%------------------------------------------------------------------------------
% 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 : n001.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 : Unsatisfiable 25.32s 4.23s
% Output : Refutation 25.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 29
% Syntax : Number of formulae : 161 ( 161 unt; 5 def)
% Number of atoms : 161 ( 160 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 26 ( 26 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 9 con; 0-3 aty)
% Number of variables : 163 ( 163 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,negated_conjecture,
! [X0,X1] : aux(X0,X1,bfalse) = unique(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
fof(f5,negated_conjecture,
! [X0] : orb(bfalse,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
fof(f6,axiom,
! [X0] : leqNat(z,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
fof(f7,plain,
! [X0] : btrue = leqNat(z,X0),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0] : leqNat(s(X0),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(f9,plain,
! [X0] : bfalse = leqNat(s(X0),z),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0,X1] : leqNat(s(X0),s(X1)) = leqNat(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
fof(f13,negated_conjecture,
! [X0,X1] : lengthNat(cons(X0,X1)) = s(lengthNat(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(f14,negated_conjecture,
! [X0] : impl(btrue,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
fof(f17,axiom,
! [X0] : elemNat(X0,nil) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(f18,plain,
! [X0] : bfalse = elemNat(X0,nil),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
! [X2,X0,X1] : elemNat(X0,cons(X1,X2)) = orb(eq(X0,X1),elemNat(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(f20,axiom,
unique(nil) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
fof(f21,plain,
btrue = unique(nil),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
! [X0,X1] : unique(cons(X0,X1)) = aux(X0,X1,elemNat(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
fof(f23,negated_conjecture,
! [X0] : append(nil,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
fof(f24,negated_conjecture,
! [X2,X0,X1] : append(cons(X0,X1),X2) = cons(X0,append(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(f25,axiom,
rev(nil) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
fof(f26,plain,
nil = rev(nil),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
! [X0,X1] : rev(cons(X0,X1)) = append(rev(X1),cons(X0,nil)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
fof(f28,negated_conjecture,
! [X0] : andb(btrue,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
fof(f33,axiom,
! [X0] : sorted(cons(X0,nil)) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
fof(f34,plain,
! [X0] : btrue = sorted(cons(X0,nil)),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
! [X2,X0,X1] : sorted(cons(X0,cons(X1,X2))) = andb(leqNat(X0,X1),sorted(cons(X1,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
fof(f36,negated_conjecture,
! [X0] : psorted_rev(X0) = impl(eq2(sorted(rev(X0)),btrue),impl(eq2(unique(X0),btrue),eq2(leqNat(lengthNat(X0),s(s(s(z)))),btrue))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
fof(f37,axiom,
eq2(bfalse,btrue) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
fof(f38,plain,
bfalse = eq2(bfalse,btrue),
inference(reorient_equations,[],[f37]) ).
fof(f41,axiom,
! [X0,X1] : eq(s(X0),s(X1)) = eq(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
fof(f42,plain,
! [X0,X1] : eq(X0,X1) = eq(s(X0),s(X1)),
inference(reorient_equations,[],[f41]) ).
fof(f45,axiom,
! [X0] : eq(s(X0),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
fof(f46,plain,
! [X0] : bfalse = eq(s(X0),z),
inference(reorient_equations,[],[f45]) ).
fof(f49,axiom,
! [X0] : eq2(X0,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
fof(f50,plain,
! [X0] : btrue = eq2(X0,X0),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
! [X0] : eq2(psorted_rev(X0),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f52,plain,
! [X0] : btrue != eq2(psorted_rev(X0),bfalse),
inference(reorient_equations,[],[f51]) ).
fof(f53,plain,
! [X0] : btrue != eq2(impl(eq2(sorted(rev(X0)),btrue),impl(eq2(unique(X0),btrue),eq2(leqNat(lengthNat(X0),s(s(s(z)))),btrue))),bfalse),
inference(definition_unfolding,[],[f52,f36]) ).
fof(f57,definition,
sF1 = unique(nil),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f58,plain,
unique(nil) = sF1,
inference(reorient_equations,[],[f57]) ).
fof(f59,plain,
btrue = sF1,
inference(definition_folding,[],[f21,f58]) ).
fof(f60,definition,
sF2 = rev(nil),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f61,plain,
rev(nil) = sF2,
inference(reorient_equations,[],[f60]) ).
