%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN135-1.006 : 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 : n005.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 12:26:54 PM UTC 2026
% Result : Unsatisfiable 3.20s 1.35s
% Output : Refutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 30
% Syntax : Number of formulae : 140 ( 140 unt; 18 def)
% Number of atoms : 140 ( 139 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 20 ( 20 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 4 con; 0-4 aty)
% Number of variables : 269 ( 269 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : minus(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule1) ).
fof(f2,negated_conjecture,
! [X0,X1] : minus(s(X0),s(X1)) = minus(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule2) ).
fof(f3,negated_conjecture,
! [X0] : '<='(zero,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule3) ).
fof(f4,negated_conjecture,
! [X0] : '<='(s(X0),zero) = false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule4) ).
fof(f5,negated_conjecture,
! [X0,X1] : '<='(s(X0),s(X1)) = '<='(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule5) ).
fof(f6,negated_conjecture,
! [X0,X1] : if(true,X0,X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule6) ).
fof(f7,negated_conjecture,
! [X0,X1] : if(false,X0,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule7) ).
fof(f10,negated_conjecture,
! [X0] : perfectp(s(X0)) = f(X0,s(zero),s(X0),s(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule9) ).
fof(f11,axiom,
! [X0,X1] : f(zero,X0,zero,X1) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule10) ).
fof(f12,plain,
! [X0,X1] : true = f(zero,X0,zero,X1),
inference(reorient_equations,[],[f11]) ).
fof(f15,negated_conjecture,
! [X2,X0,X1] : f(s(X0),zero,X1,X2) = f(X0,X2,minus(X1,s(X0)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule12) ).
fof(f16,negated_conjecture,
! [X2,X3,X0,X1] : f(s(X0),s(X1),X2,X3) = if('<='(X0,X1),f(s(X0),minus(X1,X0),X2,X3),f(X0,X3,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule13) ).
fof(f17,negated_conjecture,
! [X0] : perfectp(X0) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f18,plain,
! [X0] : true != perfectp(X0),
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
! [X0] : sF0(X0) = minus(X0,zero),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f20,plain,
! [X0] : minus(X0,zero) = sF0(X0),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f20]) ).
fof(f22,definition,
! [X0,X1] : sF1(X0,X1) = minus(s(X0),s(X1)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f23,plain,
! [X0,X1] : minus(s(X0),s(X1)) = sF1(X0,X1),
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X0,X1] : minus(X0,X1) = sF1(X0,X1),
inference(definition_folding,[],[f2,f23]) ).
fof(f25,definition,
! [X0] : sF2(X0) = '<='(zero,X0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f26,plain,
! [X0] : '<='(zero,X0) = sF2(X0),
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
! [X0] : true = sF2(X0),
inference(definition_folding,[],[f3,f26]) ).
fof(f28,definition,
! [X0] : sF3(X0) = '<='(s(X0),zero),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f29,plain,
! [X0] : '<='(s(X0),zero) = sF3(X0),
inference(reorient_equations,[],[f28]) ).
fof(f30,plain,
! [X0] : false = sF3(X0),
inference(definition_folding,[],[f4,f29]) ).
fof(f31,definition,
! [X0,X1] : sF4(X0,X1) = '<='(s(X0),s(X1)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f32,plain,
! [X0,X1] : '<='(s(X0),s(X1)) = sF4(X0,X1),
inference(reorient_equations,[],[f31]) ).
fof(f33,plain,
! [X0,X1] : '<='(X0,X1) = sF4(X0,X1),
inference(definition_folding,[],[f5,f32]) ).
fof(f34,definition,
! [X0,X1] : sF5(X0,X1) = if(true,X0,X1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f35,plain,
! [X0,X1] : if(true,X0,X1) = sF5(X0,X1),
inference(reorient_equations,[],[f34]) ).
