TSTP Solution File: GRP187-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP187-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 12:25:16 EDT 2022
% Result : Unsatisfiable 5.34s 5.80s
% Output : CNFRefutation 5.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP187-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : woody %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 06:49:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.74/1.15 ********************************************************************************
% 0.74/1.15 * W A L D M E I S T E R \| \ / \|/ *
% 0.74/1.15 * |/ | \/ | *
% 0.74/1.15 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.74/1.15 * A. Jaeger and B. Loechner | | *
% 0.74/1.15 * <waldmeister@informatik.uni-kl.de> | *
% 0.74/1.15 ********************************************************************************
% 0.74/1.15
% 0.74/1.15
% 0.74/1.15 Goals:
% 0.74/1.15 ------
% 0.74/1.15
% 0.74/1.15 ( 1) multiply(a,b) ?=? multiply(b,a)
% 0.74/1.15
% 0.74/1.15 Detected structure: VerbandsgeordneteGruppe
% 0.74/1.15 ********************************************************************************
% 0.74/1.15 ****************************** COMPLETION - PROOF ******************************
% 0.74/1.15 ********************************************************************************
% 0.74/1.15
% 5.34/5.80 joined goal: 1 multiply(a,b) ?= multiply(b,a) to multiply(b,a)
% 5.34/5.80 goal joined
% 5.34/5.80 % SZS status Unsatisfiable
% 5.34/5.80 #START OF PROOF
% 5.34/5.80 % SZS output start CNFRefutation
% 5.34/5.80 cnf('0.1.0.0',axiom,
% 5.34/5.80 ( X1 = multiply(identity,X1) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.1.1.0',plain,
% 5.34/5.80 ( X1 = multiply(identity,X1) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.1.0.0']),
% 5.34/5.80 [weight('<0,0,0,[0,0,0,1]>')]).
% 5.34/5.80 cnf('0.1.2.0',plain,
% 5.34/5.80 ( multiply(identity,X1) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_1]).
% 5.34/5.80 cnf('0.2.0.0',axiom,
% 5.34/5.80 ( X1 = least_upper_bound(X1,X1) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.2.1.0',plain,
% 5.34/5.80 ( X1 = least_upper_bound(X1,X1) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.2.0.0']),
% 5.34/5.80 [weight('<1,0,0,[0,0,0,2]>')]).
% 5.34/5.80 cnf('0.2.2.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,X1) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_2]).
% 5.34/5.80 cnf('0.3.0.0',axiom,
% 5.34/5.80 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.3.1.0',plain,
% 5.34/5.80 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.3.0.0']),
% 5.34/5.80 [weight('<2,0,0,[0,0,0,3]>')]).
% 5.34/5.80 cnf('0.3.2.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_3]).
% 5.34/5.80 cnf('0.4.0.0',axiom,
% 5.34/5.80 ( X1 = greatest_lower_bound(X1,X1) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.4.1.0',plain,
% 5.34/5.80 ( X1 = greatest_lower_bound(X1,X1) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.4.0.0']),
% 5.34/5.80 [weight('<3,0,0,[0,0,0,4]>')]).
% 5.34/5.80 cnf('0.4.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,X1) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_4]).
% 5.34/5.80 cnf('0.5.0.0',axiom,
% 5.34/5.80 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.5.1.0',plain,
% 5.34/5.80 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.5.0.0']),
% 5.34/5.80 [weight('<4,0,0,[0,0,0,5]>')]).
% 5.34/5.80 cnf('0.5.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_5]).
% 5.34/5.80 cnf('0.6.0.0',axiom,
% 5.34/5.80 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.6.1.0',plain,
% 5.34/5.80 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.6.0.0']),
% 5.34/5.80 [weight('<5,0,0,[0,0,0,6]>')]).
% 5.34/5.80 cnf('0.6.2.0',plain,
% 5.34/5.80 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_6]).
% 5.34/5.80 cnf('0.7.0.0',axiom,
% 5.34/5.80 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.7.1.0',plain,
% 5.34/5.80 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.7.0.0']),
% 5.34/5.80 [weight('<6,0,0,[0,0,0,7]>')]).
% 5.34/5.80 cnf('0.7.2.0',plain,
% 5.34/5.80 ( least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_7]).
% 5.34/5.80 cnf('0.8.0.0',axiom,
% 5.34/5.80 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.8.1.0',plain,
% 5.34/5.80 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.8.0.0']),
% 5.34/5.80 [weight('<7,0,0,[0,0,0,8]>')]).
% 5.34/5.80 cnf('0.8.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_8]).
% 5.34/5.80 cnf('0.9.0.0',axiom,
% 5.34/5.80 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.9.1.0',plain,
% 5.34/5.80 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.9.0.0']),
% 5.34/5.80 [weight('<8,0,0,[0,0,0,9]>')]).
% 5.34/5.80 cnf('0.9.2.0',plain,
% 5.34/5.80 ( least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_9]).
% 5.34/5.80 cnf('0.10.0.0',axiom,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.10.1.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.10.0.0']),
% 5.34/5.80 [weight('<9,0,0,[0,0,0,10]>')]).
% 5.34/5.80 cnf('0.10.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_10]).
% 5.34/5.80 cnf('0.11.0.0',axiom,
% 5.34/5.80 ( multiply(inverse(X1),X1) = identity ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.11.1.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),X1) = identity ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.11.0.0']),
% 5.34/5.80 [weight('<10,0,0,[0,0,0,11]>')]).
% 5.34/5.80 cnf('0.11.2.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),X1) = identity ),
% 5.34/5.80 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_11]).
% 5.34/5.80 cnf('0.12.0.0',axiom,
% 5.34/5.80 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.12.1.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.12.0.0']),
% 5.34/5.80 [weight('<11,0,0,[0,0,0,12]>')]).
% 5.34/5.80 cnf('0.12.2.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 5.34/5.80 inference(activate,[status(thm)],['0.12.1.0']),
% 5.34/5.80 [equation_1]).
% 5.34/5.80 cnf('0.13.0.0',axiom,
% 5.34/5.80 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.13.1.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.13.0.0']),
% 5.34/5.80 [weight('<12,0,0,[0,0,0,13]>')]).
% 5.34/5.80 cnf('0.13.2.0',plain,
% 5.34/5.80 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_12]).
% 5.34/5.80 cnf('0.14.0.0',axiom,
% 5.34/5.80 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.14.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.14.0.0']),
% 5.34/5.80 [weight('<13,0,0,[0,0,0,14]>')]).
% 5.34/5.80 cnf('0.14.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 5.34/5.80 inference(activate,[status(thm)],['0.14.1.0']),
% 5.34/5.80 [equation_2]).
% 5.34/5.80 cnf('0.15.0.0',axiom,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.15.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.15.0.0']),
% 5.34/5.80 [weight('<14,0,0,[0,0,0,15]>')]).
% 5.34/5.80 cnf('0.15.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_13]).
% 5.34/5.80 cnf('0.16.0.0',axiom,
% 5.34/5.80 ( greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b))) = identity ),
% 5.34/5.80 file('/tmp/WALDMEISTER_6253_n011')).
% 5.34/5.80 cnf('0.16.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b))) = identity ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.16.0.0']),
% 5.34/5.80 [weight('<15,0,0,[0,0,0,16]>')]).
% 5.34/5.80 cnf('0.16.1.1',plain,
% 5.34/5.80 ( greatest_lower_bound(least_upper_bound(b,inverse(b)),least_upper_bound(a,inverse(a))) = identity ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.16.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.80 [pos('L','L')]).
% 5.34/5.80 cnf('0.16.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(least_upper_bound(b,inverse(b)),least_upper_bound(a,inverse(a))) = identity ),
% 5.34/5.80 inference(orient,[status(thm)],['0.16.1.1',theory(equality)]),
% 5.34/5.80 [u,rule_14]).
% 5.34/5.80 cnf('0.17.0.0',plain,
% 5.34/5.80 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.5.2.0','0.12.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.17.1.0',plain,
% 5.34/5.80 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.17.0.0']),
% 5.34/5.80 [weight('<5,12,5,[0,0,0,2]>')]).
% 5.34/5.80 cnf('0.17.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_15]).
% 5.34/5.80 cnf('0.18.0.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.13.2.0','0.2.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.18.1.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.18.0.0']),
% 5.34/5.80 [weight('<5,13,2,[1,0,0,1]>')]).
% 5.34/5.80 cnf('0.18.2.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_16]).
% 5.34/5.80 cnf('0.19.0.0',plain,
% 5.34/5.80 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.3.2.0','0.14.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.19.1.0',plain,
% 5.34/5.80 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.19.0.0']),
% 5.34/5.80 [weight('<5,14,3,[0,0,0,2]>')]).
% 5.34/5.80 cnf('0.19.2.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_17]).
% 5.34/5.80 cnf('0.20.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.15.2.0','0.4.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.20.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.20.0.0']),
% 5.34/5.80 [weight('<5,15,4,[1,0,0,1]>')]).
% 5.34/5.80 cnf('0.20.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_18]).
% 5.34/5.80 cnf('0.21.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(greatest_lower_bound(X1,X2),X1) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.17.2.0','0.3.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.21.0.1',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.21.0.0','0.15.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.21.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.21.0.1']),
% 5.34/5.80 [weight('<5,17,3,[1,0,0,2]>')]).
% 5.34/5.80 cnf('0.21.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_19]).
% 5.34/5.80 cnf('0.23.0.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.23.0.1',plain,
% 5.34/5.80 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.23.0.0','0.1.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.23.1.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.23.0.1']),
% 5.34/5.80 [weight('<6,11,6,[0,0,0,1]>')]).
% 5.34/5.80 cnf('0.23.2.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_21]).
% 5.34/5.80 cnf('0.24.0.0',plain,
% 5.34/5.80 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.23.2.0','0.23.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.24.1.0',plain,
% 5.34/5.80 ( X1 = inverse(inverse(X1)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.24.0.0']),
% 5.34/5.80 [weight('<3,23,23,[0,0,0,3]>')]).
% 5.34/5.80 cnf('0.24.2.0',plain,
% 5.34/5.80 ( inverse(inverse(X1)) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_22]).
% 5.34/5.80 cnf('0.26.0.0',plain,
% 5.34/5.80 ( identity = multiply(X1,inverse(X1)) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.11.2.0','0.24.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.26.1.0',plain,
% 5.34/5.80 ( identity = multiply(X1,inverse(X1)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.26.0.0']),
% 5.34/5.80 [weight('<4,24,11,[0,0,0,1]>')]).
% 5.34/5.80 cnf('0.26.2.0',plain,
% 5.34/5.80 ( multiply(X1,inverse(X1)) = identity ),
% 5.34/5.80 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_24]).
% 5.34/5.80 cnf('0.27.0.0',plain,
% 5.34/5.80 ( identity = inverse(identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.26.2.0','0.1.2.0',theory(equality)]),
% 5.34/5.80 [pos('L','L')]).
% 5.34/5.80 cnf('0.27.1.0',plain,
% 5.34/5.80 ( identity = inverse(identity) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.27.0.0']),
% 5.34/5.80 [weight('<2,26,1,[1,0,0,0]>')]).
% 5.34/5.80 cnf('0.27.2.0',plain,
% 5.34/5.80 ( inverse(identity) = identity ),
% 5.34/5.80 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_25]).
% 5.34/5.80 cnf('0.28.0.0',plain,
% 5.34/5.80 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.23.2.0','0.26.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.28.1.0',plain,
% 5.34/5.80 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.28.0.0']),
% 5.34/5.80 [weight('<4,26,23,[0,0,0,3]>')]).
% 5.34/5.80 cnf('0.28.2.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_26]).
% 5.34/5.80 cnf('0.29.0.0',plain,
% 5.34/5.80 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.28.2.0','0.24.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.29.0.1',plain,
% 5.34/5.80 ( X1 = multiply(X1,identity) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.29.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.80 [pos('L','L')]).
% 5.34/5.80 cnf('0.29.1.0',plain,
% 5.34/5.80 ( X1 = multiply(X1,identity) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.29.0.1']),
% 5.34/5.80 [weight('<3,28,24,[1,0,0,1]>')]).
% 5.34/5.80 cnf('0.29.2.0',plain,
% 5.34/5.80 ( multiply(X1,identity) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_27]).
% 5.34/5.80 cnf('0.31.0.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(multiply(inverse(X1),X2),identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.7.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.31.1.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(multiply(inverse(X1),X2),identity) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.31.0.0']),
% 5.34/5.80 [weight('<6,11,7,[0,0,0,4]>')]).
% 5.34/5.80 cnf('0.31.1.1',plain,
% 5.34/5.80 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.31.1.0','0.12.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.31.2.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.31.1.1',theory(equality)]),
% 5.34/5.80 [u,rule_29]).
% 5.34/5.80 cnf('0.32.0.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),greatest_lower_bound(X1,X2)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.8.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.32.1.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),greatest_lower_bound(X1,X2)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.32.0.0']),
% 5.34/5.80 [weight('<6,11,8,[0,0,0,1]>')]).
% 5.34/5.80 cnf('0.32.2.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),greatest_lower_bound(X1,X2)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.32.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_30]).
% 5.34/5.80 cnf('0.33.0.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(multiply(inverse(X1),X2),identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.8.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.33.1.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(multiply(inverse(X1),X2),identity) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.33.0.0']),
% 5.34/5.80 [weight('<6,11,8,[0,0,0,4]>')]).
% 5.34/5.80 cnf('0.33.1.1',plain,
% 5.34/5.80 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.33.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.33.2.0',plain,
% 5.34/5.80 ( multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.33.1.1',theory(equality)]),
% 5.34/5.80 [u,rule_31]).
% 5.34/5.80 cnf('0.36.0.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(inverse(X1),X2),X1) = greatest_lower_bound(identity,multiply(X2,X1)) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.10.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.36.1.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(inverse(X1),X2),X1) = greatest_lower_bound(identity,multiply(X2,X1)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.36.0.0']),
% 5.34/5.80 [weight('<6,11,10,[0,0,0,1]>')]).
% 5.34/5.80 cnf('0.36.2.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(inverse(X1),X2),X1) = greatest_lower_bound(identity,multiply(X2,X1)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_34]).
% 5.34/5.80 cnf('0.37.0.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(multiply(X1,X2),identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.10.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.37.1.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(multiply(X1,X2),identity) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.37.0.0']),
% 5.34/5.80 [weight('<6,11,10,[0,0,0,4]>')]).
