%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP167-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 10:13:09 AM UTC 2026
% Result : Unsatisfiable 20.05s 4.11s
% Output : Refutation 20.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 17
% Syntax : Number of formulae : 132 ( 132 unt; 3 def)
% Number of atoms : 132 ( 131 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 104 ( 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f17,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p19) ).
fof(f18,definition,
sF0 = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f19,plain,
least_upper_bound(a,identity) = sF0,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF1 = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f21,plain,
greatest_lower_bound(a,identity) = sF1,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF2 = multiply(sF0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f23,plain,
multiply(sF0,sF1) = sF2,
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
a != sF2,
inference(definition_folding,[],[f17,f23,f21,f19]) ).
fof(f25,plain,
sF0 = least_upper_bound(identity,a),
inference(forward_demodulation,[],[f19,f6]) ).
fof(f26,plain,
sF1 = greatest_lower_bound(identity,a),
inference(forward_demodulation,[],[f21,f5]) ).
fof(f27,plain,
identity = greatest_lower_bound(identity,sF0),
inference(superposition,[],[f12,f25]) ).
fof(f28,plain,
identity = greatest_lower_bound(sF0,identity),
inference(forward_demodulation,[],[f27,f5]) ).
fof(f29,plain,
identity = least_upper_bound(identity,sF1),
inference(superposition,[],[f11,f26]) ).
fof(f32,plain,
identity = least_upper_bound(sF1,identity),
inference(forward_demodulation,[],[f29,f6]) ).
fof(f34,plain,
! [X0,X1] : least_upper_bound(X1,greatest_lower_bound(X0,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f36,plain,
! [X0,X1] : greatest_lower_bound(X1,least_upper_bound(X0,X1)) = X1,
inference(superposition,[],[f12,f6]) ).
fof(f37,plain,
a = greatest_lower_bound(a,sF0),
inference(superposition,[],[f36,f25]) ).
fof(f43,plain,
a = greatest_lower_bound(sF0,a),
inference(forward_demodulation,[],[f37,f5]) ).
fof(f44,plain,
! [X0] : multiply(sF0,greatest_lower_bound(sF1,X0)) = greatest_lower_bound(sF2,multiply(sF0,X0)),
inference(superposition,[],[f14,f23]) ).
fof(f46,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f14,f3]) ).
fof(f49,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity),
inference(superposition,[],[f14,f3]) ).
fof(f56,plain,
! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),greatest_lower_bound(X1,X0)),
inference(forward_demodulation,[],[f49,f5]) ).
fof(f65,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,inverse(X1)),X1) = greatest_lower_bound(multiply(X0,X1),identity),
inference(superposition,[],[f16,f3]) ).
fof(f76,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,inverse(X1)),X1) = greatest_lower_bound(identity,multiply(X0,X1)),
inference(forward_demodulation,[],[f65,f5]) ).
fof(f79,plain,
! [X0] : multiply(sF0,least_upper_bound(sF1,X0)) = least_upper_bound(sF2,multiply(sF0,X0)),
inference(superposition,[],[f13,f23]) ).
fof(f81,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f13,f3]) ).
fof(f84,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),identity),
inference(superposition,[],[f13,f3]) ).
fof(f93,plain,
! [X0,X1] : least_upper_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),least_upper_bound(X1,X0)),
inference(forward_demodulation,[],[f84,f6]) ).
fof(f98,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f1]) ).
fof(f118,plain,
a = least_upper_bound(a,sF1),
inference(superposition,[],[f34,f26]) ).
fof(f132,plain,
a = least_upper_bound(sF1,a),
inference(forward_demodulation,[],[f118,f6]) ).
fof(f135,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f136,plain,
! [X0] : multiply(sF0,multiply(sF1,X0)) = multiply(sF2,X0),
inference(superposition,[],[f4,f23]) ).
fof(f149,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f135,f1]) ).
fof(f178,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f149,f3]) ).
fof(f179,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f149,f149]) ).
fof(f180,plain,
sF1 = multiply(inverse(sF0),sF2),
inference(superposition,[],[f149,f23]) ).
fof(f193,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f178,f179]) ).
fof(f197,plain,
! [X0,X1] : multiply(X0,least_upper_bound(identity,X1)) = least_upper_bound(X0,multiply(X0,X1)),
inference(superposition,[],[f13,f193]) ).
