%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 : Sun Sep 27 07:28:11 AM UTC 2026
% Result : Unsatisfiable 17.05s 2.68s
% Output : CNFRefutation 17.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 21
% Syntax : Number of formulae : 166 ( 166 unt; 0 def)
% Number of atoms : 166 ( 165 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 267 ( 9 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(symmetry_of_glb,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,VAR_1) = greatest_lower_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_glb) ).
cnf(c_4,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_glb]) ).
fof(symmetry_of_lub,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,VAR_1) = least_upper_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_lub) ).
cnf(c_5,plain,
least_upper_bound(A,B) = least_upper_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_lub]) ).
fof(associativity_of_glb,axiom,
! [VAR_0,VAR_1,VAR_2] : greatest_lower_bound(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(greatest_lower_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_glb) ).
cnf(c_6,plain,
greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_glb]) ).
cnf(c_7,plain,
greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_6]) ).
fof(associativity_of_lub,axiom,
! [VAR_0,VAR_1,VAR_2] : least_upper_bound(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(least_upper_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_lub) ).
cnf(c_8,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_lub]) ).
cnf(c_9,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_8]) ).
fof(idempotence_of_lub,axiom,
! [VAR_0] : least_upper_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_lub) ).
cnf(c_10,plain,
least_upper_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_lub]) ).
fof(idempotence_of_gld,axiom,
! [VAR_0] : greatest_lower_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_gld) ).
cnf(c_11,plain,
greatest_lower_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_gld]) ).
fof(lub_absorbtion,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,greatest_lower_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',lub_absorbtion) ).
cnf(c_12,plain,
least_upper_bound(A,greatest_lower_bound(A,B)) = A,
inference(clausify,[status(thm)],[lub_absorbtion]) ).
fof(glb_absorbtion,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,least_upper_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',glb_absorbtion) ).
cnf(c_13,plain,
greatest_lower_bound(A,least_upper_bound(A,B)) = A,
inference(clausify,[status(thm)],[glb_absorbtion]) ).
fof(monotony_lub1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_lub1) ).
cnf(c_14,plain,
multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_lub1]) ).
cnf(c_15,plain,
least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_14]) ).
fof(monotony_glb1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_glb1) ).
cnf(c_16,plain,
multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_glb1]) ).
cnf(c_17,plain,
greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_16]) ).
fof(monotony_lub2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(least_upper_bound(VAR_0,VAR_1),VAR_2) = least_upper_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_lub2) ).
cnf(c_18,plain,
multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_lub2]) ).
cnf(c_19,plain,
least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B),
inference(copy,[status(thm)],[c_18]) ).
fof(monotony_glb2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(greatest_lower_bound(VAR_0,VAR_1),VAR_2) = greatest_lower_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_glb2) ).
cnf(c_20,plain,
multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_glb2]) ).
cnf(c_21,plain,
greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B),
inference(copy,[status(thm)],[c_20]) ).
fof(lat4_2,axiom,
! [VAR_0] : inverse(inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',lat4_2) ).
cnf(c_23,plain,
inverse(inverse(A)) = A,
inference(clausify,[status(thm)],[lat4_2]) ).
fof(lat4_3,axiom,
! [VAR_0,VAR_1] : inverse(multiply(VAR_0,VAR_1)) = multiply(inverse(VAR_1),inverse(VAR_0)),
file('theBenchmark.p',lat4_3) ).
cnf(c_24,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(clausify,[status(thm)],[lat4_3]) ).
cnf(c_25,plain,
multiply(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(copy,[status(thm)],[c_24]) ).
fof(lat4_4,axiom,
! [VAR_0] : positive_part(VAR_0) = least_upper_bound(VAR_0,identity),
file('theBenchmark.p',lat4_4) ).
cnf(c_26,plain,
positive_part(A) = least_upper_bound(A,identity),
inference(clausify,[status(thm)],[lat4_4]) ).
fof(lat4_5,axiom,
! [VAR_0] : negative_part(VAR_0) = greatest_lower_bound(VAR_0,identity),
file('theBenchmark.p',lat4_5) ).
cnf(c_27,plain,
negative_part(A) = greatest_lower_bound(A,identity),
inference(clausify,[status(thm)],[lat4_5]) ).
