TSTP Solution File: GRP167-3 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP167-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n014.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 12:25:03 EDT 2022
% Result : Unsatisfiable 3.03s 3.44s
% Output : CNFRefutation 3.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP167-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : woody %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 13:04:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.57/0.97 ********************************************************************************
% 0.57/0.97 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.97 * |/ | \/ | *
% 0.57/0.97 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.97 * A. Jaeger and B. Loechner | | *
% 0.57/0.97 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.97 ********************************************************************************
% 0.57/0.97
% 0.57/0.97
% 0.57/0.97 Goals:
% 0.57/0.97 ------
% 0.57/0.97
% 0.57/0.97 ( 1) multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) ?=? a
% 0.57/0.97
% 0.57/0.97 Detected structure: VerbandsgeordneteGruppe
% 0.57/0.97 ********************************************************************************
% 0.57/0.97 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.97 ********************************************************************************
% 0.57/0.97
% 3.03/3.44 joined goal: 1 multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) ?= a to a
% 3.03/3.44 goal joined
% 3.03/3.44 % SZS status Unsatisfiable
% 3.03/3.44 #START OF PROOF
% 3.03/3.44 % SZS output start CNFRefutation
% 3.03/3.44 cnf('0.1.0.0',axiom,
% 3.03/3.44 ( X1 = multiply(identity,X1) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.1.1.0',plain,
% 3.03/3.44 ( X1 = multiply(identity,X1) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.1.0.0']),
% 3.03/3.44 [weight('<0,0,0,[0,0,0,1]>')]).
% 3.03/3.44 cnf('0.1.2.0',plain,
% 3.03/3.44 ( multiply(identity,X1) = X1 ),
% 3.03/3.44 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_1]).
% 3.03/3.44 cnf('0.2.0.0',axiom,
% 3.03/3.44 ( X1 = least_upper_bound(X1,X1) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.2.1.0',plain,
% 3.03/3.44 ( X1 = least_upper_bound(X1,X1) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.2.0.0']),
% 3.03/3.44 [weight('<1,0,0,[0,0,0,2]>')]).
% 3.03/3.44 cnf('0.2.2.0',plain,
% 3.03/3.44 ( least_upper_bound(X1,X1) = X1 ),
% 3.03/3.44 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_2]).
% 3.03/3.44 cnf('0.3.0.0',axiom,
% 3.03/3.44 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.3.1.0',plain,
% 3.03/3.44 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.3.0.0']),
% 3.03/3.44 [weight('<2,0,0,[0,0,0,3]>')]).
% 3.03/3.44 cnf('0.3.2.0',plain,
% 3.03/3.44 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 3.03/3.44 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_3]).
% 3.03/3.44 cnf('0.4.0.0',axiom,
% 3.03/3.44 ( X1 = greatest_lower_bound(X1,X1) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.4.1.0',plain,
% 3.03/3.44 ( X1 = greatest_lower_bound(X1,X1) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.4.0.0']),
% 3.03/3.44 [weight('<3,0,0,[0,0,0,4]>')]).
% 3.03/3.44 cnf('0.4.2.0',plain,
% 3.03/3.44 ( greatest_lower_bound(X1,X1) = X1 ),
% 3.03/3.44 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_4]).
% 3.03/3.44 cnf('0.5.0.0',axiom,
% 3.03/3.44 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.5.1.0',plain,
% 3.03/3.44 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.5.0.0']),
% 3.03/3.44 [weight('<4,0,0,[0,0,0,5]>')]).
% 3.03/3.44 cnf('0.5.2.0',plain,
% 3.03/3.44 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 3.03/3.44 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_5]).
% 3.03/3.44 cnf('0.6.0.0',axiom,
% 3.03/3.44 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.6.1.0',plain,
% 3.03/3.44 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.6.0.0']),
% 3.03/3.44 [weight('<5,0,0,[0,0,0,6]>')]).
% 3.03/3.44 cnf('0.6.2.0',plain,
% 3.03/3.44 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 3.03/3.44 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_6]).
% 3.03/3.44 cnf('0.7.0.0',axiom,
% 3.03/3.44 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.7.1.0',plain,
% 3.03/3.44 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.7.0.0']),
% 3.03/3.44 [weight('<6,0,0,[0,0,0,7]>')]).
% 3.03/3.44 cnf('0.7.2.0',plain,
% 3.03/3.44 ( least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)) ),
% 3.03/3.44 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_7]).
% 3.03/3.44 cnf('0.8.0.0',axiom,
% 3.03/3.44 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.8.1.0',plain,
% 3.03/3.44 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.8.0.0']),
% 3.03/3.44 [weight('<7,0,0,[0,0,0,8]>')]).
% 3.03/3.44 cnf('0.8.2.0',plain,
% 3.03/3.44 ( greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)) ),
% 3.03/3.44 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_8]).
% 3.03/3.44 cnf('0.9.0.0',axiom,
% 3.03/3.44 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.9.1.0',plain,
% 3.03/3.44 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.9.0.0']),
% 3.03/3.44 [weight('<8,0,0,[0,0,0,9]>')]).
% 3.03/3.44 cnf('0.9.2.0',plain,
% 3.03/3.44 ( least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2) ),
% 3.03/3.44 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_9]).
% 3.03/3.44 cnf('0.10.0.0',axiom,
% 3.03/3.44 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.10.1.0',plain,
% 3.03/3.44 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.10.0.0']),
% 3.03/3.44 [weight('<9,0,0,[0,0,0,10]>')]).
% 3.03/3.44 cnf('0.10.2.0',plain,
% 3.03/3.44 ( greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2) ),
% 3.03/3.44 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_10]).
% 3.03/3.44 cnf('0.11.0.0',axiom,
% 3.03/3.44 ( multiply(inverse(X1),X1) = identity ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.11.1.0',plain,
% 3.03/3.44 ( multiply(inverse(X1),X1) = identity ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.11.0.0']),
% 3.03/3.44 [weight('<10,0,0,[0,0,0,11]>')]).
% 3.03/3.44 cnf('0.11.2.0',plain,
% 3.03/3.44 ( multiply(inverse(X1),X1) = identity ),
% 3.03/3.44 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 3.03/3.44 [u,rule_11]).
% 3.03/3.44 cnf('0.12.0.0',axiom,
% 3.03/3.44 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.12.1.0',plain,
% 3.03/3.44 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.12.0.0']),
% 3.03/3.44 [weight('<11,0,0,[0,0,0,12]>')]).
% 3.03/3.44 cnf('0.12.2.0',plain,
% 3.03/3.44 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 3.03/3.44 inference(activate,[status(thm)],['0.12.1.0']),
% 3.03/3.44 [equation_1]).
