TSTP Solution File: GRP169-1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : GRP169-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May  3 02:21:33 EDT 2024

% Result   : Unsatisfiable 12.25s 2.11s
% Output   : CNFRefutation 12.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   38
%            Number of leaves      :   17
% Syntax   : Number of clauses     :  157 ( 157 unt;   0 nHn;  32 RR)
%            Number of literals    :  157 ( 156 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  190 (  20 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c_49,plain,
    least_upper_bound(inverse(a),inverse(b)) = inverse(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p02a_1) ).

cnf(c_50,negated_conjecture,
    least_upper_bound(a,b) != a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p02a) ).

cnf(c_51,plain,
    greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).

cnf(c_52,plain,
    least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).

cnf(c_53,plain,
    greatest_lower_bound(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(X0,greatest_lower_bound(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).

cnf(c_54,plain,
    least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X0,least_upper_bound(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).

cnf(c_55,plain,
    least_upper_bound(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).

cnf(c_56,plain,
    greatest_lower_bound(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).

cnf(c_57,plain,
    least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).

cnf(c_58,plain,
    greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).

cnf(c_59,plain,
    least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,least_upper_bound(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).

cnf(c_60,plain,
    greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,greatest_lower_bound(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).

cnf(c_61,plain,
    least_upper_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(least_upper_bound(X0,X2),X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).

cnf(c_62,plain,
    greatest_lower_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(greatest_lower_bound(X0,X2),X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).

cnf(c_63,plain,
    multiply(identity,X0) = X0,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(c_64,plain,
    multiply(inverse(X0),X0) = identity,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).

cnf(c_65,plain,
    multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).

cnf(c_194,plain,
    least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,X2)),
    inference(superposition,[status(thm)],[c_54,c_52]) ).

cnf(c_195,plain,
    greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2)),
    inference(superposition,[status(thm)],[c_53,c_51]) ).

cnf(c_200,plain,
    least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
    inference(superposition,[status(thm)],[c_51,c_57]) ).

cnf(c_203,plain,
    greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
    inference(superposition,[status(thm)],[c_52,c_58]) ).

cnf(c_215,plain,
    greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
    inference(superposition,[status(thm)],[c_49,c_58]) ).

cnf(c_218,plain,
    greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,X1),
    inference(superposition,[status(thm)],[c_56,c_53]) ).

cnf(c_219,plain,
    greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2),
    inference(superposition,[status(thm)],[c_58,c_53]) ).

cnf(c_221,plain,
    least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0))) = X0,
    inference(superposition,[status(thm)],[c_53,c_200]) ).

cnf(c_234,plain,
    least_upper_bound(X0,least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
    inference(superposition,[status(thm)],[c_55,c_54]) ).

cnf(c_235,plain,
    least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X0,X2),
    inference(superposition,[status(thm)],[c_57,c_54]) ).

cnf(c_248,plain,
    multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
    inference(superposition,[status(thm)],[c_64,c_65]) ).

cnf(c_254,plain,
    greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) = X0,
    inference(superposition,[status(thm)],[c_54,c_203]) ).

cnf(c_300,plain,
    least_upper_bound(inverse(b),greatest_lower_bound(X0,inverse(a))) = inverse(b),
    inference(superposition,[status(thm)],[c_215,c_221]) ).

cnf(c_320,plain,
    multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
    inference(superposition,[status(thm)],[c_64,c_59]) ).

cnf(c_372,plain,
    least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(identity,X1),X0),
    inference(superposition,[status(thm)],[c_63,c_61]) ).

cnf(c_375,plain,
    least_upper_bound(multiply(X0,X1),X1) = multiply(least_upper_bound(X0,identity),X1),
    inference(superposition,[status(thm)],[c_63,c_61]) ).

cnf(c_376,plain,
    multiply(least_upper_bound(X0,inverse(X1)),X1) = least_upper_bound(multiply(X0,X1),identity),
    inference(superposition,[status(thm)],[c_64,c_61]) ).

