TSTP Solution File: GRP181-2 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP181-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n017.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 12:25:10 EDT 2022
% Result : Unsatisfiable 2.48s 2.94s
% Output : CNFRefutation 2.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : GRP181-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.09 % Command : woody %s
% 0.09/0.29 % Computer : n017.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Tue Jun 14 06:55:53 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.56/0.96 ********************************************************************************
% 0.56/0.96 * W A L D M E I S T E R \| \ / \|/ *
% 0.56/0.96 * |/ | \/ | *
% 0.56/0.96 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.56/0.96 * A. Jaeger and B. Loechner | | *
% 0.56/0.96 * <waldmeister@informatik.uni-kl.de> | *
% 0.56/0.96 ********************************************************************************
% 0.56/0.96
% 0.56/0.96
% 0.56/0.96 Goals:
% 0.56/0.96 ------
% 0.56/0.96
% 0.56/0.96 ( 1) a ?=? b
% 0.56/0.96
% 0.56/0.96 Detected structure: VerbandsgeordneteGruppe
% 0.56/0.96 ********************************************************************************
% 0.56/0.96 ****************************** COMPLETION - PROOF ******************************
% 0.56/0.96 ********************************************************************************
% 0.56/0.96
% 2.48/2.93 joined goal: 1 a ?= b to b
% 2.48/2.93 goal joined
% 2.48/2.94 % SZS status Unsatisfiable
% 2.48/2.94 #START OF PROOF
% 2.48/2.94 % SZS output start CNFRefutation
% 2.48/2.94 cnf('0.1.0.0',axiom,
% 2.48/2.94 ( X1 = multiply(identity,X1) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.1.1.0',plain,
% 2.48/2.94 ( X1 = multiply(identity,X1) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.1.0.0']),
% 2.48/2.94 [weight('<0,0,0,[0,0,0,1]>')]).
% 2.48/2.94 cnf('0.1.2.0',plain,
% 2.48/2.94 ( multiply(identity,X1) = X1 ),
% 2.48/2.94 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_1]).
% 2.48/2.94 cnf('0.3.0.0',axiom,
% 2.48/2.94 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.3.1.0',plain,
% 2.48/2.94 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.3.0.0']),
% 2.48/2.94 [weight('<2,0,0,[0,0,0,3]>')]).
% 2.48/2.94 cnf('0.3.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 2.48/2.94 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_3]).
% 2.48/2.94 cnf('0.4.0.0',axiom,
% 2.48/2.94 ( X1 = least_upper_bound(X1,X1) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.4.1.0',plain,
% 2.48/2.94 ( X1 = least_upper_bound(X1,X1) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.4.0.0']),
% 2.48/2.94 [weight('<3,0,0,[0,0,0,4]>')]).
% 2.48/2.94 cnf('0.4.2.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,X1) = X1 ),
% 2.48/2.94 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_4]).
% 2.48/2.94 cnf('0.5.0.0',axiom,
% 2.48/2.94 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.5.1.0',plain,
% 2.48/2.94 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.5.0.0']),
% 2.48/2.94 [weight('<4,0,0,[0,0,0,5]>')]).
% 2.48/2.94 cnf('0.5.2.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 2.48/2.94 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_5]).
% 2.48/2.94 cnf('0.6.0.0',axiom,
% 2.48/2.94 ( X1 = inverse(inverse(X1)) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.6.1.0',plain,
% 2.48/2.94 ( X1 = inverse(inverse(X1)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.6.0.0']),
% 2.48/2.94 [weight('<5,0,0,[0,0,0,6]>')]).
% 2.48/2.94 cnf('0.6.2.0',plain,
% 2.48/2.94 ( inverse(inverse(X1)) = X1 ),
% 2.48/2.94 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_6]).
% 2.48/2.94 cnf('0.7.0.0',axiom,
% 2.48/2.94 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.7.1.0',plain,
% 2.48/2.94 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.7.0.0']),
% 2.48/2.94 [weight('<6,0,0,[0,0,0,7]>')]).
% 2.48/2.94 cnf('0.7.2.0',plain,
% 2.48/2.94 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_7]).
% 2.48/2.94 cnf('0.8.0.0',axiom,
% 2.48/2.94 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.8.1.0',plain,
% 2.48/2.94 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.8.0.0']),
% 2.48/2.94 [weight('<7,0,0,[0,0,0,8]>')]).
% 2.48/2.94 cnf('0.8.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_8]).
% 2.48/2.94 cnf('0.9.0.0',axiom,
% 2.48/2.94 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.9.1.0',plain,
% 2.48/2.94 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.9.0.0']),
% 2.48/2.94 [weight('<8,0,0,[0,0,0,9]>')]).
% 2.48/2.94 cnf('0.9.2.0',plain,
% 2.48/2.94 ( least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_9]).
% 2.48/2.94 cnf('0.10.0.0',axiom,
% 2.48/2.94 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.10.1.0',plain,
% 2.48/2.94 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.10.0.0']),
% 2.48/2.94 [weight('<9,0,0,[0,0,0,10]>')]).
% 2.48/2.94 cnf('0.10.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_10]).
% 2.48/2.94 cnf('0.11.0.0',axiom,
% 2.48/2.94 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.11.1.0',plain,
% 2.48/2.94 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.11.0.0']),
% 2.48/2.94 [weight('<10,0,0,[0,0,0,11]>')]).
% 2.48/2.94 cnf('0.11.2.0',plain,
% 2.48/2.94 ( least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_11]).
% 2.48/2.94 cnf('0.12.0.0',axiom,
% 2.48/2.94 ( multiply(inverse(X1),X1) = identity ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.12.1.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),X1) = identity ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.12.0.0']),
% 2.48/2.94 [weight('<11,0,0,[0,0,0,12]>')]).
% 2.48/2.94 cnf('0.12.2.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),X1) = identity ),
% 2.48/2.94 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_12]).
% 2.48/2.94 cnf('0.13.0.0',axiom,
% 2.48/2.94 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.13.1.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.13.0.0']),
% 2.48/2.94 [weight('<12,0,0,[0,0,0,13]>')]).
% 2.48/2.94 cnf('0.13.2.0',plain,
% 2.48/2.94 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_13]).
% 2.48/2.94 cnf('0.14.0.0',axiom,
% 2.48/2.94 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.14.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.14.0.0']),
% 2.48/2.94 [weight('<13,0,0,[0,0,0,14]>')]).