% 5.34/5.80 cnf('0.37.1.1',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X1,X2)) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.37.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.37.2.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X1,X2)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.37.1.1',theory(equality)]),
% 5.34/5.80 [u,rule_35]).
% 5.34/5.80 cnf('0.47.0.0',plain,
% 5.34/5.80 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(multiply(X1,inverse(X2)),identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.9.2.0','0.26.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.47.1.0',plain,
% 5.34/5.80 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(multiply(X1,inverse(X2)),identity) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.47.0.0']),
% 5.34/5.80 [weight('<6,26,9,[0,0,0,4]>')]).
% 5.34/5.80 cnf('0.47.1.1',plain,
% 5.34/5.80 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.47.1.0','0.12.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.47.2.0',plain,
% 5.34/5.80 ( multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.47.1.1',theory(equality)]),
% 5.34/5.80 [u,rule_45]).
% 5.34/5.80 cnf('0.48.0.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,X2),inverse(X1)) = greatest_lower_bound(identity,multiply(X2,inverse(X1))) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.10.2.0','0.26.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.48.1.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,X2),inverse(X1)) = greatest_lower_bound(identity,multiply(X2,inverse(X1))) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.48.0.0']),
% 5.34/5.80 [weight('<6,26,10,[0,0,0,1]>')]).
% 5.34/5.80 cnf('0.48.2.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,X2),inverse(X1)) = greatest_lower_bound(identity,multiply(X2,inverse(X1))) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_46]).
% 5.34/5.80 cnf('0.49.0.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(multiply(X1,inverse(X2)),identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.10.2.0','0.26.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.49.1.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(multiply(X1,inverse(X2)),identity) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.49.0.0']),
% 5.34/5.80 [weight('<6,26,10,[0,0,0,4]>')]).
% 5.34/5.80 cnf('0.49.1.1',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X1,inverse(X2))) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.49.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.49.2.0',plain,
% 5.34/5.80 ( multiply(greatest_lower_bound(X1,X2),inverse(X2)) = greatest_lower_bound(identity,multiply(X1,inverse(X2))) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.49.1.1',theory(equality)]),
% 5.34/5.80 [u,rule_47]).
% 5.34/5.80 cnf('0.50.0.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = least_upper_bound(X1,X3) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.13.2.0','0.3.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.50.1.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = least_upper_bound(X1,X3) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.50.0.0']),
% 5.34/5.80 [weight('<7,13,3,[1,0,0,1]>')]).
% 5.34/5.80 cnf('0.50.2.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = least_upper_bound(X1,X3) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_48]).
% 5.34/5.80 cnf('0.51.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.15.2.0','0.5.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.51.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.51.0.0']),
% 5.34/5.80 [weight('<7,15,5,[1,0,0,1]>')]).
% 5.34/5.80 cnf('0.51.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.51.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_49]).
% 5.34/5.80 cnf('0.52.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(b,least_upper_bound(a,inverse(a))) = greatest_lower_bound(b,identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.51.2.0','0.16.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.52.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(b,least_upper_bound(a,inverse(a))) = greatest_lower_bound(b,identity) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.52.0.0']),
% 5.34/5.80 [weight('<6,51,16,[1,0,0,2]>')]).
% 5.34/5.80 cnf('0.52.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(b,least_upper_bound(a,inverse(a))) = greatest_lower_bound(b,identity) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.52.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_50]).
% 5.34/5.80 cnf('0.53.0.0',plain,
% 5.34/5.80 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.17.2.0','0.13.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.53.1.0',plain,
% 5.34/5.80 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.53.0.0']),
% 5.34/5.80 [weight('<7,17,13,[1,0,0,2]>')]).
% 5.34/5.80 cnf('0.53.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.53.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_51]).
% 5.34/5.80 cnf('0.54.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),X3)) = greatest_lower_bound(X1,X3) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.15.2.0','0.17.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.54.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),X3)) = greatest_lower_bound(X1,X3) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.54.0.0']),
% 5.34/5.80 [weight('<7,17,15,[0,0,0,1]>')]).
% 5.34/5.80 cnf('0.54.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),X3)) = greatest_lower_bound(X1,X3) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.54.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_52]).
% 5.34/5.80 cnf('0.56.0.0',plain,
% 5.34/5.80 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.19.2.0','0.15.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.56.1.0',plain,
% 5.34/5.80 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.56.0.0']),
% 5.34/5.80 [weight('<7,19,15,[1,0,0,2]>')]).
% 5.34/5.80 cnf('0.56.2.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_54]).
% 5.34/5.80 cnf('0.57.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(greatest_lower_bound(X2,X1),X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.15.2.0','0.21.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.1','L')]).
% 5.34/5.80 cnf('0.57.0.1',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.57.0.0','0.15.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.57.0.2',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.57.0.1','0.15.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.57.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.57.0.2']),
% 5.34/5.80 [weight('<7,21,15,[0,0,0,1]>')]).
% 5.34/5.80 cnf('0.57.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_55]).
% 5.34/5.80 cnf('0.58.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.21.2.0','0.15.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.58.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.58.0.0']),
% 5.34/5.80 [weight('<7,21,15,[1,0,0,2]>')]).
% 5.34/5.80 cnf('0.58.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.58.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_56]).
% 5.34/5.80 cnf('0.68.0.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = least_upper_bound(X1,greatest_lower_bound(X1,X3)) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.50.2.0','0.19.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.68.0.1',plain,
% 5.34/5.80 ( least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = X1 ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.68.0.0','0.3.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.68.1.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = X1 ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.68.0.1']),
% 5.34/5.80 [weight('<7,50,19,[1,0,0,2]>')]).
% 5.34/5.80 cnf('0.68.2.0',plain,
% 5.34/5.80 ( least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = X1 ),
% 5.34/5.80 inference(orient,[status(thm)],['0.68.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_66]).
% 5.34/5.80 cnf('0.69.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,X3))) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.51.2.0','0.14.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.69.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,X3))) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.69.0.0']),
% 5.34/5.80 [weight('<7,51,14,[1,0,0,2]>')]).
% 5.34/5.80 cnf('0.69.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,X3))) = greatest_lower_bound(X1,X2) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_67]).
% 5.34/5.80 cnf('0.70.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(a,b) = greatest_lower_bound(a,greatest_lower_bound(b,identity)) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.69.2.0','0.52.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.70.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(a,b) = greatest_lower_bound(a,greatest_lower_bound(b,identity)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.70.0.0']),
% 5.34/5.80 [weight('<5,69,52,[1,0,0,2]>')]).
% 5.34/5.80 cnf('0.70.1.1',plain,
% 5.34/5.80 ( greatest_lower_bound(b,a) = greatest_lower_bound(a,greatest_lower_bound(b,identity)) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.70.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.80 [pos('L','L')]).
% 5.34/5.80 cnf('0.70.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(a,greatest_lower_bound(b,identity)) = greatest_lower_bound(b,a) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.70.1.1',theory(equality)]),
% 5.34/5.80 [x,rule_68]).
% 5.34/5.80 cnf('0.71.0.0',plain,
% 5.34/5.80 ( identity = least_upper_bound(identity,greatest_lower_bound(b,a)) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.56.2.0','0.70.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.71.1.0',plain,
% 5.34/5.80 ( identity = least_upper_bound(identity,greatest_lower_bound(b,a)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.71.0.0']),
% 5.34/5.80 [weight('<5,70,56,[0,0,0,2]>')]).
% 5.34/5.80 cnf('0.71.2.0',plain,
% 5.34/5.80 ( least_upper_bound(identity,greatest_lower_bound(b,a)) = identity ),
% 5.34/5.80 inference(orient,[status(thm)],['0.71.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_69]).
% 5.34/5.80 cnf('0.73.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(a,least_upper_bound(b,inverse(b))) = greatest_lower_bound(a,identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.69.2.0','0.16.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.73.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(a,least_upper_bound(b,inverse(b))) = greatest_lower_bound(a,identity) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.73.0.0']),
% 5.34/5.80 [weight('<6,69,16,[1,0,0,2]>')]).
% 5.34/5.80 cnf('0.73.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(a,least_upper_bound(b,inverse(b))) = greatest_lower_bound(a,identity) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.73.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_71]).
% 5.34/5.80 cnf('0.74.0.0',plain,
% 5.34/5.80 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(b,a)),identity)) = multiply(inverse(greatest_lower_bound(b,a)),identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.31.2.0','0.71.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.74.0.1',plain,
% 5.34/5.80 ( least_upper_bound(identity,inverse(greatest_lower_bound(b,a))) = multiply(inverse(greatest_lower_bound(b,a)),identity) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.74.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.74.0.2',plain,
% 5.34/5.80 ( least_upper_bound(identity,inverse(greatest_lower_bound(b,a))) = inverse(greatest_lower_bound(b,a)) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.74.0.1','0.29.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.74.1.0',plain,
% 5.34/5.80 ( least_upper_bound(identity,inverse(greatest_lower_bound(b,a))) = inverse(greatest_lower_bound(b,a)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.74.0.2']),
% 5.34/5.80 [weight('<6,71,31,[0,0,0,3]>')]).
% 5.34/5.80 cnf('0.74.2.0',plain,
% 5.34/5.80 ( least_upper_bound(identity,inverse(greatest_lower_bound(b,a))) = inverse(greatest_lower_bound(b,a)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.74.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_72]).
% 5.34/5.80 cnf('0.75.0.0',plain,
% 5.34/5.80 ( identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(b,a))) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.5.2.0','0.74.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.75.1.0',plain,
% 5.34/5.80 ( identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(b,a))) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.75.0.0']),
% 5.34/5.80 [weight('<6,74,5,[0,0,0,2]>')]).
% 5.34/5.80 cnf('0.75.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(identity,inverse(greatest_lower_bound(b,a))) = identity ),
% 5.34/5.80 inference(orient,[status(thm)],['0.75.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_73]).
% 5.34/5.80 cnf('0.76.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,a))),identity)) = multiply(inverse(inverse(greatest_lower_bound(b,a))),identity) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.33.2.0','0.75.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.76.0.1',plain,
% 5.34/5.80 ( greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(b,a)))) = multiply(inverse(inverse(greatest_lower_bound(b,a))),identity) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.76.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.76.0.2',plain,
% 5.34/5.80 ( greatest_lower_bound(identity,greatest_lower_bound(b,a)) = multiply(inverse(inverse(greatest_lower_bound(b,a))),identity) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.76.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.76.0.3',plain,
% 5.34/5.80 ( greatest_lower_bound(identity,greatest_lower_bound(b,a)) = inverse(inverse(greatest_lower_bound(b,a))) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.76.0.2','0.29.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.76.0.4',plain,
% 5.34/5.80 ( greatest_lower_bound(identity,greatest_lower_bound(b,a)) = greatest_lower_bound(b,a) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.76.0.3','0.24.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.76.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(identity,greatest_lower_bound(b,a)) = greatest_lower_bound(b,a) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.76.0.4']),
% 5.34/5.80 [weight('<5,75,33,[0,0,0,3]>')]).
% 5.34/5.80 cnf('0.76.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(identity,greatest_lower_bound(b,a)) = greatest_lower_bound(b,a) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.76.1.0',theory(equality)]),
% 5.34/5.80 [u,rule_74]).
% 5.34/5.80 cnf('0.78.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(greatest_lower_bound(X1,X2),least_upper_bound(X3,X1)) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.53.2.0','0.3.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2.2','L')]).
% 5.34/5.80 cnf('0.78.0.1',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X3,X1))) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.78.0.0','0.15.2.0',theory(equality)]),
% 5.34/5.80 [pos('R','L')]).
% 5.34/5.80 cnf('0.78.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X3,X1))) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.78.0.1']),
% 5.34/5.80 [weight('<7,53,3,[1,0,0,4]>')]).
% 5.34/5.80 cnf('0.78.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X3,X1))) = greatest_lower_bound(X1,X2) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.78.1.0',theory(equality)]),
% 5.34/5.80 [x,rule_76]).
% 5.34/5.80 cnf('0.79.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(inverse(a),b) = greatest_lower_bound(inverse(a),greatest_lower_bound(b,identity)) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.78.2.0','0.52.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.79.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(inverse(a),b) = greatest_lower_bound(inverse(a),greatest_lower_bound(b,identity)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.79.0.0']),
% 5.34/5.80 [weight('<6,78,52,[1,0,0,2]>')]).
% 5.34/5.80 cnf('0.79.1.1',plain,
% 5.34/5.80 ( greatest_lower_bound(b,inverse(a)) = greatest_lower_bound(inverse(a),greatest_lower_bound(b,identity)) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.79.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.80 [pos('L','L')]).
% 5.34/5.80 cnf('0.79.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(inverse(a),greatest_lower_bound(b,identity)) = greatest_lower_bound(b,inverse(a)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.79.1.1',theory(equality)]),
% 5.34/5.80 [x,rule_77]).
% 5.34/5.80 cnf('0.80.0.0',plain,
% 5.34/5.80 ( greatest_lower_bound(inverse(b),a) = greatest_lower_bound(inverse(b),greatest_lower_bound(a,identity)) ),
% 5.34/5.80 inference(cp,[status(thm)],['0.78.2.0','0.73.2.0',theory(equality)]),
% 5.34/5.80 [pos('L.2','L')]).
% 5.34/5.80 cnf('0.80.1.0',plain,
% 5.34/5.80 ( greatest_lower_bound(inverse(b),a) = greatest_lower_bound(inverse(b),greatest_lower_bound(a,identity)) ),
% 5.34/5.80 inference(weigh,[status(thm)],['0.80.0.0']),
% 5.34/5.80 [weight('<6,78,73,[1,0,0,2]>')]).
% 5.34/5.80 cnf('0.80.1.1',plain,
% 5.34/5.80 ( greatest_lower_bound(a,inverse(b)) = greatest_lower_bound(inverse(b),greatest_lower_bound(a,identity)) ),
% 5.34/5.80 inference(reduction,[status(thm)],['0.80.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.80 [pos('L','L')]).
% 5.34/5.80 cnf('0.80.2.0',plain,
% 5.34/5.80 ( greatest_lower_bound(inverse(b),greatest_lower_bound(a,identity)) = greatest_lower_bound(a,inverse(b)) ),
% 5.34/5.80 inference(orient,[status(thm)],['0.80.1.1',theory(equality)]),
% 5.34/5.80 [x,rule_78]).
