TSTP Solution File: GRP184-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP184-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n013.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 12:25:12 EDT 2022
% Result : Unsatisfiable 0.60s 1.04s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP184-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : woody %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 13:50:29 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.60/1.01 ********************************************************************************
% 0.60/1.01 * W A L D M E I S T E R \| \ / \|/ *
% 0.60/1.01 * |/ | \/ | *
% 0.60/1.01 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.60/1.01 * A. Jaeger and B. Loechner | | *
% 0.60/1.01 * <waldmeister@informatik.uni-kl.de> | *
% 0.60/1.01 ********************************************************************************
% 0.60/1.01
% 0.60/1.01
% 0.60/1.01 Goals:
% 0.60/1.01 ------
% 0.60/1.01
% 0.60/1.01 ( 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))
% 0.60/1.01
% 0.60/1.01 Detected structure: VerbandsgeordneteGruppe
% 0.60/1.01 ********************************************************************************
% 0.60/1.01 ****************************** COMPLETION - PROOF ******************************
% 0.60/1.01 ********************************************************************************
% 0.60/1.01
% 0.60/1.04 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 least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a))))
% 0.60/1.04 goal joined
% 0.60/1.04 % SZS status Unsatisfiable
% 0.60/1.04 #START OF PROOF
% 0.60/1.04 % SZS output start CNFRefutation
% 0.60/1.04 cnf('0.1.0.0',axiom,
% 0.60/1.04 ( X1 = multiply(identity,X1) ),
% 0.60/1.04 file('/tmp/WALDMEISTER_30118_n013')).
% 0.60/1.04 cnf('0.1.1.0',plain,
% 0.60/1.04 ( X1 = multiply(identity,X1) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.60/1.04 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.60/1.04 cnf('0.1.2.0',plain,
% 0.60/1.04 ( multiply(identity,X1) = X1 ),
% 0.60/1.04 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.60/1.04 [x,rule_1]).
% 0.60/1.04 cnf('0.6.0.0',axiom,
% 0.60/1.04 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.60/1.04 file('/tmp/WALDMEISTER_30118_n013')).
% 0.60/1.04 cnf('0.6.1.0',plain,
% 0.60/1.04 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.60/1.04 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.60/1.04 cnf('0.6.2.0',plain,
% 0.60/1.04 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.60/1.04 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.60/1.04 [x,rule_6]).
% 0.60/1.04 cnf('0.7.0.0',axiom,
% 0.60/1.04 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.60/1.04 file('/tmp/WALDMEISTER_30118_n013')).
% 0.60/1.04 cnf('0.7.1.0',plain,
% 0.60/1.04 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.60/1.04 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.60/1.04 cnf('0.7.2.0',plain,
% 0.60/1.04 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.60/1.04 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.60/1.04 [u,rule_7]).
% 0.60/1.04 cnf('0.8.0.0',axiom,
% 0.60/1.04 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.60/1.04 file('/tmp/WALDMEISTER_30118_n013')).
% 0.60/1.04 cnf('0.8.1.0',plain,
% 0.60/1.04 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.60/1.04 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.60/1.04 cnf('0.8.2.0',plain,
% 0.60/1.04 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.60/1.04 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.60/1.04 [u,rule_8]).
% 0.60/1.04 cnf('0.9.0.0',axiom,
% 0.60/1.04 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.60/1.04 file('/tmp/WALDMEISTER_30118_n013')).
% 0.60/1.04 cnf('0.9.1.0',plain,
% 0.60/1.04 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.60/1.04 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.60/1.04 cnf('0.9.2.0',plain,
% 0.60/1.04 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.60/1.04 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.60/1.04 [u,rule_9]).
% 0.60/1.04 cnf('0.10.0.0',axiom,
% 0.60/1.04 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.60/1.04 file('/tmp/WALDMEISTER_30118_n013')).
% 0.60/1.04 cnf('0.10.1.0',plain,
% 0.60/1.04 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.60/1.04 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.60/1.04 cnf('0.10.2.0',plain,
% 0.60/1.04 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.60/1.04 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.60/1.04 [u,rule_10]).
% 0.60/1.04 cnf('0.11.0.0',axiom,
% 0.60/1.04 ( multiply(inverse(X1),X1) = identity ),
% 0.60/1.04 file('/tmp/WALDMEISTER_30118_n013')).
% 0.60/1.04 cnf('0.11.1.0',plain,
% 0.60/1.04 ( multiply(inverse(X1),X1) = identity ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.60/1.04 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.60/1.04 cnf('0.11.2.0',plain,
% 0.60/1.04 ( multiply(inverse(X1),X1) = identity ),
% 0.60/1.04 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.60/1.04 [u,rule_11]).
