TSTP Solution File: GRP181-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP181-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n022.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 2.03s 2.49s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP181-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : woody %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 17:43:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.59/0.98 ********************************************************************************
% 0.59/0.98 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/0.98 * |/ | \/ | *
% 0.59/0.98 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/0.98 * A. Jaeger and B. Loechner | | *
% 0.59/0.98 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/0.98 ********************************************************************************
% 0.59/0.98
% 0.59/0.98
% 0.59/0.98 Goals:
% 0.59/0.98 ------
% 0.59/0.98
% 0.59/0.98 ( 1) a ?=? b
% 0.59/0.98
% 0.59/0.98 Detected structure: VerbandsgeordneteGruppe
% 0.59/0.98 ********************************************************************************
% 0.59/0.98 ****************************** COMPLETION - PROOF ******************************
% 0.59/0.98 ********************************************************************************
% 0.59/0.98
% 2.03/2.49 joined goal: 1 a ?= b to b
% 2.03/2.49 goal joined
% 2.03/2.49 % SZS status Unsatisfiable
% 2.03/2.49 #START OF PROOF
% 2.03/2.49 % SZS output start CNFRefutation
% 2.03/2.49 cnf('0.1.0.0',axiom,
% 2.03/2.49 ( X1 = multiply(identity,X1) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.1.1.0',plain,
% 2.03/2.49 ( X1 = multiply(identity,X1) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.1.0.0']),
% 2.03/2.49 [weight('<0,0,0,[0,0,0,1]>')]).
% 2.03/2.49 cnf('0.1.2.0',plain,
% 2.03/2.49 ( multiply(identity,X1) = X1 ),
% 2.03/2.49 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_1]).
% 2.03/2.49 cnf('0.3.0.0',axiom,
% 2.03/2.49 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.3.1.0',plain,
% 2.03/2.49 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.3.0.0']),
% 2.03/2.49 [weight('<2,0,0,[0,0,0,3]>')]).
% 2.03/2.49 cnf('0.3.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 2.03/2.49 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_3]).
% 2.03/2.49 cnf('0.4.0.0',axiom,
% 2.03/2.49 ( X1 = least_upper_bound(X1,X1) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.4.1.0',plain,
% 2.03/2.49 ( X1 = least_upper_bound(X1,X1) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.4.0.0']),
% 2.03/2.49 [weight('<3,0,0,[0,0,0,4]>')]).
% 2.03/2.49 cnf('0.4.2.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,X1) = X1 ),
% 2.03/2.49 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_4]).
% 2.03/2.49 cnf('0.5.0.0',axiom,
% 2.03/2.49 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.5.1.0',plain,
% 2.03/2.49 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.5.0.0']),
% 2.03/2.49 [weight('<4,0,0,[0,0,0,5]>')]).
% 2.03/2.49 cnf('0.5.2.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 2.03/2.49 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_5]).
% 2.03/2.49 cnf('0.6.0.0',axiom,
% 2.03/2.49 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.6.1.0',plain,
% 2.03/2.49 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.6.0.0']),
% 2.03/2.49 [weight('<5,0,0,[0,0,0,6]>')]).
% 2.03/2.49 cnf('0.6.2.0',plain,
% 2.03/2.49 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_6]).
% 2.03/2.49 cnf('0.7.0.0',axiom,
% 2.03/2.49 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.7.1.0',plain,
% 2.03/2.49 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.7.0.0']),
% 2.03/2.49 [weight('<6,0,0,[0,0,0,7]>')]).
% 2.03/2.49 cnf('0.7.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_7]).
% 2.03/2.49 cnf('0.8.0.0',axiom,
% 2.03/2.49 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.8.1.0',plain,
% 2.03/2.49 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.8.0.0']),
% 2.03/2.49 [weight('<7,0,0,[0,0,0,8]>')]).
% 2.03/2.49 cnf('0.8.2.0',plain,
% 2.03/2.49 ( least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_8]).
% 2.03/2.49 cnf('0.9.0.0',axiom,
% 2.03/2.49 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.9.1.0',plain,
% 2.03/2.49 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.9.0.0']),
% 2.03/2.49 [weight('<8,0,0,[0,0,0,9]>')]).
% 2.03/2.49 cnf('0.9.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_9]).
% 2.03/2.49 cnf('0.10.0.0',axiom,
% 2.03/2.49 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.10.1.0',plain,
% 2.03/2.49 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.10.0.0']),
% 2.03/2.49 [weight('<9,0,0,[0,0,0,10]>')]).
% 2.03/2.49 cnf('0.10.2.0',plain,
% 2.03/2.49 ( least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_10]).
% 2.03/2.49 cnf('0.11.0.0',axiom,
% 2.03/2.49 ( multiply(inverse(X1),X1) = identity ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.11.1.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),X1) = identity ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.11.0.0']),
% 2.03/2.49 [weight('<10,0,0,[0,0,0,11]>')]).
% 2.03/2.49 cnf('0.11.2.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),X1) = identity ),
% 2.03/2.49 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_11]).
% 2.03/2.49 cnf('0.12.0.0',axiom,
% 2.03/2.49 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.12.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.12.0.0']),
% 2.03/2.49 [weight('<11,0,0,[0,0,0,12]>')]).
% 2.03/2.49 cnf('0.12.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 2.03/2.49 inference(activate,[status(thm)],['0.12.1.0']),
% 2.03/2.49 [equation_1]).
% 2.03/2.49 cnf('0.13.0.0',axiom,
% 2.03/2.49 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.13.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.13.0.0']),
% 2.03/2.49 [weight('<12,0,0,[0,0,0,13]>')]).
% 2.03/2.49 cnf('0.13.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_12]).
% 2.03/2.49 cnf('0.14.0.0',axiom,
% 2.03/2.49 ( greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.14.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.14.0.0']),
% 2.03/2.49 [weight('<13,0,0,[0,0,0,14]>')]).
% 2.03/2.49 cnf('0.14.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_13]).
% 2.03/2.49 cnf('0.15.0.0',axiom,
% 2.03/2.49 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.15.1.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.15.0.0']),
% 2.03/2.49 [weight('<14,0,0,[0,0,0,15]>')]).
