TSTP Solution File: GRP167-2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : GRP167-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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 : Thu Aug 31 00:58:23 EDT 2023

% Result   : Unsatisfiable 16.12s 2.65s
% Output   : CNFRefutation 16.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   40
%            Number of leaves      :   21
% Syntax   : Number of clauses     :  149 ( 149 unt;   0 nHn;   4 RR)
%            Number of literals    :  149 ( 148 equ;   2 neg)
%            Maximal clause size   :    1 (   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   :  212 (  25 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c_49,plain,
    inverse(identity) = identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_1) ).

cnf(c_50,plain,
    inverse(inverse(X0)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_2) ).

cnf(c_51,plain,
    multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_3) ).

cnf(c_52,plain,
    least_upper_bound(X0,identity) = positive_part(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_4) ).

cnf(c_53,plain,
    greatest_lower_bound(X0,identity) = negative_part(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_5) ).

cnf(c_54,plain,
    greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,X2)) = least_upper_bound(X0,greatest_lower_bound(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_6) ).

cnf(c_55,plain,
    least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,X2)) = greatest_lower_bound(X0,least_upper_bound(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_7) ).

cnf(c_56,negated_conjecture,
    multiply(positive_part(a),negative_part(a)) != a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat4) ).

cnf(c_57,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_58,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_59,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_60,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_63,plain,
    least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).

cnf(c_64,plain,
    greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).

cnf(c_65,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_66,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_67,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_68,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_69,plain,
    multiply(identity,X0) = X0,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(c_70,plain,
    multiply(inverse(X0),X0) = identity,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).

cnf(c_71,plain,
    multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).

cnf(c_257,plain,
    greatest_lower_bound(identity,X0) = negative_part(X0),
    inference(superposition,[status(thm)],[c_53,c_57]) ).

cnf(c_261,plain,
    least_upper_bound(identity,X0) = positive_part(X0),
    inference(superposition,[status(thm)],[c_52,c_58]) ).

cnf(c_265,plain,
    least_upper_bound(X0,negative_part(X0)) = X0,
    inference(superposition,[status(thm)],[c_53,c_63]) ).

cnf(c_277,plain,
    least_upper_bound(identity,negative_part(X0)) = identity,
    inference(superposition,[status(thm)],[c_257,c_63]) ).

cnf(c_288,plain,
    positive_part(greatest_lower_bound(identity,X0)) = identity,
    inference(superposition,[status(thm)],[c_261,c_63]) ).

cnf(c_289,plain,
    positive_part(negative_part(X0)) = identity,
    inference(light_normalisation,[status(thm)],[c_288,c_257]) ).

cnf(c_297,plain,
    greatest_lower_bound(X0,positive_part(X0)) = X0,
    inference(superposition,[status(thm)],[c_52,c_64]) ).

cnf(c_298,plain,
    greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
    inference(superposition,[status(thm)],[c_58,c_64]) ).

cnf(c_302,plain,
    greatest_lower_bound(identity,positive_part(X0)) = identity,
    inference(superposition,[status(thm)],[c_261,c_64]) ).

cnf(c_305,plain,
    negative_part(least_upper_bound(identity,X0)) = identity,
    inference(superposition,[status(thm)],[c_64,c_257]) ).

cnf(c_306,plain,
    negative_part(positive_part(X0)) = identity,
    inference(light_normalisation,[status(thm)],[c_305,c_261]) ).

cnf(c_314,plain,
    inverse(multiply(identity,X0)) = multiply(inverse(X0),identity),
    inference(superposition,[status(thm)],[c_49,c_51]) ).

cnf(c_315,plain,
    inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
    inference(superposition,[status(thm)],[c_50,c_51]) ).

cnf(c_322,plain,
    multiply(inverse(X0),identity) = inverse(X0),
    inference(light_normalisation,[status(thm)],[c_314,c_69]) ).

cnf(c_370,plain,
    least_upper_bound(positive_part(X0),identity) = positive_part(X0),
    inference(superposition,[status(thm)],[c_306,c_265]) ).

