%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE118+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 : 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 11:40:23 AM UTC 2026
% Result : Theorem 10.82s 2.95s
% Output : Refutation 12.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 37
% Syntax : Number of formulae : 162 ( 158 unt; 21 def)
% Number of atoms : 166 ( 165 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 26 con; 0-2 aty)
% Number of variables : 96 ( 93 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f14,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f21,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
fof(f25,axiom,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_box) ).
fof(f27,conjecture,
! [X0,X1] :
( addition(X0,X1) = X1
=> ! [X2] : addition(forward_box(X0,domain(X2)),forward_box(X1,domain(X2))) = forward_box(X0,domain(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,X1) = X1
=> ! [X2] : addition(forward_box(X0,domain(X2)),forward_box(X1,domain(X2))) = forward_box(X0,domain(X2)) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1] :
( ? [X2] : forward_box(X0,domain(X2)) != addition(forward_box(X0,domain(X2)),forward_box(X1,domain(X2)))
& addition(X0,X1) = X1 ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
( forward_box(sK0,domain(sK2)) != addition(forward_box(sK0,domain(sK2)),forward_box(sK1,domain(sK2)))
& sK1 = addition(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f42,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f43,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(cnf_transformation,[],[f14]) ).
fof(f44,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f50,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f54,plain,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(cnf_transformation,[],[f25]) ).
fof(f56,plain,
sK1 = addition(sK0,sK1),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
forward_box(sK0,domain(sK2)) != addition(forward_box(sK0,domain(sK2)),forward_box(sK1,domain(sK2))),
inference(cnf_transformation,[],[f30]) ).
fof(f58,plain,
! [X0] : c(X0) = antidomain(antidomain(antidomain(X0))),
inference(definition_unfolding,[],[f50,f45]) ).
fof(f62,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f52,f45,f45]) ).
fof(f63,plain,
! [X0,X1] : forward_box(X0,X1) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(antidomain(antidomain(antidomain(X1))))))))))),
inference(definition_unfolding,[],[f54,f58,f62,f58]) ).
fof(f64,plain,
antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK2))))))))))))) != addition(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK2))))))))))))),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK2)))))))))))))),
inference(definition_unfolding,[],[f57,f63,f45,f63,f45,f63,f45]) ).
fof(f65,definition,
sF3 = antidomain(sK2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f66,plain,
antidomain(sK2) = sF3,
inference(reorient_equations,[],[f65]) ).
fof(f67,definition,
sF4 = antidomain(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f68,plain,
antidomain(sF3) = sF4,
inference(reorient_equations,[],[f67]) ).
fof(f69,definition,
sF5 = antidomain(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f70,plain,
antidomain(sF4) = sF5,
inference(reorient_equations,[],[f69]) ).
fof(f71,definition,
sF6 = antidomain(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f72,plain,
antidomain(sF5) = sF6,
inference(reorient_equations,[],[f71]) ).
fof(f73,definition,
sF7 = antidomain(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f74,plain,
antidomain(sF6) = sF7,
inference(reorient_equations,[],[f73]) ).
fof(f75,definition,
sF8 = antidomain(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f76,plain,
antidomain(sF7) = sF8,
inference(reorient_equations,[],[f75]) ).
fof(f77,definition,
sF9 = antidomain(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f78,plain,
antidomain(sF8) = sF9,
inference(reorient_equations,[],[f77]) ).
fof(f79,definition,
sF10 = multiplication(sK0,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f80,plain,
multiplication(sK0,sF9) = sF10,
inference(reorient_equations,[],[f79]) ).
fof(f81,definition,
sF11 = antidomain(sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f82,plain,
antidomain(sF10) = sF11,
inference(reorient_equations,[],[f81]) ).
fof(f83,definition,
sF12 = antidomain(sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f84,plain,
antidomain(sF11) = sF12,
inference(reorient_equations,[],[f83]) ).
fof(f85,definition,
sF13 = antidomain(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f86,plain,
antidomain(sF12) = sF13,
inference(reorient_equations,[],[f85]) ).
fof(f87,definition,
sF14 = antidomain(sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f88,plain,
antidomain(sF13) = sF14,
inference(reorient_equations,[],[f87]) ).
fof(f89,definition,
sF15 = antidomain(sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f90,plain,
antidomain(sF14) = sF15,
inference(reorient_equations,[],[f89]) ).
