TSTP Solution File: GRP179-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP179-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n011.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 12:25:08 EDT 2022
% Result : Unsatisfiable 1.74s 2.12s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP179-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 09:47:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.62/1.02 ********************************************************************************
% 0.62/1.02 * W A L D M E I S T E R \| \ / \|/ *
% 0.62/1.02 * |/ | \/ | *
% 0.62/1.02 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.62/1.02 * A. Jaeger and B. Loechner | | *
% 0.62/1.02 * <waldmeister@informatik.uni-kl.de> | *
% 0.62/1.02 ********************************************************************************
% 0.62/1.02
% 0.62/1.02
% 0.62/1.02 Goals:
% 0.62/1.02 ------
% 0.62/1.02
% 0.62/1.02 ( 1) greatest_lower_bound(inverse(a),inverse(b)) ?=? inverse(least_upper_bound(a,b))
% 0.65/1.02
% 0.65/1.02 Detected structure: VerbandsgeordneteGruppe
% 0.65/1.02 ********************************************************************************
% 0.65/1.02 ****************************** COMPLETION - PROOF ******************************
% 0.65/1.02 ********************************************************************************
% 0.65/1.02
% 1.74/2.12 joined goal: 1 greatest_lower_bound(inverse(a),inverse(b)) ?= inverse(least_upper_bound(a,b)) to inverse(least_upper_bound(b,a))
% 1.74/2.12 goal joined
% 1.74/2.12 % SZS status Unsatisfiable
% 1.74/2.12 #START OF PROOF
% 1.74/2.12 % SZS output start CNFRefutation
% 1.74/2.12 cnf('0.1.0.0',axiom,
% 1.74/2.12 ( X1 = multiply(identity,X1) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.1.1.0',plain,
% 1.74/2.12 ( X1 = multiply(identity,X1) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.1.0.0']),
% 1.74/2.12 [weight('<0,0,0,[0,0,0,1]>')]).
% 1.74/2.12 cnf('0.1.2.0',plain,
% 1.74/2.12 ( multiply(identity,X1) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_1]).
% 1.74/2.12 cnf('0.3.0.0',axiom,
% 1.74/2.12 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.3.1.0',plain,
% 1.74/2.12 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.3.0.0']),
% 1.74/2.12 [weight('<2,0,0,[0,0,0,3]>')]).
% 1.74/2.12 cnf('0.3.2.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_3]).
% 1.74/2.12 cnf('0.5.0.0',axiom,
% 1.74/2.12 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.5.1.0',plain,
% 1.74/2.12 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.5.0.0']),
% 1.74/2.12 [weight('<4,0,0,[0,0,0,5]>')]).
% 1.74/2.12 cnf('0.5.2.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_5]).
% 1.74/2.12 cnf('0.6.0.0',axiom,
% 1.74/2.12 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.6.1.0',plain,
% 1.74/2.12 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.6.0.0']),
% 1.74/2.12 [weight('<5,0,0,[0,0,0,6]>')]).
% 1.74/2.12 cnf('0.6.2.0',plain,
% 1.74/2.12 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_6]).
% 1.74/2.12 cnf('0.8.0.0',axiom,
% 1.74/2.12 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.8.1.0',plain,
% 1.74/2.12 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.8.0.0']),
% 1.74/2.12 [weight('<7,0,0,[0,0,0,8]>')]).
% 1.74/2.12 cnf('0.8.2.0',plain,
% 1.74/2.12 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_8]).
% 1.74/2.12 cnf('0.9.0.0',axiom,
% 1.74/2.12 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.9.1.0',plain,
% 1.74/2.12 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.9.0.0']),
% 1.74/2.12 [weight('<8,0,0,[0,0,0,9]>')]).
% 1.74/2.12 cnf('0.9.2.0',plain,
% 1.74/2.12 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_9]).
% 1.74/2.12 cnf('0.10.0.0',axiom,
% 1.74/2.12 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.10.1.0',plain,
% 1.74/2.12 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.10.0.0']),
% 1.74/2.12 [weight('<9,0,0,[0,0,0,10]>')]).
% 1.74/2.12 cnf('0.10.2.0',plain,
% 1.74/2.12 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_10]).
% 1.74/2.12 cnf('0.11.0.0',axiom,
% 1.74/2.12 ( multiply(inverse(X1),X1) = identity ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.11.1.0',plain,
% 1.74/2.12 ( multiply(inverse(X1),X1) = identity ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.11.0.0']),
% 1.74/2.12 [weight('<10,0,0,[0,0,0,11]>')]).
% 1.74/2.12 cnf('0.11.2.0',plain,
% 1.74/2.12 ( multiply(inverse(X1),X1) = identity ),
% 1.74/2.12 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_11]).
% 1.74/2.12 cnf('0.12.0.0',axiom,
% 1.74/2.12 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.12.1.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.12.0.0']),
% 1.74/2.12 [weight('<11,0,0,[0,0,0,12]>')]).
% 1.74/2.12 cnf('0.12.2.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 1.74/2.12 inference(activate,[status(thm)],['0.12.1.0']),
% 1.74/2.12 [equation_1]).
% 1.74/2.12 cnf('0.13.0.0',axiom,
% 1.74/2.12 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.13.1.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.13.0.0']),
% 1.74/2.12 [weight('<12,0,0,[0,0,0,13]>')]).