% 5.34/5.80 cnf('0.81.0.0',plain,
% 5.34/5.80 ( identity = least_upper_bound(identity,greatest_lower_bound(b,inverse(a))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.56.2.0','0.79.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.81.1.0',plain,
% 5.34/5.81 ( identity = least_upper_bound(identity,greatest_lower_bound(b,inverse(a))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.81.0.0']),
% 5.34/5.81 [weight('<6,79,56,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.81.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,greatest_lower_bound(b,inverse(a))) = identity ),
% 5.34/5.81 inference(orient,[status(thm)],['0.81.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_79]).
% 5.34/5.81 cnf('0.83.0.0',plain,
% 5.34/5.81 ( identity = least_upper_bound(identity,greatest_lower_bound(a,inverse(b))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.56.2.0','0.80.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.83.1.0',plain,
% 5.34/5.81 ( identity = least_upper_bound(identity,greatest_lower_bound(a,inverse(b))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.83.0.0']),
% 5.34/5.81 [weight('<6,80,56,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.83.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,greatest_lower_bound(a,inverse(b))) = identity ),
% 5.34/5.81 inference(orient,[status(thm)],['0.83.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_81]).
% 5.34/5.81 cnf('0.85.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a))) = greatest_lower_bound(inverse(b),identity) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.54.2.0','0.16.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.85.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a))) = greatest_lower_bound(inverse(b),identity) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.85.0.0']),
% 5.34/5.81 [weight('<7,54,16,[1,0,0,2]>')]).
% 5.34/5.81 cnf('0.85.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a))) = greatest_lower_bound(identity,inverse(b)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.85.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.85.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a))) = greatest_lower_bound(identity,inverse(b)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.85.1.1',theory(equality)]),
% 5.34/5.81 [u,rule_83]).
% 5.34/5.81 cnf('0.94.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(b,identity),X1)) = greatest_lower_bound(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.15.2.0','0.70.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.94.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(identity,X1))) = greatest_lower_bound(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.94.0.0','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.94.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(identity,X1))) = greatest_lower_bound(b,greatest_lower_bound(a,X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.94.0.1','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.94.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(identity,X1))) = greatest_lower_bound(b,greatest_lower_bound(a,X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.94.0.2']),
% 5.34/5.81 [weight('<7,70,15,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.94.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(identity,X1))) = greatest_lower_bound(b,greatest_lower_bound(a,X1)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.94.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_92]).
% 5.34/5.81 cnf('0.103.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(b,a),X1)) = greatest_lower_bound(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.15.2.0','0.76.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.103.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(b,greatest_lower_bound(a,X1))) = greatest_lower_bound(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.103.0.0','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.103.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(b,greatest_lower_bound(a,X1))) = greatest_lower_bound(b,greatest_lower_bound(a,X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.103.0.1','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.103.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(b,greatest_lower_bound(a,X1))) = greatest_lower_bound(b,greatest_lower_bound(a,X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.103.0.2']),
% 5.34/5.81 [weight('<7,76,15,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.103.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(b,greatest_lower_bound(a,X1))) = greatest_lower_bound(b,greatest_lower_bound(a,X1)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.103.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_101]).
% 5.34/5.81 cnf('0.108.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(greatest_lower_bound(b,identity),a)) = multiply(greatest_lower_bound(b,inverse(a)),a) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.36.2.0','0.79.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.108.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(greatest_lower_bound(b,identity),a)) = greatest_lower_bound(identity,multiply(b,a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.108.0.0','0.37.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.108.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(greatest_lower_bound(b,identity),a)) = greatest_lower_bound(identity,multiply(b,a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.108.0.1']),
% 5.34/5.81 [weight('<7,79,36,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.108.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(greatest_lower_bound(b,identity),a)) = greatest_lower_bound(identity,multiply(b,a)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.108.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_106]).
% 5.34/5.81 cnf('0.111.0.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(b,inverse(a))),identity)) = multiply(inverse(greatest_lower_bound(b,inverse(a))),identity) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.31.2.0','0.81.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.111.0.1',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(a)))) = multiply(inverse(greatest_lower_bound(b,inverse(a))),identity) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.111.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.111.0.2',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(a)))) = inverse(greatest_lower_bound(b,inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.111.0.1','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.111.1.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(a)))) = inverse(greatest_lower_bound(b,inverse(a))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.111.0.2']),
% 5.34/5.81 [weight('<7,81,31,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.111.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(greatest_lower_bound(b,inverse(a)))) = inverse(greatest_lower_bound(b,inverse(a))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.111.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_109]).
% 5.34/5.81 cnf('0.112.0.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,inverse(b))),identity)) = multiply(inverse(greatest_lower_bound(a,inverse(b))),identity) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.31.2.0','0.83.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.112.0.1',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(greatest_lower_bound(a,inverse(b)))) = multiply(inverse(greatest_lower_bound(a,inverse(b))),identity) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.112.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.112.0.2',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(greatest_lower_bound(a,inverse(b)))) = inverse(greatest_lower_bound(a,inverse(b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.112.0.1','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.112.1.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(greatest_lower_bound(a,inverse(b)))) = inverse(greatest_lower_bound(a,inverse(b))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.112.0.2']),
% 5.34/5.81 [weight('<7,83,31,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.112.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(greatest_lower_bound(a,inverse(b)))) = inverse(greatest_lower_bound(a,inverse(b))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.112.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_110]).
% 5.34/5.81 cnf('0.113.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(a),inverse(b)) = greatest_lower_bound(inverse(a),greatest_lower_bound(identity,inverse(b))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.78.2.0','0.85.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.113.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(a),inverse(b)) = greatest_lower_bound(inverse(a),greatest_lower_bound(identity,inverse(b))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.113.0.0']),
% 5.34/5.81 [weight('<7,85,78,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.113.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(b),inverse(a)) = greatest_lower_bound(inverse(a),greatest_lower_bound(identity,inverse(b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.113.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.113.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(a),greatest_lower_bound(identity,inverse(b))) = greatest_lower_bound(inverse(b),inverse(a)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.113.1.1',theory(equality)]),
% 5.34/5.81 [x,rule_111]).
% 5.34/5.81 cnf('0.121.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(b,greatest_lower_bound(identity,greatest_lower_bound(a,X1))) = greatest_lower_bound(b,greatest_lower_bound(b,greatest_lower_bound(a,X1))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.57.2.0','0.103.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.121.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(b,greatest_lower_bound(identity,greatest_lower_bound(a,X1))) = greatest_lower_bound(b,greatest_lower_bound(a,X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.121.0.0','0.20.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.121.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(b,greatest_lower_bound(identity,greatest_lower_bound(a,X1))) = greatest_lower_bound(b,greatest_lower_bound(a,X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.121.0.1']),
% 5.34/5.81 [weight('<7,103,57,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.121.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(b,greatest_lower_bound(identity,greatest_lower_bound(a,X1))) = greatest_lower_bound(b,greatest_lower_bound(a,X1)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.121.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_119]).
% 5.34/5.81 cnf('0.123.0.0',plain,
% 5.34/5.81 ( identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(b,inverse(a)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.5.2.0','0.111.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.123.1.0',plain,
% 5.34/5.81 ( identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(b,inverse(a)))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.123.0.0']),
% 5.34/5.81 [weight('<7,111,5,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.123.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,inverse(greatest_lower_bound(b,inverse(a)))) = identity ),
% 5.34/5.81 inference(orient,[status(thm)],['0.123.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_121]).
% 5.34/5.81 cnf('0.124.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(b,inverse(a)))),identity)) = multiply(inverse(inverse(greatest_lower_bound(b,inverse(a)))),identity) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.33.2.0','0.123.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.124.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(b,inverse(a))))) = multiply(inverse(inverse(greatest_lower_bound(b,inverse(a)))),identity) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.124.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.124.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a))) = multiply(inverse(inverse(greatest_lower_bound(b,inverse(a)))),identity) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.124.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.124.0.3',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a))) = inverse(inverse(greatest_lower_bound(b,inverse(a)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.124.0.2','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.124.0.4',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a))) = greatest_lower_bound(b,inverse(a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.124.0.3','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.124.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a))) = greatest_lower_bound(b,inverse(a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.124.0.4']),
% 5.34/5.81 [weight('<6,123,33,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.124.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a))) = greatest_lower_bound(b,inverse(a)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.124.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_122]).
% 5.34/5.81 cnf('0.125.0.0',plain,
% 5.34/5.81 ( identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(a,inverse(b)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.5.2.0','0.112.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.125.1.0',plain,
% 5.34/5.81 ( identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(a,inverse(b)))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.125.0.0']),
% 5.34/5.81 [weight('<7,112,5,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.125.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,inverse(greatest_lower_bound(a,inverse(b)))) = identity ),
% 5.34/5.81 inference(orient,[status(thm)],['0.125.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_123]).
% 5.34/5.81 cnf('0.126.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(a,inverse(b)))),identity)) = multiply(inverse(inverse(greatest_lower_bound(a,inverse(b)))),identity) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.33.2.0','0.125.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.126.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,inverse(inverse(greatest_lower_bound(a,inverse(b))))) = multiply(inverse(inverse(greatest_lower_bound(a,inverse(b)))),identity) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.126.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.126.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))) = multiply(inverse(inverse(greatest_lower_bound(a,inverse(b)))),identity) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.126.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.126.0.3',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))) = inverse(inverse(greatest_lower_bound(a,inverse(b)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.126.0.2','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.126.0.4',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))) = greatest_lower_bound(a,inverse(b)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.126.0.3','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.126.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))) = greatest_lower_bound(a,inverse(b)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.126.0.4']),
% 5.34/5.81 [weight('<6,125,33,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.126.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))) = greatest_lower_bound(a,inverse(b)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.126.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_124]).
% 5.34/5.81 cnf('0.127.0.0',plain,
% 5.34/5.81 ( identity = least_upper_bound(identity,greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.68.2.0','0.113.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.127.1.0',plain,
% 5.34/5.81 ( identity = least_upper_bound(identity,greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.127.0.0']),
% 5.34/5.81 [weight('<7,113,68,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.127.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,greatest_lower_bound(inverse(b),inverse(a))) = identity ),
% 5.34/5.81 inference(orient,[status(thm)],['0.127.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_125]).
% 5.34/5.81 cnf('0.131.0.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.7.2.0','0.23.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.131.1.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.131.0.0']),
% 5.34/5.81 [weight('<8,23,7,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.131.2.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.131.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_129]).
% 5.34/5.81 cnf('0.132.0.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.7.2.0','0.23.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.132.1.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.132.0.0']),
% 5.34/5.81 [weight('<8,23,7,[0,0,0,4]>')]).
% 5.34/5.81 cnf('0.132.2.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.132.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_130]).
% 5.34/5.81 cnf('0.133.0.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(multiply(X1,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X1),X3)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.8.2.0','0.23.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.133.1.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(multiply(X1,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X1),X3)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.133.0.0']),
% 5.34/5.81 [weight('<8,23,8,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.133.2.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(multiply(X1,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X1),X3)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.133.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_131]).
% 5.34/5.81 cnf('0.134.0.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.8.2.0','0.23.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.134.1.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.134.0.0']),
% 5.34/5.81 [weight('<8,23,8,[0,0,0,4]>')]).
% 5.34/5.81 cnf('0.134.2.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.134.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_132]).
% 5.34/5.81 cnf('0.135.0.0',plain,
% 5.34/5.81 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.26.2.0','0.6.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.135.1.0',plain,
% 5.34/5.81 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.135.0.0']),
% 5.34/5.81 [weight('<8,26,6,[1,0,0,0]>')]).
% 5.34/5.81 cnf('0.135.2.0',plain,
% 5.34/5.81 ( multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity ),
% 5.34/5.81 inference(orient,[status(thm)],['0.135.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_133]).
% 5.34/5.81 cnf('0.136.0.0',plain,
% 5.34/5.81 ( multiply(X1,inverse(multiply(X2,X1))) = multiply(inverse(X2),identity) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.23.2.0','0.135.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.136.0.1',plain,
% 5.34/5.81 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.136.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.136.1.0',plain,
% 5.34/5.81 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.136.0.1']),
% 5.34/5.81 [weight('<6,135,23,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.136.2.0',plain,
% 5.34/5.81 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.136.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_134]).
% 5.34/5.81 cnf('0.137.0.0',plain,
% 5.34/5.81 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.23.2.0','0.136.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.137.1.0',plain,
% 5.34/5.81 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.137.0.0']),
% 5.34/5.81 [weight('<4,136,23,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.137.2.0',plain,
% 5.34/5.81 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.137.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_135]).
% 5.34/5.81 cnf('0.139.0.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X1)) = multiply(inverse(greatest_lower_bound(X1,X2)),X1) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.31.2.0','0.3.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.139.1.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X1)) = multiply(inverse(greatest_lower_bound(X1,X2)),X1) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.139.0.0']),
% 5.34/5.81 [weight('<8,31,3,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.139.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X1)) = multiply(inverse(greatest_lower_bound(X1,X2)),X1) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.139.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_137]).
% 5.34/5.81 cnf('0.140.0.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,X1)),identity) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.139.2.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.140.0.1',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.140.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.140.1.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.140.0.1']),
% 5.34/5.81 [weight('<6,139,29,[1,0,0,2]>')]).
% 5.34/5.81 cnf('0.140.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,X1)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.140.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_138]).
% 5.34/5.81 cnf('0.142.0.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.140.2.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1','L')]).
% 5.34/5.81 cnf('0.142.1.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.142.0.0']),
% 5.34/5.81 [weight('<6,140,14,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.142.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(identity,X1)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.142.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_140]).
% 5.34/5.81 cnf('0.151.0.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = multiply(inverse(greatest_lower_bound(X1,X2)),X2) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.31.2.0','0.19.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.151.1.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = multiply(inverse(greatest_lower_bound(X1,X2)),X2) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.151.0.0']),
% 5.34/5.81 [weight('<8,31,19,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.151.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = multiply(inverse(greatest_lower_bound(X1,X2)),X2) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.151.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_149]).
% 5.34/5.81 cnf('0.155.0.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(greatest_lower_bound(X2,X1),X3)) = greatest_lower_bound(greatest_lower_bound(identity,multiply(inverse(X1),X2)),multiply(inverse(X1),X3)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.8.2.0','0.33.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.155.0.1',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(greatest_lower_bound(identity,multiply(inverse(X1),X2)),multiply(inverse(X1),X3)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.155.0.0','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.155.0.2',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(X1),X2),multiply(inverse(X1),X3))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.155.0.1','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.155.0.3',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X3))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.155.0.2','0.8.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.155.1.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X3))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.155.0.3']),
% 5.34/5.81 [weight('<8,33,8,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.155.2.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X3))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.155.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_153]).