fof(f36,plain,
! [X0,X1] : sF5(X0,X1) = X0,
inference(definition_folding,[],[f6,f35]) ).
fof(f37,definition,
! [X0,X1] : sF6(X0,X1) = if(false,X0,X1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f38,plain,
! [X0,X1] : if(false,X0,X1) = sF6(X0,X1),
inference(reorient_equations,[],[f37]) ).
fof(f39,plain,
! [X0,X1] : sF6(X0,X1) = X1,
inference(definition_folding,[],[f7,f38]) ).
fof(f43,definition,
! [X0] : sF8(X0) = perfectp(s(X0)),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f44,plain,
! [X0] : perfectp(s(X0)) = sF8(X0),
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF9 = s(zero),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f46,plain,
s(zero) = sF9,
inference(reorient_equations,[],[f45]) ).
fof(f47,definition,
! [X0] : sF10(X0) = f(X0,sF9,s(X0),s(X0)),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f48,plain,
! [X0] : f(X0,sF9,s(X0),s(X0)) = sF10(X0),
inference(reorient_equations,[],[f47]) ).
fof(f49,plain,
! [X0] : sF8(X0) = sF10(X0),
inference(definition_folding,[],[f10,f48,f46,f44]) ).
fof(f50,definition,
! [X0,X1] : sF11(X0,X1) = f(zero,X0,zero,X1),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f51,plain,
! [X0,X1] : f(zero,X0,zero,X1) = sF11(X0,X1),
inference(reorient_equations,[],[f50]) ).
fof(f52,plain,
! [X0,X1] : true = sF11(X0,X1),
inference(definition_folding,[],[f12,f51]) ).
fof(f56,definition,
! [X2,X0,X1] : sF13(X0,X1,X2) = f(s(X0),zero,X1,X2),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f57,plain,
! [X2,X0,X1] : f(s(X0),zero,X1,X2) = sF13(X0,X1,X2),
inference(reorient_equations,[],[f56]) ).
fof(f58,definition,
! [X0,X1] : sF14(X1,X0) = minus(X1,s(X0)),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f59,plain,
! [X0,X1] : minus(X1,s(X0)) = sF14(X1,X0),
inference(reorient_equations,[],[f58]) ).
fof(f60,definition,
! [X2,X0,X1] : sF15(X0,X2,X1) = f(X0,X2,sF14(X1,X0),X2),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f61,plain,
! [X2,X0,X1] : f(X0,X2,sF14(X1,X0),X2) = sF15(X0,X2,X1),
inference(reorient_equations,[],[f60]) ).
fof(f62,plain,
! [X2,X0,X1] : sF13(X0,X1,X2) = sF15(X0,X2,X1),
inference(definition_folding,[],[f15,f61,f59,f57]) ).
fof(f63,definition,
! [X2,X3,X0,X1] : sF16(X0,X1,X2,X3) = f(s(X0),s(X1),X2,X3),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f64,plain,
! [X2,X3,X0,X1] : f(s(X0),s(X1),X2,X3) = sF16(X0,X1,X2,X3),
inference(reorient_equations,[],[f63]) ).
fof(f65,definition,
! [X2,X3,X0,X1] : sF17(X0,X1,X2,X3) = f(s(X0),minus(X1,X0),X2,X3),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f66,plain,
! [X2,X3,X0,X1] : f(s(X0),minus(X1,X0),X2,X3) = sF17(X0,X1,X2,X3),
inference(reorient_equations,[],[f65]) ).
fof(f67,definition,
! [X2,X3,X0] : sF18(X0,X3,X2) = f(X0,X3,X2,X3),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f68,plain,
! [X2,X3,X0] : f(X0,X3,X2,X3) = sF18(X0,X3,X2),
inference(reorient_equations,[],[f67]) ).