fof(f91,definition,
sF16 = multiplication(sK1,sF9),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f92,plain,
multiplication(sK1,sF9) = sF16,
inference(reorient_equations,[],[f91]) ).
fof(f93,definition,
sF17 = antidomain(sF16),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f94,plain,
antidomain(sF16) = sF17,
inference(reorient_equations,[],[f93]) ).
fof(f95,definition,
sF18 = antidomain(sF17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f96,plain,
antidomain(sF17) = sF18,
inference(reorient_equations,[],[f95]) ).
fof(f97,definition,
sF19 = antidomain(sF18),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f98,plain,
antidomain(sF18) = sF19,
inference(reorient_equations,[],[f97]) ).
fof(f99,definition,
sF20 = antidomain(sF19),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f100,plain,
antidomain(sF19) = sF20,
inference(reorient_equations,[],[f99]) ).
fof(f101,definition,
sF21 = antidomain(sF20),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f102,plain,
antidomain(sF20) = sF21,
inference(reorient_equations,[],[f101]) ).
fof(f103,definition,
sF22 = addition(sF15,sF21),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f104,plain,
addition(sF15,sF21) = sF22,
inference(reorient_equations,[],[f103]) ).
fof(f105,plain,
sF15 != sF22,
inference(definition_folding,[],[f64,f104,f102,f100,f98,f96,f94,f92,f78,f76,f74,f72,f70,f68,f66,f90,f88,f86,f84,f82,f80,f78,f76,f74,f72,f70,f68,f66,f90,f88,f86,f84,f82,f80,f78,f76,f74,f72,f70,f68,f66]) ).
fof(f106,definition,
sF23 = addition(sK0,sK1),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f107,plain,
addition(sK0,sK1) = sF23,
inference(reorient_equations,[],[f106]) ).
fof(f108,plain,
sK1 = sF23,
inference(definition_folding,[],[f56,f107]) ).
fof(f109,plain,
sK1 = addition(sK0,sK1),
inference(forward_demodulation,[],[f107,f108]) ).
fof(f128,plain,
one = addition(antidomain(sF14),sF14),
inference(superposition,[],[f44,f88]) ).
fof(f133,plain,
one = addition(antidomain(sF20),sF20),
inference(superposition,[],[f44,f100]) ).
fof(f138,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(superposition,[],[f31,f44]) ).
fof(f139,plain,
one = addition(sF21,sF20),
inference(forward_demodulation,[],[f133,f102]) ).
fof(f143,plain,
one = addition(sF15,sF14),
inference(forward_demodulation,[],[f128,f90]) ).
fof(f174,plain,
! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0),
inference(superposition,[],[f39,f37]) ).
fof(f194,plain,
! [X0] : addition(sF15,addition(sF21,X0)) = addition(sF22,X0),
inference(superposition,[],[f32,f104]) ).
fof(f210,plain,
zero = multiplication(sF11,sF10),
inference(superposition,[],[f42,f82]) ).
fof(f220,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(superposition,[],[f39,f42]) ).
fof(f222,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(superposition,[],[f38,f42]) ).
fof(f224,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[],[f222,f33]) ).
fof(f225,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,antidomain(X1)),X1),
inference(forward_demodulation,[],[f220,f33]) ).
fof(f246,plain,
! [X0] : multiplication(one,X0) = multiplication(antidomain(antidomain(X0)),X0),
inference(superposition,[],[f225,f44]) ).
fof(f253,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(forward_demodulation,[],[f246,f37]) ).
fof(f299,plain,
zero = antidomain(one),
inference(superposition,[],[f42,f36]) ).
fof(f333,plain,
! [X2,X0,X1] : multiplication(antidomain(multiplication(X1,X2)),multiplication(X0,X2)) = multiplication(antidomain(multiplication(X1,X2)),multiplication(addition(X0,X1),X2)),
inference(superposition,[],[f224,f39]) ).
fof(f362,plain,
! [X0] : multiplication(antidomain(multiplication(sK1,X0)),multiplication(sK0,X0)) = multiplication(antidomain(multiplication(sK1,X0)),multiplication(sK1,X0)),
inference(superposition,[],[f333,f109]) ).
fof(f373,plain,
! [X0] : zero = multiplication(antidomain(multiplication(sK1,X0)),multiplication(sK0,X0)),
inference(forward_demodulation,[],[f362,f42]) ).
fof(f447,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f32,f34]) ).