fof(f62,plain,
nil = sF2,
inference(definition_folding,[],[f26,f61]) ).
fof(f66,definition,
sF4 = s(z),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f67,plain,
s(z) = sF4,
inference(reorient_equations,[],[f66]) ).
fof(f68,definition,
sF5 = s(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f69,plain,
s(sF4) = sF5,
inference(reorient_equations,[],[f68]) ).
fof(f70,definition,
sF6 = s(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f71,plain,
s(sF5) = sF6,
inference(reorient_equations,[],[f70]) ).
fof(f72,plain,
! [X0] : btrue != eq2(impl(eq2(sorted(rev(X0)),btrue),impl(eq2(unique(X0),btrue),eq2(leqNat(lengthNat(X0),sF6),btrue))),bfalse),
inference(definition_folding,[],[f53,f71,f69,f67]) ).
fof(f74,plain,
btrue = unique(nil),
inference(forward_demodulation,[],[f58,f59]) ).
fof(f75,plain,
nil = rev(nil),
inference(forward_demodulation,[],[f61,f62]) ).
fof(f77,plain,
! [X0] : leqNat(z,X0) = leqNat(sF4,s(X0)),
inference(superposition,[],[f10,f67]) ).
fof(f79,plain,
! [X0] : leqNat(sF4,X0) = leqNat(sF5,s(X0)),
inference(superposition,[],[f10,f69]) ).
fof(f80,plain,
! [X0] : leqNat(X0,z) = leqNat(s(X0),sF4),
inference(superposition,[],[f10,f67]) ).
fof(f81,plain,
! [X0] : leqNat(X0,sF5) = leqNat(s(X0),sF6),
inference(superposition,[],[f10,f71]) ).
fof(f82,plain,
! [X0] : leqNat(X0,sF4) = leqNat(s(X0),sF5),
inference(superposition,[],[f10,f69]) ).
fof(f83,plain,
! [X0] : btrue = leqNat(sF4,s(X0)),
inference(forward_demodulation,[],[f77,f7]) ).
fof(f84,plain,
! [X0] : unique(cons(X0,nil)) = aux(X0,nil,bfalse),
inference(superposition,[],[f22,f18]) ).
fof(f85,plain,
! [X0] : unique(nil) = unique(cons(X0,nil)),
inference(forward_demodulation,[],[f84,f2]) ).
fof(f86,plain,
! [X0] : btrue = unique(cons(X0,nil)),
inference(forward_demodulation,[],[f85,f74]) ).
fof(f122,plain,
! [X0] : rev(cons(X0,nil)) = append(nil,cons(X0,nil)),
inference(superposition,[],[f27,f75]) ).
fof(f123,plain,
! [X0] : cons(X0,nil) = rev(cons(X0,nil)),
inference(forward_demodulation,[],[f122,f23]) ).
fof(f124,plain,
! [X0,X1] : btrue != eq2(impl(eq2(sorted(rev(cons(X1,X0))),btrue),impl(eq2(unique(cons(X1,X0)),btrue),eq2(leqNat(s(lengthNat(X0)),sF6),btrue))),bfalse),
inference(superposition,[],[f72,f13]) ).
fof(f125,plain,
! [X0,X1] : btrue != eq2(impl(eq2(sorted(rev(cons(X1,X0))),btrue),impl(eq2(unique(cons(X1,X0)),btrue),eq2(leqNat(lengthNat(X0),sF5),btrue))),bfalse),
inference(forward_demodulation,[],[f124,f81]) ).
fof(f141,plain,
bfalse = eq(sF4,z),
inference(superposition,[],[f46,f67]) ).
fof(f142,plain,
bfalse = eq(sF6,z),
inference(superposition,[],[f46,f71]) ).
fof(f143,plain,
bfalse = eq(sF5,z),
inference(superposition,[],[f46,f69]) ).
fof(f145,plain,
! [X0] : eq(sF5,X0) = eq(sF6,s(X0)),
inference(superposition,[],[f42,f71]) ).
fof(f146,plain,
! [X0] : eq(sF4,X0) = eq(sF5,s(X0)),
inference(superposition,[],[f42,f69]) ).
fof(f152,plain,
! [X0,X1] : rev(cons(X1,cons(X0,nil))) = append(cons(X0,nil),cons(X1,nil)),
inference(superposition,[],[f27,f123]) ).