% 2.48/2.94 cnf('0.14.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 2.48/2.94 inference(activate,[status(thm)],['0.14.1.0']),
% 2.48/2.94 [equation_1]).
% 2.48/2.94 cnf('0.15.0.0',axiom,
% 2.48/2.94 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.15.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.15.0.0']),
% 2.48/2.94 [weight('<14,0,0,[0,0,0,15]>')]).
% 2.48/2.94 cnf('0.15.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_14]).
% 2.48/2.94 cnf('0.16.0.0',axiom,
% 2.48/2.94 ( greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.16.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.16.0.0']),
% 2.48/2.94 [weight('<15,0,0,[0,0,0,16]>')]).
% 2.48/2.94 cnf('0.16.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_15]).
% 2.48/2.94 cnf('0.17.0.0',axiom,
% 2.48/2.94 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.17.1.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.17.0.0']),
% 2.48/2.94 [weight('<16,0,0,[0,0,0,17]>')]).
% 2.48/2.94 cnf('0.17.2.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 2.48/2.94 inference(activate,[status(thm)],['0.17.1.0']),
% 2.48/2.94 [equation_2]).
% 2.48/2.94 cnf('0.18.0.0',axiom,
% 2.48/2.94 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.18.1.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.18.0.0']),
% 2.48/2.94 [weight('<17,0,0,[0,0,0,18]>')]).
% 2.48/2.94 cnf('0.18.2.0',plain,
% 2.48/2.94 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_16]).
% 2.48/2.94 cnf('0.19.0.0',axiom,
% 2.48/2.94 ( least_upper_bound(a,c) = least_upper_bound(b,c) ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.19.1.0',plain,
% 2.48/2.94 ( least_upper_bound(a,c) = least_upper_bound(b,c) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.19.0.0']),
% 2.48/2.94 [weight('<18,0,0,[0,0,0,19]>')]).
% 2.48/2.94 cnf('0.19.2.0',plain,
% 2.48/2.94 ( least_upper_bound(a,c) = least_upper_bound(b,c) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_17]).
% 2.48/2.94 cnf('0.20.0.0',axiom,
% 2.48/2.94 ( inverse(identity) = identity ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017')).
% 2.48/2.94 cnf('0.20.1.0',plain,
% 2.48/2.94 ( inverse(identity) = identity ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.20.0.0']),
% 2.48/2.94 [weight('<19,0,0,[0,0,0,20]>')]).
% 2.48/2.94 cnf('0.20.2.0',plain,
% 2.48/2.94 ( inverse(identity) = identity ),
% 2.48/2.94 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_18]).
% 2.48/2.94 cnf('0.21.0.0',plain,
% 2.48/2.94 ( identity = multiply(X1,inverse(X1)) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.12.2.0','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.21.1.0',plain,
% 2.48/2.94 ( identity = multiply(X1,inverse(X1)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.21.0.0']),
% 2.48/2.94 [weight('<4,12,6,[1,0,0,1]>')]).
% 2.48/2.94 cnf('0.21.2.0',plain,
% 2.48/2.94 ( multiply(X1,inverse(X1)) = identity ),
% 2.48/2.94 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_19]).
% 2.48/2.94 cnf('0.22.0.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),inverse(identity)) = inverse(X1) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.13.2.0','0.1.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.22.1.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),inverse(identity)) = inverse(X1) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.22.0.0']),
% 2.48/2.94 [weight('<5,13,1,[1,0,0,1]>')]).
% 2.48/2.94 cnf('0.22.1.1',plain,
% 2.48/2.94 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.22.1.0','0.20.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.22.2.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.22.1.1',theory(equality)]),
% 2.48/2.94 [u,rule_20]).
% 2.48/2.94 cnf('0.23.0.0',plain,
% 2.48/2.94 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.22.2.0','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.23.0.1',plain,
% 2.48/2.94 ( X1 = multiply(X1,identity) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.23.0.0','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L','L')]).
% 2.48/2.94 cnf('0.23.1.0',plain,
% 2.48/2.94 ( X1 = multiply(X1,identity) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.23.0.1']),
% 2.48/2.94 [weight('<3,22,6,[1,0,0,1]>')]).
% 2.48/2.94 cnf('0.23.2.0',plain,
% 2.48/2.94 ( multiply(X1,identity) = X1 ),
% 2.48/2.94 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_21]).
% 2.48/2.94 cnf('0.24.0.0',plain,
% 2.48/2.94 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.5.2.0','0.14.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.24.1.0',plain,
% 2.48/2.94 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.24.0.0']),
% 2.48/2.94 [weight('<5,14,5,[0,0,0,2]>')]).
% 2.48/2.94 cnf('0.24.2.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1 ),
% 2.48/2.94 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_22]).
% 2.48/2.94 cnf('0.27.0.0',plain,
% 2.48/2.94 ( greatest_lower_bound(a,greatest_lower_bound(c,X1)) = greatest_lower_bound(greatest_lower_bound(b,c),X1) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.15.2.0','0.16.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.27.0.1',plain,
% 2.48/2.94 ( greatest_lower_bound(a,greatest_lower_bound(c,X1)) = greatest_lower_bound(b,greatest_lower_bound(c,X1)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.27.0.0','0.15.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.27.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(a,greatest_lower_bound(c,X1)) = greatest_lower_bound(b,greatest_lower_bound(c,X1)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.27.0.1']),
% 2.48/2.94 [weight('<5,16,15,[0,0,0,1]>')]).
% 2.48/2.94 cnf('0.27.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(a,greatest_lower_bound(c,X1)) = greatest_lower_bound(b,greatest_lower_bound(c,X1)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_25]).
% 2.48/2.94 cnf('0.28.0.0',plain,
% 2.48/2.94 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.3.2.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.28.1.0',plain,
% 2.48/2.94 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.28.0.0']),
% 2.48/2.94 [weight('<5,17,3,[0,0,0,2]>')]).
% 2.48/2.94 cnf('0.28.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1 ),
% 2.48/2.94 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_26]).
% 2.48/2.94 cnf('0.29.0.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.18.2.0','0.4.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.29.1.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.29.0.0']),
% 2.48/2.94 [weight('<5,18,4,[1,0,0,1]>')]).
% 2.48/2.94 cnf('0.29.2.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_27]).