% 2.03/2.49 cnf('0.15.2.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 2.03/2.49 inference(activate,[status(thm)],['0.15.1.0']),
% 2.03/2.49 [equation_2]).
% 2.03/2.49 cnf('0.16.0.0',axiom,
% 2.03/2.49 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.16.1.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.16.0.0']),
% 2.03/2.49 [weight('<15,0,0,[0,0,0,16]>')]).
% 2.03/2.49 cnf('0.16.2.0',plain,
% 2.03/2.49 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_14]).
% 2.03/2.49 cnf('0.17.0.0',axiom,
% 2.03/2.49 ( least_upper_bound(a,c) = least_upper_bound(b,c) ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022')).
% 2.03/2.49 cnf('0.17.1.0',plain,
% 2.03/2.49 ( least_upper_bound(a,c) = least_upper_bound(b,c) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.17.0.0']),
% 2.03/2.49 [weight('<16,0,0,[0,0,0,17]>')]).
% 2.03/2.49 cnf('0.17.2.0',plain,
% 2.03/2.49 ( least_upper_bound(a,c) = least_upper_bound(b,c) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_15]).
% 2.03/2.49 cnf('0.18.0.0',plain,
% 2.03/2.49 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.5.2.0','0.12.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.18.1.0',plain,
% 2.03/2.49 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.18.0.0']),
% 2.03/2.49 [weight('<5,12,5,[0,0,0,2]>')]).
% 2.03/2.49 cnf('0.18.2.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1 ),
% 2.03/2.49 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_16]).
% 2.03/2.49 cnf('0.21.0.0',plain,
% 2.03/2.49 ( greatest_lower_bound(a,greatest_lower_bound(c,X1)) = greatest_lower_bound(greatest_lower_bound(b,c),X1) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.13.2.0','0.14.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.21.0.1',plain,
% 2.03/2.49 ( greatest_lower_bound(a,greatest_lower_bound(c,X1)) = greatest_lower_bound(b,greatest_lower_bound(c,X1)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.21.0.0','0.13.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.21.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(a,greatest_lower_bound(c,X1)) = greatest_lower_bound(b,greatest_lower_bound(c,X1)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.21.0.1']),
% 2.03/2.49 [weight('<5,14,13,[0,0,0,1]>')]).
% 2.03/2.49 cnf('0.21.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(a,greatest_lower_bound(c,X1)) = greatest_lower_bound(b,greatest_lower_bound(c,X1)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_19]).
% 2.03/2.49 cnf('0.22.0.0',plain,
% 2.03/2.49 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.3.2.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.22.1.0',plain,
% 2.03/2.49 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.22.0.0']),
% 2.03/2.49 [weight('<5,15,3,[0,0,0,2]>')]).
% 2.03/2.49 cnf('0.22.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1 ),
% 2.03/2.49 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_20]).
% 2.03/2.49 cnf('0.23.0.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.16.2.0','0.4.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.23.1.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.23.0.0']),
% 2.03/2.49 [weight('<5,16,4,[1,0,0,1]>')]).
% 2.03/2.49 cnf('0.23.2.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_21]).
% 2.03/2.49 cnf('0.26.0.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,X2) = least_upper_bound(least_upper_bound(X1,X2),X1) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.18.2.0','0.3.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.26.0.1',plain,
% 2.03/2.49 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.26.0.0','0.16.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.26.1.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.26.0.1']),
% 2.03/2.49 [weight('<5,18,3,[1,0,0,2]>')]).
% 2.03/2.49 cnf('0.26.2.0',plain,
% 2.03/2.49 ( least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_24]).
% 2.03/2.49 cnf('0.32.0.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.32.0.1',plain,
% 2.03/2.49 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.32.0.0','0.1.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.32.1.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.32.0.1']),
% 2.03/2.49 [weight('<6,11,6,[0,0,0,1]>')]).
% 2.03/2.49 cnf('0.32.2.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 2.03/2.49 inference(orient,[status(thm)],['0.32.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_30]).
% 2.03/2.49 cnf('0.33.0.0',plain,
% 2.03/2.49 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.32.2.0','0.32.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.33.1.0',plain,
% 2.03/2.49 ( X1 = inverse(inverse(X1)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.33.0.0']),
% 2.03/2.49 [weight('<3,32,32,[0,0,0,3]>')]).
% 2.03/2.49 cnf('0.33.2.0',plain,
% 2.03/2.49 ( inverse(inverse(X1)) = X1 ),
% 2.03/2.49 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_31]).
% 2.03/2.49 cnf('0.35.0.0',plain,
% 2.03/2.49 ( identity = multiply(X1,inverse(X1)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.11.2.0','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.35.1.0',plain,
% 2.03/2.49 ( identity = multiply(X1,inverse(X1)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.35.0.0']),
% 2.03/2.49 [weight('<4,33,11,[0,0,0,1]>')]).
% 2.03/2.49 cnf('0.35.2.0',plain,
% 2.03/2.49 ( multiply(X1,inverse(X1)) = identity ),
% 2.03/2.49 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_33]).
% 2.03/2.49 cnf('0.36.0.0',plain,
% 2.03/2.49 ( identity = inverse(identity) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.35.2.0','0.1.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.36.1.0',plain,
% 2.03/2.49 ( identity = inverse(identity) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.36.0.0']),
% 2.03/2.49 [weight('<2,35,1,[1,0,0,0]>')]).
% 2.03/2.49 cnf('0.36.2.0',plain,
% 2.03/2.49 ( inverse(identity) = identity ),
% 2.03/2.49 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_34]).
% 2.03/2.49 cnf('0.37.0.0',plain,
% 2.03/2.49 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.32.2.0','0.35.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.37.1.0',plain,
% 2.03/2.49 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.37.0.0']),
% 2.03/2.49 [weight('<4,35,32,[0,0,0,3]>')]).
% 2.03/2.49 cnf('0.37.2.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_35]).
% 2.03/2.49 cnf('0.38.0.0',plain,
% 2.03/2.49 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.37.2.0','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.38.0.1',plain,
% 2.03/2.49 ( X1 = multiply(X1,identity) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.38.0.0','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.38.1.0',plain,
% 2.03/2.49 ( X1 = multiply(X1,identity) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.38.0.1']),
% 2.03/2.49 [weight('<3,37,33,[1,0,0,1]>')]).