% 5.34/5.81 cnf('0.156.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(identity),greatest_lower_bound(X1,greatest_lower_bound(b,a)))) = multiply(inverse(identity),greatest_lower_bound(X1,greatest_lower_bound(b,a))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.155.2.0','0.76.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.2','L')]).
% 5.34/5.81 cnf('0.156.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(identity,greatest_lower_bound(X1,greatest_lower_bound(b,a)))) = multiply(inverse(identity),greatest_lower_bound(X1,greatest_lower_bound(b,a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.156.0.0','0.27.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1','L')]).
% 5.34/5.81 cnf('0.156.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(X1,greatest_lower_bound(b,a))) = multiply(inverse(identity),greatest_lower_bound(X1,greatest_lower_bound(b,a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.156.0.1','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.156.0.3',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(X1,greatest_lower_bound(b,a))) = multiply(identity,greatest_lower_bound(X1,greatest_lower_bound(b,a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.156.0.2','0.27.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.156.0.4',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(X1,greatest_lower_bound(b,a))) = greatest_lower_bound(X1,greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.156.0.3','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.156.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(X1,greatest_lower_bound(b,a))) = greatest_lower_bound(X1,greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.156.0.4']),
% 5.34/5.81 [weight('<7,155,76,[1,0,0,5]>')]).
% 5.34/5.81 cnf('0.156.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(X1,greatest_lower_bound(b,a))) = greatest_lower_bound(X1,greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.156.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_154]).
% 5.34/5.81 cnf('0.179.0.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(X1,inverse(greatest_lower_bound(X1,X2)))) = multiply(X1,inverse(greatest_lower_bound(X1,X2))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.47.2.0','0.3.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.179.1.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(X1,inverse(greatest_lower_bound(X1,X2)))) = multiply(X1,inverse(greatest_lower_bound(X1,X2))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.179.0.0']),
% 5.34/5.81 [weight('<8,47,3,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.179.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(X1,inverse(greatest_lower_bound(X1,X2)))) = multiply(X1,inverse(greatest_lower_bound(X1,X2))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.179.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_177]).
% 5.34/5.81 cnf('0.180.0.0',plain,
% 5.34/5.81 ( least_upper_bound(multiply(inverse(X1),identity),inverse(greatest_lower_bound(X1,X2))) = multiply(inverse(X1),multiply(X1,inverse(greatest_lower_bound(X1,X2)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.132.2.0','0.179.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.180.0.1',plain,
% 5.34/5.81 ( least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = multiply(inverse(X1),multiply(X1,inverse(greatest_lower_bound(X1,X2)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.180.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.180.0.2',plain,
% 5.34/5.81 ( least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(greatest_lower_bound(X1,X2)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.180.0.1','0.23.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.180.1.0',plain,
% 5.34/5.81 ( least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(greatest_lower_bound(X1,X2)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.180.0.2']),
% 5.34/5.81 [weight('<7,179,132,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.180.2.0',plain,
% 5.34/5.81 ( least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(greatest_lower_bound(X1,X2)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.180.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_178]).
% 5.34/5.81 cnf('0.183.0.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.180.2.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1','L')]).
% 5.34/5.81 cnf('0.183.1.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.183.0.0']),
% 5.34/5.81 [weight('<7,180,14,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.183.2.0',plain,
% 5.34/5.81 ( least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) = inverse(greatest_lower_bound(X1,X2)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.183.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_181]).
% 5.34/5.81 cnf('0.184.0.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(least_upper_bound(X1,X2),X1)) = least_upper_bound(inverse(least_upper_bound(X1,X2)),inverse(X1)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.183.2.0','0.5.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1','L')]).
% 5.34/5.81 cnf('0.184.1.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(least_upper_bound(X1,X2),X1)) = least_upper_bound(inverse(least_upper_bound(X1,X2)),inverse(X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.184.0.0']),
% 5.34/5.81 [weight('<6,183,5,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.184.1.1',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(X1,least_upper_bound(X1,X2))) = least_upper_bound(inverse(least_upper_bound(X1,X2)),inverse(X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.184.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.184.1.2',plain,
% 5.34/5.81 ( inverse(X1) = least_upper_bound(inverse(least_upper_bound(X1,X2)),inverse(X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.184.1.1','0.5.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.184.1.3',plain,
% 5.34/5.81 ( inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.184.1.2','0.12.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.184.2.0',plain,
% 5.34/5.81 ( least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(X1) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.184.1.3',theory(equality)]),
% 5.34/5.81 [x,rule_182]).
% 5.34/5.81 cnf('0.185.0.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(least_upper_bound(X1,X2),X2)) = least_upper_bound(inverse(least_upper_bound(X1,X2)),inverse(X2)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.183.2.0','0.17.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1','L')]).
% 5.34/5.81 cnf('0.185.1.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(least_upper_bound(X1,X2),X2)) = least_upper_bound(inverse(least_upper_bound(X1,X2)),inverse(X2)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.185.0.0']),
% 5.34/5.81 [weight('<6,183,17,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.185.1.1',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(X2,least_upper_bound(X1,X2))) = least_upper_bound(inverse(least_upper_bound(X1,X2)),inverse(X2)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.185.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.185.1.2',plain,
% 5.34/5.81 ( inverse(X2) = least_upper_bound(inverse(least_upper_bound(X1,X2)),inverse(X2)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.185.1.1','0.17.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.185.1.3',plain,
% 5.34/5.81 ( inverse(X2) = least_upper_bound(inverse(X2),inverse(least_upper_bound(X1,X2))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.185.1.2','0.12.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.185.2.0',plain,
% 5.34/5.81 ( least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(X1) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.185.1.3',theory(equality)]),
% 5.34/5.81 [x,rule_183]).
% 5.34/5.81 cnf('0.198.0.0',plain,
% 5.34/5.81 ( inverse(inverse(X1)) = least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.184.2.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.198.0.1',plain,
% 5.34/5.81 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.198.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.198.1.0',plain,
% 5.34/5.81 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.198.0.1']),
% 5.34/5.81 [weight('<7,184,24,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.198.2.0',plain,
% 5.34/5.81 ( least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = X1 ),
% 5.34/5.81 inference(orient,[status(thm)],['0.198.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_196]).
% 5.34/5.81 cnf('0.202.0.0',plain,
% 5.34/5.81 ( inverse(inverse(X1)) = least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.185.2.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.202.0.1',plain,
% 5.34/5.81 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.202.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.202.1.0',plain,
% 5.34/5.81 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.202.0.1']),
% 5.34/5.81 [weight('<7,185,24,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.202.2.0',plain,
% 5.34/5.81 ( least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = X1 ),
% 5.34/5.81 inference(orient,[status(thm)],['0.202.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_200]).
% 5.34/5.81 cnf('0.210.0.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.9.2.0','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.210.1.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.210.0.0']),
% 5.34/5.81 [weight('<?,9,1,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.210.2.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)) ),
% 5.34/5.81 inference(activate,[status(thm)],['0.210.1.0']),
% 5.34/5.81 [equation_3]).
% 5.34/5.81 cnf('0.211.0.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),inverse(least_upper_bound(identity,X2))) = inverse(least_upper_bound(X1,multiply(X2,X1))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.137.2.0','0.210.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.211.1.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),inverse(least_upper_bound(identity,X2))) = inverse(least_upper_bound(X1,multiply(X2,X1))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.211.0.0']),
% 5.34/5.81 [weight('<6,210,137,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.211.2.0',plain,
% 5.34/5.81 ( inverse(least_upper_bound(X1,multiply(X2,X1))) = multiply(inverse(X1),inverse(least_upper_bound(identity,X2))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.211.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_208]).
% 5.34/5.81 cnf('0.212.0.0',plain,
% 5.34/5.81 ( multiply(inverse(inverse(X1)),inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.211.2.0','0.26.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2','L')]).
% 5.34/5.81 cnf('0.212.0.1',plain,
% 5.34/5.81 ( multiply(X1,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.212.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.212.1.0',plain,
% 5.34/5.81 ( multiply(X1,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.212.0.1']),
% 5.34/5.81 [weight('<6,211,26,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.212.1.1',plain,
% 5.34/5.81 ( multiply(X1,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.212.1.0','0.12.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.212.2.0',plain,
% 5.34/5.81 ( multiply(X1,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.212.1.1',theory(equality)]),
% 5.34/5.81 [u,rule_209]).
% 5.34/5.81 cnf('0.216.0.0',plain,
% 5.34/5.81 ( least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),X1)) = multiply(identity,X1) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.210.2.0','0.3.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.216.0.1',plain,
% 5.34/5.81 ( least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),X1)) = X1 ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.216.0.0','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.216.1.0',plain,
% 5.34/5.81 ( least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),X1)) = X1 ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.216.0.1']),
% 5.34/5.81 [weight('<7,210,3,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.216.2.0',plain,
% 5.34/5.81 ( least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),X1)) = X1 ),
% 5.34/5.81 inference(orient,[status(thm)],['0.216.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_213]).
% 5.34/5.81 cnf('0.218.0.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,X1),multiply(X2,X3)) = multiply(least_upper_bound(X2,multiply(X1,X2)),X3) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.6.2.0','0.210.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.218.1.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,X1),multiply(X2,X3)) = multiply(least_upper_bound(X2,multiply(X1,X2)),X3) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.218.0.0']),
% 5.34/5.81 [weight('<7,210,6,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.218.2.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(X1,multiply(X2,X1)),X3) = multiply(least_upper_bound(identity,X2),multiply(X1,X3)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.218.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_215]).
% 5.34/5.81 cnf('0.228.0.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(multiply(greatest_lower_bound(identity,X1),X2),X2) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.17.2.0','0.216.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.228.1.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(multiply(greatest_lower_bound(identity,X1),X2),X2) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.228.0.0']),
% 5.34/5.81 [weight('<7,216,17,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.228.1.1',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(greatest_lower_bound(identity,X1),X2)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.228.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.228.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X2),X1)) = multiply(greatest_lower_bound(identity,X2),X1) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.228.1.1',theory(equality)]),
% 5.34/5.81 [x,rule_225]).
% 5.34/5.81 cnf('0.246.0.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = multiply(X1,inverse(greatest_lower_bound(X2,X1))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.47.2.0','0.19.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.246.1.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = multiply(X1,inverse(greatest_lower_bound(X2,X1))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.246.0.0']),
% 5.34/5.81 [weight('<8,47,19,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.246.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = multiply(X1,inverse(greatest_lower_bound(X2,X1))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.246.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_242]).
% 5.34/5.81 cnf('0.253.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = multiply(greatest_lower_bound(X1,X2),inverse(greatest_lower_bound(X2,X1))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.49.2.0','0.21.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.253.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = multiply(greatest_lower_bound(X1,X2),inverse(greatest_lower_bound(X2,X1))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.253.0.0']),
% 5.34/5.81 [weight('<8,49,21,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.253.2.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(X1,X2),inverse(greatest_lower_bound(X2,X1))) = greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.253.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_249]).
% 5.34/5.81 cnf('0.331.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(b)),a)) = multiply(greatest_lower_bound(inverse(b),inverse(a)),a) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.36.2.0','0.113.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.331.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(b)),a)) = greatest_lower_bound(identity,multiply(inverse(b),a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.331.0.0','0.37.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.331.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(b)),a)) = greatest_lower_bound(identity,multiply(inverse(b),a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.331.0.1']),
% 5.34/5.81 [weight('<8,113,36,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.331.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(b)),a)) = greatest_lower_bound(identity,multiply(inverse(b),a)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.331.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_327]).
% 5.34/5.81 cnf('0.344.0.0',plain,
% 5.34/5.81 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),inverse(inverse(X1))) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.137.2.0','0.131.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.344.0.1',plain,
% 5.34/5.81 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.344.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.344.1.0',plain,
% 5.34/5.81 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.344.0.1']),
% 5.34/5.81 [weight('<8,137,131,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.344.2.0',plain,
% 5.34/5.81 ( multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.344.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_340]).
% 5.34/5.81 cnf('0.345.0.0',plain,
% 5.34/5.81 ( inverse(least_upper_bound(X1,multiply(inverse(inverse(X1)),X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.344.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.1.1','L')]).
% 5.34/5.81 cnf('0.345.0.1',plain,
% 5.34/5.81 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.345.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2.1','L')]).
% 5.34/5.81 cnf('0.345.1.0',plain,
% 5.34/5.81 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.345.0.1']),
% 5.34/5.81 [weight('<6,344,11,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.345.2.0',plain,
% 5.34/5.81 ( inverse(least_upper_bound(X1,multiply(X1,X2))) = multiply(inverse(least_upper_bound(identity,X2)),inverse(X1)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.345.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_341]).
% 5.34/5.81 cnf('0.346.0.0',plain,
% 5.34/5.81 ( multiply(inverse(least_upper_bound(identity,X1)),inverse(inverse(X1))) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.345.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2','L')]).
% 5.34/5.81 cnf('0.346.0.1',plain,
% 5.34/5.81 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.346.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.346.1.0',plain,
% 5.34/5.81 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(inverse(X1),identity)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.346.0.1']),
% 5.34/5.81 [weight('<6,345,11,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.346.1.1',plain,
% 5.34/5.81 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.346.1.0','0.12.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.346.2.0',plain,
% 5.34/5.81 ( multiply(inverse(least_upper_bound(identity,X1)),X1) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.346.1.1',theory(equality)]),
% 5.34/5.81 [u,rule_342]).
% 5.34/5.81 cnf('0.349.0.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),inverse(inverse(X1))) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.137.2.0','0.133.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.349.0.1',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),X1) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.349.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.349.1.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),X1) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.349.0.1']),
% 5.34/5.81 [weight('<8,137,133,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.349.2.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),X1) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.349.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_345]).
% 5.34/5.81 cnf('0.350.0.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(X1,multiply(inverse(inverse(X1)),X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.349.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.1.1','L')]).
% 5.34/5.81 cnf('0.350.0.1',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(X1,multiply(X1,X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.350.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2.1','L')]).
% 5.34/5.81 cnf('0.350.1.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(X1,multiply(X1,X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.350.0.1']),
% 5.34/5.81 [weight('<6,349,11,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.350.2.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(X1,multiply(X1,X2))) = multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.350.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_346]).
% 5.34/5.81 cnf('0.351.0.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,X1)),inverse(inverse(X1))) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.350.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2','L')]).