fof(f69,definition,
! [X2,X3,X0,X1] : sF19(X0,X1,X2,X3) = if('<='(X0,X1),sF17(X0,X1,X2,X3),sF18(X0,X3,X2)),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f70,plain,
! [X2,X3,X0,X1] : if('<='(X0,X1),sF17(X0,X1,X2,X3),sF18(X0,X3,X2)) = sF19(X0,X1,X2,X3),
inference(reorient_equations,[],[f69]) ).
fof(f71,plain,
! [X2,X3,X0,X1] : sF16(X0,X1,X2,X3) = sF19(X0,X1,X2,X3),
inference(definition_folding,[],[f16,f70,f68,f66,f64]) ).
fof(f72,plain,
! [X2,X3,X0,X1] : sF16(X0,X1,X2,X3) = if('<='(X0,X1),sF17(X0,X1,X2,X3),sF18(X0,X3,X2)),
inference(forward_demodulation,[],[f71,f70]) ).
fof(f73,plain,
! [X2,X0,X1] : sF13(X0,X1,X2) = f(X0,X2,sF14(X1,X0),X2),
inference(forward_demodulation,[],[f62,f61]) ).
fof(f75,plain,
! [X0,X1] : true = f(zero,X0,zero,X1),
inference(forward_demodulation,[],[f52,f51]) ).
fof(f76,plain,
! [X0] : sF8(X0) = f(X0,sF9,s(X0),s(X0)),
inference(forward_demodulation,[],[f49,f48]) ).
fof(f77,plain,
! [X0,X1] : if(false,X0,X1) = X1,
inference(forward_demodulation,[],[f39,f38]) ).
fof(f78,plain,
! [X0,X1] : if(true,X0,X1) = X0,
inference(forward_demodulation,[],[f36,f35]) ).
fof(f79,plain,
! [X0,X1] : '<='(s(X0),s(X1)) = '<='(X0,X1),
inference(forward_demodulation,[],[f33,f32]) ).
fof(f80,plain,
! [X0] : '<='(s(X0),zero) = false,
inference(forward_demodulation,[],[f30,f29]) ).
fof(f81,plain,
! [X0] : '<='(zero,X0) = true,
inference(forward_demodulation,[],[f27,f26]) ).
fof(f82,plain,
! [X0,X1] : minus(s(X0),s(X1)) = minus(X0,X1),
inference(forward_demodulation,[],[f24,f23]) ).
fof(f83,plain,
! [X0] : minus(X0,zero) = X0,
inference(forward_demodulation,[],[f21,f20]) ).
fof(f84,plain,
! [X2,X3,X0,X1] : sF16(X0,X1,X2,X3) = if('<='(X0,X1),sF17(X0,X1,X2,X3),f(X0,X3,X2,X3)),
inference(forward_demodulation,[],[f72,f68]) ).
fof(f85,plain,
! [X2,X0,X1] : f(X0,X2,minus(X1,s(X0)),X2) = sF13(X0,X1,X2),
inference(forward_demodulation,[],[f73,f59]) ).
fof(f86,plain,
! [X0] : perfectp(s(X0)) = f(X0,sF9,s(X0),s(X0)),
inference(forward_demodulation,[],[f76,f44]) ).
fof(f87,plain,
! [X2,X3,X0,X1] : if('<='(X0,X1),f(s(X0),minus(X1,X0),X2,X3),f(X0,X3,X2,X3)) = sF16(X0,X1,X2,X3),
inference(forward_demodulation,[],[f84,f66]) ).
fof(f88,plain,
! [X2,X0,X1] : f(s(X0),zero,X1,X2) = f(X0,X2,minus(X1,s(X0)),X2),
inference(forward_demodulation,[],[f85,f57]) ).
fof(f89,plain,
! [X2,X3,X0,X1] : f(s(X0),s(X1),X2,X3) = if('<='(X0,X1),f(s(X0),minus(X1,X0),X2,X3),f(X0,X3,X2,X3)),
inference(forward_demodulation,[],[f87,f64]) ).