% 2.03/2.49 cnf('0.38.2.0',plain,
% 2.03/2.49 ( multiply(X1,identity) = X1 ),
% 2.03/2.49 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_36]).
% 2.03/2.49 cnf('0.40.0.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(multiply(inverse(X1),X2),identity) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.7.2.0','0.11.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.40.1.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(multiply(inverse(X1),X2),identity) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.40.0.0']),
% 2.03/2.49 [weight('<6,11,7,[0,0,0,4]>')]).
% 2.03/2.49 cnf('0.40.1.1',plain,
% 2.03/2.49 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.40.1.0','0.12.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.40.2.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.40.1.1',theory(equality)]),
% 2.03/2.49 [u,rule_38]).
% 2.03/2.49 cnf('0.42.0.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(multiply(inverse(X1),X2),identity) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.8.2.0','0.11.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.42.1.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(multiply(inverse(X1),X2),identity) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.42.0.0']),
% 2.03/2.49 [weight('<6,11,8,[0,0,0,4]>')]).
% 2.03/2.49 cnf('0.42.1.1',plain,
% 2.03/2.49 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.42.1.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.42.2.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.42.1.1',theory(equality)]),
% 2.03/2.49 [u,rule_40]).
% 2.03/2.49 cnf('0.47.0.0',plain,
% 2.03/2.49 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.32.2.0','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.47.1.0',plain,
% 2.03/2.49 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.47.0.0']),
% 2.03/2.49 [weight('<6,33,32,[0,0,0,1]>')]).
% 2.03/2.49 cnf('0.47.2.0',plain,
% 2.03/2.49 ( multiply(X1,multiply(inverse(X1),X2)) = X2 ),
% 2.03/2.49 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_45]).
% 2.03/2.49 cnf('0.53.0.0',plain,
% 2.03/2.49 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(multiply(X1,inverse(X2)),identity) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.9.2.0','0.35.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.53.1.0',plain,
% 2.03/2.49 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(multiply(X1,inverse(X2)),identity) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.53.0.0']),
% 2.03/2.49 [weight('<6,35,9,[0,0,0,4]>')]).
% 2.03/2.49 cnf('0.53.1.1',plain,
% 2.03/2.49 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X1,inverse(X2))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.53.1.0','0.12.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.53.2.0',plain,
% 2.03/2.49 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X1,inverse(X2))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.53.1.1',theory(equality)]),
% 2.03/2.49 [u,rule_51]).
% 2.03/2.49 cnf('0.54.0.0',plain,
% 2.03/2.49 ( multiply(least_upper_bound(X1,X2),inverse(X1)) = least_upper_bound(identity,multiply(X2,inverse(X1))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.10.2.0','0.35.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.54.1.0',plain,
% 2.03/2.49 ( multiply(least_upper_bound(X1,X2),inverse(X1)) = least_upper_bound(identity,multiply(X2,inverse(X1))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.54.0.0']),
% 2.03/2.49 [weight('<6,35,10,[0,0,0,1]>')]).
% 2.03/2.49 cnf('0.54.2.0',plain,
% 2.03/2.49 ( multiply(least_upper_bound(X1,X2),inverse(X1)) = least_upper_bound(identity,multiply(X2,inverse(X1))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.54.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_52]).
% 2.03/2.49 cnf('0.55.0.0',plain,
% 2.03/2.49 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(multiply(X1,inverse(X2)),identity) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.10.2.0','0.35.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.55.1.0',plain,
% 2.03/2.49 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(multiply(X1,inverse(X2)),identity) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.55.0.0']),
% 2.03/2.49 [weight('<6,35,10,[0,0,0,4]>')]).
% 2.03/2.49 cnf('0.55.1.1',plain,
% 2.03/2.49 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.55.1.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.55.2.0',plain,
% 2.03/2.49 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.55.1.1',theory(equality)]),
% 2.03/2.49 [u,rule_53]).
% 2.03/2.49 cnf('0.62.0.0',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(c,inverse(a))) = multiply(least_upper_bound(b,c),inverse(a)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.54.2.0','0.17.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.62.1.0',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(c,inverse(a))) = multiply(least_upper_bound(b,c),inverse(a)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.62.0.0']),
% 2.03/2.49 [weight('<6,54,17,[1,0,0,1]>')]).
% 2.03/2.49 cnf('0.62.2.0',plain,
% 2.03/2.49 ( multiply(least_upper_bound(b,c),inverse(a)) = least_upper_bound(identity,multiply(c,inverse(a))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.62.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_60]).
% 2.03/2.49 cnf('0.63.0.0',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(a,inverse(c))) = multiply(least_upper_bound(b,c),inverse(c)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.55.2.0','0.17.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.63.0.1',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(a,inverse(c))) = least_upper_bound(identity,multiply(b,inverse(c))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.63.0.0','0.55.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.63.1.0',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(a,inverse(c))) = least_upper_bound(identity,multiply(b,inverse(c))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.63.0.1']),
% 2.03/2.49 [weight('<6,55,17,[1,0,0,1]>')]).
% 2.03/2.49 cnf('0.63.2.0',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(a,inverse(c))) = least_upper_bound(identity,multiply(b,inverse(c))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.63.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_61]).
% 2.03/2.49 cnf('0.69.0.0',plain,
% 2.03/2.49 ( a = least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X1))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.5.2.0','0.21.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.69.1.0',plain,
% 2.03/2.49 ( a = least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X1))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.69.0.0']),
% 2.03/2.49 [weight('<7,21,5,[0,0,0,2]>')]).
% 2.03/2.49 cnf('0.69.2.0',plain,
% 2.03/2.49 ( least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X1))) = a ),
% 2.03/2.49 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_67]).
% 2.03/2.49 cnf('0.125.0.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.7.2.0','0.32.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.125.1.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.125.0.0']),
% 2.03/2.49 [weight('<8,32,7,[0,0,0,4]>')]).
% 2.03/2.49 cnf('0.125.2.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.125.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_123]).
% 2.03/2.49 cnf('0.126.0.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.8.2.0','0.32.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.126.1.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.126.0.0']),
% 2.03/2.49 [weight('<8,32,8,[0,0,0,1]>')]).
