TSTP Solution File: GRP167-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP167-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n011.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 : Tue Aug 22 10:40:21 EDT 2023

% Result   : Unsatisfiable 246.07s 209.19s
% Output   : CNFRefutation 246.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  128 ( 120 unt;   8 typ;   0 def)
%            Number of atoms       :  120 ( 119 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            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   :  186 (; 186   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > least_upper_bound > greatest_lower_bound > #nlpp > positive_part > negative_part > inverse > identity > a

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(a,type,
    a: $i ).

tff(inverse,type,
    inverse: $i > $i ).

tff(greatest_lower_bound,type,
    greatest_lower_bound: ( $i * $i ) > $i ).

tff(least_upper_bound,type,
    least_upper_bound: ( $i * $i ) > $i ).

tff(multiply,type,
    multiply: ( $i * $i ) > $i ).

tff(negative_part,type,
    negative_part: $i > $i ).

tff(positive_part,type,
    positive_part: $i > $i ).

tff(identity,type,
    identity: $i ).

tff(f_118,axiom,
    ! [X] : ( inverse(inverse(X)) = X ),
    file(unknown,unknown) ).

tff(f_57,axiom,
    ! [X] : ( multiply(identity,X) = X ),
    file(unknown,unknown) ).

tff(f_92,axiom,
    ! [X,Y] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
    file(unknown,unknown) ).

tff(f_122,axiom,
    ! [X] : ( positive_part(X) = least_upper_bound(X,identity) ),
    file(unknown,unknown) ).

tff(f_90,axiom,
    ! [X,Y] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
    file(unknown,unknown) ).

tff(f_124,axiom,
    ! [X] : ( negative_part(X) = greatest_lower_bound(X,identity) ),
    file(unknown,unknown) ).

tff(f_104,axiom,
    ! [X,Y] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
    file(unknown,unknown) ).

tff(f_61,axiom,
    ! [X] : ( multiply(inverse(X),X) = identity ),
    file(unknown,unknown) ).

tff(f_113,axiom,
    ! [Y,Z,X] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
    file(unknown,unknown) ).

tff(f_116,axiom,
    inverse(identity) = identity,
    file(unknown,unknown) ).

tff(f_120,axiom,
    ! [X,Y] : ( inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ),
    file(unknown,unknown) ).

tff(f_111,axiom,
    ! [Y,Z,X] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
    file(unknown,unknown) ).

tff(f_64,axiom,
    ! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
    file(unknown,unknown) ).

tff(f_109,axiom,
    ! [X,Y,Z] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
    file(unknown,unknown) ).

tff(f_94,axiom,
    ! [X,Y,Z] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
    file(unknown,unknown) ).

tff(f_102,axiom,
    ! [X,Y] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
    file(unknown,unknown) ).

tff(f_128,axiom,
    ! [X,Y,Z] : ( greatest_lower_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z)) ),
    file(unknown,unknown) ).

tff(f_100,axiom,
    ! [X] : ( greatest_lower_bound(X,X) = X ),
    file(unknown,unknown) ).

tff(f_130,axiom,
    a != multiply(positive_part(a),negative_part(a)),
    file(unknown,unknown) ).

tff(c_34,plain,
    ! [X_34] : ( inverse(inverse(X_34)) = X_34 ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_2,plain,
    ! [X_1] : ( multiply(identity,X_1) = X_1 ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_182,plain,
    ! [Y_53,X_54] : ( least_upper_bound(Y_53,X_54) = least_upper_bound(X_54,Y_53) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_38,plain,
    ! [X_37] : ( least_upper_bound(X_37,identity) = positive_part(X_37) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_198,plain,
    ! [X_54] : ( least_upper_bound(identity,X_54) = positive_part(X_54) ),
    inference(superposition,[status(thm),theory(equality)],[c_182,c_38]) ).

tff(c_279,plain,
    ! [Y_56,X_57] : ( greatest_lower_bound(Y_56,X_57) = greatest_lower_bound(X_57,Y_56) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_40,plain,
    ! [X_38] : ( greatest_lower_bound(X_38,identity) = negative_part(X_38) ),
    inference(cnfTransformation,[status(thm)],[f_124]) ).

tff(c_295,plain,
    ! [X_57] : ( greatest_lower_bound(identity,X_57) = negative_part(X_57) ),
    inference(superposition,[status(thm),theory(equality)],[c_279,c_40]) ).

