TSTP Solution File: GRP184-4 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n008.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 : 600s
% DateTime : Sat Jul 16 12:25:13 EDT 2022
% Result : Unsatisfiable 0.55s 0.95s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 10:48:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.95 ********************************************************************************
% 0.55/0.95 * W A L D M E I S T E R \| \ / \|/ *
% 0.55/0.95 * |/ | \/ | *
% 0.55/0.95 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.55/0.95 * A. Jaeger and B. Loechner | | *
% 0.55/0.95 * <waldmeister@informatik.uni-kl.de> | *
% 0.55/0.95 ********************************************************************************
% 0.55/0.95
% 0.55/0.95
% 0.55/0.95 Goals:
% 0.55/0.95 ------
% 0.55/0.95
% 0.55/0.95 ( 1) multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) ?=? multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity))
% 0.55/0.95
% 0.55/0.95 Detected structure: VerbandsgeordneteGruppe
% 0.55/0.95 ********************************************************************************
% 0.55/0.95 ****************************** COMPLETION - PROOF ******************************
% 0.55/0.95 ********************************************************************************
% 0.55/0.95
% 0.55/0.95 joined goal: 1 multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) ?= multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) to inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(a),identity)))
% 0.55/0.95 goal joined
% 0.55/0.95 % SZS status Unsatisfiable
% 0.55/0.95 #START OF PROOF
% 0.55/0.95 % SZS output start CNFRefutation
% 0.55/0.95 cnf('0.1.0.0',axiom,
% 0.55/0.95 ( X1 = multiply(identity,X1) ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.1.1.0',plain,
% 0.55/0.95 ( X1 = multiply(identity,X1) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.55/0.95 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.55/0.95 cnf('0.1.2.0',plain,
% 0.55/0.95 ( multiply(identity,X1) = X1 ),
% 0.55/0.95 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.55/0.95 [x,rule_1]).
% 0.55/0.95 cnf('0.6.0.0',axiom,
% 0.55/0.95 ( X1 = inverse(inverse(X1)) ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.6.1.0',plain,
% 0.55/0.95 ( X1 = inverse(inverse(X1)) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.55/0.95 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.55/0.95 cnf('0.6.2.0',plain,
% 0.55/0.95 ( inverse(inverse(X1)) = X1 ),
% 0.55/0.95 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.55/0.95 [x,rule_6]).
% 0.55/0.95 cnf('0.8.0.0',axiom,
% 0.55/0.95 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.8.1.0',plain,
% 0.55/0.95 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.55/0.95 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.55/0.95 cnf('0.8.2.0',plain,
% 0.55/0.95 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.55/0.95 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.55/0.95 [u,rule_8]).
% 0.55/0.95 cnf('0.9.0.0',axiom,
% 0.55/0.95 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.9.1.0',plain,
% 0.55/0.95 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.55/0.95 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.55/0.95 cnf('0.9.2.0',plain,
% 0.55/0.95 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.55/0.95 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.55/0.95 [u,rule_9]).
% 0.55/0.95 cnf('0.10.0.0',axiom,
% 0.55/0.95 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.10.1.0',plain,
% 0.55/0.95 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.55/0.95 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.55/0.95 cnf('0.10.2.0',plain,
% 0.55/0.95 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.55/0.95 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.55/0.95 [u,rule_10]).
% 0.55/0.95 cnf('0.11.0.0',axiom,
% 0.55/0.95 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.11.1.0',plain,
% 0.55/0.95 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.55/0.95 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.55/0.95 cnf('0.11.2.0',plain,
% 0.55/0.95 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.55/0.95 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.55/0.95 [u,rule_11]).
% 0.55/0.95 cnf('0.12.0.0',axiom,
% 0.55/0.95 ( multiply(inverse(X1),X1) = identity ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.12.1.0',plain,
% 0.55/0.95 ( multiply(inverse(X1),X1) = identity ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.55/0.95 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.55/0.95 cnf('0.12.2.0',plain,
% 0.55/0.95 ( multiply(inverse(X1),X1) = identity ),
% 0.55/0.95 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.55/0.95 [u,rule_12]).