% 2.48/2.94 cnf('0.32.0.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,X2) = least_upper_bound(least_upper_bound(X1,X2),X1) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.24.2.0','0.3.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.32.0.1',plain,
% 2.48/2.94 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.32.0.0','0.18.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.32.1.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.32.0.1']),
% 2.48/2.94 [weight('<5,24,3,[1,0,0,2]>')]).
% 2.48/2.94 cnf('0.32.2.0',plain,
% 2.48/2.94 ( least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.32.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_30]).
% 2.48/2.94 cnf('0.38.0.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.7.2.0','0.12.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.38.0.1',plain,
% 2.48/2.94 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.38.0.0','0.1.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.38.1.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.38.0.1']),
% 2.48/2.94 [weight('<6,12,7,[0,0,0,1]>')]).
% 2.48/2.94 cnf('0.38.2.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 2.48/2.94 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_36]).
% 2.48/2.94 cnf('0.40.0.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(multiply(inverse(X1),X2),identity) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.8.2.0','0.12.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.40.1.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(multiply(inverse(X1),X2),identity) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.40.0.0']),
% 2.48/2.94 [weight('<6,12,8,[0,0,0,4]>')]).
% 2.48/2.94 cnf('0.40.1.1',plain,
% 2.48/2.94 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.40.1.0','0.14.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.40.2.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.40.1.1',theory(equality)]),
% 2.48/2.94 [u,rule_38]).
% 2.48/2.94 cnf('0.42.0.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(multiply(inverse(X1),X2),identity) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.9.2.0','0.12.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.42.1.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(multiply(inverse(X1),X2),identity) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.42.0.0']),
% 2.48/2.94 [weight('<6,12,9,[0,0,0,4]>')]).
% 2.48/2.94 cnf('0.42.1.1',plain,
% 2.48/2.94 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.42.1.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.42.2.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.42.1.1',theory(equality)]),
% 2.48/2.94 [u,rule_40]).
% 2.48/2.94 cnf('0.47.0.0',plain,
% 2.48/2.94 ( multiply(X1,multiply(inverse(X1),X2)) = multiply(identity,X2) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.7.2.0','0.21.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.47.0.1',plain,
% 2.48/2.94 ( multiply(X1,multiply(inverse(X1),X2)) = X2 ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.47.0.0','0.1.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.47.1.0',plain,
% 2.48/2.94 ( multiply(X1,multiply(inverse(X1),X2)) = X2 ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.47.0.1']),
% 2.48/2.94 [weight('<6,21,7,[0,0,0,1]>')]).
% 2.48/2.94 cnf('0.47.2.0',plain,
% 2.48/2.94 ( multiply(X1,multiply(inverse(X1),X2)) = X2 ),
% 2.48/2.94 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_45]).
% 2.48/2.94 cnf('0.53.0.0',plain,
% 2.48/2.94 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(multiply(X1,inverse(X2)),identity) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.10.2.0','0.21.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.53.1.0',plain,
% 2.48/2.94 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(multiply(X1,inverse(X2)),identity) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.53.0.0']),
% 2.48/2.94 [weight('<6,21,10,[0,0,0,4]>')]).
% 2.48/2.94 cnf('0.53.1.1',plain,
% 2.48/2.94 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X1,inverse(X2))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.53.1.0','0.14.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.53.2.0',plain,
% 2.48/2.94 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X1,inverse(X2))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.53.1.1',theory(equality)]),
% 2.48/2.94 [u,rule_51]).
% 2.48/2.94 cnf('0.54.0.0',plain,
% 2.48/2.94 ( multiply(least_upper_bound(X1,X2),inverse(X1)) = least_upper_bound(identity,multiply(X2,inverse(X1))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.11.2.0','0.21.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.54.1.0',plain,
% 2.48/2.94 ( multiply(least_upper_bound(X1,X2),inverse(X1)) = least_upper_bound(identity,multiply(X2,inverse(X1))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.54.0.0']),
% 2.48/2.94 [weight('<6,21,11,[0,0,0,1]>')]).
% 2.48/2.94 cnf('0.54.2.0',plain,
% 2.48/2.94 ( multiply(least_upper_bound(X1,X2),inverse(X1)) = least_upper_bound(identity,multiply(X2,inverse(X1))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.54.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_52]).
% 2.48/2.94 cnf('0.55.0.0',plain,
% 2.48/2.94 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(multiply(X1,inverse(X2)),identity) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.11.2.0','0.21.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.55.1.0',plain,
% 2.48/2.94 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(multiply(X1,inverse(X2)),identity) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.55.0.0']),
% 2.48/2.94 [weight('<6,21,11,[0,0,0,4]>')]).
% 2.48/2.94 cnf('0.55.1.1',plain,
% 2.48/2.94 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.55.1.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.55.2.0',plain,
% 2.48/2.94 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.55.1.1',theory(equality)]),
% 2.48/2.94 [u,rule_53]).
% 2.48/2.94 cnf('0.62.0.0',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(c,inverse(a))) = multiply(least_upper_bound(b,c),inverse(a)) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.54.2.0','0.19.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.62.1.0',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(c,inverse(a))) = multiply(least_upper_bound(b,c),inverse(a)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.62.0.0']),
% 2.48/2.94 [weight('<6,54,19,[1,0,0,1]>')]).
% 2.48/2.94 cnf('0.62.2.0',plain,
% 2.48/2.94 ( multiply(least_upper_bound(b,c),inverse(a)) = least_upper_bound(identity,multiply(c,inverse(a))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.62.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_60]).
% 2.48/2.94 cnf('0.63.0.0',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(a,inverse(c))) = multiply(least_upper_bound(b,c),inverse(c)) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.55.2.0','0.19.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.63.0.1',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(a,inverse(c))) = least_upper_bound(identity,multiply(b,inverse(c))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.63.0.0','0.55.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.63.1.0',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(a,inverse(c))) = least_upper_bound(identity,multiply(b,inverse(c))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.63.0.1']),
% 2.48/2.94 [weight('<6,55,19,[1,0,0,1]>')]).
% 2.48/2.94 cnf('0.63.2.0',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(a,inverse(c))) = least_upper_bound(identity,multiply(b,inverse(c))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.63.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_61]).