tff(c_376,plain,
    ! [X_59,Y_60] : ( greatest_lower_bound(X_59,least_upper_bound(X_59,Y_60)) = X_59 ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_390,plain,
    ! [Y_60] : ( negative_part(least_upper_bound(identity,Y_60)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_295,c_376]) ).

tff(c_409,plain,
    ! [Y_60] : ( negative_part(positive_part(Y_60)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_198,c_390]) ).

tff(c_138,plain,
    ! [X_51] : ( multiply(inverse(X_51),X_51) = identity ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_145,plain,
    ! [X_34] : ( multiply(X_34,inverse(X_34)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_34,c_138]) ).

tff(c_1510,plain,
    ! [Y_95,X_96,Z_97] : ( greatest_lower_bound(multiply(Y_95,X_96),multiply(Z_97,X_96)) = multiply(greatest_lower_bound(Y_95,Z_97),X_96) ),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_1581,plain,
    ! [Y_95,X_1] : ( multiply(greatest_lower_bound(Y_95,identity),X_1) = greatest_lower_bound(multiply(Y_95,X_1),X_1) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_1510]) ).

tff(c_12057,plain,
    ! [Y_230,X_231] : ( multiply(negative_part(Y_230),X_231) = greatest_lower_bound(multiply(Y_230,X_231),X_231) ),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_1581]) ).

tff(c_12257,plain,
    ! [X_34] : ( multiply(negative_part(X_34),inverse(X_34)) = greatest_lower_bound(identity,inverse(X_34)) ),
    inference(superposition,[status(thm),theory(equality)],[c_145,c_12057]) ).

tff(c_13051,plain,
    ! [X_238] : ( multiply(negative_part(X_238),inverse(X_238)) = negative_part(inverse(X_238)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_295,c_12257]) ).

tff(c_13126,plain,
    ! [Y_60] : ( multiply(identity,inverse(positive_part(Y_60))) = negative_part(inverse(positive_part(Y_60))) ),
    inference(superposition,[status(thm),theory(equality)],[c_409,c_13051]) ).

tff(c_13149,plain,
    ! [Y_60] : ( negative_part(inverse(positive_part(Y_60))) = inverse(positive_part(Y_60)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_13126]) ).

tff(c_32,plain,
    inverse(identity) = identity,
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_481,plain,
    ! [Y_65,X_66] : ( multiply(inverse(Y_65),inverse(X_66)) = inverse(multiply(X_66,Y_65)) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_515,plain,
    ! [Y_65] : ( multiply(inverse(Y_65),identity) = inverse(multiply(identity,Y_65)) ),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_481]) ).

tff(c_894,plain,
    ! [Y_78] : ( multiply(inverse(Y_78),identity) = inverse(Y_78) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_515]) ).

tff(c_911,plain,
    ! [X_34] : ( inverse(inverse(X_34)) = multiply(X_34,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_34,c_894]) ).

tff(c_919,plain,
    ! [X_34] : ( multiply(X_34,identity) = X_34 ),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_911]) ).

tff(c_8,plain,
    ! [Y_7,X_6] : ( greatest_lower_bound(Y_7,X_6) = greatest_lower_bound(X_6,Y_7) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_4,plain,
    ! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_1699,plain,
    ! [Y_100,X_101,Z_102] : ( least_upper_bound(multiply(Y_100,X_101),multiply(Z_102,X_101)) = multiply(least_upper_bound(Y_100,Z_102),X_101) ),
    inference(cnfTransformation,[status(thm)],[f_111]) ).

tff(c_1771,plain,
    ! [Z_102,X_1] : ( multiply(least_upper_bound(identity,Z_102),X_1) = least_upper_bound(X_1,multiply(Z_102,X_1)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_1699]) ).

tff(c_9803,plain,
    ! [Z_207,X_208] : ( multiply(positive_part(Z_207),X_208) = least_upper_bound(X_208,multiply(Z_207,X_208)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_198,c_1771]) ).

tff(c_9955,plain,
    ! [X_2] : ( multiply(positive_part(inverse(X_2)),X_2) = least_upper_bound(X_2,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_9803]) ).

tff(c_9976,plain,
    ! [X_2] : ( multiply(positive_part(inverse(X_2)),X_2) = positive_part(X_2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_9955]) ).

tff(c_921,plain,
    ! [X_79,Y_80,Z_81] : ( multiply(multiply(X_79,Y_80),Z_81) = multiply(X_79,multiply(Y_80,Z_81)) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_953,plain,
    ! [X_2,Z_81] : ( multiply(inverse(X_2),multiply(X_2,Z_81)) = multiply(identity,Z_81) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_921]) ).