% 3.03/3.44 cnf('0.13.0.0',axiom,
% 3.03/3.44 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.13.1.0',plain,
% 3.03/3.44 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.13.0.0']),
% 3.03/3.44 [weight('<12,0,0,[0,0,0,13]>')]).
% 3.03/3.44 cnf('0.13.2.0',plain,
% 3.03/3.44 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 3.03/3.44 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_12]).
% 3.03/3.44 cnf('0.14.0.0',axiom,
% 3.03/3.44 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.14.1.0',plain,
% 3.03/3.44 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.14.0.0']),
% 3.03/3.44 [weight('<13,0,0,[0,0,0,14]>')]).
% 3.03/3.44 cnf('0.14.2.0',plain,
% 3.03/3.44 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 3.03/3.44 inference(activate,[status(thm)],['0.14.1.0']),
% 3.03/3.44 [equation_2]).
% 3.03/3.44 cnf('0.15.0.0',axiom,
% 3.03/3.44 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 3.03/3.44 file('/tmp/WALDMEISTER_27856_n014')).
% 3.03/3.44 cnf('0.15.1.0',plain,
% 3.03/3.44 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 3.03/3.44 inference(weigh,[status(thm)],['0.15.0.0']),
% 3.03/3.44 [weight('<14,0,0,[0,0,0,15]>')]).
% 3.03/3.44 cnf('0.15.2.0',plain,
% 3.03/3.44 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 3.03/3.44 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 3.03/3.44 [x,rule_13]).
% 3.03/3.44 cnf('0.16.0.0',plain,
% 3.03/3.44 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 3.03/3.44 inference(cp,[status(thm)],['0.5.2.0','0.12.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.16.1.0',plain,
% 3.03/3.45 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.16.0.0']),
% 3.03/3.45 [weight('<5,12,5,[0,0,0,2]>')]).
% 3.03/3.45 cnf('0.16.2.0',plain,
% 3.03/3.45 ( greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1 ),
% 3.03/3.45 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_14]).
% 3.03/3.45 cnf('0.17.0.0',plain,
% 3.03/3.45 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.13.2.0','0.2.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.17.1.0',plain,
% 3.03/3.45 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.17.0.0']),
% 3.03/3.45 [weight('<5,13,2,[1,0,0,1]>')]).
% 3.03/3.45 cnf('0.17.2.0',plain,
% 3.03/3.45 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_15]).
% 3.03/3.45 cnf('0.18.0.0',plain,
% 3.03/3.45 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.3.2.0','0.14.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.18.1.0',plain,
% 3.03/3.45 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.18.0.0']),
% 3.03/3.45 [weight('<5,14,3,[0,0,0,2]>')]).
% 3.03/3.45 cnf('0.18.2.0',plain,
% 3.03/3.45 ( least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1 ),
% 3.03/3.45 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_16]).
% 3.03/3.45 cnf('0.19.0.0',plain,
% 3.03/3.45 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.15.2.0','0.4.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.19.1.0',plain,
% 3.03/3.45 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.19.0.0']),
% 3.03/3.45 [weight('<5,15,4,[1,0,0,1]>')]).
% 3.03/3.45 cnf('0.19.2.0',plain,
% 3.03/3.45 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_17]).
% 3.03/3.45 cnf('0.20.0.0',plain,
% 3.03/3.45 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(greatest_lower_bound(X1,X2),X1) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.16.2.0','0.3.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.20.0.1',plain,
% 3.03/3.45 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.20.0.0','0.15.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.20.1.0',plain,
% 3.03/3.45 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.20.0.1']),
% 3.03/3.45 [weight('<5,16,3,[1,0,0,2]>')]).
% 3.03/3.45 cnf('0.20.2.0',plain,
% 3.03/3.45 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_18]).
% 3.03/3.45 cnf('0.22.0.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.22.0.1',plain,
% 3.03/3.45 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.22.0.0','0.1.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.22.1.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.22.0.1']),
% 3.03/3.45 [weight('<6,11,6,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.22.2.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 3.03/3.45 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_20]).
% 3.03/3.45 cnf('0.23.0.0',plain,
% 3.03/3.45 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.22.2.0','0.22.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.23.1.0',plain,
% 3.03/3.45 ( X1 = inverse(inverse(X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.23.0.0']),
% 3.03/3.45 [weight('<3,22,22,[0,0,0,3]>')]).
% 3.03/3.45 cnf('0.23.2.0',plain,
% 3.03/3.45 ( inverse(inverse(X1)) = X1 ),
% 3.03/3.45 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_21]).
% 3.03/3.45 cnf('0.25.0.0',plain,
% 3.03/3.45 ( identity = multiply(X1,inverse(X1)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.11.2.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.25.1.0',plain,
% 3.03/3.45 ( identity = multiply(X1,inverse(X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.25.0.0']),
% 3.03/3.45 [weight('<4,23,11,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.25.2.0',plain,
% 3.03/3.45 ( multiply(X1,inverse(X1)) = identity ),
% 3.03/3.45 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_23]).
% 3.03/3.45 cnf('0.26.0.0',plain,
% 3.03/3.45 ( identity = inverse(identity) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.25.2.0','0.1.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('0.26.1.0',plain,
% 3.03/3.45 ( identity = inverse(identity) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.26.0.0']),
% 3.03/3.45 [weight('<2,25,1,[1,0,0,0]>')]).
% 3.03/3.45 cnf('0.26.2.0',plain,
% 3.03/3.45 ( inverse(identity) = identity ),
% 3.03/3.45 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_24]).
% 3.03/3.45 cnf('0.27.0.0',plain,
% 3.03/3.45 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.22.2.0','0.25.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.27.1.0',plain,
% 3.03/3.45 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.27.0.0']),
% 3.03/3.45 [weight('<4,25,22,[0,0,0,3]>')]).
% 3.03/3.45 cnf('0.27.2.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_25]).
% 3.03/3.45 cnf('0.28.0.0',plain,
% 3.03/3.45 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.27.2.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.28.0.1',plain,
% 3.03/3.45 ( X1 = multiply(X1,identity) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.28.0.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('0.28.1.0',plain,
% 3.03/3.45 ( X1 = multiply(X1,identity) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.28.0.1']),
% 3.03/3.45 [weight('<3,27,23,[1,0,0,1]>')]).
% 3.03/3.45 cnf('0.28.2.0',plain,
% 3.03/3.45 ( multiply(X1,identity) = X1 ),
% 3.03/3.45 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_26]).