fof(f94,plain,
! [X0] : '<='(zero,X0) = '<='(sF9,s(X0)),
inference(superposition,[],[f79,f46]) ).
fof(f96,plain,
! [X0] : true = '<='(sF9,s(X0)),
inference(forward_demodulation,[],[f94,f81]) ).
fof(f97,plain,
true = '<='(sF9,sF9),
inference(superposition,[],[f96,f46]) ).
fof(f101,plain,
! [X0] : minus(X0,zero) = minus(s(X0),sF9),
inference(superposition,[],[f82,f46]) ).
fof(f102,plain,
! [X0] : minus(s(X0),sF9) = X0,
inference(forward_demodulation,[],[f101,f83]) ).
fof(f103,plain,
zero = minus(sF9,sF9),
inference(superposition,[],[f102,f46]) ).
fof(f107,plain,
! [X0] : true != f(X0,sF9,s(X0),s(X0)),
inference(superposition,[],[f18,f86]) ).
fof(f113,plain,
! [X0,X1] : f(sF9,zero,X0,X1) = f(zero,X1,minus(X0,sF9),X1),
inference(superposition,[],[f88,f46]) ).
fof(f114,plain,
! [X2,X0,X1] : f(s(X1),zero,s(X0),X2) = f(X1,X2,minus(X0,X1),X2),
inference(superposition,[],[f88,f82]) ).
fof(f117,plain,
! [X0] : f(sF9,zero,sF9,X0) = f(zero,X0,zero,X0),
inference(superposition,[],[f113,f103]) ).
fof(f118,plain,
! [X0] : true = f(sF9,zero,sF9,X0),
inference(forward_demodulation,[],[f117,f75]) ).
fof(f139,plain,
! [X2,X0,X1] : f(s(s(X1)),zero,s(s(X0)),X2) = f(s(X1),X2,minus(X0,X1),X2),
inference(superposition,[],[f114,f82]) ).
fof(f140,plain,
! [X0,X1] : f(s(sF9),zero,s(s(X0)),X1) = f(sF9,X1,X0,X1),
inference(superposition,[],[f114,f102]) ).
fof(f162,plain,
! [X2,X0,X1] : f(s(s(X0)),s(zero),X1,X2) = if(false,f(s(s(X0)),minus(zero,s(X0)),X1,X2),f(s(X0),X2,X1,X2)),
inference(superposition,[],[f89,f80]) ).
fof(f169,plain,
! [X2,X0,X1] : f(s(zero),s(X0),X1,X2) = if('<='(zero,X0),f(s(zero),X0,X1,X2),f(zero,X2,X1,X2)),
inference(superposition,[],[f89,f83]) ).
fof(f170,plain,
! [X2,X3,X0,X1] : f(s(s(X1)),s(s(X0)),X2,X3) = if('<='(s(X1),s(X0)),f(s(s(X1)),minus(X0,X1),X2,X3),f(s(X1),X3,X2,X3)),
inference(superposition,[],[f89,f82]) ).
fof(f171,plain,
! [X2,X0,X1] : f(s(sF9),s(s(X0)),X1,X2) = if('<='(sF9,s(X0)),f(s(sF9),X0,X1,X2),f(sF9,X2,X1,X2)),
inference(superposition,[],[f89,f102]) ).
fof(f172,plain,
! [X0,X1] : f(s(sF9),s(sF9),X0,X1) = if('<='(sF9,sF9),f(s(sF9),zero,X0,X1),f(sF9,X1,X0,X1)),
inference(superposition,[],[f89,f103]) ).
fof(f193,plain,
! [X0,X1] : f(s(sF9),s(sF9),X0,X1) = if(true,f(s(sF9),zero,X0,X1),f(sF9,X1,X0,X1)),
inference(forward_demodulation,[],[f172,f97]) ).