tff(c_963,plain,
    ! [X_2,Z_81] : ( multiply(inverse(X_2),multiply(X_2,Z_81)) = Z_81 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_953]) ).

tff(c_14638,plain,
    ! [X_252,Y_253] : ( inverse(multiply(inverse(X_252),Y_253)) = multiply(inverse(Y_253),X_252) ),
    inference(superposition,[status(thm),theory(equality)],[c_34,c_481]) ).

tff(c_14919,plain,
    ! [X_256,Z_257] : ( multiply(inverse(multiply(X_256,Z_257)),X_256) = inverse(Z_257) ),
    inference(superposition,[status(thm),theory(equality)],[c_963,c_14638]) ).

tff(c_15034,plain,
    ! [X_2] : ( multiply(inverse(positive_part(X_2)),positive_part(inverse(X_2))) = inverse(X_2) ),
    inference(superposition,[status(thm),theory(equality)],[c_9976,c_14919]) ).

tff(c_2559,plain,
    ! [X_116,Y_117,Z_118] : ( greatest_lower_bound(multiply(X_116,Y_117),multiply(X_116,Z_118)) = multiply(X_116,greatest_lower_bound(Y_117,Z_118)) ),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_2607,plain,
    ! [X_34,Z_118] : ( multiply(X_34,greatest_lower_bound(identity,Z_118)) = greatest_lower_bound(X_34,multiply(X_34,Z_118)) ),
    inference(superposition,[status(thm),theory(equality)],[c_919,c_2559]) ).

tff(c_238557,plain,
    ! [X_996,Z_997] : ( multiply(X_996,negative_part(Z_997)) = greatest_lower_bound(X_996,multiply(X_996,Z_997)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_295,c_2607]) ).

tff(c_239323,plain,
    ! [X_2] : ( multiply(inverse(positive_part(X_2)),negative_part(positive_part(inverse(X_2)))) = greatest_lower_bound(inverse(positive_part(X_2)),inverse(X_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_15034,c_238557]) ).

tff(c_239719,plain,
    ! [X_2] : ( greatest_lower_bound(inverse(X_2),inverse(positive_part(X_2))) = inverse(positive_part(X_2)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_919,c_409,c_8,c_239323]) ).

tff(c_655,plain,
    ! [X_71,Y_72,Z_73] : ( greatest_lower_bound(greatest_lower_bound(X_71,Y_72),Z_73) = greatest_lower_bound(X_71,greatest_lower_bound(Y_72,Z_73)) ),
    inference(cnfTransformation,[status(thm)],[f_94]) ).

tff(c_682,plain,
    ! [X_71,Y_72] : ( greatest_lower_bound(X_71,greatest_lower_bound(Y_72,identity)) = negative_part(greatest_lower_bound(X_71,Y_72)) ),
    inference(superposition,[status(thm),theory(equality)],[c_655,c_40]) ).

tff(c_743,plain,
    ! [X_71,Y_72] : ( greatest_lower_bound(X_71,negative_part(Y_72)) = negative_part(greatest_lower_bound(X_71,Y_72)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_682]) ).

tff(c_411,plain,
    ! [X_61,Y_62] : ( least_upper_bound(X_61,greatest_lower_bound(X_61,Y_62)) = X_61 ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_421,plain,
    ! [Y_62] : ( positive_part(greatest_lower_bound(identity,Y_62)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_411,c_198]) ).

tff(c_449,plain,
    ! [Y_62] : ( positive_part(negative_part(Y_62)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_295,c_421]) ).

tff(c_9952,plain,
    ! [X_34] : ( multiply(positive_part(X_34),inverse(X_34)) = least_upper_bound(inverse(X_34),identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_145,c_9803]) ).

tff(c_10580,plain,
    ! [X_218] : ( multiply(positive_part(X_218),inverse(X_218)) = positive_part(inverse(X_218)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_9952]) ).

tff(c_10643,plain,
    ! [Y_62] : ( multiply(identity,inverse(negative_part(Y_62))) = positive_part(inverse(negative_part(Y_62))) ),
    inference(superposition,[status(thm),theory(equality)],[c_449,c_10580]) ).

tff(c_11033,plain,
    ! [Y_222] : ( positive_part(inverse(negative_part(Y_222))) = inverse(negative_part(Y_222)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_10643]) ).

