TSTP Solution File: GRP164-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP164-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n023.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 12:25:00 EDT 2022
% Result : Unsatisfiable 5.12s 5.51s
% Output : CNFRefutation 5.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP164-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.14 % Command : woody %s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 17:12:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.64/1.01 ********************************************************************************
% 0.64/1.01 * W A L D M E I S T E R \| \ / \|/ *
% 0.64/1.01 * |/ | \/ | *
% 0.64/1.01 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.64/1.01 * A. Jaeger and B. Loechner | | *
% 0.64/1.01 * <waldmeister@informatik.uni-kl.de> | *
% 0.64/1.01 ********************************************************************************
% 0.64/1.01
% 0.64/1.01
% 0.64/1.01 Goals:
% 0.64/1.01 ------
% 0.64/1.01
% 0.64/1.01 ( 1) greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) ?=? least_upper_bound(a,greatest_lower_bound(b,c))
% 0.64/1.01
% 0.64/1.01 Detected structure: VerbandsgeordneteGruppe
% 0.64/1.01 ********************************************************************************
% 0.64/1.01 ****************************** COMPLETION - PROOF ******************************
% 0.64/1.01 ********************************************************************************
% 0.64/1.01
% 5.12/5.51 joined goal: 1 greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) ?= least_upper_bound(a,greatest_lower_bound(b,c)) to least_upper_bound(a,greatest_lower_bound(c,b))
% 5.12/5.51 goal joined
% 5.12/5.51 % SZS status Unsatisfiable
% 5.12/5.51 #START OF PROOF
% 5.12/5.51 % SZS output start CNFRefutation
% 5.12/5.51 cnf('0.1.0.0',axiom,
% 5.12/5.51 ( X1 = multiply(identity,X1) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.1.1.0',plain,
% 5.12/5.51 ( X1 = multiply(identity,X1) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1.0.0']),
% 5.12/5.51 [weight('<0,0,0,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.1.2.0',plain,
% 5.12/5.51 ( multiply(identity,X1) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_1]).
% 5.12/5.51 cnf('0.2.0.0',axiom,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,X1) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.2.1.0',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,X1) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.2.0.0']),
% 5.12/5.51 [weight('<1,0,0,[0,0,0,2]>')]).
% 5.12/5.51 cnf('0.2.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,X1) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_2]).
% 5.12/5.51 cnf('0.3.0.0',axiom,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.3.1.0',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.3.0.0']),
% 5.12/5.51 [weight('<2,0,0,[0,0,0,3]>')]).
% 5.12/5.51 cnf('0.3.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_3]).
% 5.12/5.51 cnf('0.4.0.0',axiom,
% 5.12/5.51 ( X1 = least_upper_bound(X1,X1) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.4.1.0',plain,
% 5.12/5.51 ( X1 = least_upper_bound(X1,X1) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.4.0.0']),
% 5.12/5.51 [weight('<3,0,0,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.4.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X1) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_4]).
% 5.12/5.51 cnf('0.5.0.0',axiom,
% 5.12/5.51 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.5.1.0',plain,
% 5.12/5.51 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.5.0.0']),
% 5.12/5.51 [weight('<4,0,0,[0,0,0,5]>')]).
% 5.12/5.51 cnf('0.5.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_5]).
% 5.12/5.51 cnf('0.6.0.0',axiom,
% 5.12/5.51 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.6.1.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.6.0.0']),
% 5.12/5.51 [weight('<5,0,0,[0,0,0,6]>')]).
% 5.12/5.51 cnf('0.6.2.0',plain,
% 5.12/5.51 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_6]).
% 5.12/5.51 cnf('0.7.0.0',axiom,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.7.1.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.7.0.0']),
% 5.12/5.51 [weight('<6,0,0,[0,0,0,7]>')]).
% 5.12/5.51 cnf('0.7.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_7]).
% 5.12/5.51 cnf('0.8.0.0',axiom,
% 5.12/5.51 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.8.1.0',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.8.0.0']),
% 5.12/5.51 [weight('<7,0,0,[0,0,0,8]>')]).
% 5.12/5.51 cnf('0.8.2.0',plain,
% 5.12/5.51 ( least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_8]).
% 5.12/5.51 cnf('0.9.0.0',axiom,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.9.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.9.0.0']),
% 5.12/5.51 [weight('<8,0,0,[0,0,0,9]>')]).
% 5.12/5.51 cnf('0.9.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_9]).
% 5.12/5.51 cnf('0.10.0.0',axiom,
% 5.12/5.51 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.10.1.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.10.0.0']),
% 5.12/5.51 [weight('<9,0,0,[0,0,0,10]>')]).
% 5.12/5.51 cnf('0.10.2.0',plain,
% 5.12/5.51 ( least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_10]).
% 5.12/5.51 cnf('0.11.0.0',axiom,
% 5.12/5.51 ( multiply(inverse(X1),X1) = identity ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.11.1.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),X1) = identity ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.11.0.0']),
% 5.12/5.51 [weight('<10,0,0,[0,0,0,11]>')]).
% 5.12/5.51 cnf('0.11.2.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),X1) = identity ),
% 5.12/5.51 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_11]).
% 5.12/5.51 cnf('0.12.0.0',axiom,
% 5.12/5.51 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.12.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.12.0.0']),
% 5.12/5.51 [weight('<11,0,0,[0,0,0,12]>')]).
% 5.12/5.51 cnf('0.12.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 5.12/5.51 inference(activate,[status(thm)],['0.12.1.0']),
% 5.12/5.51 [equation_1]).
% 5.12/5.51 cnf('0.13.0.0',axiom,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.13.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.13.0.0']),
% 5.12/5.51 [weight('<12,0,0,[0,0,0,13]>')]).
% 5.12/5.51 cnf('0.13.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_12]).
% 5.12/5.51 cnf('0.14.0.0',axiom,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.14.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.14.0.0']),
% 5.12/5.51 [weight('<13,0,0,[0,0,0,14]>')]).
% 5.12/5.51 cnf('0.14.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 5.12/5.51 inference(activate,[status(thm)],['0.14.1.0']),
% 5.12/5.51 [equation_2]).
% 5.12/5.51 cnf('0.15.0.0',axiom,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 5.12/5.51 file('/tmp/WALDMEISTER_28551_n023')).
% 5.12/5.51 cnf('0.15.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.15.0.0']),
% 5.12/5.51 [weight('<14,0,0,[0,0,0,15]>')]).
% 5.12/5.51 cnf('0.15.2.0',plain,
% 5.12/5.51 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_13]).
% 5.12/5.51 cnf('0.16.0.0',plain,
% 5.12/5.51 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.5.2.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.16.1.0',plain,
% 5.12/5.51 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.16.0.0']),
% 5.12/5.51 [weight('<5,12,5,[0,0,0,2]>')]).
% 5.12/5.51 cnf('0.16.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_14]).
% 5.12/5.51 cnf('0.17.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.13.2.0','0.2.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.17.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.17.0.0']),
% 5.12/5.51 [weight('<5,13,2,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.17.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_15]).
% 5.12/5.51 cnf('0.18.0.0',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.3.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.18.1.0',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.18.0.0']),
% 5.12/5.51 [weight('<5,14,3,[0,0,0,2]>')]).
% 5.12/5.51 cnf('0.18.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_16]).
% 5.12/5.51 cnf('0.19.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.15.2.0','0.4.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.19.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.19.0.0']),
% 5.12/5.51 [weight('<5,15,4,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.19.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_17]).
% 5.12/5.51 cnf('0.20.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(least_upper_bound(X1,X2),X1) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.16.2.0','0.3.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.20.0.1',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.20.0.0','0.15.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.20.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.20.0.1']),
% 5.12/5.51 [weight('<5,16,3,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.20.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_18]).
% 5.12/5.51 cnf('0.21.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.17.2.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.21.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.21.0.0']),
% 5.12/5.51 [weight('<5,17,12,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.21.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_19]).
% 5.12/5.51 cnf('0.22.0.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.22.0.1',plain,
% 5.12/5.51 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.22.0.0','0.1.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.22.1.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.22.0.1']),
% 5.12/5.51 [weight('<6,11,6,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.22.2.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_20]).
% 5.12/5.51 cnf('0.23.0.0',plain,
% 5.12/5.51 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.22.2.0','0.22.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.23.1.0',plain,
% 5.12/5.51 ( X1 = inverse(inverse(X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.23.0.0']),
% 5.12/5.51 [weight('<3,22,22,[0,0,0,3]>')]).
% 5.12/5.51 cnf('0.23.2.0',plain,
% 5.12/5.51 ( inverse(inverse(X1)) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_21]).
% 5.12/5.51 cnf('0.25.0.0',plain,
% 5.12/5.51 ( identity = multiply(X1,inverse(X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.11.2.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.25.1.0',plain,
% 5.12/5.51 ( identity = multiply(X1,inverse(X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.25.0.0']),
% 5.12/5.51 [weight('<4,23,11,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.25.2.0',plain,
% 5.12/5.51 ( multiply(X1,inverse(X1)) = identity ),
% 5.12/5.51 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_23]).
% 5.12/5.51 cnf('0.26.0.0',plain,
% 5.12/5.51 ( identity = inverse(identity) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.25.2.0','0.1.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.26.1.0',plain,
% 5.12/5.51 ( identity = inverse(identity) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.26.0.0']),
% 5.12/5.51 [weight('<2,25,1,[1,0,0,0]>')]).
% 5.12/5.51 cnf('0.26.2.0',plain,
% 5.12/5.51 ( inverse(identity) = identity ),
% 5.12/5.51 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_24]).
% 5.12/5.51 cnf('0.27.0.0',plain,
% 5.12/5.51 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.22.2.0','0.25.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.27.1.0',plain,
% 5.12/5.51 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.27.0.0']),
% 5.12/5.51 [weight('<4,25,22,[0,0,0,3]>')]).
% 5.12/5.51 cnf('0.27.2.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_25]).
% 5.12/5.51 cnf('0.28.0.0',plain,
% 5.12/5.51 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.27.2.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.28.0.1',plain,
% 5.12/5.51 ( X1 = multiply(X1,identity) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.28.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.28.1.0',plain,
% 5.12/5.51 ( X1 = multiply(X1,identity) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.28.0.1']),
% 5.12/5.51 [weight('<3,27,23,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.28.2.0',plain,
% 5.12/5.51 ( multiply(X1,identity) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_26]).
% 5.12/5.51 cnf('0.30.0.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(multiply(inverse(X1),X2),identity) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.7.2.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.30.1.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(multiply(inverse(X1),X2),identity) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.30.0.0']),
% 5.12/5.51 [weight('<6,11,7,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.30.1.1',plain,
% 5.12/5.51 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.30.1.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.30.2.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.30.1.1',theory(equality)]),
% 5.12/5.51 [u,rule_28]).
% 5.12/5.51 cnf('0.31.0.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.8.2.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.31.1.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.31.0.0']),
% 5.12/5.51 [weight('<6,11,8,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.31.2.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_29]).
% 5.12/5.51 cnf('0.34.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(multiply(X1,X2),identity) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.9.2.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.34.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(multiply(X1,X2),identity) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.34.0.0']),
% 5.12/5.51 [weight('<6,11,9,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.34.1.1',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X1,X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.34.1.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.34.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X1,X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.34.1.1',theory(equality)]),
% 5.12/5.51 [u,rule_32]).
% 5.12/5.51 cnf('0.37.0.0',plain,
% 5.12/5.51 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.22.2.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.37.1.0',plain,
% 5.12/5.51 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.37.0.0']),
% 5.12/5.51 [weight('<6,23,22,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.37.2.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(inverse(X1),X2)) = X2 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_35]).
% 5.12/5.51 cnf('0.38.0.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(identity,multiply(X1,X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.7.2.0','0.25.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.38.1.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(identity,multiply(X1,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.38.0.0']),
% 5.12/5.51 [weight('<6,25,7,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.38.2.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(identity,multiply(X1,X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_36]).
% 5.12/5.51 cnf('0.40.0.0',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(inverse(X1),X2)) = least_upper_bound(identity,multiply(X1,X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.8.2.0','0.25.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.40.1.0',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(inverse(X1),X2)) = least_upper_bound(identity,multiply(X1,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.40.0.0']),
% 5.12/5.51 [weight('<6,25,8,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.40.2.0',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(inverse(X1),X2)) = least_upper_bound(identity,multiply(X1,X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_38]).
% 5.12/5.51 cnf('0.43.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(multiply(X1,inverse(X2)),identity) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.9.2.0','0.25.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.43.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(multiply(X1,inverse(X2)),identity) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.43.0.0']),
% 5.12/5.51 [weight('<6,25,9,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.43.1.1',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X1,inverse(X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.43.1.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.43.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X1,inverse(X2))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.43.1.1',theory(equality)]),
% 5.12/5.51 [u,rule_41]).
% 5.12/5.51 cnf('0.45.0.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(multiply(X1,inverse(X2)),identity) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.10.2.0','0.25.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.45.1.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(multiply(X1,inverse(X2)),identity) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.45.0.0']),
% 5.12/5.51 [weight('<6,25,10,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.45.1.1',plain,
% 5.12/5.51 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.45.1.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.45.2.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.45.1.1',theory(equality)]),
% 5.12/5.51 [u,rule_43]).
% 5.12/5.51 cnf('0.46.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.13.2.0','0.3.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.46.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.46.0.0']),
% 5.12/5.51 [weight('<7,13,3,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.46.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_44]).
% 5.12/5.51 cnf('0.47.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = least_upper_bound(X1,X3) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.15.2.0','0.5.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.47.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = least_upper_bound(X1,X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.47.0.0']),
% 5.12/5.51 [weight('<7,15,5,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.47.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = least_upper_bound(X1,X3) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_45]).
% 5.12/5.51 cnf('0.48.0.0',plain,
% 5.12/5.51 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.16.2.0','0.13.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.48.1.0',plain,
% 5.12/5.51 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.48.0.0']),
% 5.12/5.51 [weight('<7,16,13,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.48.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_46]).
% 5.12/5.51 cnf('0.50.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),X3)) = greatest_lower_bound(X1,X3) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.13.2.0','0.18.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.50.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),X3)) = greatest_lower_bound(X1,X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.50.0.0']),
% 5.12/5.51 [weight('<7,18,13,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.50.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),X3)) = greatest_lower_bound(X1,X3) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_48]).
% 5.12/5.51 cnf('0.51.0.0',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.18.2.0','0.15.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.51.1.0',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.51.0.0']),
% 5.12/5.51 [weight('<7,18,15,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.51.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.51.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_49]).
% 5.12/5.51 cnf('0.52.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(least_upper_bound(X2,X1),X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.15.2.0','0.20.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.52.0.1',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.52.0.0','0.15.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.52.0.2',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.52.0.1','0.15.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.52.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.52.0.2']),
% 5.12/5.51 [weight('<7,20,15,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.52.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.52.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_50]).
% 5.12/5.51 cnf('0.55.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(greatest_lower_bound(X2,X1),X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.13.2.0','0.21.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.55.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.55.0.0','0.13.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.55.0.2',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.55.0.1','0.13.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.55.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.55.0.2']),
% 5.12/5.51 [weight('<7,21,13,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.55.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_53]).