cnf(c_388,plain,
    least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(X1,identity),X0),
    inference(theory_normalisation,[status(thm)],[c_375,c_54,c_52,c_53,c_51]) ).

cnf(c_390,plain,
    multiply(least_upper_bound(X0,inverse(X1)),X1) = least_upper_bound(identity,multiply(X0,X1)),
    inference(theory_normalisation,[status(thm)],[c_376,c_54,c_52,c_53,c_51]) ).

cnf(c_403,plain,
    greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
    inference(superposition,[status(thm)],[c_63,c_62]) ).

cnf(c_407,plain,
    multiply(greatest_lower_bound(X0,inverse(X1)),X1) = greatest_lower_bound(multiply(X0,X1),identity),
    inference(superposition,[status(thm)],[c_64,c_62]) ).

cnf(c_423,plain,
    multiply(greatest_lower_bound(X0,inverse(X1)),X1) = greatest_lower_bound(identity,multiply(X0,X1)),
    inference(theory_normalisation,[status(thm)],[c_407,c_54,c_52,c_53,c_51]) ).

cnf(c_465,plain,
    greatest_lower_bound(greatest_lower_bound(X0,X1),least_upper_bound(X2,X0)) = greatest_lower_bound(X0,X1),
    inference(superposition,[status(thm)],[c_57,c_254]) ).

cnf(c_479,plain,
    greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(X2,X0))) = greatest_lower_bound(X0,X1),
    inference(theory_normalisation,[status(thm)],[c_465,c_54,c_52,c_53,c_51]) ).

cnf(c_551,plain,
    multiply(inverse(identity),X0) = X0,
    inference(superposition,[status(thm)],[c_63,c_248]) ).

cnf(c_552,plain,
    multiply(inverse(inverse(X0)),identity) = multiply(identity,X0),
    inference(superposition,[status(thm)],[c_64,c_248]) ).

cnf(c_565,plain,
    multiply(inverse(inverse(X0)),identity) = X0,
    inference(light_normalisation,[status(thm)],[c_552,c_63]) ).

cnf(c_585,plain,
    multiply(inverse(inverse(identity)),X0) = multiply(identity,X0),
    inference(superposition,[status(thm)],[c_551,c_248]) ).

cnf(c_595,plain,
    multiply(inverse(inverse(identity)),X0) = X0,
    inference(light_normalisation,[status(thm)],[c_585,c_63]) ).

cnf(c_612,plain,
    multiply(inverse(inverse(X0)),multiply(identity,X1)) = multiply(X0,X1),
    inference(superposition,[status(thm)],[c_565,c_65]) ).

cnf(c_783,plain,
    inverse(identity) = identity,
    inference(superposition,[status(thm)],[c_595,c_64]) ).

cnf(c_805,plain,
    least_upper_bound(inverse(b),greatest_lower_bound(inverse(a),X0)) = inverse(b),
    inference(superposition,[status(thm)],[c_51,c_300]) ).

cnf(c_885,plain,
    greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(X0,X2))) = greatest_lower_bound(X0,X1),
    inference(superposition,[status(thm)],[c_51,c_219]) ).

cnf(c_946,plain,
    least_upper_bound(X0,least_upper_bound(X1,greatest_lower_bound(X0,X2))) = least_upper_bound(X0,X1),
    inference(superposition,[status(thm)],[c_52,c_235]) ).

cnf(c_1317,plain,
    multiply(least_upper_bound(identity,inverse(X0)),X0) = least_upper_bound(X0,identity),
    inference(superposition,[status(thm)],[c_64,c_372]) ).

cnf(c_1358,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X0))),least_upper_bound(X0,identity)) = multiply(identity,X0),
    inference(superposition,[status(thm)],[c_1317,c_248]) ).

cnf(c_1369,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X0))),least_upper_bound(X0,identity)) = X0,
    inference(light_normalisation,[status(thm)],[c_1358,c_63]) ).

cnf(c_1466,plain,
    multiply(greatest_lower_bound(identity,inverse(X0)),X0) = greatest_lower_bound(X0,identity),
    inference(superposition,[status(thm)],[c_64,c_403]) ).

