%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP179-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 10:13:13 AM UTC 2026
% Result : Unsatisfiable 4.82s 1.74s
% Output : Refutation 6.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 20
% Syntax : Number of formulae : 159 ( 159 unt; 4 def)
% Number of atoms : 159 ( 158 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 149 ( 149 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f7,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
fof(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18_3) ).
fof(f21,negated_conjecture,
least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p18) ).
fof(f25,definition,
sF1 = inverse(a),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f26,plain,
inverse(a) = sF1,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF2 = least_upper_bound(sF1,identity),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f28,plain,
least_upper_bound(sF1,identity) = sF2,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF3 = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f30,plain,
greatest_lower_bound(a,identity) = sF3,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF4 = inverse(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f32,plain,
inverse(sF3) = sF4,
inference(reorient_equations,[],[f31]) ).
fof(f33,plain,
sF2 != sF4,
inference(definition_folding,[],[f21,f32,f30,f28,f26]) ).
fof(f35,plain,
sF3 = greatest_lower_bound(identity,a),
inference(forward_demodulation,[],[f30,f5]) ).
fof(f36,plain,
identity = least_upper_bound(identity,sF3),
inference(superposition,[],[f11,f35]) ).
fof(f37,plain,
identity = least_upper_bound(sF3,identity),
inference(forward_demodulation,[],[f36,f6]) ).
fof(f38,plain,
sF1 = greatest_lower_bound(sF1,sF2),
inference(superposition,[],[f12,f28]) ).
fof(f42,plain,
! [X0,X1] : greatest_lower_bound(X1,least_upper_bound(X0,X1)) = X1,
inference(superposition,[],[f12,f6]) ).
fof(f44,plain,
a = inverse(sF1),
inference(superposition,[],[f19,f26]) ).
fof(f45,plain,
sF3 = inverse(sF4),
inference(superposition,[],[f19,f32]) ).
fof(f47,plain,
! [X0,X1] : least_upper_bound(X1,greatest_lower_bound(X0,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f50,plain,
identity = multiply(sF1,a),
inference(superposition,[],[f3,f26]) ).
fof(f51,plain,
identity = multiply(sF4,sF3),
inference(superposition,[],[f3,f32]) ).
fof(f52,plain,
identity = greatest_lower_bound(identity,sF2),
inference(superposition,[],[f42,f28]) ).
fof(f58,plain,
a = least_upper_bound(a,sF3),
inference(superposition,[],[f47,f35]) ).
fof(f68,plain,
a = least_upper_bound(sF3,a),
inference(forward_demodulation,[],[f58,f6]) ).
fof(f69,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f13,f3]) ).
fof(f71,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),identity),
inference(superposition,[],[f13,f3]) ).
fof(f82,plain,
! [X0,X1] : least_upper_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),least_upper_bound(X1,X0)),
inference(forward_demodulation,[],[f71,f6]) ).
fof(f84,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f92,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f84,f1]) ).
fof(f99,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f92,f19]) ).
fof(f100,plain,
! [X0] : multiply(sF1,multiply(a,X0)) = X0,
inference(superposition,[],[f92,f26]) ).
fof(f102,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f92,f3]) ).
fof(f104,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f92,f4]) ).
fof(f111,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f102,f19]) ).
fof(f118,plain,
! [X0,X1] : multiply(X0,least_upper_bound(X1,identity)) = least_upper_bound(multiply(X0,X1),X0),
inference(superposition,[],[f13,f111]) ).
fof(f121,plain,
! [X0,X1] : multiply(X0,least_upper_bound(X1,identity)) = least_upper_bound(X0,multiply(X0,X1)),
inference(forward_demodulation,[],[f118,f6]) ).
fof(f123,plain,
! [X0,X1] : inverse(multiply(X1,inverse(X0))) = multiply(X0,inverse(X1)),
inference(superposition,[],[f20,f19]) ).
fof(f127,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[],[f20,f19]) ).