% 1.74/2.12 cnf('0.13.2.0',plain,
% 1.74/2.12 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_12]).
% 1.74/2.12 cnf('0.14.0.0',axiom,
% 1.74/2.12 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.14.1.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.14.0.0']),
% 1.74/2.12 [weight('<13,0,0,[0,0,0,14]>')]).
% 1.74/2.12 cnf('0.14.2.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 1.74/2.12 inference(activate,[status(thm)],['0.14.1.0']),
% 1.74/2.12 [equation_2]).
% 1.74/2.12 cnf('0.15.0.0',axiom,
% 1.74/2.12 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011')).
% 1.74/2.12 cnf('0.15.1.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.15.0.0']),
% 1.74/2.12 [weight('<14,0,0,[0,0,0,15]>')]).
% 1.74/2.12 cnf('0.15.2.0',plain,
% 1.74/2.12 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_13]).
% 1.74/2.12 cnf('0.16.0.0',plain,
% 1.74/2.12 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.5.2.0','0.12.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.16.1.0',plain,
% 1.74/2.12 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.16.0.0']),
% 1.74/2.12 [weight('<41,12,5,[0,0,0,2]>')]).
% 1.74/2.12 cnf('0.16.2.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_14]).
% 1.74/2.12 cnf('0.17.0.0',plain,
% 1.74/2.12 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.3.2.0','0.14.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.17.1.0',plain,
% 1.74/2.12 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.17.0.0']),
% 1.74/2.12 [weight('<41,14,3,[0,0,0,2]>')]).
% 1.74/2.12 cnf('0.17.2.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_15]).
% 1.74/2.12 cnf('0.22.0.0',plain,
% 1.74/2.12 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.22.0.1',plain,
% 1.74/2.12 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.22.0.0','0.1.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.22.1.0',plain,
% 1.74/2.12 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.22.0.1']),
% 1.74/2.12 [weight('<55,11,6,[0,0,0,1]>')]).
% 1.74/2.12 cnf('0.22.2.0',plain,
% 1.74/2.12 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_20]).
% 1.74/2.12 cnf('0.23.0.0',plain,
% 1.74/2.12 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.22.2.0','0.22.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.23.1.0',plain,
% 1.74/2.12 ( X1 = inverse(inverse(X1)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.23.0.0']),
% 1.74/2.12 [weight('<19,22,22,[0,0,0,3]>')]).
% 1.74/2.12 cnf('0.23.2.0',plain,
% 1.74/2.12 ( inverse(inverse(X1)) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_21]).
% 1.74/2.12 cnf('0.25.0.0',plain,
% 1.74/2.12 ( identity = multiply(X1,inverse(X1)) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.11.2.0','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.25.1.0',plain,
% 1.74/2.12 ( identity = multiply(X1,inverse(X1)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.25.0.0']),
% 1.74/2.12 [weight('<29,23,11,[0,0,0,1]>')]).
% 1.74/2.12 cnf('0.25.2.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(X1)) = identity ),
% 1.74/2.12 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_23]).
% 1.74/2.12 cnf('0.26.0.0',plain,
% 1.74/2.12 ( identity = inverse(identity) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.25.2.0','0.1.2.0',theory(equality)]),
% 1.74/2.12 [pos('L','L')]).
% 1.74/2.12 cnf('0.26.1.0',plain,
% 1.74/2.12 ( identity = inverse(identity) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.26.0.0']),
% 1.74/2.12 [weight('<11,25,1,[1,0,0,0]>')]).
% 1.74/2.12 cnf('0.26.2.0',plain,
% 1.74/2.12 ( inverse(identity) = identity ),
% 1.74/2.12 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_24]).
% 1.74/2.12 cnf('0.27.0.0',plain,
% 1.74/2.12 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.22.2.0','0.25.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.27.1.0',plain,
% 1.74/2.12 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.27.0.0']),
% 1.74/2.12 [weight('<34,25,22,[0,0,0,3]>')]).
% 1.74/2.12 cnf('0.27.2.0',plain,
% 1.74/2.12 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_25]).
% 1.74/2.12 cnf('0.28.0.0',plain,
% 1.74/2.12 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.27.2.0','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.28.0.1',plain,
% 1.74/2.12 ( X1 = multiply(X1,identity) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.28.0.0','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('L','L')]).
% 1.74/2.12 cnf('0.28.1.0',plain,
% 1.74/2.12 ( X1 = multiply(X1,identity) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.28.0.1']),
% 1.74/2.12 [weight('<19,27,23,[1,0,0,1]>')]).
% 1.74/2.12 cnf('0.28.2.0',plain,
% 1.74/2.12 ( multiply(X1,identity) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_26]).
% 1.74/2.12 cnf('0.44.0.0',plain,
% 1.74/2.12 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.25.2.0','0.6.2.0',theory(equality)]),
% 1.74/2.12 [pos('L','L')]).
% 1.74/2.12 cnf('0.44.1.0',plain,
% 1.74/2.12 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.44.0.0']),
% 1.74/2.12 [weight('<89,25,6,[1,0,0,0]>')]).
% 1.74/2.12 cnf('0.44.2.0',plain,
% 1.74/2.12 ( multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity ),
% 1.74/2.12 inference(orient,[status(thm)],['0.44.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_42]).