tff(c_11106,plain,
    ! [Y_222] : ( negative_part(inverse(negative_part(Y_222))) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_11033,c_409]) ).

tff(c_2637,plain,
    ! [X_2,Z_118] : ( multiply(inverse(X_2),greatest_lower_bound(X_2,Z_118)) = greatest_lower_bound(identity,multiply(inverse(X_2),Z_118)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_2559]) ).

tff(c_53504,plain,
    ! [X_456,Z_457] : ( multiply(inverse(X_456),greatest_lower_bound(X_456,Z_457)) = negative_part(multiply(inverse(X_456),Z_457)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_295,c_2637]) ).

tff(c_53809,plain,
    ! [X_38] : ( multiply(inverse(X_38),negative_part(X_38)) = negative_part(multiply(inverse(X_38),identity)) ),
    inference(superposition,[status(thm),theory(equality)],[c_40,c_53504]) ).

tff(c_54145,plain,
    ! [X_459] : ( multiply(inverse(X_459),negative_part(X_459)) = negative_part(inverse(X_459)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_919,c_53809]) ).

tff(c_36,plain,
    ! [Y_36,X_35] : ( multiply(inverse(Y_36),inverse(X_35)) = inverse(multiply(X_35,Y_36)) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_2739,plain,
    ! [X_120,Z_121] : ( multiply(inverse(X_120),multiply(X_120,Z_121)) = Z_121 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_953]) ).

tff(c_2787,plain,
    ! [Y_36,X_35] : ( multiply(inverse(inverse(Y_36)),inverse(multiply(X_35,Y_36))) = inverse(X_35) ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_2739]) ).

tff(c_2809,plain,
    ! [Y_36,X_35] : ( multiply(Y_36,inverse(multiply(X_35,Y_36))) = inverse(X_35) ),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_2787]) ).

tff(c_54172,plain,
    ! [X_459] : ( multiply(negative_part(X_459),inverse(negative_part(inverse(X_459)))) = inverse(inverse(X_459)) ),
    inference(superposition,[status(thm),theory(equality)],[c_54145,c_2809]) ).

tff(c_54294,plain,
    ! [X_459] : ( multiply(negative_part(X_459),inverse(negative_part(inverse(X_459)))) = X_459 ),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_54172]) ).

tff(c_525,plain,
    ! [X_67] : ( greatest_lower_bound(X_67,positive_part(X_67)) = X_67 ),
    inference(superposition,[status(thm),theory(equality)],[c_38,c_376]) ).

tff(c_1358,plain,
    ! [Y_92] : ( greatest_lower_bound(negative_part(Y_92),identity) = negative_part(Y_92) ),
    inference(superposition,[status(thm),theory(equality)],[c_449,c_525]) ).

tff(c_1383,plain,
    ! [Y_92] : ( negative_part(negative_part(Y_92)) = negative_part(Y_92) ),
    inference(superposition,[status(thm),theory(equality)],[c_1358,c_40]) ).

tff(c_54503,plain,
    ! [X_461] : ( multiply(negative_part(X_461),inverse(negative_part(inverse(X_461)))) = X_461 ),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_54172]) ).

tff(c_1578,plain,
    ! [Z_97,X_1] : ( multiply(greatest_lower_bound(identity,Z_97),X_1) = greatest_lower_bound(X_1,multiply(Z_97,X_1)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_1510]) ).

tff(c_1592,plain,
    ! [Z_97,X_1] : ( multiply(negative_part(Z_97),X_1) = greatest_lower_bound(X_1,multiply(Z_97,X_1)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_295,c_1578]) ).

tff(c_54527,plain,
    ! [X_461] : ( multiply(negative_part(negative_part(X_461)),inverse(negative_part(inverse(X_461)))) = greatest_lower_bound(inverse(negative_part(inverse(X_461))),X_461) ),
    inference(superposition,[status(thm),theory(equality)],[c_54503,c_1592]) ).

tff(c_54658,plain,
    ! [X_461] : ( greatest_lower_bound(X_461,inverse(negative_part(inverse(X_461)))) = X_461 ),
    inference(demodulation,[status(thm),theory(equality)],[c_54294,c_1383,c_8,c_54527]) ).

tff(c_2018,plain,
    ! [X_107,Y_108,Z_109] : ( least_upper_bound(greatest_lower_bound(X_107,Y_108),greatest_lower_bound(X_107,Z_109)) = greatest_lower_bound(X_107,least_upper_bound(Y_108,Z_109)) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_65619,plain,
    ! [X_511,Y_512,Y_513] : ( least_upper_bound(greatest_lower_bound(X_511,Y_512),greatest_lower_bound(Y_513,X_511)) = greatest_lower_bound(X_511,least_upper_bound(Y_512,Y_513)) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_2018]) ).