fof(lat4_7,axiom,
! [VAR_0,VAR_1,VAR_2] : greatest_lower_bound(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(greatest_lower_bound(VAR_0,VAR_1),greatest_lower_bound(VAR_0,VAR_2)),
file('theBenchmark.p',lat4_7) ).
cnf(c_30,plain,
greatest_lower_bound(A,least_upper_bound(B,C)) = least_upper_bound(greatest_lower_bound(A,B),greatest_lower_bound(A,C)),
inference(clausify,[status(thm)],[lat4_7]) ).
cnf(c_31,plain,
least_upper_bound(greatest_lower_bound(A,B),greatest_lower_bound(A,C)) = greatest_lower_bound(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_30]) ).
fof(prove_lat4,axiom,
a != multiply(positive_part(a),negative_part(a)),
file('theBenchmark.p',prove_lat4) ).
cnf(c_32,plain,
a != multiply(positive_part(a),negative_part(a)),
inference(clausify,[status(thm)],[prove_lat4]) ).
cnf(c_5226,plain,
a != multiply(least_upper_bound(a,identity),negative_part(a)),
inference(paramod,[status(thm)],[c_26,c_32]) ).
cnf(c_5227,plain,
a != multiply(least_upper_bound(identity,a),negative_part(a)),
inference(paramod,[status(thm)],[c_5,c_5226]) ).
cnf(c_5228,plain,
a != multiply(least_upper_bound(identity,a),greatest_lower_bound(a,identity)),
inference(paramod,[status(thm)],[c_27,c_5227]) ).
cnf(c_5229,plain,
a != multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)),
inference(paramod,[status(thm)],[c_4,c_5228]) ).
cnf(c_33,plain,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(copy,[status(thm)],[c_5229]) ).
cnf(c_5230,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_5231,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_5230]) ).
cnf(c_34,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_5231]) ).
cnf(c_5232,plain,
least_upper_bound(least_upper_bound(A,B),B) = least_upper_bound(A,B),
inference(paramod,[status(thm)],[c_10,c_9]) ).
cnf(c_41,plain,
least_upper_bound(A,least_upper_bound(B,A)) = least_upper_bound(B,A),
inference(paramod,[status(thm)],[c_5,c_5232]) ).
cnf(c_5233,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(A,greatest_lower_bound(A,B)),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_42,plain,
greatest_lower_bound(A,greatest_lower_bound(A,B)) = greatest_lower_bound(A,B),
inference(copy,[status(thm)],[c_5233]) ).
cnf(c_5234,plain,
least_upper_bound(A,B) = least_upper_bound(A,least_upper_bound(greatest_lower_bound(A,C),B)),
inference(paramod,[status(thm)],[c_12,c_9]) ).
cnf(c_46,plain,
least_upper_bound(A,least_upper_bound(greatest_lower_bound(A,B),C)) = least_upper_bound(A,C),
inference(copy,[status(thm)],[c_5234]) ).
cnf(c_48,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_57,plain,
least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_5235,plain,
least_upper_bound(multiply(A,B),B) = multiply(least_upper_bound(A,identity),B),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_58,plain,
least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A),
inference(paramod,[status(thm)],[c_5,c_5235]) ).
cnf(c_64,plain,
greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_5236,plain,
greatest_lower_bound(multiply(A,B),B) = multiply(greatest_lower_bound(A,identity),B),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_65,plain,
greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(B,identity),A),
inference(paramod,[status(thm)],[c_4,c_5236]) ).
cnf(c_71,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_5237,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_34]) ).
cnf(c_107,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_23,c_5237]) ).
cnf(c_5238,plain,
multiply(inverse(multiply(A,B)),inverse(inverse(A))) = inverse(B),
inference(paramod,[status(thm)],[c_34,c_25]) ).
cnf(c_118,plain,
multiply(inverse(multiply(A,B)),A) = inverse(B),
inference(paramod,[status(thm)],[c_23,c_5238]) ).
cnf(c_120,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(identity,B)),
inference(paramod,[status(thm)],[c_107,c_15]) ).
cnf(c_5239,plain,
least_upper_bound(multiply(A,B),A) = multiply(A,least_upper_bound(B,identity)),
inference(paramod,[status(thm)],[c_107,c_15]) ).