% 1.74/2.12 cnf('0.45.0.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(multiply(X2,X1))) = multiply(inverse(X2),identity) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.22.2.0','0.44.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.45.0.1',plain,
% 1.74/2.12 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.45.0.0','0.28.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.45.1.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.45.0.1']),
% 1.74/2.12 [weight('<62,44,22,[0,0,0,3]>')]).
% 1.74/2.12 cnf('0.45.2.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_43]).
% 1.74/2.12 cnf('0.47.0.0',plain,
% 1.74/2.12 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.22.2.0','0.45.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.47.1.0',plain,
% 1.74/2.12 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.47.0.0']),
% 1.74/2.12 [weight('<99,45,22,[0,0,0,3]>')]).
% 1.74/2.12 cnf('0.47.2.0',plain,
% 1.74/2.12 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 1.74/2.12 inference(activate,[status(thm)],['0.47.1.0']),
% 1.74/2.12 [equation_3]).
% 1.74/2.12 cnf('0.68.0.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X2,X1),X3) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.15.2.0','0.14.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.68.0.1',plain,
% 1.74/2.12 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.68.0.0','0.15.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.68.1.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.68.0.1']),
% 1.74/2.12 [weight('<120,15,14,[1,0,0,1]>')]).
% 1.74/2.12 cnf('0.68.2.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)) ),
% 1.74/2.12 inference(activate,[status(thm)],['0.68.1.0']),
% 1.74/2.12 [equation_10]).
% 1.74/2.12 cnf('0.72.0.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,X2) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,greatest_lower_bound(X2,X3))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.5.2.0','0.13.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.72.1.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,X2) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,greatest_lower_bound(X2,X3))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.72.0.0']),
% 1.74/2.12 [weight('<129,13,5,[0,0,0,2]>')]).
% 1.74/2.12 cnf('0.72.2.0',plain,
% 1.74/2.12 ( least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,greatest_lower_bound(X2,X3))) = greatest_lower_bound(X1,X2) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.72.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_60]).
% 1.74/2.12 cnf('0.140.0.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(X1,X2)) = multiply(X3,inverse(greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.45.2.0','0.9.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1','L')]).
% 1.74/2.12 cnf('0.140.1.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(X1,X2)) = multiply(X3,inverse(greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.140.0.0']),
% 1.74/2.12 [weight('<164,45,9,[1,0,0,3]>')]).
% 1.74/2.12 cnf('0.140.2.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(greatest_lower_bound(multiply(X2,X1),multiply(X3,X1)))) = inverse(greatest_lower_bound(X2,X3)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.140.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_128]).
% 1.74/2.12 cnf('0.141.0.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,X1)) = multiply(X2,inverse(greatest_lower_bound(X2,multiply(X1,X2)))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.140.2.0','0.1.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1.1','L')]).
% 1.74/2.12 cnf('0.141.1.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,X1)) = multiply(X2,inverse(greatest_lower_bound(X2,multiply(X1,X2)))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.141.0.0']),
% 1.74/2.12 [weight('<116,140,1,[1,0,0,4]>')]).
% 1.74/2.12 cnf('0.141.2.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(greatest_lower_bound(X1,multiply(X2,X1)))) = inverse(greatest_lower_bound(identity,X2)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.141.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_129]).
% 1.74/2.12 cnf('0.142.0.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(X1))) = multiply(X1,inverse(greatest_lower_bound(X1,identity))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.141.2.0','0.11.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1.2','L')]).
% 1.74/2.12 cnf('0.142.1.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(X1))) = multiply(X1,inverse(greatest_lower_bound(X1,identity))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.142.0.0']),
% 1.74/2.12 [weight('<83,141,11,[1,0,0,5]>')]).
% 1.74/2.12 cnf('0.142.2.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.142.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_130]).
% 1.74/2.12 cnf('0.143.0.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(X1))) = multiply(X1,inverse(greatest_lower_bound(identity,X1))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.142.2.0','0.12.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1','L')]).
% 1.74/2.12 cnf('0.143.1.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(X1))) = multiply(X1,inverse(greatest_lower_bound(identity,X1))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.143.0.0']),
% 1.74/2.12 [weight('<83,142,12,[1,0,0,3]>')]).
% 1.74/2.12 cnf('0.143.2.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.143.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_131]).
% 1.74/2.12 cnf('0.144.0.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1)))) = multiply(least_upper_bound(identity,X1),inverse(identity)) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.143.2.0','0.3.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1','L')]).
% 1.74/2.12 cnf('0.144.0.1',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1)))) = least_upper_bound(multiply(identity,inverse(identity)),multiply(X1,inverse(identity))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.144.0.0','0.10.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.144.0.2',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1)))) = least_upper_bound(inverse(identity),multiply(X1,inverse(identity))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.144.0.1','0.1.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.1','L')]).
% 1.74/2.12 cnf('0.144.0.3',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1)))) = least_upper_bound(identity,multiply(X1,inverse(identity))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.144.0.2','0.26.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.1','L')]).
% 1.74/2.12 cnf('0.144.0.4',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1)))) = least_upper_bound(identity,multiply(X1,identity)) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.144.0.3','0.26.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.2.2','L')]).
% 1.74/2.12 cnf('0.144.0.5',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1)))) = least_upper_bound(identity,X1) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.144.0.4','0.28.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.2','L')]).