% 0.55/0.95 cnf('0.13.0.0',axiom,
% 0.55/0.95 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.13.1.0',plain,
% 0.55/0.95 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.55/0.95 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.55/0.95 cnf('0.13.2.0',plain,
% 0.55/0.95 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.55/0.95 inference(activate,[status(thm)],['0.13.1.0']),
% 0.55/0.95 [equation_1]).
% 0.55/0.95 cnf('0.14.0.0',axiom,
% 0.55/0.95 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.14.1.0',plain,
% 0.55/0.95 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.55/0.95 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.55/0.95 cnf('0.14.2.0',plain,
% 0.55/0.95 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.55/0.95 inference(activate,[status(thm)],['0.14.1.0']),
% 0.55/0.95 [equation_2]).
% 0.55/0.95 cnf('0.17.0.0',axiom,
% 0.55/0.95 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.17.1.0',plain,
% 0.55/0.95 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.55/0.95 [weight('<16,0,0,[0,0,0,17]>')]).
% 0.55/0.95 cnf('0.17.2.0',plain,
% 0.55/0.95 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.55/0.95 inference(activate,[status(thm)],['0.17.1.0']),
% 0.55/0.95 [equation_3]).
% 0.55/0.95 cnf('0.19.0.0',axiom,
% 0.55/0.95 ( greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X1,X2)) ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.19.1.0',plain,
% 0.55/0.95 ( greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X1,X2)) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.55/0.95 [weight('<18,0,0,[0,0,0,19]>')]).
% 0.55/0.95 cnf('0.19.2.0',plain,
% 0.55/0.95 ( inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(X2)) ),
% 0.55/0.95 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.55/0.95 [x,rule_16]).
% 0.55/0.95 cnf('0.20.0.0',axiom,
% 0.55/0.95 ( inverse(identity) = identity ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008')).
% 0.55/0.95 cnf('0.20.1.0',plain,
% 0.55/0.95 ( inverse(identity) = identity ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.55/0.95 [weight('<19,0,0,[0,0,0,20]>')]).
% 0.55/0.95 cnf('0.20.2.0',plain,
% 0.55/0.95 ( inverse(identity) = identity ),
% 0.55/0.95 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.55/0.95 [u,rule_17]).
% 0.55/0.95 cnf('0.21.0.0',plain,
% 0.55/0.95 ( inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)) ),
% 0.55/0.95 inference(cp,[status(thm)],['0.13.2.0','0.20.2.0',theory(equality)]),
% 0.55/0.95 [pos('L.1','L')]).
% 0.55/0.95 cnf('0.21.0.1',plain,
% 0.55/0.95 ( inverse(multiply(X1,identity)) = inverse(X1) ),
% 0.55/0.95 inference(reduction,[status(thm)],['0.21.0.0','0.1.2.0',theory(equality)]),
% 0.55/0.95 [pos('R','L')]).
% 0.55/0.95 cnf('0.21.1.0',plain,
% 0.55/0.95 ( multiply(X1,identity) = X1 ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.21.0.1']),
% 0.55/0.95 [weight('<19,20,13,[0,0,0,1]>')]).
% 0.55/0.95 cnf('0.21.2.0',plain,
% 0.55/0.95 ( multiply(X1,identity) = X1 ),
% 0.55/0.95 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.55/0.95 [u,rule_18]).
% 0.55/0.95 cnf('0.22.0.0',plain,
% 0.55/0.95 ( identity = multiply(X1,inverse(X1)) ),
% 0.55/0.95 inference(cp,[status(thm)],['0.12.2.0','0.6.2.0',theory(equality)]),
% 0.55/0.95 [pos('L.1','L')]).
% 0.55/0.95 cnf('0.22.1.0',plain,
% 0.55/0.95 ( identity = multiply(X1,inverse(X1)) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.22.0.0']),
% 0.55/0.95 [weight('<29,12,6,[1,0,0,1]>')]).
% 0.55/0.95 cnf('0.22.2.0',plain,
% 0.55/0.95 ( multiply(X1,inverse(X1)) = identity ),
% 0.55/0.95 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.55/0.95 [x,rule_19]).