% 5.12/5.51 cnf('0.60.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,X3))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.47.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.60.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,X3))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.60.0.0']),
% 5.12/5.51 [weight('<7,47,14,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.60.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,X3))) = least_upper_bound(X1,X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.60.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_58]).
% 5.12/5.51 cnf('0.62.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(least_upper_bound(X1,X2),greatest_lower_bound(X3,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.48.2.0','0.3.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.2','L')]).
% 5.12/5.51 cnf('0.62.0.1',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.62.0.0','0.15.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.62.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.62.0.1']),
% 5.12/5.51 [weight('<7,48,3,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.62.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) = least_upper_bound(X1,X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.62.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_60]).
% 5.12/5.51 cnf('0.64.0.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),greatest_lower_bound(multiply(X1,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X1),X3)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.7.2.0','0.22.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.64.1.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),greatest_lower_bound(multiply(X1,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X1),X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.64.0.0']),
% 5.12/5.51 [weight('<8,22,7,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.64.2.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),greatest_lower_bound(multiply(X1,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X1),X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_62]).
% 5.12/5.51 cnf('0.65.0.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.7.2.0','0.22.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.65.1.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.65.0.0']),
% 5.12/5.51 [weight('<8,22,7,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.65.2.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.65.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_63]).
% 5.12/5.51 cnf('0.66.0.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.8.2.0','0.22.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.66.1.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.66.0.0']),
% 5.12/5.51 [weight('<8,22,8,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.66.2.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.66.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_64]).
% 5.12/5.51 cnf('0.67.0.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.8.2.0','0.22.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.67.1.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.67.0.0']),
% 5.12/5.51 [weight('<8,22,8,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.67.2.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.67.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_65]).
% 5.12/5.51 cnf('0.68.0.0',plain,
% 5.12/5.51 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.25.2.0','0.6.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.68.1.0',plain,
% 5.12/5.51 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.68.0.0']),
% 5.12/5.51 [weight('<8,25,6,[1,0,0,0]>')]).
% 5.12/5.51 cnf('0.68.2.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity ),
% 5.12/5.51 inference(orient,[status(thm)],['0.68.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_66]).
% 5.12/5.51 cnf('0.69.0.0',plain,
% 5.12/5.51 ( multiply(X1,inverse(multiply(X2,X1))) = multiply(inverse(X2),identity) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.22.2.0','0.68.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.69.0.1',plain,
% 5.12/5.51 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.69.0.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.69.1.0',plain,
% 5.12/5.51 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.69.0.1']),
% 5.12/5.51 [weight('<6,68,22,[0,0,0,3]>')]).
% 5.12/5.51 cnf('0.69.2.0',plain,
% 5.12/5.51 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_67]).
% 5.12/5.51 cnf('0.70.0.0',plain,
% 5.12/5.51 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.22.2.0','0.69.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.70.1.0',plain,
% 5.12/5.51 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.70.0.0']),
% 5.12/5.51 [weight('<4,69,22,[0,0,0,3]>')]).
% 5.12/5.51 cnf('0.70.2.0',plain,
% 5.12/5.51 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.70.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_68]).
% 5.12/5.51 cnf('0.72.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),X1) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.30.2.0','0.3.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.72.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),X1) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.72.0.0']),
% 5.12/5.51 [weight('<8,30,3,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.72.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),X1) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.72.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_70]).
% 5.12/5.51 cnf('0.73.0.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X1)),identity) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.72.2.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.73.0.1',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.73.0.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.73.1.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.73.0.1']),
% 5.12/5.51 [weight('<6,72,28,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.73.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.73.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_71]).
% 5.12/5.51 cnf('0.75.0.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.73.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.75.1.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.75.0.0']),
% 5.12/5.51 [weight('<6,73,14,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.75.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) = inverse(least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.75.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_73]).
% 5.12/5.51 cnf('0.79.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X1)) = multiply(inverse(greatest_lower_bound(X1,X2)),greatest_lower_bound(X1,X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.30.2.0','0.17.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.79.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X1)) = identity ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.79.0.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.79.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X1)) = identity ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.79.0.1']),
% 5.12/5.51 [weight('<8,30,17,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.79.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X1)) = identity ),
% 5.12/5.51 inference(orient,[status(thm)],['0.79.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_77]).
% 5.12/5.51 cnf('0.80.0.0',plain,
% 5.12/5.51 ( identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.79.2.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.80.1.0',plain,
% 5.12/5.51 ( identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.80.0.0']),
% 5.12/5.51 [weight('<6,79,28,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.80.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) = identity ),
% 5.12/5.51 inference(orient,[status(thm)],['0.80.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_78]).
% 5.12/5.51 cnf('0.82.0.0',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(inverse(greatest_lower_bound(identity,X1)),identity) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.16.2.0','0.80.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.82.1.0',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(inverse(greatest_lower_bound(identity,X1)),identity) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.82.0.0']),
% 5.12/5.51 [weight('<6,80,16,[0,0,0,2]>')]).
% 5.12/5.51 cnf('0.82.1.1',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.82.1.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.82.2.0',plain,
% 5.12/5.51 ( least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.82.1.1',theory(equality)]),
% 5.12/5.51 [x,rule_80]).
% 5.12/5.51 cnf('0.84.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X2)) = multiply(inverse(least_upper_bound(X1,X2)),X2) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.30.2.0','0.18.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.84.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X2)) = multiply(inverse(least_upper_bound(X1,X2)),X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.84.0.0']),
% 5.12/5.51 [weight('<8,30,18,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.84.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X2)) = multiply(inverse(least_upper_bound(X1,X2)),X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.84.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_82]).
% 5.12/5.51 cnf('0.98.0.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.7.2.0','0.37.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.98.1.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.98.0.0']),
% 5.12/5.51 [weight('<8,37,7,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.98.2.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.98.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_96]).
% 5.12/5.51 cnf('0.105.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = multiply(X1,inverse(least_upper_bound(X1,X2))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.43.2.0','0.3.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.105.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = multiply(X1,inverse(least_upper_bound(X1,X2))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.105.0.0']),
% 5.12/5.51 [weight('<8,43,3,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.105.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = multiply(X1,inverse(least_upper_bound(X1,X2))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.105.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_103]).
% 5.12/5.51 cnf('0.106.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(multiply(inverse(X1),identity),inverse(least_upper_bound(X1,X2))) = multiply(inverse(X1),multiply(X1,inverse(least_upper_bound(X1,X2)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.65.2.0','0.105.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.106.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = multiply(inverse(X1),multiply(X1,inverse(least_upper_bound(X1,X2)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.106.0.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.106.0.2',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(least_upper_bound(X1,X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.106.0.1','0.22.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.106.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(least_upper_bound(X1,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.106.0.2']),
% 5.12/5.51 [weight('<7,105,65,[0,0,0,3]>')]).
% 5.12/5.51 cnf('0.106.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(least_upper_bound(X1,X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.106.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_104]).
% 5.12/5.51 cnf('0.107.0.0',plain,
% 5.12/5.51 ( 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)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.98.2.0','0.105.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.107.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = multiply(X1,multiply(inverse(X1),inverse(least_upper_bound(inverse(X1),X2)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.107.0.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.107.0.2',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.107.0.1','0.37.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.107.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.107.0.2']),
% 5.12/5.51 [weight('<7,105,98,[0,0,0,2]>')]).
% 5.12/5.51 cnf('0.107.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.107.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_105]).
% 5.12/5.51 cnf('0.109.0.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.106.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.109.1.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.109.0.0']),
% 5.12/5.51 [weight('<7,106,14,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.109.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(least_upper_bound(X1,X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.109.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_107]).
% 5.12/5.51 cnf('0.110.0.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(greatest_lower_bound(X1,X2),X1)) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.109.2.0','0.5.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.110.1.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(greatest_lower_bound(X1,X2),X1)) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.110.0.0']),
% 5.12/5.51 [weight('<6,109,5,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.110.1.1',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,greatest_lower_bound(X1,X2))) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.110.1.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.110.1.2',plain,
% 5.12/5.51 ( inverse(X1) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.110.1.1','0.5.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.110.1.3',plain,
% 5.12/5.51 ( inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.110.1.2','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.110.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(X1) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.110.1.3',theory(equality)]),
% 5.12/5.51 [x,rule_108]).
% 5.12/5.51 cnf('0.111.0.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(greatest_lower_bound(X1,X2),X2)) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.109.2.0','0.16.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.111.1.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(greatest_lower_bound(X1,X2),X2)) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.111.0.0']),
% 5.12/5.51 [weight('<6,109,16,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.111.1.1',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X2,greatest_lower_bound(X1,X2))) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.111.1.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.111.1.2',plain,
% 5.12/5.51 ( inverse(X2) = greatest_lower_bound(inverse(greatest_lower_bound(X1,X2)),inverse(X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.111.1.1','0.16.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.111.1.3',plain,
% 5.12/5.51 ( inverse(X2) = greatest_lower_bound(inverse(X2),inverse(greatest_lower_bound(X1,X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.111.1.2','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.111.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) = inverse(X1) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.111.1.3',theory(equality)]),
% 5.12/5.51 [x,rule_109]).
% 5.12/5.51 cnf('0.116.0.0',plain,
% 5.12/5.51 ( inverse(inverse(X1)) = greatest_lower_bound(X1,inverse(greatest_lower_bound(inverse(X1),X2))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.110.2.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.116.0.1',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,inverse(greatest_lower_bound(inverse(X1),X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.116.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.116.1.0',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,inverse(greatest_lower_bound(inverse(X1),X2))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.116.0.1']),
% 5.12/5.51 [weight('<7,110,23,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.116.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,inverse(greatest_lower_bound(inverse(X1),X2))) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.116.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_114]).
% 5.12/5.51 cnf('0.125.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(X1,inverse(least_upper_bound(X2,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.43.2.0','0.18.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.125.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(X1,inverse(least_upper_bound(X2,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.125.0.0']),
% 5.12/5.51 [weight('<8,43,18,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.125.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(X1,inverse(least_upper_bound(X2,X1))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.125.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_123]).
% 5.12/5.51 cnf('0.132.0.0',plain,
% 5.12/5.51 ( least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(least_upper_bound(X1,X2),inverse(least_upper_bound(X2,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.45.2.0','0.20.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.132.1.0',plain,
% 5.12/5.51 ( least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = multiply(least_upper_bound(X1,X2),inverse(least_upper_bound(X2,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.132.0.0']),
% 5.12/5.51 [weight('<8,45,20,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.132.2.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(X1,X2),inverse(least_upper_bound(X2,X1))) = least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.132.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_130]).
% 5.12/5.51 cnf('0.133.0.0',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),inverse(inverse(X1))) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.70.2.0','0.64.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.133.0.1',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),X1) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.133.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.133.1.0',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),X1) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.133.0.1']),
% 5.12/5.51 [weight('<8,70,64,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.133.2.0',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),X1) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.133.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_131]).
% 5.12/5.51 cnf('0.134.0.0',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(X1,multiply(inverse(inverse(X1)),X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.133.2.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.1.1','L')]).
% 5.12/5.51 cnf('0.134.0.1',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(X1,multiply(X1,X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.134.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2.1','L')]).
% 5.12/5.51 cnf('0.134.1.0',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(X1,multiply(X1,X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.134.0.1']),
% 5.12/5.51 [weight('<6,133,11,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.134.2.0',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(X1,multiply(X1,X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.134.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_132]).
% 5.12/5.51 cnf('0.135.0.0',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(identity,X1)),inverse(inverse(X1))) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.134.2.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2','L')]).
% 5.12/5.51 cnf('0.135.0.1',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.135.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.135.1.0',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.135.0.1']),
% 5.12/5.51 [weight('<6,134,11,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.135.1.1',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.135.1.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.135.2.0',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.135.1.1',theory(equality)]),
% 5.12/5.51 [u,rule_133]).
% 5.12/5.51 cnf('0.137.0.0',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(X1,multiply(X2,X3))),inverse(inverse(X2))) = inverse(greatest_lower_bound(multiply(inverse(X2),X1),X3)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.70.2.0','0.65.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.137.0.1',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(X1,multiply(X2,X3))),X2) = inverse(greatest_lower_bound(multiply(inverse(X2),X1),X3)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.137.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.137.1.0',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(X1,multiply(X2,X3))),X2) = inverse(greatest_lower_bound(multiply(inverse(X2),X1),X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.137.0.1']),
% 5.12/5.51 [weight('<8,70,65,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.137.2.0',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(X1,multiply(X2,X3))),X2) = inverse(greatest_lower_bound(multiply(inverse(X2),X1),X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.137.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_135]).
% 5.12/5.51 cnf('0.138.0.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),inverse(inverse(X1))) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.70.2.0','0.66.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.138.0.1',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.138.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.138.1.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.138.0.1']),
% 5.12/5.51 [weight('<8,70,66,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.138.2.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.138.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_136]).
% 5.12/5.51 cnf('0.139.0.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,multiply(inverse(inverse(X1)),X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.138.2.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.1.1','L')]).
% 5.12/5.51 cnf('0.139.0.1',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.139.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2.1','L')]).
% 5.12/5.51 cnf('0.139.1.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.139.0.1']),
% 5.12/5.51 [weight('<6,138,11,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.139.2.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.139.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_137]).
% 5.12/5.51 cnf('0.140.0.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X1)),inverse(inverse(X1))) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.139.2.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2','L')]).
% 5.12/5.51 cnf('0.140.0.1',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.140.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.140.1.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.140.0.1']),
% 5.12/5.51 [weight('<6,139,11,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.140.1.1',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.140.1.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.140.2.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.140.1.1',theory(equality)]),
% 5.12/5.51 [u,rule_138]).
% 5.12/5.51 cnf('0.142.0.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(X1,multiply(X2,X3))),inverse(inverse(X2))) = inverse(least_upper_bound(multiply(inverse(X2),X1),X3)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.70.2.0','0.67.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.142.0.1',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(X1,multiply(X2,X3))),X2) = inverse(least_upper_bound(multiply(inverse(X2),X1),X3)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.142.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.142.1.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(X1,multiply(X2,X3))),X2) = inverse(least_upper_bound(multiply(inverse(X2),X1),X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.142.0.1']),
% 5.12/5.51 [weight('<8,70,67,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.142.2.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(X1,multiply(X2,X3))),X2) = inverse(least_upper_bound(multiply(inverse(X2),X1),X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.142.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_140]).
% 5.12/5.51 cnf('0.152.0.0',plain,
% 5.12/5.51 ( 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))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.30.2.0','0.75.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.152.0.1',plain,
% 5.12/5.51 ( 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))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.152.0.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.152.0.2',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,least_upper_bound(X1,identity)) = multiply(inverse(inverse(least_upper_bound(X1,identity))),inverse(least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.152.0.1','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.152.0.3',plain,
% 5.12/5.51 ( identity = multiply(inverse(inverse(least_upper_bound(X1,identity))),inverse(least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.152.0.2','0.18.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.152.0.4',plain,
% 5.12/5.51 ( identity = multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.152.0.3','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.152.1.0',plain,
% 5.12/5.51 ( identity = multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.152.0.4']),
% 5.12/5.51 [weight('<8,75,30,[0,0,0,3]>')]).