% 1.74/2.12 cnf('0.144.1.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1)))) = least_upper_bound(identity,X1) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.144.0.5']),
% 1.74/2.12 [weight('<87,143,3,[1,0,0,3]>')]).
% 1.74/2.12 cnf('0.144.2.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1)))) = least_upper_bound(identity,X1) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.144.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_132]).
% 1.74/2.12 cnf('0.145.0.0',plain,
% 1.74/2.12 ( greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.23.2.0','0.144.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.145.1.0',plain,
% 1.74/2.12 ( greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.145.0.0']),
% 1.74/2.12 [weight('<76,144,23,[0,0,0,1]>')]).
% 1.74/2.12 cnf('0.145.2.0',plain,
% 1.74/2.12 ( greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.145.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_133]).
% 1.74/2.12 cnf('0.146.0.0',plain,
% 1.74/2.12 ( identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.5.2.0','0.145.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.146.1.0',plain,
% 1.74/2.12 ( identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.146.0.0']),
% 1.74/2.12 [weight('<55,145,5,[0,0,0,2]>')]).
% 1.74/2.12 cnf('0.146.2.0',plain,
% 1.74/2.12 ( least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) = identity ),
% 1.74/2.12 inference(orient,[status(thm)],['0.146.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_134]).
% 1.74/2.12 cnf('0.150.0.0',plain,
% 1.74/2.12 ( least_upper_bound(multiply(X1,identity),multiply(X1,inverse(least_upper_bound(identity,X2)))) = multiply(X1,identity) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.8.2.0','0.146.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.150.0.1',plain,
% 1.74/2.12 ( least_upper_bound(X1,multiply(X1,inverse(least_upper_bound(identity,X2)))) = multiply(X1,identity) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.150.0.0','0.28.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.150.0.2',plain,
% 1.74/2.12 ( least_upper_bound(X1,multiply(X1,inverse(least_upper_bound(identity,X2)))) = X1 ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.150.0.1','0.28.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.150.1.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,multiply(X1,inverse(least_upper_bound(identity,X2)))) = X1 ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.150.0.2']),
% 1.74/2.12 [weight('<89,146,8,[0,0,0,2]>')]).
% 1.74/2.12 cnf('0.150.2.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,multiply(X1,inverse(least_upper_bound(identity,X2)))) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.150.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_138]).
% 1.74/2.12 cnf('0.151.0.0',plain,
% 1.74/2.12 ( least_upper_bound(multiply(identity,X1),multiply(inverse(least_upper_bound(identity,X2)),X1)) = multiply(identity,X1) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.10.2.0','0.146.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.151.0.1',plain,
% 1.74/2.12 ( least_upper_bound(X1,multiply(inverse(least_upper_bound(identity,X2)),X1)) = multiply(identity,X1) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.151.0.0','0.1.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.151.0.2',plain,
% 1.74/2.12 ( least_upper_bound(X1,multiply(inverse(least_upper_bound(identity,X2)),X1)) = X1 ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.151.0.1','0.1.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.151.1.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,multiply(inverse(least_upper_bound(identity,X2)),X1)) = X1 ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.151.0.2']),
% 1.74/2.12 [weight('<89,146,10,[0,0,0,1]>')]).
% 1.74/2.12 cnf('0.151.2.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,multiply(inverse(least_upper_bound(identity,X2)),X1)) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.151.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_139]).
% 1.74/2.12 cnf('0.171.0.0',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(multiply(least_upper_bound(identity,X2),X1))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.150.2.0','0.47.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','R')]).
% 1.74/2.12 cnf('0.171.0.1',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(multiply(identity,X1),multiply(X2,X1)))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.171.0.0','0.10.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.2.1','L')]).
% 1.74/2.12 cnf('0.171.0.2',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,multiply(X2,X1)))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.171.0.1','0.1.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.2.1.1','L')]).
% 1.74/2.12 cnf('0.171.1.0',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,multiply(X2,X1)))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.171.0.2']),
% 1.74/2.12 [weight('<119,150,47,[1,0,1,2]>')]).
% 1.74/2.12 cnf('0.171.2.0',plain,
% 1.74/2.12 ( least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,multiply(X2,X1)))) = inverse(X1) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.171.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_159]).
% 1.74/2.12 cnf('0.172.0.0',plain,
% 1.74/2.12 ( inverse(inverse(X1)) = least_upper_bound(inverse(inverse(X1)),inverse(least_upper_bound(inverse(X1),identity))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.171.2.0','0.25.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1.2','L')]).
% 1.74/2.12 cnf('0.172.0.1',plain,
% 1.74/2.12 ( X1 = least_upper_bound(inverse(inverse(X1)),inverse(least_upper_bound(inverse(X1),identity))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.172.0.0','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('L','L')]).
% 1.74/2.12 cnf('0.172.0.2',plain,
% 1.74/2.12 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),identity))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.172.0.1','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.1','L')]).
% 1.74/2.12 cnf('0.172.1.0',plain,
% 1.74/2.12 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),identity))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.172.0.2']),
% 1.74/2.12 [weight('<71,171,25,[1,0,0,6]>')]).
% 1.74/2.12 cnf('0.172.1.1',plain,
% 1.74/2.12 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(identity,inverse(X1)))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.172.1.0','0.14.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.2.1','L')]).
% 1.74/2.12 cnf('0.172.2.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,inverse(least_upper_bound(identity,inverse(X1)))) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.172.1.1',theory(equality)]),
% 1.74/2.12 [x,rule_160]).