% 3.03/3.45 cnf('0.30.0.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(multiply(inverse(X1),X2),identity) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.7.2.0','0.11.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.30.1.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(multiply(inverse(X1),X2),identity) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.30.0.0']),
% 3.03/3.45 [weight('<6,11,7,[0,0,0,4]>')]).
% 3.03/3.45 cnf('0.30.1.1',plain,
% 3.03/3.45 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.30.1.0','0.12.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.30.2.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.30.1.1',theory(equality)]),
% 3.03/3.45 [u,rule_28]).
% 3.03/3.45 cnf('0.31.0.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),greatest_lower_bound(X1,X2)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.8.2.0','0.11.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.31.1.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),greatest_lower_bound(X1,X2)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.31.0.0']),
% 3.03/3.45 [weight('<6,11,8,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.31.2.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),greatest_lower_bound(X1,X2)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_29]).
% 3.03/3.45 cnf('0.34.0.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(multiply(X1,X2),identity) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.9.2.0','0.11.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.34.1.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(multiply(X1,X2),identity) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.34.0.0']),
% 3.03/3.45 [weight('<6,11,9,[0,0,0,4]>')]).
% 3.03/3.45 cnf('0.34.1.1',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(identity,multiply(X1,X2)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.34.1.0','0.12.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.34.2.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(identity,multiply(X1,X2)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.34.1.1',theory(equality)]),
% 3.03/3.45 [u,rule_32]).
% 3.03/3.45 cnf('0.43.0.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(multiply(X1,inverse(X2)),identity) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.9.2.0','0.25.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.43.1.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(multiply(X1,inverse(X2)),identity) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.43.0.0']),
% 3.03/3.45 [weight('<6,25,9,[0,0,0,4]>')]).
% 3.03/3.45 cnf('0.43.1.1',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.43.1.0','0.12.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.43.2.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.43.1.1',theory(equality)]),
% 3.03/3.45 [u,rule_41]).
% 3.03/3.45 cnf('0.45.0.0',plain,
% 3.03/3.45 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(multiply(X1,inverse(X2)),identity) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.10.2.0','0.25.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.45.1.0',plain,
% 3.03/3.45 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(multiply(X1,inverse(X2)),identity) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.45.0.0']),
% 3.03/3.45 [weight('<6,25,10,[0,0,0,4]>')]).
% 3.03/3.45 cnf('0.45.1.1',plain,
% 3.03/3.45 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X1,inverse(X2))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.45.1.0','0.14.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.45.2.0',plain,
% 3.03/3.45 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X1,inverse(X2))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.45.1.1',theory(equality)]),
% 3.03/3.45 [u,rule_43]).
% 3.03/3.45 cnf('0.46.0.0',plain,
% 3.03/3.45 ( least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = least_upper_bound(X1,X3) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.13.2.0','0.3.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.46.1.0',plain,
% 3.03/3.45 ( least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = least_upper_bound(X1,X3) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.46.0.0']),
% 3.03/3.45 [weight('<7,13,3,[1,0,0,1]>')]).
% 3.03/3.45 cnf('0.46.2.0',plain,
% 3.03/3.45 ( least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = least_upper_bound(X1,X3) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_44]).
% 3.03/3.45 cnf('0.47.0.0',plain,
% 3.03/3.45 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.15.2.0','0.5.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.47.1.0',plain,
% 3.03/3.45 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.47.0.0']),
% 3.03/3.45 [weight('<7,15,5,[1,0,0,1]>')]).
% 3.03/3.45 cnf('0.47.2.0',plain,
% 3.03/3.45 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_45]).
% 3.03/3.45 cnf('0.64.0.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.7.2.0','0.22.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.64.1.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.64.0.0']),
% 3.03/3.45 [weight('<8,22,7,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.64.2.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_62]).
% 3.03/3.45 cnf('0.66.0.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),greatest_lower_bound(multiply(X1,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X1),X3)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.8.2.0','0.22.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.66.1.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),greatest_lower_bound(multiply(X1,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X1),X3)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.66.0.0']),
% 3.03/3.45 [weight('<8,22,8,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.66.2.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),greatest_lower_bound(multiply(X1,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X1),X3)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.66.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_64]).
% 3.03/3.45 cnf('0.68.0.0',plain,
% 3.03/3.45 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.25.2.0','0.6.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('0.68.1.0',plain,
% 3.03/3.45 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.68.0.0']),
% 3.03/3.45 [weight('<8,25,6,[1,0,0,0]>')]).
% 3.03/3.45 cnf('0.68.2.0',plain,
% 3.03/3.45 ( multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity ),
% 3.03/3.45 inference(orient,[status(thm)],['0.68.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_66]).
% 3.03/3.45 cnf('0.69.0.0',plain,
% 3.03/3.45 ( multiply(X1,inverse(multiply(X2,X1))) = multiply(inverse(X2),identity) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.22.2.0','0.68.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.69.0.1',plain,
% 3.03/3.45 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.69.0.0','0.28.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.69.1.0',plain,
% 3.03/3.45 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.69.0.1']),
% 3.03/3.45 [weight('<6,68,22,[0,0,0,3]>')]).
% 3.03/3.45 cnf('0.69.2.0',plain,
% 3.03/3.45 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_67]).
% 3.03/3.45 cnf('0.70.0.0',plain,
% 3.03/3.45 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.22.2.0','0.69.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.70.1.0',plain,
% 3.03/3.45 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.70.0.0']),
% 3.03/3.45 [weight('<4,69,22,[0,0,0,3]>')]).
% 3.03/3.45 cnf('0.70.2.0',plain,
% 3.03/3.45 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.70.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_68]).
% 3.03/3.45 cnf('0.72.0.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X1)) = multiply(inverse(greatest_lower_bound(X1,X2)),X1) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.30.2.0','0.3.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.72.1.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X1)) = multiply(inverse(greatest_lower_bound(X1,X2)),X1) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.72.0.0']),
% 3.03/3.45 [weight('<8,30,3,[1,0,0,3]>')]).
% 3.03/3.45 cnf('0.72.2.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X1)) = multiply(inverse(greatest_lower_bound(X1,X2)),X1) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.72.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_70]).
% 3.03/3.45 cnf('0.73.0.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,X1)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.72.2.0','0.28.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.73.0.1',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.73.0.0','0.28.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('0.73.1.0',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.73.0.1']),
% 3.03/3.45 [weight('<6,72,28,[1,0,0,2]>')]).
% 3.03/3.45 cnf('0.73.2.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,X1)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.73.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_71]).
% 3.03/3.45 cnf('0.75.0.0',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.73.2.0','0.14.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2.1','L')]).