tff(c_66283,plain,
    ! [X_38,Y_513] : ( least_upper_bound(negative_part(X_38),greatest_lower_bound(Y_513,X_38)) = greatest_lower_bound(X_38,least_upper_bound(identity,Y_513)) ),
    inference(superposition,[status(thm),theory(equality)],[c_40,c_65619]) ).

tff(c_522261,plain,
    ! [X_1457,Y_1458] : ( least_upper_bound(negative_part(X_1457),greatest_lower_bound(Y_1458,X_1457)) = greatest_lower_bound(X_1457,positive_part(Y_1458)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_198,c_66283]) ).

tff(c_523396,plain,
    ! [X_461] : ( least_upper_bound(negative_part(inverse(negative_part(inverse(X_461)))),X_461) = greatest_lower_bound(inverse(negative_part(inverse(X_461))),positive_part(X_461)) ),
    inference(superposition,[status(thm),theory(equality)],[c_54658,c_522261]) ).

tff(c_739649,plain,
    ! [X_1734] : ( greatest_lower_bound(positive_part(X_1734),inverse(negative_part(inverse(X_1734)))) = positive_part(X_1734) ),
    inference(demodulation,[status(thm),theory(equality)],[c_198,c_11106,c_8,c_523396]) ).

tff(c_18,plain,
    ! [X_17] : ( greatest_lower_bound(X_17,X_17) = X_17 ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_736,plain,
    ! [X_17,Z_73] : ( greatest_lower_bound(X_17,greatest_lower_bound(X_17,Z_73)) = greatest_lower_bound(X_17,Z_73) ),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_655]) ).

tff(c_2640,plain,
    ! [X_2,Y_117] : ( multiply(inverse(X_2),greatest_lower_bound(Y_117,X_2)) = greatest_lower_bound(multiply(inverse(X_2),Y_117),identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_2559]) ).

tff(c_54981,plain,
    ! [X_463,Y_464] : ( multiply(inverse(X_463),greatest_lower_bound(Y_464,X_463)) = negative_part(multiply(inverse(X_463),Y_464)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_2640]) ).

tff(c_55242,plain,
    ! [X_17,Z_73] : ( multiply(inverse(greatest_lower_bound(X_17,Z_73)),greatest_lower_bound(X_17,Z_73)) = negative_part(multiply(inverse(greatest_lower_bound(X_17,Z_73)),X_17)) ),
    inference(superposition,[status(thm),theory(equality)],[c_736,c_54981]) ).

tff(c_55346,plain,
    ! [X_17,Z_73] : ( negative_part(multiply(inverse(greatest_lower_bound(X_17,Z_73)),X_17)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_55242]) ).

tff(c_1571,plain,
    ! [Y_95,X_2] : ( multiply(greatest_lower_bound(Y_95,inverse(X_2)),X_2) = greatest_lower_bound(multiply(Y_95,X_2),identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_1510]) ).

tff(c_18023,plain,
    ! [Y_275,X_276] : ( multiply(greatest_lower_bound(Y_275,inverse(X_276)),X_276) = negative_part(multiply(Y_275,X_276)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_1571]) ).

tff(c_684846,plain,
    ! [Y_1667,X_1668] : ( multiply(inverse(greatest_lower_bound(Y_1667,inverse(X_1668))),negative_part(multiply(Y_1667,X_1668))) = X_1668 ),
    inference(superposition,[status(thm),theory(equality)],[c_18023,c_963]) ).

tff(c_685620,plain,
    ! [X_17,Z_73] : ( multiply(inverse(greatest_lower_bound(inverse(greatest_lower_bound(X_17,Z_73)),inverse(X_17))),identity) = X_17 ),
    inference(superposition,[status(thm),theory(equality)],[c_55346,c_684846]) ).

tff(c_686088,plain,
    ! [X_1669,Z_1670] : ( inverse(greatest_lower_bound(inverse(X_1669),inverse(greatest_lower_bound(X_1669,Z_1670)))) = X_1669 ),
    inference(demodulation,[status(thm),theory(equality)],[c_919,c_8,c_685620]) ).