% 5.34/5.81 cnf('0.351.0.1',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.351.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.351.1.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(inverse(X1),identity)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.351.0.1']),
% 5.34/5.81 [weight('<6,350,11,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.351.1.1',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.351.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.351.2.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,X1)),X1) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.351.1.1',theory(equality)]),
% 5.34/5.81 [u,rule_347]).
% 5.34/5.81 cnf('0.353.0.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(X1,multiply(X2,X3))),inverse(inverse(X2))) = inverse(greatest_lower_bound(multiply(inverse(X2),X1),X3)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.137.2.0','0.134.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.353.0.1',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(X1,multiply(X2,X3))),X2) = inverse(greatest_lower_bound(multiply(inverse(X2),X1),X3)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.353.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.353.1.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(X1,multiply(X2,X3))),X2) = inverse(greatest_lower_bound(multiply(inverse(X2),X1),X3)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.353.0.1']),
% 5.34/5.81 [weight('<8,137,134,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.353.2.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(X1,multiply(X2,X3))),X2) = inverse(greatest_lower_bound(multiply(inverse(X2),X1),X3)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.353.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_349]).
% 5.34/5.81 cnf('0.365.0.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X1,identity))),identity)) = multiply(inverse(inverse(greatest_lower_bound(X1,identity))),inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.31.2.0','0.142.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.365.0.1',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(inverse(greatest_lower_bound(X1,identity)))) = multiply(inverse(inverse(greatest_lower_bound(X1,identity))),inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.365.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.365.0.2',plain,
% 5.34/5.81 ( least_upper_bound(identity,greatest_lower_bound(X1,identity)) = multiply(inverse(inverse(greatest_lower_bound(X1,identity))),inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.365.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.365.0.3',plain,
% 5.34/5.81 ( identity = multiply(inverse(inverse(greatest_lower_bound(X1,identity))),inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.365.0.2','0.19.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.365.0.4',plain,
% 5.34/5.81 ( identity = multiply(greatest_lower_bound(X1,identity),inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.365.0.3','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.365.1.0',plain,
% 5.34/5.81 ( identity = multiply(greatest_lower_bound(X1,identity),inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.365.0.4']),
% 5.34/5.81 [weight('<8,142,31,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.365.1.1',plain,
% 5.34/5.81 ( identity = greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(identity,X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.365.1.0','0.253.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.365.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(identity,X1)))) = identity ),
% 5.34/5.81 inference(orient,[status(thm)],['0.365.1.1',theory(equality)]),
% 5.34/5.81 [x,rule_361]).
% 5.34/5.81 cnf('0.366.0.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(identity,X1))))),multiply(X1,inverse(greatest_lower_bound(identity,X1)))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.151.2.0','0.365.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1.1','L')]).
% 5.34/5.81 cnf('0.366.0.1',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,inverse(multiply(X1,inverse(greatest_lower_bound(identity,X1)))))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.366.0.0','0.351.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.366.0.2',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,multiply(inverse(inverse(greatest_lower_bound(identity,X1))),inverse(X1)))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.366.0.1','0.137.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2','L')]).
% 5.34/5.81 cnf('0.366.0.3',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X1),inverse(X1)))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.366.0.2','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2.1','L')]).
% 5.34/5.81 cnf('0.366.0.4',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,multiply(identity,inverse(X1))))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.366.0.3','0.49.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2','L')]).
% 5.34/5.81 cnf('0.366.0.5',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,multiply(identity,inverse(X1)))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.366.0.4','0.20.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.366.0.6',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),inverse(identity)) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.366.0.5','0.350.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.366.0.7',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),identity) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.366.0.6','0.27.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.366.0.8',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,multiply(inverse(identity),multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.366.0.7','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.366.0.9',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,multiply(identity,multiply(X1,inverse(greatest_lower_bound(identity,X1))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.366.0.8','0.27.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2.1','L')]).
% 5.34/5.81 cnf('0.366.0.10',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,multiply(X1,inverse(greatest_lower_bound(identity,X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.366.0.9','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.366.0.11',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,inverse(X1))) = multiply(X1,inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.366.0.10','0.246.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.366.1.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,inverse(X1))) = multiply(X1,inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.366.0.11']),
% 5.34/5.81 [weight('<6,365,151,[0,0,0,4]>')]).
% 5.34/5.81 cnf('0.366.2.0',plain,
% 5.34/5.81 ( multiply(X1,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.366.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_362]).
% 5.34/5.81 cnf('0.424.0.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,greatest_lower_bound(inverse(X1),X2)),X1) = least_upper_bound(X1,greatest_lower_bound(identity,multiply(X2,X1))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.210.2.0','0.36.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.424.1.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,greatest_lower_bound(inverse(X1),X2)),X1) = least_upper_bound(X1,greatest_lower_bound(identity,multiply(X2,X1))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.424.0.0']),
% 5.34/5.81 [weight('<8,210,36,[1,1,0,2]>')]).
% 5.34/5.81 cnf('0.424.2.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,greatest_lower_bound(inverse(X1),X2)),X1) = least_upper_bound(X1,greatest_lower_bound(identity,multiply(X2,X1))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.424.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_419]).
% 5.34/5.81 cnf('0.425.0.0',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(greatest_lower_bound(b,identity),a))) = multiply(least_upper_bound(identity,greatest_lower_bound(b,inverse(a))),a) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.424.2.0','0.79.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2','L')]).
% 5.34/5.81 cnf('0.425.0.1',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(b,a))) = multiply(least_upper_bound(identity,greatest_lower_bound(b,inverse(a))),a) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.425.0.0','0.108.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.425.0.2',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(b,a))) = multiply(identity,a) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.425.0.1','0.81.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.425.0.3',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(b,a))) = a ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.425.0.2','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.425.1.0',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(b,a))) = a ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.425.0.3']),
% 5.34/5.81 [weight('<7,424,79,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.425.2.0',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(b,a))) = a ),
% 5.34/5.81 inference(orient,[status(thm)],['0.425.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_420]).
% 5.34/5.81 cnf('0.427.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(b,a)) = greatest_lower_bound(greatest_lower_bound(identity,multiply(b,a)),a) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.17.2.0','0.425.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.427.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(b,a)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.427.0.0','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.427.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(b,a)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.427.0.1']),
% 5.34/5.81 [weight('<7,425,17,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.427.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(b,a)) = greatest_lower_bound(identity,greatest_lower_bound(a,multiply(b,a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.427.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.427.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,multiply(b,a))) = greatest_lower_bound(identity,multiply(b,a)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.427.1.1',theory(equality)]),
% 5.34/5.81 [x,rule_422]).
% 5.34/5.81 cnf('0.429.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(b,greatest_lower_bound(a,multiply(b,a))) = greatest_lower_bound(b,greatest_lower_bound(identity,multiply(b,a))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.121.2.0','0.427.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.429.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(b,greatest_lower_bound(a,multiply(b,a))) = greatest_lower_bound(b,greatest_lower_bound(identity,multiply(b,a))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.429.0.0']),
% 5.34/5.81 [weight('<7,427,121,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.429.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(b,greatest_lower_bound(identity,multiply(b,a))) = greatest_lower_bound(b,greatest_lower_bound(a,multiply(b,a))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.429.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_424]).
% 5.34/5.81 cnf('0.444.0.0',plain,
% 5.34/5.81 ( least_upper_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),X1)) = multiply(inverse(greatest_lower_bound(identity,X2)),X1) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.210.2.0','0.140.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.444.1.0',plain,
% 5.34/5.81 ( least_upper_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),X1)) = multiply(inverse(greatest_lower_bound(identity,X2)),X1) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.444.0.0']),
% 5.34/5.81 [weight('<8,210,140,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.444.2.0',plain,
% 5.34/5.81 ( least_upper_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),X1)) = multiply(inverse(greatest_lower_bound(identity,X2)),X1) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.444.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_439]).
% 5.34/5.81 cnf('0.445.0.0',plain,
% 5.34/5.81 ( X1 = least_upper_bound(X1,inverse(multiply(inverse(greatest_lower_bound(identity,X2)),inverse(X1)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.198.2.0','0.444.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1','L')]).
% 5.34/5.81 cnf('0.445.0.1',plain,
% 5.34/5.81 ( X1 = least_upper_bound(X1,multiply(inverse(inverse(X1)),inverse(inverse(greatest_lower_bound(identity,X2))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.445.0.0','0.137.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.445.0.2',plain,
% 5.34/5.81 ( X1 = least_upper_bound(X1,multiply(X1,inverse(inverse(greatest_lower_bound(identity,X2))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.445.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2.1','L')]).
% 5.34/5.81 cnf('0.445.0.3',plain,
% 5.34/5.81 ( X1 = least_upper_bound(X1,multiply(X1,greatest_lower_bound(identity,X2))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.445.0.2','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2.2','L')]).
% 5.34/5.81 cnf('0.445.1.0',plain,
% 5.34/5.81 ( X1 = least_upper_bound(X1,multiply(X1,greatest_lower_bound(identity,X2))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.445.0.3']),
% 5.34/5.81 [weight('<7,444,198,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.445.2.0',plain,
% 5.34/5.81 ( least_upper_bound(X1,multiply(X1,greatest_lower_bound(identity,X2))) = X1 ),
% 5.34/5.81 inference(orient,[status(thm)],['0.445.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_440]).
% 5.34/5.81 cnf('0.458.0.0',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.7.2.0','0.212.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.458.1.0',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.458.0.0']),
% 5.34/5.81 [weight('<8,212,7,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.458.2.0',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.458.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_453]).
% 5.34/5.81 cnf('0.478.0.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,inverse(X1)),multiply(X1,X2)) = multiply(least_upper_bound(X1,identity),X2) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.218.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2','L')]).
% 5.34/5.81 cnf('0.478.1.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,inverse(X1)),multiply(X1,X2)) = multiply(least_upper_bound(X1,identity),X2) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.478.0.0']),
% 5.34/5.81 [weight('<8,218,11,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.478.2.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,inverse(X1)),multiply(X1,X2)) = multiply(least_upper_bound(X1,identity),X2) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.478.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_473]).
% 5.34/5.81 cnf('0.486.0.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))),X1) = greatest_lower_bound(X1,multiply(greatest_lower_bound(a,inverse(b)),X1)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.228.2.0','0.126.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1','L')]).
% 5.34/5.81 cnf('0.486.0.1',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(a,inverse(b)),X1) = greatest_lower_bound(X1,multiply(greatest_lower_bound(a,inverse(b)),X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.486.0.0','0.126.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.486.1.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(a,inverse(b)),X1) = greatest_lower_bound(X1,multiply(greatest_lower_bound(a,inverse(b)),X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.486.0.1']),
% 5.34/5.81 [weight('<8,228,126,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.486.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(X1,multiply(greatest_lower_bound(a,inverse(b)),X1)) = multiply(greatest_lower_bound(a,inverse(b)),X1) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.486.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_481]).
% 5.34/5.81 cnf('0.487.0.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(a,inverse(b)),b) = greatest_lower_bound(b,greatest_lower_bound(identity,multiply(a,b))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.486.2.0','0.37.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.487.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(b,greatest_lower_bound(identity,multiply(a,b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.487.0.0','0.37.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.487.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(b,greatest_lower_bound(identity,multiply(a,b))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.487.0.1']),
% 5.34/5.81 [weight('<7,486,37,[1,0,0,2]>')]).
% 5.34/5.81 cnf('0.487.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(b,greatest_lower_bound(identity,multiply(a,b))) = greatest_lower_bound(identity,multiply(a,b)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.487.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_482]).
% 5.34/5.81 cnf('0.488.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(b,greatest_lower_bound(a,multiply(a,b))) = greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,b))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.94.2.0','0.487.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.488.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(b,greatest_lower_bound(a,multiply(a,b))) = greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,b))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.488.0.0']),
% 5.34/5.81 [weight('<7,487,94,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.488.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(a,greatest_lower_bound(identity,multiply(a,b))) = greatest_lower_bound(b,greatest_lower_bound(a,multiply(a,b))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.488.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_483]).
% 5.34/5.81 cnf('0.489.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(greatest_lower_bound(identity,multiply(a,b)),a) = greatest_lower_bound(greatest_lower_bound(identity,multiply(a,b)),greatest_lower_bound(b,greatest_lower_bound(a,multiply(a,b)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.21.2.0','0.488.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.489.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),a)) = greatest_lower_bound(greatest_lower_bound(identity,multiply(a,b)),greatest_lower_bound(b,greatest_lower_bound(a,multiply(a,b)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.489.0.0','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.489.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),a)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),greatest_lower_bound(b,greatest_lower_bound(a,multiply(a,b))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.489.0.1','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.489.0.3',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),a)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),greatest_lower_bound(b,a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.489.0.2','0.58.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.489.0.4',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),a)) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.489.0.3','0.156.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.489.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),a)) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.489.0.4']),
% 5.34/5.81 [weight('<7,488,21,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.489.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,multiply(a,b))) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.489.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.489.1.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,multiply(a,b))) = greatest_lower_bound(greatest_lower_bound(b,a),multiply(a,b)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.489.1.1','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.489.1.3',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,multiply(a,b))) = greatest_lower_bound(b,greatest_lower_bound(a,multiply(a,b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.489.1.2','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.489.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,multiply(a,b))) = greatest_lower_bound(b,greatest_lower_bound(a,multiply(a,b))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.489.1.3',theory(equality)]),
% 5.34/5.81 [u,rule_484]).
% 5.34/5.81 cnf('0.591.0.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(inverse(least_upper_bound(identity,X1)),X2),X1) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),multiply(X2,X1)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.9.2.0','0.346.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.591.1.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(inverse(least_upper_bound(identity,X1)),X2),X1) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),multiply(X2,X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.591.0.0']),
% 5.34/5.81 [weight('<8,346,9,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.591.2.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(inverse(least_upper_bound(identity,X1)),X2),X1) = least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),multiply(X2,X1)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.591.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_586]).
% 5.34/5.81 cnf('0.602.0.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,X1)),multiply(X1,X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.6.2.0','0.351.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.602.1.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,X1)),multiply(X1,X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.602.0.0']),
% 5.34/5.81 [weight('<8,351,6,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.602.2.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,X1)),multiply(X1,X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.602.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_597]).
% 5.34/5.81 cnf('0.637.0.0',plain,
% 5.34/5.81 ( multiply(X1,multiply(inverse(greatest_lower_bound(identity,X1)),X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.6.2.0','0.366.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.637.1.0',plain,
% 5.34/5.81 ( multiply(X1,multiply(inverse(greatest_lower_bound(identity,X1)),X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.637.0.0']),
% 5.34/5.81 [weight('<8,366,6,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.637.2.0',plain,
% 5.34/5.81 ( multiply(X1,multiply(inverse(greatest_lower_bound(identity,X1)),X2)) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X2) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.637.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_632]).