% 5.12/5.51 cnf('0.152.1.1',plain,
% 5.12/5.51 ( identity = least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(identity,X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.152.1.0','0.132.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.152.2.0',plain,
% 5.12/5.51 ( least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(identity,X1)))) = identity ),
% 5.12/5.51 inference(orient,[status(thm)],['0.152.1.1',theory(equality)]),
% 5.12/5.51 [x,rule_150]).
% 5.12/5.51 cnf('0.153.0.0',plain,
% 5.12/5.51 ( 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))))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.84.2.0','0.152.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1.1','L')]).
% 5.12/5.51 cnf('0.153.0.1',plain,
% 5.12/5.51 ( 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))))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.153.0.0','0.140.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.153.0.2',plain,
% 5.12/5.51 ( 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))))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.153.0.1','0.70.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2','L')]).
% 5.12/5.51 cnf('0.153.0.3',plain,
% 5.12/5.51 ( 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))))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.153.0.2','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2.1','L')]).
% 5.12/5.51 cnf('0.153.0.4',plain,
% 5.12/5.51 ( 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))))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.153.0.3','0.45.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2','L')]).
% 5.12/5.51 cnf('0.153.0.5',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,multiply(identity,inverse(X1)))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.153.0.4','0.19.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.153.0.6',plain,
% 5.12/5.51 ( 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))))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.153.0.5','0.139.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.153.0.7',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,inverse(X1))),identity) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.153.0.6','0.26.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.153.0.8',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,multiply(inverse(identity),multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.153.0.7','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.153.0.9',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,multiply(identity,multiply(X1,inverse(least_upper_bound(identity,X1))))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.153.0.8','0.26.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2.1','L')]).
% 5.12/5.51 cnf('0.153.0.10',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,multiply(X1,inverse(least_upper_bound(identity,X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.153.0.9','0.1.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2','L')]).
% 5.12/5.51 cnf('0.153.0.11',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.153.0.10','0.125.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.153.1.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.153.0.11']),
% 5.12/5.51 [weight('<6,152,84,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.153.2.0',plain,
% 5.12/5.51 ( multiply(X1,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.153.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_151]).
% 5.12/5.51 cnf('0.193.0.0',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),inverse(inverse(X1)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.116.2.0','0.134.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.193.0.1',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.193.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2.2','L')]).
% 5.12/5.51 cnf('0.193.1.0',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.193.0.1']),
% 5.12/5.51 [weight('<8,134,116,[0,0,0,2]>')]).
% 5.12/5.51 cnf('0.193.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),X1)) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.193.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_191]).
% 5.12/5.51 cnf('0.194.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(multiply(greatest_lower_bound(identity,X1),X2),X2) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.193.2.0','0.22.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.194.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(multiply(greatest_lower_bound(identity,X1),X2),X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.194.0.0']),
% 5.12/5.51 [weight('<7,193,22,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.194.1.1',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.194.1.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.194.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X2),X1)) = multiply(greatest_lower_bound(identity,X2),X1) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.194.1.1',theory(equality)]),
% 5.12/5.51 [x,rule_192]).
% 5.12/5.51 cnf('0.208.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,X1)),X2),X1) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X1))),multiply(X2,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.9.2.0','0.135.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.208.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,X1)),X2),X1) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X1))),multiply(X2,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.208.0.0']),
% 5.12/5.51 [weight('<8,135,9,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.208.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(inverse(greatest_lower_bound(identity,X1)),X2),X1) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X1))),multiply(X2,X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.208.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_206]).
% 5.12/5.51 cnf('0.210.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.9.2.0','0.1.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.210.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.210.0.0']),
% 5.12/5.51 [weight('<?,9,1,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.210.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)) ),
% 5.12/5.51 inference(activate,[status(thm)],['0.210.1.0']),
% 5.12/5.51 [equation_3]).
% 5.12/5.51 cnf('0.211.0.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,X2))) = inverse(greatest_lower_bound(X1,multiply(X2,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.70.2.0','0.210.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.211.1.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,X2))) = inverse(greatest_lower_bound(X1,multiply(X2,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.211.0.0']),
% 5.12/5.51 [weight('<6,210,70,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.211.2.0',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(X1,multiply(X2,X1))) = multiply(inverse(X1),inverse(greatest_lower_bound(identity,X2))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.211.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_208]).
% 5.12/5.51 cnf('0.212.0.0',plain,
% 5.12/5.51 ( multiply(inverse(inverse(X1)),inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.211.2.0','0.25.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2','L')]).
% 5.12/5.51 cnf('0.212.0.1',plain,
% 5.12/5.51 ( multiply(X1,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.212.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.212.1.0',plain,
% 5.12/5.51 ( multiply(X1,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.212.0.1']),
% 5.12/5.51 [weight('<6,211,25,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.212.1.1',plain,
% 5.12/5.51 ( multiply(X1,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.212.1.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.212.2.0',plain,
% 5.12/5.51 ( multiply(X1,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.212.1.1',theory(equality)]),
% 5.12/5.51 [u,rule_209]).
% 5.12/5.51 cnf('0.214.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,multiply(X1,X2)),X3) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.6.2.0','0.210.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.214.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,multiply(X1,X2)),X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.214.0.0']),
% 5.12/5.51 [weight('<7,210,6,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.214.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,multiply(X2,X1)),X3) = multiply(greatest_lower_bound(identity,X2),multiply(X1,X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.214.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_211]).
% 5.12/5.51 cnf('0.231.0.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(inverse(X1),multiply(inverse(X1),X2))) = greatest_lower_bound(X1,multiply(inverse(least_upper_bound(identity,X2)),inverse(inverse(X1)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.107.2.0','0.139.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.231.0.1',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X2)),inverse(inverse(X1))) = greatest_lower_bound(X1,multiply(inverse(least_upper_bound(identity,X2)),inverse(inverse(X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.231.0.0','0.139.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.231.0.2',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X2)),X1) = greatest_lower_bound(X1,multiply(inverse(least_upper_bound(identity,X2)),inverse(inverse(X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.231.0.1','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.231.0.3',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X2)),X1) = greatest_lower_bound(X1,multiply(inverse(least_upper_bound(identity,X2)),X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.231.0.2','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2.2','L')]).
% 5.12/5.51 cnf('0.231.1.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X2)),X1) = greatest_lower_bound(X1,multiply(inverse(least_upper_bound(identity,X2)),X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.231.0.3']),
% 5.12/5.51 [weight('<8,139,107,[0,0,0,2]>')]).
% 5.12/5.51 cnf('0.231.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(inverse(least_upper_bound(identity,X2)),X1)) = multiply(inverse(least_upper_bound(identity,X2)),X1) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.231.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_228]).
% 5.12/5.51 cnf('0.232.0.0',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,inverse(multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.116.2.0','0.231.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.232.0.1',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,multiply(inverse(inverse(X1)),inverse(inverse(least_upper_bound(identity,X2))))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.232.0.0','0.70.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2','L')]).
% 5.12/5.51 cnf('0.232.0.2',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,multiply(X1,inverse(inverse(least_upper_bound(identity,X2))))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.232.0.1','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2.1','L')]).
% 5.12/5.51 cnf('0.232.0.3',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,multiply(X1,least_upper_bound(identity,X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.232.0.2','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2.2','L')]).
% 5.12/5.51 cnf('0.232.1.0',plain,
% 5.12/5.51 ( X1 = greatest_lower_bound(X1,multiply(X1,least_upper_bound(identity,X2))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.232.0.3']),
% 5.12/5.51 [weight('<7,231,116,[0,0,0,3]>')]).
% 5.12/5.51 cnf('0.232.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(X1,least_upper_bound(identity,X2))) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.232.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_229]).
% 5.12/5.51 cnf('0.237.0.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X1)),multiply(X1,X2)) = multiply(inverse(least_upper_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.6.2.0','0.140.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.237.1.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X1)),multiply(X1,X2)) = multiply(inverse(least_upper_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.237.0.0']),
% 5.12/5.51 [weight('<8,140,6,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.237.2.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X1)),multiply(X1,X2)) = multiply(inverse(least_upper_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.237.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_234]).
% 5.12/5.51 cnf('0.259.0.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(inverse(least_upper_bound(identity,X1)),X2)) = multiply(inverse(least_upper_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.6.2.0','0.153.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.259.1.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(inverse(least_upper_bound(identity,X1)),X2)) = multiply(inverse(least_upper_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.259.0.0']),
% 5.12/5.51 [weight('<8,153,6,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.259.2.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(inverse(least_upper_bound(identity,X1)),X2)) = multiply(inverse(least_upper_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.259.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_256]).
% 5.12/5.51 cnf('0.260.0.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,inverse(X1))),X1) = multiply(X1,inverse(least_upper_bound(identity,inverse(X1)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.259.2.0','0.140.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.260.1.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,inverse(X1))),X1) = multiply(X1,inverse(least_upper_bound(identity,inverse(X1)))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.260.0.0']),
% 5.12/5.51 [weight('<7,259,140,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.260.2.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,inverse(X1))),X1) = multiply(X1,inverse(least_upper_bound(identity,inverse(X1)))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.260.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_257]).
% 5.12/5.51 cnf('0.261.0.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),inverse(least_upper_bound(identity,inverse(inverse(X1))))) = multiply(inverse(least_upper_bound(identity,X1)),inverse(X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.260.2.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.1.2','L')]).
% 5.12/5.51 cnf('0.261.0.1',plain,
% 5.12/5.51 ( multiply(inverse(X1),inverse(least_upper_bound(identity,X1))) = multiply(inverse(least_upper_bound(identity,X1)),inverse(X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.261.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1.2','L')]).
% 5.12/5.51 cnf('0.261.1.0',plain,
% 5.12/5.51 ( multiply(inverse(X1),inverse(least_upper_bound(identity,X1))) = multiply(inverse(least_upper_bound(identity,X1)),inverse(X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.261.0.1']),
% 5.12/5.51 [weight('<7,260,23,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.261.2.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X1)),inverse(X1)) = multiply(inverse(X1),inverse(least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.261.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_258]).
% 5.12/5.51 cnf('0.262.0.0',plain,
% 5.12/5.51 ( multiply(inverse(inverse(X1)),inverse(inverse(least_upper_bound(identity,X1)))) = inverse(multiply(inverse(X1),inverse(least_upper_bound(identity,X1)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.70.2.0','0.261.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.262.0.1',plain,
% 5.12/5.51 ( multiply(X1,inverse(inverse(least_upper_bound(identity,X1)))) = inverse(multiply(inverse(X1),inverse(least_upper_bound(identity,X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.262.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.262.0.2',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(identity,X1)) = inverse(multiply(inverse(X1),inverse(least_upper_bound(identity,X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.262.0.1','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.262.0.3',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(identity,X1)) = multiply(inverse(inverse(least_upper_bound(identity,X1))),inverse(inverse(X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.262.0.2','0.70.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.262.0.4',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),inverse(inverse(X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.262.0.3','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.262.0.5',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),X1) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.262.0.4','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2','L')]).
% 5.12/5.51 cnf('0.262.1.0',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),X1) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.262.0.5']),
% 5.12/5.51 [weight('<5,261,70,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.262.2.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.262.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_259]).
% 5.12/5.51 cnf('0.269.0.0',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(inverse(least_upper_bound(identity,X1)),X2)) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),multiply(X1,X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.8.2.0','0.153.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.269.1.0',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(inverse(least_upper_bound(identity,X1)),X2)) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),multiply(X1,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.269.0.0']),
% 5.12/5.51 [weight('<8,153,8,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.269.2.0',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(inverse(least_upper_bound(identity,X1)),X2)) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),multiply(X1,X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.269.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_266]).
% 5.12/5.51 cnf('0.317.0.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(inverse(greatest_lower_bound(identity,X1)),X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.6.2.0','0.212.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.317.1.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(inverse(greatest_lower_bound(identity,X1)),X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.317.0.0']),
% 5.12/5.51 [weight('<8,212,6,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.317.2.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(inverse(greatest_lower_bound(identity,X1)),X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.317.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_314]).
% 5.12/5.51 cnf('0.327.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,inverse(X1)),multiply(X1,X2)) = multiply(greatest_lower_bound(X1,identity),X2) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.214.2.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2','L')]).
% 5.12/5.51 cnf('0.327.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,inverse(X1)),multiply(X1,X2)) = multiply(greatest_lower_bound(X1,identity),X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.327.0.0']),
% 5.12/5.51 [weight('<8,214,11,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.327.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,inverse(X1)),multiply(X1,X2)) = multiply(greatest_lower_bound(X1,identity),X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.327.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_324]).
% 5.12/5.51 cnf('0.328.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(least_upper_bound(identity,X1),identity),X1) = multiply(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))),multiply(X1,least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.327.2.0','0.262.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.328.0.1',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(least_upper_bound(identity,X1),identity),X1) = multiply(inverse(least_upper_bound(identity,X1)),multiply(X1,least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.328.0.0','0.73.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.328.0.2',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(least_upper_bound(identity,X1),identity),X1) = multiply(inverse(least_upper_bound(identity,inverse(X1))),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.328.0.1','0.237.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.328.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(least_upper_bound(identity,X1),identity),X1) = multiply(inverse(least_upper_bound(identity,inverse(X1))),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.328.0.2']),
% 5.12/5.51 [weight('<7,327,262,[1,0,0,5]>')]).
% 5.12/5.51 cnf('0.328.1.1',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,least_upper_bound(identity,X1)),X1) = multiply(inverse(least_upper_bound(identity,inverse(X1))),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.328.1.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.328.1.2',plain,
% 5.12/5.51 ( multiply(identity,X1) = multiply(inverse(least_upper_bound(identity,inverse(X1))),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.328.1.1','0.3.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.328.1.3',plain,
% 5.12/5.51 ( X1 = multiply(inverse(least_upper_bound(identity,inverse(X1))),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.328.1.2','0.1.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.328.2.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,inverse(X1))),least_upper_bound(identity,X1)) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.328.1.3',theory(equality)]),
% 5.12/5.51 [x,rule_325]).
% 5.12/5.51 cnf('0.514.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(multiply(X1,X2),X3),X4) = greatest_lower_bound(multiply(X1,multiply(X2,X4)),multiply(X3,X4)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.9.2.0','0.6.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.514.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(multiply(X1,X2),X3),X4) = greatest_lower_bound(multiply(X1,multiply(X2,X4)),multiply(X3,X4)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.514.0.0']),
% 5.12/5.51 [weight('<9,9,6,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.514.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(multiply(X1,multiply(X2,X3)),multiply(X4,X3)) = multiply(greatest_lower_bound(multiply(X1,X2),X4),X3) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.514.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_510]).
% 5.12/5.51 cnf('0.515.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(multiply(X1,inverse(X2)),X3),X2) = greatest_lower_bound(multiply(X1,identity),multiply(X3,X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.514.2.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2','L')]).
% 5.12/5.51 cnf('0.515.0.1',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(multiply(X1,inverse(X2)),X3),X2) = greatest_lower_bound(X1,multiply(X3,X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.515.0.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.515.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(multiply(X1,inverse(X2)),X3),X2) = greatest_lower_bound(X1,multiply(X3,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.515.0.1']),
% 5.12/5.51 [weight('<8,514,11,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.515.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(multiply(X1,inverse(X2)),X3),X2) = greatest_lower_bound(X1,multiply(X3,X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.515.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_511]).