fof(f155,plain,
! [X0,X1] : rev(cons(X1,cons(X0,nil))) = cons(X0,append(nil,cons(X1,nil))),
inference(forward_demodulation,[],[f152,f24]) ).
fof(f157,plain,
! [X0,X1] : rev(cons(X1,cons(X0,nil))) = cons(X0,cons(X1,nil)),
inference(forward_demodulation,[],[f155,f23]) ).
fof(f168,plain,
! [X2,X0,X1] : sorted(cons(s(X0),cons(s(X1),X2))) = andb(leqNat(X0,X1),sorted(cons(s(X1),X2))),
inference(superposition,[],[f35,f10]) ).
fof(f171,plain,
! [X0,X1] : sorted(cons(X0,cons(X1,nil))) = andb(leqNat(X0,X1),btrue),
inference(superposition,[],[f35,f34]) ).
fof(f175,plain,
leqNat(sF4,sF5) = leqNat(sF5,sF6),
inference(superposition,[],[f79,f71]) ).
fof(f188,plain,
eq(sF4,z) = eq(sF5,sF4),
inference(superposition,[],[f146,f67]) ).
fof(f192,plain,
bfalse = eq(sF5,sF4),
inference(forward_demodulation,[],[f188,f141]) ).
fof(f193,plain,
eq(sF5,z) = eq(sF6,sF4),
inference(superposition,[],[f145,f67]) ).
fof(f195,plain,
eq(sF5,sF4) = eq(sF6,sF5),
inference(superposition,[],[f145,f69]) ).
fof(f196,plain,
bfalse = eq(sF6,sF5),
inference(forward_demodulation,[],[f195,f192]) ).
fof(f198,plain,
bfalse = eq(sF6,sF4),
inference(forward_demodulation,[],[f193,f143]) ).
fof(f201,plain,
btrue = leqNat(sF4,sF5),
inference(superposition,[],[f83,f69]) ).
fof(f204,plain,
btrue = leqNat(sF5,sF6),
inference(backward_demodulation,[],[f175,f201]) ).
fof(f207,plain,
! [X0] : sorted(cons(sF5,cons(sF6,X0))) = andb(btrue,sorted(cons(sF6,X0))),
inference(superposition,[],[f35,f204]) ).
fof(f208,plain,
! [X0] : sorted(cons(sF5,cons(sF6,X0))) = sorted(cons(sF6,X0)),
inference(forward_demodulation,[],[f207,f28]) ).
fof(f222,plain,
! [X2,X0,X1] : elemNat(s(X0),cons(s(X1),X2)) = orb(eq(X0,X1),elemNat(s(X0),X2)),
inference(superposition,[],[f19,f42]) ).
fof(f230,plain,
! [X0] : elemNat(sF6,cons(sF5,X0)) = orb(bfalse,elemNat(sF6,X0)),
inference(superposition,[],[f19,f196]) ).
fof(f231,plain,
! [X0,X1] : elemNat(X0,cons(X1,nil)) = orb(eq(X0,X1),bfalse),
inference(superposition,[],[f19,f18]) ).
fof(f232,plain,
! [X0] : elemNat(sF6,cons(sF5,X0)) = elemNat(sF6,X0),
inference(forward_demodulation,[],[f230,f5]) ).
fof(f255,plain,
! [X0] : orb(bfalse,elemNat(sF6,X0)) = elemNat(sF6,cons(z,X0)),
inference(superposition,[],[f19,f142]) ).
fof(f256,plain,
! [X0] : elemNat(sF6,X0) = elemNat(sF6,cons(z,X0)),
inference(forward_demodulation,[],[f255,f5]) ).
fof(f263,plain,
! [X0] : orb(bfalse,elemNat(sF6,X0)) = elemNat(sF6,cons(sF4,X0)),
inference(superposition,[],[f19,f198]) ).
fof(f264,plain,
! [X0] : elemNat(sF6,X0) = elemNat(sF6,cons(sF4,X0)),
inference(forward_demodulation,[],[f263,f5]) ).
fof(f274,plain,
! [X0] : unique(cons(sF6,cons(sF5,X0))) = aux(sF6,cons(sF5,X0),elemNat(sF6,X0)),
inference(superposition,[],[f22,f232]) ).
fof(f298,plain,
! [X0,X1] : sorted(cons(s(X0),cons(sF6,X1))) = andb(leqNat(X0,sF5),sorted(cons(sF6,X1))),
inference(superposition,[],[f35,f81]) ).