fof(f129,plain,
! [X0] : inverse(multiply(sF3,X0)) = multiply(inverse(X0),sF4),
inference(superposition,[],[f20,f32]) ).
fof(f132,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(inverse(X1)),inverse(multiply(X0,X1))),
inference(superposition,[],[f92,f20]) ).
fof(f133,plain,
! [X2,X0,X1] : multiply(inverse(X1),multiply(inverse(X0),X2)) = multiply(inverse(multiply(X0,X1)),X2),
inference(superposition,[],[f4,f20]) ).
fof(f136,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(multiply(X0,X1),inverse(X1))),
inference(forward_demodulation,[],[f132,f20]) ).
fof(f141,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f136,f123]) ).
fof(f148,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))),
inference(superposition,[],[f141,f141]) ).
fof(f161,plain,
! [X0,X1] : inverse(X1) = inverse(multiply(inverse(X0),multiply(X0,X1))),
inference(forward_demodulation,[],[f148,f20]) ).
fof(f169,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(forward_demodulation,[],[f161,f127]) ).
fof(f178,plain,
! [X0,X1] : multiply(X0,greatest_lower_bound(identity,X1)) = greatest_lower_bound(X0,multiply(X0,X1)),
inference(superposition,[],[f14,f111]) ).
fof(f182,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity),
inference(superposition,[],[f14,f3]) ).
fof(f200,plain,
! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),greatest_lower_bound(X1,X0)),
inference(forward_demodulation,[],[f182,f5]) ).
fof(f232,plain,
! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0)),
inference(superposition,[],[f15,f3]) ).
fof(f233,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f1]) ).
fof(f270,plain,
! [X0] : multiply(a,multiply(sF1,X0)) = X0,
inference(superposition,[],[f92,f44]) ).
fof(f273,plain,
! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)),
inference(superposition,[],[f16,f3]) ).
fof(f274,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f16,f1]) ).
fof(f312,plain,
! [X0] : greatest_lower_bound(identity,greatest_lower_bound(a,X0)) = greatest_lower_bound(sF3,X0),
inference(superposition,[],[f7,f35]) ).
fof(f332,plain,
! [X0] : multiply(sF3,multiply(sF4,X0)) = X0,
inference(superposition,[],[f99,f32]) ).
fof(f344,plain,
! [X2,X0,X1] : multiply(X1,least_upper_bound(X2,multiply(inverse(X1),X0))) = least_upper_bound(multiply(X1,X2),X0),
inference(superposition,[],[f13,f99]) ).
fof(f346,plain,
! [X2,X0,X1] : multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X0))) = greatest_lower_bound(multiply(X1,X2),X0),
inference(superposition,[],[f14,f99]) ).
fof(f371,plain,
! [X0] : least_upper_bound(sF1,least_upper_bound(identity,X0)) = least_upper_bound(sF2,X0),
inference(superposition,[],[f8,f28]) ).
fof(f552,plain,
! [X0] : multiply(greatest_lower_bound(identity,a),multiply(sF1,X0)) = greatest_lower_bound(multiply(sF1,X0),X0),
inference(superposition,[],[f274,f270]) ).
fof(f577,plain,
! [X0] : multiply(greatest_lower_bound(identity,a),multiply(sF1,X0)) = greatest_lower_bound(X0,multiply(sF1,X0)),
inference(forward_demodulation,[],[f552,f5]) ).
fof(f597,plain,
! [X0] : multiply(greatest_lower_bound(identity,a),multiply(sF1,X0)) = multiply(greatest_lower_bound(identity,sF1),X0),
inference(forward_demodulation,[],[f577,f274]) ).
fof(f607,plain,
! [X0] : multiply(greatest_lower_bound(identity,a),multiply(sF1,X0)) = multiply(greatest_lower_bound(sF1,identity),X0),
inference(forward_demodulation,[],[f597,f5]) ).
fof(f613,plain,
! [X0] : multiply(greatest_lower_bound(sF1,identity),X0) = multiply(sF3,multiply(sF1,X0)),
inference(forward_demodulation,[],[f607,f35]) ).