% 2.48/2.94 cnf('0.69.0.0',plain,
% 2.48/2.94 ( a = least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X1))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.5.2.0','0.27.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.69.1.0',plain,
% 2.48/2.94 ( a = least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X1))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.69.0.0']),
% 2.48/2.94 [weight('<7,27,5,[0,0,0,2]>')]).
% 2.48/2.94 cnf('0.69.2.0',plain,
% 2.48/2.94 ( least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X1))) = a ),
% 2.48/2.94 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_67]).
% 2.48/2.94 cnf('0.95.0.0',plain,
% 2.48/2.94 ( multiply(inverse(inverse(a)),inverse(least_upper_bound(b,c))) = inverse(least_upper_bound(identity,multiply(c,inverse(a)))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.13.2.0','0.62.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.95.0.1',plain,
% 2.48/2.94 ( multiply(a,inverse(least_upper_bound(b,c))) = inverse(least_upper_bound(identity,multiply(c,inverse(a)))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.95.0.0','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.95.1.0',plain,
% 2.48/2.94 ( multiply(a,inverse(least_upper_bound(b,c))) = inverse(least_upper_bound(identity,multiply(c,inverse(a)))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.95.0.1']),
% 2.48/2.94 [weight('<7,62,13,[0,0,0,1]>')]).
% 2.48/2.94 cnf('0.95.2.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(c,inverse(a)))) = multiply(a,inverse(least_upper_bound(b,c))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.95.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_93]).
% 2.48/2.94 cnf('0.129.0.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.8.2.0','0.38.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.129.1.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.129.0.0']),
% 2.48/2.94 [weight('<8,38,8,[0,0,0,4]>')]).
% 2.48/2.94 cnf('0.129.2.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.129.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_127]).
% 2.48/2.94 cnf('0.130.0.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.9.2.0','0.38.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.130.1.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.130.0.0']),
% 2.48/2.94 [weight('<8,38,9,[0,0,0,1]>')]).
% 2.48/2.94 cnf('0.130.2.0',plain,
% 2.48/2.94 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.130.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_128]).
% 2.48/2.94 cnf('0.134.0.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),X1) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.40.2.0','0.3.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.134.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),X1) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.134.0.0']),
% 2.48/2.94 [weight('<8,40,3,[1,0,0,3]>')]).
% 2.48/2.94 cnf('0.134.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),X1) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.134.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_132]).
% 2.48/2.94 cnf('0.135.0.0',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(identity,X1)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.134.2.0','0.23.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.135.0.1',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.135.0.0','0.23.2.0',theory(equality)]),
% 2.48/2.94 [pos('L','L')]).
% 2.48/2.94 cnf('0.135.1.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.135.0.1']),
% 2.48/2.94 [weight('<6,134,23,[1,0,0,2]>')]).
% 2.48/2.94 cnf('0.135.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.135.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_133]).
% 2.48/2.94 cnf('0.137.0.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.135.2.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2.1','L')]).
% 2.48/2.94 cnf('0.137.1.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.137.0.0']),
% 2.48/2.94 [weight('<6,135,17,[1,0,0,3]>')]).
% 2.48/2.94 cnf('0.137.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) = inverse(least_upper_bound(identity,X1)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.137.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_135]).
% 2.48/2.94 cnf('0.147.0.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X2)) = multiply(inverse(least_upper_bound(X1,X2)),X2) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.40.2.0','0.28.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.147.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X2)) = multiply(inverse(least_upper_bound(X1,X2)),X2) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.147.0.0']),
% 2.48/2.94 [weight('<8,40,28,[1,0,0,3]>')]).
% 2.48/2.94 cnf('0.147.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X2)) = multiply(inverse(least_upper_bound(X1,X2)),X2) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.147.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_145]).
% 2.48/2.94 cnf('0.165.0.0',plain,
% 2.48/2.94 ( multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.8.2.0','0.47.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.165.1.0',plain,
% 2.48/2.94 ( multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.165.0.0']),
% 2.48/2.94 [weight('<8,47,8,[0,0,0,4]>')]).
% 2.48/2.94 cnf('0.165.2.0',plain,
% 2.48/2.94 ( multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.165.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_163]).
% 2.48/2.94 cnf('0.173.0.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = multiply(X1,inverse(least_upper_bound(X1,X2))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.53.2.0','0.3.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.173.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = multiply(X1,inverse(least_upper_bound(X1,X2))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.173.0.0']),
% 2.48/2.94 [weight('<8,53,3,[1,0,0,1]>')]).
% 2.48/2.94 cnf('0.173.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = multiply(X1,inverse(least_upper_bound(X1,X2))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.173.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_171]).
% 2.48/2.94 cnf('0.174.0.0',plain,
% 2.48/2.94 ( greatest_lower_bound(multiply(inverse(X1),identity),inverse(least_upper_bound(X1,X2))) = multiply(inverse(X1),multiply(X1,inverse(least_upper_bound(X1,X2)))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.129.2.0','0.173.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.174.0.1',plain,
% 2.48/2.94 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = multiply(inverse(X1),multiply(X1,inverse(least_upper_bound(X1,X2)))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.174.0.0','0.23.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.174.0.2',plain,
% 2.48/2.94 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(least_upper_bound(X1,X2)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.174.0.1','0.38.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.174.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(least_upper_bound(X1,X2)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.174.0.2']),
% 2.48/2.94 [weight('<7,173,129,[0,0,0,3]>')]).
% 2.48/2.94 cnf('0.174.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(least_upper_bound(X1,X2)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.174.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_172]).
% 2.48/2.94 cnf('0.175.0.0',plain,
% 2.48/2.94 ( greatest_lower_bound(multiply(X1,identity),inverse(least_upper_bound(inverse(X1),X2))) = multiply(X1,multiply(inverse(X1),inverse(least_upper_bound(inverse(X1),X2)))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.165.2.0','0.173.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.175.0.1',plain,
% 2.48/2.94 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = multiply(X1,multiply(inverse(X1),inverse(least_upper_bound(inverse(X1),X2)))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.175.0.0','0.23.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.175.0.2',plain,
% 2.48/2.94 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.175.0.1','0.47.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.175.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.175.0.2']),
% 2.48/2.94 [weight('<7,173,165,[0,0,0,2]>')]).
% 2.48/2.94 cnf('0.175.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.175.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_173]).
% 2.48/2.94 cnf('0.176.0.0',plain,
% 2.48/2.94 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.5.2.0','0.174.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.176.1.0',plain,
% 2.48/2.94 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.176.0.0']),
% 2.48/2.94 [weight('<7,174,5,[0,0,0,2]>')]).