fof(f199,plain,
! [X0,X1] : multiply(X0,greatest_lower_bound(identity,X1)) = greatest_lower_bound(X0,multiply(X0,X1)),
inference(superposition,[],[f14,f193]) ).
fof(f208,plain,
multiply(sF0,least_upper_bound(sF1,identity)) = least_upper_bound(sF2,sF0),
inference(superposition,[],[f79,f193]) ).
fof(f209,plain,
multiply(sF0,greatest_lower_bound(sF1,identity)) = greatest_lower_bound(sF2,sF0),
inference(superposition,[],[f44,f193]) ).
fof(f210,plain,
multiply(sF0,greatest_lower_bound(sF1,identity)) = greatest_lower_bound(sF0,sF2),
inference(forward_demodulation,[],[f209,f5]) ).
fof(f211,plain,
multiply(sF0,least_upper_bound(sF1,identity)) = least_upper_bound(sF0,sF2),
inference(forward_demodulation,[],[f208,f6]) ).
fof(f219,plain,
multiply(sF0,identity) = least_upper_bound(sF0,sF2),
inference(forward_demodulation,[],[f211,f32]) ).
fof(f220,plain,
sF0 = least_upper_bound(sF0,sF2),
inference(forward_demodulation,[],[f219,f193]) ).
fof(f221,plain,
sF2 = greatest_lower_bound(sF2,sF0),
inference(superposition,[],[f36,f220]) ).
fof(f223,plain,
sF2 = greatest_lower_bound(sF0,sF2),
inference(forward_demodulation,[],[f221,f5]) ).
fof(f224,plain,
sF2 = multiply(sF0,greatest_lower_bound(sF1,identity)),
inference(backward_demodulation,[],[f210,f223]) ).
fof(f238,plain,
multiply(inverse(sF0),sF2) = greatest_lower_bound(sF1,identity),
inference(superposition,[],[f149,f224]) ).
fof(f239,plain,
sF1 = greatest_lower_bound(sF1,identity),
inference(forward_demodulation,[],[f238,f180]) ).
fof(f272,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,X1),greatest_lower_bound(multiply(X0,X2),X3)) = greatest_lower_bound(multiply(X0,greatest_lower_bound(X1,X2)),X3),
inference(superposition,[],[f7,f14]) ).
fof(f299,plain,
! [X2,X3,X0,X1] : least_upper_bound(multiply(X0,X1),least_upper_bound(multiply(X0,X2),X3)) = least_upper_bound(multiply(X0,least_upper_bound(X1,X2)),X3),
inference(superposition,[],[f8,f13]) ).
fof(f476,plain,
! [X0] : greatest_lower_bound(identity,inverse(X0)) = multiply(inverse(X0),greatest_lower_bound(identity,X0)),
inference(superposition,[],[f56,f193]) ).
fof(f773,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f3,f179]) ).
fof(f774,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f149,f179]) ).
fof(f845,plain,
multiply(sF0,identity) = multiply(sF2,inverse(sF1)),
inference(superposition,[],[f136,f773]) ).
fof(f846,plain,
sF0 = multiply(sF2,inverse(sF1)),
inference(forward_demodulation,[],[f845,f193]) ).
fof(f958,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = multiply(inverse(X0),greatest_lower_bound(X1,X0)),
inference(superposition,[],[f56,f46]) ).
fof(f1079,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = multiply(inverse(X0),least_upper_bound(X1,X0)),
inference(superposition,[],[f93,f81]) ).
fof(f1775,plain,
multiply(inverse(a),sF1) = greatest_lower_bound(identity,inverse(a)),
inference(superposition,[],[f476,f26]) ).
fof(f1862,plain,
greatest_lower_bound(identity,multiply(identity,a)) = multiply(multiply(inverse(a),sF1),a),
inference(superposition,[],[f76,f1775]) ).
fof(f1873,plain,
greatest_lower_bound(identity,multiply(identity,a)) = multiply(inverse(a),multiply(sF1,a)),
inference(forward_demodulation,[],[f1862,f4]) ).
fof(f1878,plain,
multiply(inverse(a),multiply(sF1,a)) = multiply(identity,greatest_lower_bound(identity,a)),
inference(forward_demodulation,[],[f1873,f199]) ).
fof(f1883,plain,
greatest_lower_bound(identity,a) = multiply(inverse(a),multiply(sF1,a)),
inference(forward_demodulation,[],[f1878,f1]) ).