fof(f655,plain,
! [X0,X1] : inverse(greatest_lower_bound(inverse(X1),X0)) = multiply(X1,inverse(greatest_lower_bound(identity,multiply(X0,X1)))),
inference(superposition,[],[f141,f273]) ).
fof(f740,plain,
! [X0,X1] : inverse(least_upper_bound(inverse(X1),X0)) = multiply(X1,inverse(least_upper_bound(identity,multiply(X0,X1)))),
inference(superposition,[],[f141,f232]) ).
fof(f945,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(least_upper_bound(X1,X0),inverse(least_upper_bound(identity,multiply(inverse(X0),X1)))),
inference(superposition,[],[f141,f82]) ).
fof(f947,plain,
! [X0,X1] : multiply(least_upper_bound(X1,X0),inverse(least_upper_bound(identity,multiply(inverse(X0),X1)))) = X0,
inference(forward_demodulation,[],[f945,f19]) ).
fof(f1006,plain,
multiply(least_upper_bound(identity,sF1),a) = least_upper_bound(a,identity),
inference(superposition,[],[f233,f50]) ).
fof(f1027,plain,
least_upper_bound(identity,a) = multiply(least_upper_bound(identity,sF1),a),
inference(forward_demodulation,[],[f1006,f6]) ).
fof(f1043,plain,
least_upper_bound(identity,a) = multiply(least_upper_bound(sF1,identity),a),
inference(forward_demodulation,[],[f1027,f6]) ).
fof(f1054,plain,
least_upper_bound(identity,a) = multiply(sF2,a),
inference(forward_demodulation,[],[f1043,f28]) ).
fof(f1127,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(greatest_lower_bound(X1,X0),inverse(greatest_lower_bound(identity,multiply(inverse(X0),X1)))),
inference(superposition,[],[f141,f200]) ).
fof(f1131,plain,
! [X0,X1] : multiply(greatest_lower_bound(X1,X0),inverse(greatest_lower_bound(identity,multiply(inverse(X0),X1)))) = X0,
inference(forward_demodulation,[],[f1127,f19]) ).
fof(f1453,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(least_upper_bound(X0,X1),inverse(least_upper_bound(identity,multiply(inverse(X0),X1)))),
inference(superposition,[],[f141,f69]) ).
fof(f1466,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(least_upper_bound(identity,multiply(inverse(X0),X1)))) = X0,
inference(forward_demodulation,[],[f1453,f19]) ).
fof(f1704,plain,
! [X0,X1] : inverse(least_upper_bound(X1,X0)) = multiply(inverse(least_upper_bound(identity,multiply(inverse(X0),X1))),inverse(X0)),
inference(superposition,[],[f141,f947]) ).
fof(f1709,plain,
! [X0,X1] : inverse(least_upper_bound(X1,X0)) = inverse(multiply(X0,least_upper_bound(identity,multiply(inverse(X0),X1)))),
inference(forward_demodulation,[],[f1704,f20]) ).
fof(f1744,plain,
! [X0,X1] : inverse(least_upper_bound(X1,X0)) = inverse(least_upper_bound(multiply(X0,identity),X1)),
inference(forward_demodulation,[],[f1709,f344]) ).
fof(f1768,plain,
! [X0,X1] : inverse(least_upper_bound(X1,X0)) = inverse(least_upper_bound(X0,X1)),
inference(forward_demodulation,[],[f1744,f111]) ).
fof(f1819,plain,
! [X2,X0,X1] : multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X0),X1))),multiply(inverse(X0),multiply(greatest_lower_bound(X1,X0),X2))) = X2,
inference(superposition,[],[f104,f200]) ).
fof(f1945,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,greatest_lower_bound(identity,multiply(inverse(X0),X1)))),multiply(greatest_lower_bound(X1,X0),X2)) = X2,
inference(forward_demodulation,[],[f1819,f133]) ).