% 2.48/2.94 cnf('0.176.2.0',plain,
% 2.48/2.94 ( least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(X1) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.176.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_174]).
% 2.48/2.94 cnf('0.177.0.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.174.2.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2.1','L')]).
% 2.48/2.94 cnf('0.177.1.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.177.0.0']),
% 2.48/2.94 [weight('<7,174,17,[1,0,0,4]>')]).
% 2.48/2.94 cnf('0.177.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(least_upper_bound(X1,X2)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.177.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_175]).
% 2.48/2.94 cnf('0.178.0.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(greatest_lower_bound(X1,X2),X1)) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.177.2.0','0.5.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2.1','L')]).
% 2.48/2.94 cnf('0.178.1.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(greatest_lower_bound(X1,X2),X1)) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.178.0.0']),
% 2.48/2.94 [weight('<6,177,5,[1,0,0,4]>')]).
% 2.48/2.94 cnf('0.178.1.1',plain,
% 2.48/2.94 ( inverse(least_upper_bound(X1,greatest_lower_bound(X1,X2))) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.178.1.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.178.1.2',plain,
% 2.48/2.94 ( inverse(X1) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.178.1.1','0.5.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.178.1.3',plain,
% 2.48/2.94 ( inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.178.1.2','0.14.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.178.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(X1) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.178.1.3',theory(equality)]),
% 2.48/2.94 [x,rule_176]).
% 2.48/2.94 cnf('0.183.0.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.175.2.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2.1','L')]).
% 2.48/2.94 cnf('0.183.1.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.183.0.0']),
% 2.48/2.94 [weight('<7,175,17,[1,0,0,3]>')]).
% 2.48/2.94 cnf('0.183.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.183.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_181]).
% 2.48/2.94 cnf('0.184.0.0',plain,
% 2.48/2.94 ( greatest_lower_bound(b,greatest_lower_bound(c,inverse(least_upper_bound(inverse(c),X1)))) = greatest_lower_bound(a,inverse(least_upper_bound(inverse(c),X1))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.27.2.0','0.175.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.184.0.1',plain,
% 2.48/2.94 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1))) = greatest_lower_bound(a,inverse(least_upper_bound(inverse(c),X1))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.184.0.0','0.175.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.184.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1))) = greatest_lower_bound(a,inverse(least_upper_bound(inverse(c),X1))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.184.0.1']),
% 2.48/2.94 [weight('<7,175,27,[0,0,0,2]>')]).
% 2.48/2.94 cnf('0.184.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(a,inverse(least_upper_bound(inverse(c),X1))) = greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.184.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_182]).
% 2.48/2.94 cnf('0.185.0.0',plain,
% 2.48/2.94 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.176.2.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2.1','L')]).
% 2.48/2.94 cnf('0.185.1.0',plain,
% 2.48/2.94 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.185.0.0']),
% 2.48/2.94 [weight('<7,176,17,[1,0,0,4]>')]).
% 2.48/2.94 cnf('0.185.2.0',plain,
% 2.48/2.94 ( least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(X1) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.185.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_183]).
% 2.48/2.94 cnf('0.188.0.0',plain,
% 2.48/2.94 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.24.2.0','0.178.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.188.1.0',plain,
% 2.48/2.94 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.188.0.0']),
% 2.48/2.94 [weight('<7,178,24,[0,0,0,2]>')]).
% 2.48/2.94 cnf('0.188.1.1',plain,
% 2.48/2.94 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.188.1.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.188.2.0',plain,
% 2.48/2.94 ( least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(greatest_lower_bound(X1,X2)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.188.1.1',theory(equality)]),
% 2.48/2.94 [x,rule_186]).
% 2.48/2.94 cnf('0.202.0.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(X1,inverse(least_upper_bound(X2,X1))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.53.2.0','0.28.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.202.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(X1,inverse(least_upper_bound(X2,X1))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.202.0.0']),
% 2.48/2.94 [weight('<8,53,28,[1,0,0,1]>')]).
% 2.48/2.94 cnf('0.202.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(X1,inverse(least_upper_bound(X2,X1))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.202.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_200]).
% 2.48/2.94 cnf('0.246.0.0',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(least_upper_bound(X1,X2),inverse(least_upper_bound(X2,X1))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.55.2.0','0.32.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.246.1.0',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(least_upper_bound(X1,X2),inverse(least_upper_bound(X2,X1))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.246.0.0']),
% 2.48/2.94 [weight('<8,55,32,[1,0,0,1]>')]).
% 2.48/2.94 cnf('0.246.2.0',plain,
% 2.48/2.94 ( multiply(least_upper_bound(X1,X2),inverse(least_upper_bound(X2,X1))) = least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.246.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_242]).
% 2.48/2.94 cnf('0.274.0.0',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),inverse(inverse(X1))) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.13.2.0','0.130.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.274.0.1',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.274.0.0','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.274.1.0',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.274.0.1']),
% 2.48/2.94 [weight('<8,130,13,[0,0,0,1]>')]).
% 2.48/2.94 cnf('0.274.2.0',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.274.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_270]).
% 2.48/2.94 cnf('0.275.0.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(X1,multiply(inverse(inverse(X1)),X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.274.2.0','0.12.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1.1.1','L')]).
% 2.48/2.94 cnf('0.275.0.1',plain,
% 2.48/2.94 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.275.0.0','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1.2.1','L')]).
% 2.48/2.94 cnf('0.275.1.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.275.0.1']),
% 2.48/2.94 [weight('<6,274,12,[1,0,0,3]>')]).
% 2.48/2.94 cnf('0.275.2.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.275.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_271]).
% 2.48/2.94 cnf('0.276.0.0',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(identity,X1)),inverse(inverse(X1))) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.275.2.0','0.12.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1.2','L')]).
% 2.48/2.94 cnf('0.276.0.1',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.276.0.0','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.276.1.0',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.276.0.1']),
% 2.48/2.94 [weight('<6,275,12,[1,0,0,3]>')]).
% 2.48/2.94 cnf('0.276.1.1',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.276.1.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('R.1','L')]).
% 2.48/2.94 cnf('0.276.2.0',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.276.1.1',theory(equality)]),
% 2.48/2.94 [u,rule_272]).