% 5.12/5.51 cnf('0.517.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(X2,X3)) = multiply(greatest_lower_bound(X2,multiply(X1,inverse(X3))),X3) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.515.2.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.517.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(X2,X3)) = multiply(greatest_lower_bound(X2,multiply(X1,inverse(X3))),X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.517.0.0']),
% 5.12/5.51 [weight('<8,515,12,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.517.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(X1,multiply(X2,inverse(X3))),X3) = greatest_lower_bound(X2,multiply(X1,X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.517.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_513]).
% 5.12/5.51 cnf('0.522.0.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(multiply(X1,X2),X3),X4) = least_upper_bound(multiply(X1,multiply(X2,X4)),multiply(X3,X4)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.10.2.0','0.6.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.522.1.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(multiply(X1,X2),X3),X4) = least_upper_bound(multiply(X1,multiply(X2,X4)),multiply(X3,X4)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.522.0.0']),
% 5.12/5.51 [weight('<9,10,6,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.522.2.0',plain,
% 5.12/5.51 ( least_upper_bound(multiply(X1,multiply(X2,X3)),multiply(X4,X3)) = multiply(least_upper_bound(multiply(X1,X2),X4),X3) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.522.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_518]).
% 5.12/5.51 cnf('0.523.0.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(multiply(X1,inverse(X2)),X3),X2) = least_upper_bound(multiply(X1,identity),multiply(X3,X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.522.2.0','0.11.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2','L')]).
% 5.12/5.51 cnf('0.523.0.1',plain,
% 5.12/5.51 ( multiply(least_upper_bound(multiply(X1,inverse(X2)),X3),X2) = least_upper_bound(X1,multiply(X3,X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.523.0.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.523.1.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(multiply(X1,inverse(X2)),X3),X2) = least_upper_bound(X1,multiply(X3,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.523.0.1']),
% 5.12/5.51 [weight('<8,522,11,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.523.2.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(multiply(X1,inverse(X2)),X3),X2) = least_upper_bound(X1,multiply(X3,X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.523.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_519]).
% 5.12/5.51 cnf('0.525.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,multiply(X2,X3)) = multiply(least_upper_bound(X2,multiply(X1,inverse(X3))),X3) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.523.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.525.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,multiply(X2,X3)) = multiply(least_upper_bound(X2,multiply(X1,inverse(X3))),X3) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.525.0.0']),
% 5.12/5.51 [weight('<8,523,14,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.525.2.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(X1,multiply(X2,inverse(X3))),X3) = least_upper_bound(X2,multiply(X1,X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.525.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_521]).
% 5.12/5.51 cnf('0.585.0.0',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(X2,greatest_lower_bound(inverse(X1),X3))) = least_upper_bound(multiply(X1,X2),greatest_lower_bound(identity,multiply(X1,X3))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.8.2.0','0.38.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.585.1.0',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(X2,greatest_lower_bound(inverse(X1),X3))) = least_upper_bound(multiply(X1,X2),greatest_lower_bound(identity,multiply(X1,X3))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.585.0.0']),
% 5.12/5.51 [weight('<9,38,8,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.585.2.0',plain,
% 5.12/5.51 ( least_upper_bound(multiply(X1,X2),greatest_lower_bound(identity,multiply(X1,X3))) = multiply(X1,least_upper_bound(X2,greatest_lower_bound(inverse(X1),X3))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.585.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_579]).
% 5.12/5.51 cnf('0.586.0.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(least_upper_bound(inverse(X1),X2),X3)) = greatest_lower_bound(least_upper_bound(identity,multiply(X1,X2)),multiply(X1,X3)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.7.2.0','0.40.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.586.1.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(least_upper_bound(inverse(X1),X2),X3)) = greatest_lower_bound(least_upper_bound(identity,multiply(X1,X2)),multiply(X1,X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.586.0.0']),
% 5.12/5.51 [weight('<9,40,7,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.586.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,multiply(X1,X2)),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(least_upper_bound(inverse(X1),X2),X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.586.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_580]).
% 5.12/5.51 cnf('0.595.0.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(X2,least_upper_bound(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),least_upper_bound(identity,multiply(X1,X3))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.7.2.0','0.40.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.595.1.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(X2,least_upper_bound(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),least_upper_bound(identity,multiply(X1,X3))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.595.0.0']),
% 5.12/5.51 [weight('<9,40,7,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.595.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(multiply(X1,X2),least_upper_bound(identity,multiply(X1,X3))) = multiply(X1,greatest_lower_bound(X2,least_upper_bound(inverse(X1),X3))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.595.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_589]).
% 5.12/5.51 cnf('0.603.0.0',plain,
% 5.12/5.51 ( least_upper_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X2),X3),least_upper_bound(X1,X3)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.18.2.0','0.47.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.603.1.0',plain,
% 5.12/5.51 ( least_upper_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X2),X3),least_upper_bound(X1,X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.603.0.0']),
% 5.12/5.51 [weight('<9,47,18,[0,0,0,2]>')]).
% 5.12/5.51 cnf('0.603.1.1',plain,
% 5.12/5.51 ( least_upper_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(least_upper_bound(X1,X3),least_upper_bound(greatest_lower_bound(X1,X2),X3)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.603.1.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.603.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(greatest_lower_bound(X1,X3),X2)) = least_upper_bound(greatest_lower_bound(X1,X3),X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.603.1.1',theory(equality)]),
% 5.12/5.51 [x,rule_596]).
% 5.12/5.51 cnf('0.612.0.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.10.2.0','0.1.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.612.1.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.612.0.0']),
% 5.12/5.51 [weight('<?,10,1,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.612.2.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)) ),
% 5.12/5.51 inference(activate,[status(thm)],['0.612.1.0']),
% 5.12/5.51 [equation_8]).
% 5.12/5.51 cnf('0.630.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(greatest_lower_bound(least_upper_bound(X1,X2),X3),greatest_lower_bound(X2,X3)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.16.2.0','0.50.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.630.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(greatest_lower_bound(least_upper_bound(X1,X2),X3),greatest_lower_bound(X2,X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.630.0.0']),
% 5.12/5.51 [weight('<9,50,16,[0,0,0,2]>')]).
% 5.12/5.51 cnf('0.630.1.1',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(greatest_lower_bound(X2,X3),greatest_lower_bound(least_upper_bound(X1,X2),X3)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.630.1.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.630.2.0',plain,
% 5.12/5.51 ( least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(least_upper_bound(X3,X1),X2)) = greatest_lower_bound(least_upper_bound(X3,X1),X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.630.1.1',theory(equality)]),
% 5.12/5.51 [x,rule_622]).
% 5.12/5.51 cnf('0.640.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,least_upper_bound(X3,X2))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.51.2.0','0.52.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.640.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,least_upper_bound(X3,X2))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.640.0.0']),
% 5.12/5.51 [weight('<9,52,51,[0,0,0,2]>')]).
% 5.12/5.51 cnf('0.640.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,least_upper_bound(X3,X2))) = least_upper_bound(X1,X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.640.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_632]).
% 5.12/5.51 cnf('0.691.0.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,least_upper_bound(X2,X3))) = greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,least_upper_bound(X3,X1)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.109.2.0','0.15.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.691.1.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,least_upper_bound(X2,X3))) = greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,least_upper_bound(X3,X1)))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.691.0.0']),
% 5.12/5.51 [weight('<9,109,15,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.691.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,least_upper_bound(X3,X1)))) = inverse(least_upper_bound(X1,least_upper_bound(X2,X3))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.691.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_683]).
% 5.12/5.51 cnf('0.703.0.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,least_upper_bound(X2,X3))) = greatest_lower_bound(inverse(least_upper_bound(X1,least_upper_bound(X2,X3))),inverse(X3)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.111.2.0','0.51.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.703.1.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,least_upper_bound(X2,X3))) = greatest_lower_bound(inverse(least_upper_bound(X1,least_upper_bound(X2,X3))),inverse(X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.703.0.0']),
% 5.12/5.51 [weight('<9,111,51,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.703.1.1',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,least_upper_bound(X2,X3))) = greatest_lower_bound(inverse(X3),inverse(least_upper_bound(X1,least_upper_bound(X2,X3)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.703.1.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.703.1.2',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,least_upper_bound(X2,X3))) = inverse(least_upper_bound(X3,least_upper_bound(X1,X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.703.1.1','0.691.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.703.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)) ),
% 5.12/5.51 inference(activate,[status(thm)],['0.703.1.2']),
% 5.12/5.51 [equation_9]).
% 5.12/5.51 cnf('0.805.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,multiply(greatest_lower_bound(identity,X3),X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.60.2.0','0.194.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.2','L')]).
% 5.12/5.51 cnf('0.805.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,multiply(greatest_lower_bound(identity,X3),X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.805.0.0']),
% 5.12/5.51 [weight('<9,194,60,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.805.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,least_upper_bound(X2,multiply(greatest_lower_bound(identity,X3),X1))) = least_upper_bound(X1,X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.805.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_796]).
% 5.12/5.51 cnf('0.862.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity)))),multiply(X2,least_upper_bound(X1,identity))) = multiply(greatest_lower_bound(inverse(identity),X2),least_upper_bound(X1,identity)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.208.2.0','0.18.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.1.1','L')]).
% 5.12/5.51 cnf('0.862.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(inverse(least_upper_bound(identity,X1))),multiply(X2,least_upper_bound(X1,identity))) = multiply(greatest_lower_bound(inverse(identity),X2),least_upper_bound(X1,identity)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.862.0.0','0.75.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.1','L')]).
% 5.12/5.51 cnf('0.862.0.2',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),multiply(X2,least_upper_bound(X1,identity))) = multiply(greatest_lower_bound(inverse(identity),X2),least_upper_bound(X1,identity)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.862.0.1','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.862.0.3',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),multiply(X2,least_upper_bound(X1,identity))) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(X1,identity)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.862.0.2','0.26.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1.1','L')]).
% 5.12/5.51 cnf('0.862.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),multiply(X2,least_upper_bound(X1,identity))) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(X1,identity)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.862.0.3']),
% 5.12/5.51 [weight('<9,208,18,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.862.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),multiply(X2,least_upper_bound(X1,identity))) = multiply(greatest_lower_bound(identity,X2),least_upper_bound(X1,identity)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.862.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_852]).
% 5.12/5.51 cnf('0.863.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(X1,identity)) = greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,multiply(inverse(X1),identity))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.862.2.0','0.31.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.863.0.1',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(X1,identity)) = greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.863.0.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2.2','L')]).
% 5.12/5.51 cnf('0.863.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(X1,identity)) = greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.863.0.1']),
% 5.12/5.51 [weight('<8,862,31,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.863.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(X1,identity)) = greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.863.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_853]).
% 5.12/5.51 cnf('0.865.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.863.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.865.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.865.0.0']),
% 5.12/5.51 [weight('<8,863,14,[1,0,0,5]>')]).
% 5.12/5.51 cnf('0.865.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) = greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.865.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_855]).
% 5.12/5.51 cnf('0.872.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(X2,least_upper_bound(X1,X3))) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X2),least_upper_bound(X1,X3))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.46.2.0','0.210.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','R')]).
% 5.12/5.51 cnf('0.872.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(X2,least_upper_bound(X1,X3))) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X2),least_upper_bound(X1,X3))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.872.0.0']),
% 5.12/5.51 [weight('<9,210,46,[0,1,0,2]>')]).
% 5.12/5.51 cnf('0.872.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X2),least_upper_bound(X1,X3))) = greatest_lower_bound(X1,multiply(X2,least_upper_bound(X1,X3))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.872.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_861]).
% 5.12/5.51 cnf('0.908.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,least_upper_bound(identity,X3)))) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.55.2.0','0.232.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.2','L')]).
% 5.12/5.51 cnf('0.908.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,least_upper_bound(identity,X3)))) = greatest_lower_bound(X1,X2) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.908.0.0','0.21.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.908.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,least_upper_bound(identity,X3)))) = greatest_lower_bound(X1,X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.908.0.1']),
% 5.12/5.51 [weight('<9,232,55,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.908.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,least_upper_bound(identity,X3)))) = greatest_lower_bound(X1,X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.908.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_897]).
% 5.12/5.51 cnf('0.935.0.0',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(identity,X1)),inverse(least_upper_bound(identity,X1))) = inverse(greatest_lower_bound(least_upper_bound(identity,X1),multiply(X1,least_upper_bound(identity,X1)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.134.2.0','0.262.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2','L')]).
% 5.12/5.51 cnf('0.935.0.1',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(identity,X1)),inverse(least_upper_bound(identity,X1))) = multiply(inverse(least_upper_bound(identity,X1)),inverse(greatest_lower_bound(identity,X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.935.0.0','0.211.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.935.1.0',plain,
% 5.12/5.51 ( multiply(inverse(greatest_lower_bound(identity,X1)),inverse(least_upper_bound(identity,X1))) = multiply(inverse(least_upper_bound(identity,X1)),inverse(greatest_lower_bound(identity,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.935.0.1']),
% 5.12/5.51 [weight('<9,262,134,[0,0,0,3]>')]).
% 5.12/5.51 cnf('0.935.2.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,X1)),inverse(greatest_lower_bound(identity,X1))) = multiply(inverse(greatest_lower_bound(identity,X1)),inverse(least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.935.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_924]).
% 5.12/5.51 cnf('0.936.0.0',plain,
% 5.12/5.51 ( multiply(inverse(inverse(greatest_lower_bound(identity,X1))),inverse(inverse(least_upper_bound(identity,X1)))) = inverse(multiply(inverse(greatest_lower_bound(identity,X1)),inverse(least_upper_bound(identity,X1)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.70.2.0','0.935.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.936.0.1',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),inverse(inverse(least_upper_bound(identity,X1)))) = inverse(multiply(inverse(greatest_lower_bound(identity,X1)),inverse(least_upper_bound(identity,X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.936.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.936.0.2',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = inverse(multiply(inverse(greatest_lower_bound(identity,X1)),inverse(least_upper_bound(identity,X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.936.0.1','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.936.0.3',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = multiply(inverse(inverse(least_upper_bound(identity,X1))),inverse(inverse(greatest_lower_bound(identity,X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.936.0.2','0.70.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.936.0.4',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),inverse(inverse(greatest_lower_bound(identity,X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.936.0.3','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.936.0.5',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.936.0.4','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2','L')]).
% 5.12/5.51 cnf('0.936.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.936.0.5']),
% 5.12/5.51 [weight('<7,935,70,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.936.2.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.936.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_925]).
% 5.12/5.51 cnf('0.937.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.936.2.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.937.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.937.0.0']),
% 5.12/5.51 [weight('<7,936,12,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.937.2.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.937.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_926]).
% 5.12/5.51 cnf('0.952.0.0',plain,
% 5.12/5.51 ( least_upper_bound(inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1)))),multiply(greatest_lower_bound(identity,X1),X2)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(inverse(identity),X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.269.2.0','0.5.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1.1','L')]).
% 5.12/5.51 cnf('0.952.0.1',plain,
% 5.12/5.51 ( least_upper_bound(inverse(inverse(greatest_lower_bound(identity,X1))),multiply(greatest_lower_bound(identity,X1),X2)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(inverse(identity),X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.952.0.0','0.82.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.1','L')]).
