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