% 5.34/5.81 cnf('0.638.0.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X1) = multiply(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.637.2.0','0.351.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.638.1.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X1) = multiply(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.638.0.0']),
% 5.34/5.81 [weight('<7,637,351,[1,0,0,2]>')]).
% 5.34/5.81 cnf('0.638.2.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),X1) = multiply(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.638.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_633]).
% 5.34/5.81 cnf('0.639.0.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,inverse(inverse(X1))))) = multiply(inverse(greatest_lower_bound(identity,X1)),inverse(X1)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.638.2.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.1.2','L')]).
% 5.34/5.81 cnf('0.639.0.1',plain,
% 5.34/5.81 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1))) = multiply(inverse(greatest_lower_bound(identity,X1)),inverse(X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.639.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1.2','L')]).
% 5.34/5.81 cnf('0.639.1.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1))) = multiply(inverse(greatest_lower_bound(identity,X1)),inverse(X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.639.0.1']),
% 5.34/5.81 [weight('<7,638,24,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.639.2.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,X1)),inverse(X1)) = multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.639.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_634]).
% 5.34/5.81 cnf('0.640.0.0',plain,
% 5.34/5.81 ( multiply(inverse(inverse(X1)),inverse(inverse(greatest_lower_bound(identity,X1)))) = inverse(multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.137.2.0','0.639.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.640.0.1',plain,
% 5.34/5.81 ( multiply(X1,inverse(inverse(greatest_lower_bound(identity,X1)))) = inverse(multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.640.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.640.0.2',plain,
% 5.34/5.81 ( multiply(X1,greatest_lower_bound(identity,X1)) = inverse(multiply(inverse(X1),inverse(greatest_lower_bound(identity,X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.640.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.640.0.3',plain,
% 5.34/5.81 ( multiply(X1,greatest_lower_bound(identity,X1)) = multiply(inverse(inverse(greatest_lower_bound(identity,X1))),inverse(inverse(X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.640.0.2','0.137.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.640.0.4',plain,
% 5.34/5.81 ( multiply(X1,greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),inverse(inverse(X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.640.0.3','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.640.0.5',plain,
% 5.34/5.81 ( multiply(X1,greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),X1) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.640.0.4','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.640.1.0',plain,
% 5.34/5.81 ( multiply(X1,greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),X1) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.640.0.5']),
% 5.34/5.81 [weight('<5,639,137,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.640.2.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,X1),X1) = multiply(X1,greatest_lower_bound(identity,X1)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.640.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_635]).
% 5.34/5.81 cnf('0.644.0.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(greatest_lower_bound(identity,X1),identity),X1) = multiply(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))),multiply(X1,greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.478.2.0','0.640.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.644.0.1',plain,
% 5.34/5.81 ( multiply(least_upper_bound(greatest_lower_bound(identity,X1),identity),X1) = multiply(inverse(greatest_lower_bound(identity,X1)),multiply(X1,greatest_lower_bound(identity,X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.644.0.0','0.140.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.644.0.2',plain,
% 5.34/5.81 ( multiply(least_upper_bound(greatest_lower_bound(identity,X1),identity),X1) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.644.0.1','0.602.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.644.1.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(greatest_lower_bound(identity,X1),identity),X1) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.644.0.2']),
% 5.34/5.81 [weight('<7,640,478,[0,0,0,5]>')]).
% 5.34/5.81 cnf('0.644.1.1',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,greatest_lower_bound(identity,X1)),X1) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.644.1.0','0.12.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.644.1.2',plain,
% 5.34/5.81 ( multiply(identity,X1) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.644.1.1','0.3.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.644.1.3',plain,
% 5.34/5.81 ( X1 = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.644.1.2','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.644.2.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) = X1 ),
% 5.34/5.81 inference(orient,[status(thm)],['0.644.1.3',theory(equality)]),
% 5.34/5.81 [x,rule_639]).
% 5.34/5.81 cnf('0.694.0.0',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(b)),a))) = multiply(least_upper_bound(identity,greatest_lower_bound(inverse(b),inverse(a))),a) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.424.2.0','0.113.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2','L')]).
% 5.34/5.81 cnf('0.694.0.1',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(b),a))) = multiply(least_upper_bound(identity,greatest_lower_bound(inverse(b),inverse(a))),a) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.694.0.0','0.331.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.694.0.2',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(b),a))) = multiply(identity,a) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.694.0.1','0.127.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.694.0.3',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(b),a))) = a ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.694.0.2','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.694.1.0',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(b),a))) = a ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.694.0.3']),
% 5.34/5.81 [weight('<8,424,113,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.694.2.0',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(b),a))) = a ),
% 5.34/5.81 inference(orient,[status(thm)],['0.694.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_689]).
% 5.34/5.81 cnf('0.695.0.0',plain,
% 5.34/5.81 ( least_upper_bound(b,greatest_lower_bound(identity,multiply(inverse(a),b))) = multiply(identity,b) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.424.2.0','0.127.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.695.0.1',plain,
% 5.34/5.81 ( least_upper_bound(b,greatest_lower_bound(identity,multiply(inverse(a),b))) = b ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.695.0.0','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.695.1.0',plain,
% 5.34/5.81 ( least_upper_bound(b,greatest_lower_bound(identity,multiply(inverse(a),b))) = b ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.695.0.1']),
% 5.34/5.81 [weight('<8,424,127,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.695.2.0',plain,
% 5.34/5.81 ( least_upper_bound(b,greatest_lower_bound(identity,multiply(inverse(a),b))) = b ),
% 5.34/5.81 inference(orient,[status(thm)],['0.695.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_690]).
% 5.34/5.81 cnf('0.696.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(identity,multiply(b,a)))) = multiply(inverse(b),greatest_lower_bound(b,greatest_lower_bound(a,multiply(b,a)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.32.2.0','0.429.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.696.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(b),identity),a)) = multiply(inverse(b),greatest_lower_bound(b,greatest_lower_bound(a,multiply(b,a)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.696.0.0','0.134.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.696.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(inverse(b),a)) = multiply(inverse(b),greatest_lower_bound(b,greatest_lower_bound(a,multiply(b,a)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.696.0.1','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1','L')]).
% 5.34/5.81 cnf('0.696.0.3',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(inverse(b),a)) = greatest_lower_bound(identity,multiply(inverse(b),greatest_lower_bound(a,multiply(b,a)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.696.0.2','0.32.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.696.0.4',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(inverse(b),a)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(b),a),a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.696.0.3','0.134.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.696.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(inverse(b),a)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(b),a),a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.696.0.4']),
% 5.34/5.81 [weight('<8,429,32,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.696.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))) = greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(b),a),a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.696.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.696.1.2',plain,
% 5.34/5.81 ( greatest_lower_bound(a,inverse(b)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(b),a),a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.696.1.1','0.126.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.696.1.3',plain,
% 5.34/5.81 ( greatest_lower_bound(a,inverse(b)) = greatest_lower_bound(identity,greatest_lower_bound(a,multiply(inverse(b),a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.696.1.2','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.696.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(a,multiply(inverse(b),a))) = greatest_lower_bound(a,inverse(b)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.696.1.3',theory(equality)]),
% 5.34/5.81 [x,rule_691]).
% 5.34/5.81 cnf('0.700.0.0',plain,
% 5.34/5.81 ( X1 = least_upper_bound(X1,multiply(X1,greatest_lower_bound(b,inverse(a)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.445.2.0','0.124.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.2','L')]).
% 5.34/5.81 cnf('0.700.1.0',plain,
% 5.34/5.81 ( X1 = least_upper_bound(X1,multiply(X1,greatest_lower_bound(b,inverse(a)))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.700.0.0']),
% 5.34/5.81 [weight('<8,445,124,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.700.2.0',plain,
% 5.34/5.81 ( least_upper_bound(X1,multiply(X1,greatest_lower_bound(b,inverse(a)))) = X1 ),
% 5.34/5.81 inference(orient,[status(thm)],['0.700.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_695]).
% 5.34/5.81 cnf('0.701.0.0',plain,
% 5.34/5.81 ( inverse(inverse(a)) = least_upper_bound(inverse(inverse(a)),greatest_lower_bound(identity,multiply(inverse(inverse(a)),b))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.700.2.0','0.33.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.701.0.1',plain,
% 5.34/5.81 ( a = least_upper_bound(inverse(inverse(a)),greatest_lower_bound(identity,multiply(inverse(inverse(a)),b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.701.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.701.0.2',plain,
% 5.34/5.81 ( a = least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(inverse(a)),b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.701.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.701.0.3',plain,
% 5.34/5.81 ( a = least_upper_bound(a,greatest_lower_bound(identity,multiply(a,b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.701.0.2','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2.2.1','L')]).
% 5.34/5.81 cnf('0.701.1.0',plain,
% 5.34/5.81 ( a = least_upper_bound(a,greatest_lower_bound(identity,multiply(a,b))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.701.0.3']),
% 5.34/5.81 [weight('<7,700,33,[1,0,0,2]>')]).
% 5.34/5.81 cnf('0.701.2.0',plain,
% 5.34/5.81 ( least_upper_bound(a,greatest_lower_bound(identity,multiply(a,b))) = a ),
% 5.34/5.81 inference(orient,[status(thm)],['0.701.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_696]).
% 5.34/5.81 cnf('0.702.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(greatest_lower_bound(identity,multiply(a,b)),a) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.17.2.0','0.701.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.702.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.702.0.0','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.702.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.702.0.1']),
% 5.34/5.81 [weight('<7,701,17,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.702.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(identity,greatest_lower_bound(a,multiply(a,b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.702.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.702.1.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(b,greatest_lower_bound(a,multiply(a,b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.702.1.1','0.489.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.702.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(b,greatest_lower_bound(a,multiply(a,b))) = greatest_lower_bound(identity,multiply(a,b)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.702.1.2',theory(equality)]),
% 5.34/5.81 [x,rule_697]).
% 5.34/5.81 cnf('0.726.0.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(inverse(least_upper_bound(identity,X1)),identity),X1) = multiply(least_upper_bound(identity,inverse(inverse(least_upper_bound(identity,X1)))),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.478.2.0','0.346.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.726.0.1',plain,
% 5.34/5.81 ( multiply(least_upper_bound(inverse(least_upper_bound(identity,X1)),identity),X1) = multiply(least_upper_bound(identity,least_upper_bound(identity,X1)),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.726.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1.2','L')]).
% 5.34/5.81 cnf('0.726.0.2',plain,
% 5.34/5.81 ( multiply(least_upper_bound(inverse(least_upper_bound(identity,X1)),identity),X1) = multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.726.0.1','0.18.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.726.1.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(inverse(least_upper_bound(identity,X1)),identity),X1) = multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.726.0.2']),
% 5.34/5.81 [weight('<8,478,346,[1,0,0,5]>')]).
% 5.34/5.81 cnf('0.726.1.1',plain,
% 5.34/5.81 ( least_upper_bound(inverse(least_upper_bound(identity,inverse(X1))),multiply(identity,X1)) = multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.726.1.0','0.591.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.726.1.2',plain,
% 5.34/5.81 ( least_upper_bound(multiply(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) = multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.726.1.1','0.12.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.726.1.3',plain,
% 5.34/5.81 ( least_upper_bound(X1,inverse(least_upper_bound(identity,inverse(X1)))) = multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.726.1.2','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.726.1.4',plain,
% 5.34/5.81 ( X1 = multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.726.1.3','0.202.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.726.2.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) = X1 ),
% 5.34/5.81 inference(orient,[status(thm)],['0.726.1.4',theory(equality)]),
% 5.34/5.81 [x,rule_720]).
% 5.34/5.81 cnf('0.813.0.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(X1,multiply(X2,X3)),X4) = least_upper_bound(multiply(X1,X4),multiply(X2,multiply(X3,X4))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.9.2.0','0.6.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.813.1.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(X1,multiply(X2,X3)),X4) = least_upper_bound(multiply(X1,X4),multiply(X2,multiply(X3,X4))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.813.0.0']),
% 5.34/5.81 [weight('<?,9,6,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.813.2.0',plain,
% 5.34/5.81 ( least_upper_bound(multiply(X1,X2),multiply(X3,multiply(X4,X2))) = multiply(least_upper_bound(X1,multiply(X3,X4)),X2) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.813.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_807]).
% 5.34/5.81 cnf('0.881.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(b),a)) = greatest_lower_bound(greatest_lower_bound(identity,multiply(inverse(b),a)),a) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.17.2.0','0.694.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.881.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(b),a)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(b),a),a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.881.0.0','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.881.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(b),a)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(b),a),a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.881.0.1']),
% 5.34/5.81 [weight('<8,694,17,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.881.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(b),a)) = greatest_lower_bound(identity,greatest_lower_bound(a,multiply(inverse(b),a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.881.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.881.1.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(b),a)) = greatest_lower_bound(a,inverse(b)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.881.1.1','0.696.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.881.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(b),a)) = greatest_lower_bound(a,inverse(b)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.881.1.2',theory(equality)]),
% 5.34/5.81 [u,rule_875]).
% 5.34/5.81 cnf('0.882.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(multiply(inverse(inverse(b)),identity),a) = multiply(inverse(inverse(b)),greatest_lower_bound(a,inverse(b))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.134.2.0','0.881.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.882.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(inverse(b)),a) = multiply(inverse(inverse(b)),greatest_lower_bound(a,inverse(b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.882.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.882.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(b,a) = multiply(inverse(inverse(b)),greatest_lower_bound(a,inverse(b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.882.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.882.0.3',plain,
% 5.34/5.81 ( greatest_lower_bound(b,a) = greatest_lower_bound(identity,multiply(inverse(inverse(b)),a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.882.0.2','0.33.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.882.0.4',plain,
% 5.34/5.81 ( greatest_lower_bound(b,a) = greatest_lower_bound(identity,multiply(b,a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.882.0.3','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2.1','L')]).
% 5.34/5.81 cnf('0.882.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(b,a) = greatest_lower_bound(identity,multiply(b,a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.882.0.4']),
% 5.34/5.81 [weight('<5,881,134,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.882.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(b,a)) = greatest_lower_bound(b,a) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.882.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_876]).