% 0.55/0.95 cnf('0.23.0.0',plain,
% 0.55/0.95 ( least_upper_bound(X1,X2) = inverse(greatest_lower_bound(inverse(X1),inverse(X2))) ),
% 0.55/0.95 inference(cp,[status(thm)],['0.6.2.0','0.19.2.0',theory(equality)]),
% 0.55/0.95 [pos('L.1','L')]).
% 0.55/0.95 cnf('0.23.1.0',plain,
% 0.55/0.95 ( least_upper_bound(X1,X2) = inverse(greatest_lower_bound(inverse(X1),inverse(X2))) ),
% 0.55/0.95 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.55/0.95 [weight('<39,19,6,[0,0,0,1]>')]).
% 0.55/0.95 cnf('0.23.2.0',plain,
% 0.55/0.95 ( least_upper_bound(X1,X2) = inverse(greatest_lower_bound(inverse(X1),inverse(X2))) ),
% 0.55/0.95 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.55/0.95 [u,rule_20]).
% 0.55/0.95 cnf('1.0.0.0',conjecture,
% 0.55/0.95 ( multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.55/0.95 file('/tmp/WALDMEISTER_2496_n008',conjecture_1)).
% 0.55/0.95 cnf('1.0.0.1',plain,
% 0.55/0.95 ( least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),multiply(identity,inverse(greatest_lower_bound(a,identity)))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.55/0.95 inference(reduction,[status(thm)],['1.0.0.0','0.10.2.0',theory(equality)]),
% 0.55/0.95 [pos('L','L')]).
% 0.55/0.95 cnf('1.0.0.2',plain,
% 0.55/0.96 ( least_upper_bound(multiply(identity,inverse(greatest_lower_bound(a,identity))),multiply(a,inverse(greatest_lower_bound(a,identity)))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.55/0.96 inference(reduction,[status(thm)],['1.0.0.1','0.14.2.0',theory(equality)]),
% 0.55/0.96 [pos('L','L')]).
% 0.55/0.96 cnf('1.0.0.3',plain,
% 0.55/0.96 ( least_upper_bound(multiply(identity,inverse(greatest_lower_bound(a,identity))),multiply(a,inverse(greatest_lower_bound(identity,a)))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.55/0.96 inference(reduction,[status(thm)],['1.0.0.2','0.17.2.0',theory(equality)]),
% 0.55/0.96 [pos('L.2.2.1','L')]).
% 0.55/0.96 cnf('1.0.0.4',plain,
% 0.55/0.96 ( least_upper_bound(multiply(identity,inverse(greatest_lower_bound(a,identity))),multiply(a,inverse(greatest_lower_bound(identity,a)))) = multiply(inverse(greatest_lower_bound(a,inverse(identity))),least_upper_bound(a,identity)) ),
% 0.55/0.96 inference(reduction,[status(thm)],['1.0.0.3','0.20.2.0',theory(equality)]),
% 0.55/0.96 [pos('R.1.1.2','R')]).
% 0.55/0.96 cnf('1.0.0.5',plain,
% 0.55/0.96 ( least_upper_bound(multiply(inverse(identity),inverse(greatest_lower_bound(a,identity))),multiply(a,inverse(greatest_lower_bound(identity,a)))) = multiply(inverse(greatest_lower_bound(a,inverse(identity))),least_upper_bound(a,identity)) ),
% 0.55/0.96 inference(reduction,[status(thm)],['1.0.0.4','0.20.2.0',theory(equality)]),
% 0.55/0.96 [pos('L.1.1','R')]).
% 0.55/0.96 cnf('1.0.0.6',plain,
% 0.55/0.96 ( least_upper_bound(inverse(multiply(greatest_lower_bound(a,identity),identity)),multiply(a,inverse(greatest_lower_bound(identity,a)))) = multiply(inverse(greatest_lower_bound(a,inverse(identity))),least_upper_bound(a,identity)) ),
% 0.55/0.96 inference(reduction,[status(thm)],['1.0.0.5','0.13.2.0',theory(equality)]),
% 0.55/0.96 [pos('L.1','L')]).