fof(f313,plain,
! [X2,X0,X1] : btrue != eq2(impl(eq2(sorted(rev(cons(X1,cons(X2,X0)))),btrue),impl(eq2(unique(cons(X1,cons(X2,X0))),btrue),eq2(leqNat(s(lengthNat(X0)),sF5),btrue))),bfalse),
inference(superposition,[],[f125,f13]) ).
fof(f314,plain,
! [X2,X0,X1] : btrue != eq2(impl(eq2(sorted(rev(cons(X1,cons(X2,X0)))),btrue),impl(eq2(unique(cons(X1,cons(X2,X0))),btrue),eq2(leqNat(lengthNat(X0),sF4),btrue))),bfalse),
inference(forward_demodulation,[],[f313,f82]) ).
fof(f407,plain,
! [X0] : andb(btrue,sorted(cons(s(sF6),X0))) = sorted(cons(s(sF5),cons(s(sF6),X0))),
inference(superposition,[],[f168,f204]) ).
fof(f423,plain,
! [X0] : andb(btrue,sorted(cons(s(sF6),X0))) = sorted(cons(sF6,cons(s(sF6),X0))),
inference(forward_demodulation,[],[f407,f71]) ).
fof(f439,plain,
! [X0] : sorted(cons(s(sF6),X0)) = sorted(cons(sF6,cons(s(sF6),X0))),
inference(forward_demodulation,[],[f423,f28]) ).
fof(f505,plain,
! [X0,X1] : elemNat(s(s(X0)),cons(s(z),X1)) = orb(bfalse,elemNat(s(s(X0)),X1)),
inference(superposition,[],[f222,f46]) ).
fof(f521,plain,
! [X0] : orb(bfalse,elemNat(s(sF6),X0)) = elemNat(s(sF6),cons(s(sF5),X0)),
inference(superposition,[],[f222,f196]) ).
fof(f526,plain,
! [X0,X1] : orb(eq(X0,X1),bfalse) = elemNat(s(X0),cons(s(X1),nil)),
inference(superposition,[],[f222,f18]) ).
fof(f529,plain,
! [X0,X1] : elemNat(X0,cons(X1,nil)) = elemNat(s(X0),cons(s(X1),nil)),
inference(forward_demodulation,[],[f526,f231]) ).
fof(f531,plain,
! [X0] : orb(bfalse,elemNat(s(sF6),X0)) = elemNat(s(sF6),cons(sF6,X0)),
inference(forward_demodulation,[],[f521,f71]) ).
fof(f545,plain,
! [X0,X1] : elemNat(s(s(X0)),cons(s(z),X1)) = elemNat(s(s(X0)),X1),
inference(forward_demodulation,[],[f505,f5]) ).
fof(f551,plain,
! [X0] : elemNat(s(sF6),X0) = elemNat(s(sF6),cons(sF6,X0)),
inference(forward_demodulation,[],[f531,f5]) ).
fof(f562,plain,
! [X0,X1] : elemNat(s(s(X0)),X1) = elemNat(s(s(X0)),cons(sF4,X1)),
inference(forward_demodulation,[],[f545,f67]) ).
fof(f591,plain,
! [X0,X1] : unique(cons(s(s(X0)),cons(sF4,X1))) = aux(s(s(X0)),cons(sF4,X1),elemNat(s(s(X0)),X1)),
inference(superposition,[],[f22,f562]) ).
fof(f610,plain,
! [X0] : elemNat(X0,cons(z,nil)) = elemNat(s(X0),cons(sF4,nil)),
inference(superposition,[],[f529,f67]) ).
fof(f639,plain,
! [X0,X1] : elemNat(s(X0),cons(s(X1),cons(sF4,nil))) = orb(eq(X0,X1),elemNat(X0,cons(z,nil))),
inference(superposition,[],[f222,f610]) ).
fof(f647,plain,
! [X0,X1] : elemNat(s(X0),cons(s(X1),cons(sF4,nil))) = elemNat(X0,cons(X1,cons(z,nil))),
inference(forward_demodulation,[],[f639,f19]) ).
fof(f741,plain,
! [X0] : unique(cons(s(sF6),cons(sF6,X0))) = aux(s(sF6),cons(sF6,X0),elemNat(s(sF6),X0)),
inference(superposition,[],[f22,f551]) ).