% 5.34/5.81 cnf('0.905.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(a),b)) = greatest_lower_bound(greatest_lower_bound(identity,multiply(inverse(a),b)),b) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.17.2.0','0.695.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.905.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(a),b)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(a),b),b)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.905.0.0','0.15.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.905.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(a),b)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(a),b),b)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.905.0.1']),
% 5.34/5.81 [weight('<8,695,17,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.905.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(a),b)) = greatest_lower_bound(identity,greatest_lower_bound(b,multiply(inverse(a),b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.905.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.905.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(b,multiply(inverse(a),b))) = greatest_lower_bound(identity,multiply(inverse(a),b)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.905.1.1',theory(equality)]),
% 5.34/5.81 [x,rule_899]).
% 5.34/5.81 cnf('0.910.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(a),greatest_lower_bound(b,multiply(a,b)))) = multiply(inverse(a),greatest_lower_bound(identity,multiply(a,b))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.155.2.0','0.702.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.910.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(a),b),b)) = multiply(inverse(a),greatest_lower_bound(identity,multiply(a,b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.910.0.0','0.134.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.910.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(a),b),b)) = greatest_lower_bound(multiply(inverse(a),identity),b) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.910.0.1','0.134.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.910.0.3',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(a),b),b)) = greatest_lower_bound(inverse(a),b) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.910.0.2','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.910.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(a),b),b)) = greatest_lower_bound(inverse(a),b) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.910.0.3']),
% 5.34/5.81 [weight('<8,702,155,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.910.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,greatest_lower_bound(b,multiply(inverse(a),b))) = greatest_lower_bound(inverse(a),b) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.910.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.910.1.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(a),b)) = greatest_lower_bound(inverse(a),b) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.910.1.1','0.905.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.910.1.3',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(a),b)) = greatest_lower_bound(b,inverse(a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.910.1.2','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.910.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(a),b)) = greatest_lower_bound(b,inverse(a)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.910.1.3',theory(equality)]),
% 5.34/5.81 [u,rule_904]).
% 5.34/5.81 cnf('0.911.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(multiply(inverse(inverse(a)),identity),b) = multiply(inverse(inverse(a)),greatest_lower_bound(b,inverse(a))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.134.2.0','0.910.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.911.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(inverse(a)),b) = multiply(inverse(inverse(a)),greatest_lower_bound(b,inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.911.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.911.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(a,b) = multiply(inverse(inverse(a)),greatest_lower_bound(b,inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.911.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.911.0.3',plain,
% 5.34/5.81 ( greatest_lower_bound(a,b) = greatest_lower_bound(identity,multiply(inverse(inverse(a)),b)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.911.0.2','0.33.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.911.0.4',plain,
% 5.34/5.81 ( greatest_lower_bound(a,b) = greatest_lower_bound(identity,multiply(a,b)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.911.0.3','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2.1','L')]).
% 5.34/5.81 cnf('0.911.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(a,b) = greatest_lower_bound(identity,multiply(a,b)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.911.0.4']),
% 5.34/5.81 [weight('<5,910,134,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.911.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(b,a) = greatest_lower_bound(identity,multiply(a,b)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.911.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.911.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(b,a) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.911.1.1',theory(equality)]),
% 5.34/5.81 [x,rule_905]).
% 5.34/5.81 cnf('0.1006.0.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(X1,multiply(X2,inverse(X3))),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,identity)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.813.2.0','0.11.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.2','L')]).
% 5.34/5.81 cnf('0.1006.0.1',plain,
% 5.34/5.81 ( multiply(least_upper_bound(X1,multiply(X2,inverse(X3))),X3) = least_upper_bound(multiply(X1,X3),X2) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1006.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.1006.1.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(X1,multiply(X2,inverse(X3))),X3) = least_upper_bound(multiply(X1,X3),X2) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1006.0.1']),
% 5.34/5.81 [weight('<8,813,11,[1,0,0,6]>')]).
% 5.34/5.81 cnf('0.1006.2.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(X1,multiply(X2,inverse(X3))),X3) = least_upper_bound(multiply(X1,X3),X2) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1006.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_1000]).
% 5.34/5.81 cnf('0.1014.0.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.10.2.0','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.1014.1.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1014.0.0']),
% 5.34/5.81 [weight('<?,10,1,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.1014.2.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)) ),
% 5.34/5.81 inference(activate,[status(thm)],['0.1014.1.0']),
% 5.34/5.81 [equation_7]).
% 5.34/5.81 cnf('0.1015.0.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,X2))) = inverse(greatest_lower_bound(X1,multiply(X2,X1))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.137.2.0','0.1014.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.1015.1.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,X2))) = inverse(greatest_lower_bound(X1,multiply(X2,X1))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1015.0.0']),
% 5.34/5.81 [weight('<6,1014,137,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.1015.2.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(X1,multiply(X2,X1))) = multiply(inverse(X1),inverse(greatest_lower_bound(identity,X2))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1015.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_1008]).
% 5.34/5.81 cnf('0.1017.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(X1,multiply(multiply(b,a),X1)) = multiply(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.1014.2.0','0.882.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.1017.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(X1,multiply(b,multiply(a,X1))) = multiply(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1017.0.0','0.6.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.1017.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(X1,multiply(b,multiply(a,X1))) = multiply(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1017.0.1']),
% 5.34/5.81 [weight('<7,1014,882,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.1017.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(X1,multiply(b,multiply(a,X1))) = multiply(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1017.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_1010]).
% 5.34/5.81 cnf('0.1018.0.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(b,a),inverse(a)) = greatest_lower_bound(inverse(a),multiply(b,identity)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.1017.2.0','0.26.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.2','L')]).
% 5.34/5.81 cnf('0.1018.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(b,inverse(a))) = greatest_lower_bound(inverse(a),multiply(b,identity)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1018.0.0','0.49.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.1018.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(b,inverse(a))) = greatest_lower_bound(inverse(a),b) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1018.0.1','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.1018.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(b,inverse(a))) = greatest_lower_bound(inverse(a),b) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1018.0.2']),
% 5.34/5.81 [weight('<6,1017,26,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.1018.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(b,inverse(a))) = greatest_lower_bound(b,inverse(a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1018.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.1018.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(b,inverse(a))) = greatest_lower_bound(b,inverse(a)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1018.1.1',theory(equality)]),
% 5.34/5.81 [u,rule_1011]).
% 5.34/5.81 cnf('0.1019.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(X1,multiply(multiply(a,b),X1)) = multiply(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.1014.2.0','0.911.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.1019.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(X1,multiply(a,multiply(b,X1))) = multiply(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1019.0.0','0.6.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.1019.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(X1,multiply(a,multiply(b,X1))) = multiply(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1019.0.1']),
% 5.34/5.81 [weight('<7,1014,911,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.1019.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(X1,multiply(a,multiply(b,X1))) = multiply(greatest_lower_bound(b,a),X1) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1019.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_1012]).
% 5.34/5.81 cnf('0.1020.0.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(b,a),inverse(b)) = greatest_lower_bound(inverse(b),multiply(a,identity)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.1019.2.0','0.26.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.2','L')]).
% 5.34/5.81 cnf('0.1020.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,inverse(b))) = greatest_lower_bound(inverse(b),multiply(a,identity)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1020.0.0','0.48.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.1020.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,inverse(b))) = greatest_lower_bound(inverse(b),a) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1020.0.1','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.1020.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,inverse(b))) = greatest_lower_bound(inverse(b),a) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1020.0.2']),
% 5.34/5.81 [weight('<6,1019,26,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.1020.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,inverse(b))) = greatest_lower_bound(a,inverse(b)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1020.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.1020.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(a,inverse(b))) = greatest_lower_bound(a,inverse(b)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1020.1.1',theory(equality)]),
% 5.34/5.81 [u,rule_1013]).
% 5.34/5.81 cnf('0.1025.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(multiply(inverse(b),identity),inverse(a)) = multiply(inverse(b),greatest_lower_bound(b,inverse(a))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.134.2.0','0.1018.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.1025.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(b),inverse(a)) = multiply(inverse(b),greatest_lower_bound(b,inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1025.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.1025.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(b),inverse(a)) = greatest_lower_bound(identity,multiply(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1025.0.1','0.32.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.1025.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(b),inverse(a)) = greatest_lower_bound(identity,multiply(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1025.0.2']),
% 5.34/5.81 [weight('<7,1018,134,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.1025.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(b),inverse(a))) = greatest_lower_bound(inverse(b),inverse(a)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1025.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_1018]).
% 5.34/5.81 cnf('0.1030.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(multiply(inverse(a),identity),inverse(b)) = multiply(inverse(a),greatest_lower_bound(a,inverse(b))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.134.2.0','0.1020.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.1030.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(a),inverse(b)) = multiply(inverse(a),greatest_lower_bound(a,inverse(b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1030.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.1030.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(a),inverse(b)) = greatest_lower_bound(identity,multiply(inverse(a),inverse(b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1030.0.1','0.32.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.1030.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(a),inverse(b)) = greatest_lower_bound(identity,multiply(inverse(a),inverse(b))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1030.0.2']),
% 5.34/5.81 [weight('<7,1020,134,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.1030.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(b),inverse(a)) = greatest_lower_bound(identity,multiply(inverse(a),inverse(b))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1030.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.1030.2.0',plain,
% 5.34/5.81 ( greatest_lower_bound(identity,multiply(inverse(a),inverse(b))) = greatest_lower_bound(inverse(b),inverse(a)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1030.1.1',theory(equality)]),
% 5.34/5.81 [x,rule_1023]).
% 5.34/5.81 cnf('0.1187.0.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,multiply(X2,X3)))) = inverse(greatest_lower_bound(X1,multiply(X2,multiply(X3,X1)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.1015.2.0','0.6.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2','L')]).
% 5.34/5.81 cnf('0.1187.1.0',plain,
% 5.34/5.81 ( multiply(inverse(X1),inverse(greatest_lower_bound(identity,multiply(X2,X3)))) = inverse(greatest_lower_bound(X1,multiply(X2,multiply(X3,X1)))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1187.0.0']),
% 5.34/5.81 [weight('<8,1015,6,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.1187.2.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(X1,multiply(X2,multiply(X3,X1)))) = multiply(inverse(X1),inverse(greatest_lower_bound(identity,multiply(X2,X3)))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1187.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_1180]).
% 5.34/5.81 cnf('0.1298.0.0',plain,
% 5.34/5.81 ( multiply(inverse(inverse(X1)),inverse(greatest_lower_bound(identity,multiply(X2,X1)))) = inverse(greatest_lower_bound(inverse(X1),multiply(X2,identity))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.1187.2.0','0.26.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2.2','L')]).
% 5.34/5.81 cnf('0.1298.0.1',plain,
% 5.34/5.81 ( multiply(X1,inverse(greatest_lower_bound(identity,multiply(X2,X1)))) = inverse(greatest_lower_bound(inverse(X1),multiply(X2,identity))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1298.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.1298.0.2',plain,
% 5.34/5.81 ( multiply(X1,inverse(greatest_lower_bound(identity,multiply(X2,X1)))) = inverse(greatest_lower_bound(inverse(X1),X2)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1298.0.1','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1.2','L')]).
% 5.34/5.81 cnf('0.1298.1.0',plain,
% 5.34/5.81 ( multiply(X1,inverse(greatest_lower_bound(identity,multiply(X2,X1)))) = inverse(greatest_lower_bound(inverse(X1),X2)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1298.0.2']),
% 5.34/5.81 [weight('<8,1187,26,[1,0,0,5]>')]).
% 5.34/5.81 cnf('0.1298.2.0',plain,
% 5.34/5.81 ( multiply(X1,inverse(greatest_lower_bound(identity,multiply(X2,X1)))) = inverse(greatest_lower_bound(inverse(X1),X2)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1298.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_1290]).
% 5.34/5.81 cnf('0.1386.0.0',plain,
% 5.34/5.81 ( multiply(inverse(inverse(greatest_lower_bound(identity,multiply(X1,X2)))),inverse(X2)) = inverse(inverse(greatest_lower_bound(inverse(X2),X1))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.137.2.0','0.1298.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.1386.0.1',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,multiply(X1,X2)),inverse(X2)) = inverse(inverse(greatest_lower_bound(inverse(X2),X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1386.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.1386.0.2',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,multiply(X1,X2)),inverse(X2)) = greatest_lower_bound(inverse(X2),X1) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1386.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.1386.1.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,multiply(X1,X2)),inverse(X2)) = greatest_lower_bound(inverse(X2),X1) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1386.0.2']),
% 5.34/5.81 [weight('<8,1298,137,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.1386.2.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,multiply(X1,X2)),inverse(X2)) = greatest_lower_bound(inverse(X2),X1) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1386.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_1378]).
% 5.34/5.81 cnf('0.1433.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(inverse(inverse(least_upper_bound(identity,inverse(X1)))),least_upper_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),inverse(inverse(least_upper_bound(identity,inverse(X1))))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.1386.2.0','0.726.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2','L')]).
% 5.34/5.81 cnf('0.1433.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(least_upper_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),inverse(inverse(least_upper_bound(identity,inverse(X1))))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1433.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.1433.0.2',plain,
% 5.34/5.81 ( greatest_lower_bound(least_upper_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1433.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.1433.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(least_upper_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1433.0.2']),
% 5.34/5.81 [weight('<8,1386,726,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.1433.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1433.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.1433.2.0',plain,
% 5.34/5.81 ( multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1433.1.1',theory(equality)]),
% 5.34/5.81 [x,rule_1425]).
% 5.34/5.81 cnf('0.1447.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(least_upper_bound(identity,inverse(X1)),least_upper_bound(identity,inverse(inverse(X1)))) = multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.1433.2.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.2','L')]).
% 5.34/5.81 cnf('0.1447.0.1',plain,
% 5.34/5.81 ( greatest_lower_bound(least_upper_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) = multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1447.0.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.2','L')]).
% 5.34/5.81 cnf('0.1447.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(least_upper_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) = multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1447.0.1']),
% 5.34/5.81 [weight('<8,1433,24,[1,0,0,6]>')]).
% 5.34/5.81 cnf('0.1447.1.1',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1447.1.0','0.14.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.1447.2.0',plain,
% 5.34/5.81 ( 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))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1447.1.1',theory(equality)]),
% 5.34/5.81 [x,rule_1439]).