% 5.12/5.51 cnf('0.952.0.2',plain,
% 5.12/5.51 ( least_upper_bound(greatest_lower_bound(identity,X1),multiply(greatest_lower_bound(identity,X1),X2)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(inverse(identity),X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.952.0.1','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.952.0.3',plain,
% 5.12/5.51 ( least_upper_bound(greatest_lower_bound(identity,X1),multiply(greatest_lower_bound(identity,X1),X2)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.952.0.2','0.26.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2.1','L')]).
% 5.12/5.51 cnf('0.952.1.0',plain,
% 5.12/5.51 ( least_upper_bound(greatest_lower_bound(identity,X1),multiply(greatest_lower_bound(identity,X1),X2)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.952.0.3']),
% 5.12/5.51 [weight('<9,269,5,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.952.2.0',plain,
% 5.12/5.51 ( least_upper_bound(greatest_lower_bound(identity,X1),multiply(greatest_lower_bound(identity,X1),X2)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.952.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_941]).
% 5.12/5.51 cnf('0.953.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) = least_upper_bound(greatest_lower_bound(identity,inverse(X1)),greatest_lower_bound(identity,multiply(identity,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.952.2.0','0.34.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.953.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = least_upper_bound(greatest_lower_bound(identity,inverse(X1)),greatest_lower_bound(identity,multiply(identity,X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.953.0.0','0.865.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.953.0.2',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = least_upper_bound(greatest_lower_bound(identity,inverse(X1)),greatest_lower_bound(identity,X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.953.0.1','0.1.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2.2','L')]).
% 5.12/5.51 cnf('0.953.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = least_upper_bound(greatest_lower_bound(identity,inverse(X1)),greatest_lower_bound(identity,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.953.0.2']),
% 5.12/5.51 [weight('<8,952,34,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.953.1.1',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.953.1.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.953.2.0',plain,
% 5.12/5.51 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.953.1.1',theory(equality)]),
% 5.12/5.51 [x,rule_942]).
% 5.12/5.51 cnf('0.955.0.0',plain,
% 5.12/5.51 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.603.2.0','0.953.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.955.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(least_upper_bound(identity,greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.955.0.0','0.953.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.955.0.2',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.955.0.1','0.5.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.955.0.3',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,least_upper_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.955.0.2','0.46.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.955.0.4',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = identity ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.955.0.3','0.3.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.955.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = identity ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.955.0.4']),
% 5.12/5.51 [weight('<8,953,603,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.955.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = identity ),
% 5.12/5.51 inference(orient,[status(thm)],['0.955.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_944]).
% 5.12/5.51 cnf('0.956.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,multiply(inverse(least_upper_bound(identity,inverse(X1))),least_upper_bound(identity,X1))) = multiply(inverse(least_upper_bound(identity,inverse(X1))),identity) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.30.2.0','0.955.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.956.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,X1) = multiply(inverse(least_upper_bound(identity,inverse(X1))),identity) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.956.0.0','0.328.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.956.0.2',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.956.0.1','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.956.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.956.0.2']),
% 5.12/5.51 [weight('<5,955,30,[0,0,0,3]>')]).
% 5.12/5.51 cnf('0.956.2.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(identity,X1) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.956.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_945]).
% 5.12/5.51 cnf('0.957.0.0',plain,
% 5.12/5.51 ( least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(identity,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.23.2.0','0.956.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.957.1.0',plain,
% 5.12/5.51 ( least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(identity,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.957.0.0']),
% 5.12/5.51 [weight('<4,956,23,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.957.2.0',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.957.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_946]).
% 5.12/5.51 cnf('0.958.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,inverse(X1)) = inverse(least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.956.2.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.2','L')]).
% 5.12/5.51 cnf('0.958.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(identity,inverse(X1)) = inverse(least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.958.0.0']),
% 5.12/5.51 [weight('<4,956,23,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.958.2.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.958.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_947]).
% 5.12/5.51 cnf('0.961.0.0',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(multiply(inverse(X1),identity),X2)) = multiply(least_upper_bound(identity,inverse(multiply(X1,X2))),X1) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.137.2.0','0.957.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.961.0.1',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(inverse(X1),X2)) = multiply(least_upper_bound(identity,inverse(multiply(X1,X2))),X1) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.961.0.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.1','L')]).
% 5.12/5.51 cnf('0.961.0.2',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(inverse(X1),X2)) = multiply(least_upper_bound(identity,multiply(inverse(X2),inverse(X1))),X1) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.961.0.1','0.70.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1.2','L')]).
% 5.12/5.51 cnf('0.961.0.3',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(inverse(X2),multiply(identity,X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.961.0.2','0.525.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.961.0.4',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(inverse(X2),X1) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.961.0.3','0.1.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2','L')]).
% 5.12/5.51 cnf('0.961.1.0',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(inverse(X2),X1) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.961.0.4']),
% 5.12/5.51 [weight('<5,957,137,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.961.2.0',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(inverse(X2),X1) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.961.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_950]).
% 5.12/5.51 cnf('0.962.0.0',plain,
% 5.12/5.51 ( least_upper_bound(inverse(X1),inverse(X2)) = inverse(greatest_lower_bound(X2,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.961.2.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.1','L')]).
% 5.12/5.51 cnf('0.962.1.0',plain,
% 5.12/5.51 ( least_upper_bound(inverse(X1),inverse(X2)) = inverse(greatest_lower_bound(X2,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.962.0.0']),
% 5.12/5.51 [weight('<4,961,23,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.962.2.0',plain,
% 5.12/5.51 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(X2),inverse(X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.962.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_951]).
% 5.12/5.51 cnf('0.963.0.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(multiply(inverse(X1),identity),X2)) = multiply(greatest_lower_bound(identity,inverse(multiply(X1,X2))),X1) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.142.2.0','0.958.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.963.0.1',plain,
% 5.12/5.51 ( inverse(least_upper_bound(inverse(X1),X2)) = multiply(greatest_lower_bound(identity,inverse(multiply(X1,X2))),X1) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.963.0.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.1','L')]).
% 5.12/5.51 cnf('0.963.0.2',plain,
% 5.12/5.51 ( inverse(least_upper_bound(inverse(X1),X2)) = multiply(greatest_lower_bound(identity,multiply(inverse(X2),inverse(X1))),X1) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.963.0.1','0.70.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1.2','L')]).
% 5.12/5.51 cnf('0.963.0.3',plain,
% 5.12/5.51 ( inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(X2),multiply(identity,X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.963.0.2','0.517.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.963.0.4',plain,
% 5.12/5.51 ( inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(X2),X1) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.963.0.3','0.1.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2','L')]).
% 5.12/5.51 cnf('0.963.1.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(X2),X1) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.963.0.4']),
% 5.12/5.51 [weight('<5,958,142,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.963.2.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(X2),X1) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.963.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_952]).
% 5.12/5.51 cnf('0.964.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X2,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.963.2.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1.1','L')]).
% 5.12/5.51 cnf('0.964.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X2,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.964.0.0']),
% 5.12/5.51 [weight('<4,963,23,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.964.2.0',plain,
% 5.12/5.51 ( inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X2),inverse(X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.964.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_953]).
% 5.12/5.51 cnf('0.973.0.0',plain,
% 5.12/5.51 ( multiply(inverse(least_upper_bound(identity,inverse(X1))),least_upper_bound(identity,X1)) = X1 ),
% 5.12/5.51 inference(interreduction_right,[status(thm)],['0.328.2.0'])).
% 5.12/5.51 cnf('0.973.0.1',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = X1 ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.973.0.0','0.956.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.973.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = X1 ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.973.0.1']),
% 5.12/5.51 [weight('<7,328,956,[0,0,0,0]>')]).
% 5.12/5.51 cnf('0.973.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.973.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_960]).
% 5.12/5.51 cnf('0.976.0.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(interreduction_right,[status(thm)],['0.937.2.0'])).
% 5.12/5.51 cnf('0.976.0.1',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) = X1 ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.976.0.0','0.973.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.976.1.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) = X1 ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.976.0.1']),
% 5.12/5.51 [weight('<7,937,973,[0,0,0,0]>')]).
% 5.12/5.51 cnf('0.976.2.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.976.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_963]).
% 5.12/5.51 cnf('0.985.0.0',plain,
% 5.12/5.51 ( X1 = multiply(greatest_lower_bound(identity,X1),least_upper_bound(X1,identity)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.973.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.985.1.0',plain,
% 5.12/5.51 ( X1 = multiply(greatest_lower_bound(identity,X1),least_upper_bound(X1,identity)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.985.0.0']),
% 5.12/5.51 [weight('<7,973,14,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.985.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(X1,identity)) = X1 ),
% 5.12/5.51 inference(orient,[status(thm)],['0.985.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_972]).
% 5.12/5.51 cnf('0.989.0.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(inverse(least_upper_bound(identity,X1)),X2)) = multiply(inverse(least_upper_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(interreduction_right,[status(thm)],['0.259.2.0'])).
% 5.12/5.51 cnf('0.989.0.1',plain,
% 5.12/5.51 ( multiply(X1,multiply(inverse(least_upper_bound(identity,X1)),X2)) = multiply(greatest_lower_bound(identity,X1),X2) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.989.0.0','0.956.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.989.1.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(inverse(least_upper_bound(identity,X1)),X2)) = multiply(greatest_lower_bound(identity,X1),X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.989.0.1']),
% 5.12/5.51 [weight('<8,259,956,[0,0,0,0]>')]).
% 5.12/5.51 cnf('0.989.1.1',plain,
% 5.12/5.51 ( multiply(X1,multiply(greatest_lower_bound(inverse(X1),inverse(identity)),X2)) = multiply(greatest_lower_bound(identity,X1),X2) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.989.1.0','0.964.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.989.1.2',plain,
% 5.12/5.51 ( multiply(X1,multiply(greatest_lower_bound(inverse(X1),identity),X2)) = multiply(greatest_lower_bound(identity,X1),X2) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.989.1.1','0.26.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1.2','L')]).
% 5.12/5.51 cnf('0.989.1.3',plain,
% 5.12/5.51 ( multiply(X1,multiply(greatest_lower_bound(identity,inverse(X1)),X2)) = multiply(greatest_lower_bound(identity,X1),X2) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.989.1.2','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.989.2.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(greatest_lower_bound(identity,inverse(X1)),X2)) = multiply(greatest_lower_bound(identity,X1),X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.989.1.3',theory(equality)]),
% 5.12/5.51 [u,rule_976]).
% 5.12/5.51 cnf('0.992.0.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(inverse(greatest_lower_bound(identity,X1)),X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(interreduction_right,[status(thm)],['0.317.2.0'])).
% 5.12/5.51 cnf('0.992.0.1',plain,
% 5.12/5.51 ( multiply(X1,multiply(least_upper_bound(identity,inverse(X1)),X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.992.0.0','0.957.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.992.0.2',plain,
% 5.12/5.51 ( multiply(X1,multiply(least_upper_bound(identity,inverse(X1)),X2)) = multiply(least_upper_bound(identity,inverse(inverse(X1))),X2) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.992.0.1','0.957.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1','L')]).
% 5.12/5.51 cnf('0.992.0.3',plain,
% 5.12/5.51 ( multiply(X1,multiply(least_upper_bound(identity,inverse(X1)),X2)) = multiply(least_upper_bound(identity,X1),X2) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.992.0.2','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.1.2','L')]).
% 5.12/5.51 cnf('0.992.1.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(least_upper_bound(identity,inverse(X1)),X2)) = multiply(least_upper_bound(identity,X1),X2) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.992.0.3']),
% 5.12/5.51 [weight('<8,317,957,[0,0,0,0]>')]).
% 5.12/5.51 cnf('0.992.2.0',plain,
% 5.12/5.51 ( multiply(X1,multiply(least_upper_bound(identity,inverse(X1)),X2)) = multiply(least_upper_bound(identity,X1),X2) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.992.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_977]).
% 5.12/5.51 cnf('0.1014.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X3,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.12.2.0','0.13.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.1014.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X3,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1014.0.0']),
% 5.12/5.51 [weight('<?,13,12,[0,0,0,0]>')]).
% 5.12/5.51 cnf('0.1014.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X3,X1)) ),
% 5.12/5.51 inference(activate,[status(thm)],['0.1014.1.0']),
% 5.12/5.51 [equation_18]).
% 5.12/5.51 cnf('0.1205.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,multiply(X2,greatest_lower_bound(X1,X3))) = least_upper_bound(X1,multiply(least_upper_bound(identity,X2),greatest_lower_bound(X1,X3))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.47.2.0','0.612.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','R')]).
% 5.12/5.51 cnf('0.1205.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,multiply(X2,greatest_lower_bound(X1,X3))) = least_upper_bound(X1,multiply(least_upper_bound(identity,X2),greatest_lower_bound(X1,X3))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1205.0.0']),
% 5.12/5.51 [weight('<9,612,47,[0,1,0,2]>')]).
% 5.12/5.51 cnf('0.1205.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,multiply(least_upper_bound(identity,X2),greatest_lower_bound(X1,X3))) = least_upper_bound(X1,multiply(X2,greatest_lower_bound(X1,X3))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1205.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_1182]).
% 5.12/5.51 cnf('0.1232.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.630.2.0','0.18.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.1232.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1232.0.0']),
% 5.12/5.51 [weight('<9,630,18,[1,0,0,1]>')]).
% 5.12/5.51 cnf('0.1232.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(X3,X1))) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(X3,X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1232.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_1207]).
% 5.12/5.51 cnf('0.1257.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),X3)) = least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),least_upper_bound(X3,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.805.2.0','0.8.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.1257.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),X3)) = least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),least_upper_bound(X3,X1))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1257.0.0']),
% 5.12/5.51 [weight('<9,805,8,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.1257.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),least_upper_bound(X3,X1))) = least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1257.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_1229]).
% 5.12/5.51 cnf('0.1352.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(X2,least_upper_bound(identity,X3))) = greatest_lower_bound(X1,multiply(greatest_lower_bound(X2,X1),least_upper_bound(identity,X3))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.908.2.0','0.9.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.1352.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(X2,least_upper_bound(identity,X3))) = greatest_lower_bound(X1,multiply(greatest_lower_bound(X2,X1),least_upper_bound(identity,X3))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1352.0.0']),
% 5.12/5.51 [weight('<9,908,9,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.1352.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(greatest_lower_bound(X2,X1),least_upper_bound(identity,X3))) = greatest_lower_bound(X1,multiply(X2,least_upper_bound(identity,X3))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1352.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_1320]).
% 5.12/5.51 cnf('0.1407.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(least_upper_bound(identity,X1),X2)) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.7.2.0','0.973.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.1407.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(least_upper_bound(identity,X1),X2)) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1407.0.0']),
% 5.12/5.51 [weight('<9,973,7,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.1407.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(least_upper_bound(identity,X1),X2)) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1407.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_1375]).
% 5.12/5.51 cnf('0.1408.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(X2,least_upper_bound(identity,X1))) = greatest_lower_bound(multiply(greatest_lower_bound(identity,X1),X2),X1) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.7.2.0','0.973.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.1408.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(X2,least_upper_bound(identity,X1))) = greatest_lower_bound(multiply(greatest_lower_bound(identity,X1),X2),X1) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1408.0.0']),
% 5.12/5.51 [weight('<9,973,7,[0,0,0,4]>')]).