fof(f884,plain,
! [X2,X0,X1] : rev(cons(X2,cons(X1,cons(X0,nil)))) = append(cons(X0,cons(X1,nil)),cons(X2,nil)),
inference(superposition,[],[f27,f157]) ).
fof(f887,plain,
! [X2,X0,X1] : rev(cons(X2,cons(X1,cons(X0,nil)))) = cons(X0,append(cons(X1,nil),cons(X2,nil))),
inference(forward_demodulation,[],[f884,f24]) ).
fof(f890,plain,
! [X2,X0,X1] : rev(cons(X2,cons(X1,cons(X0,nil)))) = cons(X0,cons(X1,append(nil,cons(X2,nil)))),
inference(forward_demodulation,[],[f887,f24]) ).
fof(f893,plain,
! [X2,X0,X1] : cons(X0,cons(X1,cons(X2,nil))) = rev(cons(X2,cons(X1,cons(X0,nil)))),
inference(forward_demodulation,[],[f890,f23]) ).
fof(f1204,plain,
! [X0,X1] : sorted(cons(X1,cons(sF5,cons(sF6,X0)))) = andb(leqNat(X1,sF5),sorted(cons(sF6,X0))),
inference(superposition,[],[f35,f208]) ).
fof(f1205,plain,
! [X0,X1] : sorted(cons(X1,cons(sF5,cons(sF6,X0)))) = sorted(cons(s(X1),cons(sF6,X0))),
inference(forward_demodulation,[],[f1204,f298]) ).
fof(f1756,plain,
! [X0,X1] : sorted(cons(X1,cons(sF6,cons(s(sF6),X0)))) = andb(leqNat(X1,sF6),sorted(cons(s(sF6),X0))),
inference(superposition,[],[f35,f439]) ).
fof(f1757,plain,
! [X0,X1] : sorted(cons(X1,cons(sF6,cons(s(sF6),X0)))) = sorted(cons(s(X1),cons(s(sF6),X0))),
inference(forward_demodulation,[],[f1756,f168]) ).
fof(f1823,plain,
! [X0] : unique(cons(s(s(X0)),cons(sF4,nil))) = aux(s(s(X0)),cons(sF4,nil),bfalse),
inference(superposition,[],[f591,f18]) ).
fof(f1826,plain,
! [X0] : unique(cons(sF4,nil)) = unique(cons(s(s(X0)),cons(sF4,nil))),
inference(forward_demodulation,[],[f1823,f2]) ).
fof(f1832,plain,
! [X0] : btrue = unique(cons(s(s(X0)),cons(sF4,nil))),
inference(forward_demodulation,[],[f1826,f86]) ).
fof(f1836,plain,
btrue = unique(cons(s(sF4),cons(sF4,nil))),
inference(superposition,[],[f1832,f67]) ).
fof(f1844,plain,
btrue = unique(cons(sF5,cons(sF4,nil))),
inference(forward_demodulation,[],[f1836,f69]) ).
fof(f2302,plain,
! [X0] : unique(cons(sF6,cons(sF5,cons(sF4,X0)))) = aux(sF6,cons(sF5,cons(sF4,X0)),elemNat(sF6,X0)),
inference(superposition,[],[f274,f264]) ).
fof(f19183,plain,
unique(cons(sF6,cons(sF5,cons(sF4,nil)))) = aux(sF6,cons(sF5,cons(sF4,nil)),bfalse),
inference(superposition,[],[f2302,f18]) ).
fof(f19187,plain,
unique(cons(sF5,cons(sF4,nil))) = unique(cons(sF6,cons(sF5,cons(sF4,nil)))),
inference(forward_demodulation,[],[f19183,f2]) ).
fof(f19189,plain,
btrue = unique(cons(sF6,cons(sF5,cons(sF4,nil)))),
inference(forward_demodulation,[],[f19187,f1844]) ).
fof(f29263,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,[],[f27,f893]) ).
fof(f29266,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,[],[f29263,f24]) ).
fof(f29294,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,[],[f29266,f24]) ).
fof(f29322,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,[],[f29294,f24]) ).
fof(f29350,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,[],[f29322,f23]) ).
fof(f37093,plain,
! [X0] : elemNat(X0,cons(sF4,cons(z,nil))) = elemNat(s(X0),cons(sF5,cons(sF4,nil))),
inference(superposition,[],[f647,f69]) ).