fof(f481,plain,
! [X0,X1] : multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(antidomain(multiplication(X0,antidomain(antidomain(X1)))),multiplication(X0,antidomain(antidomain(X1)))),
inference(superposition,[],[f225,f43]) ).
fof(f487,plain,
! [X0,X1] : zero = multiplication(antidomain(multiplication(X0,X1)),multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[],[f481,f42]) ).
fof(f787,plain,
one = addition(sF15,one),
inference(superposition,[],[f447,f143]) ).
fof(f959,plain,
zero = multiplication(antidomain(multiplication(sK1,sF9)),sF10),
inference(superposition,[],[f373,f80]) ).
fof(f981,plain,
zero = multiplication(antidomain(sF16),sF10),
inference(forward_demodulation,[],[f959,f92]) ).
fof(f985,plain,
zero = multiplication(sF17,sF10),
inference(forward_demodulation,[],[f981,f94]) ).
fof(f990,plain,
! [X0] : multiplication(addition(X0,sF17),sF10) = addition(multiplication(X0,sF10),zero),
inference(superposition,[],[f39,f985]) ).
fof(f1006,plain,
! [X0] : multiplication(X0,sF10) = multiplication(addition(X0,sF17),sF10),
inference(forward_demodulation,[],[f990,f33]) ).
fof(f1039,plain,
one = addition(sF11,antidomain(sF11)),
inference(superposition,[],[f138,f82]) ).
fof(f1053,plain,
! [X0] : multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)) = multiplication(antidomain(antidomain(antidomain(X0))),one),
inference(superposition,[],[f224,f138]) ).
fof(f1055,plain,
! [X0] : antidomain(antidomain(antidomain(X0))) = multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)),
inference(forward_demodulation,[],[f1053,f36]) ).
fof(f1066,plain,
one = addition(sF11,sF12),
inference(forward_demodulation,[],[f1039,f84]) ).
fof(f1073,plain,
! [X0] : antidomain(X0) = antidomain(antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f1055,f253]) ).
fof(f1083,plain,
sF11 = antidomain(antidomain(sF11)),
inference(superposition,[],[f1073,f82]) ).
fof(f1085,plain,
sF13 = antidomain(antidomain(sF13)),
inference(superposition,[],[f1073,f86]) ).
fof(f1088,plain,
sF17 = antidomain(antidomain(sF17)),
inference(superposition,[],[f1073,f94]) ).
fof(f1089,plain,
sF18 = antidomain(antidomain(sF18)),
inference(superposition,[],[f1073,f96]) ).
fof(f1090,plain,
sF19 = antidomain(antidomain(sF19)),
inference(superposition,[],[f1073,f98]) ).
fof(f1109,plain,
sF19 = antidomain(sF20),
inference(forward_demodulation,[],[f1090,f100]) ).
fof(f1110,plain,
sF18 = antidomain(sF19),
inference(forward_demodulation,[],[f1089,f98]) ).
fof(f1111,plain,
sF17 = antidomain(sF18),
inference(forward_demodulation,[],[f1088,f96]) ).
fof(f1113,plain,
sF13 = antidomain(sF14),
inference(forward_demodulation,[],[f1085,f88]) ).
fof(f1115,plain,
sF11 = antidomain(sF12),
inference(forward_demodulation,[],[f1083,f84]) ).
fof(f1122,plain,
sF19 = sF21,
inference(forward_demodulation,[],[f1109,f102]) ).
fof(f1123,plain,
sF18 = sF20,
inference(forward_demodulation,[],[f1110,f100]) ).
fof(f1124,plain,
sF17 = sF19,
inference(forward_demodulation,[],[f1111,f98]) ).
fof(f1125,plain,
sF13 = sF15,
inference(forward_demodulation,[],[f1113,f90]) ).
fof(f1127,plain,
sF11 = sF13,
inference(forward_demodulation,[],[f1115,f86]) ).
fof(f1139,plain,
sF22 = addition(sF13,sF21),
inference(superposition,[],[f104,f1125]) ).
fof(f1140,plain,
sF22 = addition(sF13,sF19),
inference(forward_demodulation,[],[f1139,f1122]) ).
fof(f1144,plain,
sF22 = addition(sF13,sF17),
inference(forward_demodulation,[],[f1140,f1124]) ).
fof(f1146,plain,
sF22 = addition(sF11,sF17),
inference(forward_demodulation,[],[f1144,f1127]) ).