% 1.74/2.12 cnf('0.174.0.0',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(identity,X1))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.172.2.0','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1.2','L')]).
% 1.74/2.12 cnf('0.174.1.0',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(identity,X1))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.174.0.0']),
% 1.74/2.12 [weight('<79,172,23,[1,0,0,5]>')]).
% 1.74/2.12 cnf('0.174.2.0',plain,
% 1.74/2.12 ( least_upper_bound(inverse(X1),inverse(least_upper_bound(identity,X1))) = inverse(X1) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.174.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_162]).
% 1.74/2.12 cnf('0.178.0.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(X1,identity)) = least_upper_bound(inverse(greatest_lower_bound(X1,identity)),inverse(identity)) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.174.2.0','0.16.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1','L')]).
% 1.74/2.12 cnf('0.178.0.1',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(X1,identity)) = least_upper_bound(inverse(greatest_lower_bound(X1,identity)),identity) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.178.0.0','0.26.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.2','L')]).
% 1.74/2.12 cnf('0.178.1.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(X1,identity)) = least_upper_bound(inverse(greatest_lower_bound(X1,identity)),identity) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.178.0.1']),
% 1.74/2.12 [weight('<76,174,16,[1,0,0,4]>')]).
% 1.74/2.12 cnf('0.178.1.1',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(X1,identity)) = least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.178.1.0','0.14.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.178.2.0',plain,
% 1.74/2.12 ( least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(X1,identity)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.178.1.1',theory(equality)]),
% 1.74/2.12 [x,rule_166]).
% 1.74/2.12 cnf('0.227.0.0',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(multiply(X1,least_upper_bound(identity,X2)))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.151.2.0','0.47.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','R')]).
% 1.74/2.12 cnf('0.227.0.1',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(multiply(X1,identity),multiply(X1,X2)))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.227.0.0','0.8.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.2.1','L')]).
% 1.74/2.12 cnf('0.227.0.2',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,multiply(X1,X2)))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.227.0.1','0.28.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.2.1.1','L')]).
% 1.74/2.12 cnf('0.227.1.0',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,multiply(X1,X2)))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.227.0.2']),
% 1.74/2.12 [weight('<119,151,47,[1,0,1,2]>')]).
% 1.74/2.12 cnf('0.227.2.0',plain,
% 1.74/2.12 ( least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,multiply(X1,X2)))) = inverse(X1) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.227.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_215]).
% 1.74/2.12 cnf('0.228.0.0',plain,
% 1.74/2.12 ( inverse(inverse(X1)) = least_upper_bound(inverse(inverse(X1)),inverse(least_upper_bound(inverse(X1),X2))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.227.2.0','0.22.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1.2','L')]).
% 1.74/2.12 cnf('0.228.0.1',plain,
% 1.74/2.12 ( X1 = least_upper_bound(inverse(inverse(X1)),inverse(least_upper_bound(inverse(X1),X2))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.228.0.0','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('L','L')]).
% 1.74/2.12 cnf('0.228.0.2',plain,
% 1.74/2.12 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.228.0.1','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.1','L')]).
% 1.74/2.12 cnf('0.228.1.0',plain,
% 1.74/2.12 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.228.0.2']),
% 1.74/2.12 [weight('<71,227,22,[1,0,0,6]>')]).
% 1.74/2.12 cnf('0.228.2.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.228.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_216]).
% 1.74/2.12 cnf('0.229.0.0',plain,
% 1.74/2.12 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.228.2.0','0.14.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1','L')]).
% 1.74/2.12 cnf('0.229.1.0',plain,
% 1.74/2.12 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.229.0.0']),
% 1.74/2.12 [weight('<71,228,14,[1,0,0,3]>')]).
% 1.74/2.12 cnf('0.229.2.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = X1 ),
% 1.74/2.12 inference(orient,[status(thm)],['0.229.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_217]).
% 1.74/2.12 cnf('0.231.0.0',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.229.2.0','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1.2','L')]).
% 1.74/2.12 cnf('0.231.1.0',plain,
% 1.74/2.12 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.231.0.0']),
% 1.74/2.12 [weight('<79,229,23,[1,0,0,5]>')]).
% 1.74/2.12 cnf('0.231.2.0',plain,
% 1.74/2.12 ( least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(X1) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.231.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_219]).
% 1.74/2.12 cnf('0.233.0.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.231.2.0','0.5.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1','L')]).
% 1.74/2.12 cnf('0.233.1.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.233.0.0']),
% 1.74/2.12 [weight('<95,231,5,[1,0,0,4]>')]).
% 1.74/2.12 cnf('0.233.1.1',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.233.1.0','0.14.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.233.2.0',plain,
% 1.74/2.12 ( least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(greatest_lower_bound(X1,X2)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.233.1.1',theory(equality)]),
% 1.74/2.12 [x,rule_221]).
% 1.74/2.12 cnf('0.241.0.0',plain,
% 1.74/2.12 ( inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(inverse(least_upper_bound(X1,inverse(X2))),X2) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.17.2.0','0.229.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.241.1.0',plain,
% 1.74/2.12 ( inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(inverse(least_upper_bound(X1,inverse(X2))),X2) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.241.0.0']),
% 1.74/2.12 [weight('<103,229,17,[0,0,0,2]>')]).