fof(f37222,plain,
unique(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil))))) = aux(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil))),elemNat(sF6,cons(sF4,cons(z,nil)))),
inference(superposition,[],[f741,f37093]) ).
fof(f37242,plain,
unique(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil))))) = aux(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil))),elemNat(sF6,cons(z,nil))),
inference(forward_demodulation,[],[f37222,f264]) ).
fof(f37276,plain,
unique(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil))))) = aux(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil))),elemNat(sF6,nil)),
inference(forward_demodulation,[],[f37242,f256]) ).
fof(f37302,plain,
unique(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil))))) = aux(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil))),bfalse),
inference(forward_demodulation,[],[f37276,f18]) ).
fof(f37324,plain,
unique(cons(sF6,cons(sF5,cons(sF4,nil)))) = unique(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil))))),
inference(forward_demodulation,[],[f37302,f2]) ).
fof(f37340,plain,
btrue = unique(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil))))),
inference(forward_demodulation,[],[f37324,f19189]) ).
fof(f38022,plain,
btrue != eq2(impl(eq2(sorted(rev(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(sF5,cons(sF4,nil))),sF4),btrue))),bfalse),
inference(superposition,[],[f314,f37340]) ).
fof(f38027,plain,
btrue != eq2(impl(eq2(sorted(rev(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(s(lengthNat(cons(sF4,nil))),sF4),btrue))),bfalse),
inference(forward_demodulation,[],[f38022,f13]) ).
fof(f38030,plain,
btrue != eq2(impl(eq2(sorted(rev(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(sF4,nil)),z),btrue))),bfalse),
inference(forward_demodulation,[],[f38027,f80]) ).
fof(f38033,plain,
btrue != eq2(impl(eq2(sorted(rev(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(s(lengthNat(nil)),z),btrue))),bfalse),
inference(forward_demodulation,[],[f38030,f13]) ).
fof(f38036,plain,
btrue != eq2(impl(eq2(sorted(rev(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(bfalse,btrue))),bfalse),
inference(forward_demodulation,[],[f38033,f9]) ).
fof(f38039,plain,
btrue != eq2(impl(eq2(sorted(rev(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil)))))),btrue),impl(eq2(btrue,btrue),bfalse)),bfalse),
inference(forward_demodulation,[],[f38036,f38]) ).
fof(f38042,plain,
btrue != eq2(impl(eq2(sorted(rev(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil)))))),btrue),impl(btrue,bfalse)),bfalse),
inference(forward_demodulation,[],[f38039,f50]) ).
fof(f38045,plain,
btrue != eq2(impl(eq2(sorted(rev(cons(s(sF6),cons(sF6,cons(sF5,cons(sF4,nil)))))),btrue),bfalse),bfalse),
inference(forward_demodulation,[],[f38042,f14]) ).
fof(f38048,plain,
btrue != eq2(impl(eq2(sorted(cons(sF4,cons(sF5,cons(sF6,cons(s(sF6),nil))))),btrue),bfalse),bfalse),
inference(forward_demodulation,[],[f38045,f29350]) ).
fof(f38051,plain,
btrue != eq2(impl(eq2(sorted(cons(s(sF4),cons(sF6,cons(s(sF6),nil)))),btrue),bfalse),bfalse),
inference(forward_demodulation,[],[f38048,f1205]) ).
fof(f38054,plain,
btrue != eq2(impl(eq2(sorted(cons(s(s(sF4)),cons(s(sF6),nil))),btrue),bfalse),bfalse),
inference(forward_demodulation,[],[f38051,f1757]) ).
fof(f38057,plain,
btrue != eq2(impl(eq2(andb(leqNat(s(s(sF4)),s(sF6)),btrue),btrue),bfalse),bfalse),
inference(forward_demodulation,[],[f38054,f171]) ).
fof(f38060,plain,
btrue != eq2(impl(eq2(andb(leqNat(s(sF4),sF6),btrue),btrue),bfalse),bfalse),
inference(forward_demodulation,[],[f38057,f10]) ).
fof(f38063,plain,
btrue != eq2(impl(eq2(andb(leqNat(sF4,sF5),btrue),btrue),bfalse),bfalse),
inference(forward_demodulation,[],[f38060,f81]) ).