% 5.12/5.51 cnf('0.1408.1.1',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(X2,least_upper_bound(identity,X1))) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1408.1.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.1408.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(X2,least_upper_bound(identity,X1))) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1408.1.1',theory(equality)]),
% 5.12/5.51 [u,rule_1376]).
% 5.12/5.51 cnf('0.1436.0.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),least_upper_bound(greatest_lower_bound(X1,identity),X2)) = least_upper_bound(X1,multiply(least_upper_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.8.2.0','0.976.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.1436.1.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),least_upper_bound(greatest_lower_bound(X1,identity),X2)) = least_upper_bound(X1,multiply(least_upper_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1436.0.0']),
% 5.12/5.51 [weight('<9,976,8,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.1436.2.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),least_upper_bound(greatest_lower_bound(X1,identity),X2)) = least_upper_bound(X1,multiply(least_upper_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1436.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_1403]).
% 5.12/5.51 cnf('0.1480.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(least_upper_bound(X1,identity),X2)) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.7.2.0','0.985.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.1480.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(least_upper_bound(X1,identity),X2)) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1480.0.0']),
% 5.12/5.51 [weight('<9,985,7,[0,0,0,1]>')]).
% 5.12/5.51 cnf('0.1480.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(least_upper_bound(X1,identity),X2)) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1480.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_1447]).
% 5.12/5.51 cnf('0.1500.0.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X1))),X2)) = multiply(X1,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.989.2.0','0.38.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.1500.0.1',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(least_upper_bound(inverse(inverse(X1)),inverse(identity)),X2)) = multiply(X1,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1500.0.0','0.962.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.1500.0.2',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(least_upper_bound(X1,inverse(identity)),X2)) = multiply(X1,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1500.0.1','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1.1','L')]).
% 5.12/5.51 cnf('0.1500.0.3',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(least_upper_bound(X1,identity),X2)) = multiply(X1,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1500.0.2','0.26.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1.2','L')]).
% 5.12/5.51 cnf('0.1500.1.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(least_upper_bound(X1,identity),X2)) = multiply(X1,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1500.0.3']),
% 5.12/5.51 [weight('<9,989,38,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.1500.1.1',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2)) = multiply(X1,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1500.1.0','0.1480.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.1500.2.0',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X1)),X2))) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1500.1.1',theory(equality)]),
% 5.12/5.51 [x,rule_1467]).
% 5.12/5.51 cnf('0.1505.0.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),X2)) = multiply(X1,least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.992.2.0','0.40.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.1505.0.1',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),least_upper_bound(greatest_lower_bound(inverse(inverse(X1)),inverse(identity)),X2)) = multiply(X1,least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1505.0.0','0.964.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.1505.0.2',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),least_upper_bound(greatest_lower_bound(X1,inverse(identity)),X2)) = multiply(X1,least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1505.0.1','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1.1','L')]).
% 5.12/5.51 cnf('0.1505.0.3',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),least_upper_bound(greatest_lower_bound(X1,identity),X2)) = multiply(X1,least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1505.0.2','0.26.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1.2','L')]).
% 5.12/5.51 cnf('0.1505.1.0',plain,
% 5.12/5.51 ( multiply(least_upper_bound(identity,X1),least_upper_bound(greatest_lower_bound(X1,identity),X2)) = multiply(X1,least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1505.0.3']),
% 5.12/5.51 [weight('<9,992,40,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.1505.1.1',plain,
% 5.12/5.51 ( least_upper_bound(X1,multiply(least_upper_bound(identity,X1),X2)) = multiply(X1,least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X1)),X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1505.1.0','0.1436.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.1505.2.0',plain,
% 5.12/5.51 ( multiply(X1,least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X1)),X2))) = least_upper_bound(X1,multiply(least_upper_bound(identity,X1),X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1505.1.1',theory(equality)]),
% 5.12/5.51 [x,rule_1471]).
% 5.12/5.51 cnf('0.1522.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X2),X3),greatest_lower_bound(X4,X1)) = greatest_lower_bound(X4,greatest_lower_bound(X1,X3)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.1014.2.0','0.46.2.0',theory(equality)]),
% 5.12/5.51 [pos('R.2','L')]).
% 5.12/5.51 cnf('0.1522.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),greatest_lower_bound(X3,greatest_lower_bound(X4,X1))) = greatest_lower_bound(X4,greatest_lower_bound(X1,X3)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1522.0.0','0.13.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.1522.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),greatest_lower_bound(X3,greatest_lower_bound(X4,X1))) = greatest_lower_bound(X4,greatest_lower_bound(X1,X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1522.0.1']),
% 5.12/5.51 [weight('<9,1014,46,[1,1,0,2]>')]).
% 5.12/5.51 cnf('0.1522.2.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),greatest_lower_bound(X3,greatest_lower_bound(X4,X1))) = greatest_lower_bound(X4,greatest_lower_bound(X1,X3)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1522.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_1488]).
% 5.12/5.51 cnf('0.1759.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),multiply(greatest_lower_bound(identity,least_upper_bound(X1,X2)),least_upper_bound(identity,X2))) = multiply(greatest_lower_bound(identity,least_upper_bound(X1,X2)),least_upper_bound(identity,X2)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.1408.2.0','0.640.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.1759.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),multiply(identity,least_upper_bound(identity,X2))) = multiply(greatest_lower_bound(identity,least_upper_bound(X1,X2)),least_upper_bound(identity,X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1759.0.0','0.1352.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.1759.0.2',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(identity,X2)) = multiply(greatest_lower_bound(identity,least_upper_bound(X1,X2)),least_upper_bound(identity,X2)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1759.0.1','0.1.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.1759.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(identity,X2)) = multiply(greatest_lower_bound(identity,least_upper_bound(X1,X2)),least_upper_bound(identity,X2)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1759.0.2']),
% 5.12/5.51 [weight('<9,1408,640,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.1759.2.0',plain,
% 5.12/5.51 ( multiply(greatest_lower_bound(identity,least_upper_bound(X1,X2)),least_upper_bound(identity,X2)) = greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(identity,X2)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1759.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_1716]).
% 5.12/5.51 cnf('0.1760.0.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,multiply(greatest_lower_bound(identity,least_upper_bound(X2,X1)),identity)) = least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.1257.2.0','0.1759.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.1760.0.1',plain,
% 5.12/5.51 ( least_upper_bound(X1,greatest_lower_bound(identity,least_upper_bound(X2,X1))) = least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(identity,X1))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1760.0.0','0.28.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.1760.0.2',plain,
% 5.12/5.51 ( least_upper_bound(X1,greatest_lower_bound(identity,least_upper_bound(X2,X1))) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1760.0.1','0.1232.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.1760.1.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,greatest_lower_bound(identity,least_upper_bound(X2,X1))) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1760.0.2']),
% 5.12/5.51 [weight('<7,1759,1257,[0,0,0,2]>')]).
% 5.12/5.51 cnf('0.1760.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,greatest_lower_bound(identity,least_upper_bound(X2,X1))) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(identity,X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1760.1.0',theory(equality)]),
% 5.12/5.51 [u,rule_1717]).
% 5.12/5.51 cnf('0.1770.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(multiply(X1,X2),multiply(X1,X3)),least_upper_bound(identity,multiply(X1,X3))) = least_upper_bound(multiply(X1,X3),greatest_lower_bound(identity,multiply(X1,least_upper_bound(X2,X3)))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.1760.2.0','0.8.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.2','L')]).
% 5.12/5.51 cnf('0.1770.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(multiply(X1,least_upper_bound(X2,X3)),least_upper_bound(identity,multiply(X1,X3))) = least_upper_bound(multiply(X1,X3),greatest_lower_bound(identity,multiply(X1,least_upper_bound(X2,X3)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1770.0.0','0.8.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.1770.0.2',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(least_upper_bound(X2,X3),least_upper_bound(inverse(X1),X3))) = least_upper_bound(multiply(X1,X3),greatest_lower_bound(identity,multiply(X1,least_upper_bound(X2,X3)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1770.0.1','0.595.2.0',theory(equality)]),
% 5.12/5.51 [pos('L','L')]).
% 5.12/5.51 cnf('0.1770.0.3',plain,
% 5.12/5.51 ( multiply(X1,greatest_lower_bound(least_upper_bound(X2,X3),least_upper_bound(inverse(X1),X3))) = multiply(X1,least_upper_bound(X3,greatest_lower_bound(inverse(X1),least_upper_bound(X2,X3)))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1770.0.2','0.585.2.0',theory(equality)]),
% 5.12/5.51 [pos('R','L')]).
% 5.12/5.51 cnf('0.1770.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X2,X3),least_upper_bound(inverse(X1),X3)) = least_upper_bound(X3,greatest_lower_bound(inverse(X1),least_upper_bound(X2,X3))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1770.0.3']),
% 5.12/5.51 [weight('<8,1760,8,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.1770.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,greatest_lower_bound(inverse(X2),least_upper_bound(X3,X1))) = greatest_lower_bound(least_upper_bound(X3,X1),least_upper_bound(inverse(X2),X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1770.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_1727]).
% 5.12/5.51 cnf('0.1771.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(inverse(inverse(X3)),X2)) = least_upper_bound(X2,greatest_lower_bound(X3,least_upper_bound(X1,X2))) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.1770.2.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.1771.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(X3,least_upper_bound(X1,X2))) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1771.0.0','0.23.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.1','L')]).
% 5.12/5.51 cnf('0.1771.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(X3,least_upper_bound(X1,X2))) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1771.0.1']),
% 5.12/5.51 [weight('<7,1770,23,[1,0,0,3]>')]).
% 5.12/5.51 cnf('0.1771.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,greatest_lower_bound(X2,least_upper_bound(X3,X1))) = greatest_lower_bound(least_upper_bound(X3,X1),least_upper_bound(X2,X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1771.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_1728]).
% 5.12/5.51 cnf('0.1772.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,greatest_lower_bound(X1,X2)),least_upper_bound(X3,greatest_lower_bound(X1,X2))) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X3,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.1771.2.0','0.5.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2.2','L')]).
% 5.12/5.51 cnf('0.1772.0.1',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,least_upper_bound(X3,greatest_lower_bound(X1,X2))) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X3,X1)) ),
% 5.12/5.51 inference(reduction,[status(thm)],['0.1772.0.0','0.5.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.1','L')]).
% 5.12/5.51 cnf('0.1772.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(X1,least_upper_bound(X3,greatest_lower_bound(X1,X2))) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X3,X1)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1772.0.1']),
% 5.12/5.51 [weight('<7,1771,5,[1,0,0,4]>')]).
% 5.12/5.51 cnf('0.1772.2.0',plain,
% 5.12/5.51 ( least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X3,X1)) = greatest_lower_bound(X1,least_upper_bound(X3,greatest_lower_bound(X1,X2))) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1772.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_1729]).
% 5.12/5.51 cnf('0.1773.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X2),X3)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.1771.2.0','0.12.2.0',theory(equality)]),
% 5.12/5.51 [pos('L.2','L')]).
% 5.12/5.51 cnf('0.1773.1.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X2),X3)) ),
% 5.12/5.51 inference(weigh,[status(thm)],['0.1773.0.0']),
% 5.12/5.51 [weight('<7,1771,12,[1,0,0,2]>')]).
% 5.12/5.51 cnf('0.1773.2.0',plain,
% 5.12/5.51 ( least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),X3)) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(X3,X1)) ),
% 5.12/5.51 inference(orient,[status(thm)],['0.1773.1.0',theory(equality)]),
% 5.12/5.51 [x,rule_1730]).
% 5.12/5.51 cnf('0.1775.0.0',plain,
% 5.12/5.51 ( greatest_lower_bound(least_upper_bound(X1,greatest_lower_bound(X2,X1)),least_upper_bound(X3,greatest_lower_bound(X2,X1))) = least_upper_bound(greatest_lower_bound(X2,X1),greatest_lower_bound(X3,X1)) ),
% 5.12/5.51 inference(cp,[status(thm)],['0.1771.2.0','0.16.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2','L')]).
% 5.12/5.52 cnf('0.1775.0.1',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X3,greatest_lower_bound(X2,X1))) = least_upper_bound(greatest_lower_bound(X2,X1),greatest_lower_bound(X3,X1)) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1775.0.0','0.16.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.1','L')]).
% 5.12/5.52 cnf('0.1775.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X3,greatest_lower_bound(X2,X1))) = least_upper_bound(greatest_lower_bound(X2,X1),greatest_lower_bound(X3,X1)) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.1775.0.1']),
% 5.12/5.52 [weight('<7,1771,16,[1,0,0,4]>')]).
% 5.12/5.52 cnf('0.1775.2.0',plain,
% 5.12/5.52 ( least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X3,X2)) = greatest_lower_bound(X2,least_upper_bound(X3,greatest_lower_bound(X1,X2))) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.1775.1.0',theory(equality)]),
% 5.12/5.52 [x,rule_1732]).
% 5.12/5.52 cnf('0.1776.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,X3))) = least_upper_bound(greatest_lower_bound(X2,X1),greatest_lower_bound(X1,X3)) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1772.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.52 [pos('L','L')]).
% 5.12/5.52 cnf('0.1776.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,X3))) = least_upper_bound(greatest_lower_bound(X2,X1),greatest_lower_bound(X1,X3)) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.1776.0.0']),
% 5.12/5.52 [weight('<7,1772,0,[1,0,0,0]>')]).
% 5.12/5.52 cnf('0.1776.2.0',plain,
% 5.12/5.52 ( least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,least_upper_bound(X1,greatest_lower_bound(X2,X3))) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.1776.1.0',theory(equality)]),
% 5.12/5.52 [x,rule_1733]).
% 5.12/5.52 cnf('0.1778.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X2,X1),X3)) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1773.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.1','L')]).
% 5.12/5.52 cnf('0.1778.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X2,X1),X3)) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.1778.0.0']),
% 5.12/5.52 [weight('<7,1773,0,[1,0,0,3]>')]).
% 5.12/5.52 cnf('0.1778.2.0',plain,
% 5.12/5.52 ( least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(X3,X1)) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.1778.1.0',theory(equality)]),
% 5.12/5.52 [x,rule_1735]).
% 5.12/5.52 cnf('0.1779.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) = least_upper_bound(greatest_lower_bound(X3,X1),greatest_lower_bound(X1,X2)) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1775.2.0','0.12.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2','L')]).
% 5.12/5.52 cnf('0.1779.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) = least_upper_bound(greatest_lower_bound(X3,X1),greatest_lower_bound(X1,X2)) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.1779.0.0']),
% 5.12/5.52 [weight('<7,1775,12,[1,0,0,4]>')]).
% 5.12/5.52 cnf('0.1779.1.1',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) = greatest_lower_bound(X1,least_upper_bound(X3,greatest_lower_bound(X1,X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1779.1.0','0.1776.2.0',theory(equality)]),
% 5.12/5.52 [pos('R','L')]).
% 5.12/5.52 cnf('0.1779.2.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) = greatest_lower_bound(X1,least_upper_bound(X3,greatest_lower_bound(X1,X2))) ),
% 5.12/5.52 inference(activate,[status(thm)],['0.1779.1.1']),
% 5.12/5.52 [equation_44]).