fof(f2008,plain,
! [X2,X0,X1] : multiply(inverse(greatest_lower_bound(multiply(X0,identity),X1)),multiply(greatest_lower_bound(X1,X0),X2)) = X2,
inference(forward_demodulation,[],[f1945,f346]) ).
fof(f2035,plain,
! [X2,X0,X1] : multiply(inverse(greatest_lower_bound(X0,X1)),multiply(greatest_lower_bound(X1,X0),X2)) = X2,
inference(forward_demodulation,[],[f2008,f111]) ).
fof(f2229,plain,
! [X2,X0,X1] : multiply(greatest_lower_bound(X2,X1),X0) = multiply(greatest_lower_bound(X1,X2),X0),
inference(superposition,[],[f99,f2035]) ).
fof(f2924,plain,
sF3 = multiply(a,inverse(least_upper_bound(identity,multiply(inverse(sF3),a)))),
inference(superposition,[],[f1466,f68]) ).
fof(f2929,plain,
sF3 = inverse(least_upper_bound(inverse(a),inverse(sF3))),
inference(forward_demodulation,[],[f2924,f740]) ).
fof(f2933,plain,
sF3 = inverse(least_upper_bound(inverse(sF3),inverse(a))),
inference(forward_demodulation,[],[f2929,f1768]) ).
fof(f2935,plain,
sF3 = inverse(least_upper_bound(inverse(sF3),sF1)),
inference(forward_demodulation,[],[f2933,f26]) ).
fof(f2936,plain,
sF3 = inverse(least_upper_bound(sF1,inverse(sF3))),
inference(forward_demodulation,[],[f2935,f1768]) ).
fof(f2937,plain,
sF3 = inverse(least_upper_bound(sF1,sF4)),
inference(forward_demodulation,[],[f2936,f32]) ).
fof(f2940,plain,
inverse(sF3) = least_upper_bound(sF1,sF4),
inference(superposition,[],[f19,f2937]) ).
fof(f2968,plain,
sF4 = least_upper_bound(sF1,sF4),
inference(forward_demodulation,[],[f2940,f32]) ).
fof(f3066,plain,
least_upper_bound(sF1,identity) = multiply(sF1,least_upper_bound(a,identity)),
inference(superposition,[],[f121,f50]) ).
fof(f3067,plain,
multiply(sF4,least_upper_bound(sF3,identity)) = least_upper_bound(sF4,identity),
inference(superposition,[],[f121,f51]) ).
fof(f3097,plain,
least_upper_bound(identity,sF4) = multiply(sF4,least_upper_bound(sF3,identity)),
inference(forward_demodulation,[],[f3067,f6]) ).
fof(f3098,plain,
least_upper_bound(sF1,identity) = multiply(sF1,least_upper_bound(identity,a)),
inference(forward_demodulation,[],[f3066,f6]) ).
fof(f3139,plain,
multiply(sF4,identity) = least_upper_bound(identity,sF4),
inference(forward_demodulation,[],[f3097,f37]) ).
fof(f3140,plain,
least_upper_bound(sF1,identity) = multiply(sF1,multiply(sF2,a)),
inference(forward_demodulation,[],[f3098,f1054]) ).
fof(f3169,plain,
sF4 = least_upper_bound(identity,sF4),
inference(forward_demodulation,[],[f3139,f111]) ).
fof(f3170,plain,
sF2 = multiply(sF1,multiply(sF2,a)),
inference(forward_demodulation,[],[f3140,f28]) ).
fof(f3184,plain,
least_upper_bound(sF1,sF4) = least_upper_bound(sF2,sF4),
inference(superposition,[],[f371,f3169]) ).
fof(f3197,plain,
sF4 = least_upper_bound(sF2,sF4),
inference(forward_demodulation,[],[f3184,f2968]) ).
fof(f3210,plain,
sF2 = multiply(sF4,inverse(least_upper_bound(identity,multiply(inverse(sF2),sF4)))),
inference(superposition,[],[f1466,f3197]) ).