fof(f38066,plain,
btrue != eq2(impl(eq2(andb(btrue,btrue),btrue),bfalse),bfalse),
inference(forward_demodulation,[],[f38063,f201]) ).
fof(f38069,plain,
btrue != eq2(impl(eq2(btrue,btrue),bfalse),bfalse),
inference(forward_demodulation,[],[f38066,f28]) ).
fof(f38072,plain,
btrue != eq2(impl(btrue,bfalse),bfalse),
inference(forward_demodulation,[],[f38069,f50]) ).
fof(f38075,plain,
btrue != eq2(bfalse,bfalse),
inference(forward_demodulation,[],[f38072,f14]) ).
fof(f38078,plain,
$false,
inference(forward_subsumption_resolution,[],[f38075,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 : n001.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 15:16:03 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 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
% 25.32/4.23 % (420150)Detected a unit-equality problem, will run specialized UEQ schedule.
% 25.32/4.23 % (420157)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3788393527:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 25.32/4.23 % (420160)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3359324992:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 25.32/4.23 % (420155)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=4141192063:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 25.32/4.23 % (420158)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1777803601:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 25.32/4.23 % (420161)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=442561540:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 25.32/4.23 % (420159)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2383304886:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 25.32/4.23 % (420156)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3040429319:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 25.32/4.23 % (420158)Instruction limit reached!
% 25.32/4.23 % (420158)------------------------------
% 25.32/4.23 % (420158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.32/4.23 % (420158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.32/4.23 % (420158)CaDiCaL version: 2.1.3
% 25.32/4.23 % (420158)Termination reason: Instruction limit
% 25.32/4.23 % (420158)Termination phase: Saturation
% 25.32/4.23 % (420158)Time elapsed: 0.079 s
% 25.32/4.23 % (420158)Peak memory usage: 88 MB
% 25.32/4.23 % (420158)Instructions burned: 137 (million)
% 25.32/4.23 % (420159)Instruction limit reached!
% 25.32/4.23 % (420159)------------------------------
% 25.32/4.23 % (420159)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.32/4.23 % (420159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.32/4.23 % (420159)CaDiCaL version: 2.1.3
% 25.32/4.23 % (420159)Termination reason: Instruction limit
% 25.32/4.23 % (420159)Termination phase: Saturation
% 25.32/4.23 % (420159)Time elapsed: 0.102 s
% 25.32/4.23 % (420159)Peak memory usage: 89 MB
% 25.32/4.23 % (420159)Instructions burned: 181 (million)
% 25.32/4.23 % (420160)Instruction limit reached!
% 25.32/4.23 % (420160)------------------------------
% 25.32/4.23 % (420160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.32/4.23 % (420160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.32/4.23 % (420160)CaDiCaL version: 2.1.3
% 25.32/4.23 % (420160)Termination reason: Instruction limit
% 25.32/4.23 % (420160)Termination phase: Saturation
% 25.32/4.23 % (420160)Time elapsed: 0.157 s
% 25.32/4.23 % (420160)Peak memory usage: 89 MB
% 25.32/4.23 % (420160)Instructions burned: 258 (million)
% 25.32/4.23 % (420169)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3487567189:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 25.32/4.23 % (420170)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1204878895:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 25.32/4.23 % (420171)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3642884136:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 25.32/4.23 % (420171)Instruction limit reached!
% 25.32/4.23 % (420171)------------------------------
% 25.32/4.23 % (420171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.32/4.23 % (420171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.32/4.23 % (420171)CaDiCaL version: 2.1.3
% 25.32/4.23 % (420171)Termination reason: Instruction limit
% 25.32/4.23 % (420171)Termination phase: Saturation
% 25.32/4.23 % (420171)Time elapsed: 0.109 s
% 25.32/4.23 % (420171)Peak memory usage: 90 MB
% 25.32/4.23 % (420171)Instructions burned: 216 (million)
% 25.32/4.23 % (420175)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=3382298151:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 25.32/4.23 % (420161)Instruction limit reached!
% 25.32/4.23 % (420161)------------------------------
% 25.32/4.23 % (420161)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.32/4.23 % (420161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.32/4.23 % (420161)CaDiCaL version: 2.1.3
% 25.32/4.23 % (420161)Termination reason: Instruction limit
% 25.32/4.23 % (420161)Termination phase: Saturation
% 25.32/4.23 % (420161)Time elapsed: 0.634 s
% 25.32/4.23 % (420161)Peak memory usage: 94 MB
% 25.32/4.23 % (420161)Instructions burned: 1188 (million)
% 25.32/4.23 % (420175)Instruction limit reached!