fof(f1179,plain,
sF22 = addition(sF11,sF22),
inference(superposition,[],[f447,f1146]) ).
fof(f1508,plain,
one = multiplication(antidomain(zero),one),
inference(superposition,[],[f253,f299]) ).
fof(f1512,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f1508,f36]) ).
fof(f1968,plain,
addition(sF15,one) = addition(sF22,sF20),
inference(superposition,[],[f194,f139]) ).
fof(f1993,plain,
addition(sF15,one) = addition(sF22,sF18),
inference(forward_demodulation,[],[f1968,f1123]) ).
fof(f2007,plain,
one = addition(sF22,sF18),
inference(forward_demodulation,[],[f1993,f787]) ).
fof(f2040,plain,
one = addition(sF22,one),
inference(superposition,[],[f447,f2007]) ).
fof(f7231,plain,
multiplication(sF11,sF10) = multiplication(sF22,sF10),
inference(superposition,[],[f1006,f1146]) ).
fof(f7265,plain,
zero = multiplication(sF22,sF10),
inference(forward_demodulation,[],[f7231,f210]) ).
fof(f7294,plain,
zero = multiplication(antidomain(zero),multiplication(sF22,antidomain(antidomain(sF10)))),
inference(superposition,[],[f487,f7265]) ).
fof(f7298,plain,
zero = multiplication(antidomain(zero),multiplication(sF22,antidomain(sF11))),
inference(forward_demodulation,[],[f7294,f82]) ).
fof(f7312,plain,
zero = multiplication(antidomain(zero),multiplication(sF22,sF12)),
inference(forward_demodulation,[],[f7298,f84]) ).
fof(f7317,plain,
zero = multiplication(one,multiplication(sF22,sF12)),
inference(forward_demodulation,[],[f7312,f1512]) ).
fof(f7321,plain,
zero = multiplication(sF22,sF12),
inference(forward_demodulation,[],[f7317,f37]) ).
fof(f7326,plain,
! [X0] : addition(multiplication(sF22,X0),zero) = multiplication(sF22,addition(X0,sF12)),
inference(superposition,[],[f38,f7321]) ).
fof(f7353,plain,
! [X0] : multiplication(sF22,X0) = multiplication(sF22,addition(X0,sF12)),
inference(forward_demodulation,[],[f7326,f33]) ).
fof(f7373,plain,
multiplication(sF22,one) = multiplication(sF22,sF11),
inference(superposition,[],[f7353,f1066]) ).
fof(f7400,plain,
sF22 = multiplication(sF22,sF11),
inference(forward_demodulation,[],[f7373,f36]) ).
fof(f7412,plain,
addition(sF22,sF11) = multiplication(addition(sF22,one),sF11),
inference(superposition,[],[f174,f7400]) ).
fof(f7424,plain,
multiplication(one,sF11) = addition(sF22,sF11),
inference(forward_demodulation,[],[f7412,f2040]) ).
fof(f7430,plain,
sF11 = addition(sF22,sF11),
inference(forward_demodulation,[],[f7424,f37]) ).
fof(f9579,plain,
sF11 = addition(sF11,sF22),
inference(superposition,[],[f31,f7430]) ).
fof(f9604,plain,
sF11 = sF22,
inference(forward_demodulation,[],[f9579,f1179]) ).
fof(f9616,plain,
sF11 != sF15,
inference(superposition,[],[f105,f9604]) ).
fof(f9631,plain,
sF11 != sF13,
inference(forward_demodulation,[],[f9616,f1125]) ).
fof(f9633,plain,
$false,
inference(forward_subsumption_resolution,[],[f9631,f1127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE118+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 % Computer : n004.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sun Sep 27 13:10:51 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.54 Running first-order theorem proving
% 0.27/0.54 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
% 10.82/2.95 % (3510478)Detected formulas, will run a generic FOF schedule.
% 10.82/2.95 % (3510500)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=2104395313:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.82/2.95 % (3510502)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=3196974210:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.82/2.95 % (3510503)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1054909505:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.82/2.95 % (3510501)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=672900335:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.82/2.95 % (3510504)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=85716872:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.82/2.95 % (3510505)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3500444838:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.82/2.95 % (3510506)dis-21_1_sil=8000:lcm=predicate:random_seed=2131840014: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)
% 10.82/2.95 % (3510506)Refutation not found, incomplete strategy
% 10.82/2.95 % (3510506)------------------------------
% 10.82/2.95 % (3510506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.82/2.95 % (3510506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.82/2.95 % (3510506)CaDiCaL version: 2.1.3
% 10.82/2.95 % (3510506)Termination reason: Refutation not found, incomplete strategy
% 10.82/2.95 % (3510506)Time elapsed: 0.003 s
% 10.82/2.95 % (3510506)Peak memory usage: 88 MB
% 10.82/2.95 % (3510506)Instructions burned: 1 (million)
% 10.82/2.95 % (3510503)Instruction limit reached!