% 1.74/2.12 cnf('0.241.1.1',plain,
% 1.74/2.12 ( inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(X2,inverse(least_upper_bound(X1,inverse(X2)))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.241.1.0','0.12.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.241.2.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = inverse(least_upper_bound(X2,inverse(X1))) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.241.1.1',theory(equality)]),
% 1.74/2.12 [x,rule_229]).
% 1.74/2.12 cnf('0.277.0.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(inverse(X1),X2)) = multiply(X1,inverse(greatest_lower_bound(identity,multiply(X2,X1)))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.140.2.0','0.11.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1.1','L')]).
% 1.74/2.12 cnf('0.277.1.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(inverse(X1),X2)) = multiply(X1,inverse(greatest_lower_bound(identity,multiply(X2,X1)))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.277.0.0']),
% 1.74/2.12 [weight('<125,140,11,[1,0,0,4]>')]).
% 1.74/2.12 cnf('0.277.2.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(greatest_lower_bound(identity,multiply(X2,X1)))) = inverse(greatest_lower_bound(inverse(X1),X2)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.277.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_265]).
% 1.74/2.12 cnf('0.279.0.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(inverse(multiply(X1,X2)),inverse(X1))) = multiply(multiply(X1,X2),inverse(greatest_lower_bound(identity,X2))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.277.2.0','0.22.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1.2','L')]).
% 1.74/2.12 cnf('0.279.0.1',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(inverse(multiply(X1,X2)),inverse(X1))) = multiply(X1,multiply(X2,inverse(greatest_lower_bound(identity,X2)))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.279.0.0','0.6.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.279.0.2',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(inverse(multiply(X1,X2)),inverse(X1))) = multiply(X1,inverse(greatest_lower_bound(identity,inverse(X2)))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.279.0.1','0.143.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.2','L')]).
% 1.74/2.12 cnf('0.279.1.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(inverse(multiply(X1,X2)),inverse(X1))) = multiply(X1,inverse(greatest_lower_bound(identity,inverse(X2)))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.279.0.2']),
% 1.74/2.12 [weight('<127,277,22,[1,0,0,5]>')]).
% 1.74/2.12 cnf('0.279.1.1',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,X2)))) = multiply(X1,inverse(greatest_lower_bound(identity,inverse(X2)))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.279.1.0','0.12.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.279.2.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(greatest_lower_bound(identity,inverse(X2)))) = inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,X2)))) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.279.1.1',theory(equality)]),
% 1.74/2.12 [x,rule_267]).
% 1.74/2.12 cnf('0.280.0.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,inverse(X2))))) = multiply(X1,inverse(greatest_lower_bound(identity,X2))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.279.2.0','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1.2','L')]).
% 1.74/2.12 cnf('0.280.1.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,inverse(X2))))) = multiply(X1,inverse(greatest_lower_bound(identity,X2))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.280.0.0']),
% 1.74/2.12 [weight('<111,279,23,[1,0,0,5]>')]).
% 1.74/2.12 cnf('0.280.2.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(greatest_lower_bound(identity,X2))) = inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,inverse(X2))))) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.280.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_268]).
% 1.74/2.12 cnf('0.353.0.0',plain,
% 1.74/2.12 ( least_upper_bound(identity,least_upper_bound(X1,inverse(greatest_lower_bound(X2,identity)))) = least_upper_bound(X1,inverse(greatest_lower_bound(X2,identity))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.68.2.0','0.178.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.353.1.0',plain,
% 1.74/2.12 ( least_upper_bound(identity,least_upper_bound(X1,inverse(greatest_lower_bound(X2,identity)))) = least_upper_bound(X1,inverse(greatest_lower_bound(X2,identity))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.353.0.0']),
% 1.74/2.12 [weight('<134,178,68,[0,0,0,2]>')]).
% 1.74/2.12 cnf('0.353.2.0',plain,
% 1.74/2.12 ( least_upper_bound(identity,least_upper_bound(X1,inverse(greatest_lower_bound(X2,identity)))) = least_upper_bound(X1,inverse(greatest_lower_bound(X2,identity))) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.353.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_341]).
% 1.74/2.12 cnf('0.443.0.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,identity) = least_upper_bound(greatest_lower_bound(X1,identity),greatest_lower_bound(X1,inverse(least_upper_bound(identity,X2)))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.72.2.0','0.145.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.2','L')]).
% 1.74/2.12 cnf('0.443.1.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,identity) = least_upper_bound(greatest_lower_bound(X1,identity),greatest_lower_bound(X1,inverse(least_upper_bound(identity,X2)))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.443.0.0']),
% 1.74/2.12 [weight('<153,145,72,[0,0,0,6]>')]).
% 1.74/2.12 cnf('0.443.2.0',plain,
% 1.74/2.12 ( least_upper_bound(greatest_lower_bound(X1,identity),greatest_lower_bound(X1,inverse(least_upper_bound(identity,X2)))) = greatest_lower_bound(X1,identity) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.443.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_431]).
% 1.74/2.12 cnf('0.444.0.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,identity) = least_upper_bound(greatest_lower_bound(X1,identity),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.443.2.0','0.241.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.444.1.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,identity) = least_upper_bound(greatest_lower_bound(X1,identity),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.444.0.0']),
% 1.74/2.12 [weight('<129,443,241,[1,0,0,4]>')]).