cnf(c_372,plain,
    least_upper_bound(identity,positive_part(X0)) = positive_part(X0),
    inference(theory_normalisation,[status(thm)],[c_370,c_60,c_58,c_59,c_57]) ).

cnf(c_377,plain,
    greatest_lower_bound(negative_part(X0),identity) = negative_part(X0),
    inference(superposition,[status(thm)],[c_289,c_297]) ).

cnf(c_382,plain,
    greatest_lower_bound(identity,negative_part(X0)) = negative_part(X0),
    inference(theory_normalisation,[status(thm)],[c_377,c_60,c_58,c_59,c_57]) ).

cnf(c_409,plain,
    multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
    inference(superposition,[status(thm)],[c_70,c_71]) ).

cnf(c_419,plain,
    greatest_lower_bound(positive_part(X0),least_upper_bound(X0,X1)) = least_upper_bound(X0,greatest_lower_bound(identity,X1)),
    inference(superposition,[status(thm)],[c_52,c_54]) ).

cnf(c_474,plain,
    least_upper_bound(negative_part(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,least_upper_bound(identity,X1)),
    inference(superposition,[status(thm)],[c_53,c_55]) ).

cnf(c_491,plain,
    greatest_lower_bound(X0,least_upper_bound(X1,positive_part(X0))) = least_upper_bound(greatest_lower_bound(X0,X1),X0),
    inference(superposition,[status(thm)],[c_297,c_55]) ).

cnf(c_503,plain,
    greatest_lower_bound(X0,least_upper_bound(X1,positive_part(X0))) = least_upper_bound(X0,greatest_lower_bound(X0,X1)),
    inference(theory_normalisation,[status(thm)],[c_491,c_60,c_58,c_59,c_57]) ).

cnf(c_504,plain,
    greatest_lower_bound(X0,least_upper_bound(X1,positive_part(X0))) = X0,
    inference(light_normalisation,[status(thm)],[c_503,c_63]) ).

cnf(c_574,plain,
    greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) = X0,
    inference(superposition,[status(thm)],[c_60,c_298]) ).

cnf(c_580,plain,
    greatest_lower_bound(negative_part(X0),X0) = negative_part(X0),
    inference(superposition,[status(thm)],[c_265,c_298]) ).

cnf(c_591,plain,
    greatest_lower_bound(X0,negative_part(X0)) = negative_part(X0),
    inference(theory_normalisation,[status(thm)],[c_580,c_60,c_58,c_59,c_57]) ).

cnf(c_604,plain,
    multiply(X0,identity) = X0,
    inference(superposition,[status(thm)],[c_50,c_322]) ).

cnf(c_612,plain,
    least_upper_bound(X0,multiply(X0,X1)) = multiply(X0,least_upper_bound(identity,X1)),
    inference(superposition,[status(thm)],[c_604,c_65]) ).

cnf(c_647,plain,
    greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(identity,X1)),
    inference(superposition,[status(thm)],[c_604,c_66]) ).

cnf(c_685,plain,
    least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(identity,X1),X0),
    inference(superposition,[status(thm)],[c_69,c_67]) ).

cnf(c_686,plain,
    multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0)),
    inference(superposition,[status(thm)],[c_70,c_67]) ).

cnf(c_731,plain,
    greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
    inference(superposition,[status(thm)],[c_69,c_68]) ).

cnf(c_732,plain,
    multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)),
    inference(superposition,[status(thm)],[c_70,c_68]) ).

cnf(c_812,plain,
    negative_part(negative_part(X0)) = negative_part(X0),
    inference(superposition,[status(thm)],[c_382,c_257]) ).

cnf(c_850,plain,
    least_upper_bound(greatest_lower_bound(X0,X1),negative_part(X0)) = greatest_lower_bound(X0,least_upper_bound(X1,negative_part(X0))),
    inference(superposition,[status(thm)],[c_591,c_55]) ).

