TSTP Solution File: GRP167-5 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP167-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 12:25:03 EDT 2022
% Result : Unsatisfiable 0.62s 1.04s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP167-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : woody %s
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Tue Jun 14 14:09:51 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.62/1.03 ********************************************************************************
% 0.62/1.03 * W A L D M E I S T E R \| \ / \|/ *
% 0.62/1.03 * |/ | \/ | *
% 0.62/1.03 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.62/1.03 * A. Jaeger and B. Loechner | | *
% 0.62/1.03 * <waldmeister@informatik.uni-kl.de> | *
% 0.62/1.03 ********************************************************************************
% 0.62/1.03
% 0.62/1.03
% 0.62/1.03 Goals:
% 0.62/1.03 ------
% 0.62/1.03
% 0.62/1.03 ( 1) multiply(positive_part(a),negative_part(a)) ?=? a
% 0.62/1.03
% 0.62/1.03 Detected structure: VerbandsgeordneteGruppe
% 0.62/1.03 ********************************************************************************
% 0.62/1.03 ****************************** COMPLETION - PROOF ******************************
% 0.62/1.03 ********************************************************************************
% 0.62/1.03
% 0.62/1.04 joined goal: 1 multiply(positive_part(a),negative_part(a)) ?= a to a
% 0.62/1.04 goal joined
% 0.62/1.04 % SZS status Unsatisfiable
% 0.62/1.04 #START OF PROOF
% 0.62/1.04 % SZS output start CNFRefutation
% 0.62/1.04 cnf('0.1.0.0',axiom,
% 0.62/1.04 ( X1 = greatest_lower_bound(X1,X1) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.1.1.0',plain,
% 0.62/1.04 ( X1 = greatest_lower_bound(X1,X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.62/1.04 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.1.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,X1) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_1]).
% 0.62/1.04 cnf('0.4.0.0',axiom,
% 0.62/1.04 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.4.1.0',plain,
% 0.62/1.04 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.62/1.04 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.62/1.04 cnf('0.4.2.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_4]).
% 0.62/1.04 cnf('0.5.0.0',axiom,
% 0.62/1.04 ( X1 = multiply(identity,X1) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.5.1.0',plain,
% 0.62/1.04 ( X1 = multiply(identity,X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.62/1.04 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.62/1.04 cnf('0.5.2.0',plain,
% 0.62/1.04 ( multiply(identity,X1) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_5]).
% 0.62/1.04 cnf('0.6.0.0',axiom,
% 0.62/1.04 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.6.1.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.62/1.04 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.62/1.04 cnf('0.6.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.62/1.04 inference(activate,[status(thm)],['0.6.1.0']),
% 0.62/1.04 [equation_1]).
% 0.62/1.04 cnf('0.7.0.0',axiom,
% 0.62/1.04 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.7.1.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.62/1.04 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.62/1.04 cnf('0.7.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_6]).
% 0.62/1.04 cnf('0.9.0.0',axiom,
% 0.62/1.04 ( greatest_lower_bound(X1,identity) = negative_part(X1) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.9.1.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,identity) = negative_part(X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.62/1.04 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.62/1.04 cnf('0.9.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,identity) = negative_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_8]).
% 0.62/1.04 cnf('0.11.0.0',axiom,
% 0.62/1.04 ( greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.11.1.0',plain,
% 0.62/1.04 ( greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.62/1.04 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.62/1.04 cnf('0.11.2.0',plain,
% 0.62/1.04 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_10]).
% 0.62/1.04 cnf('0.13.0.0',axiom,
% 0.62/1.04 ( greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X1,X2)) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.13.1.0',plain,
% 0.62/1.04 ( greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X1,X2)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.62/1.04 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.62/1.04 cnf('0.13.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X1,X2)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_12]).
% 0.62/1.04 cnf('0.14.0.0',axiom,
% 0.62/1.04 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.14.1.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.62/1.04 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.62/1.04 cnf('0.14.2.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.62/1.04 inference(activate,[status(thm)],['0.14.1.0']),
% 0.62/1.04 [equation_2]).
% 0.62/1.04 cnf('0.15.0.0',axiom,
% 0.62/1.04 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.15.1.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.62/1.04 [weight('<14,0,0,[0,0,0,15]>')]).
% 0.62/1.04 cnf('0.15.2.0',plain,
% 0.62/1.04 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_13]).