fof(f1885,plain,
sF1 = multiply(inverse(a),multiply(sF1,a)),
inference(forward_demodulation,[],[f1883,f26]) ).
fof(f1886,plain,
multiply(sF1,a) = multiply(a,sF1),
inference(superposition,[],[f774,f1885]) ).
fof(f1970,plain,
least_upper_bound(sF1,multiply(sF1,a)) = multiply(least_upper_bound(identity,a),sF1),
inference(superposition,[],[f98,f1886]) ).
fof(f1976,plain,
multiply(sF0,sF1) = least_upper_bound(sF1,multiply(sF1,a)),
inference(forward_demodulation,[],[f1970,f25]) ).
fof(f1986,plain,
multiply(sF0,sF1) = multiply(sF1,least_upper_bound(identity,a)),
inference(forward_demodulation,[],[f1976,f197]) ).
fof(f1993,plain,
multiply(sF0,sF1) = multiply(sF1,sF0),
inference(forward_demodulation,[],[f1986,f25]) ).
fof(f1997,plain,
sF2 = multiply(sF1,sF0),
inference(forward_demodulation,[],[f1993,f23]) ).
fof(f2001,plain,
! [X0] : multiply(sF2,X0) = multiply(sF1,multiply(sF0,X0)),
inference(superposition,[],[f4,f1997]) ).
fof(f2039,plain,
multiply(sF1,identity) = multiply(sF2,inverse(sF0)),
inference(superposition,[],[f2001,f773]) ).
fof(f2066,plain,
sF1 = multiply(sF2,inverse(sF0)),
inference(forward_demodulation,[],[f2039,f193]) ).
fof(f2479,plain,
inverse(sF0) = multiply(inverse(sF2),sF1),
inference(superposition,[],[f149,f2066]) ).
fof(f2503,plain,
! [X0] : multiply(inverse(sF2),least_upper_bound(sF1,X0)) = least_upper_bound(inverse(sF0),multiply(inverse(sF2),X0)),
inference(superposition,[],[f13,f2479]) ).
fof(f2516,plain,
multiply(inverse(sF2),greatest_lower_bound(identity,sF1)) = greatest_lower_bound(inverse(sF2),inverse(sF0)),
inference(superposition,[],[f199,f2479]) ).
fof(f2517,plain,
multiply(inverse(sF2),greatest_lower_bound(identity,sF1)) = greatest_lower_bound(inverse(sF0),inverse(sF2)),
inference(forward_demodulation,[],[f2516,f5]) ).
fof(f2530,plain,
greatest_lower_bound(inverse(sF0),inverse(sF2)) = multiply(inverse(sF2),greatest_lower_bound(sF1,identity)),
inference(forward_demodulation,[],[f2517,f5]) ).
fof(f2535,plain,
multiply(inverse(sF2),sF1) = greatest_lower_bound(inverse(sF0),inverse(sF2)),
inference(forward_demodulation,[],[f2530,f239]) ).
fof(f2538,plain,
inverse(sF0) = greatest_lower_bound(inverse(sF0),inverse(sF2)),
inference(forward_demodulation,[],[f2535,f2479]) ).
fof(f2583,plain,
inverse(sF2) = least_upper_bound(inverse(sF2),inverse(sF0)),
inference(superposition,[],[f34,f2538]) ).
fof(f2591,plain,
inverse(sF2) = least_upper_bound(inverse(sF0),inverse(sF2)),
inference(forward_demodulation,[],[f2583,f6]) ).
fof(f3143,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,greatest_lower_bound(X3,X2)),multiply(X1,X2)) = greatest_lower_bound(multiply(X0,X3),multiply(greatest_lower_bound(X0,X1),X2)),
inference(superposition,[],[f272,f16]) ).
fof(f3286,plain,
! [X0,X1] : greatest_lower_bound(multiply(X0,identity),multiply(greatest_lower_bound(X0,X1),a)) = greatest_lower_bound(multiply(X0,sF1),multiply(X1,a)),
inference(superposition,[],[f3143,f26]) ).
fof(f3490,plain,
! [X0,X1] : greatest_lower_bound(multiply(X0,sF1),multiply(X1,a)) = greatest_lower_bound(X0,multiply(greatest_lower_bound(X0,X1),a)),
inference(forward_demodulation,[],[f3286,f193]) ).
fof(f4546,plain,
multiply(inverse(sF2),sF0) = inverse(sF1),
inference(superposition,[],[f149,f846]) ).