% 2.48/2.94 cnf('0.293.0.0',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,multiply(inverse(inverse(least_upper_bound(X1,identity))),identity)) = multiply(inverse(inverse(least_upper_bound(X1,identity))),inverse(least_upper_bound(identity,X1))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.40.2.0','0.137.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.293.0.1',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,inverse(inverse(least_upper_bound(X1,identity)))) = multiply(inverse(inverse(least_upper_bound(X1,identity))),inverse(least_upper_bound(identity,X1))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.293.0.0','0.23.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.293.0.2',plain,
% 2.48/2.94 ( greatest_lower_bound(identity,least_upper_bound(X1,identity)) = multiply(inverse(inverse(least_upper_bound(X1,identity))),inverse(least_upper_bound(identity,X1))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.293.0.1','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.293.0.3',plain,
% 2.48/2.94 ( identity = multiply(inverse(inverse(least_upper_bound(X1,identity))),inverse(least_upper_bound(identity,X1))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.293.0.2','0.28.2.0',theory(equality)]),
% 2.48/2.94 [pos('L','L')]).
% 2.48/2.94 cnf('0.293.0.4',plain,
% 2.48/2.94 ( identity = multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,X1))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.293.0.3','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('R.1','L')]).
% 2.48/2.94 cnf('0.293.1.0',plain,
% 2.48/2.94 ( identity = multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,X1))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.293.0.4']),
% 2.48/2.94 [weight('<8,137,40,[0,0,0,3]>')]).
% 2.48/2.94 cnf('0.293.1.1',plain,
% 2.48/2.94 ( identity = least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(identity,X1)))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.293.1.0','0.246.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.293.2.0',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(identity,X1)))) = identity ),
% 2.48/2.94 inference(orient,[status(thm)],['0.293.1.1',theory(equality)]),
% 2.48/2.94 [x,rule_289]).
% 2.48/2.94 cnf('0.294.0.0',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(identity,X1))))),multiply(X1,inverse(least_upper_bound(identity,X1)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.147.2.0','0.293.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2.1.1','L')]).
% 2.48/2.94 cnf('0.294.0.1',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,inverse(multiply(X1,inverse(least_upper_bound(identity,X1)))))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.294.0.0','0.276.2.0',theory(equality)]),
% 2.48/2.94 [pos('L','L')]).
% 2.48/2.94 cnf('0.294.0.2',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(inverse(inverse(least_upper_bound(identity,X1))),inverse(X1)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.294.0.1','0.13.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1.2','L')]).
% 2.48/2.94 cnf('0.294.0.3',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(least_upper_bound(identity,X1),inverse(X1)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.294.0.2','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1.2.1','L')]).
% 2.48/2.94 cnf('0.294.0.4',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,least_upper_bound(identity,multiply(identity,inverse(X1))))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.294.0.3','0.55.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1.2','L')]).
% 2.48/2.94 cnf('0.294.0.5',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(identity,inverse(X1)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.294.0.4','0.29.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.294.0.6',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(identity,inverse(X1))),inverse(identity)) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.294.0.5','0.275.2.0',theory(equality)]),
% 2.48/2.94 [pos('L','L')]).
% 2.48/2.94 cnf('0.294.0.7',plain,
% 2.48/2.94 ( multiply(inverse(least_upper_bound(identity,inverse(X1))),identity) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.294.0.6','0.20.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.294.0.8',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.294.0.7','0.23.2.0',theory(equality)]),
% 2.48/2.94 [pos('L','L')]).
% 2.48/2.94 cnf('0.294.0.9',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,multiply(identity,multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.294.0.8','0.20.2.0',theory(equality)]),
% 2.48/2.94 [pos('R.2.1','L')]).
% 2.48/2.94 cnf('0.294.0.10',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(identity,X1)))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.294.0.9','0.1.2.0',theory(equality)]),
% 2.48/2.94 [pos('R.2','L')]).
% 2.48/2.94 cnf('0.294.0.11',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(identity,X1))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.294.0.10','0.202.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.294.1.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(identity,X1))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.294.0.11']),
% 2.48/2.94 [weight('<6,293,147,[0,0,0,4]>')]).
% 2.48/2.94 cnf('0.294.2.0',plain,
% 2.48/2.94 ( multiply(X1,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.294.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_290]).
% 2.48/2.94 cnf('0.296.0.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,inverse(multiply(c,inverse(a))))) = multiply(multiply(c,inverse(a)),multiply(a,inverse(least_upper_bound(b,c)))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.294.2.0','0.95.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.296.0.1',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(inverse(inverse(a)),inverse(c)))) = multiply(multiply(c,inverse(a)),multiply(a,inverse(least_upper_bound(b,c)))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.296.0.0','0.13.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1.2','L')]).
% 2.48/2.94 cnf('0.296.0.2',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(a,inverse(c)))) = multiply(multiply(c,inverse(a)),multiply(a,inverse(least_upper_bound(b,c)))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.296.0.1','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1.2.1','L')]).
% 2.48/2.94 cnf('0.296.0.3',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(b,inverse(c)))) = multiply(multiply(c,inverse(a)),multiply(a,inverse(least_upper_bound(b,c)))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.296.0.2','0.63.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.296.0.4',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(b,inverse(c)))) = multiply(c,multiply(inverse(a),multiply(a,inverse(least_upper_bound(b,c))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.296.0.3','0.7.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.296.0.5',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(b,inverse(c)))) = multiply(c,inverse(least_upper_bound(b,c))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.296.0.4','0.38.2.0',theory(equality)]),
% 2.48/2.94 [pos('R.2','L')]).
% 2.48/2.94 cnf('0.296.1.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(b,inverse(c)))) = multiply(c,inverse(least_upper_bound(b,c))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.296.0.5']),
% 2.48/2.94 [weight('<7,294,95,[1,0,0,2]>')]).
% 2.48/2.94 cnf('0.296.2.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(b,inverse(c)))) = multiply(c,inverse(least_upper_bound(b,c))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.296.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_292]).
% 2.48/2.94 cnf('0.297.0.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,inverse(multiply(b,inverse(c))))) = multiply(multiply(b,inverse(c)),multiply(c,inverse(least_upper_bound(b,c)))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.294.2.0','0.296.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.297.0.1',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(inverse(inverse(c)),inverse(b)))) = multiply(multiply(b,inverse(c)),multiply(c,inverse(least_upper_bound(b,c)))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.297.0.0','0.13.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1.2','L')]).