% 2.03/2.49 cnf('0.126.2.0',plain,
% 2.03/2.49 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.126.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_124]).
% 2.03/2.49 cnf('0.128.0.0',plain,
% 2.03/2.49 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.35.2.0','0.6.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.128.1.0',plain,
% 2.03/2.49 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.128.0.0']),
% 2.03/2.49 [weight('<8,35,6,[1,0,0,0]>')]).
% 2.03/2.49 cnf('0.128.2.0',plain,
% 2.03/2.49 ( multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity ),
% 2.03/2.49 inference(orient,[status(thm)],['0.128.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_126]).
% 2.03/2.49 cnf('0.129.0.0',plain,
% 2.03/2.49 ( multiply(X1,inverse(multiply(X2,X1))) = multiply(inverse(X2),identity) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.32.2.0','0.128.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.129.0.1',plain,
% 2.03/2.49 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.129.0.0','0.38.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.129.1.0',plain,
% 2.03/2.49 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.129.0.1']),
% 2.03/2.49 [weight('<6,128,32,[0,0,0,3]>')]).
% 2.03/2.49 cnf('0.129.2.0',plain,
% 2.03/2.49 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.129.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_127]).
% 2.03/2.49 cnf('0.130.0.0',plain,
% 2.03/2.49 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.32.2.0','0.129.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.130.1.0',plain,
% 2.03/2.49 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.130.0.0']),
% 2.03/2.49 [weight('<4,129,32,[0,0,0,3]>')]).
% 2.03/2.49 cnf('0.130.2.0',plain,
% 2.03/2.49 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.130.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_128]).
% 2.03/2.49 cnf('0.134.0.0',plain,
% 2.03/2.49 ( multiply(inverse(inverse(a)),inverse(least_upper_bound(b,c))) = inverse(least_upper_bound(identity,multiply(c,inverse(a)))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.130.2.0','0.62.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.134.0.1',plain,
% 2.03/2.49 ( multiply(a,inverse(least_upper_bound(b,c))) = inverse(least_upper_bound(identity,multiply(c,inverse(a)))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.134.0.0','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.134.1.0',plain,
% 2.03/2.49 ( multiply(a,inverse(least_upper_bound(b,c))) = inverse(least_upper_bound(identity,multiply(c,inverse(a)))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.134.0.1']),
% 2.03/2.49 [weight('<7,130,62,[1,0,0,1]>')]).
% 2.03/2.49 cnf('0.134.2.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(c,inverse(a)))) = multiply(a,inverse(least_upper_bound(b,c))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.134.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_132]).
% 2.03/2.49 cnf('0.137.0.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),X1) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.40.2.0','0.3.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.137.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),X1) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.137.0.0']),
% 2.03/2.49 [weight('<8,40,3,[1,0,0,3]>')]).
% 2.03/2.49 cnf('0.137.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),X1) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.137.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_135]).
% 2.03/2.49 cnf('0.138.0.0',plain,
% 2.03/2.49 ( multiply(inverse(least_upper_bound(identity,X1)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.137.2.0','0.38.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.138.0.1',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.138.0.0','0.38.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.138.1.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.138.0.1']),
% 2.03/2.49 [weight('<6,137,38,[1,0,0,2]>')]).
% 2.03/2.49 cnf('0.138.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.138.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_136]).
% 2.03/2.49 cnf('0.140.0.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.138.2.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2.1','L')]).
% 2.03/2.49 cnf('0.140.1.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.140.0.0']),
% 2.03/2.49 [weight('<6,138,15,[1,0,0,3]>')]).
% 2.03/2.49 cnf('0.140.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) = inverse(least_upper_bound(identity,X1)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.140.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_138]).
% 2.03/2.49 cnf('0.150.0.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X2)) = multiply(inverse(least_upper_bound(X1,X2)),X2) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.40.2.0','0.22.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.150.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X2)) = multiply(inverse(least_upper_bound(X1,X2)),X2) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.150.0.0']),
% 2.03/2.49 [weight('<8,40,22,[1,0,0,3]>')]).
% 2.03/2.49 cnf('0.150.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X2)) = multiply(inverse(least_upper_bound(X1,X2)),X2) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.150.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_148]).
% 2.03/2.49 cnf('0.168.0.0',plain,
% 2.03/2.49 ( multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.7.2.0','0.47.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.168.1.0',plain,
% 2.03/2.49 ( multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.168.0.0']),
% 2.03/2.49 [weight('<8,47,7,[0,0,0,4]>')]).
% 2.03/2.49 cnf('0.168.2.0',plain,
% 2.03/2.49 ( multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.168.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_166]).
% 2.03/2.49 cnf('0.176.0.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = multiply(X1,inverse(least_upper_bound(X1,X2))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.53.2.0','0.3.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.176.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = multiply(X1,inverse(least_upper_bound(X1,X2))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.176.0.0']),
% 2.03/2.49 [weight('<8,53,3,[1,0,0,1]>')]).
% 2.03/2.49 cnf('0.176.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = multiply(X1,inverse(least_upper_bound(X1,X2))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.176.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_174]).
% 2.03/2.49 cnf('0.177.0.0',plain,
% 2.03/2.49 ( greatest_lower_bound(multiply(inverse(X1),identity),inverse(least_upper_bound(X1,X2))) = multiply(inverse(X1),multiply(X1,inverse(least_upper_bound(X1,X2)))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.125.2.0','0.176.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.177.0.1',plain,
% 2.03/2.49 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = multiply(inverse(X1),multiply(X1,inverse(least_upper_bound(X1,X2)))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.177.0.0','0.38.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.177.0.2',plain,
% 2.03/2.49 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(least_upper_bound(X1,X2)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.177.0.1','0.32.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.177.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(least_upper_bound(X1,X2)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.177.0.2']),
% 2.03/2.49 [weight('<7,176,125,[0,0,0,3]>')]).
% 2.03/2.49 cnf('0.177.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(least_upper_bound(X1,X2)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.177.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_175]).