% 0.60/1.04 cnf('0.12.0.0',axiom,
% 0.60/1.04 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.60/1.04 file('/tmp/WALDMEISTER_30118_n013')).
% 0.60/1.04 cnf('0.12.1.0',plain,
% 0.60/1.04 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.60/1.04 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.60/1.04 cnf('0.12.2.0',plain,
% 0.60/1.04 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.60/1.04 inference(activate,[status(thm)],['0.12.1.0']),
% 0.60/1.04 [equation_1]).
% 0.60/1.04 cnf('0.14.0.0',axiom,
% 0.60/1.04 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.60/1.04 file('/tmp/WALDMEISTER_30118_n013')).
% 0.60/1.04 cnf('0.14.1.0',plain,
% 0.60/1.04 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.60/1.04 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.60/1.04 cnf('0.14.2.0',plain,
% 0.60/1.04 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.60/1.04 inference(activate,[status(thm)],['0.14.1.0']),
% 0.60/1.04 [equation_2]).
% 0.60/1.04 cnf('0.22.0.0',plain,
% 0.60/1.04 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1','L')]).
% 0.60/1.04 cnf('0.22.0.1',plain,
% 0.60/1.04 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.60/1.04 inference(reduction,[status(thm)],['0.22.0.0','0.1.2.0',theory(equality)]),
% 0.60/1.04 [pos('R','L')]).
% 0.60/1.04 cnf('0.22.1.0',plain,
% 0.60/1.04 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.22.0.1']),
% 0.60/1.04 [weight('<55,11,6,[0,0,0,1]>')]).
% 0.60/1.04 cnf('0.22.2.0',plain,
% 0.60/1.04 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.60/1.04 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.60/1.04 [u,rule_20]).
% 0.60/1.04 cnf('0.23.0.0',plain,
% 0.60/1.04 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.22.2.0','0.22.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.2','L')]).
% 0.60/1.04 cnf('0.23.1.0',plain,
% 0.60/1.04 ( X1 = inverse(inverse(X1)) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.60/1.04 [weight('<19,22,22,[0,0,0,3]>')]).
% 0.60/1.04 cnf('0.23.2.0',plain,
% 0.60/1.04 ( inverse(inverse(X1)) = X1 ),
% 0.60/1.04 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.60/1.04 [x,rule_21]).
% 0.60/1.04 cnf('0.25.0.0',plain,
% 0.60/1.04 ( identity = multiply(X1,inverse(X1)) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.11.2.0','0.23.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1','L')]).
% 0.60/1.04 cnf('0.25.1.0',plain,
% 0.60/1.04 ( identity = multiply(X1,inverse(X1)) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.60/1.04 [weight('<29,23,11,[0,0,0,1]>')]).
% 0.60/1.04 cnf('0.25.2.0',plain,
% 0.60/1.04 ( multiply(X1,inverse(X1)) = identity ),
% 0.60/1.04 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.60/1.04 [x,rule_23]).
% 0.60/1.04 cnf('0.26.0.0',plain,
% 0.60/1.04 ( identity = inverse(identity) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.25.2.0','0.1.2.0',theory(equality)]),
% 0.60/1.04 [pos('L','L')]).
% 0.60/1.04 cnf('0.26.1.0',plain,
% 0.60/1.04 ( identity = inverse(identity) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.26.0.0']),
% 0.60/1.04 [weight('<11,25,1,[1,0,0,0]>')]).
% 0.60/1.04 cnf('0.26.2.0',plain,
% 0.60/1.04 ( inverse(identity) = identity ),
% 0.60/1.04 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 0.60/1.04 [x,rule_24]).
% 0.60/1.04 cnf('0.27.0.0',plain,
% 0.60/1.04 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.22.2.0','0.25.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.2','L')]).
% 0.60/1.04 cnf('0.27.1.0',plain,
% 0.60/1.04 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.27.0.0']),
% 0.60/1.04 [weight('<34,25,22,[0,0,0,3]>')]).
% 0.60/1.04 cnf('0.27.2.0',plain,
% 0.60/1.04 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 0.60/1.04 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 0.60/1.04 [x,rule_25]).
% 0.60/1.04 cnf('0.28.0.0',plain,
% 0.60/1.04 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.27.2.0','0.23.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1','L')]).