% 2.48/2.94 cnf('0.297.0.2',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(multiply(b,inverse(c)),multiply(c,inverse(least_upper_bound(b,c)))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.297.0.1','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1.2.1','L')]).
% 2.48/2.94 cnf('0.297.0.3',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(b,multiply(inverse(c),multiply(c,inverse(least_upper_bound(b,c))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.297.0.2','0.7.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.297.0.4',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(b,inverse(least_upper_bound(b,c))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.297.0.3','0.38.2.0',theory(equality)]),
% 2.48/2.94 [pos('R.2','L')]).
% 2.48/2.94 cnf('0.297.1.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(b,inverse(least_upper_bound(b,c))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.297.0.4']),
% 2.48/2.94 [weight('<7,296,294,[0,0,0,2]>')]).
% 2.48/2.94 cnf('0.297.2.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(b,inverse(least_upper_bound(b,c))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.297.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_293]).
% 2.48/2.94 cnf('0.350.0.0',plain,
% 2.48/2.94 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),inverse(a)))) = inverse(least_upper_bound(inverse(a),inverse(c))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.184.2.0','0.183.2.0',theory(equality)]),
% 2.48/2.94 [pos('L','L')]).
% 2.48/2.94 cnf('0.350.1.0',plain,
% 2.48/2.94 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),inverse(a)))) = inverse(least_upper_bound(inverse(a),inverse(c))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.350.0.0']),
% 2.48/2.94 [weight('<8,184,183,[1,0,0,0]>')]).
% 2.48/2.94 cnf('0.350.1.1',plain,
% 2.48/2.94 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(a),inverse(c)))) = inverse(least_upper_bound(inverse(a),inverse(c))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.350.1.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2.1','L')]).
% 2.48/2.94 cnf('0.350.2.0',plain,
% 2.48/2.94 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(a),inverse(c)))) = inverse(least_upper_bound(inverse(a),inverse(c))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.350.1.1',theory(equality)]),
% 2.48/2.94 [u,rule_346]).
% 2.48/2.94 cnf('0.536.0.0',plain,
% 2.48/2.94 ( inverse(greatest_lower_bound(b,inverse(least_upper_bound(inverse(a),inverse(c))))) = least_upper_bound(inverse(b),inverse(inverse(least_upper_bound(inverse(a),inverse(c))))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.188.2.0','0.350.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2.1','L')]).
% 2.48/2.94 cnf('0.536.0.1',plain,
% 2.48/2.94 ( inverse(inverse(least_upper_bound(inverse(a),inverse(c)))) = least_upper_bound(inverse(b),inverse(inverse(least_upper_bound(inverse(a),inverse(c))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.536.0.0','0.350.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.536.0.2',plain,
% 2.48/2.94 ( least_upper_bound(inverse(a),inverse(c)) = least_upper_bound(inverse(b),inverse(inverse(least_upper_bound(inverse(a),inverse(c))))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.536.0.1','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L','L')]).
% 2.48/2.94 cnf('0.536.0.3',plain,
% 2.48/2.94 ( least_upper_bound(inverse(a),inverse(c)) = least_upper_bound(inverse(b),least_upper_bound(inverse(a),inverse(c))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.536.0.2','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('R.2','L')]).
% 2.48/2.94 cnf('0.536.1.0',plain,
% 2.48/2.94 ( least_upper_bound(inverse(a),inverse(c)) = least_upper_bound(inverse(b),least_upper_bound(inverse(a),inverse(c))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.536.0.3']),
% 2.48/2.94 [weight('<8,350,188,[0,0,0,4]>')]).
% 2.48/2.94 cnf('0.536.2.0',plain,
% 2.48/2.94 ( least_upper_bound(inverse(b),least_upper_bound(inverse(a),inverse(c))) = least_upper_bound(inverse(a),inverse(c)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.536.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_531]).
% 2.48/2.94 cnf('0.1145.0.0',plain,
% 2.48/2.94 ( a = least_upper_bound(a,greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1)))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.69.2.0','0.175.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2.2','L')]).
% 2.48/2.94 cnf('0.1145.1.0',plain,
% 2.48/2.94 ( a = least_upper_bound(a,greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1)))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.1145.0.0']),
% 2.48/2.94 [weight('<9,175,69,[0,0,0,4]>')]).
% 2.48/2.94 cnf('0.1145.2.0',plain,
% 2.48/2.94 ( least_upper_bound(a,greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1)))) = a ),
% 2.48/2.94 inference(orient,[status(thm)],['0.1145.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_1135]).
% 2.48/2.94 cnf('0.1146.0.0',plain,
% 2.48/2.94 ( a = least_upper_bound(a,inverse(least_upper_bound(inverse(b),inverse(c)))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.1145.2.0','0.183.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.1146.1.0',plain,
% 2.48/2.94 ( a = least_upper_bound(a,inverse(least_upper_bound(inverse(b),inverse(c)))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.1146.0.0']),
% 2.48/2.94 [weight('<8,1145,183,[1,0,0,2]>')]).
% 2.48/2.94 cnf('0.1146.2.0',plain,
% 2.48/2.94 ( least_upper_bound(a,inverse(least_upper_bound(inverse(b),inverse(c)))) = a ),
% 2.48/2.94 inference(orient,[status(thm)],['0.1146.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_1136]).
% 2.48/2.94 cnf('0.1147.0.0',plain,
% 2.48/2.94 ( inverse(inverse(least_upper_bound(inverse(b),inverse(c)))) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(b),inverse(c)))),inverse(a)) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.185.2.0','0.1146.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2.1','L')]).
% 2.48/2.94 cnf('0.1147.0.1',plain,
% 2.48/2.94 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(b),inverse(c)))),inverse(a)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.1147.0.0','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L','L')]).
% 2.48/2.94 cnf('0.1147.0.2',plain,
% 2.48/2.94 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(least_upper_bound(inverse(b),inverse(c)),inverse(a)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.1147.0.1','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('R.1','L')]).
% 2.48/2.94 cnf('0.1147.0.3',plain,
% 2.48/2.94 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(b),least_upper_bound(inverse(c),inverse(a))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.1147.0.2','0.18.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.1147.1.0',plain,
% 2.48/2.94 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(b),least_upper_bound(inverse(c),inverse(a))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.1147.0.3']),
% 2.48/2.94 [weight('<8,1146,185,[0,0,0,4]>')]).