% 0.62/1.04 cnf('0.16.0.0',axiom,
% 0.62/1.04 ( least_upper_bound(X1,identity) = positive_part(X1) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.16.1.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,identity) = positive_part(X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.62/1.04 [weight('<15,0,0,[0,0,0,16]>')]).
% 0.62/1.04 cnf('0.16.2.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,identity) = positive_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_14]).
% 0.62/1.04 cnf('0.19.0.0',axiom,
% 0.62/1.04 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.19.1.0',plain,
% 0.62/1.04 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.62/1.04 [weight('<18,0,0,[0,0,0,19]>')]).
% 0.62/1.04 cnf('0.19.2.0',plain,
% 0.62/1.04 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_17]).
% 0.62/1.04 cnf('0.20.0.0',axiom,
% 0.62/1.04 ( multiply(inverse(X1),X1) = identity ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026')).
% 0.62/1.04 cnf('0.20.1.0',plain,
% 0.62/1.04 ( multiply(inverse(X1),X1) = identity ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.62/1.04 [weight('<19,0,0,[0,0,0,20]>')]).
% 0.62/1.04 cnf('0.20.2.0',plain,
% 0.62/1.04 ( multiply(inverse(X1),X1) = identity ),
% 0.62/1.04 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_18]).
% 0.62/1.04 cnf('0.21.0.0',plain,
% 0.62/1.04 ( negative_part(identity) = identity ),
% 0.62/1.04 inference(cp,[status(thm)],['0.9.2.0','0.1.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.21.1.0',plain,
% 0.62/1.04 ( negative_part(identity) = identity ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.62/1.04 [weight('<11,9,1,[1,0,0,0]>')]).
% 0.62/1.04 cnf('0.21.2.0',plain,
% 0.62/1.04 ( negative_part(identity) = identity ),
% 0.62/1.04 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_19]).
% 0.62/1.04 cnf('0.23.0.0',plain,
% 0.62/1.04 ( negative_part(X1) = greatest_lower_bound(identity,X1) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.9.2.0','0.6.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.23.1.0',plain,
% 0.62/1.04 ( negative_part(X1) = greatest_lower_bound(identity,X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.62/1.04 [weight('<23,9,6,[1,0,0,0]>')]).
% 0.62/1.04 cnf('0.23.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(identity,X1) = negative_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_21]).
% 0.62/1.04 cnf('0.24.0.0',plain,
% 0.62/1.04 ( positive_part(X1) = least_upper_bound(identity,X1) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.16.2.0','0.14.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.24.1.0',plain,
% 0.62/1.04 ( positive_part(X1) = least_upper_bound(identity,X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.24.0.0']),
% 0.62/1.04 [weight('<23,16,14,[1,0,0,0]>')]).
% 0.62/1.04 cnf('0.24.2.0',plain,
% 0.62/1.04 ( least_upper_bound(identity,X1) = positive_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_22]).
% 0.62/1.04 cnf('0.25.0.0',plain,
% 0.62/1.04 ( positive_part(greatest_lower_bound(identity,X1)) = identity ),
% 0.62/1.04 inference(cp,[status(thm)],['0.24.2.0','0.4.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.25.0.1',plain,
% 0.62/1.04 ( positive_part(negative_part(X1)) = identity ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.25.0.0','0.23.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.25.1.0',plain,
% 0.62/1.04 ( positive_part(negative_part(X1)) = identity ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.25.0.1']),
% 0.62/1.04 [weight('<24,24,4,[1,0,0,0]>')]).
% 0.62/1.04 cnf('0.25.2.0',plain,
% 0.62/1.04 ( positive_part(negative_part(X1)) = identity ),
% 0.62/1.04 inference(activate,[status(thm)],['0.25.1.0']),
% 0.62/1.04 [equation_3]).
% 0.62/1.04 cnf('0.25.2.2',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = identity ),
% 0.62/1.04 inference(instl,[status(thm)],['0.25.2.0',theory(equality)])).
% 0.62/1.04 cnf('0.26.0.0',plain,
% 0.62/1.04 ( negative_part(identity) = identity ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.21.2.0'])).
% 0.62/1.04 cnf('0.26.1.0',plain,
% 0.62/1.04 ( negative_part(identity) = identity ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.26.0.0']),
% 0.62/1.04 [weight('<11,21,25,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.26.1.1',plain,
% 0.62/1.04 ( negative_part(positive_part(negative_part(a))) = identity ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.26.1.0','0.25.2.2',theory(equality)]),
% 0.62/1.04 [pos('L.1','R')]).