% 2.03/2.49 cnf('0.178.0.0',plain,
% 2.03/2.49 ( 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)))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.168.2.0','0.176.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.178.0.1',plain,
% 2.03/2.49 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = multiply(X1,multiply(inverse(X1),inverse(least_upper_bound(inverse(X1),X2)))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.178.0.0','0.38.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.178.0.2',plain,
% 2.03/2.49 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.178.0.1','0.47.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.178.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.178.0.2']),
% 2.03/2.49 [weight('<7,176,168,[0,0,0,2]>')]).
% 2.03/2.49 cnf('0.178.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.178.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_176]).
% 2.03/2.49 cnf('0.179.0.0',plain,
% 2.03/2.49 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.5.2.0','0.177.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.179.1.0',plain,
% 2.03/2.49 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.179.0.0']),
% 2.03/2.49 [weight('<7,177,5,[0,0,0,2]>')]).
% 2.03/2.49 cnf('0.179.2.0',plain,
% 2.03/2.49 ( least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(X1) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.179.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_177]).
% 2.03/2.49 cnf('0.180.0.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.177.2.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2.1','L')]).
% 2.03/2.49 cnf('0.180.1.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.180.0.0']),
% 2.03/2.49 [weight('<7,177,15,[1,0,0,4]>')]).
% 2.03/2.49 cnf('0.180.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(least_upper_bound(X1,X2)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.180.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_178]).
% 2.03/2.49 cnf('0.181.0.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(greatest_lower_bound(X1,X2),X1)) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.180.2.0','0.5.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2.1','L')]).
% 2.03/2.49 cnf('0.181.1.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(greatest_lower_bound(X1,X2),X1)) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.181.0.0']),
% 2.03/2.49 [weight('<6,180,5,[1,0,0,4]>')]).
% 2.03/2.49 cnf('0.181.1.1',plain,
% 2.03/2.49 ( inverse(least_upper_bound(X1,greatest_lower_bound(X1,X2))) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.181.1.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.181.1.2',plain,
% 2.03/2.49 ( inverse(X1) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.181.1.1','0.5.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.181.1.3',plain,
% 2.03/2.49 ( inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.181.1.2','0.12.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.181.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(X1) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.181.1.3',theory(equality)]),
% 2.03/2.49 [x,rule_179]).
% 2.03/2.49 cnf('0.186.0.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.178.2.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2.1','L')]).
% 2.03/2.49 cnf('0.186.1.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.186.0.0']),
% 2.03/2.49 [weight('<7,178,15,[1,0,0,3]>')]).
% 2.03/2.49 cnf('0.186.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.186.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_184]).
% 2.03/2.49 cnf('0.187.0.0',plain,
% 2.03/2.49 ( 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))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.21.2.0','0.178.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.187.0.1',plain,
% 2.03/2.49 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1))) = greatest_lower_bound(a,inverse(least_upper_bound(inverse(c),X1))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.187.0.0','0.178.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.187.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1))) = greatest_lower_bound(a,inverse(least_upper_bound(inverse(c),X1))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.187.0.1']),
% 2.03/2.49 [weight('<7,178,21,[0,0,0,2]>')]).
% 2.03/2.49 cnf('0.187.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(a,inverse(least_upper_bound(inverse(c),X1))) = greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.187.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_185]).
% 2.03/2.49 cnf('0.188.0.0',plain,
% 2.03/2.49 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.179.2.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2.1','L')]).
% 2.03/2.49 cnf('0.188.1.0',plain,
% 2.03/2.49 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.188.0.0']),
% 2.03/2.49 [weight('<7,179,15,[1,0,0,4]>')]).
% 2.03/2.49 cnf('0.188.2.0',plain,
% 2.03/2.49 ( least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(X1) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.188.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_186]).
% 2.03/2.49 cnf('0.190.0.0',plain,
% 2.03/2.49 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.18.2.0','0.181.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.190.1.0',plain,
% 2.03/2.49 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.190.0.0']),
% 2.03/2.49 [weight('<7,181,18,[0,0,0,2]>')]).
% 2.03/2.49 cnf('0.190.1.1',plain,
% 2.03/2.49 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.190.1.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.190.2.0',plain,
% 2.03/2.49 ( least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(greatest_lower_bound(X1,X2)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.190.1.1',theory(equality)]),
% 2.03/2.49 [x,rule_188]).
% 2.03/2.49 cnf('0.205.0.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(X1,inverse(least_upper_bound(X2,X1))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.53.2.0','0.22.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.205.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(X1,inverse(least_upper_bound(X2,X1))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.205.0.0']),
% 2.03/2.49 [weight('<8,53,22,[1,0,0,1]>')]).
% 2.03/2.49 cnf('0.205.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(X1,inverse(least_upper_bound(X2,X1))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.205.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_203]).
% 2.03/2.49 cnf('0.249.0.0',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(least_upper_bound(X1,X2),inverse(least_upper_bound(X2,X1))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.55.2.0','0.26.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.249.1.0',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(least_upper_bound(X1,X2),inverse(least_upper_bound(X2,X1))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.249.0.0']),
% 2.03/2.49 [weight('<8,55,26,[1,0,0,1]>')]).
% 2.03/2.49 cnf('0.249.2.0',plain,
% 2.03/2.49 ( multiply(least_upper_bound(X1,X2),inverse(least_upper_bound(X2,X1))) = least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.249.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_245]).
% 2.03/2.49 cnf('0.277.0.0',plain,
% 2.03/2.49 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),inverse(inverse(X1))) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.130.2.0','0.126.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.277.0.1',plain,
% 2.03/2.49 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.277.0.0','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.277.1.0',plain,
% 2.03/2.49 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.277.0.1']),
% 2.03/2.49 [weight('<8,130,126,[1,0,0,1]>')]).
% 2.03/2.49 cnf('0.277.2.0',plain,
% 2.03/2.49 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.277.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_273]).
% 2.03/2.49 cnf('0.278.0.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(X1,multiply(inverse(inverse(X1)),X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.277.2.0','0.11.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1.1.1','L')]).
% 2.03/2.49 cnf('0.278.0.1',plain,
% 2.03/2.49 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.278.0.0','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1.2.1','L')]).
% 2.03/2.49 cnf('0.278.1.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.278.0.1']),
% 2.03/2.49 [weight('<6,277,11,[1,0,0,3]>')]).
% 2.03/2.49 cnf('0.278.2.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.278.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_274]).