cnf(c_121,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(B,identity)),
inference(paramod,[status(thm)],[c_5,c_5239]) ).
cnf(c_122,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_107,c_17]) ).
cnf(c_5240,plain,
greatest_lower_bound(multiply(A,B),A) = multiply(A,greatest_lower_bound(B,identity)),
inference(paramod,[status(thm)],[c_107,c_17]) ).
cnf(c_123,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(B,identity)),
inference(paramod,[status(thm)],[c_4,c_5240]) ).
cnf(c_5241,plain,
least_upper_bound(multiply(A,B),identity) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_71,c_15]) ).
cnf(c_5242,plain,
least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))),
inference(paramod,[status(thm)],[c_5,c_5241]) ).
cnf(c_125,plain,
multiply(A,least_upper_bound(B,inverse(A))) = least_upper_bound(identity,multiply(A,B)),
inference(copy,[status(thm)],[c_5242]) ).
cnf(c_5243,plain,
least_upper_bound(A,least_upper_bound(B,least_upper_bound(C,A))) = least_upper_bound(least_upper_bound(B,C),A),
inference(paramod,[status(thm)],[c_9,c_41]) ).
cnf(c_142,plain,
least_upper_bound(A,least_upper_bound(B,least_upper_bound(C,A))) = least_upper_bound(B,least_upper_bound(C,A)),
inference(paramod,[status(thm)],[c_9,c_5243]) ).
cnf(c_5244,plain,
least_upper_bound(greatest_lower_bound(A,B),greatest_lower_bound(A,C)) = greatest_lower_bound(A,least_upper_bound(B,greatest_lower_bound(A,C))),
inference(paramod,[status(thm)],[c_42,c_31]) ).
cnf(c_5245,plain,
greatest_lower_bound(A,least_upper_bound(B,C)) = greatest_lower_bound(A,least_upper_bound(B,greatest_lower_bound(A,C))),
inference(paramod,[status(thm)],[c_31,c_5244]) ).
cnf(c_157,plain,
greatest_lower_bound(A,least_upper_bound(B,greatest_lower_bound(A,C))) = greatest_lower_bound(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_5245]) ).
cnf(c_5246,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_71,c_64]) ).
cnf(c_5247,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(identity,A),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_5246]) ).
cnf(c_228,plain,
multiply(greatest_lower_bound(identity,A),inverse(A)) = greatest_lower_bound(identity,inverse(A)),
inference(copy,[status(thm)],[c_5247]) ).
cnf(c_5248,plain,
greatest_lower_bound(inverse(A),identity) = multiply(greatest_lower_bound(A,identity),inverse(A)),
inference(paramod,[status(thm)],[c_71,c_65]) ).
cnf(c_5249,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(greatest_lower_bound(A,identity),inverse(A)),
inference(paramod,[status(thm)],[c_4,c_5248]) ).
cnf(c_248,plain,
multiply(greatest_lower_bound(A,identity),inverse(A)) = greatest_lower_bound(identity,inverse(A)),
inference(copy,[status(thm)],[c_5249]) ).
cnf(c_265,plain,
greatest_lower_bound(A,multiply(A,least_upper_bound(identity,B))) = A,
inference(paramod,[status(thm)],[c_120,c_13]) ).
cnf(c_5250,plain,
multiply(A,least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),A),
inference(paramod,[status(thm)],[c_120,c_57]) ).
cnf(c_282,plain,
multiply(least_upper_bound(identity,A),A) = multiply(A,least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_5250]) ).
cnf(c_5251,plain,
multiply(A,least_upper_bound(identity,A)) = multiply(least_upper_bound(A,identity),A),
inference(paramod,[status(thm)],[c_120,c_58]) ).
cnf(c_285,plain,
multiply(least_upper_bound(A,identity),A) = multiply(A,least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_5251]) ).
cnf(c_329,plain,
least_upper_bound(greatest_lower_bound(A,B),multiply(A,greatest_lower_bound(identity,C))) = greatest_lower_bound(A,least_upper_bound(B,multiply(A,C))),
inference(paramod,[status(thm)],[c_122,c_31]) ).
cnf(c_5252,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(least_upper_bound(identity,a),a)) != a,
inference(paramod,[status(thm)],[c_122,c_33]) ).