tff(c_691052,plain,
    ! [X_1675,Z_1676] : ( greatest_lower_bound(inverse(X_1675),inverse(greatest_lower_bound(X_1675,Z_1676))) = inverse(X_1675) ),
    inference(superposition,[status(thm),theory(equality)],[c_686088,c_34]) ).

tff(c_692422,plain,
    ! [Y_7,X_6] : ( greatest_lower_bound(inverse(Y_7),inverse(greatest_lower_bound(X_6,Y_7))) = inverse(Y_7) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_691052]) ).

tff(c_739691,plain,
    ! [X_1734] : ( greatest_lower_bound(inverse(inverse(negative_part(inverse(X_1734)))),inverse(positive_part(X_1734))) = inverse(inverse(negative_part(inverse(X_1734)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_739649,c_692422]) ).

tff(c_740508,plain,
    ! [X_1734] : ( negative_part(inverse(X_1734)) = inverse(positive_part(X_1734)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_13149,c_239719,c_8,c_743,c_8,c_34,c_34,c_739691]) ).

tff(c_12263,plain,
    ! [X_2] : ( multiply(negative_part(inverse(X_2)),X_2) = greatest_lower_bound(identity,X_2) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_12057]) ).

tff(c_12308,plain,
    ! [X_232] : ( multiply(negative_part(inverse(X_232)),X_232) = negative_part(X_232) ),
    inference(demodulation,[status(thm),theory(equality)],[c_295,c_12263]) ).

tff(c_12340,plain,
    ! [X_232] : ( multiply(inverse(negative_part(inverse(X_232))),negative_part(X_232)) = X_232 ),
    inference(superposition,[status(thm),theory(equality)],[c_12308,c_963]) ).

tff(c_740759,plain,
    ! [X_232] : ( multiply(inverse(inverse(positive_part(X_232))),negative_part(X_232)) = X_232 ),
    inference(demodulation,[status(thm),theory(equality)],[c_740508,c_12340]) ).

tff(c_740779,plain,
    ! [X_232] : ( multiply(positive_part(X_232),negative_part(X_232)) = X_232 ),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_740759]) ).

tff(c_46,plain,
    multiply(positive_part(a),negative_part(a)) != a,
    inference(cnfTransformation,[status(thm)],[f_130]) ).

tff(c_744916,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_740779,c_46]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : GRP167-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36  % Computer : n011.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 21:54:21 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 246.07/209.19  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 246.18/209.21  
% 246.18/209.21  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 246.18/209.25  
% 246.18/209.25  Inference rules
% 246.18/209.25  ----------------------
% 246.18/209.25  #Ref     : 0
% 246.18/209.25  #Sup     : 193004
% 246.18/209.25  #Fact    : 0
% 246.18/209.25  #Define  : 0
% 246.18/209.25  #Split   : 0
% 246.18/209.25  #Chain   : 0
% 246.18/209.25  #Close   : 0
% 246.18/209.25  
% 246.18/209.25  Ordering : KBO
% 246.18/209.25  
% 246.18/209.25  Simplification rules
% 246.18/209.25  ----------------------
% 246.18/209.25  #Subsume      : 2910
% 246.18/209.25  #Demod        : 330031
% 246.18/209.25  #Tautology    : 104671
% 246.18/209.25  #SimpNegUnit  : 0
% 246.18/209.25  #BackRed      : 81
% 246.18/209.25  
% 246.18/209.25  #Partial instantiations: 0
% 246.18/209.25  #Strategies tried      : 1
% 246.18/209.25  
% 246.18/209.25  Timing (in seconds)
% 246.18/209.25  ----------------------
% 246.18/209.26  Preprocessing        : 0.48
% 246.18/209.26  Parsing              : 0.23
% 246.18/209.26  CNF conversion       : 0.02
% 246.18/209.26  Main loop            : 207.61
% 246.18/209.26  Inferencing          : 10.01
% 246.18/209.26  Reduction            : 138.45
% 246.18/209.26  Demodulation         : 130.07
% 246.18/209.26  BG Simplification    : 1.31
% 246.18/209.26  Subsumption          : 39.38
% 246.18/209.26  Abstraction          : 2.91
% 246.18/209.26  MUC search           : 0.00
% 246.18/209.26  Cooper               : 0.00
% 246.18/209.26  Total                : 208.16
% 246.18/209.26  Index Insertion      : 0.00
% 246.18/209.26  Index Deletion       : 0.00
% 246.18/209.26  Index Matching       : 0.00
% 246.18/209.26  BG Taut test         : 0.00
%------------------------------------------------------------------------------