% 0.62/1.04 cnf('0.26.1.2',plain,
% 0.62/1.04 ( negative_part(positive_part(negative_part(a))) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.26.1.1','0.25.2.2',theory(equality)]),
% 0.62/1.04 [pos('R','R')]).
% 0.62/1.04 cnf('0.26.2.0',plain,
% 0.62/1.04 ( negative_part(positive_part(negative_part(a))) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.26.1.2',theory(equality)]),
% 0.62/1.04 [u,rule_23]).
% 0.62/1.04 cnf('0.28.0.0',plain,
% 0.62/1.04 ( multiply(identity,X1) = X1 ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.5.2.0'])).
% 0.62/1.04 cnf('0.28.1.0',plain,
% 0.62/1.04 ( multiply(identity,X1) = X1 ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.28.0.0']),
% 0.62/1.04 [weight('<19,5,25,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.28.1.1',plain,
% 0.62/1.04 ( multiply(positive_part(negative_part(a)),X1) = X1 ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.28.1.0','0.25.2.2',theory(equality)]),
% 0.62/1.04 [pos('L.1','R')]).
% 0.62/1.04 cnf('0.28.2.0',plain,
% 0.62/1.04 ( multiply(positive_part(negative_part(a)),X1) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.28.1.1',theory(equality)]),
% 0.62/1.04 [u,rule_25]).
% 0.62/1.04 cnf('0.29.0.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,identity) = negative_part(X1) ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.9.2.0'])).
% 0.62/1.04 cnf('0.29.1.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,identity) = negative_part(X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.29.0.0']),
% 0.62/1.04 [weight('<23,9,25,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.29.1.1',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,positive_part(negative_part(a))) = negative_part(X1) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.29.1.0','0.25.2.2',theory(equality)]),
% 0.62/1.04 [pos('L.2','R')]).
% 0.62/1.04 cnf('0.29.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,positive_part(negative_part(a))) = negative_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.29.1.1',theory(equality)]),
% 0.62/1.04 [u,rule_26]).
% 0.62/1.04 cnf('0.30.0.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,identity) = positive_part(X1) ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.16.2.0'])).
% 0.62/1.04 cnf('0.30.1.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,identity) = positive_part(X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.30.0.0']),
% 0.62/1.04 [weight('<23,16,25,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.30.1.1',plain,
% 0.62/1.04 ( least_upper_bound(X1,positive_part(negative_part(a))) = positive_part(X1) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.30.1.0','0.25.2.2',theory(equality)]),
% 0.62/1.04 [pos('L.2','R')]).
% 0.62/1.04 cnf('0.30.2.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,positive_part(negative_part(a))) = positive_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.30.1.1',theory(equality)]),
% 0.62/1.04 [u,rule_27]).
% 0.62/1.04 cnf('0.31.0.0',plain,
% 0.62/1.04 ( greatest_lower_bound(identity,X1) = negative_part(X1) ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.23.2.0'])).
% 0.62/1.04 cnf('0.31.1.0',plain,
% 0.62/1.04 ( greatest_lower_bound(identity,X1) = negative_part(X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.31.0.0']),
% 0.62/1.04 [weight('<23,23,25,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.31.1.1',plain,
% 0.62/1.04 ( greatest_lower_bound(positive_part(negative_part(a)),X1) = negative_part(X1) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.31.1.0','0.25.2.2',theory(equality)]),
% 0.62/1.04 [pos('L.1','R')]).
% 0.62/1.04 cnf('0.31.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(positive_part(negative_part(a)),X1) = negative_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.31.1.1',theory(equality)]),
% 0.62/1.04 [u,rule_28]).
% 0.62/1.04 cnf('0.32.0.0',plain,
% 0.62/1.04 ( least_upper_bound(identity,X1) = positive_part(X1) ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.24.2.0'])).
% 0.62/1.04 cnf('0.32.1.0',plain,
% 0.62/1.04 ( least_upper_bound(identity,X1) = positive_part(X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.32.0.0']),
% 0.62/1.04 [weight('<23,24,25,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.32.1.1',plain,
% 0.62/1.04 ( least_upper_bound(positive_part(negative_part(a)),X1) = positive_part(X1) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.32.1.0','0.25.2.2',theory(equality)]),
% 0.62/1.04 [pos('L.1','R')]).