cnf(c_856,plain,
    least_upper_bound(negative_part(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,least_upper_bound(X1,negative_part(X0))),
    inference(theory_normalisation,[status(thm)],[c_850,c_60,c_58,c_59,c_57]) ).

cnf(c_857,plain,
    greatest_lower_bound(X0,least_upper_bound(X1,negative_part(X0))) = greatest_lower_bound(X0,least_upper_bound(identity,X1)),
    inference(light_normalisation,[status(thm)],[c_856,c_474]) ).

cnf(c_899,plain,
    greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,positive_part(X0)))) = X0,
    inference(superposition,[status(thm)],[c_60,c_504]) ).

cnf(c_1487,plain,
    greatest_lower_bound(greatest_lower_bound(X0,X1),least_upper_bound(X2,X0)) = greatest_lower_bound(X0,X1),
    inference(superposition,[status(thm)],[c_63,c_574]) ).

cnf(c_1525,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_1487,c_60,c_58,c_59,c_57]) ).

cnf(c_3921,plain,
    multiply(inverse(inverse(X0)),inverse(multiply(X1,X0))) = multiply(identity,inverse(X1)),
    inference(superposition,[status(thm)],[c_51,c_409]) ).

cnf(c_3943,plain,
    multiply(X0,inverse(multiply(X1,X0))) = multiply(identity,inverse(X1)),
    inference(light_normalisation,[status(thm)],[c_3921,c_50]) ).

cnf(c_4110,plain,
    greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X3,positive_part(X0))))) = X0,
    inference(superposition,[status(thm)],[c_60,c_899]) ).

cnf(c_5693,plain,
    multiply(inverse(X0),least_upper_bound(identity,X0)) = least_upper_bound(inverse(X0),identity),
    inference(superposition,[status(thm)],[c_70,c_612]) ).

cnf(c_5727,plain,
    multiply(inverse(X0),least_upper_bound(identity,X0)) = least_upper_bound(identity,inverse(X0)),
    inference(theory_normalisation,[status(thm)],[c_5693,c_60,c_58,c_59,c_57]) ).

cnf(c_5728,plain,
    multiply(inverse(X0),positive_part(X0)) = least_upper_bound(identity,inverse(X0)),
    inference(light_normalisation,[status(thm)],[c_5727,c_261]) ).

cnf(c_5761,plain,
    multiply(X0,positive_part(inverse(X0))) = least_upper_bound(identity,X0),
    inference(superposition,[status(thm)],[c_50,c_5728]) ).

cnf(c_5765,plain,
    multiply(inverse(negative_part(X0)),identity) = least_upper_bound(identity,inverse(negative_part(X0))),
    inference(superposition,[status(thm)],[c_289,c_5728]) ).

cnf(c_5785,plain,
    multiply(X0,positive_part(inverse(X0))) = positive_part(X0),
    inference(light_normalisation,[status(thm)],[c_5761,c_261]) ).

cnf(c_5858,plain,
    multiply(inverse(X0),positive_part(X0)) = positive_part(inverse(X0)),
    inference(superposition,[status(thm)],[c_50,c_5785]) ).

cnf(c_5867,plain,
    multiply(X0,multiply(positive_part(inverse(X0)),X1)) = multiply(positive_part(X0),X1),
    inference(superposition,[status(thm)],[c_5785,c_71]) ).

cnf(c_6024,plain,
    multiply(inverse(negative_part(X0)),identity) = positive_part(inverse(negative_part(X0))),
    inference(superposition,[status(thm)],[c_289,c_5858]) ).

cnf(c_6177,plain,
    multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(inverse(X0),identity),
    inference(superposition,[status(thm)],[c_70,c_647]) ).

cnf(c_6213,plain,
    multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)),
    inference(theory_normalisation,[status(thm)],[c_6177,c_60,c_58,c_59,c_57]) ).

cnf(c_6214,plain,
    multiply(inverse(X0),negative_part(X0)) = greatest_lower_bound(identity,inverse(X0)),
    inference(light_normalisation,[status(thm)],[c_6213,c_257]) ).