fof(f194,plain,
! [X2,X0,X1] : f(s(sF9),s(s(X0)),X1,X2) = if(true,f(s(sF9),X0,X1,X2),f(sF9,X2,X1,X2)),
inference(forward_demodulation,[],[f171,f96]) ).
fof(f195,plain,
! [X2,X3,X0,X1] : f(s(s(X1)),s(s(X0)),X2,X3) = if('<='(X1,X0),f(s(s(X1)),minus(X0,X1),X2,X3),f(s(X1),X3,X2,X3)),
inference(forward_demodulation,[],[f170,f79]) ).
fof(f196,plain,
! [X2,X0,X1] : f(sF9,s(X0),X1,X2) = if('<='(zero,X0),f(sF9,X0,X1,X2),f(zero,X2,X1,X2)),
inference(forward_demodulation,[],[f169,f46]) ).
fof(f203,plain,
! [X2,X0,X1] : f(s(s(X0)),s(zero),X1,X2) = f(s(X0),X2,X1,X2),
inference(forward_demodulation,[],[f162,f77]) ).
fof(f209,plain,
! [X0,X1] : f(s(sF9),s(sF9),X0,X1) = f(s(sF9),zero,X0,X1),
inference(forward_demodulation,[],[f193,f78]) ).
fof(f210,plain,
! [X2,X0,X1] : f(s(sF9),s(s(X0)),X1,X2) = f(s(sF9),X0,X1,X2),
inference(forward_demodulation,[],[f194,f78]) ).
fof(f211,plain,
! [X2,X0,X1] : f(sF9,s(X0),X1,X2) = if(true,f(sF9,X0,X1,X2),f(zero,X2,X1,X2)),
inference(forward_demodulation,[],[f196,f81]) ).
fof(f216,plain,
! [X2,X0,X1] : f(s(X0),X2,X1,X2) = f(s(s(X0)),sF9,X1,X2),
inference(forward_demodulation,[],[f203,f46]) ).
fof(f222,plain,
! [X2,X0,X1] : f(sF9,s(X0),X1,X2) = f(sF9,X0,X1,X2),
inference(forward_demodulation,[],[f211,f78]) ).
fof(f229,plain,
! [X0,X1] : f(sF9,zero,X0,X1) = f(sF9,sF9,X0,X1),
inference(superposition,[],[f222,f46]) ).
fof(f271,plain,
! [X0] : true != f(s(X0),s(s(s(X0))),s(s(s(X0))),s(s(s(X0)))),
inference(superposition,[],[f107,f216]) ).
fof(f288,plain,
! [X2,X0,X1] : f(s(s(s(X0))),s(s(zero)),X1,X2) = if(false,f(s(s(s(X0))),minus(zero,s(X0)),X1,X2),f(s(s(X0)),X2,X1,X2)),
inference(superposition,[],[f195,f80]) ).
fof(f295,plain,
! [X2,X3,X0,X1] : f(s(s(s(X1))),s(s(s(X0))),X2,X3) = if('<='(s(X1),s(X0)),f(s(s(s(X1))),minus(X0,X1),X2,X3),f(s(s(X1)),X3,X2,X3)),
inference(superposition,[],[f195,f82]) ).
fof(f296,plain,
! [X2,X0,X1] : f(s(s(sF9)),s(s(s(X0))),X1,X2) = if('<='(sF9,s(X0)),f(s(s(sF9)),X0,X1,X2),f(s(sF9),X2,X1,X2)),
inference(superposition,[],[f195,f102]) ).
fof(f297,plain,
! [X0,X1] : f(s(s(sF9)),s(s(sF9)),X0,X1) = if('<='(sF9,sF9),f(s(s(sF9)),zero,X0,X1),f(s(sF9),X1,X0,X1)),
inference(superposition,[],[f195,f103]) ).
fof(f314,plain,
! [X0,X1] : f(s(s(sF9)),s(s(sF9)),X0,X1) = if(true,f(s(s(sF9)),zero,X0,X1),f(s(sF9),X1,X0,X1)),
inference(forward_demodulation,[],[f297,f97]) ).