% 2.48/2.94 cnf('0.1147.1.1',plain,
% 2.48/2.94 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(b),least_upper_bound(inverse(a),inverse(c))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.1147.1.0','0.17.2.0',theory(equality)]),
% 2.48/2.94 [pos('R.2','L')]).
% 2.48/2.94 cnf('0.1147.1.2',plain,
% 2.48/2.94 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(a),inverse(c)) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.1147.1.1','0.536.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.1147.2.0',plain,
% 2.48/2.94 ( least_upper_bound(inverse(a),inverse(c)) = least_upper_bound(inverse(b),inverse(c)) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.1147.1.2',theory(equality)]),
% 2.48/2.94 [x,rule_1137]).
% 2.48/2.94 cnf('0.1150.0.0',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(inverse(inverse(c)),inverse(a))) = multiply(inverse(inverse(c)),least_upper_bound(inverse(b),inverse(c))) ),
% 2.48/2.94 inference(cp,[status(thm)],['0.42.2.0','0.1147.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2','L')]).
% 2.48/2.94 cnf('0.1150.0.1',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(c,inverse(a))) = multiply(inverse(inverse(c)),least_upper_bound(inverse(b),inverse(c))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.1150.0.0','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.2.1','L')]).
% 2.48/2.94 cnf('0.1150.0.2',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(c,inverse(a))) = least_upper_bound(identity,multiply(inverse(inverse(c)),inverse(b))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.1150.0.1','0.42.2.0',theory(equality)]),
% 2.48/2.94 [pos('R','L')]).
% 2.48/2.94 cnf('0.1150.0.3',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(c,inverse(a))) = least_upper_bound(identity,multiply(c,inverse(b))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.1150.0.2','0.6.2.0',theory(equality)]),
% 2.48/2.94 [pos('R.2.1','L')]).
% 2.48/2.94 cnf('0.1150.1.0',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(c,inverse(a))) = least_upper_bound(identity,multiply(c,inverse(b))) ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.1150.0.3']),
% 2.48/2.94 [weight('<6,1147,42,[0,0,0,3]>')]).
% 2.48/2.94 cnf('0.1150.2.0',plain,
% 2.48/2.94 ( least_upper_bound(identity,multiply(c,inverse(a))) = least_upper_bound(identity,multiply(c,inverse(b))) ),
% 2.48/2.94 inference(orient,[status(thm)],['0.1150.1.0',theory(equality)]),
% 2.48/2.94 [u,rule_1140]).
% 2.48/2.94 cnf('0.1151.0.0',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(c,inverse(a)))) = multiply(a,inverse(least_upper_bound(b,c))) ),
% 2.48/2.94 inference(interreduction_right,[status(thm)],['0.95.2.0'])).
% 2.48/2.94 cnf('0.1151.0.1',plain,
% 2.48/2.94 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(a,inverse(least_upper_bound(b,c))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.1151.0.0','0.1150.2.0',theory(equality)]),
% 2.48/2.94 [pos('L.1','L')]).
% 2.48/2.94 cnf('0.1151.0.2',plain,
% 2.48/2.94 ( multiply(b,inverse(least_upper_bound(b,c))) = multiply(a,inverse(least_upper_bound(b,c))) ),
% 2.48/2.94 inference(reduction,[status(thm)],['0.1151.0.1','0.297.2.0',theory(equality)]),
% 2.48/2.94 [pos('L','L')]).
% 2.48/2.94 cnf('0.1151.1.0',plain,
% 2.48/2.94 ( b = a ),
% 2.48/2.94 inference(weigh,[status(thm)],['0.1151.0.2']),
% 2.48/2.94 [weight('<1,95,1150,[0,0,0,0]>')]).
% 2.48/2.94 cnf('0.1151.2.0',plain,
% 2.48/2.94 ( a = b ),
% 2.48/2.94 inference(orient,[status(thm)],['0.1151.1.0',theory(equality)]),
% 2.48/2.94 [x,rule_1141]).
% 2.48/2.94 cnf('1.0.0.0',conjecture,
% 2.48/2.94 ( a = b ),
% 2.48/2.94 file('/tmp/WALDMEISTER_5376_n017',conjecture_1)).
% 2.48/2.94 cnf('1.0.0.1',plain,
% 2.48/2.94 ( b = b ),
% 2.48/2.94 inference(reduction,[status(thm)],['1.0.0.0','0.1151.2.0',theory(equality)]),
% 2.48/2.94 [pos('L','L')]).
% 2.48/2.94 cnf('1.0.0.2',plain,
% 2.48/2.94 ( $true ),
% 2.48/2.94 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 2.48/2.94 [conjecture_1]).
% 2.48/2.94
% 2.48/2.94 Proved Goals:
% 2.48/2.94 No. 1: a ?= b joined, current: b = b
% 2.48/2.94 1 goal was specified, which was proved.
% 2.48/2.94 % SZS output end CNFRefutation
% 2.48/2.94 #END OF PROOF
% 2.48/2.94
% 2.48/2.94 Problem WALDMEISTER_5376_n017
% 2.48/2.94 CPs.gen 223162
% 2.48/2.94 CPs.reexp 0
% 2.48/2.94 Select 13159
% 2.48/2.94 R 1141
% 2.48/2.94 E 10
% 2.48/2.94 vsize 8.9M
% 2.48/2.94 rss 4.5M
% 2.48/2.94 process.time 1.219s
% 2.48/2.94 wallclock.time 1.982s
% 2.48/2.94 status S
% 2.48/2.94
% 2.48/2.94
% 2.48/2.94 Waldmeister states: Goal proved.
% 2.48/2.94 % SZS status Unsatisfiable
% 2.48/2.94
% 2.48/2.94 Problem WALDMEISTER_5376_n017
% 2.48/2.94 CPs.gen 176380
% 2.48/2.94 CPs.reexp 0
% 2.48/2.94 Select 16273
% 2.48/2.94 R 990
% 2.48/2.94 E 12
% 2.48/2.94 vsize 7.5M
% 2.48/2.94 rss 4.8M
% 2.48/2.94 process.time 0.741s
% 2.48/2.94 wallclock.time 1.983s
% 2.48/2.94 status S
%------------------------------------------------------------------------------