% 5.12/5.52 cnf('0.1781.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X2,X1),X3)) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1779.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2','L')]).
% 5.12/5.52 cnf('0.1781.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X2,X1),X3)) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.1781.0.0']),
% 5.12/5.52 [weight('<7,1779,14,[1,0,0,2]>')]).
% 5.12/5.52 cnf('0.1781.2.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X2,X1),X3)) = greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,X3))) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.1781.1.0',theory(equality)]),
% 5.12/5.52 [x,rule_1736]).
% 5.12/5.52 cnf('0.1782.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) = greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1779.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.52 [pos('R.2','L')]).
% 5.12/5.52 cnf('0.1782.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) = greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.1782.0.0']),
% 5.12/5.52 [weight('<7,1779,14,[1,1,0,2]>')]).
% 5.12/5.52 cnf('0.1782.2.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.1782.1.0',theory(equality)]),
% 5.12/5.52 [x,rule_1737]).
% 5.12/5.52 cnf('0.1849.0.0',plain,
% 5.12/5.52 ( least_upper_bound(identity,multiply(X1,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))),X2)))) = least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X1),multiply(greatest_lower_bound(identity,least_upper_bound(identity,X1)),X2))) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1205.2.0','0.1500.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2','L')]).
% 5.12/5.52 cnf('0.1849.0.1',plain,
% 5.12/5.52 ( least_upper_bound(identity,multiply(X1,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,greatest_lower_bound(inverse(X1),inverse(identity))),X2)))) = least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X1),multiply(greatest_lower_bound(identity,least_upper_bound(identity,X1)),X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1849.0.0','0.964.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2.2.1.2','L')]).
% 5.12/5.52 cnf('0.1849.0.2',plain,
% 5.12/5.52 ( least_upper_bound(identity,multiply(X1,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,greatest_lower_bound(inverse(X1),identity)),X2)))) = least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X1),multiply(greatest_lower_bound(identity,least_upper_bound(identity,X1)),X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1849.0.1','0.26.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2.2.1.2.2','L')]).
% 5.12/5.52 cnf('0.1849.0.3',plain,
% 5.12/5.52 ( least_upper_bound(identity,multiply(X1,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X1)),X2)))) = least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X1),multiply(greatest_lower_bound(identity,least_upper_bound(identity,X1)),X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1849.0.2','0.21.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2.2.1','L')]).
% 5.12/5.52 cnf('0.1849.0.4',plain,
% 5.12/5.52 ( least_upper_bound(identity,greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))) = least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X1),multiply(greatest_lower_bound(identity,least_upper_bound(identity,X1)),X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1849.0.3','0.1500.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2','L')]).
% 5.12/5.52 cnf('0.1849.0.5',plain,
% 5.12/5.52 ( least_upper_bound(identity,greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))) = least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X1),multiply(identity,X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1849.0.4','0.3.2.0',theory(equality)]),
% 5.12/5.52 [pos('R.2.2.1','L')]).
% 5.12/5.52 cnf('0.1849.0.6',plain,
% 5.12/5.52 ( least_upper_bound(identity,greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))) = least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X1),X2)) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1849.0.5','0.1.2.0',theory(equality)]),
% 5.12/5.52 [pos('R.2.2','L')]).
% 5.12/5.52 cnf('0.1849.1.0',plain,
% 5.12/5.52 ( least_upper_bound(identity,greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))) = least_upper_bound(identity,greatest_lower_bound(least_upper_bound(identity,X1),X2)) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.1849.0.6']),
% 5.12/5.52 [weight('<9,1500,1205,[0,0,0,2]>')]).
% 5.12/5.52 cnf('0.1849.1.1',plain,
% 5.12/5.52 ( least_upper_bound(identity,greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))) = greatest_lower_bound(least_upper_bound(X1,identity),least_upper_bound(X2,identity)) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1849.1.0','0.1778.2.0',theory(equality)]),
% 5.12/5.52 [pos('R','L')]).
% 5.12/5.52 cnf('0.1849.2.0',plain,
% 5.12/5.52 ( least_upper_bound(identity,greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))) = greatest_lower_bound(least_upper_bound(X1,identity),least_upper_bound(X2,identity)) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.1849.1.1',theory(equality)]),
% 5.12/5.52 [u,rule_1801]).
% 5.12/5.52 cnf('0.1854.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,multiply(X1,least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))),X2)))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X1),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X1)),X2))) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.872.2.0','0.1505.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2','L')]).
% 5.12/5.52 cnf('0.1854.0.1',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,multiply(X1,least_upper_bound(identity,multiply(least_upper_bound(identity,least_upper_bound(inverse(X1),inverse(identity))),X2)))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X1),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X1)),X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1854.0.0','0.962.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2.2.1.2','L')]).
% 5.12/5.52 cnf('0.1854.0.2',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,multiply(X1,least_upper_bound(identity,multiply(least_upper_bound(identity,least_upper_bound(inverse(X1),identity)),X2)))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X1),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X1)),X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1854.0.1','0.26.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2.2.1.2.2','L')]).
% 5.12/5.52 cnf('0.1854.0.3',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,multiply(X1,least_upper_bound(identity,multiply(least_upper_bound(identity,inverse(X1)),X2)))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X1),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X1)),X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1854.0.2','0.20.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2.2.1','L')]).
% 5.12/5.52 cnf('0.1854.0.4',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,multiply(least_upper_bound(identity,X1),X2))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X1),multiply(least_upper_bound(identity,greatest_lower_bound(identity,X1)),X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1854.0.3','0.1505.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2','L')]).
% 5.12/5.52 cnf('0.1854.0.5',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,multiply(least_upper_bound(identity,X1),X2))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X1),multiply(identity,X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1854.0.4','0.5.2.0',theory(equality)]),
% 5.12/5.52 [pos('R.2.2.1','L')]).
% 5.12/5.52 cnf('0.1854.0.6',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,multiply(least_upper_bound(identity,X1),X2))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1854.0.5','0.1.2.0',theory(equality)]),
% 5.12/5.52 [pos('R.2.2','L')]).
% 5.12/5.52 cnf('0.1854.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,multiply(least_upper_bound(identity,X1),X2))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X1),X2)) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.1854.0.6']),
% 5.12/5.52 [weight('<9,1505,872,[0,0,0,2]>')]).
% 5.12/5.52 cnf('0.1854.1.1',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,multiply(least_upper_bound(identity,X1),X2))) = greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(X2,identity))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1854.1.0','0.1782.2.0',theory(equality)]),
% 5.12/5.52 [pos('R','L')]).
% 5.12/5.52 cnf('0.1854.2.0',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,multiply(least_upper_bound(identity,X1),X2))) = greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(X2,identity))) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.1854.1.1',theory(equality)]),
% 5.12/5.52 [u,rule_1805]).
% 5.12/5.52 cnf('0.1956.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(greatest_lower_bound(X3,X4),X2)) = least_upper_bound(X2,greatest_lower_bound(X3,greatest_lower_bound(X4,least_upper_bound(X1,X2)))) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1771.2.0','0.13.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2','L')]).
% 5.12/5.52 cnf('0.1956.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(greatest_lower_bound(X3,X4),X2)) = least_upper_bound(X2,greatest_lower_bound(X3,greatest_lower_bound(X4,least_upper_bound(X1,X2)))) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.1956.0.0']),
% 5.12/5.52 [weight('<9,1771,13,[1,0,0,2]>')]).
% 5.12/5.52 cnf('0.1956.2.0',plain,
% 5.12/5.52 ( least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,least_upper_bound(X4,X1)))) = greatest_lower_bound(least_upper_bound(X4,X1),least_upper_bound(greatest_lower_bound(X2,X3),X1)) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.1956.1.0',theory(equality)]),
% 5.12/5.52 [x,rule_1906]).
% 5.12/5.52 cnf('0.1958.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X2),X3),least_upper_bound(X4,X3)) = least_upper_bound(X3,greatest_lower_bound(X4,least_upper_bound(X1,least_upper_bound(X2,X3)))) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1771.2.0','0.15.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2','L')]).
% 5.12/5.52 cnf('0.1958.0.1',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(X1,least_upper_bound(X2,X3)),least_upper_bound(X4,X3)) = least_upper_bound(X3,greatest_lower_bound(X4,least_upper_bound(X1,least_upper_bound(X2,X3)))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1958.0.0','0.15.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.1','L')]).
% 5.12/5.52 cnf('0.1958.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(X1,least_upper_bound(X2,X3)),least_upper_bound(X4,X3)) = least_upper_bound(X3,greatest_lower_bound(X4,least_upper_bound(X1,least_upper_bound(X2,X3)))) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.1958.0.1']),
% 5.12/5.52 [weight('<9,1771,15,[1,0,0,4]>')]).
% 5.12/5.52 cnf('0.1958.2.0',plain,
% 5.12/5.52 ( least_upper_bound(X1,greatest_lower_bound(X2,least_upper_bound(X3,least_upper_bound(X4,X1)))) = greatest_lower_bound(least_upper_bound(X3,least_upper_bound(X4,X1)),least_upper_bound(X2,X1)) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.1958.1.0',theory(equality)]),
% 5.12/5.52 [x,rule_1908]).
% 5.12/5.52 cnf('0.1996.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X2,least_upper_bound(X1,X3)),X4)) = greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X3),least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X3),X4)))) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.46.2.0','0.1781.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2','L')]).
% 5.12/5.52 cnf('0.1996.0.1',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X2,least_upper_bound(X1,X3)),X4)) = greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X3),X4))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.1996.0.0','0.46.2.0',theory(equality)]),
% 5.12/5.52 [pos('R','L')]).
% 5.12/5.52 cnf('0.1996.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X2,least_upper_bound(X1,X3)),X4)) = greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X3),X4))) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.1996.0.1']),
% 5.12/5.52 [weight('<9,1781,46,[0,0,0,2]>')]).
% 5.12/5.52 cnf('0.1996.2.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X2,least_upper_bound(X1,X3)),X4)) = greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X3),X4))) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.1996.1.0',theory(equality)]),
% 5.12/5.52 [u,rule_1945]).
% 5.12/5.52 cnf('0.2048.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(X2,identity))) = greatest_lower_bound(identity,least_upper_bound(X1,least_upper_bound(X2,multiply(X1,X2)))) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1854.2.0','0.612.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2','L')]).
% 5.12/5.52 cnf('0.2048.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(X2,identity))) = greatest_lower_bound(identity,least_upper_bound(X1,least_upper_bound(X2,multiply(X1,X2)))) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.2048.0.0']),
% 5.12/5.52 [weight('<9,1854,612,[1,0,0,4]>')]).
% 5.12/5.52 cnf('0.2048.2.0',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,least_upper_bound(X2,multiply(X1,X2)))) = greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(X2,identity))) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.2048.1.0',theory(equality)]),
% 5.12/5.52 [x,rule_1994]).
% 5.12/5.52 cnf('0.2083.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(greatest_lower_bound(X3,X4),X2)) = least_upper_bound(X2,greatest_lower_bound(X3,greatest_lower_bound(X4,least_upper_bound(X2,X1)))) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1956.2.0','0.14.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2.2','L')]).
% 5.12/5.52 cnf('0.2083.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(greatest_lower_bound(X3,X4),X2)) = least_upper_bound(X2,greatest_lower_bound(X3,greatest_lower_bound(X4,least_upper_bound(X2,X1)))) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.2083.0.0']),
% 5.12/5.52 [weight('<9,1956,14,[1,0,0,6]>')]).
% 5.12/5.52 cnf('0.2083.2.0',plain,
% 5.12/5.52 ( least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,least_upper_bound(X1,X4)))) = greatest_lower_bound(least_upper_bound(X4,X1),least_upper_bound(greatest_lower_bound(X2,X3),X1)) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.2083.1.0',theory(equality)]),
% 5.12/5.52 [x,rule_2029]).
% 5.12/5.52 cnf('0.2090.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))),least_upper_bound(X4,greatest_lower_bound(X3,X1))) = least_upper_bound(greatest_lower_bound(X3,X1),greatest_lower_bound(X4,least_upper_bound(X1,X2))) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1958.2.0','0.62.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2','L')]).
% 5.12/5.52 cnf('0.2090.0.1',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X4,greatest_lower_bound(X3,X1))) = least_upper_bound(greatest_lower_bound(X3,X1),greatest_lower_bound(X4,least_upper_bound(X1,X2))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.2090.0.0','0.62.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.1','L')]).
% 5.12/5.52 cnf('0.2090.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X4,greatest_lower_bound(X3,X1))) = least_upper_bound(greatest_lower_bound(X3,X1),greatest_lower_bound(X4,least_upper_bound(X1,X2))) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.2090.0.1']),
% 5.12/5.52 [weight('<9,1958,62,[1,0,0,4]>')]).
% 5.12/5.52 cnf('0.2090.2.0',plain,
% 5.12/5.52 ( least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X3,least_upper_bound(X2,X4))) = greatest_lower_bound(least_upper_bound(X2,X4),least_upper_bound(X3,greatest_lower_bound(X1,X2))) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.2090.1.0',theory(equality)]),
% 5.12/5.52 [x,rule_2036]).
% 5.12/5.52 cnf('0.2115.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X3),X4))) = greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(least_upper_bound(X1,X3),X2),X4)) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.1996.2.0','0.12.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.1','L')]).
% 5.12/5.52 cnf('0.2115.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X3),X4))) = greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(least_upper_bound(X1,X3),X2),X4)) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.2115.0.0']),
% 5.12/5.52 [weight('<9,1996,12,[1,0,0,3]>')]).
% 5.12/5.52 cnf('0.2115.2.0',plain,
% 5.12/5.52 ( greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(least_upper_bound(X1,X2),X3),X4)) = greatest_lower_bound(X1,least_upper_bound(X3,greatest_lower_bound(least_upper_bound(X1,X2),X4))) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.2115.1.0',theory(equality)]),
% 5.12/5.52 [x,rule_2056]).
% 5.12/5.52 cnf('0.2143.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(X2,identity))) = greatest_lower_bound(identity,least_upper_bound(X2,least_upper_bound(multiply(X1,X2),X1))) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.2048.2.0','0.703.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2','R')]).
% 5.12/5.52 cnf('0.2143.1.0',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(X2,identity))) = greatest_lower_bound(identity,least_upper_bound(X2,least_upper_bound(multiply(X1,X2),X1))) ),
% 5.12/5.52 inference(weigh,[status(thm)],['0.2143.0.0']),
% 5.12/5.52 [weight('<9,2048,703,[1,0,1,2]>')]).
% 5.12/5.52 cnf('0.2143.1.1',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(X2,identity))) = greatest_lower_bound(identity,least_upper_bound(X2,least_upper_bound(X1,multiply(X1,X2)))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.2143.1.0','0.14.2.0',theory(equality)]),
% 5.12/5.52 [pos('R.2.2','L')]).
% 5.12/5.52 cnf('0.2143.2.0',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,least_upper_bound(X2,multiply(X2,X1)))) = greatest_lower_bound(identity,least_upper_bound(X2,greatest_lower_bound(X1,identity))) ),
% 5.12/5.52 inference(orient,[status(thm)],['0.2143.1.1',theory(equality)]),
% 5.12/5.52 [x,rule_2084]).