% 0.62/1.04 cnf('0.32.2.0',plain,
% 0.62/1.04 ( least_upper_bound(positive_part(negative_part(a)),X1) = positive_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.32.1.1',theory(equality)]),
% 0.62/1.04 [u,rule_29]).
% 0.62/1.04 cnf('0.33.0.0',plain,
% 0.62/1.04 ( multiply(inverse(X1),X1) = identity ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.20.2.0'])).
% 0.62/1.04 cnf('0.33.1.0',plain,
% 0.62/1.04 ( multiply(inverse(X1),X1) = identity ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.33.0.0']),
% 0.62/1.04 [weight('<29,20,25,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.33.1.1',plain,
% 0.62/1.04 ( multiply(inverse(X1),X1) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.33.1.0','0.25.2.2',theory(equality)]),
% 0.62/1.04 [pos('R','R')]).
% 0.62/1.04 cnf('0.33.2.0',plain,
% 0.62/1.04 ( multiply(inverse(X1),X1) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.33.1.1',theory(equality)]),
% 0.62/1.04 [u,rule_30]).
% 0.62/1.04 cnf('0.34.0.0',plain,
% 0.62/1.04 ( X1 = least_upper_bound(X1,negative_part(X1)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.4.2.0','0.29.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.34.1.0',plain,
% 0.62/1.04 ( X1 = least_upper_bound(X1,negative_part(X1)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.34.0.0']),
% 0.62/1.04 [weight('<29,29,4,[0,0,0,2]>')]).
% 0.62/1.04 cnf('0.34.2.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,negative_part(X1)) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_31]).
% 0.62/1.04 cnf('0.36.0.0',plain,
% 0.62/1.04 ( negative_part(greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X2,positive_part(negative_part(a)))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.29.2.0','0.7.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.36.0.1',plain,
% 0.62/1.04 ( negative_part(greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,negative_part(X2)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.36.0.0','0.29.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2','L')]).
% 0.62/1.04 cnf('0.36.1.0',plain,
% 0.62/1.04 ( negative_part(greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,negative_part(X2)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.36.0.1']),
% 0.62/1.04 [weight('<44,29,7,[1,0,0,0]>')]).
% 0.62/1.04 cnf('0.36.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,negative_part(X2)) = negative_part(greatest_lower_bound(X1,X2)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_33]).
% 0.62/1.04 cnf('0.37.0.0',plain,
% 0.62/1.04 ( negative_part(greatest_lower_bound(X1,positive_part(negative_part(a)))) = greatest_lower_bound(X1,positive_part(negative_part(a))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.36.2.0','0.26.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.37.0.1',plain,
% 0.62/1.04 ( negative_part(negative_part(X1)) = greatest_lower_bound(X1,positive_part(negative_part(a))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.37.0.0','0.29.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.37.0.2',plain,
% 0.62/1.04 ( negative_part(negative_part(X1)) = negative_part(X1) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.37.0.1','0.29.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.37.1.0',plain,
% 0.62/1.04 ( negative_part(negative_part(X1)) = negative_part(X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.37.0.2']),
% 0.62/1.04 [weight('<23,36,26,[1,0,0,2]>')]).
% 0.62/1.04 cnf('0.37.2.0',plain,
% 0.62/1.04 ( negative_part(negative_part(X1)) = negative_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_34]).
% 0.62/1.04 cnf('0.38.0.0',plain,
% 0.62/1.04 ( identity = positive_part(negative_part(X1)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.25.2.0','0.37.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.38.1.0',plain,
% 0.62/1.04 ( identity = positive_part(negative_part(X1)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.38.0.0']),
% 0.62/1.04 [weight('<24,37,25,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.38.1.1',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = positive_part(negative_part(X1)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.38.1.0','0.25.2.2',theory(equality)]),
% 0.62/1.04 [pos('L','R')]).
% 0.62/1.04 cnf('0.38.2.0',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = positive_part(negative_part(X1)) ),
% 0.62/1.04 inference(activate,[status(thm)],['0.38.1.1']),
% 0.62/1.04 [equation_4]).
% 0.62/1.04 cnf('0.38.2.1',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(instr,[status(thm)],['0.38.2.0',theory(equality)])).
% 0.62/1.04 cnf('0.40.0.0',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(negative_part(X2)),X1) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.28.2.0','0.38.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.40.1.0',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(negative_part(X2)),X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.40.0.0']),
% 0.62/1.04 [weight('<41,38,28,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.40.2.0',plain,
% 0.62/1.04 ( multiply(positive_part(negative_part(X1)),X2) = X2 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_36]).