% 3.03/3.45 cnf('0.75.1.0',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.75.0.0']),
% 3.03/3.45 [weight('<6,73,14,[1,0,0,3]>')]).
% 3.03/3.45 cnf('0.75.2.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(identity,X1)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.75.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_73]).
% 3.03/3.45 cnf('0.79.0.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),least_upper_bound(X1,X2)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.30.2.0','0.17.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.79.0.1',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = identity ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.79.0.0','0.11.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.79.1.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = identity ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.79.0.1']),
% 3.03/3.45 [weight('<8,30,17,[1,0,0,3]>')]).
% 3.03/3.45 cnf('0.79.2.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = identity ),
% 3.03/3.45 inference(orient,[status(thm)],['0.79.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_77]).
% 3.03/3.45 cnf('0.80.0.0',plain,
% 3.03/3.45 ( identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.79.2.0','0.28.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.80.1.0',plain,
% 3.03/3.45 ( identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.80.0.0']),
% 3.03/3.45 [weight('<6,79,28,[1,0,0,2]>')]).
% 3.03/3.45 cnf('0.80.2.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) = identity ),
% 3.03/3.45 inference(orient,[status(thm)],['0.80.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_78]).
% 3.03/3.45 cnf('0.82.0.0',plain,
% 3.03/3.45 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(inverse(least_upper_bound(identity,X1)),identity) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.16.2.0','0.80.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.82.1.0',plain,
% 3.03/3.45 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(inverse(least_upper_bound(identity,X1)),identity) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.82.0.0']),
% 3.03/3.45 [weight('<6,80,16,[0,0,0,2]>')]).
% 3.03/3.45 cnf('0.82.1.1',plain,
% 3.03/3.45 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.82.1.0','0.14.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.82.2.0',plain,
% 3.03/3.45 ( greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.82.1.1',theory(equality)]),
% 3.03/3.45 [x,rule_80]).
% 3.03/3.45 cnf('0.84.0.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = multiply(inverse(greatest_lower_bound(X1,X2)),X2) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.30.2.0','0.18.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.84.1.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = multiply(inverse(greatest_lower_bound(X1,X2)),X2) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.84.0.0']),
% 3.03/3.45 [weight('<8,30,18,[1,0,0,3]>')]).
% 3.03/3.45 cnf('0.84.2.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = multiply(inverse(greatest_lower_bound(X1,X2)),X2) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.84.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_82]).
% 3.03/3.45 cnf('0.125.0.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = multiply(X1,inverse(greatest_lower_bound(X2,X1))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.43.2.0','0.18.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.125.1.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = multiply(X1,inverse(greatest_lower_bound(X2,X1))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.125.0.0']),
% 3.03/3.45 [weight('<8,43,18,[1,0,0,1]>')]).
% 3.03/3.45 cnf('0.125.2.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = multiply(X1,inverse(greatest_lower_bound(X2,X1))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.125.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_123]).
% 3.03/3.45 cnf('0.132.0.0',plain,
% 3.03/3.45 ( greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = multiply(greatest_lower_bound(X1,X2),inverse(greatest_lower_bound(X2,X1))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.45.2.0','0.20.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.132.1.0',plain,
% 3.03/3.45 ( greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = multiply(greatest_lower_bound(X1,X2),inverse(greatest_lower_bound(X2,X1))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.132.0.0']),
% 3.03/3.45 [weight('<8,45,20,[1,0,0,1]>')]).
% 3.03/3.45 cnf('0.132.2.0',plain,
% 3.03/3.45 ( multiply(greatest_lower_bound(X1,X2),inverse(greatest_lower_bound(X2,X1))) = greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.132.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_130]).
% 3.03/3.45 cnf('0.133.0.0',plain,
% 3.03/3.45 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),inverse(inverse(X1))) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.70.2.0','0.64.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.133.0.1',plain,
% 3.03/3.45 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.133.0.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.133.1.0',plain,
% 3.03/3.45 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.133.0.1']),
% 3.03/3.45 [weight('<8,70,64,[1,0,0,1]>')]).
% 3.03/3.45 cnf('0.133.2.0',plain,
% 3.03/3.45 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.133.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_131]).
% 3.03/3.45 cnf('0.134.0.0',plain,
% 3.03/3.45 ( inverse(least_upper_bound(X1,multiply(inverse(inverse(X1)),X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.133.2.0','0.11.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.1.1','L')]).
% 3.03/3.45 cnf('0.134.0.1',plain,
% 3.03/3.45 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.134.0.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.2.1','L')]).
% 3.03/3.45 cnf('0.134.1.0',plain,
% 3.03/3.45 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.134.0.1']),
% 3.03/3.45 [weight('<6,133,11,[1,0,0,3]>')]).
% 3.03/3.45 cnf('0.134.2.0',plain,
% 3.03/3.45 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.134.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_132]).
% 3.03/3.45 cnf('0.135.0.0',plain,
% 3.03/3.45 ( multiply(inverse(least_upper_bound(identity,X1)),inverse(inverse(X1))) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.134.2.0','0.11.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.2','L')]).
% 3.03/3.45 cnf('0.135.0.1',plain,
% 3.03/3.45 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.135.0.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.135.1.0',plain,
% 3.03/3.45 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.135.0.1']),
% 3.03/3.45 [weight('<6,134,11,[1,0,0,3]>')]).
% 3.03/3.45 cnf('0.135.1.1',plain,
% 3.03/3.45 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.135.1.0','0.12.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.1','L')]).
% 3.03/3.45 cnf('0.135.2.0',plain,
% 3.03/3.45 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.135.1.1',theory(equality)]),
% 3.03/3.45 [u,rule_133]).
% 3.03/3.45 cnf('0.136.0.0',plain,
% 3.03/3.45 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(inverse(least_upper_bound(X1,identity)),X1) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.135.2.0','0.12.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.1','L')]).
% 3.03/3.45 cnf('0.136.1.0',plain,
% 3.03/3.45 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(inverse(least_upper_bound(X1,identity)),X1) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.136.0.0']),
% 3.03/3.45 [weight('<6,135,12,[1,0,0,2]>')]).
% 3.03/3.45 cnf('0.136.2.0',plain,
% 3.03/3.45 ( multiply(inverse(least_upper_bound(X1,identity)),X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.136.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_134]).
% 3.03/3.45 cnf('0.138.0.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),inverse(inverse(X1))) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.70.2.0','0.66.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.138.0.1',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),X1) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.138.0.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.138.1.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),X1) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.138.0.1']),
% 3.03/3.45 [weight('<8,70,66,[1,0,0,1]>')]).
% 3.03/3.45 cnf('0.138.2.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),X1) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.138.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_136]).
