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