cnf(c_1514,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X0))),greatest_lower_bound(X0,identity)) = multiply(identity,X0),
    inference(superposition,[status(thm)],[c_1466,c_248]) ).

cnf(c_1527,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X0))),greatest_lower_bound(X0,identity)) = X0,
    inference(light_normalisation,[status(thm)],[c_1514,c_63]) ).

cnf(c_1978,plain,
    multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
    inference(superposition,[status(thm)],[c_63,c_612]) ).

cnf(c_1998,plain,
    multiply(X0,identity) = X0,
    inference(demodulation,[status(thm)],[c_565,c_1978]) ).

cnf(c_2026,plain,
    greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(identity,X1)),
    inference(superposition,[status(thm)],[c_1998,c_60]) ).

cnf(c_2027,plain,
    least_upper_bound(X0,multiply(X0,X1)) = multiply(X0,least_upper_bound(identity,X1)),
    inference(superposition,[status(thm)],[c_1998,c_59]) ).

cnf(c_2076,plain,
    multiply(X0,inverse(X0)) = identity,
    inference(superposition,[status(thm)],[c_1978,c_64]) ).

cnf(c_2077,plain,
    multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
    inference(superposition,[status(thm)],[c_1978,c_248]) ).

cnf(c_2078,plain,
    inverse(inverse(X0)) = multiply(X0,identity),
    inference(superposition,[status(thm)],[c_1978,c_1998]) ).

cnf(c_2079,plain,
    inverse(inverse(X0)) = X0,
    inference(light_normalisation,[status(thm)],[c_2078,c_1998]) ).

cnf(c_2120,plain,
    multiply(X0,greatest_lower_bound(inverse(X0),X1)) = greatest_lower_bound(identity,multiply(X0,X1)),
    inference(superposition,[status(thm)],[c_2076,c_60]) ).

cnf(c_2121,plain,
    multiply(X0,least_upper_bound(inverse(X0),X1)) = least_upper_bound(identity,multiply(X0,X1)),
    inference(superposition,[status(thm)],[c_2076,c_59]) ).

cnf(c_2124,plain,
    multiply(X0,least_upper_bound(X1,inverse(X0))) = least_upper_bound(multiply(X0,X1),identity),
    inference(superposition,[status(thm)],[c_2076,c_59]) ).

cnf(c_2132,plain,
    multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
    inference(superposition,[status(thm)],[c_2076,c_65]) ).

cnf(c_2137,plain,
    multiply(X0,least_upper_bound(X1,inverse(X0))) = least_upper_bound(identity,multiply(X0,X1)),
    inference(theory_normalisation,[status(thm)],[c_2124,c_54,c_52,c_53,c_51]) ).

cnf(c_2551,plain,
    multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(inverse(X0),identity),
    inference(superposition,[status(thm)],[c_64,c_2026]) ).

cnf(c_2559,plain,
    multiply(X0,greatest_lower_bound(identity,inverse(X0))) = greatest_lower_bound(X0,identity),
    inference(superposition,[status(thm)],[c_2076,c_2026]) ).

cnf(c_2584,plain,
    multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)),
    inference(theory_normalisation,[status(thm)],[c_2551,c_54,c_52,c_53,c_51]) ).

cnf(c_2626,plain,
    multiply(inverse(X0),least_upper_bound(identity,X0)) = least_upper_bound(inverse(X0),identity),
    inference(superposition,[status(thm)],[c_64,c_2027]) ).

cnf(c_2634,plain,
    multiply(X0,least_upper_bound(identity,inverse(X0))) = least_upper_bound(X0,identity),
    inference(superposition,[status(thm)],[c_2076,c_2027]) ).

cnf(c_2659,plain,
    multiply(inverse(X0),least_upper_bound(identity,X0)) = least_upper_bound(identity,inverse(X0)),
    inference(theory_normalisation,[status(thm)],[c_2626,c_54,c_52,c_53,c_51]) ).