% 5.34/5.81 cnf('0.1568.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(greatest_lower_bound(least_upper_bound(X1,X2),X3),greatest_lower_bound(X1,X3)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.19.2.0','0.51.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.1568.1.0',plain,
% 5.34/5.81 ( greatest_lower_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(greatest_lower_bound(least_upper_bound(X1,X2),X3),greatest_lower_bound(X1,X3)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.1568.0.0']),
% 5.34/5.81 [weight('<9,51,19,[0,0,0,2]>')]).
% 5.34/5.81 cnf('0.1568.1.1',plain,
% 5.34/5.81 ( greatest_lower_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(greatest_lower_bound(X1,X3),greatest_lower_bound(least_upper_bound(X1,X2),X3)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.1568.1.0','0.12.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.1568.2.0',plain,
% 5.34/5.81 ( least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(least_upper_bound(X1,X3),X2)) = greatest_lower_bound(least_upper_bound(X1,X3),X2) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.1568.1.1',theory(equality)]),
% 5.34/5.81 [x,rule_1558]).
% 5.34/5.81 cnf('0.2186.0.0',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.458.2.0','0.3.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1.1','L')]).
% 5.34/5.81 cnf('0.2186.0.1',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2186.0.0','0.140.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.1','L')]).
% 5.34/5.81 cnf('0.2186.0.2',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2186.0.1','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.2186.0.3',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2186.0.2','0.27.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2.1','L')]).
% 5.34/5.81 cnf('0.2186.1.0',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2186.0.3']),
% 5.34/5.81 [weight('<9,458,3,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.2186.2.0',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2186.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_2168]).
% 5.34/5.81 cnf('0.2187.0.0',plain,
% 5.34/5.81 ( 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))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.2186.2.0','0.37.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.2187.0.1',plain,
% 5.34/5.81 ( 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))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2187.0.0','0.1447.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.2187.0.2',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2187.0.1','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2.2','L')]).
% 5.34/5.81 cnf('0.2187.1.0',plain,
% 5.34/5.81 ( 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)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2187.0.2']),
% 5.34/5.81 [weight('<8,2186,37,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.2187.1.1',plain,
% 5.34/5.81 ( 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))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2187.1.0','0.12.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.2187.2.0',plain,
% 5.34/5.81 ( 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))) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2187.1.1',theory(equality)]),
% 5.34/5.81 [u,rule_2169]).
% 5.34/5.81 cnf('0.2193.0.0',plain,
% 5.34/5.81 ( greatest_lower_bound(least_upper_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X1))),least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.1568.2.0','0.2187.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.2193.0.1',plain,
% 5.34/5.81 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(greatest_lower_bound(identity,least_upper_bound(identity,inverse(X1))),least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2193.0.0','0.2187.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('0.2193.0.2',plain,
% 5.34/5.81 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1)))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2193.0.1','0.5.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.2193.0.3',plain,
% 5.34/5.81 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,greatest_lower_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2193.0.2','0.50.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.2193.0.4',plain,
% 5.34/5.81 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = identity ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2193.0.3','0.3.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.2193.1.0',plain,
% 5.34/5.81 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = identity ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2193.0.4']),
% 5.34/5.81 [weight('<8,2187,1568,[0,0,0,4]>')]).
% 5.34/5.81 cnf('0.2193.2.0',plain,
% 5.34/5.81 ( least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = identity ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2193.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_2175]).
% 5.34/5.81 cnf('0.2194.0.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1))) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),identity) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.31.2.0','0.2193.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.2194.0.1',plain,
% 5.34/5.81 ( least_upper_bound(identity,X1) = multiply(inverse(greatest_lower_bound(identity,inverse(X1))),identity) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2194.0.0','0.644.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.2194.0.2',plain,
% 5.34/5.81 ( least_upper_bound(identity,X1) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2194.0.1','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.2194.1.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,X1) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2194.0.2']),
% 5.34/5.81 [weight('<5,2193,31,[0,0,0,3]>')]).
% 5.34/5.81 cnf('0.2194.2.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,X1) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2194.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_2176]).
% 5.34/5.81 cnf('0.2196.0.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(identity,X1)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.2194.2.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.2','L')]).
% 5.34/5.81 cnf('0.2196.1.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(identity,X1)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2196.0.0']),
% 5.34/5.81 [weight('<4,2194,24,[1,0,0,3]>')]).
% 5.34/5.81 cnf('0.2196.2.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(X1)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2196.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_2178]).
% 5.34/5.81 cnf('0.2200.0.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(multiply(inverse(X1),identity),X2)) = multiply(least_upper_bound(identity,inverse(multiply(X1,X2))),X1) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.353.2.0','0.2196.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.2200.0.1',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(inverse(X1),X2)) = multiply(least_upper_bound(identity,inverse(multiply(X1,X2))),X1) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2200.0.0','0.29.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.1','L')]).
% 5.34/5.81 cnf('0.2200.0.2',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(inverse(X1),X2)) = multiply(least_upper_bound(identity,multiply(inverse(X2),inverse(X1))),X1) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2200.0.1','0.137.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1.2','L')]).
% 5.34/5.81 cnf('0.2200.0.3',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(multiply(identity,X1),inverse(X2)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2200.0.2','0.1006.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.2200.0.4',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(X1,inverse(X2)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2200.0.3','0.1.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.2200.1.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(X1,inverse(X2)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2200.0.4']),
% 5.34/5.81 [weight('<5,2196,353,[0,0,0,1]>')]).
% 5.34/5.81 cnf('0.2200.2.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(X1,inverse(X2)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2200.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_2182]).
% 5.34/5.81 cnf('0.2201.0.0',plain,
% 5.34/5.81 ( least_upper_bound(inverse(X1),inverse(X2)) = inverse(greatest_lower_bound(X1,X2)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.2200.2.0','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1.1','L')]).
% 5.34/5.81 cnf('0.2201.1.0',plain,
% 5.34/5.81 ( least_upper_bound(inverse(X1),inverse(X2)) = inverse(greatest_lower_bound(X1,X2)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2201.0.0']),
% 5.34/5.81 [weight('<4,2200,24,[1,0,0,2]>')]).
% 5.34/5.81 cnf('0.2201.2.0',plain,
% 5.34/5.81 ( inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(X1),inverse(X2)) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2201.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_2183]).
% 5.34/5.81 cnf('0.2208.0.0',plain,
% 5.34/5.81 ( least_upper_bound(inverse(identity),inverse(multiply(inverse(b),inverse(a)))) = inverse(greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.2201.2.0','0.1025.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.2208.0.1',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(multiply(inverse(b),inverse(a)))) = inverse(greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2208.0.0','0.27.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.2208.0.2',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(inverse(a)),inverse(inverse(b)))) = inverse(greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2208.0.1','0.137.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.2208.0.3',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(a,inverse(inverse(b)))) = inverse(greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2208.0.2','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1','L')]).
% 5.34/5.81 cnf('0.2208.0.4',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(a,b)) = inverse(greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2208.0.3','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.2','L')]).
% 5.34/5.81 cnf('0.2208.0.5',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(a,b)) = least_upper_bound(inverse(inverse(b)),inverse(inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2208.0.4','0.2201.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.2208.0.6',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(a,b)) = least_upper_bound(b,inverse(inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2208.0.5','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.2208.0.7',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(a,b)) = least_upper_bound(b,a) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2208.0.6','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.2208.1.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(a,b)) = least_upper_bound(b,a) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2208.0.7']),
% 5.34/5.81 [weight('<5,2201,1025,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.2208.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(a,b)) = least_upper_bound(b,a) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2208.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_2190]).
% 5.34/5.81 cnf('0.2209.0.0',plain,
% 5.34/5.81 ( least_upper_bound(inverse(identity),inverse(multiply(inverse(a),inverse(b)))) = inverse(greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.2201.2.0','0.1030.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.2209.0.1',plain,
% 5.34/5.81 ( least_upper_bound(identity,inverse(multiply(inverse(a),inverse(b)))) = inverse(greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2209.0.0','0.27.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.2209.0.2',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(inverse(inverse(b)),inverse(inverse(a)))) = inverse(greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2209.0.1','0.137.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.2209.0.3',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(b,inverse(inverse(a)))) = inverse(greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2209.0.2','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.1','L')]).
% 5.34/5.81 cnf('0.2209.0.4',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(b,a)) = inverse(greatest_lower_bound(inverse(b),inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2209.0.3','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2.2','L')]).
% 5.34/5.81 cnf('0.2209.0.5',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(b,a)) = least_upper_bound(inverse(inverse(b)),inverse(inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2209.0.4','0.2201.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.2209.0.6',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(b,a)) = least_upper_bound(b,inverse(inverse(a))) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2209.0.5','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.2209.0.7',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(b,a)) = least_upper_bound(b,a) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2209.0.6','0.24.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.2','L')]).
% 5.34/5.81 cnf('0.2209.1.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(b,a)) = least_upper_bound(b,a) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2209.0.7']),
% 5.34/5.81 [weight('<5,2201,1030,[1,0,0,1]>')]).
% 5.34/5.81 cnf('0.2209.2.0',plain,
% 5.34/5.81 ( least_upper_bound(identity,multiply(b,a)) = least_upper_bound(b,a) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2209.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_2191]).
% 5.34/5.81 cnf('0.2233.0.0',plain,
% 5.34/5.81 ( multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) = X1 ),
% 5.34/5.81 inference(interreduction_right,[status(thm)],['0.644.2.0'])).
% 5.34/5.81 cnf('0.2233.0.1',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) = X1 ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2233.0.0','0.2194.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.1','L')]).
% 5.34/5.81 cnf('0.2233.1.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) = X1 ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2233.0.1']),
% 5.34/5.81 [weight('<7,644,2194,[0,0,0,0]>')]).
% 5.34/5.81 cnf('0.2233.2.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) = X1 ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2233.1.0',theory(equality)]),
% 5.34/5.81 [u,rule_2213]).
% 5.34/5.81 cnf('0.2318.0.0',plain,
% 5.34/5.81 ( multiply(b,a) = multiply(least_upper_bound(identity,multiply(b,a)),greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.2233.2.0','0.882.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.2318.0.1',plain,
% 5.34/5.81 ( multiply(b,a) = multiply(least_upper_bound(b,a),greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2318.0.0','0.2209.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.2318.1.0',plain,
% 5.34/5.81 ( multiply(b,a) = multiply(least_upper_bound(b,a),greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2318.0.1']),
% 5.34/5.81 [weight('<7,2233,882,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.2318.2.0',plain,
% 5.34/5.81 ( multiply(least_upper_bound(b,a),greatest_lower_bound(b,a)) = multiply(b,a) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2318.1.0',theory(equality)]),
% 5.34/5.81 [x,rule_2298]).
% 5.34/5.81 cnf('0.2319.0.0',plain,
% 5.34/5.81 ( multiply(a,b) = multiply(least_upper_bound(identity,multiply(a,b)),greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(cp,[status(thm)],['0.2233.2.0','0.911.2.0',theory(equality)]),
% 5.34/5.81 [pos('L.2','L')]).
% 5.34/5.81 cnf('0.2319.0.1',plain,
% 5.34/5.81 ( multiply(a,b) = multiply(least_upper_bound(b,a),greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2319.0.0','0.2208.2.0',theory(equality)]),
% 5.34/5.81 [pos('R.1','L')]).
% 5.34/5.81 cnf('0.2319.1.0',plain,
% 5.34/5.81 ( multiply(a,b) = multiply(least_upper_bound(b,a),greatest_lower_bound(b,a)) ),
% 5.34/5.81 inference(weigh,[status(thm)],['0.2319.0.1']),
% 5.34/5.81 [weight('<7,2233,911,[1,0,0,4]>')]).
% 5.34/5.81 cnf('0.2319.1.1',plain,
% 5.34/5.81 ( multiply(a,b) = multiply(b,a) ),
% 5.34/5.81 inference(reduction,[status(thm)],['0.2319.1.0','0.2318.2.0',theory(equality)]),
% 5.34/5.81 [pos('R','L')]).
% 5.34/5.81 cnf('0.2319.2.0',plain,
% 5.34/5.81 ( multiply(a,b) = multiply(b,a) ),
% 5.34/5.81 inference(orient,[status(thm)],['0.2319.1.1',theory(equality)]),
% 5.34/5.81 [u,rule_2299]).
% 5.34/5.81 cnf('1.0.0.0',conjecture,
% 5.34/5.81 ( multiply(a,b) = multiply(b,a) ),
% 5.34/5.81 file('/tmp/WALDMEISTER_6253_n011',conjecture_1)).
% 5.34/5.81 cnf('1.0.0.1',plain,
% 5.34/5.81 ( multiply(b,a) = multiply(b,a) ),
% 5.34/5.81 inference(reduction,[status(thm)],['1.0.0.0','0.2319.2.0',theory(equality)]),
% 5.34/5.81 [pos('L','L')]).
% 5.34/5.81 cnf('1.0.0.2',plain,
% 5.34/5.81 ( $true ),
% 5.34/5.81 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 5.34/5.81 [conjecture_1]).
% 5.34/5.81
% 5.34/5.81 Proved Goals:
% 5.34/5.81 No. 1: multiply(a,b) ?= multiply(b,a) joined, current: multiply(b,a) = multiply(b,a)
% 5.34/5.81 1 goal was specified, which was proved.
% 5.34/5.81 % SZS output end CNFRefutation
% 5.34/5.81 #END OF PROOF
% 5.34/5.81
% 5.34/5.81 Problem WALDMEISTER_6253_n011
% 5.34/5.81 CPs.gen 577998
% 5.34/5.81 CPs.reexp 0
% 5.34/5.81 Select 36056
% 5.34/5.81 R 2299
% 5.34/5.81 E 20
% 5.34/5.81 vsize 9.4M
% 5.34/5.81 rss 5.0M
% 5.34/5.81 process.time 3.560s
% 5.34/5.81 wallclock.time 4.660s
% 5.34/5.81 status S
% 5.34/5.81
% 5.34/5.81
% 5.34/5.81 Waldmeister states: Goal proved.
% 5.34/5.81 % SZS status Unsatisfiable
% 5.34/5.81
% 5.34/5.81 Problem WALDMEISTER_6253_n011
% 5.34/5.81 CPs.gen 222951
% 5.34/5.81 CPs.reexp 0
% 5.34/5.81 Select 16913
% 5.34/5.81 R 1358
% 5.34/5.81 E 12
% 5.34/5.81 vsize 7.6M
% 5.34/5.81 rss 5.0M
% 5.34/5.81 process.time 1.099s
% 5.34/5.81 wallclock.time 4.660s
% 5.34/5.81 status S
%------------------------------------------------------------------------------