fof(f3215,plain,
sF2 = inverse(least_upper_bound(inverse(sF4),inverse(sF2))),
inference(forward_demodulation,[],[f3210,f740]) ).
fof(f3219,plain,
sF2 = inverse(least_upper_bound(inverse(sF2),inverse(sF4))),
inference(forward_demodulation,[],[f3215,f1768]) ).
fof(f3221,plain,
sF2 = inverse(least_upper_bound(inverse(sF2),sF3)),
inference(forward_demodulation,[],[f3219,f45]) ).
fof(f3222,plain,
sF2 = inverse(least_upper_bound(sF3,inverse(sF2))),
inference(forward_demodulation,[],[f3221,f1768]) ).
fof(f3223,plain,
multiply(sF2,a) = multiply(a,sF2),
inference(superposition,[],[f270,f3170]) ).
fof(f3238,plain,
multiply(greatest_lower_bound(identity,sF1),multiply(sF2,a)) = greatest_lower_bound(multiply(sF2,a),sF2),
inference(superposition,[],[f274,f3170]) ).
fof(f3239,plain,
multiply(greatest_lower_bound(identity,sF1),multiply(sF2,a)) = greatest_lower_bound(sF2,multiply(sF2,a)),
inference(forward_demodulation,[],[f3238,f5]) ).
fof(f3258,plain,
multiply(greatest_lower_bound(identity,sF1),multiply(sF2,a)) = multiply(sF2,greatest_lower_bound(identity,a)),
inference(forward_demodulation,[],[f3239,f178]) ).
fof(f3268,plain,
multiply(greatest_lower_bound(identity,sF1),multiply(sF2,a)) = multiply(sF2,sF3),
inference(forward_demodulation,[],[f3258,f35]) ).
fof(f3277,plain,
multiply(sF2,sF3) = multiply(greatest_lower_bound(sF1,identity),multiply(sF2,a)),
inference(forward_demodulation,[],[f3268,f2229]) ).
fof(f3282,plain,
multiply(sF2,sF3) = multiply(sF3,multiply(sF1,multiply(sF2,a))),
inference(forward_demodulation,[],[f3277,f613]) ).
fof(f3286,plain,
multiply(sF2,sF3) = multiply(sF3,multiply(sF1,multiply(a,sF2))),
inference(forward_demodulation,[],[f3282,f3223]) ).
fof(f3287,plain,
multiply(sF2,sF3) = multiply(sF3,sF2),
inference(forward_demodulation,[],[f3286,f100]) ).
fof(f3300,plain,
inverse(sF3) = multiply(inverse(multiply(sF3,sF2)),sF2),
inference(superposition,[],[f169,f3287]) ).
fof(f3305,plain,
inverse(sF3) = multiply(multiply(inverse(sF2),sF4),sF2),
inference(forward_demodulation,[],[f3300,f129]) ).
fof(f3313,plain,
inverse(sF3) = multiply(inverse(sF2),multiply(sF4,sF2)),
inference(forward_demodulation,[],[f3305,f4]) ).
fof(f3316,plain,
sF4 = multiply(inverse(sF2),multiply(sF4,sF2)),
inference(forward_demodulation,[],[f3313,f32]) ).
fof(f3821,plain,
inverse(sF2) = least_upper_bound(sF3,inverse(sF2)),
inference(superposition,[],[f19,f3222]) ).
fof(f3875,plain,
sF3 = greatest_lower_bound(sF3,inverse(sF2)),
inference(superposition,[],[f12,f3821]) ).
fof(f4396,plain,
multiply(sF4,sF2) = multiply(sF2,sF4),
inference(superposition,[],[f99,f3316]) ).
fof(f4511,plain,
sF2 = multiply(sF3,multiply(sF2,sF4)),
inference(superposition,[],[f332,f4396]) ).
fof(f4558,plain,
inverse(sF3) = multiply(multiply(sF2,sF4),inverse(sF2)),
inference(superposition,[],[f141,f4511]) ).