cnf(c_2724,plain,
    multiply(identity,greatest_lower_bound(identity,inverse(inverse(X0)))) = multiply(X0,greatest_lower_bound(inverse(X0),identity)),
    inference(superposition,[status(thm)],[c_2559,c_2077]) ).

cnf(c_2728,plain,
    multiply(identity,greatest_lower_bound(identity,inverse(inverse(X0)))) = multiply(X0,greatest_lower_bound(identity,inverse(X0))),
    inference(theory_normalisation,[status(thm)],[c_2724,c_54,c_52,c_53,c_51]) ).

cnf(c_2729,plain,
    multiply(identity,greatest_lower_bound(identity,X0)) = greatest_lower_bound(X0,identity),
    inference(light_normalisation,[status(thm)],[c_2728,c_2079,c_2559]) ).

cnf(c_2777,plain,
    greatest_lower_bound(greatest_lower_bound(identity,X0),identity) = multiply(identity,greatest_lower_bound(identity,X0)),
    inference(superposition,[status(thm)],[c_218,c_2729]) ).

cnf(c_2817,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X0,identity)) = multiply(identity,greatest_lower_bound(identity,X0)),
    inference(theory_normalisation,[status(thm)],[c_2777,c_54,c_52,c_53,c_51]) ).

cnf(c_2818,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X0,identity)) = greatest_lower_bound(X0,identity),
    inference(light_normalisation,[status(thm)],[c_2817,c_2729]) ).

cnf(c_3089,plain,
    multiply(identity,least_upper_bound(identity,inverse(inverse(X0)))) = multiply(X0,least_upper_bound(inverse(X0),identity)),
    inference(superposition,[status(thm)],[c_2634,c_2077]) ).

cnf(c_3094,plain,
    multiply(identity,least_upper_bound(identity,inverse(inverse(X0)))) = multiply(X0,least_upper_bound(identity,inverse(X0))),
    inference(theory_normalisation,[status(thm)],[c_3089,c_54,c_52,c_53,c_51]) ).

cnf(c_3095,plain,
    multiply(identity,least_upper_bound(identity,X0)) = least_upper_bound(X0,identity),
    inference(light_normalisation,[status(thm)],[c_3094,c_2079,c_2634]) ).

cnf(c_3138,plain,
    least_upper_bound(least_upper_bound(identity,X0),identity) = multiply(identity,least_upper_bound(identity,X0)),
    inference(superposition,[status(thm)],[c_234,c_3095]) ).

cnf(c_3178,plain,
    least_upper_bound(identity,least_upper_bound(X0,identity)) = multiply(identity,least_upper_bound(identity,X0)),
    inference(theory_normalisation,[status(thm)],[c_3138,c_54,c_52,c_53,c_51]) ).

cnf(c_3179,plain,
    least_upper_bound(identity,least_upper_bound(X0,identity)) = least_upper_bound(X0,identity),
    inference(light_normalisation,[status(thm)],[c_3178,c_3095]) ).

cnf(c_3339,plain,
    greatest_lower_bound(identity,inverse(identity)) = multiply(inverse(identity),identity),
    inference(superposition,[status(thm)],[c_56,c_2584]) ).

cnf(c_3376,plain,
    greatest_lower_bound(identity,identity) = multiply(identity,identity),
    inference(light_normalisation,[status(thm)],[c_3339,c_783]) ).

cnf(c_3433,plain,
    greatest_lower_bound(multiply(identity,identity),X0) = greatest_lower_bound(identity,greatest_lower_bound(identity,X0)),
    inference(superposition,[status(thm)],[c_3376,c_53]) ).

cnf(c_3436,plain,
    least_upper_bound(identity,multiply(identity,identity)) = identity,
    inference(superposition,[status(thm)],[c_3376,c_200]) ).

cnf(c_3440,plain,
    greatest_lower_bound(X0,multiply(identity,identity)) = greatest_lower_bound(identity,greatest_lower_bound(X0,identity)),
    inference(superposition,[status(thm)],[c_3376,c_195]) ).

cnf(c_3451,plain,
    greatest_lower_bound(X0,multiply(identity,identity)) = greatest_lower_bound(X0,identity),
    inference(light_normalisation,[status(thm)],[c_3440,c_2818]) ).