% 2.03/2.49 cnf('0.279.0.0',plain,
% 2.03/2.49 ( multiply(inverse(least_upper_bound(identity,X1)),inverse(inverse(X1))) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.278.2.0','0.11.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1.2','L')]).
% 2.03/2.49 cnf('0.279.0.1',plain,
% 2.03/2.49 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.279.0.0','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.279.1.0',plain,
% 2.03/2.49 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.279.0.1']),
% 2.03/2.49 [weight('<6,278,11,[1,0,0,3]>')]).
% 2.03/2.49 cnf('0.279.1.1',plain,
% 2.03/2.49 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.279.1.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('R.1','L')]).
% 2.03/2.49 cnf('0.279.2.0',plain,
% 2.03/2.49 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.279.1.1',theory(equality)]),
% 2.03/2.49 [u,rule_275]).
% 2.03/2.49 cnf('0.296.0.0',plain,
% 2.03/2.49 ( 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))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.40.2.0','0.140.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.296.0.1',plain,
% 2.03/2.49 ( 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))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.296.0.0','0.38.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.296.0.2',plain,
% 2.03/2.49 ( greatest_lower_bound(identity,least_upper_bound(X1,identity)) = multiply(inverse(inverse(least_upper_bound(X1,identity))),inverse(least_upper_bound(identity,X1))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.296.0.1','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.296.0.3',plain,
% 2.03/2.49 ( identity = multiply(inverse(inverse(least_upper_bound(X1,identity))),inverse(least_upper_bound(identity,X1))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.296.0.2','0.22.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.296.0.4',plain,
% 2.03/2.49 ( identity = multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,X1))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.296.0.3','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('R.1','L')]).
% 2.03/2.49 cnf('0.296.1.0',plain,
% 2.03/2.49 ( identity = multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,X1))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.296.0.4']),
% 2.03/2.49 [weight('<8,140,40,[0,0,0,3]>')]).
% 2.03/2.49 cnf('0.296.1.1',plain,
% 2.03/2.49 ( identity = least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(identity,X1)))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.296.1.0','0.249.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.296.2.0',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(identity,X1)))) = identity ),
% 2.03/2.49 inference(orient,[status(thm)],['0.296.1.1',theory(equality)]),
% 2.03/2.49 [x,rule_292]).
% 2.03/2.49 cnf('0.297.0.0',plain,
% 2.03/2.49 ( 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))))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.150.2.0','0.296.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2.1.1','L')]).
% 2.03/2.49 cnf('0.297.0.1',plain,
% 2.03/2.49 ( 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))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.297.0.0','0.279.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.297.0.2',plain,
% 2.03/2.49 ( 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))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.297.0.1','0.130.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1.2','L')]).
% 2.03/2.49 cnf('0.297.0.3',plain,
% 2.03/2.49 ( 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))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.297.0.2','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1.2.1','L')]).
% 2.03/2.49 cnf('0.297.0.4',plain,
% 2.03/2.49 ( 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))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.297.0.3','0.55.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1.2','L')]).
% 2.03/2.49 cnf('0.297.0.5',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(identity,inverse(X1)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.297.0.4','0.23.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.297.0.6',plain,
% 2.03/2.49 ( 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))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.297.0.5','0.278.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.297.0.7',plain,
% 2.03/2.49 ( multiply(inverse(least_upper_bound(identity,inverse(X1))),identity) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.297.0.6','0.36.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.297.0.8',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.297.0.7','0.38.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.297.0.9',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,multiply(identity,multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.297.0.8','0.36.2.0',theory(equality)]),
% 2.03/2.49 [pos('R.2.1','L')]).
% 2.03/2.49 cnf('0.297.0.10',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(identity,X1)))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.297.0.9','0.1.2.0',theory(equality)]),
% 2.03/2.49 [pos('R.2','L')]).
% 2.03/2.49 cnf('0.297.0.11',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(identity,X1))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.297.0.10','0.205.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.297.1.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(identity,X1))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.297.0.11']),
% 2.03/2.49 [weight('<6,296,150,[0,0,0,4]>')]).
% 2.03/2.49 cnf('0.297.2.0',plain,
% 2.03/2.49 ( multiply(X1,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.297.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_293]).
% 2.03/2.49 cnf('0.299.0.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,inverse(multiply(c,inverse(a))))) = multiply(multiply(c,inverse(a)),multiply(a,inverse(least_upper_bound(b,c)))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.297.2.0','0.134.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.299.0.1',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(inverse(inverse(a)),inverse(c)))) = multiply(multiply(c,inverse(a)),multiply(a,inverse(least_upper_bound(b,c)))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.299.0.0','0.130.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1.2','L')]).
% 2.03/2.49 cnf('0.299.0.2',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(a,inverse(c)))) = multiply(multiply(c,inverse(a)),multiply(a,inverse(least_upper_bound(b,c)))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.299.0.1','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1.2.1','L')]).
% 2.03/2.49 cnf('0.299.0.3',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(b,inverse(c)))) = multiply(multiply(c,inverse(a)),multiply(a,inverse(least_upper_bound(b,c)))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.299.0.2','0.63.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.299.0.4',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(b,inverse(c)))) = multiply(c,multiply(inverse(a),multiply(a,inverse(least_upper_bound(b,c))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.299.0.3','0.6.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.299.0.5',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(b,inverse(c)))) = multiply(c,inverse(least_upper_bound(b,c))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.299.0.4','0.32.2.0',theory(equality)]),
% 2.03/2.49 [pos('R.2','L')]).
% 2.03/2.49 cnf('0.299.1.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(b,inverse(c)))) = multiply(c,inverse(least_upper_bound(b,c))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.299.0.5']),
% 2.03/2.49 [weight('<7,297,134,[1,0,0,2]>')]).
% 2.03/2.49 cnf('0.299.2.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(b,inverse(c)))) = multiply(c,inverse(least_upper_bound(b,c))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.299.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_295]).
% 2.03/2.49 cnf('0.300.0.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,inverse(multiply(b,inverse(c))))) = multiply(multiply(b,inverse(c)),multiply(c,inverse(least_upper_bound(b,c)))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.297.2.0','0.299.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.300.0.1',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(inverse(inverse(c)),inverse(b)))) = multiply(multiply(b,inverse(c)),multiply(c,inverse(least_upper_bound(b,c)))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.300.0.0','0.130.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1.2','L')]).