% 3.03/3.45 cnf('0.139.0.0',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(X1,multiply(inverse(inverse(X1)),X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.138.2.0','0.11.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.1.1','L')]).
% 3.03/3.45 cnf('0.139.0.1',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(X1,multiply(X1,X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.139.0.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.2.1','L')]).
% 3.03/3.45 cnf('0.139.1.0',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(X1,multiply(X1,X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.139.0.1']),
% 3.03/3.45 [weight('<6,138,11,[1,0,0,3]>')]).
% 3.03/3.45 cnf('0.139.2.0',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(X1,multiply(X1,X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.139.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_137]).
% 3.03/3.45 cnf('0.140.0.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,X1)),inverse(inverse(X1))) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.139.2.0','0.11.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.2','L')]).
% 3.03/3.45 cnf('0.140.0.1',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.140.0.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.140.1.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.140.0.1']),
% 3.03/3.45 [weight('<6,139,11,[1,0,0,3]>')]).
% 3.03/3.45 cnf('0.140.1.1',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.140.1.0','0.14.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.1','L')]).
% 3.03/3.45 cnf('0.140.2.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.140.1.1',theory(equality)]),
% 3.03/3.45 [u,rule_138]).
% 3.03/3.45 cnf('0.152.0.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X1,identity))),identity)) = multiply(inverse(inverse(greatest_lower_bound(X1,identity))),inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.30.2.0','0.75.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.152.0.1',plain,
% 3.03/3.45 ( least_upper_bound(identity,inverse(inverse(greatest_lower_bound(X1,identity)))) = multiply(inverse(inverse(greatest_lower_bound(X1,identity))),inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.152.0.0','0.28.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.152.0.2',plain,
% 3.03/3.45 ( least_upper_bound(identity,greatest_lower_bound(X1,identity)) = multiply(inverse(inverse(greatest_lower_bound(X1,identity))),inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.152.0.1','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.152.0.3',plain,
% 3.03/3.45 ( identity = multiply(inverse(inverse(greatest_lower_bound(X1,identity))),inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.152.0.2','0.18.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('0.152.0.4',plain,
% 3.03/3.45 ( identity = multiply(greatest_lower_bound(X1,identity),inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.152.0.3','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.1','L')]).
% 3.03/3.45 cnf('0.152.1.0',plain,
% 3.03/3.45 ( identity = multiply(greatest_lower_bound(X1,identity),inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.152.0.4']),
% 3.03/3.45 [weight('<8,75,30,[0,0,0,3]>')]).
% 3.03/3.45 cnf('0.152.1.1',plain,
% 3.03/3.45 ( identity = greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(identity,X1)))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.152.1.0','0.132.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.152.2.0',plain,
% 3.03/3.45 ( greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(identity,X1)))) = identity ),
% 3.03/3.45 inference(orient,[status(thm)],['0.152.1.1',theory(equality)]),
% 3.03/3.45 [x,rule_150]).
% 3.03/3.45 cnf('0.153.0.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(identity,X1))))),multiply(X1,inverse(greatest_lower_bound(identity,X1)))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.84.2.0','0.152.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2.1.1','L')]).
% 3.03/3.45 cnf('0.153.0.1',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,inverse(multiply(X1,inverse(greatest_lower_bound(identity,X1)))))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.153.0.0','0.140.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('0.153.0.2',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(identity,X1))),inverse(X1)))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.153.0.1','0.70.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.2','L')]).
% 3.03/3.45 cnf('0.153.0.3',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X1),inverse(X1)))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.153.0.2','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.2.1','L')]).
% 3.03/3.45 cnf('0.153.0.4',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(identity,inverse(X1))))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.153.0.3','0.45.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.2','L')]).
% 3.03/3.45 cnf('0.153.0.5',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,multiply(identity,inverse(X1)))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.153.0.4','0.19.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.153.0.6',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),inverse(identity)) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.153.0.5','0.139.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('0.153.0.7',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),identity) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.153.0.6','0.26.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.153.0.8',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.153.0.7','0.28.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('0.153.0.9',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,multiply(identity,multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.153.0.8','0.26.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.2.1','L')]).
% 3.03/3.45 cnf('0.153.0.10',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,multiply(X1,inverse(greatest_lower_bound(identity,X1)))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.153.0.9','0.1.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.2','L')]).
% 3.03/3.45 cnf('0.153.0.11',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,inverse(X1))) = multiply(X1,inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.153.0.10','0.125.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.153.1.0',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,inverse(X1))) = multiply(X1,inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.153.0.11']),
% 3.03/3.45 [weight('<6,152,84,[0,0,0,4]>')]).
% 3.03/3.45 cnf('0.153.2.0',plain,
% 3.03/3.45 ( multiply(X1,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.153.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_151]).
% 3.03/3.45 cnf('0.208.0.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(inverse(least_upper_bound(identity,X1)),X2),X1) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),multiply(X2,X1)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.9.2.0','0.135.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.208.1.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(inverse(least_upper_bound(identity,X1)),X2),X1) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),multiply(X2,X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.208.0.0']),
% 3.03/3.45 [weight('<8,135,9,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.208.2.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(inverse(least_upper_bound(identity,X1)),X2),X1) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),multiply(X2,X1)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.208.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_206]).
% 3.03/3.45 cnf('0.210.0.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.9.2.0','0.1.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.210.1.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.210.0.0']),
% 3.03/3.45 [weight('<?,9,1,[1,0,0,1]>')]).
% 3.03/3.45 cnf('0.210.2.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)) ),
% 3.03/3.45 inference(activate,[status(thm)],['0.210.1.0']),
% 3.03/3.45 [equation_3]).
% 3.03/3.45 cnf('0.214.0.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,X1),multiply(X2,X3)) = multiply(least_upper_bound(X2,multiply(X1,X2)),X3) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.6.2.0','0.210.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.214.1.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,X1),multiply(X2,X3)) = multiply(least_upper_bound(X2,multiply(X1,X2)),X3) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.214.0.0']),
% 3.03/3.45 [weight('<7,210,6,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.214.2.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,multiply(X2,X1)),X3) = multiply(least_upper_bound(identity,X2),multiply(X1,X3)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.214.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_211]).
% 3.03/3.45 cnf('0.237.0.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,X1)),multiply(X1,X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.6.2.0','0.140.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.237.1.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,X1)),multiply(X1,X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.237.0.0']),
% 3.03/3.45 [weight('<8,140,6,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.237.2.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,X1)),multiply(X1,X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.237.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_234]).