% 1.74/2.12 cnf('0.444.1.1',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,identity) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),greatest_lower_bound(X1,identity)) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.444.1.0','0.14.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.444.2.0',plain,
% 1.74/2.12 ( least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),greatest_lower_bound(X1,identity)) = greatest_lower_bound(X1,identity) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.444.1.1',theory(equality)]),
% 1.74/2.12 [x,rule_432]).
% 1.74/2.12 cnf('0.445.0.0',plain,
% 1.74/2.12 ( least_upper_bound(identity,inverse(X1)) = least_upper_bound(least_upper_bound(identity,inverse(X1)),inverse(greatest_lower_bound(X1,identity))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.228.2.0','0.444.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1','L')]).
% 1.74/2.12 cnf('0.445.0.1',plain,
% 1.74/2.12 ( least_upper_bound(identity,inverse(X1)) = least_upper_bound(identity,least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,identity)))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.445.0.0','0.15.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.445.0.2',plain,
% 1.74/2.12 ( least_upper_bound(identity,inverse(X1)) = least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,identity))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.445.0.1','0.353.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.445.0.3',plain,
% 1.74/2.12 ( least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(X1,identity)) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.445.0.2','0.233.2.0',theory(equality)]),
% 1.74/2.12 [pos('R','L')]).
% 1.74/2.12 cnf('0.445.1.0',plain,
% 1.74/2.12 ( least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(X1,identity)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.445.0.3']),
% 1.74/2.12 [weight('<44,444,228,[0,0,0,3]>')]).
% 1.74/2.12 cnf('0.445.2.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(X1,identity)) = least_upper_bound(identity,inverse(X1)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.445.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_433]).
% 1.74/2.12 cnf('0.446.0.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,identity) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.23.2.0','0.445.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.446.1.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,identity) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.446.0.0']),
% 1.74/2.12 [weight('<35,445,23,[0,0,0,1]>')]).
% 1.74/2.12 cnf('0.446.2.0',plain,
% 1.74/2.12 ( greatest_lower_bound(X1,identity) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.446.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_434]).
% 1.74/2.12 cnf('0.447.0.0',plain,
% 1.74/2.12 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,X1) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.446.2.0','0.12.2.0',theory(equality)]),
% 1.74/2.12 [pos('L','L')]).
% 1.74/2.12 cnf('0.447.1.0',plain,
% 1.74/2.12 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,X1) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.447.0.0']),
% 1.74/2.12 [weight('<35,446,12,[1,0,0,0]>')]).
% 1.74/2.12 cnf('0.447.2.0',plain,
% 1.74/2.12 ( greatest_lower_bound(identity,X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.447.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_435]).
% 1.74/2.12 cnf('0.965.0.0',plain,
% 1.74/2.12 ( multiply(X1,inverse(greatest_lower_bound(identity,X2))) = inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,inverse(X2))))) ),
% 1.74/2.12 inference(interreduction_right,[status(thm)],['0.280.2.0'])).
% 1.74/2.12 cnf('0.965.0.1',plain,
% 1.74/2.12 ( multiply(X1,inverse(inverse(least_upper_bound(identity,inverse(X2))))) = inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,inverse(X2))))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.965.0.0','0.447.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2.1','L')]).
% 1.74/2.12 cnf('0.965.0.2',plain,
% 1.74/2.12 ( multiply(X1,least_upper_bound(identity,inverse(X2))) = inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,inverse(X2))))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.965.0.1','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.965.0.3',plain,
% 1.74/2.12 ( least_upper_bound(multiply(X1,identity),multiply(X1,inverse(X2))) = inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,inverse(X2))))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.965.0.2','0.8.2.0',theory(equality)]),
% 1.74/2.12 [pos('L','L')]).
% 1.74/2.12 cnf('0.965.0.4',plain,
% 1.74/2.12 ( least_upper_bound(X1,multiply(X1,inverse(X2))) = inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,inverse(X2))))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.965.0.3','0.28.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.965.1.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,multiply(X1,inverse(X2))) = inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,inverse(X2))))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.965.0.4']),
% 1.74/2.12 [weight('<159,280,447,[0,0,0,0]>')]).
% 1.74/2.12 cnf('0.965.2.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(inverse(X1),inverse(multiply(X1,inverse(X2))))) = least_upper_bound(X1,multiply(X1,inverse(X2))) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.965.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_953]).
% 1.74/2.12 cnf('0.966.0.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,multiply(X1,inverse(multiply(X2,X1)))) = inverse(greatest_lower_bound(inverse(X1),inverse(inverse(X2)))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.965.2.0','0.45.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1.2.1','L')]).
% 1.74/2.12 cnf('0.966.0.1',plain,
% 1.74/2.12 ( least_upper_bound(X1,inverse(X2)) = inverse(greatest_lower_bound(inverse(X1),inverse(inverse(X2)))) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.966.0.0','0.45.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.2','L')]).
% 1.74/2.12 cnf('0.966.0.2',plain,
% 1.74/2.12 ( least_upper_bound(X1,inverse(X2)) = inverse(greatest_lower_bound(inverse(X1),X2)) ),
% 1.74/2.12 inference(reduction,[status(thm)],['0.966.0.1','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.1.2','L')]).
