
| ~ spl0_2 ),
inference(resolution,[],[f720,f46]) ).
fof(f786,plain,
! [X2,X3,X0,X1] :
( unique(cons(X3,cons(X1,cons(X0,cons(X2,nil)))))
| X1 = X2
| X0 = X2
| X0 = X1
| X2 = X3
| X1 = X3
| X0 = X3 ),
inference(resolution,[],[f231,f146]) ).
fof(f897,definition,
( spl0_28
<=> ! [X0,X1] :
( X0 = X1
| ~ leqNat(X1,s(s(z)))
| ~ leqNat(X0,X1)
| s(s(z)) = X0
| s(s(s(z))) = X1
| s(s(s(z))) = X0
| s(s(z)) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f898,plain,
( ! [X0,X1] :
( ~ leqNat(X1,s(s(z)))
| X0 = X1
| ~ leqNat(X0,X1)
| s(s(z)) = X0
| s(s(s(z))) = X1
| s(s(s(z))) = X0
| s(s(z)) = X1 )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f935,plain,
( s(z) = proj1S(s(z))
| ~ spl0_10 ),
inference(superposition,[],[f36,f257]) ).
fof(f952,plain,
( z = s(z)
| ~ spl0_10 ),
inference(forward_demodulation,[],[f935,f36]) ).
fof(f963,plain,
( $false
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f952,f37]) ).
fof(f964,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[],[f963]) ).
fof(f965,plain,
( leqNat(s(s(s(z))),s(s(z)))
| ~ spl0_6 ),
inference(resolution,[],[f212,f40]) ).
fof(f967,plain,
( leqNat(s(s(z)),s(z))
| ~ spl0_6 ),
inference(resolution,[],[f965,f40]) ).
fof(f972,plain,
( leqNat(s(z),z)
| ~ spl0_6 ),
inference(resolution,[],[f967,f40]) ).
fof(f975,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f972,f39]) ).
fof(f976,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f975]) ).
fof(f980,plain,
( ! [X2,X3,X0,X1] :
( ~ sorted(cons(X0,cons(X1,cons(X2,cons(X3,nil)))))
| X0 = X2
| X0 = X1
| X1 = X2
| X0 = X3
| X2 = X3
| X1 = X3 )
| ~ spl0_5 ),
inference(resolution,[],[f208,f786]) ).
fof(f1005,plain,
( s(s(z)) = proj1S(s(s(z)))
| ~ spl0_8 ),
inference(superposition,[],[f36,f249]) ).
fof(f1022,plain,
( s(z) = s(s(z))
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1005,f36]) ).
fof(f1025,plain,
( $false
| ~ spl0_8
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f1022,f256]) ).
fof(f1026,plain,
( ~ spl0_8
| spl0_10 ),
inference(avatar_contradiction_clause,[],[f1025]) ).
fof(f1034,plain,
( ! [X0,X1] :
( s(s(z)) = X0
| X0 = X1
| s(s(z)) = X1
| s(s(s(z))) = X0
| s(s(z)) = s(s(s(z)))
| s(s(s(z))) = X1
| ~ leqNat(X0,X1)
| ~ leqNat(X1,s(s(z))) )
| ~ spl0_2
| ~ spl0_5 ),
inference(resolution,[],[f980,f732]) ).
fof(f1045,plain,
( ! [X0,X1] :
( s(s(z)) = X0
| X0 = X1
| s(s(z)) = X1
| s(s(s(z))) = X0
| s(s(s(z))) = X1
| ~ leqNat(X0,X1)
| ~ leqNat(X1,s(s(z))) )
| ~ spl0_2
| ~ spl0_5
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f1034,f248]) ).
fof(f1047,plain,
( spl0_28
| ~ spl0_2
| ~ spl0_5
| spl0_8 ),
inference(avatar_split_clause,[],[f1045,f247,f207,f129,f897]) ).
fof(f1119,plain,
( ! [X0] :
( s(z) = X0
| ~ leqNat(X0,s(z))
| s(s(z)) = X0
| s(z) = s(s(s(z)))
| s(s(s(z))) = X0
| s(z) = s(s(z)) )
| ~ spl0_2
| ~ spl0_28 ),
inference(resolution,[],[f898,f133]) ).
fof(f1124,plain,
( ! [X0] :
( s(z) = X0
| ~ leqNat(X0,s(z))
| s(s(z)) = X0
| s(z) = s(s(s(z)))
| s(s(s(z))) = X0 )
| ~ spl0_2
| spl0_10
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f1119,f256]) ).
fof(f1127,definition,
( spl0_32
<=> s(z) = s(s(s(z))) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f1129,plain,
( s(z) = s(s(s(z)))
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f1131,definition,
( spl0_33
<=> ! [X0] :
( s(z) = X0
| s(s(s(z))) = X0
| s(s(z)) = X0
| ~ leqNat(X0,s(z)) ) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f1132,plain,
( ! [X0] :
( ~ leqNat(X0,s(z))
| s(s(s(z))) = X0
| s(s(z)) = X0
| s(z) = X0 )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f1133,plain,
( spl0_32
| spl0_33
| ~ spl0_2
| spl0_10
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f1124,f897,f255,f129,f1131,f1127]) ).
fof(f1163,plain,
( s(s(z)) = proj1S(s(z))
| ~ spl0_32 ),
inference(superposition,[],[f36,f1129]) ).
fof(f1184,plain,
( z = s(s(z))
| ~ spl0_32 ),
inference(forward_demodulation,[],[f1163,f36]) ).