cnf(c_6262,plain,
    multiply(X0,negative_part(inverse(X0))) = greatest_lower_bound(identity,X0),
    inference(superposition,[status(thm)],[c_50,c_6214]) ).

cnf(c_6289,plain,
    multiply(X0,negative_part(inverse(X0))) = negative_part(X0),
    inference(light_normalisation,[status(thm)],[c_6262,c_257]) ).

cnf(c_6487,plain,
    multiply(inverse(X0),negative_part(X0)) = negative_part(inverse(X0)),
    inference(superposition,[status(thm)],[c_50,c_6289]) ).

cnf(c_6506,plain,
    multiply(inverse(negative_part(inverse(inverse(X0)))),X0) = inverse(negative_part(inverse(X0))),
    inference(superposition,[status(thm)],[c_6289,c_315]) ).

cnf(c_6510,plain,
    multiply(inverse(negative_part(X0)),X0) = inverse(negative_part(inverse(X0))),
    inference(light_normalisation,[status(thm)],[c_6506,c_50]) ).

cnf(c_6543,plain,
    multiply(inverse(negative_part(X0)),negative_part(X0)) = negative_part(inverse(negative_part(X0))),
    inference(superposition,[status(thm)],[c_812,c_6487]) ).

cnf(c_7012,plain,
    multiply(greatest_lower_bound(identity,X0),positive_part(inverse(X0))) = greatest_lower_bound(positive_part(inverse(X0)),positive_part(X0)),
    inference(superposition,[status(thm)],[c_5785,c_731]) ).

cnf(c_7060,plain,
    multiply(greatest_lower_bound(identity,X0),positive_part(inverse(X0))) = greatest_lower_bound(positive_part(X0),positive_part(inverse(X0))),
    inference(theory_normalisation,[status(thm)],[c_7012,c_60,c_58,c_59,c_57]) ).

cnf(c_7061,plain,
    multiply(negative_part(X0),positive_part(inverse(X0))) = greatest_lower_bound(positive_part(X0),positive_part(inverse(X0))),
    inference(light_normalisation,[status(thm)],[c_7060,c_257]) ).

cnf(c_8670,plain,
    multiply(positive_part(X0),inverse(positive_part(inverse(X0)))) = multiply(identity,inverse(inverse(X0))),
    inference(superposition,[status(thm)],[c_5858,c_3943]) ).

cnf(c_8672,plain,
    multiply(negative_part(X0),inverse(negative_part(inverse(X0)))) = multiply(identity,inverse(inverse(X0))),
    inference(superposition,[status(thm)],[c_6487,c_3943]) ).

cnf(c_8707,plain,
    multiply(negative_part(X0),inverse(negative_part(inverse(X0)))) = X0,
    inference(light_normalisation,[status(thm)],[c_8672,c_50,c_69]) ).

cnf(c_8708,plain,
    multiply(positive_part(X0),inverse(positive_part(inverse(X0)))) = X0,
    inference(light_normalisation,[status(thm)],[c_8670,c_50,c_69]) ).

cnf(c_8922,plain,
    multiply(greatest_lower_bound(identity,negative_part(X0)),inverse(negative_part(inverse(X0)))) = greatest_lower_bound(inverse(negative_part(inverse(X0))),X0),
    inference(superposition,[status(thm)],[c_8707,c_731]) ).

cnf(c_8947,plain,
    multiply(greatest_lower_bound(identity,negative_part(X0)),inverse(negative_part(inverse(X0)))) = greatest_lower_bound(X0,inverse(negative_part(inverse(X0)))),
    inference(theory_normalisation,[status(thm)],[c_8922,c_60,c_58,c_59,c_57]) ).

cnf(c_8948,plain,
    greatest_lower_bound(X0,inverse(negative_part(inverse(X0)))) = X0,
    inference(light_normalisation,[status(thm)],[c_8947,c_382,c_8707]) ).