% 0.62/1.04 cnf('0.41.0.0',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X2,positive_part(negative_part(a)))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.30.2.0','0.15.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.41.0.1',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(X1,X2)) = least_upper_bound(X1,positive_part(X2)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.41.0.0','0.30.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2','L')]).
% 0.62/1.04 cnf('0.41.1.0',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(X1,X2)) = least_upper_bound(X1,positive_part(X2)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.41.0.1']),
% 0.62/1.04 [weight('<44,30,15,[1,0,0,0]>')]).
% 0.62/1.04 cnf('0.41.2.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,positive_part(X2)) = positive_part(least_upper_bound(X1,X2)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_37]).
% 0.62/1.04 cnf('0.43.0.0',plain,
% 0.62/1.04 ( least_upper_bound(positive_part(negative_part(a)),least_upper_bound(X1,X2)) = least_upper_bound(positive_part(X1),X2) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.15.2.0','0.32.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.43.0.1',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(X1,X2)) = least_upper_bound(positive_part(X1),X2) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.43.0.0','0.32.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.43.1.0',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(X1,X2)) = least_upper_bound(positive_part(X1),X2) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.43.0.1']),
% 0.62/1.04 [weight('<44,32,15,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.43.2.0',plain,
% 0.62/1.04 ( least_upper_bound(positive_part(X1),X2) = positive_part(least_upper_bound(X1,X2)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.43.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_39]).
% 0.62/1.04 cnf('0.46.0.0',plain,
% 0.62/1.04 ( least_upper_bound(positive_part(negative_part(a)),X1) = positive_part(X1) ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.32.2.0'])).
% 0.62/1.04 cnf('0.46.0.1',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(negative_part(a),X1)) = positive_part(X1) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.46.0.0','0.43.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.46.1.0',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(negative_part(a),X1)) = positive_part(X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.46.0.1']),
% 0.62/1.04 [weight('<47,32,43,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.46.2.0',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(negative_part(a),X1)) = positive_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_42]).
% 0.62/1.04 cnf('0.47.0.0',plain,
% 0.62/1.04 ( negative_part(X1) = greatest_lower_bound(X1,positive_part(negative_part(X2))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.29.2.0','0.38.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.47.1.0',plain,
% 0.62/1.04 ( negative_part(X1) = greatest_lower_bound(X1,positive_part(negative_part(X2))) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.47.0.0']),
% 0.62/1.04 [weight('<47,38,29,[0,0,0,2]>')]).
% 0.62/1.04 cnf('0.47.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,positive_part(negative_part(X2))) = negative_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_43]).
% 0.62/1.04 cnf('0.49.0.0',plain,
% 0.62/1.04 ( negative_part(X1) = greatest_lower_bound(positive_part(negative_part(X2)),X1) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.31.2.0','0.38.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.49.1.0',plain,
% 0.62/1.04 ( negative_part(X1) = greatest_lower_bound(positive_part(negative_part(X2)),X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.49.0.0']),
% 0.62/1.04 [weight('<47,38,31,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.49.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(positive_part(negative_part(X1)),X2) = negative_part(X2) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.49.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_45]).
% 0.62/1.04 cnf('0.51.0.0',plain,
% 0.62/1.04 ( greatest_lower_bound(multiply(X1,X2),multiply(positive_part(negative_part(X3)),X2)) = multiply(negative_part(X1),X2) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.11.2.0','0.47.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.51.0.1',plain,
% 0.62/1.04 ( greatest_lower_bound(multiply(X1,X2),X2) = multiply(negative_part(X1),X2) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.51.0.0','0.40.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.51.1.0',plain,
% 0.62/1.04 ( greatest_lower_bound(multiply(X1,X2),X2) = multiply(negative_part(X1),X2) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.51.0.1']),
% 0.62/1.04 [weight('<49,47,11,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.51.1.1',plain,
% 0.62/1.04 ( greatest_lower_bound(X2,multiply(X1,X2)) = multiply(negative_part(X1),X2) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.51.1.0','0.6.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.51.2.0',plain,
% 0.62/1.04 ( multiply(negative_part(X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.51.1.1',theory(equality)]),
% 0.62/1.04 [x,rule_46]).