fof(f4583,plain,
! [X0] : multiply(inverse(sF2),greatest_lower_bound(sF0,X0)) = greatest_lower_bound(inverse(sF1),multiply(inverse(sF2),X0)),
inference(superposition,[],[f14,f4546]) ).
fof(f4595,plain,
multiply(inverse(sF2),greatest_lower_bound(identity,sF0)) = greatest_lower_bound(inverse(sF2),inverse(sF1)),
inference(superposition,[],[f199,f4546]) ).
fof(f4602,plain,
multiply(inverse(sF2),greatest_lower_bound(identity,sF0)) = greatest_lower_bound(inverse(sF1),inverse(sF2)),
inference(forward_demodulation,[],[f4595,f5]) ).
fof(f4617,plain,
greatest_lower_bound(inverse(sF1),inverse(sF2)) = multiply(inverse(sF2),greatest_lower_bound(sF0,identity)),
inference(forward_demodulation,[],[f4602,f5]) ).
fof(f4623,plain,
multiply(inverse(sF2),identity) = greatest_lower_bound(inverse(sF1),inverse(sF2)),
inference(forward_demodulation,[],[f4617,f28]) ).
fof(f4627,plain,
inverse(sF2) = greatest_lower_bound(inverse(sF1),inverse(sF2)),
inference(forward_demodulation,[],[f4623,f193]) ).
fof(f4641,plain,
greatest_lower_bound(multiply(inverse(sF1),sF1),multiply(inverse(sF2),a)) = greatest_lower_bound(inverse(sF1),multiply(inverse(sF2),a)),
inference(superposition,[],[f3490,f4627]) ).
fof(f4642,plain,
greatest_lower_bound(multiply(inverse(sF1),sF1),multiply(inverse(sF2),a)) = multiply(inverse(sF2),greatest_lower_bound(sF0,a)),
inference(forward_demodulation,[],[f4641,f4583]) ).
fof(f4650,plain,
multiply(inverse(sF2),a) = greatest_lower_bound(multiply(inverse(sF1),sF1),multiply(inverse(sF2),a)),
inference(forward_demodulation,[],[f4642,f43]) ).
fof(f4655,plain,
multiply(inverse(sF2),a) = greatest_lower_bound(identity,multiply(inverse(sF2),a)),
inference(forward_demodulation,[],[f4650,f3]) ).
fof(f4659,plain,
multiply(inverse(sF2),a) = multiply(inverse(sF2),greatest_lower_bound(sF2,a)),
inference(forward_demodulation,[],[f4655,f46]) ).
fof(f4661,plain,
multiply(inverse(sF2),a) = multiply(inverse(sF2),greatest_lower_bound(a,sF2)),
inference(forward_demodulation,[],[f4659,f958]) ).
fof(f4706,plain,
greatest_lower_bound(a,sF2) = multiply(inverse(inverse(sF2)),multiply(inverse(sF2),a)),
inference(superposition,[],[f149,f4661]) ).
fof(f4719,plain,
a = greatest_lower_bound(a,sF2),
inference(forward_demodulation,[],[f4706,f149]) ).
fof(f4766,plain,
sF2 = least_upper_bound(sF2,a),
inference(superposition,[],[f34,f4719]) ).
fof(f4774,plain,
sF2 = least_upper_bound(a,sF2),
inference(forward_demodulation,[],[f4766,f6]) ).
fof(f5565,plain,
! [X2,X3,X0,X1] : least_upper_bound(multiply(X0,least_upper_bound(X3,X2)),multiply(X1,X2)) = least_upper_bound(multiply(X0,X3),multiply(least_upper_bound(X0,X1),X2)),
inference(superposition,[],[f299,f15]) ).
fof(f5741,plain,
! [X0,X1] : least_upper_bound(multiply(X0,identity),multiply(least_upper_bound(X0,X1),a)) = least_upper_bound(multiply(X0,sF0),multiply(X1,a)),
inference(superposition,[],[f5565,f25]) ).
fof(f6002,plain,
! [X0,X1] : least_upper_bound(multiply(X0,sF0),multiply(X1,a)) = least_upper_bound(X0,multiply(least_upper_bound(X0,X1),a)),
inference(forward_demodulation,[],[f5741,f193]) ).