cnf(c_9004,plain,
    greatest_lower_bound(X0,greatest_lower_bound(inverse(negative_part(inverse(X0))),X1)) = greatest_lower_bound(X0,X1),
    inference(superposition,[status(thm)],[c_8948,c_59]) ).

cnf(c_9081,plain,
    multiply(least_upper_bound(identity,positive_part(X0)),inverse(positive_part(inverse(X0)))) = least_upper_bound(inverse(positive_part(inverse(X0))),X0),
    inference(superposition,[status(thm)],[c_8708,c_685]) ).

cnf(c_9099,plain,
    multiply(least_upper_bound(identity,positive_part(X0)),inverse(positive_part(inverse(X0)))) = least_upper_bound(X0,inverse(positive_part(inverse(X0)))),
    inference(theory_normalisation,[status(thm)],[c_9081,c_60,c_58,c_59,c_57]) ).

cnf(c_9100,plain,
    least_upper_bound(X0,inverse(positive_part(inverse(X0)))) = X0,
    inference(light_normalisation,[status(thm)],[c_9099,c_372,c_8708]) ).

cnf(c_9136,plain,
    least_upper_bound(inverse(X0),inverse(positive_part(X0))) = inverse(X0),
    inference(superposition,[status(thm)],[c_50,c_9100]) ).

cnf(c_9265,plain,
    least_upper_bound(inverse(negative_part(X0)),inverse(identity)) = inverse(negative_part(X0)),
    inference(superposition,[status(thm)],[c_289,c_9136]) ).

cnf(c_9294,plain,
    least_upper_bound(inverse(identity),inverse(negative_part(X0))) = inverse(negative_part(X0)),
    inference(theory_normalisation,[status(thm)],[c_9265,c_60,c_58,c_59,c_57]) ).

cnf(c_9295,plain,
    positive_part(inverse(negative_part(X0))) = inverse(negative_part(X0)),
    inference(light_normalisation,[status(thm)],[c_9294,c_49,c_5765,c_6024]) ).

cnf(c_9708,plain,
    negative_part(inverse(negative_part(X0))) = identity,
    inference(superposition,[status(thm)],[c_9295,c_306]) ).

cnf(c_12242,plain,
    greatest_lower_bound(X0,least_upper_bound(X1,greatest_lower_bound(identity,X0))) = greatest_lower_bound(X0,positive_part(X1)),
    inference(superposition,[status(thm)],[c_419,c_1525]) ).

cnf(c_12262,plain,
    greatest_lower_bound(X0,least_upper_bound(identity,X1)) = greatest_lower_bound(X0,positive_part(X1)),
    inference(light_normalisation,[status(thm)],[c_12242,c_257,c_857]) ).

cnf(c_12800,plain,
    least_upper_bound(negative_part(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,positive_part(X1)),
    inference(light_normalisation,[status(thm)],[c_474,c_12262]) ).

cnf(c_12824,plain,
    least_upper_bound(negative_part(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(X0,positive_part(X1)),
    inference(superposition,[status(thm)],[c_57,c_12800]) ).

cnf(c_15083,plain,
    multiply(positive_part(inverse(X0)),X0) = least_upper_bound(identity,multiply(identity,X0)),
    inference(superposition,[status(thm)],[c_52,c_686]) ).

cnf(c_15091,plain,
    least_upper_bound(identity,multiply(negative_part(inverse(X0)),X0)) = multiply(inverse(X0),X0),
    inference(superposition,[status(thm)],[c_265,c_686]) ).

cnf(c_15152,plain,
    multiply(positive_part(inverse(X0)),X0) = positive_part(X0),
    inference(light_normalisation,[status(thm)],[c_15083,c_69,c_261]) ).

cnf(c_15154,plain,
    least_upper_bound(identity,multiply(negative_part(inverse(X0)),X0)) = identity,
    inference(light_normalisation,[status(thm)],[c_15091,c_70]) ).

cnf(c_15234,plain,
    multiply(positive_part(inverse(X0)),greatest_lower_bound(identity,X0)) = greatest_lower_bound(positive_part(inverse(X0)),positive_part(X0)),
    inference(superposition,[status(thm)],[c_15152,c_647]) ).