cnf(c_3472,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X0,identity)) = greatest_lower_bound(identity,X0),
    inference(superposition,[status(thm)],[c_3436,c_885]) ).

cnf(c_3475,plain,
    greatest_lower_bound(multiply(identity,identity),greatest_lower_bound(X0,identity)) = greatest_lower_bound(multiply(identity,identity),X0),
    inference(superposition,[status(thm)],[c_3436,c_479]) ).

cnf(c_3478,plain,
    multiply(least_upper_bound(identity,identity),identity) = identity,
    inference(superposition,[status(thm)],[c_3436,c_388]) ).

cnf(c_3487,plain,
    greatest_lower_bound(identity,greatest_lower_bound(X0,multiply(identity,identity))) = greatest_lower_bound(multiply(identity,identity),X0),
    inference(theory_normalisation,[status(thm)],[c_3475,c_54,c_52,c_53,c_51]) ).

cnf(c_3488,plain,
    greatest_lower_bound(identity,greatest_lower_bound(identity,X0)) = greatest_lower_bound(X0,identity),
    inference(light_normalisation,[status(thm)],[c_3487,c_2818,c_3433,c_3451]) ).

cnf(c_3607,plain,
    least_upper_bound(identity,inverse(identity)) = multiply(inverse(identity),identity),
    inference(superposition,[status(thm)],[c_55,c_2659]) ).

cnf(c_3645,plain,
    least_upper_bound(identity,identity) = multiply(identity,identity),
    inference(light_normalisation,[status(thm)],[c_3607,c_783]) ).

cnf(c_3671,plain,
    multiply(multiply(identity,identity),identity) = identity,
    inference(demodulation,[status(thm)],[c_3478,c_3645]) ).

cnf(c_3707,plain,
    greatest_lower_bound(identity,multiply(identity,identity)) = identity,
    inference(superposition,[status(thm)],[c_3645,c_203]) ).

cnf(c_3711,plain,
    least_upper_bound(X0,multiply(identity,identity)) = least_upper_bound(identity,least_upper_bound(X0,identity)),
    inference(superposition,[status(thm)],[c_3645,c_194]) ).

cnf(c_3724,plain,
    least_upper_bound(X0,multiply(identity,identity)) = least_upper_bound(X0,identity),
    inference(light_normalisation,[status(thm)],[c_3711,c_3179]) ).

cnf(c_3865,plain,
    multiply(multiply(identity,identity),multiply(identity,X0)) = multiply(identity,X0),
    inference(superposition,[status(thm)],[c_3671,c_65]) ).

cnf(c_3883,plain,
    multiply(multiply(identity,identity),X0) = X0,
    inference(light_normalisation,[status(thm)],[c_3865,c_63]) ).

cnf(c_3899,plain,
    least_upper_bound(identity,least_upper_bound(X0,identity)) = least_upper_bound(identity,X0),
    inference(superposition,[status(thm)],[c_3707,c_946]) ).

cnf(c_3995,plain,
    greatest_lower_bound(multiply(identity,identity),X0) = greatest_lower_bound(X0,identity),
    inference(light_normalisation,[status(thm)],[c_3433,c_3488]) ).

cnf(c_4409,plain,
    least_upper_bound(multiply(identity,identity),X0) = least_upper_bound(X0,identity),
    inference(superposition,[status(thm)],[c_3724,c_52]) ).

cnf(c_5906,plain,
    least_upper_bound(identity,multiply(multiply(identity,identity),X0)) = multiply(least_upper_bound(inverse(X0),identity),X0),
    inference(superposition,[status(thm)],[c_4409,c_390]) ).

cnf(c_5936,plain,
    least_upper_bound(identity,multiply(multiply(identity,identity),X0)) = multiply(least_upper_bound(identity,inverse(X0)),X0),
    inference(theory_normalisation,[status(thm)],[c_5906,c_54,c_52,c_53,c_51]) ).