fof(f6136,plain,
least_upper_bound(multiply(inverse(sF0),sF0),multiply(inverse(sF2),a)) = least_upper_bound(inverse(sF0),multiply(inverse(sF2),a)),
inference(superposition,[],[f6002,f2591]) ).
fof(f6217,plain,
least_upper_bound(multiply(inverse(sF0),sF0),multiply(inverse(sF2),a)) = multiply(inverse(sF2),least_upper_bound(sF1,a)),
inference(forward_demodulation,[],[f6136,f2503]) ).
fof(f6251,plain,
multiply(inverse(sF2),a) = least_upper_bound(multiply(inverse(sF0),sF0),multiply(inverse(sF2),a)),
inference(forward_demodulation,[],[f6217,f132]) ).
fof(f6276,plain,
multiply(inverse(sF2),a) = least_upper_bound(identity,multiply(inverse(sF2),a)),
inference(forward_demodulation,[],[f6251,f3]) ).
fof(f6285,plain,
multiply(inverse(sF2),a) = multiply(inverse(sF2),least_upper_bound(sF2,a)),
inference(forward_demodulation,[],[f6276,f81]) ).
fof(f6291,plain,
multiply(inverse(sF2),a) = multiply(inverse(sF2),least_upper_bound(a,sF2)),
inference(forward_demodulation,[],[f6285,f1079]) ).
fof(f6295,plain,
multiply(inverse(sF2),sF2) = multiply(inverse(sF2),a),
inference(forward_demodulation,[],[f6291,f4774]) ).
fof(f6297,plain,
identity = multiply(inverse(sF2),a),
inference(forward_demodulation,[],[f6295,f3]) ).
fof(f6305,plain,
a = multiply(sF2,identity),
inference(superposition,[],[f774,f6297]) ).
fof(f6364,plain,
a = sF2,
inference(forward_demodulation,[],[f6305,f193]) ).
fof(f6383,plain,
$false,
inference(forward_subsumption_resolution,[],[f6364,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP167-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 % Computer : n002.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Sun Sep 27 09:37:21 UTC 2026
% 0.21/0.49 % CPUTime :
% 0.21/0.49 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.54 Running first-order theorem proving
% 0.25/0.54 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
% 20.05/4.11 % (3289770)Detected a unit-equality problem, will run specialized UEQ schedule.
% 20.05/4.11 % (3289779)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3785290133:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 20.05/4.11 % (3289777)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=718962489:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 20.05/4.11 % (3289776)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=2923835629:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 20.05/4.11 % (3289775)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=1615426469:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 20.05/4.11 % (3289778)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4031210821:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 20.05/4.11 % (3289780)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4289930501:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 20.05/4.11 % (3289781)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=617550445:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 20.05/4.11 % (3289779)Instruction limit reached!
% 20.05/4.11 % (3289779)------------------------------
% 20.05/4.11 % (3289779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.05/4.11 % (3289779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.05/4.11 % (3289779)CaDiCaL version: 2.1.3
% 20.05/4.11 % (3289779)Termination reason: Instruction limit
% 20.05/4.11 % (3289779)Termination phase: Saturation
% 20.05/4.11 % (3289779)Time elapsed: 0.095 s
% 20.05/4.11 % (3289779)Peak memory usage: 89 MB
% 20.05/4.11 % (3289779)Instructions burned: 182 (million)
% 20.05/4.11 % (3289778)Instruction limit reached!
% 20.05/4.11 % (3289778)------------------------------
% 20.05/4.11 % (3289778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.05/4.11 % (3289778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.05/4.11 % (3289778)CaDiCaL version: 2.1.3
% 20.05/4.11 % (3289778)Termination reason: Instruction limit
% 20.05/4.11 % (3289778)Termination phase: Saturation
% 20.05/4.11 % (3289778)Time elapsed: 0.125 s
% 20.05/4.11 % (3289778)Peak memory usage: 88 MB
% 20.05/4.11 % (3289778)Instructions burned: 136 (million)
% 20.05/4.11 % (3289780)Instruction limit reached!
% 20.05/4.11 % (3289780)------------------------------
% 20.05/4.11 % (3289780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.05/4.11 % (3289780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.05/4.11 % (3289789)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4228469158:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 20.05/4.11 % (3289780)CaDiCaL version: 2.1.3
% 20.05/4.11 % (3289780)Termination reason: Instruction limit
% 20.05/4.11 % (3289780)Termination phase: Saturation
% 20.05/4.11 % (3289780)Time elapsed: 0.271 s
% 20.05/4.11 % (3289780)Peak memory usage: 90 MB
% 20.05/4.11 % (3289780)Instructions burned: 258 (million)
% 20.05/4.11 % (3289792)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=207484569:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 20.05/4.11 % (3289794)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3784905094:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 20.05/4.11 % (3289794)Instruction limit reached!