cnf(c_5253,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(a,least_upper_bound(identity,a))) != a,
inference(paramod,[status(thm)],[c_282,c_5252]) ).
cnf(c_330,plain,
multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)) != a,
inference(paramod,[status(thm)],[c_64,c_5253]) ).
cnf(c_5254,plain,
multiply(A,greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),A),
inference(paramod,[status(thm)],[c_122,c_64]) ).
cnf(c_337,plain,
multiply(greatest_lower_bound(identity,A),A) = multiply(A,greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_5254]) ).
cnf(c_5255,plain,
multiply(A,greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(A,identity),A),
inference(paramod,[status(thm)],[c_122,c_65]) ).
cnf(c_340,plain,
multiply(greatest_lower_bound(A,identity),A) = multiply(A,greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_5255]) ).
cnf(c_5256,plain,
greatest_lower_bound(inverse(A),identity) = multiply(inverse(A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_2,c_123]) ).
cnf(c_5257,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_4,c_5256]) ).
cnf(c_343,plain,
multiply(inverse(A),greatest_lower_bound(A,identity)) = greatest_lower_bound(identity,inverse(A)),
inference(copy,[status(thm)],[c_5257]) ).
cnf(c_5258,plain,
least_upper_bound(A,least_upper_bound(greatest_lower_bound(A,B),least_upper_bound(C,A))) = least_upper_bound(C,A),
inference(paramod,[status(thm)],[c_41,c_46]) ).
cnf(c_381,plain,
least_upper_bound(greatest_lower_bound(A,B),least_upper_bound(C,A)) = least_upper_bound(C,A),
inference(paramod,[status(thm)],[c_142,c_5258]) ).
cnf(c_390,plain,
least_upper_bound(A,multiply(greatest_lower_bound(A,B),least_upper_bound(identity,C))) = least_upper_bound(A,multiply(greatest_lower_bound(A,B),C)),
inference(paramod,[status(thm)],[c_120,c_46]) ).
cnf(c_5259,plain,
multiply(identity,inverse(least_upper_bound(A,identity))) = greatest_lower_bound(identity,inverse(least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_48,c_228]) ).
cnf(c_5260,plain,
inverse(least_upper_bound(A,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_1,c_5259]) ).
cnf(c_414,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(A,identity))) = inverse(least_upper_bound(A,identity)),
inference(copy,[status(thm)],[c_5260]) ).
cnf(c_5261,plain,
least_upper_bound(least_upper_bound(identity,least_upper_bound(A,identity)),multiply(least_upper_bound(identity,least_upper_bound(A,identity)),A)) = multiply(least_upper_bound(A,identity),least_upper_bound(identity,least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_282,c_121]) ).
cnf(c_5262,plain,
least_upper_bound(least_upper_bound(A,identity),multiply(least_upper_bound(identity,least_upper_bound(A,identity)),A)) = multiply(least_upper_bound(A,identity),least_upper_bound(identity,least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_41,c_5261]) ).
cnf(c_5263,plain,
least_upper_bound(least_upper_bound(A,identity),multiply(least_upper_bound(A,identity),A)) = multiply(least_upper_bound(A,identity),least_upper_bound(identity,least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_41,c_5262]) ).
cnf(c_5264,plain,
least_upper_bound(least_upper_bound(A,identity),multiply(A,least_upper_bound(identity,A))) = multiply(least_upper_bound(A,identity),least_upper_bound(identity,least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_285,c_5263]) ).
cnf(c_5265,plain,
least_upper_bound(A,least_upper_bound(identity,multiply(A,least_upper_bound(identity,A)))) = multiply(least_upper_bound(A,identity),least_upper_bound(identity,least_upper_bound(A,identity))),
inference(paramod,[status(thm)],[c_9,c_5264]) ).
cnf(c_452,plain,
least_upper_bound(A,least_upper_bound(identity,multiply(A,least_upper_bound(identity,A)))) = multiply(least_upper_bound(A,identity),least_upper_bound(A,identity)),
inference(paramod,[status(thm)],[c_41,c_5265]) ).
cnf(c_5266,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(A,least_upper_bound(identity,A))) = multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_282,c_122]) ).
cnf(c_5267,plain,
multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_64,c_5266]) ).