fof(f315,plain,
! [X2,X0,X1] : f(s(s(sF9)),s(s(s(X0))),X1,X2) = if(true,f(s(s(sF9)),X0,X1,X2),f(s(sF9),X2,X1,X2)),
inference(forward_demodulation,[],[f296,f96]) ).
fof(f316,plain,
! [X2,X3,X0,X1] : f(s(s(s(X1))),s(s(s(X0))),X2,X3) = if('<='(X1,X0),f(s(s(s(X1))),minus(X0,X1),X2,X3),f(s(s(X1)),X3,X2,X3)),
inference(forward_demodulation,[],[f295,f79]) ).
fof(f323,plain,
! [X2,X0,X1] : f(s(s(s(X0))),s(s(zero)),X1,X2) = f(s(s(X0)),X2,X1,X2),
inference(forward_demodulation,[],[f288,f77]) ).
fof(f326,plain,
! [X0,X1] : f(s(s(sF9)),s(s(sF9)),X0,X1) = f(s(s(sF9)),zero,X0,X1),
inference(forward_demodulation,[],[f314,f78]) ).
fof(f327,plain,
! [X2,X0,X1] : f(s(s(sF9)),s(s(s(X0))),X1,X2) = f(s(s(sF9)),X0,X1,X2),
inference(forward_demodulation,[],[f315,f78]) ).
fof(f332,plain,
! [X2,X0,X1] : f(s(s(X0)),X2,X1,X2) = f(s(s(s(X0))),s(sF9),X1,X2),
inference(forward_demodulation,[],[f323,f46]) ).
fof(f670,plain,
! [X0,X1] : f(s(sF9),X1,X0,X1) = f(s(s(sF9)),zero,s(s(s(X0))),X1),
inference(superposition,[],[f139,f102]) ).
fof(f2657,plain,
! [X2,X0,X1] : f(s(s(s(sF9))),s(s(s(s(X0)))),X1,X2) = if('<='(sF9,s(X0)),f(s(s(s(sF9))),X0,X1,X2),f(s(s(sF9)),X2,X1,X2)),
inference(superposition,[],[f316,f102]) ).
fof(f2702,plain,
! [X2,X0,X1] : f(s(s(s(sF9))),s(s(s(s(X0)))),X1,X2) = if(true,f(s(s(s(sF9))),X0,X1,X2),f(s(s(sF9)),X2,X1,X2)),
inference(forward_demodulation,[],[f2657,f96]) ).
fof(f2714,plain,
! [X2,X0,X1] : f(s(s(s(sF9))),s(s(s(s(X0)))),X1,X2) = f(s(s(s(sF9))),X0,X1,X2),
inference(forward_demodulation,[],[f2702,f78]) ).
fof(f2759,plain,
true != f(s(s(s(sF9))),s(sF9),s(s(s(s(s(sF9))))),s(s(s(s(s(sF9)))))),
inference(superposition,[],[f271,f2714]) ).
fof(f2774,plain,
true != f(s(s(sF9)),s(s(s(s(s(sF9))))),s(s(s(s(s(sF9))))),s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2759,f332]) ).
fof(f2776,plain,
true != f(s(s(sF9)),s(s(sF9)),s(s(s(s(s(sF9))))),s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2774,f327]) ).
fof(f2778,plain,
true != f(s(s(sF9)),zero,s(s(s(s(s(sF9))))),s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2776,f326]) ).
fof(f2779,plain,
true != f(s(sF9),s(s(s(s(s(sF9))))),s(s(sF9)),s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2778,f670]) ).
fof(f2780,plain,
true != f(s(sF9),s(s(s(sF9))),s(s(sF9)),s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2779,f210]) ).
fof(f2781,plain,
true != f(s(sF9),s(sF9),s(s(sF9)),s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2780,f210]) ).