% 0.62/1.04 cnf('0.56.0.0',plain,
% 0.62/1.04 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(positive_part(negative_part(a)),X2) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.19.2.0','0.33.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.56.0.1',plain,
% 0.62/1.04 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.56.0.0','0.28.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.56.1.0',plain,
% 0.62/1.04 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.56.0.1']),
% 0.62/1.04 [weight('<55,33,19,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.56.2.0',plain,
% 0.62/1.04 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_51]).
% 0.62/1.04 cnf('0.57.0.0',plain,
% 0.62/1.04 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.56.2.0','0.56.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.57.1.0',plain,
% 0.62/1.04 ( X1 = inverse(inverse(X1)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.57.0.0']),
% 0.62/1.04 [weight('<19,56,56,[0,0,0,3]>')]).
% 0.62/1.04 cnf('0.57.2.0',plain,
% 0.62/1.04 ( inverse(inverse(X1)) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_52]).
% 0.62/1.04 cnf('0.58.0.0',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = multiply(X1,inverse(X1)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.33.2.0','0.57.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.58.1.0',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = multiply(X1,inverse(X1)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.58.0.0']),
% 0.62/1.04 [weight('<39,57,33,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.58.2.0',plain,
% 0.62/1.04 ( multiply(X1,inverse(X1)) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.58.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_53]).
% 0.62/1.04 cnf('0.59.0.0',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = inverse(positive_part(negative_part(X1))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.58.2.0','0.40.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.59.1.0',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = inverse(positive_part(negative_part(X1))) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.59.0.0']),
% 0.62/1.04 [weight('<39,58,40,[1,0,0,0]>')]).
% 0.62/1.04 cnf('0.59.2.0',plain,
% 0.62/1.04 ( inverse(positive_part(negative_part(X1))) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.59.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_54]).
% 0.62/1.04 cnf('0.60.0.0',plain,
% 0.62/1.04 ( inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(X1,inverse(X2)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.13.2.0','0.57.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.60.1.0',plain,
% 0.62/1.04 ( inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(X1,inverse(X2)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.60.0.0']),
% 0.62/1.04 [weight('<49,57,13,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.60.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,inverse(X2)) = inverse(least_upper_bound(inverse(X1),X2)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.60.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_55]).
% 0.62/1.04 cnf('0.61.0.0',plain,
% 0.62/1.04 ( inverse(least_upper_bound(inverse(positive_part(negative_part(X1))),X2)) = negative_part(inverse(X2)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.60.2.0','0.49.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.61.0.1',plain,
% 0.62/1.04 ( inverse(least_upper_bound(positive_part(negative_part(a)),X2)) = negative_part(inverse(X2)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.61.0.0','0.59.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1.1','L')]).
% 0.62/1.04 cnf('0.61.0.2',plain,
% 0.62/1.04 ( inverse(positive_part(least_upper_bound(negative_part(a),X2))) = negative_part(inverse(X2)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.61.0.1','0.43.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.61.0.3',plain,
% 0.62/1.04 ( inverse(positive_part(X2)) = negative_part(inverse(X2)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.61.0.2','0.46.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.61.1.0',plain,
% 0.62/1.04 ( inverse(positive_part(X2)) = negative_part(inverse(X2)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.61.0.3']),
% 0.62/1.04 [weight('<27,60,49,[1,0,0,0]>')]).
% 0.62/1.04 cnf('0.61.2.0',plain,
% 0.62/1.04 ( inverse(positive_part(X1)) = negative_part(inverse(X1)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.61.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_56]).
% 0.62/1.04 cnf('0.62.0.0',plain,
% 0.62/1.04 ( positive_part(X1) = inverse(negative_part(inverse(X1))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.57.2.0','0.61.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.62.1.0',plain,
% 0.62/1.04 ( positive_part(X1) = inverse(negative_part(inverse(X1))) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.62.0.0']),
% 0.62/1.04 [weight('<34,61,57,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.62.2.0',plain,
% 0.62/1.04 ( inverse(negative_part(inverse(X1))) = positive_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.62.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_57]).
% 0.62/1.04 cnf('0.63.0.0',plain,
% 0.62/1.04 ( positive_part(inverse(X1)) = inverse(negative_part(X1)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.62.2.0','0.57.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1.1','L')]).
% 0.62/1.04 cnf('0.63.1.0',plain,
% 0.62/1.04 ( positive_part(inverse(X1)) = inverse(negative_part(X1)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.63.0.0']),
% 0.62/1.04 [weight('<27,62,57,[1,0,0,2]>')]).