cnf(c_15242,plain,
    multiply(positive_part(inverse(X0)),multiply(X0,X1)) = multiply(positive_part(X0),X1),
    inference(superposition,[status(thm)],[c_15152,c_71]) ).

cnf(c_15276,plain,
    multiply(positive_part(inverse(X0)),greatest_lower_bound(identity,X0)) = greatest_lower_bound(positive_part(X0),positive_part(inverse(X0))),
    inference(theory_normalisation,[status(thm)],[c_15234,c_60,c_58,c_59,c_57]) ).

cnf(c_15277,plain,
    multiply(positive_part(inverse(X0)),negative_part(X0)) = multiply(negative_part(X0),positive_part(inverse(X0))),
    inference(light_normalisation,[status(thm)],[c_15276,c_257,c_7061]) ).

cnf(c_16128,plain,
    least_upper_bound(identity,greatest_lower_bound(X0,multiply(negative_part(inverse(X1)),X1))) = greatest_lower_bound(least_upper_bound(identity,X0),identity),
    inference(superposition,[status(thm)],[c_15154,c_54]) ).

cnf(c_16163,plain,
    least_upper_bound(identity,greatest_lower_bound(X0,multiply(negative_part(inverse(X1)),X1))) = greatest_lower_bound(identity,least_upper_bound(identity,X0)),
    inference(theory_normalisation,[status(thm)],[c_16128,c_60,c_58,c_59,c_57]) ).

cnf(c_16164,plain,
    least_upper_bound(identity,greatest_lower_bound(X0,multiply(negative_part(inverse(X1)),X1))) = identity,
    inference(light_normalisation,[status(thm)],[c_16163,c_261,c_302]) ).

cnf(c_16586,plain,
    least_upper_bound(identity,greatest_lower_bound(multiply(negative_part(inverse(X0)),X0),X1)) = identity,
    inference(superposition,[status(thm)],[c_57,c_16164]) ).

cnf(c_16698,plain,
    least_upper_bound(identity,multiply(negative_part(inverse(X0)),greatest_lower_bound(X0,X1))) = identity,
    inference(superposition,[status(thm)],[c_66,c_16586]) ).

cnf(c_17393,plain,
    least_upper_bound(identity,multiply(negative_part(X0),greatest_lower_bound(inverse(X0),X1))) = identity,
    inference(superposition,[status(thm)],[c_50,c_16698]) ).

cnf(c_19014,plain,
    multiply(negative_part(inverse(X0)),X0) = greatest_lower_bound(identity,multiply(identity,X0)),
    inference(superposition,[status(thm)],[c_53,c_732]) ).

cnf(c_19086,plain,
    multiply(negative_part(inverse(X0)),X0) = negative_part(X0),
    inference(light_normalisation,[status(thm)],[c_19014,c_69,c_257]) ).

cnf(c_19172,plain,
    multiply(negative_part(X0),inverse(X0)) = negative_part(inverse(X0)),
    inference(superposition,[status(thm)],[c_50,c_19086]) ).

cnf(c_20941,plain,
    greatest_lower_bound(inverse(negative_part(X0)),inverse(negative_part(inverse(X0)))) = multiply(inverse(negative_part(X0)),greatest_lower_bound(identity,X0)),
    inference(superposition,[status(thm)],[c_6510,c_647]) ).

cnf(c_20988,plain,
    greatest_lower_bound(inverse(negative_part(X0)),inverse(negative_part(inverse(X0)))) = identity,
    inference(light_normalisation,[status(thm)],[c_20941,c_257,c_6543,c_9708]) ).

cnf(c_21322,plain,
    least_upper_bound(identity,multiply(negative_part(X0),inverse(X0))) = identity,
    inference(superposition,[status(thm)],[c_4110,c_17393]) ).

cnf(c_21332,plain,
    least_upper_bound(identity,negative_part(inverse(X0))) = identity,
    inference(light_normalisation,[status(thm)],[c_21322,c_19172]) ).