fof(f2782,plain,
true != f(s(sF9),zero,s(s(sF9)),s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2781,f209]) ).
fof(f2783,plain,
true != f(sF9,s(s(s(s(s(sF9))))),sF9,s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2782,f140]) ).
fof(f2784,plain,
true != f(sF9,s(s(s(s(sF9)))),sF9,s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2783,f222]) ).
fof(f2785,plain,
true != f(sF9,s(s(s(sF9))),sF9,s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2784,f222]) ).
fof(f2786,plain,
true != f(sF9,s(s(sF9)),sF9,s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2785,f222]) ).
fof(f2787,plain,
true != f(sF9,s(sF9),sF9,s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2786,f222]) ).
fof(f2788,plain,
true != f(sF9,sF9,sF9,s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2787,f222]) ).
fof(f2789,plain,
true != f(sF9,zero,sF9,s(s(s(s(s(sF9)))))),
inference(forward_demodulation,[],[f2788,f229]) ).
fof(f2790,plain,
true != true,
inference(forward_demodulation,[],[f2789,f118]) ).
fof(f2791,plain,
$false,
inference(trivial_inequality_removal,[],[f2790]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN135-1.006 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n005.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:05:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.20/1.35 % (213428)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.20/1.35 % (213439)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4023877029:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.20/1.35 % (213438)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2632928152:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.20/1.35 % (213435)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3951944276:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.20/1.35 % (213437)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3439111932:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.20/1.35 % (213436)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1932266994:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.20/1.35 % (213434)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=1083658973:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.20/1.35 % (213433)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=1208179441:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.20/1.35 % (213436)Instruction limit reached!
% 3.20/1.35 % (213436)------------------------------
% 3.20/1.35 % (213436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.20/1.35 % (213436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/1.35 % (213436)CaDiCaL version: 2.1.3
% 3.20/1.35 % (213436)Termination reason: Instruction limit
% 3.20/1.35 % (213436)Termination phase: Saturation
% 3.20/1.35 % (213436)Time elapsed: 0.074 s
% 3.20/1.35 % (213436)Peak memory usage: 88 MB
% 3.20/1.35 % (213436)Instructions burned: 137 (million)
% 3.20/1.35 % (213437)First to succeed.
% 3.20/1.35 % (213437)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-213428"
% 3.20/1.35 % (213439)Also succeeded, but the first one will report.
% 3.20/1.35 % (213438)Instruction limit reached!
% 3.20/1.35 % (213438)------------------------------
% 3.20/1.35 % (213438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.20/1.35 % (213438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/1.35 % (213438)CaDiCaL version: 2.1.3
% 3.20/1.35 % (213438)Termination reason: Instruction limit
% 3.20/1.35 % (213438)Termination phase: Saturation
% 3.20/1.35 % (213438)Time elapsed: 0.142 s
% 3.20/1.35 % (213438)Peak memory usage: 89 MB
% 3.20/1.35 % (213438)Instructions burned: 258 (million)
% 3.20/1.35 % (213447)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2687193093:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.20/1.35 % (213448)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1782610838:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.20/1.35 % (213437)Refutation found. Thanks to Tanya!
% 3.20/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.20/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.13/1.54 % (213437)------------------------------
% 4.13/1.54 % (213437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.54 % (213437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.54 % (213437)CaDiCaL version: 2.1.3
% 4.13/1.54 % (213437)Termination reason: Refutation
% 4.13/1.54 % (213437)Time elapsed: 0.090 s
% 4.13/1.54 % (213437)Peak memory usage: 89 MB
% 4.13/1.54 % (213437)Instructions burned: 153 (million)
% 4.13/1.54 % (213437)------------------------------
% 4.13/1.54 % (213437)------------------------------
% 4.13/1.54 % (213428)Success in time 0.496 s
% 4.13/1.54 % Vampire exiting
%------------------------------------------------------------------------------