% 3.03/3.45 cnf('0.259.0.0',plain,
% 3.03/3.45 ( multiply(X1,multiply(inverse(greatest_lower_bound(identity,X1)),X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.6.2.0','0.153.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.259.1.0',plain,
% 3.03/3.45 ( multiply(X1,multiply(inverse(greatest_lower_bound(identity,X1)),X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.259.0.0']),
% 3.03/3.45 [weight('<8,153,6,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.259.2.0',plain,
% 3.03/3.45 ( multiply(X1,multiply(inverse(greatest_lower_bound(identity,X1)),X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.259.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_256]).
% 3.03/3.45 cnf('0.260.0.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X1) = multiply(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.259.2.0','0.140.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.260.1.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X1) = multiply(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.260.0.0']),
% 3.03/3.45 [weight('<7,259,140,[1,0,0,2]>')]).
% 3.03/3.45 cnf('0.260.2.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X1) = multiply(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.260.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_257]).
% 3.03/3.45 cnf('0.261.0.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,inverse(inverse(X1))))) = multiply(inverse(greatest_lower_bound(identity,X1)),inverse(X1)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.260.2.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.1.2','L')]).
% 3.03/3.45 cnf('0.261.0.1',plain,
% 3.03/3.45 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1))) = multiply(inverse(greatest_lower_bound(identity,X1)),inverse(X1)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.261.0.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2.1.2','L')]).
% 3.03/3.45 cnf('0.261.1.0',plain,
% 3.03/3.45 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1))) = multiply(inverse(greatest_lower_bound(identity,X1)),inverse(X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.261.0.1']),
% 3.03/3.45 [weight('<7,260,23,[1,0,0,4]>')]).
% 3.03/3.45 cnf('0.261.2.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,X1)),inverse(X1)) = multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.261.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_258]).
% 3.03/3.45 cnf('0.262.0.0',plain,
% 3.03/3.45 ( multiply(inverse(inverse(X1)),inverse(inverse(greatest_lower_bound(identity,X1)))) = inverse(multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1)))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.70.2.0','0.261.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.262.0.1',plain,
% 3.03/3.45 ( multiply(X1,inverse(inverse(greatest_lower_bound(identity,X1)))) = inverse(multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1)))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.262.0.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.262.0.2',plain,
% 3.03/3.45 ( multiply(X1,greatest_lower_bound(identity,X1)) = inverse(multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1)))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.262.0.1','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.262.0.3',plain,
% 3.03/3.45 ( multiply(X1,greatest_lower_bound(identity,X1)) = multiply(inverse(inverse(greatest_lower_bound(identity,X1))),inverse(inverse(X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.262.0.2','0.70.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.262.0.4',plain,
% 3.03/3.45 ( multiply(X1,greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),inverse(inverse(X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.262.0.3','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.1','L')]).
% 3.03/3.45 cnf('0.262.0.5',plain,
% 3.03/3.45 ( multiply(X1,greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),X1) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.262.0.4','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.2','L')]).
% 3.03/3.45 cnf('0.262.1.0',plain,
% 3.03/3.45 ( multiply(X1,greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),X1) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.262.0.5']),
% 3.03/3.45 [weight('<5,261,70,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.262.2.0',plain,
% 3.03/3.45 ( multiply(greatest_lower_bound(identity,X1),X1) = multiply(X1,greatest_lower_bound(identity,X1)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.262.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_259]).
% 3.03/3.45 cnf('0.269.0.0',plain,
% 3.03/3.45 ( multiply(X1,greatest_lower_bound(inverse(greatest_lower_bound(identity,X1)),X2)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X1))),multiply(X1,X2)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.8.2.0','0.153.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.269.1.0',plain,
% 3.03/3.45 ( multiply(X1,greatest_lower_bound(inverse(greatest_lower_bound(identity,X1)),X2)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X1))),multiply(X1,X2)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.269.0.0']),
% 3.03/3.45 [weight('<8,153,8,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.269.2.0',plain,
% 3.03/3.45 ( multiply(X1,greatest_lower_bound(inverse(greatest_lower_bound(identity,X1)),X2)) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X1))),multiply(X1,X2)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.269.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_266]).
% 3.03/3.45 cnf('0.327.0.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,inverse(X1)),multiply(X1,X2)) = multiply(least_upper_bound(X1,identity),X2) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.214.2.0','0.11.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.2','L')]).
% 3.03/3.45 cnf('0.327.1.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,inverse(X1)),multiply(X1,X2)) = multiply(least_upper_bound(X1,identity),X2) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.327.0.0']),
% 3.03/3.45 [weight('<8,214,11,[1,0,0,3]>')]).
% 3.03/3.45 cnf('0.327.2.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,inverse(X1)),multiply(X1,X2)) = multiply(least_upper_bound(X1,identity),X2) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.327.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_324]).
% 3.03/3.45 cnf('0.328.0.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(greatest_lower_bound(identity,X1),identity),X1) = multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))),multiply(X1,greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.327.2.0','0.262.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.328.0.1',plain,
% 3.03/3.45 ( multiply(least_upper_bound(greatest_lower_bound(identity,X1),identity),X1) = multiply(inverse(greatest_lower_bound(identity,X1)),multiply(X1,greatest_lower_bound(identity,X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.328.0.0','0.73.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.1','L')]).
% 3.03/3.45 cnf('0.328.0.2',plain,
% 3.03/3.45 ( multiply(least_upper_bound(greatest_lower_bound(identity,X1),identity),X1) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.328.0.1','0.237.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.328.1.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(greatest_lower_bound(identity,X1),identity),X1) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.328.0.2']),
% 3.03/3.45 [weight('<7,327,262,[1,0,0,5]>')]).
% 3.03/3.45 cnf('0.328.1.1',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,greatest_lower_bound(identity,X1)),X1) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.328.1.0','0.12.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.328.1.2',plain,
% 3.03/3.45 ( multiply(identity,X1) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.328.1.1','0.3.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.328.1.3',plain,
% 3.03/3.45 ( X1 = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.328.1.2','0.1.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('0.328.2.0',plain,
% 3.03/3.45 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) = X1 ),
% 3.03/3.45 inference(orient,[status(thm)],['0.328.1.3',theory(equality)]),
% 3.03/3.45 [x,rule_325]).
% 3.03/3.45 cnf('0.603.0.0',plain,
% 3.03/3.45 ( greatest_lower_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(greatest_lower_bound(least_upper_bound(X1,X2),X3),greatest_lower_bound(X1,X3)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.18.2.0','0.47.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.603.1.0',plain,
% 3.03/3.45 ( greatest_lower_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(greatest_lower_bound(least_upper_bound(X1,X2),X3),greatest_lower_bound(X1,X3)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.603.0.0']),
% 3.03/3.45 [weight('<9,47,18,[0,0,0,2]>')]).