% 5.12/5.52 cnf('0.2144.0.0',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,X1),X2),identity))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X1),X2),least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))))) ),
% 5.12/5.52 inference(cp,[status(thm)],['0.2143.2.0','0.1407.2.0',theory(equality)]),
% 5.12/5.52 [pos('L.2.2.2','L')]).
% 5.12/5.52 cnf('0.2144.0.1',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,X1),X2),identity),identity))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X1),X2),least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.2144.0.0','0.1782.2.0',theory(equality)]),
% 5.12/5.52 [pos('L','L')]).
% 5.12/5.52 cnf('0.2144.0.2',plain,
% 5.12/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(greatest_lower_bound(least_upper_bound(identity,X1),X2),greatest_lower_bound(identity,identity)))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X1),X2),least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))))) ),
% 5.12/5.52 inference(reduction,[status(thm)],['0.2144.0.1','0.13.2.0',theory(equality)]),
% 5.13/5.52 [pos('L.2.2','L')]).
% 5.13/5.52 cnf('0.2144.0.3',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(least_upper_bound(identity,X1),greatest_lower_bound(X2,greatest_lower_bound(identity,identity))))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X1),X2),least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.2','0.13.2.0',theory(equality)]),
% 5.13/5.52 [pos('L.2.2','L')]).
% 5.13/5.52 cnf('0.2144.0.4',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,greatest_lower_bound(identity,X2)))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X1),X2),least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.3','0.1522.2.0',theory(equality)]),
% 5.13/5.52 [pos('L.2.2','L')]).
% 5.13/5.52 cnf('0.2144.0.5',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X1),X2),least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.4','0.17.2.0',theory(equality)]),
% 5.13/5.52 [pos('L.2.2','L')]).
% 5.13/5.52 cnf('0.2144.0.6',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2)))))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.5','0.2115.2.0',theory(equality)]),
% 5.13/5.52 [pos('R','L')]).
% 5.13/5.52 cnf('0.2144.0.7',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(identity,X1),greatest_lower_bound(X1,least_upper_bound(identity,greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),X2))))))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.6','0.1776.2.0',theory(equality)]),
% 5.13/5.52 [pos('R.2.2.2','L')]).
% 5.13/5.52 cnf('0.2144.0.8',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(identity,X1),greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,identity),least_upper_bound(X2,identity)))))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.7','0.1849.2.0',theory(equality)]),
% 5.13/5.52 [pos('R.2.2.2.2','L')]).
% 5.13/5.52 cnf('0.2144.0.9',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(identity,X1),greatest_lower_bound(X1,least_upper_bound(X2,identity))))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.8','0.46.2.0',theory(equality)]),
% 5.13/5.52 [pos('R.2.2.2','L')]).
% 5.13/5.52 cnf('0.2144.0.10',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X2),least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X1),X1),X2))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.9','0.2083.2.0',theory(equality)]),
% 5.13/5.52 [pos('R.2','L')]).
% 5.13/5.52 cnf('0.2144.0.11',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,least_upper_bound(greatest_lower_bound(least_upper_bound(identity,X1),X1),X2)) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.10','0.46.2.0',theory(equality)]),
% 5.13/5.52 [pos('R','L')]).
% 5.13/5.52 cnf('0.2144.0.12',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(least_upper_bound(identity,X1),X2))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.11','0.2115.2.0',theory(equality)]),
% 5.13/5.52 [pos('R','L')]).
% 5.13/5.52 cnf('0.2144.0.13',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(X2,X1))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.12','0.1773.2.0',theory(equality)]),
% 5.13/5.52 [pos('R.2','L')]).
% 5.13/5.52 cnf('0.2144.0.14',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,least_upper_bound(X2,X1)) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2144.0.13','0.46.2.0',theory(equality)]),
% 5.13/5.52 [pos('R','L')]).
% 5.13/5.52 cnf('0.2144.1.0',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,least_upper_bound(X2,X1)) ),
% 5.13/5.52 inference(weigh,[status(thm)],['0.2144.0.14']),
% 5.13/5.52 [weight('<7,2143,1407,[1,0,0,6]>')]).
% 5.13/5.52 cnf('0.2144.2.0',plain,
% 5.13/5.52 ( greatest_lower_bound(identity,least_upper_bound(X1,greatest_lower_bound(identity,X2))) = greatest_lower_bound(identity,least_upper_bound(X2,X1)) ),
% 5.13/5.52 inference(orient,[status(thm)],['0.2144.1.0',theory(equality)]),
% 5.13/5.52 [u,rule_2085]).
% 5.13/5.52 cnf('0.2146.0.0',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(identity,X2)) = least_upper_bound(least_upper_bound(X1,greatest_lower_bound(identity,X2)),greatest_lower_bound(identity,least_upper_bound(X2,X1))) ),
% 5.13/5.52 inference(cp,[status(thm)],['0.16.2.0','0.2144.2.0',theory(equality)]),
% 5.13/5.52 [pos('L.2','L')]).
% 5.13/5.52 cnf('0.2146.0.1',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(identity,X2)) = least_upper_bound(X1,least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,least_upper_bound(X2,X1)))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2146.0.0','0.15.2.0',theory(equality)]),
% 5.13/5.52 [pos('R','L')]).
% 5.13/5.52 cnf('0.2146.0.2',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(identity,X2)) = least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(identity,greatest_lower_bound(identity,X2)))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2146.0.1','0.2090.2.0',theory(equality)]),
% 5.13/5.52 [pos('R.2','L')]).
% 5.13/5.52 cnf('0.2146.0.3',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(least_upper_bound(identity,greatest_lower_bound(identity,X2)),X1)) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2146.0.2','0.1773.2.0',theory(equality)]),
% 5.13/5.52 [pos('R','L')]).
% 5.13/5.52 cnf('0.2146.0.4',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X2),X1))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2146.0.3','0.15.2.0',theory(equality)]),
% 5.13/5.52 [pos('R.2','L')]).
% 5.13/5.52 cnf('0.2146.0.5',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(identity,X1)) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2146.0.4','0.47.2.0',theory(equality)]),
% 5.13/5.52 [pos('R.2','L')]).
% 5.13/5.52 cnf('0.2146.1.0',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(identity,X1)) ),
% 5.13/5.52 inference(weigh,[status(thm)],['0.2146.0.5']),
% 5.13/5.52 [weight('<7,2144,16,[0,0,0,2]>')]).
% 5.13/5.52 cnf('0.2146.2.0',plain,
% 5.13/5.52 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(identity,X2)) = least_upper_bound(X2,greatest_lower_bound(identity,X1)) ),
% 5.13/5.52 inference(orient,[status(thm)],['0.2146.1.0',theory(equality)]),
% 5.13/5.52 [x,rule_2087]).
% 5.13/5.52 cnf('0.2149.0.0',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(X2,X1)) ),
% 5.13/5.52 inference(cp,[status(thm)],['0.2146.2.0','0.12.2.0',theory(equality)]),
% 5.13/5.52 [pos('L','L')]).
% 5.13/5.52 cnf('0.2149.1.0',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(X2,X1)) ),
% 5.13/5.52 inference(weigh,[status(thm)],['0.2149.0.0']),
% 5.13/5.52 [weight('<7,2146,0,[1,0,0,0]>')]).
% 5.13/5.52 cnf('0.2149.2.0',plain,
% 5.13/5.52 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(X2,X1)) = least_upper_bound(X1,greatest_lower_bound(identity,X2)) ),
% 5.13/5.52 inference(orient,[status(thm)],['0.2149.1.0',theory(equality)]),
% 5.13/5.52 [x,rule_2090]).
% 5.13/5.52 cnf('0.2163.0.0',plain,
% 5.13/5.52 ( least_upper_bound(multiply(X1,X2),greatest_lower_bound(identity,multiply(X1,X3))) = greatest_lower_bound(least_upper_bound(identity,multiply(X1,X2)),multiply(X1,least_upper_bound(X3,X2))) ),
% 5.13/5.52 inference(cp,[status(thm)],['0.2149.2.0','0.8.2.0',theory(equality)]),
% 5.13/5.52 [pos('L.2','L')]).
% 5.13/5.52 cnf('0.2163.0.1',plain,
% 5.13/5.52 ( multiply(X1,least_upper_bound(X2,greatest_lower_bound(inverse(X1),X3))) = greatest_lower_bound(least_upper_bound(identity,multiply(X1,X2)),multiply(X1,least_upper_bound(X3,X2))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2163.0.0','0.585.2.0',theory(equality)]),
% 5.13/5.52 [pos('L','L')]).
% 5.13/5.52 cnf('0.2163.0.2',plain,
% 5.13/5.52 ( multiply(X1,least_upper_bound(X2,greatest_lower_bound(inverse(X1),X3))) = multiply(X1,greatest_lower_bound(least_upper_bound(inverse(X1),X2),least_upper_bound(X3,X2))) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2163.0.1','0.586.2.0',theory(equality)]),
% 5.13/5.52 [pos('R','L')]).
% 5.13/5.52 cnf('0.2163.1.0',plain,
% 5.13/5.52 ( least_upper_bound(X2,greatest_lower_bound(inverse(X1),X3)) = greatest_lower_bound(least_upper_bound(inverse(X1),X2),least_upper_bound(X3,X2)) ),
% 5.13/5.52 inference(weigh,[status(thm)],['0.2163.0.2']),
% 5.13/5.52 [weight('<8,2149,8,[1,0,0,4]>')]).
% 5.13/5.52 cnf('0.2163.2.0',plain,
% 5.13/5.52 ( greatest_lower_bound(least_upper_bound(inverse(X1),X2),least_upper_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(inverse(X1),X3)) ),
% 5.13/5.52 inference(orient,[status(thm)],['0.2163.1.0',theory(equality)]),
% 5.13/5.52 [x,rule_2104]).
% 5.13/5.52 cnf('0.2164.0.0',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(inverse(inverse(X2)),X3)) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(X3,X1)) ),
% 5.13/5.52 inference(cp,[status(thm)],['0.2163.2.0','0.23.2.0',theory(equality)]),
% 5.13/5.52 [pos('L.1.1','L')]).
% 5.13/5.52 cnf('0.2164.0.1',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(X3,X1)) ),
% 5.13/5.52 inference(reduction,[status(thm)],['0.2164.0.0','0.23.2.0',theory(equality)]),
% 5.13/5.52 [pos('L.2.1','L')]).
% 5.13/5.52 cnf('0.2164.1.0',plain,
% 5.13/5.52 ( least_upper_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(least_upper_bound(X2,X1),least_upper_bound(X3,X1)) ),
% 5.13/5.52 inference(weigh,[status(thm)],['0.2164.0.1']),
% 5.13/5.52 [weight('<7,2163,23,[1,0,0,2]>')]).
% 5.13/5.52 cnf('0.2164.2.0',plain,
% 5.13/5.52 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(X1,X3)) ),
% 5.13/5.52 inference(orient,[status(thm)],['0.2164.1.0',theory(equality)]),
% 5.13/5.52 [x,rule_2105]).
% 5.13/5.52 cnf('1.0.0.0',conjecture,
% 5.13/5.52 ( greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) = least_upper_bound(a,greatest_lower_bound(b,c)) ),
% 5.13/5.52 file('/tmp/WALDMEISTER_28551_n023',conjecture_1)).
% 5.13/5.52 cnf('1.0.0.1',plain,
% 5.13/5.52 ( greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(a,b)) = least_upper_bound(a,greatest_lower_bound(b,c)) ),
% 5.13/5.52 inference(reduction,[status(thm)],['1.0.0.0','0.12.2.0',theory(equality)]),
% 5.13/5.52 [pos('L','L')]).
% 5.13/5.52 cnf('1.0.0.2',plain,
% 5.13/5.52 ( greatest_lower_bound(least_upper_bound(c,a),least_upper_bound(a,b)) = least_upper_bound(a,greatest_lower_bound(b,c)) ),
% 5.13/5.52 inference(reduction,[status(thm)],['1.0.0.1','0.14.2.0',theory(equality)]),
% 5.13/5.52 [pos('L.1','L')]).
% 5.13/5.52 cnf('1.0.0.3',plain,
% 5.13/5.52 ( greatest_lower_bound(least_upper_bound(c,a),least_upper_bound(b,a)) = least_upper_bound(a,greatest_lower_bound(b,c)) ),
% 5.13/5.52 inference(reduction,[status(thm)],['1.0.0.2','0.14.2.0',theory(equality)]),
% 5.13/5.52 [pos('L.2','L')]).
% 5.13/5.52 cnf('1.0.0.4',plain,
% 5.13/5.52 ( least_upper_bound(a,greatest_lower_bound(c,b)) = least_upper_bound(a,greatest_lower_bound(b,c)) ),
% 5.13/5.52 inference(reduction,[status(thm)],['1.0.0.3','0.2164.2.0',theory(equality)]),
% 5.13/5.52 [pos('L','L')]).
% 5.13/5.52 cnf('1.0.0.5',plain,
% 5.13/5.52 ( least_upper_bound(a,greatest_lower_bound(c,b)) = least_upper_bound(a,greatest_lower_bound(c,b)) ),
% 5.13/5.52 inference(reduction,[status(thm)],['1.0.0.4','0.12.2.0',theory(equality)]),
% 5.13/5.52 [pos('R.2','L')]).
% 5.13/5.52 cnf('1.0.0.6',plain,
% 5.13/5.52 ( $true ),
% 5.13/5.52 inference(trivial,[status(thm)],['1.0.0.5',theory(equality)]),
% 5.13/5.52 [conjecture_1]).
% 5.13/5.52
% 5.13/5.52 Proved Goals:
% 5.13/5.52 No. 1: greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)) ?= least_upper_bound(a,greatest_lower_bound(b,c)) joined, current: least_upper_bound(a,greatest_lower_bound(c,b)) = least_upper_bound(a,greatest_lower_bound(c,b))
% 5.13/5.52 1 goal was specified, which was proved.
% 5.13/5.52 % SZS output end CNFRefutation
% 5.13/5.52 #END OF PROOF
% 5.13/5.52
% 5.13/5.52 Problem WALDMEISTER_28551_n023
% 5.13/5.52 CPs.gen 836560
% 5.13/5.52 CPs.reexp 0
% 5.13/5.52 Select 44205
% 5.13/5.52 R 2105
% 5.13/5.52 E 59
% 5.13/5.52 vsize 9.9M
% 5.13/5.52 rss 5.4M
% 5.13/5.52 process.time 3.646s
% 5.13/5.52 wallclock.time 4.503s
% 5.13/5.52 status S
% 5.13/5.52
% 5.13/5.52
% 5.13/5.52 Waldmeister states: Goal proved.
% 5.13/5.52 % SZS status Unsatisfiable
% 5.13/5.52
% 5.13/5.52 Problem WALDMEISTER_28551_n023
% 5.13/5.52 CPs.gen 267811
% 5.13/5.52 CPs.reexp 0
% 5.13/5.52 Select 16995
% 5.13/5.52 R 1101
% 5.13/5.52 E 12
% 5.13/5.52 vsize 7.1M
% 5.13/5.52 rss 4.5M
% 5.13/5.52 process.time 0.858s
% 5.13/5.52 wallclock.time 4.504s
% 5.13/5.52 status S
%------------------------------------------------------------------------------