cnf(c_5937,plain,
    multiply(least_upper_bound(identity,inverse(X0)),X0) = least_upper_bound(identity,X0),
    inference(light_normalisation,[status(thm)],[c_5936,c_3883]) ).

cnf(c_6163,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X0))),least_upper_bound(identity,X0)) = multiply(identity,X0),
    inference(superposition,[status(thm)],[c_5937,c_248]) ).

cnf(c_6183,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X0))),least_upper_bound(identity,X0)) = X0,
    inference(light_normalisation,[status(thm)],[c_6163,c_63]) ).

cnf(c_6835,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X0))),least_upper_bound(identity,least_upper_bound(X0,identity))) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X0))),X0),
    inference(superposition,[status(thm)],[c_1369,c_2027]) ).

cnf(c_6874,plain,
    multiply(inverse(least_upper_bound(identity,inverse(X0))),least_upper_bound(identity,least_upper_bound(X0,identity))) = least_upper_bound(X0,inverse(least_upper_bound(identity,inverse(X0)))),
    inference(theory_normalisation,[status(thm)],[c_6835,c_54,c_52,c_53,c_51]) ).

cnf(c_6875,plain,
    least_upper_bound(X0,inverse(least_upper_bound(identity,inverse(X0)))) = X0,
    inference(light_normalisation,[status(thm)],[c_6874,c_3899,c_6183]) ).

cnf(c_6921,plain,
    least_upper_bound(inverse(X0),inverse(least_upper_bound(identity,X0))) = inverse(X0),
    inference(superposition,[status(thm)],[c_2079,c_6875]) ).

cnf(c_7197,plain,
    greatest_lower_bound(identity,multiply(multiply(identity,identity),X0)) = multiply(greatest_lower_bound(inverse(X0),identity),X0),
    inference(superposition,[status(thm)],[c_3995,c_423]) ).

cnf(c_7225,plain,
    greatest_lower_bound(identity,multiply(multiply(identity,identity),X0)) = multiply(greatest_lower_bound(identity,inverse(X0)),X0),
    inference(theory_normalisation,[status(thm)],[c_7197,c_54,c_52,c_53,c_51]) ).

cnf(c_7226,plain,
    multiply(greatest_lower_bound(identity,inverse(X0)),X0) = greatest_lower_bound(identity,X0),
    inference(light_normalisation,[status(thm)],[c_7225,c_3883]) ).

cnf(c_7525,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X0))),greatest_lower_bound(identity,X0)) = multiply(identity,X0),
    inference(superposition,[status(thm)],[c_7226,c_248]) ).

cnf(c_7545,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X0))),greatest_lower_bound(identity,X0)) = X0,
    inference(light_normalisation,[status(thm)],[c_7525,c_63]) ).

cnf(c_7900,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X0))),greatest_lower_bound(identity,greatest_lower_bound(X0,identity))) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X0))),X0),
    inference(superposition,[status(thm)],[c_1527,c_2026]) ).

cnf(c_7936,plain,
    multiply(inverse(greatest_lower_bound(identity,inverse(X0))),greatest_lower_bound(identity,greatest_lower_bound(X0,identity))) = greatest_lower_bound(X0,inverse(greatest_lower_bound(identity,inverse(X0)))),
    inference(theory_normalisation,[status(thm)],[c_7900,c_54,c_52,c_53,c_51]) ).

cnf(c_7937,plain,
    greatest_lower_bound(X0,inverse(greatest_lower_bound(identity,inverse(X0)))) = X0,
    inference(light_normalisation,[status(thm)],[c_7936,c_3472,c_7545]) ).

cnf(c_7970,plain,
    greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(identity,X0))) = inverse(X0),
    inference(superposition,[status(thm)],[c_2079,c_7937]) ).

cnf(c_9407,plain,
    greatest_lower_bound(identity,multiply(X0,inverse(greatest_lower_bound(identity,X0)))) = multiply(X0,inverse(X0)),
    inference(superposition,[status(thm)],[c_7970,c_2120]) ).