% 3.03/3.45 cnf('0.603.1.1',plain,
% 3.03/3.45 ( greatest_lower_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(greatest_lower_bound(X1,X3),greatest_lower_bound(least_upper_bound(X1,X2),X3)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.603.1.0','0.12.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.603.2.0',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(least_upper_bound(X1,X3),X2)) = greatest_lower_bound(least_upper_bound(X1,X3),X2) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.603.1.1',theory(equality)]),
% 3.03/3.45 [x,rule_596]).
% 3.03/3.45 cnf('0.755.0.0',plain,
% 3.03/3.45 ( X1 = multiply(inverse(inverse(least_upper_bound(X1,identity))),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.22.2.0','0.136.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.755.0.1',plain,
% 3.03/3.45 ( X1 = multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.755.0.0','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.1','L')]).
% 3.03/3.45 cnf('0.755.1.0',plain,
% 3.03/3.45 ( X1 = multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.755.0.1']),
% 3.03/3.45 [weight('<9,136,22,[0,0,0,3]>')]).
% 3.03/3.45 cnf('0.755.2.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,inverse(X1)))) = X1 ),
% 3.03/3.45 inference(orient,[status(thm)],['0.755.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_746]).
% 3.03/3.45 cnf('0.862.0.0',plain,
% 3.03/3.45 ( least_upper_bound(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity)))),multiply(X2,greatest_lower_bound(X1,identity))) = multiply(least_upper_bound(inverse(identity),X2),greatest_lower_bound(X1,identity)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.208.2.0','0.18.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.1.1','L')]).
% 3.03/3.45 cnf('0.862.0.1',plain,
% 3.03/3.45 ( least_upper_bound(inverse(inverse(greatest_lower_bound(identity,X1))),multiply(X2,greatest_lower_bound(X1,identity))) = multiply(least_upper_bound(inverse(identity),X2),greatest_lower_bound(X1,identity)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.862.0.0','0.75.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.1','L')]).
% 3.03/3.45 cnf('0.862.0.2',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),multiply(X2,greatest_lower_bound(X1,identity))) = multiply(least_upper_bound(inverse(identity),X2),greatest_lower_bound(X1,identity)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.862.0.1','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.862.0.3',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),multiply(X2,greatest_lower_bound(X1,identity))) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(X1,identity)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.862.0.2','0.26.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.1.1','L')]).
% 3.03/3.45 cnf('0.862.1.0',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),multiply(X2,greatest_lower_bound(X1,identity))) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(X1,identity)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.862.0.3']),
% 3.03/3.45 [weight('<9,208,18,[1,0,0,3]>')]).
% 3.03/3.45 cnf('0.862.2.0',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),multiply(X2,greatest_lower_bound(X1,identity))) = multiply(least_upper_bound(identity,X2),greatest_lower_bound(X1,identity)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.862.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_852]).
% 3.03/3.45 cnf('0.863.0.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)) = least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,multiply(inverse(X1),identity))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.862.2.0','0.31.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.863.0.1',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)) = least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.863.0.0','0.28.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.2.2','L')]).
% 3.03/3.45 cnf('0.863.1.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)) = least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.863.0.1']),
% 3.03/3.45 [weight('<8,862,31,[1,0,0,4]>')]).
% 3.03/3.45 cnf('0.863.2.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)) = least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.863.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_853]).
% 3.03/3.45 cnf('0.865.0.0',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(identity,X1)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.863.2.0','0.14.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.865.1.0',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(identity,X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.865.0.0']),
% 3.03/3.45 [weight('<8,863,14,[1,0,0,5]>')]).
% 3.03/3.45 cnf('0.865.2.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(identity,X1)) = least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.865.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_855]).
% 3.03/3.45 cnf('0.952.0.0',plain,
% 3.03/3.45 ( greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1)))),multiply(least_upper_bound(identity,X1),X2)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(inverse(identity),X2)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.269.2.0','0.5.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2.1.1','L')]).
% 3.03/3.45 cnf('0.952.0.1',plain,
% 3.03/3.45 ( greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X1))),multiply(least_upper_bound(identity,X1),X2)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(inverse(identity),X2)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.952.0.0','0.82.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1.1','L')]).
% 3.03/3.45 cnf('0.952.0.2',plain,
% 3.03/3.45 ( greatest_lower_bound(least_upper_bound(identity,X1),multiply(least_upper_bound(identity,X1),X2)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(inverse(identity),X2)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.952.0.1','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.952.0.3',plain,
% 3.03/3.45 ( greatest_lower_bound(least_upper_bound(identity,X1),multiply(least_upper_bound(identity,X1),X2)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X2)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.952.0.2','0.26.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.2.1','L')]).
% 3.03/3.45 cnf('0.952.1.0',plain,
% 3.03/3.45 ( greatest_lower_bound(least_upper_bound(identity,X1),multiply(least_upper_bound(identity,X1),X2)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X2)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.952.0.3']),
% 3.03/3.45 [weight('<9,269,5,[1,0,0,4]>')]).
% 3.03/3.45 cnf('0.952.2.0',plain,
% 3.03/3.45 ( greatest_lower_bound(least_upper_bound(identity,X1),multiply(least_upper_bound(identity,X1),X2)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X2)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.952.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_941]).
% 3.03/3.45 cnf('0.953.0.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(identity,X1)) = greatest_lower_bound(least_upper_bound(identity,inverse(X1)),least_upper_bound(identity,multiply(identity,X1))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.952.2.0','0.34.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.953.0.1',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = greatest_lower_bound(least_upper_bound(identity,inverse(X1)),least_upper_bound(identity,multiply(identity,X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.953.0.0','0.865.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('0.953.0.2',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = greatest_lower_bound(least_upper_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.953.0.1','0.1.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.2.2','L')]).
% 3.03/3.45 cnf('0.953.1.0',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = greatest_lower_bound(least_upper_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.953.0.2']),
% 3.03/3.45 [weight('<8,952,34,[1,0,0,4]>')]).
% 3.03/3.45 cnf('0.953.1.1',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.953.1.0','0.14.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.953.2.0',plain,
% 3.03/3.45 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.953.1.1',theory(equality)]),
% 3.03/3.45 [x,rule_942]).
% 3.03/3.45 cnf('0.955.0.0',plain,
% 3.03/3.45 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X1))),least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1)))) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.603.2.0','0.953.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.955.0.1',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X1))),least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1)))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.955.0.0','0.953.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('0.955.0.2',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1)))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.955.0.1','0.5.2.0',theory(equality)]),
% 3.03/3.45 [pos('R.1','L')]).