cnf(c_22150,plain,
    greatest_lower_bound(X0,greatest_lower_bound(X1,inverse(negative_part(inverse(X0))))) = greatest_lower_bound(X0,X1),
    inference(superposition,[status(thm)],[c_57,c_9004]) ).

cnf(c_24639,plain,
    multiply(positive_part(inverse(inverse(X0))),negative_part(inverse(X0))) = multiply(positive_part(inverse(X0)),negative_part(X0)),
    inference(superposition,[status(thm)],[c_6487,c_15242]) ).

cnf(c_24694,plain,
    multiply(positive_part(X0),negative_part(inverse(X0))) = multiply(negative_part(X0),positive_part(inverse(X0))),
    inference(light_normalisation,[status(thm)],[c_24639,c_50,c_15277]) ).

cnf(c_53258,plain,
    greatest_lower_bound(X0,inverse(negative_part(X0))) = greatest_lower_bound(X0,identity),
    inference(superposition,[status(thm)],[c_20988,c_22150]) ).

cnf(c_53261,plain,
    greatest_lower_bound(X0,inverse(negative_part(X0))) = negative_part(X0),
    inference(light_normalisation,[status(thm)],[c_53258,c_53]) ).

cnf(c_53497,plain,
    least_upper_bound(negative_part(inverse(negative_part(X0))),negative_part(X0)) = greatest_lower_bound(inverse(negative_part(X0)),positive_part(X0)),
    inference(superposition,[status(thm)],[c_53261,c_12824]) ).

cnf(c_53625,plain,
    least_upper_bound(negative_part(X0),negative_part(inverse(negative_part(X0)))) = greatest_lower_bound(positive_part(X0),inverse(negative_part(X0))),
    inference(theory_normalisation,[status(thm)],[c_53497,c_60,c_58,c_59,c_57]) ).

cnf(c_53626,plain,
    greatest_lower_bound(positive_part(X0),inverse(negative_part(X0))) = least_upper_bound(negative_part(X0),identity),
    inference(light_normalisation,[status(thm)],[c_53625,c_9708]) ).

cnf(c_53627,plain,
    greatest_lower_bound(positive_part(X0),inverse(negative_part(X0))) = least_upper_bound(identity,negative_part(X0)),
    inference(theory_normalisation,[status(thm)],[c_53626,c_60,c_58,c_59,c_57]) ).

cnf(c_53628,plain,
    greatest_lower_bound(positive_part(X0),inverse(negative_part(X0))) = identity,
    inference(light_normalisation,[status(thm)],[c_53627,c_277]) ).

cnf(c_53815,plain,
    greatest_lower_bound(X0,positive_part(inverse(X0))) = greatest_lower_bound(X0,identity),
    inference(superposition,[status(thm)],[c_53628,c_22150]) ).

cnf(c_53825,plain,
    greatest_lower_bound(X0,positive_part(inverse(X0))) = negative_part(X0),
    inference(light_normalisation,[status(thm)],[c_53815,c_53]) ).

cnf(c_55545,plain,
    greatest_lower_bound(inverse(X0),positive_part(X0)) = negative_part(inverse(X0)),
    inference(superposition,[status(thm)],[c_50,c_53825]) ).

cnf(c_56114,plain,
    least_upper_bound(negative_part(positive_part(X0)),negative_part(inverse(X0))) = greatest_lower_bound(positive_part(X0),positive_part(inverse(X0))),
    inference(superposition,[status(thm)],[c_55545,c_12824]) ).

cnf(c_56174,plain,
    least_upper_bound(negative_part(inverse(X0)),negative_part(positive_part(X0))) = greatest_lower_bound(positive_part(X0),positive_part(inverse(X0))),
    inference(theory_normalisation,[status(thm)],[c_56114,c_60,c_58,c_59,c_57]) ).