% 20.05/4.11 % (3289794)------------------------------
% 20.05/4.11 % (3289794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.05/4.11 % (3289794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.05/4.11 % (3289794)CaDiCaL version: 2.1.3
% 20.05/4.11 % (3289794)Termination reason: Instruction limit
% 20.05/4.11 % (3289794)Termination phase: Saturation
% 20.05/4.11 % (3289794)Time elapsed: 0.186 s
% 20.05/4.11 % (3289794)Peak memory usage: 90 MB
% 20.05/4.11 % (3289794)Instructions burned: 215 (million)
% 20.05/4.11 % (3289797)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=2886472076:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2989 on theBenchmark for (2989ds/317Mi)
% 20.05/4.11 % (3289781)Instruction limit reached!
% 20.05/4.11 % (3289781)------------------------------
% 20.05/4.11 % (3289781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.05/4.11 % (3289781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.05/4.11 % (3289781)CaDiCaL version: 2.1.3
% 20.05/4.11 % (3289781)Termination reason: Instruction limit
% 20.05/4.11 % (3289781)Termination phase: Saturation
% 20.05/4.11 % (3289781)Time elapsed: 1.087 s
% 20.05/4.11 % (3289781)Peak memory usage: 99 MB
% 20.05/4.11 % (3289781)Instructions burned: 1188 (million)
% 20.05/4.11 % (3289797)Instruction limit reached!
% 20.05/4.11 % (3289797)------------------------------
% 20.05/4.11 % (3289797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.05/4.11 % (3289797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.05/4.11 % (3289797)CaDiCaL version: 2.1.3
% 20.05/4.11 % (3289797)Termination reason: Instruction limit
% 20.05/4.11 % (3289797)Termination phase: Saturation
% 20.05/4.11 % (3289797)Time elapsed: 0.164 s
% 20.05/4.11 % (3289797)Peak memory usage: 90 MB
% 20.05/4.11 % (3289797)Instructions burned: 318 (million)
% 20.05/4.11 % (3289800)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=504608659:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2985 on theBenchmark for (2985ds/2836Mi)
% 20.05/4.11 % (3289799)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=1781956808:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 20.05/4.11 % (3289777)First to succeed.
% 20.05/4.11 % (3289777)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3289770"
% 20.05/4.11 % (3289789)Instruction limit reached!
% 20.05/4.11 % (3289789)------------------------------
% 20.05/4.11 % (3289789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.05/4.11 % (3289789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.05/4.11 % (3289789)CaDiCaL version: 2.1.3
% 20.05/4.11 % (3289789)Termination reason: Instruction limit
% 20.05/4.11 % (3289789)Termination phase: Saturation
% 20.05/4.11 % (3289789)Time elapsed: 1.873 s
% 20.05/4.11 % (3289789)Peak memory usage: 142 MB
% 20.05/4.11 % (3289789)Instructions burned: 2051 (million)
% 20.05/4.11 % (3289806)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=1002733851:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2975 on theBenchmark for (2975ds/14534Mi)
% 20.05/4.11 % (3289777)Refutation found. Thanks to Tanya!
% 20.05/4.11 % SZS status Unsatisfiable for theBenchmark
% 20.05/4.11 % SZS output start Proof for theBenchmark
% See solution above
% 20.80/4.34 % (3289777)------------------------------
% 20.80/4.34 % (3289777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.80/4.34 % (3289777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.80/4.34 % (3289777)CaDiCaL version: 2.1.3
% 20.80/4.34 % (3289777)Termination reason: Refutation
% 20.80/4.34 % (3289777)Time elapsed: 2.092 s
% 20.80/4.34 % (3289777)Peak memory usage: 140 MB
% 20.80/4.34 % (3289777)Instructions burned: 2020 (million)
% 20.80/4.34 % (3289777)------------------------------
% 20.80/4.34 % (3289777)------------------------------
% 20.80/4.34 % (3289770)Success in time 2.804 s
% 20.80/4.34 % Vampire exiting
%------------------------------------------------------------------------------