% 0.55/0.96 cnf('1.0.0.7',plain,
% 0.55/0.96 ( least_upper_bound(inverse(greatest_lower_bound(multiply(a,identity),multiply(identity,identity))),multiply(a,inverse(greatest_lower_bound(identity,a)))) = multiply(inverse(greatest_lower_bound(a,inverse(identity))),least_upper_bound(a,identity)) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.6','0.11.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.8',plain,
% 0.59/0.96 ( least_upper_bound(inverse(greatest_lower_bound(multiply(a,identity),multiply(identity,identity))),multiply(a,inverse(greatest_lower_bound(identity,a)))) = least_upper_bound(multiply(inverse(greatest_lower_bound(a,inverse(identity))),a),multiply(inverse(greatest_lower_bound(a,inverse(identity))),identity)) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.7','0.8.2.0',theory(equality)]),
% 0.59/0.96 [pos('R','L')]).
% 0.59/0.96 cnf('1.0.0.9',plain,
% 0.59/0.96 ( least_upper_bound(inverse(greatest_lower_bound(a,multiply(identity,identity))),multiply(a,inverse(greatest_lower_bound(identity,a)))) = least_upper_bound(multiply(inverse(greatest_lower_bound(a,inverse(identity))),a),multiply(inverse(greatest_lower_bound(a,inverse(identity))),identity)) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.8','0.21.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.10',plain,
% 0.59/0.96 ( least_upper_bound(inverse(greatest_lower_bound(a,multiply(identity,identity))),multiply(a,inverse(greatest_lower_bound(identity,a)))) = least_upper_bound(multiply(inverse(greatest_lower_bound(a,inverse(identity))),a),inverse(greatest_lower_bound(a,inverse(identity)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.9','0.21.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.2','L')]).
% 0.59/0.96 cnf('1.0.0.11',plain,
% 0.59/0.96 ( least_upper_bound(inverse(greatest_lower_bound(a,multiply(identity,identity))),multiply(a,inverse(greatest_lower_bound(identity,a)))) = least_upper_bound(multiply(inverse(greatest_lower_bound(inverse(identity),a)),a),inverse(greatest_lower_bound(a,inverse(identity)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.10','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.12',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,multiply(identity,identity)))),inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))))) = least_upper_bound(multiply(inverse(greatest_lower_bound(inverse(identity),a)),a),inverse(greatest_lower_bound(a,inverse(identity)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.11','0.23.2.0',theory(equality)]),
% 0.59/0.96 [pos('L','L')]).
% 0.59/0.96 cnf('1.0.0.13',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,multiply(identity,identity)))),inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))))) = inverse(greatest_lower_bound(inverse(multiply(inverse(greatest_lower_bound(inverse(identity),a)),a)),inverse(inverse(greatest_lower_bound(a,inverse(identity)))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.12','0.23.2.0',theory(equality)]),
% 0.59/0.96 [pos('R','L')]).
% 0.59/0.96 cnf('1.0.0.14',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,multiply(identity,identity)))),inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))))) = inverse(greatest_lower_bound(multiply(inverse(a),inverse(inverse(greatest_lower_bound(inverse(identity),a)))),inverse(inverse(greatest_lower_bound(a,inverse(identity)))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.13','0.13.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.1','R')]).
% 0.59/0.96 cnf('1.0.0.15',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,multiply(identity,identity)))),multiply(inverse(inverse(greatest_lower_bound(identity,a))),inverse(a)))) = inverse(greatest_lower_bound(multiply(inverse(a),inverse(inverse(greatest_lower_bound(inverse(identity),a)))),inverse(inverse(greatest_lower_bound(a,inverse(identity)))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.14','0.13.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.2','R')]).