% 2.03/2.49 cnf('0.300.0.2',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(multiply(b,inverse(c)),multiply(c,inverse(least_upper_bound(b,c)))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.300.0.1','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1.2.1','L')]).
% 2.03/2.49 cnf('0.300.0.3',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(b,multiply(inverse(c),multiply(c,inverse(least_upper_bound(b,c))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.300.0.2','0.6.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.300.0.4',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(b,inverse(least_upper_bound(b,c))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.300.0.3','0.32.2.0',theory(equality)]),
% 2.03/2.49 [pos('R.2','L')]).
% 2.03/2.49 cnf('0.300.1.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(b,inverse(least_upper_bound(b,c))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.300.0.4']),
% 2.03/2.49 [weight('<7,299,297,[0,0,0,2]>')]).
% 2.03/2.49 cnf('0.300.2.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(b,inverse(least_upper_bound(b,c))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.300.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_296]).
% 2.03/2.49 cnf('0.353.0.0',plain,
% 2.03/2.49 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),inverse(a)))) = inverse(least_upper_bound(inverse(a),inverse(c))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.187.2.0','0.186.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.353.1.0',plain,
% 2.03/2.49 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),inverse(a)))) = inverse(least_upper_bound(inverse(a),inverse(c))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.353.0.0']),
% 2.03/2.49 [weight('<8,187,186,[1,0,0,0]>')]).
% 2.03/2.49 cnf('0.353.1.1',plain,
% 2.03/2.49 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(a),inverse(c)))) = inverse(least_upper_bound(inverse(a),inverse(c))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.353.1.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2.1','L')]).
% 2.03/2.49 cnf('0.353.2.0',plain,
% 2.03/2.49 ( greatest_lower_bound(b,inverse(least_upper_bound(inverse(a),inverse(c)))) = inverse(least_upper_bound(inverse(a),inverse(c))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.353.1.1',theory(equality)]),
% 2.03/2.49 [u,rule_349]).
% 2.03/2.49 cnf('0.539.0.0',plain,
% 2.03/2.49 ( 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))))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.190.2.0','0.353.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2.1','L')]).
% 2.03/2.49 cnf('0.539.0.1',plain,
% 2.03/2.49 ( inverse(inverse(least_upper_bound(inverse(a),inverse(c)))) = least_upper_bound(inverse(b),inverse(inverse(least_upper_bound(inverse(a),inverse(c))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.539.0.0','0.353.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.539.0.2',plain,
% 2.03/2.49 ( least_upper_bound(inverse(a),inverse(c)) = least_upper_bound(inverse(b),inverse(inverse(least_upper_bound(inverse(a),inverse(c))))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.539.0.1','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.539.0.3',plain,
% 2.03/2.49 ( least_upper_bound(inverse(a),inverse(c)) = least_upper_bound(inverse(b),least_upper_bound(inverse(a),inverse(c))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.539.0.2','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('R.2','L')]).
% 2.03/2.49 cnf('0.539.1.0',plain,
% 2.03/2.49 ( least_upper_bound(inverse(a),inverse(c)) = least_upper_bound(inverse(b),least_upper_bound(inverse(a),inverse(c))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.539.0.3']),
% 2.03/2.49 [weight('<8,353,190,[0,0,0,4]>')]).
% 2.03/2.49 cnf('0.539.2.0',plain,
% 2.03/2.49 ( least_upper_bound(inverse(b),least_upper_bound(inverse(a),inverse(c))) = least_upper_bound(inverse(a),inverse(c)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.539.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_534]).
% 2.03/2.49 cnf('0.1148.0.0',plain,
% 2.03/2.49 ( a = least_upper_bound(a,greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1)))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.69.2.0','0.178.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2.2','L')]).
% 2.03/2.49 cnf('0.1148.1.0',plain,
% 2.03/2.49 ( a = least_upper_bound(a,greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1)))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.1148.0.0']),
% 2.03/2.49 [weight('<9,178,69,[0,0,0,4]>')]).
% 2.03/2.49 cnf('0.1148.2.0',plain,
% 2.03/2.49 ( least_upper_bound(a,greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1)))) = a ),
% 2.03/2.49 inference(orient,[status(thm)],['0.1148.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_1138]).
% 2.03/2.49 cnf('0.1149.0.0',plain,
% 2.03/2.49 ( a = least_upper_bound(a,inverse(least_upper_bound(inverse(b),inverse(c)))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.1148.2.0','0.186.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.1149.1.0',plain,
% 2.03/2.49 ( a = least_upper_bound(a,inverse(least_upper_bound(inverse(b),inverse(c)))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.1149.0.0']),
% 2.03/2.49 [weight('<8,1148,186,[1,0,0,2]>')]).
% 2.03/2.49 cnf('0.1149.2.0',plain,
% 2.03/2.49 ( least_upper_bound(a,inverse(least_upper_bound(inverse(b),inverse(c)))) = a ),
% 2.03/2.49 inference(orient,[status(thm)],['0.1149.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_1139]).
% 2.03/2.49 cnf('0.1150.0.0',plain,
% 2.03/2.49 ( inverse(inverse(least_upper_bound(inverse(b),inverse(c)))) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(b),inverse(c)))),inverse(a)) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.188.2.0','0.1149.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2.1','L')]).
% 2.03/2.49 cnf('0.1150.0.1',plain,
% 2.03/2.49 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(b),inverse(c)))),inverse(a)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.1150.0.0','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.1150.0.2',plain,
% 2.03/2.49 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(least_upper_bound(inverse(b),inverse(c)),inverse(a)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.1150.0.1','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('R.1','L')]).
% 2.03/2.49 cnf('0.1150.0.3',plain,
% 2.03/2.49 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(b),least_upper_bound(inverse(c),inverse(a))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.1150.0.2','0.16.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.1150.1.0',plain,
% 2.03/2.49 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(b),least_upper_bound(inverse(c),inverse(a))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.1150.0.3']),
% 2.03/2.49 [weight('<8,1149,188,[0,0,0,4]>')]).