cnf(c_453,plain,
multiply(least_upper_bound(identity,A),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_5267]) ).
cnf(c_5268,plain,
greatest_lower_bound(least_upper_bound(identity,A),multiply(A,least_upper_bound(identity,A))) = multiply(least_upper_bound(identity,A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_282,c_123]) ).
cnf(c_5269,plain,
multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),greatest_lower_bound(A,identity)),
inference(paramod,[status(thm)],[c_64,c_5268]) ).
cnf(c_454,plain,
multiply(least_upper_bound(identity,A),greatest_lower_bound(A,identity)) = multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_5269]) ).
cnf(c_5270,plain,
least_upper_bound(greatest_lower_bound(A,identity),multiply(A,greatest_lower_bound(identity,A))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(A,identity)),
inference(paramod,[status(thm)],[c_340,c_121]) ).
cnf(c_524,plain,
greatest_lower_bound(A,least_upper_bound(identity,multiply(A,A))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(A,identity)),
inference(paramod,[status(thm)],[c_329,c_5270]) ).
cnf(c_5271,plain,
multiply(inverse(greatest_lower_bound(A,identity)),inverse(inverse(A))) = inverse(greatest_lower_bound(identity,inverse(A))),
inference(paramod,[status(thm)],[c_343,c_25]) ).
cnf(c_530,plain,
multiply(inverse(greatest_lower_bound(A,identity)),A) = inverse(greatest_lower_bound(identity,inverse(A))),
inference(paramod,[status(thm)],[c_23,c_5271]) ).
cnf(c_667,plain,
least_upper_bound(greatest_lower_bound(A,B),least_upper_bound(C,B)) = least_upper_bound(C,B),
inference(paramod,[status(thm)],[c_4,c_381]) ).
cnf(c_5272,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(A))),greatest_lower_bound(A,identity)) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_248,c_118]) ).
cnf(c_900,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(A))),greatest_lower_bound(A,identity)) = A,
inference(paramod,[status(thm)],[c_23,c_5272]) ).
cnf(c_1059,plain,
least_upper_bound(A,least_upper_bound(B,multiply(A,least_upper_bound(identity,C)))) = least_upper_bound(B,multiply(A,least_upper_bound(identity,C))),
inference(paramod,[status(thm)],[c_265,c_667]) ).
cnf(c_1061,plain,
least_upper_bound(identity,multiply(A,least_upper_bound(identity,A))) = multiply(least_upper_bound(A,identity),least_upper_bound(A,identity)),
inference(paramod,[status(thm)],[c_1059,c_452]) ).
cnf(c_1274,plain,
multiply(least_upper_bound(A,identity),greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5,c_453]) ).
cnf(c_1301,plain,
multiply(least_upper_bound(A,identity),greatest_lower_bound(A,identity)) = multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)),
inference(paramod,[status(thm)],[c_5,c_454]) ).
cnf(c_1683,plain,
least_upper_bound(greatest_lower_bound(identity,A),inverse(least_upper_bound(B,identity))) = greatest_lower_bound(identity,least_upper_bound(A,inverse(least_upper_bound(B,identity)))),
inference(paramod,[status(thm)],[c_414,c_31]) ).
cnf(c_5273,plain,
greatest_lower_bound(A,least_upper_bound(identity,multiply(A,B))) = multiply(A,greatest_lower_bound(identity,least_upper_bound(B,inverse(A)))),
inference(paramod,[status(thm)],[c_125,c_122]) ).
cnf(c_2481,plain,
multiply(A,greatest_lower_bound(identity,least_upper_bound(B,inverse(A)))) = greatest_lower_bound(A,least_upper_bound(identity,multiply(A,B))),
inference(copy,[status(thm)],[c_5273]) ).
cnf(c_5274,plain,
multiply(least_upper_bound(A,identity),least_upper_bound(greatest_lower_bound(identity,A),inverse(least_upper_bound(A,identity)))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_1274,c_125]) ).
cnf(c_5275,plain,
multiply(least_upper_bound(A,identity),greatest_lower_bound(identity,least_upper_bound(A,inverse(least_upper_bound(A,identity))))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_1683,c_5274]) ).
cnf(c_5276,plain,
greatest_lower_bound(least_upper_bound(A,identity),least_upper_bound(identity,multiply(least_upper_bound(A,identity),A))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_2481,c_5275]) ).