cnf(c_9449,plain,
    greatest_lower_bound(identity,multiply(X0,inverse(greatest_lower_bound(identity,X0)))) = identity,
    inference(light_normalisation,[status(thm)],[c_9407,c_2076]) ).

cnf(c_10003,plain,
    least_upper_bound(identity,multiply(a,inverse(b))) = multiply(a,inverse(b)),
    inference(superposition,[status(thm)],[c_49,c_2121]) ).

cnf(c_10178,plain,
    greatest_lower_bound(identity,multiply(a,inverse(b))) = identity,
    inference(superposition,[status(thm)],[c_10003,c_58]) ).

cnf(c_10235,plain,
    greatest_lower_bound(identity,multiply(multiply(a,inverse(b)),inverse(identity))) = identity,
    inference(superposition,[status(thm)],[c_10178,c_9449]) ).

cnf(c_10251,plain,
    greatest_lower_bound(identity,multiply(multiply(a,inverse(b)),identity)) = identity,
    inference(light_normalisation,[status(thm)],[c_10235,c_783]) ).

cnf(c_10633,plain,
    greatest_lower_bound(identity,multiply(a,multiply(inverse(b),identity))) = identity,
    inference(superposition,[status(thm)],[c_65,c_10251]) ).

cnf(c_11290,plain,
    least_upper_bound(identity,multiply(b,inverse(a))) = multiply(b,inverse(b)),
    inference(superposition,[status(thm)],[c_49,c_2137]) ).

cnf(c_21480,plain,
    least_upper_bound(identity,multiply(inverse(X0),greatest_lower_bound(X1,X0))) = multiply(inverse(X0),X0),
    inference(superposition,[status(thm)],[c_200,c_320]) ).

cnf(c_21634,plain,
    least_upper_bound(identity,multiply(inverse(X0),greatest_lower_bound(X1,X0))) = identity,
    inference(light_normalisation,[status(thm)],[c_21480,c_64]) ).

cnf(c_21988,plain,
    least_upper_bound(identity,multiply(inverse(least_upper_bound(X0,X1)),X0)) = identity,
    inference(superposition,[status(thm)],[c_58,c_21634]) ).

cnf(c_22809,plain,
    least_upper_bound(identity,inverse(least_upper_bound(identity,X0))) = identity,
    inference(superposition,[status(thm)],[c_1998,c_21988]) ).

cnf(c_22840,plain,
    least_upper_bound(identity,multiply(inverse(inverse(b)),inverse(b))) = identity,
    inference(superposition,[status(thm)],[c_805,c_21988]) ).

cnf(c_23362,plain,
    least_upper_bound(identity,inverse(multiply(b,inverse(b)))) = identity,
    inference(superposition,[status(thm)],[c_11290,c_22809]) ).

cnf(c_26582,plain,
    least_upper_bound(identity,multiply(b,inverse(b))) = identity,
    inference(superposition,[status(thm)],[c_2079,c_22840]) ).

cnf(c_26716,plain,
    least_upper_bound(inverse(multiply(b,inverse(b))),inverse(identity)) = inverse(multiply(b,inverse(b))),
    inference(superposition,[status(thm)],[c_26582,c_6921]) ).

cnf(c_26742,plain,
    least_upper_bound(inverse(identity),inverse(multiply(b,inverse(b)))) = inverse(multiply(b,inverse(b))),
    inference(theory_normalisation,[status(thm)],[c_26716,c_54,c_52,c_53,c_51]) ).

cnf(c_26743,plain,
    inverse(multiply(b,inverse(b))) = identity,
    inference(light_normalisation,[status(thm)],[c_26742,c_783,c_23362]) ).

cnf(c_26847,plain,
    multiply(b,multiply(inverse(b),identity)) = identity,
    inference(superposition,[status(thm)],[c_26743,c_2132]) ).

cnf(c_27920,plain,
    greatest_lower_bound(identity,multiply(X0,multiply(inverse(b),identity))) = multiply(greatest_lower_bound(b,X0),multiply(inverse(b),identity)),
    inference(superposition,[status(thm)],[c_26847,c_62]) ).