% 2.03/2.49 cnf('0.1150.1.1',plain,
% 2.03/2.49 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(b),least_upper_bound(inverse(a),inverse(c))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.1150.1.0','0.15.2.0',theory(equality)]),
% 2.03/2.49 [pos('R.2','L')]).
% 2.03/2.49 cnf('0.1150.1.2',plain,
% 2.03/2.49 ( least_upper_bound(inverse(b),inverse(c)) = least_upper_bound(inverse(a),inverse(c)) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.1150.1.1','0.539.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.1150.2.0',plain,
% 2.03/2.49 ( least_upper_bound(inverse(a),inverse(c)) = least_upper_bound(inverse(b),inverse(c)) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.1150.1.2',theory(equality)]),
% 2.03/2.49 [x,rule_1140]).
% 2.03/2.49 cnf('0.1153.0.0',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(inverse(inverse(c)),inverse(a))) = multiply(inverse(inverse(c)),least_upper_bound(inverse(b),inverse(c))) ),
% 2.03/2.49 inference(cp,[status(thm)],['0.42.2.0','0.1150.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2','L')]).
% 2.03/2.49 cnf('0.1153.0.1',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(c,inverse(a))) = multiply(inverse(inverse(c)),least_upper_bound(inverse(b),inverse(c))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.1153.0.0','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.2.1','L')]).
% 2.03/2.49 cnf('0.1153.0.2',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(c,inverse(a))) = least_upper_bound(identity,multiply(inverse(inverse(c)),inverse(b))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.1153.0.1','0.42.2.0',theory(equality)]),
% 2.03/2.49 [pos('R','L')]).
% 2.03/2.49 cnf('0.1153.0.3',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(c,inverse(a))) = least_upper_bound(identity,multiply(c,inverse(b))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.1153.0.2','0.33.2.0',theory(equality)]),
% 2.03/2.49 [pos('R.2.1','L')]).
% 2.03/2.49 cnf('0.1153.1.0',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(c,inverse(a))) = least_upper_bound(identity,multiply(c,inverse(b))) ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.1153.0.3']),
% 2.03/2.49 [weight('<6,1150,42,[0,0,0,3]>')]).
% 2.03/2.49 cnf('0.1153.2.0',plain,
% 2.03/2.49 ( least_upper_bound(identity,multiply(c,inverse(a))) = least_upper_bound(identity,multiply(c,inverse(b))) ),
% 2.03/2.49 inference(orient,[status(thm)],['0.1153.1.0',theory(equality)]),
% 2.03/2.49 [u,rule_1143]).
% 2.03/2.49 cnf('0.1154.0.0',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(c,inverse(a)))) = multiply(a,inverse(least_upper_bound(b,c))) ),
% 2.03/2.49 inference(interreduction_right,[status(thm)],['0.134.2.0'])).
% 2.03/2.49 cnf('0.1154.0.1',plain,
% 2.03/2.49 ( inverse(least_upper_bound(identity,multiply(c,inverse(b)))) = multiply(a,inverse(least_upper_bound(b,c))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.1154.0.0','0.1153.2.0',theory(equality)]),
% 2.03/2.49 [pos('L.1','L')]).
% 2.03/2.49 cnf('0.1154.0.2',plain,
% 2.03/2.49 ( multiply(b,inverse(least_upper_bound(b,c))) = multiply(a,inverse(least_upper_bound(b,c))) ),
% 2.03/2.49 inference(reduction,[status(thm)],['0.1154.0.1','0.300.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('0.1154.1.0',plain,
% 2.03/2.49 ( b = a ),
% 2.03/2.49 inference(weigh,[status(thm)],['0.1154.0.2']),
% 2.03/2.49 [weight('<1,134,1153,[0,0,0,0]>')]).
% 2.03/2.49 cnf('0.1154.2.0',plain,
% 2.03/2.49 ( a = b ),
% 2.03/2.49 inference(orient,[status(thm)],['0.1154.1.0',theory(equality)]),
% 2.03/2.49 [x,rule_1144]).
% 2.03/2.49 cnf('1.0.0.0',conjecture,
% 2.03/2.49 ( a = b ),
% 2.03/2.49 file('/tmp/WALDMEISTER_29188_n022',conjecture_1)).
% 2.03/2.49 cnf('1.0.0.1',plain,
% 2.03/2.49 ( b = b ),
% 2.03/2.49 inference(reduction,[status(thm)],['1.0.0.0','0.1154.2.0',theory(equality)]),
% 2.03/2.49 [pos('L','L')]).
% 2.03/2.49 cnf('1.0.0.2',plain,
% 2.03/2.49 ( $true ),
% 2.03/2.49 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 2.03/2.49 [conjecture_1]).
% 2.03/2.49
% 2.03/2.49 Proved Goals:
% 2.03/2.49 No. 1: a ?= b joined, current: b = b
% 2.03/2.49 1 goal was specified, which was proved.
% 2.03/2.49 % SZS output end CNFRefutation
% 2.03/2.49 #END OF PROOF
% 2.03/2.49
% 2.03/2.49 Problem WALDMEISTER_29188_n022
% 2.03/2.49 CPs.gen 223268
% 2.03/2.49 CPs.reexp 0
% 2.03/2.49 Select 13160
% 2.03/2.49 R 1144
% 2.03/2.49 E 10
% 2.03/2.49 vsize 8.9M
% 2.03/2.49 rss 4.4M
% 2.03/2.49 process.time 0.872s
% 2.03/2.49 wallclock.time 1.511s
% 2.03/2.49 status S
% 2.03/2.49
% 2.03/2.49
% 2.03/2.49 Waldmeister states: Goal proved.
% 2.03/2.49 % SZS status Unsatisfiable
% 2.03/2.49
% 2.03/2.49 Problem WALDMEISTER_29188_n022
% 2.03/2.49 CPs.gen 179104
% 2.03/2.49 CPs.reexp 0
% 2.03/2.49 Select 16273
% 2.03/2.49 R 1016
% 2.03/2.49 E 12
% 2.03/2.49 vsize 7.5M
% 2.03/2.49 rss 4.8M
% 2.03/2.49 process.time 0.640s
% 2.03/2.49 wallclock.time 1.512s
% 2.03/2.49 status S
%------------------------------------------------------------------------------