fof(f1189,plain,
( $false
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f1184,f37]) ).
fof(f1190,plain,
~ spl0_32,
inference(avatar_contradiction_clause,[],[f1189]) ).
fof(f1217,plain,
( z = s(s(s(z)))
| z = s(s(z))
| z = s(z)
| ~ spl0_33 ),
inference(resolution,[],[f1132,f38]) ).
fof(f1220,plain,
( z = s(s(s(z)))
| z = s(s(z))
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1217,f37]) ).
fof(f1221,plain,
( z = s(s(s(z)))
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1220,f37]) ).
fof(f1222,plain,
( $false
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1221,f37]) ).
fof(f1223,plain,
~ spl0_33,
inference(avatar_contradiction_clause,[],[f1222]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f213]) ).
cnf(s6,plain,
spl0_2,
inference(sat_conversion,[],[f263]) ).
cnf(s122,plain,
~ spl0_10,
inference(sat_conversion,[],[f964]) ).
cnf(s123,plain,
~ spl0_6,
inference(sat_conversion,[],[f976]) ).
cnf(s125,plain,
( ~ spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f1026]) ).
cnf(s126,plain,
( ~ spl0_2
| ~ spl0_5
| spl0_8
| spl0_28 ),
inference(sat_conversion,[],[f1047]) ).
cnf(s129,plain,
( ~ spl0_2
| spl0_10
| ~ spl0_28
| spl0_32
| spl0_33 ),
inference(sat_conversion,[],[f1133]) ).
cnf(s132,plain,
~ spl0_32,
inference(sat_conversion,[],[f1190]) ).
cnf(s134,plain,
~ spl0_33,
inference(sat_conversion,[],[f1223]) ).
cnf(s135,plain,
( ~ spl0_2
| spl0_10
| ~ spl0_28 ),
inference(rat,[],[s129,s134,s132]) ).
cnf(s136,plain,
~ spl0_8,
inference(rat,[],[s125,s122]) ).
cnf(s139,plain,
~ spl0_28,
inference(rat,[],[s135,s122,s6]) ).
cnf(s140,plain,
~ spl0_5,
inference(rat,[],[s126,s139,s136,s6]) ).
cnf(s143,plain,
$false,
inference(rat,[],[s3,s123,s140]) ).
fof(f1224,plain,
$false,
inference(avatar_sat_refutation,[],[s143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX203+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 15:10:07 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.73/1.11 % (449775)Detected formulas, will run a generic FOF schedule.
% 2.73/1.11 % (449803)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=884907644:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/1.11 % (449807)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=553090732:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/1.11 % (449807)First to succeed.
% 2.73/1.11 % (449807)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-449775"
% 2.73/1.11 % (449802)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=3961490966:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/1.11 % (449805)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2174889458:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/1.11 % (449801)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=4103440363:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/1.11 % (449806)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1019442702:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/1.11 % (449808)dis-21_1_sil=8000:lcm=predicate:random_seed=1016825807: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)
% 2.73/1.11 % (449805)Instruction limit reached!
% 2.73/1.11 % (449805)------------------------------
% 2.73/1.11 % (449805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.11 % (449805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.11 % (449805)CaDiCaL version: 2.1.3
% 2.73/1.11 % (449805)Termination reason: Instruction limit
% 2.73/1.11 % (449805)Termination phase: Saturation
% 2.73/1.11 % (449805)Time elapsed: 0.080 s
% 2.73/1.11 % (449805)Peak memory usage: 89 MB
% 2.73/1.11 % (449805)Instructions burned: 109 (million)
% 2.73/1.11 % (449808)Instruction limit reached!
% 2.73/1.11 % (449808)------------------------------
% 2.73/1.11 % (449808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.11 % (449808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.11 % (449808)CaDiCaL version: 2.1.3
% 2.73/1.11 % (449808)Termination reason: Instruction limit
% 2.73/1.11 % (449808)Termination phase: Saturation
% 2.73/1.11 % (449808)Time elapsed: 0.094 s
% 2.73/1.11 % (449808)Peak memory usage: 89 MB
% 2.73/1.11 % (449808)Instructions burned: 129 (million)
% 2.73/1.11 % (449806)Instruction limit reached!
% 2.73/1.11 % (449806)------------------------------
% 2.73/1.11 % (449806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.11 % (449806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.11 % (449806)CaDiCaL version: 2.1.3
% 2.73/1.11 % (449806)Termination reason: Instruction limit
% 2.73/1.11 % (449806)Termination phase: Saturation
% 2.73/1.11 % (449806)Time elapsed: 0.112 s
% 2.73/1.11 % (449806)Peak memory usage: 88 MB
% 2.73/1.11 % (449806)Instructions burned: 119 (million)
% 2.73/1.11 % (449807)Refutation found. Thanks to Tanya!
% 2.73/1.11 % SZS status Theorem for theBenchmark
% 2.73/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.35 % (449807)------------------------------
% 3.50/1.35 % (449807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.35 % (449807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.35 % (449807)CaDiCaL version: 2.1.3
% 3.50/1.35 % (449807)Termination reason: Refutation
% 3.50/1.35 % (449807)Time elapsed: 0.032 s
% 3.50/1.35 % (449807)Peak memory usage: 90 MB
% 3.50/1.35 % (449807)Instructions burned: 53 (million)
% 3.50/1.35 % (449807)------------------------------
% 3.50/1.35 % (449807)------------------------------
% 3.50/1.35 % (449775)Success in time 0.391 s
% 3.50/1.35 % Vampire exiting
%------------------------------------------------------------------------------