cnf(c_5277,plain,
greatest_lower_bound(least_upper_bound(A,identity),least_upper_bound(identity,multiply(A,least_upper_bound(identity,A)))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_285,c_5276]) ).
cnf(c_5278,plain,
greatest_lower_bound(least_upper_bound(A,identity),multiply(least_upper_bound(A,identity),least_upper_bound(A,identity))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_1061,c_5277]) ).
cnf(c_5279,plain,
multiply(least_upper_bound(A,identity),greatest_lower_bound(identity,least_upper_bound(A,identity))) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_122,c_5278]) ).
cnf(c_5280,plain,
multiply(least_upper_bound(A,identity),identity) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_48,c_5279]) ).
cnf(c_5281,plain,
least_upper_bound(A,identity) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A))),
inference(paramod,[status(thm)],[c_107,c_5280]) ).
cnf(c_5282,plain,
least_upper_bound(A,identity) = least_upper_bound(identity,multiply(greatest_lower_bound(identity,A),A)),
inference(paramod,[status(thm)],[c_390,c_5281]) ).
cnf(c_5283,plain,
least_upper_bound(A,identity) = least_upper_bound(identity,multiply(A,greatest_lower_bound(identity,A))),
inference(paramod,[status(thm)],[c_337,c_5282]) ).
cnf(c_2484,plain,
least_upper_bound(identity,multiply(A,greatest_lower_bound(identity,A))) = least_upper_bound(A,identity),
inference(copy,[status(thm)],[c_5283]) ).
cnf(c_2500,plain,
least_upper_bound(identity,greatest_lower_bound(A,multiply(A,A))) = least_upper_bound(A,identity),
inference(paramod,[status(thm)],[c_122,c_2484]) ).
cnf(c_5284,plain,
greatest_lower_bound(A,least_upper_bound(A,identity)) = greatest_lower_bound(A,least_upper_bound(identity,multiply(A,A))),
inference(paramod,[status(thm)],[c_2500,c_157]) ).
cnf(c_5285,plain,
A = greatest_lower_bound(A,least_upper_bound(identity,multiply(A,A))),
inference(paramod,[status(thm)],[c_13,c_5284]) ).
cnf(c_5042,plain,
greatest_lower_bound(A,least_upper_bound(identity,multiply(A,A))) = A,
inference(copy,[status(thm)],[c_5285]) ).
cnf(c_5286,plain,
A = multiply(greatest_lower_bound(A,identity),least_upper_bound(A,identity)),
inference(paramod,[status(thm)],[c_5042,c_524]) ).
cnf(c_5061,plain,
multiply(greatest_lower_bound(A,identity),least_upper_bound(A,identity)) = A,
inference(copy,[status(thm)],[c_5286]) ).
cnf(c_5287,plain,
multiply(inverse(greatest_lower_bound(A,identity)),A) = least_upper_bound(A,identity),
inference(paramod,[status(thm)],[c_5061,c_34]) ).
cnf(c_5076,plain,
inverse(greatest_lower_bound(identity,inverse(A))) = least_upper_bound(A,identity),
inference(paramod,[status(thm)],[c_530,c_5287]) ).
cnf(c_5288,plain,
multiply(least_upper_bound(A,identity),greatest_lower_bound(A,identity)) = A,
inference(paramod,[status(thm)],[c_5076,c_900]) ).
cnf(c_5224,plain,
multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)) = A,
inference(paramod,[status(thm)],[c_1301,c_5288]) ).
cnf(c_5225,plain,
$false,
inference(resolve,[status(thm)],[c_5224,c_330]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n018.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 14:35:06 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 2175508 was started by sandbox on n018,
% 0.16/0.44 % Fri Sep 25 14:35:06 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 17.05/2.68
% 17.05/2.68 % SZS status Unsatisfiable for theBenchmark
% 17.05/2.68
% 17.05/2.68 % Proof 1 at 1.67 (+ 0.51) seconds.
% 17.05/2.68 % Length of proof is 82.
% 17.05/2.68 % Level of proof is 14.
% 17.05/2.68 % Maximum clause weight is 44.000.
% 17.05/2.68 % Given clauses 209.
% 17.05/2.68
% 17.05/2.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------