% 10.82/2.95 % (3510503)------------------------------
% 10.82/2.95 % (3510503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.82/2.95 % (3510503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.82/2.95 % (3510503)CaDiCaL version: 2.1.3
% 10.82/2.95 % (3510503)Termination reason: Instruction limit
% 10.82/2.95 % (3510503)Termination phase: Saturation
% 10.82/2.95 % (3510503)Time elapsed: 0.094 s
% 10.82/2.95 % (3510503)Peak memory usage: 89 MB
% 10.82/2.95 % (3510503)Instructions burned: 110 (million)
% 10.82/2.95 % (3510504)Instruction limit reached!
% 10.82/2.95 % (3510504)------------------------------
% 10.82/2.95 % (3510504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.82/2.95 % (3510504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.82/2.95 % (3510504)CaDiCaL version: 2.1.3
% 10.82/2.95 % (3510504)Termination reason: Instruction limit
% 10.82/2.95 % (3510504)Termination phase: Saturation
% 10.82/2.95 % (3510504)Time elapsed: 0.107 s
% 10.82/2.95 % (3510504)Peak memory usage: 88 MB
% 10.82/2.95 % (3510504)Instructions burned: 120 (million)
% 10.82/2.95 % (3510505)Instruction limit reached!
% 10.82/2.95 % (3510505)------------------------------
% 10.82/2.95 % (3510505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.82/2.95 % (3510505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.82/2.95 % (3510505)CaDiCaL version: 2.1.3
% 10.82/2.95 % (3510505)Termination reason: Instruction limit
% 10.82/2.95 % (3510505)Termination phase: Saturation
% 10.82/2.95 % (3510505)Time elapsed: 0.136 s
% 10.82/2.95 % (3510505)Peak memory usage: 89 MB
% 10.82/2.95 % (3510505)Instructions burned: 139 (million)
% 10.82/2.95 % (3510514)lrs+10_1_sil=8000:sp=occurrence:random_seed=4067001103:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 10.82/2.95 % (3510506)------------------------------
% 10.82/2.95 % (3510506)------------------------------
% 10.82/2.95 % (3510515)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1386325521:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 10.82/2.95 % (3510516)lrs+1011_1_sil=32000:sp=occurrence:random_seed=26508807:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 10.82/2.95 % (3510515)Instruction limit reached!
% 10.82/2.95 % (3510515)------------------------------
% 10.82/2.95 % (3510515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.82/2.95 % (3510515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.82/2.95 % (3510515)CaDiCaL version: 2.1.3
% 10.82/2.95 % (3510515)Termination reason: Instruction limit
% 10.82/2.95 % (3510515)Termination phase: Saturation
% 10.82/2.95 % (3510515)Time elapsed: 0.147 s
% 10.82/2.95 % (3510515)Peak memory usage: 89 MB
% 10.82/2.95 % (3510515)Instructions burned: 158 (million)
% 10.82/2.95 % (3510514)Instruction limit reached!
% 10.82/2.95 % (3510514)------------------------------
% 10.82/2.95 % (3510514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.82/2.95 % (3510514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.82/2.95 % (3510514)CaDiCaL version: 2.1.3
% 10.82/2.95 % (3510514)Termination reason: Instruction limit
% 10.82/2.95 % (3510514)Termination phase: Saturation
% 10.82/2.95 % (3510514)Time elapsed: 0.275 s
% 10.82/2.95 % (3510514)Peak memory usage: 92 MB
% 10.82/2.95 % (3510514)Instructions burned: 285 (million)
% 10.82/2.95 % (3510519)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=3700312829:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 10.82/2.95 % (3510516)Instruction limit reached!