cnf(c_56175,plain,
    multiply(positive_part(X0),negative_part(inverse(X0))) = least_upper_bound(negative_part(inverse(X0)),identity),
    inference(light_normalisation,[status(thm)],[c_56174,c_306,c_7061,c_24694]) ).

cnf(c_56176,plain,
    multiply(positive_part(X0),negative_part(inverse(X0))) = least_upper_bound(identity,negative_part(inverse(X0))),
    inference(theory_normalisation,[status(thm)],[c_56175,c_60,c_58,c_59,c_57]) ).

cnf(c_56177,plain,
    multiply(positive_part(X0),negative_part(inverse(X0))) = identity,
    inference(light_normalisation,[status(thm)],[c_56176,c_21332]) ).

cnf(c_56776,plain,
    multiply(positive_part(X0),negative_part(inverse(inverse(X0)))) = multiply(X0,identity),
    inference(superposition,[status(thm)],[c_56177,c_5867]) ).

cnf(c_56790,plain,
    multiply(positive_part(X0),negative_part(X0)) = X0,
    inference(light_normalisation,[status(thm)],[c_56776,c_50,c_604]) ).

cnf(c_56836,plain,
    a != a,
    inference(demodulation,[status(thm)],[c_56,c_56790]) ).

cnf(c_56837,plain,
    $false,
    inference(equality_resolution_simp,[status(thm)],[c_56836]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : GRP167-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.12  % Command  : run_iprover %s %d THM
% 0.13/0.33  % Computer : n023.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Mon Aug 28 19:56:10 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.19/0.45  Running UEQ theorem proving
% 0.19/0.45  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule casc_29_ueq --heuristic_context ueq --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.12/2.65  % SZS status Started for theBenchmark.p
% 16.12/2.65  % SZS status Unsatisfiable for theBenchmark.p
% 16.12/2.65  
% 16.12/2.65  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 16.12/2.65  
% 16.12/2.65  ------  iProver source info
% 16.12/2.65  
% 16.12/2.65  git: date: 2023-05-31 18:12:56 +0000
% 16.12/2.65  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 16.12/2.65  git: non_committed_changes: false
% 16.12/2.65  git: last_make_outside_of_git: false
% 16.12/2.65  
% 16.12/2.65  ------ Parsing...successful
% 16.12/2.65  
% 16.12/2.65  
% 16.12/2.65  
% 16.12/2.65  ------ Preprocessing... sup_sim: 0  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 16.12/2.65  
% 16.12/2.65  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 16.12/2.65  
% 16.12/2.65  ------ Preprocessing... sf_s  rm: 0 0s  sf_e 
% 16.12/2.65  ------ Proving...
% 16.12/2.65  ------ Problem Properties 
% 16.12/2.65  
% 16.12/2.65  
% 16.12/2.65  clauses                                 23
% 16.12/2.65  conjectures                             1
% 16.12/2.65  EPR                                     0
% 16.12/2.65  Horn                                    23
% 16.12/2.65  unary                                   23
% 16.12/2.65  binary                                  0
% 16.12/2.65  lits                                    23
% 16.12/2.65  lits eq                                 23
% 16.12/2.65  fd_pure                                 0
% 16.12/2.65  fd_pseudo                               0
% 16.12/2.65  fd_cond                                 0
% 16.12/2.65  fd_pseudo_cond                          0
% 16.12/2.65  AC symbols                              2
% 16.12/2.65  
% 16.12/2.65  ------ Input Options Time Limit: Unbounded
% 16.12/2.65  
% 16.12/2.65  
% 16.12/2.65  ------ 
% 16.12/2.65  Current options:
% 16.12/2.65  ------ 
% 16.12/2.65  
% 16.12/2.65  
% 16.12/2.65  
% 16.12/2.65  
% 16.12/2.65  ------ Proving...
% 16.12/2.65  
% 16.12/2.65  
% 16.12/2.65  % SZS status Unsatisfiable for theBenchmark.p
% 16.12/2.65  
% 16.12/2.65  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.12/2.65  
% 16.12/2.65  
%------------------------------------------------------------------------------