% 1.74/2.12 cnf('0.966.1.0',plain,
% 1.74/2.12 ( least_upper_bound(X1,inverse(X2)) = inverse(greatest_lower_bound(inverse(X1),X2)) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.966.0.2']),
% 1.74/2.12 [weight('<59,965,45,[1,0,0,5]>')]).
% 1.74/2.12 cnf('0.966.2.0',plain,
% 1.74/2.12 ( inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(X1,inverse(X2)) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.966.1.0',theory(equality)]),
% 1.74/2.12 [x,rule_954]).
% 1.74/2.12 cnf('0.967.0.0',plain,
% 1.74/2.12 ( greatest_lower_bound(inverse(X1),X2) = inverse(least_upper_bound(X1,inverse(X2))) ),
% 1.74/2.12 inference(cp,[status(thm)],['0.23.2.0','0.966.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1','L')]).
% 1.74/2.12 cnf('0.967.1.0',plain,
% 1.74/2.12 ( greatest_lower_bound(inverse(X1),X2) = inverse(least_upper_bound(X1,inverse(X2))) ),
% 1.74/2.12 inference(weigh,[status(thm)],['0.967.0.0']),
% 1.74/2.12 [weight('<49,966,23,[0,0,0,1]>')]).
% 1.74/2.12 cnf('0.967.2.0',plain,
% 1.74/2.12 ( greatest_lower_bound(inverse(X1),X2) = inverse(least_upper_bound(X1,inverse(X2))) ),
% 1.74/2.12 inference(orient,[status(thm)],['0.967.1.0',theory(equality)]),
% 1.74/2.12 [u,rule_955]).
% 1.74/2.12 cnf('1.0.0.0',conjecture,
% 1.74/2.12 ( greatest_lower_bound(inverse(a),inverse(b)) = inverse(least_upper_bound(a,b)) ),
% 1.74/2.12 file('/tmp/WALDMEISTER_26522_n011',conjecture_1)).
% 1.74/2.12 cnf('1.0.0.1',plain,
% 1.74/2.12 ( greatest_lower_bound(inverse(b),inverse(a)) = inverse(least_upper_bound(a,b)) ),
% 1.74/2.12 inference(reduction,[status(thm)],['1.0.0.0','0.12.2.0',theory(equality)]),
% 1.74/2.12 [pos('L','L')]).
% 1.74/2.12 cnf('1.0.0.2',plain,
% 1.74/2.12 ( greatest_lower_bound(inverse(b),inverse(a)) = inverse(least_upper_bound(b,a)) ),
% 1.74/2.12 inference(reduction,[status(thm)],['1.0.0.1','0.14.2.0',theory(equality)]),
% 1.74/2.12 [pos('R.1','L')]).
% 1.74/2.12 cnf('1.0.0.3',plain,
% 1.74/2.12 ( inverse(least_upper_bound(b,inverse(inverse(a)))) = inverse(least_upper_bound(b,a)) ),
% 1.74/2.12 inference(reduction,[status(thm)],['1.0.0.2','0.967.2.0',theory(equality)]),
% 1.74/2.12 [pos('L','L')]).
% 1.74/2.12 cnf('1.0.0.4',plain,
% 1.74/2.12 ( inverse(least_upper_bound(b,a)) = inverse(least_upper_bound(b,a)) ),
% 1.74/2.12 inference(reduction,[status(thm)],['1.0.0.3','0.23.2.0',theory(equality)]),
% 1.74/2.12 [pos('L.1.2','L')]).
% 1.74/2.12 cnf('1.0.0.5',plain,
% 1.74/2.12 ( $true ),
% 1.74/2.12 inference(trivial,[status(thm)],['1.0.0.4',theory(equality)]),
% 1.74/2.12 [conjecture_1]).
% 1.74/2.12
% 1.74/2.12 Proved Goals:
% 1.74/2.12 No. 1: greatest_lower_bound(inverse(a),inverse(b)) ?= inverse(least_upper_bound(a,b)) joined, current: inverse(least_upper_bound(b,a)) = inverse(least_upper_bound(b,a))
% 1.74/2.12 1 goal was specified, which was proved.
% 1.74/2.12 % SZS output end CNFRefutation
% 1.74/2.12 #END OF PROOF
% 1.74/2.12
% 1.74/2.12 Problem WALDMEISTER_26522_n011
% 1.74/2.12 CPs.gen 233729
% 1.74/2.12 CPs.reexp 0
% 1.74/2.12 Select 15208
% 1.74/2.12 R 955
% 1.74/2.12 E 12
% 1.74/2.12 vsize 6.8M
% 1.74/2.12 rss 4.1M
% 1.74/2.12 process.time 0.574s
% 1.74/2.12 wallclock.time 1.108s
% 1.74/2.12 status S
% 1.74/2.12
% 1.74/2.12
% 1.74/2.12 Waldmeister states: Goal proved.
% 1.74/2.12 % SZS status Unsatisfiable
% 1.74/2.12
% 1.74/2.12 Problem WALDMEISTER_26522_n011
% 1.74/2.12 CPs.gen 110726
% 1.74/2.12 CPs.reexp 0
% 1.74/2.12 Select 7545
% 1.74/2.12 R 627
% 1.74/2.12 E 8
% 1.74/2.12 vsize 6.6M
% 1.74/2.12 rss 4.1M
% 1.74/2.12 process.time 0.535s
% 1.74/2.12 wallclock.time 1.107s
% 1.74/2.12 status S
%------------------------------------------------------------------------------