% 0.60/1.04 cnf('0.28.0.1',plain,
% 0.60/1.04 ( X1 = multiply(X1,identity) ),
% 0.60/1.04 inference(reduction,[status(thm)],['0.28.0.0','0.23.2.0',theory(equality)]),
% 0.60/1.04 [pos('L','L')]).
% 0.60/1.04 cnf('0.28.1.0',plain,
% 0.60/1.04 ( X1 = multiply(X1,identity) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.28.0.1']),
% 0.60/1.04 [weight('<19,27,23,[1,0,0,1]>')]).
% 0.60/1.04 cnf('0.28.2.0',plain,
% 0.60/1.04 ( multiply(X1,identity) = X1 ),
% 0.60/1.04 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 0.60/1.04 [x,rule_26]).
% 0.60/1.04 cnf('0.29.0.0',plain,
% 0.60/1.04 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.22.2.0','0.23.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1','L')]).
% 0.60/1.04 cnf('0.29.1.0',plain,
% 0.60/1.04 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.29.0.0']),
% 0.60/1.04 [weight('<55,23,22,[0,0,0,1]>')]).
% 0.60/1.04 cnf('0.29.2.0',plain,
% 0.60/1.04 ( multiply(X1,multiply(inverse(X1),X2)) = X2 ),
% 0.60/1.04 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.60/1.04 [x,rule_27]).
% 0.60/1.04 cnf('0.44.0.0',plain,
% 0.60/1.04 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.25.2.0','0.6.2.0',theory(equality)]),
% 0.60/1.04 [pos('L','L')]).
% 0.60/1.04 cnf('0.44.1.0',plain,
% 0.60/1.04 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.44.0.0']),
% 0.60/1.04 [weight('<89,25,6,[1,0,0,0]>')]).
% 0.60/1.04 cnf('0.44.2.0',plain,
% 0.60/1.04 ( multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity ),
% 0.60/1.04 inference(orient,[status(thm)],['0.44.1.0',theory(equality)]),
% 0.60/1.04 [x,rule_42]).
% 0.60/1.04 cnf('0.45.0.0',plain,
% 0.60/1.04 ( multiply(X1,inverse(multiply(X2,X1))) = multiply(inverse(X2),identity) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.22.2.0','0.44.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.2','L')]).
% 0.60/1.04 cnf('0.45.0.1',plain,
% 0.60/1.04 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 0.60/1.04 inference(reduction,[status(thm)],['0.45.0.0','0.28.2.0',theory(equality)]),
% 0.60/1.04 [pos('R','L')]).
% 0.60/1.04 cnf('0.45.1.0',plain,
% 0.60/1.04 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.45.0.1']),
% 0.60/1.04 [weight('<62,44,22,[0,0,0,3]>')]).
% 0.60/1.04 cnf('0.45.2.0',plain,
% 0.60/1.04 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 0.60/1.04 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 0.60/1.04 [u,rule_43]).
% 0.60/1.04 cnf('0.47.0.0',plain,
% 0.60/1.04 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.22.2.0','0.45.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.2','L')]).
% 0.60/1.04 cnf('0.47.1.0',plain,
% 0.60/1.04 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.47.0.0']),
% 0.60/1.04 [weight('<99,45,22,[0,0,0,3]>')]).
% 0.60/1.04 cnf('0.47.2.0',plain,
% 0.60/1.04 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 0.60/1.04 inference(activate,[status(thm)],['0.47.1.0']),
% 0.60/1.04 [equation_3]).
% 0.60/1.04 cnf('0.49.0.0',plain,
% 0.60/1.04 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.29.2.0','0.45.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.2','L')]).
% 0.60/1.04 cnf('0.49.1.0',plain,
% 0.60/1.04 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.49.0.0']),
% 0.60/1.04 [weight('<99,45,29,[0,0,0,2]>')]).
% 0.60/1.04 cnf('0.49.2.0',plain,
% 0.60/1.04 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.60/1.04 inference(activate,[status(thm)],['0.49.1.0']),
% 0.60/1.04 [equation_4]).
% 0.60/1.04 cnf('0.50.0.0',plain,
% 0.60/1.04 ( multiply(X1,X2) = inverse(multiply(inverse(X2),inverse(X1))) ),
% 0.60/1.04 inference(cp,[status(thm)],['0.23.2.0','0.47.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1','L')]).
% 0.60/1.04 cnf('0.50.1.0',plain,
% 0.60/1.04 ( multiply(X1,X2) = inverse(multiply(inverse(X2),inverse(X1))) ),
% 0.60/1.04 inference(weigh,[status(thm)],['0.50.0.0']),
% 0.60/1.04 [weight('<99,47,23,[0,0,0,1]>')]).