% 25.32/4.23 % (420175)------------------------------
% 25.32/4.23 % (420175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.32/4.23 % (420175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.32/4.23 % (420175)CaDiCaL version: 2.1.3
% 25.32/4.23 % (420175)Termination reason: Instruction limit
% 25.32/4.23 % (420175)Termination phase: Saturation
% 25.32/4.23 % (420175)Time elapsed: 0.149 s
% 25.32/4.23 % (420175)Peak memory usage: 94 MB
% 25.32/4.23 % (420175)Instructions burned: 318 (million)
% 25.32/4.23 % (420177)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2356998470:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 25.32/4.23 % (420178)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3106014068:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 25.32/4.23 % (420169)Instruction limit reached!
% 25.32/4.23 % (420169)------------------------------
% 25.32/4.23 % (420169)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.32/4.23 % (420169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.32/4.23 % (420169)CaDiCaL version: 2.1.3
% 25.32/4.23 % (420169)Termination reason: Instruction limit
% 25.32/4.23 % (420169)Termination phase: Saturation
% 25.32/4.23 % (420169)Time elapsed: 1.312 s
% 25.32/4.23 % (420169)Peak memory usage: 139 MB
% 25.32/4.23 % (420169)Instructions burned: 2051 (million)
% 25.32/4.23 % (420181)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=4149496604:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2982 on theBenchmark for (2982ds/14534Mi)
% 25.32/4.23 % (420178)Instruction limit reached!
% 25.32/4.23 % (420178)------------------------------
% 25.32/4.23 % (420178)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.32/4.23 % (420178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.32/4.23 % (420178)CaDiCaL version: 2.1.3
% 25.32/4.23 % (420178)Termination reason: Instruction limit
% 25.32/4.23 % (420178)Termination phase: Saturation
% 25.32/4.23 % (420178)Time elapsed: 1.390 s
% 25.32/4.23 % (420178)Peak memory usage: 109 MB
% 25.32/4.23 % (420178)Instructions burned: 2836 (million)
% 25.32/4.23 % (420183)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=2295545279:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2975 on theBenchmark for (2975ds/11832Mi)
% 25.32/4.23 % (420170)Instruction limit reached!
% 25.32/4.23 % (420170)------------------------------
% 25.32/4.23 % (420170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.32/4.23 % (420170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.32/4.23 % (420170)CaDiCaL version: 2.1.3
% 25.32/4.23 % (420170)Termination reason: Instruction limit
% 25.32/4.23 % (420170)Termination phase: Saturation
% 25.32/4.23 % (420170)Time elapsed: 2.920 s
% 25.32/4.23 % (420170)Peak memory usage: 154 MB
% 25.32/4.23 % (420170)Instructions burned: 4949 (million)
% 25.32/4.23 % (420157)First to succeed.
% 25.32/4.23 % (420157)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-420150"
% 25.32/4.23 % (420185)lrs+10_1_to=lpo:ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:drc=off:fde=unused:sp=const_min:spb=goal:fd=preordered:random_seed=902927153:i=2279:fgj=on:bd=all_2966 on theBenchmark for (2966ds/2279Mi)
% 25.32/4.23 % (420157)Refutation found. Thanks to Tanya!
% 25.32/4.23 % SZS status Unsatisfiable for theBenchmark
% 25.32/4.23 % SZS output start Proof for theBenchmark
% See solution above
% 25.91/4.43 % (420157)------------------------------
% 25.91/4.43 % (420157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.91/4.43 % (420157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.91/4.43 % (420157)CaDiCaL version: 2.1.3
% 25.91/4.43 % (420157)Termination reason: Refutation
% 25.91/4.43 % (420157)Time elapsed: 3.251 s
% 25.91/4.43 % (420157)Peak memory usage: 204 MB
% 25.91/4.43 % (420157)Instructions burned: 9280 (million)
% 25.91/4.43 % (420157)------------------------------
% 25.91/4.43 % (420157)------------------------------
% 25.91/4.43 % (420150)Success in time 3.567 s
% 25.91/4.43 % Vampire exiting
%------------------------------------------------------------------------------