% 3.03/3.45 cnf('0.955.0.3',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,greatest_lower_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.955.0.2','0.46.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.955.0.4',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = identity ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.955.0.3','0.3.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.955.1.0',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = identity ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.955.0.4']),
% 3.03/3.45 [weight('<8,953,603,[0,0,0,4]>')]).
% 3.03/3.45 cnf('0.955.2.0',plain,
% 3.03/3.45 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = identity ),
% 3.03/3.45 inference(orient,[status(thm)],['0.955.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_944]).
% 3.03/3.45 cnf('0.956.0.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1))) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),identity) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.30.2.0','0.955.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.956.0.1',plain,
% 3.03/3.45 ( least_upper_bound(identity,X1) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),identity) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.956.0.0','0.328.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.956.0.2',plain,
% 3.03/3.45 ( least_upper_bound(identity,X1) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.956.0.1','0.28.2.0',theory(equality)]),
% 3.03/3.45 [pos('R','L')]).
% 3.03/3.45 cnf('0.956.1.0',plain,
% 3.03/3.45 ( least_upper_bound(identity,X1) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.956.0.2']),
% 3.03/3.45 [weight('<5,955,30,[0,0,0,3]>')]).
% 3.03/3.45 cnf('0.956.2.0',plain,
% 3.03/3.45 ( inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,X1) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.956.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_945]).
% 3.03/3.45 cnf('0.957.0.0',plain,
% 3.03/3.45 ( greatest_lower_bound(identity,inverse(X1)) = inverse(least_upper_bound(identity,X1)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.23.2.0','0.956.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.1','L')]).
% 3.03/3.45 cnf('0.957.1.0',plain,
% 3.03/3.45 ( greatest_lower_bound(identity,inverse(X1)) = inverse(least_upper_bound(identity,X1)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.957.0.0']),
% 3.03/3.45 [weight('<4,956,23,[0,0,0,1]>')]).
% 3.03/3.45 cnf('0.957.2.0',plain,
% 3.03/3.45 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)) ),
% 3.03/3.45 inference(orient,[status(thm)],['0.957.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_946]).
% 3.03/3.45 cnf('0.974.0.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,inverse(X1)))) = X1 ),
% 3.03/3.45 inference(interreduction_right,[status(thm)],['0.755.2.0'])).
% 3.03/3.45 cnf('0.974.0.1',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,identity),greatest_lower_bound(identity,inverse(inverse(X1)))) = X1 ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.974.0.0','0.957.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.974.0.2',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,identity),greatest_lower_bound(identity,X1)) = X1 ),
% 3.03/3.45 inference(reduction,[status(thm)],['0.974.0.1','0.23.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2.2','L')]).
% 3.03/3.45 cnf('0.974.1.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,identity),greatest_lower_bound(identity,X1)) = X1 ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.974.0.2']),
% 3.03/3.45 [weight('<7,755,957,[0,0,0,0]>')]).
% 3.03/3.45 cnf('0.974.2.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,identity),greatest_lower_bound(identity,X1)) = X1 ),
% 3.03/3.45 inference(orient,[status(thm)],['0.974.1.0',theory(equality)]),
% 3.03/3.45 [u,rule_961]).
% 3.03/3.45 cnf('0.986.0.0',plain,
% 3.03/3.45 ( X1 = multiply(least_upper_bound(X1,identity),greatest_lower_bound(X1,identity)) ),
% 3.03/3.45 inference(cp,[status(thm)],['0.974.2.0','0.14.2.0',theory(equality)]),
% 3.03/3.45 [pos('L.2','L')]).
% 3.03/3.45 cnf('0.986.1.0',plain,
% 3.03/3.45 ( X1 = multiply(least_upper_bound(X1,identity),greatest_lower_bound(X1,identity)) ),
% 3.03/3.45 inference(weigh,[status(thm)],['0.986.0.0']),
% 3.03/3.45 [weight('<7,974,14,[1,0,0,4]>')]).
% 3.03/3.45 cnf('0.986.2.0',plain,
% 3.03/3.45 ( multiply(least_upper_bound(X1,identity),greatest_lower_bound(X1,identity)) = X1 ),
% 3.03/3.45 inference(orient,[status(thm)],['0.986.1.0',theory(equality)]),
% 3.03/3.45 [x,rule_973]).
% 3.03/3.45 cnf('1.0.0.0',conjecture,
% 3.03/3.45 ( multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) = a ),
% 3.03/3.45 file('/tmp/WALDMEISTER_27856_n014',conjecture_1)).
% 3.03/3.45 cnf('1.0.0.1',plain,
% 3.03/3.45 ( a = a ),
% 3.03/3.45 inference(reduction,[status(thm)],['1.0.0.0','0.986.2.0',theory(equality)]),
% 3.03/3.45 [pos('L','L')]).
% 3.03/3.45 cnf('1.0.0.2',plain,
% 3.03/3.45 ( $true ),
% 3.03/3.45 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 3.03/3.45 [conjecture_1]).
% 3.03/3.45
% 3.03/3.45 Proved Goals:
% 3.03/3.45 No. 1: multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) ?= a joined, current: a = a
% 3.03/3.45 1 goal was specified, which was proved.
% 3.03/3.45 % SZS output end CNFRefutation
% 3.03/3.45 #END OF PROOF
% 3.03/3.45
% 3.03/3.45 Problem WALDMEISTER_27856_n014
% 3.03/3.45 CPs.gen 280554
% 3.03/3.45 CPs.reexp 0
% 3.03/3.45 Select 14502
% 3.03/3.45 R 973
% 3.03/3.45 E 13
% 3.03/3.45 vsize 8.5M
% 3.03/3.45 rss 4.2M
% 3.03/3.45 process.time 1.550s
% 3.03/3.45 wallclock.time 2.480s
% 3.03/3.45 status S
% 3.03/3.45
% 3.03/3.45
% 3.03/3.45 Waldmeister states: Goal proved.
% 3.03/3.45 % SZS status Unsatisfiable
% 3.03/3.45
% 3.03/3.45 Problem WALDMEISTER_27856_n014
% 3.03/3.45 CPs.gen 257149
% 3.03/3.45 CPs.reexp 0
% 3.03/3.45 Select 16391
% 3.03/3.45 R 1063
% 3.03/3.45 E 12
% 3.03/3.45 vsize 7.5M
% 3.03/3.45 rss 4.8M
% 3.03/3.45 process.time 0.931s
% 3.03/3.45 wallclock.time 2.481s
% 3.03/3.45 status S
%------------------------------------------------------------------------------