% 0.60/1.04 cnf('0.50.2.0',plain,
% 0.60/1.04 ( multiply(X1,X2) = inverse(multiply(inverse(X2),inverse(X1))) ),
% 0.60/1.04 inference(activate,[status(thm)],['0.50.1.0']),
% 0.60/1.04 [equation_5]).
% 0.60/1.04 cnf('1.0.0.0',conjecture,
% 0.60/1.04 ( multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 file('/tmp/WALDMEISTER_30118_n013',conjecture_1)).
% 0.60/1.04 cnf('1.0.0.1',plain,
% 0.60/1.04 ( 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)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.0','0.9.2.0',theory(equality)]),
% 0.60/1.04 [pos('L','L')]).
% 0.60/1.04 cnf('1.0.0.2',plain,
% 0.60/1.04 ( 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)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.1','0.12.2.0',theory(equality)]),
% 0.60/1.04 [pos('L','L')]).
% 0.60/1.04 cnf('1.0.0.3',plain,
% 0.60/1.04 ( 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)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.2','0.14.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.2.2.1','L')]).
% 0.60/1.04 cnf('1.0.0.4',plain,
% 0.60/1.04 ( 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,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.3','0.26.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1.1','R')]).
% 0.60/1.04 cnf('1.0.0.5',plain,
% 0.60/1.04 ( 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,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.4','0.47.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1','R')]).
% 0.60/1.04 cnf('1.0.0.6',plain,
% 0.60/1.04 ( 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,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.5','0.10.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1.1','L')]).
% 0.60/1.04 cnf('1.0.0.7',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(multiply(a,identity),identity)),multiply(a,inverse(greatest_lower_bound(identity,a)))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.6','0.1.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1.1.2','L')]).
% 0.60/1.04 cnf('1.0.0.8',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(multiply(a,identity),identity)),inverse(multiply(greatest_lower_bound(identity,a),inverse(a)))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.7','0.49.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.2','R')]).
% 0.60/1.04 cnf('1.0.0.9',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(multiply(a,identity),identity)),inverse(inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.8','0.49.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.2.1','R')]).
% 0.60/1.04 cnf('1.0.0.10',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(multiply(a,identity),identity)),inverse(inverse(multiply(a,inverse(greatest_lower_bound(a,identity)))))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.9','0.14.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.2.1.1.2.1','L')]).
% 0.60/1.04 cnf('1.0.0.11',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(multiply(a,identity),identity)),inverse(inverse(inverse(multiply(greatest_lower_bound(a,identity),inverse(a)))))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.10','0.49.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.2.1.1','R')]).
% 0.60/1.04 cnf('1.0.0.12',plain,
% 0.60/1.04 ( least_upper_bound(inverse(inverse(inverse(multiply(greatest_lower_bound(a,identity),inverse(a))))),inverse(greatest_lower_bound(multiply(a,identity),identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.11','0.12.2.0',theory(equality)]),
% 0.60/1.04 [pos('L','L')]).
% 0.60/1.04 cnf('1.0.0.13',plain,
% 0.60/1.04 ( least_upper_bound(inverse(inverse(inverse(greatest_lower_bound(multiply(a,inverse(a)),multiply(identity,inverse(a)))))),inverse(greatest_lower_bound(multiply(a,identity),identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.12','0.10.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1.1.1.1','L')]).
% 0.60/1.04 cnf('1.0.0.14',plain,
% 0.60/1.04 ( least_upper_bound(inverse(inverse(inverse(greatest_lower_bound(identity,multiply(identity,inverse(a)))))),inverse(greatest_lower_bound(multiply(a,identity),identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.13','0.25.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1.1.1.1.1','L')]).
% 0.60/1.04 cnf('1.0.0.15',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(identity,multiply(identity,inverse(a)))),inverse(greatest_lower_bound(multiply(a,identity),identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.14','0.23.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1','L')]).
% 0.60/1.04 cnf('1.0.0.16',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(multiply(a,identity),identity)),inverse(greatest_lower_bound(identity,multiply(identity,inverse(a))))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.15','0.12.2.0',theory(equality)]),
% 0.60/1.04 [pos('L','L')]).
% 0.60/1.04 cnf('1.0.0.17',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,multiply(identity,inverse(a))))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.16','0.28.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.1.1.1','L')]).
% 0.60/1.04 cnf('1.0.0.18',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.17','0.1.2.0',theory(equality)]),
% 0.60/1.04 [pos('L.2.1.2','L')]).