% 0.59/0.96 cnf('1.0.0.16',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,multiply(identity,identity)))),multiply(inverse(inverse(greatest_lower_bound(identity,a))),inverse(a)))) = inverse(greatest_lower_bound(multiply(inverse(a),inverse(inverse(greatest_lower_bound(inverse(identity),a)))),inverse(inverse(greatest_lower_bound(inverse(identity),a))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.15','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.2.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.17',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,multiply(identity,identity)))),multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)))) = inverse(greatest_lower_bound(multiply(inverse(a),inverse(inverse(greatest_lower_bound(inverse(identity),a)))),inverse(inverse(greatest_lower_bound(inverse(identity),a))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.16','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.2.1.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.18',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,multiply(identity,identity)))),multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)))) = inverse(greatest_lower_bound(multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,inverse(identity))))),inverse(inverse(greatest_lower_bound(inverse(identity),a))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.17','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.1.2.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.19',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(multiply(identity,identity),a))),multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)))) = inverse(greatest_lower_bound(multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,inverse(identity))))),inverse(inverse(greatest_lower_bound(inverse(identity),a))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.18','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.1.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.20',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(multiply(identity,identity),a))),multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(identity),a))),multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,inverse(identity))))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.19','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1','L')]).
% 0.59/0.96 cnf('1.0.0.21',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)),inverse(inverse(greatest_lower_bound(multiply(identity,identity),a))))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(identity),a))),multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,inverse(identity))))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.20','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1','L')]).
% 0.59/0.96 cnf('1.0.0.22',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)),inverse(inverse(greatest_lower_bound(multiply(identity,identity),a))))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,inverse(identity)))),multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,inverse(identity))))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.21','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.1.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.23',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)),inverse(inverse(greatest_lower_bound(identity,a))))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,inverse(identity)))),multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,inverse(identity))))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.22','0.1.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.2.1.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.24',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)),inverse(inverse(greatest_lower_bound(identity,a))))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,inverse(identity)))),multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,identity)))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.23','0.20.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.2.2.1.1.2','L')]).
% 0.59/0.96 cnf('1.0.0.25',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)),inverse(inverse(greatest_lower_bound(a,identity))))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,inverse(identity)))),multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,identity)))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.24','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.2.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.26',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)),inverse(inverse(greatest_lower_bound(a,identity))))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,inverse(identity)))),multiply(inverse(a),inverse(inverse(greatest_lower_bound(identity,a)))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.25','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.2.2.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.27',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)),greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,inverse(identity)))),multiply(inverse(a),inverse(inverse(greatest_lower_bound(identity,a)))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.26','0.6.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.2','L')]).
% 0.59/0.96 cnf('1.0.0.28',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)),greatest_lower_bound(a,identity))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(identity),a))),multiply(inverse(a),inverse(inverse(greatest_lower_bound(identity,a)))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.27','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.1.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.29',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(identity),a))),multiply(inverse(a),inverse(inverse(greatest_lower_bound(identity,a)))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.28','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1','L')]).
% 0.59/0.96 cnf('1.0.0.30',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(identity),a))),multiply(inverse(a),greatest_lower_bound(identity,a)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.29','0.6.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.2.2','L')]).
% 0.59/0.96 cnf('1.0.0.31',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(inverse(identity),a))),multiply(inverse(a),greatest_lower_bound(a,identity)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.30','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.2.2','L')]).
% 0.59/0.96 cnf('1.0.0.32',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)))) = inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(a,identity)),inverse(inverse(greatest_lower_bound(inverse(identity),a))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.31','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1','L')]).
% 0.59/0.96 cnf('1.0.0.33',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),multiply(inverse(inverse(greatest_lower_bound(a,identity))),inverse(a)))) = inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(a,identity)),inverse(inverse(greatest_lower_bound(a,inverse(identity)))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.32','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.2.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.34',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),multiply(greatest_lower_bound(a,identity),inverse(a)))) = inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(a,identity)),inverse(inverse(greatest_lower_bound(a,inverse(identity)))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.33','0.6.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.2.1','L')]).
% 0.59/0.96 cnf('1.0.0.35',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),multiply(greatest_lower_bound(a,identity),inverse(a)))) = inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(a,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.34','0.20.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.2.1.1.2','L')]).
% 0.59/0.96 cnf('1.0.0.36',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(multiply(a,inverse(a)),multiply(identity,inverse(a))))) = inverse(greatest_lower_bound(multiply(inverse(a),greatest_lower_bound(a,identity)),inverse(inverse(greatest_lower_bound(a,identity))))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.35','0.11.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.2','L')]).
% 0.59/0.96 cnf('1.0.0.37',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(multiply(a,inverse(a)),multiply(identity,inverse(a))))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,identity))),multiply(inverse(a),greatest_lower_bound(a,identity)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.36','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1','L')]).