% 10.82/2.95 % (3510516)------------------------------
% 10.82/2.95 % (3510516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.82/2.95 % (3510516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.82/2.95 % (3510516)CaDiCaL version: 2.1.3
% 10.82/2.95 % (3510516)Termination reason: Instruction limit
% 10.82/2.95 % (3510516)Termination phase: Saturation
% 10.82/2.95 % (3510516)Time elapsed: 0.317 s
% 10.82/2.95 % (3510516)Peak memory usage: 92 MB
% 10.82/2.95 % (3510516)Instructions burned: 325 (million)
% 10.82/2.95 % (3510521)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2749064569:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 10.82/2.95 % (3510522)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=475038239:i=2350_2990 on theBenchmark for (2990ds/2350Mi)
% 10.82/2.95 % (3510519)Instruction limit reached!
% 10.82/2.95 % (3510519)------------------------------
% 10.82/2.95 % (3510519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.82/2.95 % (3510519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.82/2.95 % (3510519)CaDiCaL version: 2.1.3
% 10.82/2.95 % (3510519)Termination reason: Instruction limit
% 10.82/2.95 % (3510519)Termination phase: Saturation
% 10.82/2.95 % (3510519)Time elapsed: 0.239 s
% 10.82/2.95 % (3510519)Peak memory usage: 91 MB
% 10.82/2.95 % (3510519)Instructions burned: 248 (million)
% 10.82/2.95 % (3510524)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2386752263:cts=off:i=113:fsr=off:ss=included:sgt=4_2989 on theBenchmark for (2989ds/113Mi)
% 10.82/2.95 % (3510500)First to succeed.
% 10.82/2.95 % (3510500)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3510478"
% 10.82/2.95 % (3510521)Instruction limit reached!
% 10.82/2.95 % (3510521)------------------------------
% 10.82/2.95 % (3510521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.82/2.95 % (3510521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.82/2.95 % (3510521)CaDiCaL version: 2.1.3
% 10.82/2.95 % (3510521)Termination reason: Instruction limit
% 10.82/2.95 % (3510521)Termination phase: Saturation
% 10.82/2.95 % (3510521)Time elapsed: 0.249 s
% 10.82/2.95 % (3510521)Peak memory usage: 91 MB
% 10.82/2.95 % (3510521)Instructions burned: 295 (million)
% 10.82/2.95 % (3510524)Instruction limit reached!
% 10.82/2.95 % (3510524)------------------------------
% 10.82/2.95 % (3510524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.82/2.95 % (3510524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.82/2.95 % (3510524)CaDiCaL version: 2.1.3
% 10.82/2.95 % (3510524)Termination reason: Instruction limit
% 10.82/2.95 % (3510524)Termination phase: Saturation
% 10.82/2.95 % (3510524)Time elapsed: 0.110 s
% 10.82/2.95 % (3510524)Peak memory usage: 90 MB
% 10.82/2.95 % (3510524)Instructions burned: 113 (million)
% 10.82/2.95 % (3510527)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2928450028:i=127:av=off:fsr=off:sup=off_2987 on theBenchmark for (2987ds/127Mi)
% 10.82/2.95 % (3510527)Refutation not found, incomplete strategy
% 10.82/2.95 % (3510527)------------------------------
% 10.82/2.95 % (3510527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.82/2.95 % (3510527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.82/2.95 % (3510527)CaDiCaL version: 2.1.3
% 10.82/2.95 % (3510527)Termination reason: Refutation not found, incomplete strategy
% 10.82/2.95 % (3510527)Time elapsed: 0.002 s
% 10.82/2.95 % (3510527)Peak memory usage: 88 MB
% 10.82/2.95 % (3510527)Instructions burned: 1 (million)
% 10.82/2.95 % (3510500)Refutation found. Thanks to Tanya!
% 10.82/2.95 % SZS status Theorem for theBenchmark
% 10.82/2.95 % SZS output start Proof for theBenchmark
% See solution above
% 12.66/3.33 % (3510500)------------------------------
% 12.66/3.33 % (3510500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.66/3.33 % (3510500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.66/3.33 % (3510500)CaDiCaL version: 2.1.3
% 12.66/3.33 % (3510500)Termination reason: Refutation
% 12.66/3.33 % (3510500)Time elapsed: 1.152 s
% 12.66/3.33 % (3510500)Peak memory usage: 139 MB
% 12.66/3.33 % (3510500)Instructions burned: 1938 (million)
% 12.66/3.33 % (3510500)------------------------------
% 12.66/3.33 % (3510500)------------------------------
% 12.66/3.33 % (3510478)Success in time 1.635 s
% 12.66/3.33 % Vampire exiting
%------------------------------------------------------------------------------