cnf(c_27946,plain,
    multiply(greatest_lower_bound(b,a),multiply(inverse(b),identity)) = identity,
    inference(demodulation,[status(thm)],[c_10633,c_27920]) ).

cnf(c_27947,plain,
    multiply(greatest_lower_bound(a,b),multiply(inverse(b),identity)) = identity,
    inference(theory_normalisation,[status(thm)],[c_27946,c_54,c_52,c_53,c_51]) ).

cnf(c_27958,plain,
    multiply(greatest_lower_bound(a,b),inverse(b)) = identity,
    inference(superposition,[status(thm)],[c_1998,c_27947]) ).

cnf(c_28422,plain,
    multiply(greatest_lower_bound(a,b),multiply(inverse(b),X0)) = multiply(identity,X0),
    inference(superposition,[status(thm)],[c_27958,c_65]) ).

cnf(c_28432,plain,
    multiply(greatest_lower_bound(a,b),multiply(inverse(b),X0)) = X0,
    inference(light_normalisation,[status(thm)],[c_28422,c_63]) ).

cnf(c_28588,plain,
    multiply(greatest_lower_bound(a,b),identity) = b,
    inference(superposition,[status(thm)],[c_64,c_28432]) ).

cnf(c_28686,plain,
    greatest_lower_bound(a,b) = b,
    inference(superposition,[status(thm)],[c_28588,c_1998]) ).

cnf(c_28907,plain,
    least_upper_bound(a,b) = a,
    inference(superposition,[status(thm)],[c_28686,c_57]) ).

cnf(c_28925,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_28907,c_50]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : GRP169-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.02/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n026.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Fri May  3 00:07:36 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.17/0.43  Running UEQ theorem proving
% 0.17/0.43  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule casc_24_ueq --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.25/2.11  % SZS status Started for theBenchmark.p
% 12.25/2.11  % SZS status Unsatisfiable for theBenchmark.p
% 12.25/2.11  
% 12.25/2.11  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 12.25/2.11  
% 12.25/2.11  ------  iProver source info
% 12.25/2.11  
% 12.25/2.11  git: date: 2024-05-02 19:28:25 +0000
% 12.25/2.11  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 12.25/2.11  git: non_committed_changes: false
% 12.25/2.11  
% 12.25/2.11  ------ Parsing...successful
% 12.25/2.11  
% 12.25/2.11  
% 12.25/2.11  
% 12.25/2.11  ------ Preprocessing... sup_sim: 0  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 12.25/2.11  
% 12.25/2.11  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 12.25/2.11  
% 12.25/2.11  ------ Preprocessing... sf_s  rm: 0 0s  sf_e 
% 12.25/2.11  ------ Proving...
% 12.25/2.11  ------ Problem Properties 
% 12.25/2.11  
% 12.25/2.11  
% 12.25/2.11  clauses                                 17
% 12.25/2.11  conjectures                             1
% 12.25/2.11  EPR                                     0
% 12.25/2.11  Horn                                    17
% 12.25/2.11  unary                                   17
% 12.25/2.11  binary                                  0
% 12.25/2.11  lits                                    17
% 12.25/2.11  lits eq                                 17
% 12.25/2.11  fd_pure                                 0
% 12.25/2.11  fd_pseudo                               0
% 12.25/2.11  fd_cond                                 0
% 12.25/2.11  fd_pseudo_cond                          0
% 12.25/2.11  AC symbols                              2
% 12.25/2.11  
% 12.25/2.11  ------ Input Options Time Limit: Unbounded
% 12.25/2.11  
% 12.25/2.11  
% 12.25/2.11  ------ 
% 12.25/2.11  Current options:
% 12.25/2.11  ------ 
% 12.25/2.11  
% 12.25/2.11  
% 12.25/2.11  
% 12.25/2.11  
% 12.25/2.11  ------ Proving...
% 12.25/2.11  
% 12.25/2.11  
% 12.25/2.11  % SZS status Unsatisfiable for theBenchmark.p
% 12.25/2.11  
% 12.25/2.11  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.25/2.11  
% 12.25/2.12  
%------------------------------------------------------------------------------