% 0.59/0.96 cnf('1.0.0.38',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(multiply(a,inverse(a)),inverse(a)))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,identity))),multiply(inverse(a),greatest_lower_bound(a,identity)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.37','0.1.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.2.2','L')]).
% 0.59/0.96 cnf('1.0.0.39',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(multiply(a,inverse(a)),inverse(a)))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,identity))),greatest_lower_bound(multiply(inverse(a),a),multiply(inverse(a),identity)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.38','0.9.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.2','L')]).
% 0.59/0.96 cnf('1.0.0.40',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(a),multiply(a,inverse(a))))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,identity))),greatest_lower_bound(multiply(inverse(a),a),multiply(inverse(a),identity)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.39','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.2','L')]).
% 0.59/0.96 cnf('1.0.0.41',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(a),multiply(a,inverse(a))))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,identity))),greatest_lower_bound(multiply(inverse(a),a),inverse(a)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.40','0.21.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.2.2','L')]).
% 0.59/0.96 cnf('1.0.0.42',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(a),identity))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,identity))),greatest_lower_bound(multiply(inverse(a),a),inverse(a)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.41','0.22.2.0',theory(equality)]),
% 0.59/0.96 [pos('L.1.2.2','L')]).
% 0.59/0.96 cnf('1.0.0.43',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(a),identity))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,identity))),greatest_lower_bound(inverse(a),multiply(inverse(a),a)))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.42','0.17.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.2','L')]).
% 0.59/0.96 cnf('1.0.0.44',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(a),identity))) = inverse(greatest_lower_bound(inverse(inverse(greatest_lower_bound(a,identity))),greatest_lower_bound(inverse(a),identity))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.43','0.12.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.2.2','L')]).
% 0.59/0.96 cnf('1.0.0.45',plain,
% 0.59/0.96 ( inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(a),identity))) = inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(a),identity))) ),
% 0.59/0.96 inference(reduction,[status(thm)],['1.0.0.44','0.6.2.0',theory(equality)]),
% 0.59/0.96 [pos('R.1.1','L')]).
% 0.59/0.96 cnf('1.0.0.46',plain,
% 0.59/0.96 ( $true ),
% 0.59/0.96 inference(trivial,[status(thm)],['1.0.0.45',theory(equality)]),
% 0.59/0.96 [conjecture_1]).
% 0.59/0.96
% 0.59/0.96 Proved Goals:
% 0.59/0.96 No. 1: multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) ?= multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) joined, current: inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(a),identity))) = inverse(greatest_lower_bound(greatest_lower_bound(a,identity),greatest_lower_bound(inverse(a),identity)))
% 0.59/0.96 1 goal was specified, which was proved.
% 0.59/0.96 % SZS output end CNFRefutation
% 0.59/0.96 #END OF PROOF
% 0.59/0.96
% 0.59/0.96 Problem WALDMEISTER_2496_n008
% 0.59/0.96 CPs.gen 121
% 0.59/0.96 CPs.reexp 0
% 0.59/0.96 Select 24
% 0.59/0.96 R 20
% 0.59/0.96 E 3
% 0.59/0.96 vsize 6.5M
% 0.59/0.96 rss 3.7M
% 0.59/0.96 process.time 0.006s
% 0.59/0.96 wallclock.time 0.007s
% 0.59/0.96 status S
% 0.59/0.96
% 0.59/0.96
% 0.59/0.96 Waldmeister states: Goal proved.
% 0.59/0.96 % SZS status Unsatisfiable
% 0.59/0.96
% 0.59/0.96 Problem WALDMEISTER_2496_n008
% 0.59/0.96 CPs.gen 0
% 0.59/0.96 CPs.reexp 0
% 0.59/0.96 Select 0
% 0.59/0.96 R 0
% 0.59/0.96 E 0
% 0.59/0.96 vsize 6.0M
% 0.59/0.96 rss 3.2M
% 0.59/0.96 process.time 0.001s
% 0.59/0.96 wallclock.time 0.006s
% 0.59/0.96 status S
%------------------------------------------------------------------------------