fof(f4565,plain,
inverse(sF3) = multiply(sF2,multiply(sF4,inverse(sF2))),
inference(forward_demodulation,[],[f4558,f4]) ).
fof(f4575,plain,
sF4 = multiply(sF2,multiply(sF4,inverse(sF2))),
inference(forward_demodulation,[],[f4565,f32]) ).
fof(f5124,plain,
sF2 = multiply(sF1,inverse(greatest_lower_bound(identity,multiply(inverse(sF2),sF1)))),
inference(superposition,[],[f1131,f38]) ).
fof(f5131,plain,
sF2 = inverse(greatest_lower_bound(inverse(sF1),inverse(sF2))),
inference(forward_demodulation,[],[f5124,f655]) ).
fof(f5137,plain,
sF2 = inverse(greatest_lower_bound(a,inverse(sF2))),
inference(forward_demodulation,[],[f5131,f44]) ).
fof(f5141,plain,
inverse(sF2) = greatest_lower_bound(a,inverse(sF2)),
inference(superposition,[],[f19,f5137]) ).
fof(f5206,plain,
greatest_lower_bound(sF3,inverse(sF2)) = greatest_lower_bound(identity,inverse(sF2)),
inference(superposition,[],[f312,f5141]) ).
fof(f5229,plain,
sF3 = greatest_lower_bound(identity,inverse(sF2)),
inference(forward_demodulation,[],[f5206,f3875]) ).
fof(f5608,plain,
multiply(greatest_lower_bound(identity,sF2),multiply(sF4,inverse(sF2))) = greatest_lower_bound(multiply(sF4,inverse(sF2)),sF4),
inference(superposition,[],[f274,f4575]) ).
fof(f5611,plain,
multiply(greatest_lower_bound(identity,sF2),multiply(sF4,inverse(sF2))) = greatest_lower_bound(sF4,multiply(sF4,inverse(sF2))),
inference(forward_demodulation,[],[f5608,f5]) ).
fof(f5624,plain,
multiply(greatest_lower_bound(identity,sF2),multiply(sF4,inverse(sF2))) = multiply(sF4,greatest_lower_bound(identity,inverse(sF2))),
inference(forward_demodulation,[],[f5611,f178]) ).
fof(f5630,plain,
multiply(sF4,sF3) = multiply(greatest_lower_bound(identity,sF2),multiply(sF4,inverse(sF2))),
inference(forward_demodulation,[],[f5624,f5229]) ).
fof(f5636,plain,
multiply(sF4,sF3) = multiply(identity,multiply(sF4,inverse(sF2))),
inference(forward_demodulation,[],[f5630,f52]) ).
fof(f5640,plain,
multiply(sF4,sF3) = multiply(sF4,inverse(sF2)),
inference(forward_demodulation,[],[f5636,f1]) ).
fof(f5642,plain,
identity = multiply(sF4,inverse(sF2)),
inference(forward_demodulation,[],[f5640,f51]) ).
fof(f5643,plain,
sF4 = multiply(sF2,identity),
inference(backward_demodulation,[],[f4575,f5642]) ).
fof(f5657,plain,
sF2 = sF4,
inference(forward_demodulation,[],[f5643,f111]) ).
fof(f5662,plain,
$false,
inference(forward_subsumption_resolution,[],[f5657,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP179-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n026.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 09:38:41 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.82/1.74 % (2579253)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.82/1.74 % (2579260)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1052816283:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.82/1.74 % (2579262)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3352752062:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.82/1.74 % (2579263)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3102196208:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.82/1.74 % (2579261)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=603807378:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.82/1.74 % (2579258)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=256189174:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.82/1.74 % (2579259)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=1175716841:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.82/1.74 % (2579264)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1717675038:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.82/1.74 % (2579261)Instruction limit reached!