% 0.60/1.04 cnf('1.0.0.19',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))) = least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.18','0.7.2.0',theory(equality)]),
% 0.60/1.04 [pos('R','L')]).
% 0.60/1.04 cnf('1.0.0.20',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))) = least_upper_bound(inverse(multiply(inverse(a),inverse(inverse(greatest_lower_bound(a,identity))))),multiply(inverse(greatest_lower_bound(a,identity)),identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.19','0.50.2.0',theory(equality)]),
% 0.60/1.04 [pos('R.1','L')]).
% 0.60/1.04 cnf('1.0.0.21',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))) = least_upper_bound(inverse(multiply(inverse(a),greatest_lower_bound(a,identity))),multiply(inverse(greatest_lower_bound(a,identity)),identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.20','0.23.2.0',theory(equality)]),
% 0.60/1.04 [pos('R.1.1.2','L')]).
% 0.60/1.04 cnf('1.0.0.22',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))) = least_upper_bound(inverse(greatest_lower_bound(multiply(inverse(a),a),multiply(inverse(a),identity))),multiply(inverse(greatest_lower_bound(a,identity)),identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.21','0.8.2.0',theory(equality)]),
% 0.60/1.04 [pos('R.1.1','L')]).
% 0.60/1.04 cnf('1.0.0.23',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))) = least_upper_bound(inverse(greatest_lower_bound(identity,multiply(inverse(a),identity))),multiply(inverse(greatest_lower_bound(a,identity)),identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.22','0.11.2.0',theory(equality)]),
% 0.60/1.04 [pos('R.1.1.1','L')]).
% 0.60/1.04 cnf('1.0.0.24',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))) = least_upper_bound(inverse(greatest_lower_bound(identity,inverse(a))),multiply(inverse(greatest_lower_bound(a,identity)),identity)) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.23','0.28.2.0',theory(equality)]),
% 0.60/1.04 [pos('R.1.1.2','L')]).
% 0.60/1.04 cnf('1.0.0.25',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))) = least_upper_bound(inverse(greatest_lower_bound(identity,inverse(a))),inverse(greatest_lower_bound(a,identity))) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.24','0.28.2.0',theory(equality)]),
% 0.60/1.04 [pos('R.2','L')]).
% 0.60/1.04 cnf('1.0.0.26',plain,
% 0.60/1.04 ( least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))) = least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))) ),
% 0.60/1.04 inference(reduction,[status(thm)],['1.0.0.25','0.12.2.0',theory(equality)]),
% 0.60/1.04 [pos('R','L')]).
% 0.60/1.04 cnf('1.0.0.27',plain,
% 0.60/1.04 ( $true ),
% 0.60/1.04 inference(trivial,[status(thm)],['1.0.0.26',theory(equality)]),
% 0.60/1.04 [conjecture_1]).
% 0.60/1.04
% 0.60/1.04 Proved Goals:
% 0.60/1.04 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: least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a)))) = least_upper_bound(inverse(greatest_lower_bound(a,identity)),inverse(greatest_lower_bound(identity,inverse(a))))
% 0.60/1.04 1 goal was specified, which was proved.
% 0.60/1.04 % SZS output end CNFRefutation
% 0.60/1.04 #END OF PROOF
% 0.60/1.04
% 0.60/1.04 Problem WALDMEISTER_30118_n013
% 0.60/1.04 CPs.gen 748
% 0.60/1.04 CPs.reexp 0
% 0.60/1.04 Select 71
% 0.60/1.04 R 45
% 0.60/1.04 E 5
% 0.60/1.04 vsize 7.0M
% 0.60/1.04 rss 4.1M
% 0.60/1.04 process.time 0.027s
% 0.60/1.04 wallclock.time 0.028s
% 0.60/1.04 status S
% 0.60/1.04
% 0.60/1.04
% 0.60/1.04 Waldmeister states: Goal proved.
% 0.60/1.04 % SZS status Unsatisfiable
% 0.60/1.04
% 0.60/1.04 Problem WALDMEISTER_30118_n013
% 0.60/1.04 CPs.gen 0
% 0.60/1.04 CPs.reexp 0
% 0.60/1.04 Select 0
% 0.60/1.04 R 0
% 0.60/1.04 E 0
% 0.60/1.04 vsize 6.0M
% 0.60/1.04 rss 3.2M
% 0.60/1.04 process.time 0.001s
% 0.60/1.04 wallclock.time 0.027s
% 0.60/1.04 status S
%------------------------------------------------------------------------------