% 4.82/1.74 % (2579261)------------------------------
% 4.82/1.74 % (2579261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.74 % (2579261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.74 % (2579261)CaDiCaL version: 2.1.3
% 4.82/1.74 % (2579261)Termination reason: Instruction limit
% 4.82/1.74 % (2579261)Termination phase: Saturation
% 4.82/1.74 % (2579261)Time elapsed: 0.084 s
% 4.82/1.74 % (2579261)Peak memory usage: 89 MB
% 4.82/1.74 % (2579261)Instructions burned: 137 (million)
% 4.82/1.74 % (2579262)Instruction limit reached!
% 4.82/1.74 % (2579262)------------------------------
% 4.82/1.74 % (2579262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.74 % (2579262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.74 % (2579262)CaDiCaL version: 2.1.3
% 4.82/1.74 % (2579262)Termination reason: Instruction limit
% 4.82/1.74 % (2579262)Termination phase: Saturation
% 4.82/1.74 % (2579262)Time elapsed: 0.109 s
% 4.82/1.74 % (2579262)Peak memory usage: 89 MB
% 4.82/1.74 % (2579262)Instructions burned: 183 (million)
% 4.82/1.74 % (2579263)Instruction limit reached!
% 4.82/1.74 % (2579263)------------------------------
% 4.82/1.74 % (2579263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.74 % (2579263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.74 % (2579263)CaDiCaL version: 2.1.3
% 4.82/1.74 % (2579263)Termination reason: Instruction limit
% 4.82/1.74 % (2579263)Termination phase: Saturation
% 4.82/1.74 % (2579263)Time elapsed: 0.156 s
% 4.82/1.74 % (2579263)Peak memory usage: 90 MB
% 4.82/1.74 % (2579263)Instructions burned: 257 (million)
% 4.82/1.74 % (2579272)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1942188791:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.82/1.74 % (2579273)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2740947452:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 4.82/1.74 % (2579274)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=59177543:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 4.82/1.74 % (2579274)Instruction limit reached!
% 4.82/1.74 % (2579274)------------------------------
% 4.82/1.74 % (2579274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.74 % (2579274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.74 % (2579274)CaDiCaL version: 2.1.3
% 4.82/1.74 % (2579274)Termination reason: Instruction limit
% 4.82/1.74 % (2579274)Termination phase: Saturation
% 4.82/1.74 % (2579274)Time elapsed: 0.119 s
% 4.82/1.74 % (2579274)Peak memory usage: 92 MB
% 4.82/1.74 % (2579274)Instructions burned: 216 (million)
% 4.82/1.74 % (2579278)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=3517022854: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)
% 4.82/1.74 % (2579260)First to succeed.
% 4.82/1.74 % (2579260)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2579253"
% 4.82/1.74 % (2579264)Instruction limit reached!
% 4.82/1.74 % (2579264)------------------------------
% 4.82/1.74 % (2579264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.74 % (2579264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.74 % (2579264)CaDiCaL version: 2.1.3
% 4.82/1.74 % (2579264)Termination reason: Instruction limit
% 4.82/1.74 % (2579264)Termination phase: Saturation
% 4.82/1.74 % (2579264)Time elapsed: 0.643 s
% 4.82/1.74 % (2579264)Peak memory usage: 99 MB
% 4.82/1.74 % (2579264)Instructions burned: 1187 (million)
% 4.82/1.74 % (2579260)Refutation found. Thanks to Tanya!
% 4.82/1.74 % SZS status Unsatisfiable for theBenchmark
% 4.82/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 6.82/1.93 % (2579260)------------------------------
% 6.82/1.93 % (2579260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/1.93 % (2579260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.93 % (2579260)CaDiCaL version: 2.1.3
% 6.82/1.93 % (2579260)Termination reason: Refutation
% 6.82/1.93 % (2579260)Time elapsed: 0.614 s
% 6.82/1.93 % (2579260)Peak memory usage: 136 MB
% 6.82/1.93 % (2579260)Instructions burned: 1682 (million)
% 6.82/1.93 % (2579260)------------------------------
% 6.82/1.93 % (2579260)------------------------------
% 6.82/1.93 % (2579253)Success in time 0.876 s
% 6.82/1.93 % Vampire exiting
%------------------------------------------------------------------------------