% 0.62/1.04 cnf('0.63.2.0',plain,
% 0.62/1.04 ( inverse(negative_part(X1)) = positive_part(inverse(X1)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.63.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_58]).
% 0.62/1.04 cnf('0.64.0.0',plain,
% 0.62/1.04 ( inverse(positive_part(negative_part(X1))) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.59.2.0'])).
% 0.62/1.04 cnf('0.64.0.1',plain,
% 0.62/1.04 ( negative_part(inverse(negative_part(X1))) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.64.0.0','0.61.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.64.1.0',plain,
% 0.62/1.04 ( negative_part(inverse(negative_part(X1))) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.64.0.1']),
% 0.62/1.04 [weight('<39,59,61,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.64.1.1',plain,
% 0.62/1.04 ( negative_part(positive_part(inverse(X1))) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.64.1.0','0.63.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.64.2.0',plain,
% 0.62/1.04 ( negative_part(positive_part(inverse(X1))) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.64.1.1',theory(equality)]),
% 0.62/1.04 [u,rule_59]).
% 0.62/1.04 cnf('0.65.0.0',plain,
% 0.62/1.04 ( inverse(least_upper_bound(inverse(X1),inverse(X2))) = greatest_lower_bound(X1,X2) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.60.2.0','0.57.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.65.1.0',plain,
% 0.62/1.04 ( inverse(least_upper_bound(inverse(X1),inverse(X2))) = greatest_lower_bound(X1,X2) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.65.0.0']),
% 0.62/1.04 [weight('<39,60,57,[1,0,0,2]>')]).
% 0.62/1.04 cnf('0.65.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,X2) = inverse(least_upper_bound(inverse(X1),inverse(X2))) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.65.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_60]).
% 0.62/1.04 cnf('0.66.0.0',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = negative_part(positive_part(X1)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.64.2.0','0.57.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1.1','L')]).
% 0.62/1.04 cnf('0.66.1.0',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = negative_part(positive_part(X1)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.66.0.0']),
% 0.62/1.04 [weight('<48,64,57,[1,0,0,2]>')]).
% 0.62/1.04 cnf('0.66.2.0',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = negative_part(positive_part(X1)) ),
% 0.62/1.04 inference(activate,[status(thm)],['0.66.1.0']),
% 0.62/1.04 [equation_6]).
% 0.62/1.04 cnf('0.66.2.1',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(instr,[status(thm)],['0.66.2.0',theory(equality)])).
% 0.62/1.04 cnf('0.67.0.0',plain,
% 0.62/1.04 ( multiply(inverse(X1),X1) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.33.2.0'])).
% 0.62/1.04 cnf('0.67.1.0',plain,
% 0.62/1.04 ( multiply(inverse(X1),X1) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.67.0.0']),
% 0.62/1.04 [weight('<39,33,66,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.67.1.1',plain,
% 0.62/1.04 ( multiply(inverse(X1),X1) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.67.1.0','0.66.2.1',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.67.2.0',plain,
% 0.62/1.04 ( multiply(inverse(X1),X1) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.67.1.1',theory(equality)]),
% 0.62/1.04 [u,rule_61]).
% 0.62/1.04 cnf('0.68.0.0',plain,
% 0.62/1.04 ( multiply(X1,inverse(X1)) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.58.2.0'])).
% 0.62/1.04 cnf('0.68.1.0',plain,
% 0.62/1.04 ( multiply(X1,inverse(X1)) = positive_part(negative_part(a)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.68.0.0']),
% 0.62/1.04 [weight('<39,58,66,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.68.1.1',plain,
% 0.62/1.04 ( multiply(X1,inverse(X1)) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.68.1.0','0.66.2.1',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.68.2.0',plain,
% 0.62/1.04 ( multiply(X1,inverse(X1)) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.68.1.1',theory(equality)]),
% 0.62/1.04 [u,rule_62]).
% 0.62/1.04 cnf('0.70.0.0',plain,
% 0.62/1.04 ( X1 = multiply(inverse(inverse(X1)),negative_part(positive_part(a))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.56.2.0','0.67.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.70.0.1',plain,
% 0.62/1.04 ( X1 = multiply(X1,negative_part(positive_part(a))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.70.0.0','0.57.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.1','L')]).
% 0.62/1.04 cnf('0.70.1.0',plain,
% 0.62/1.04 ( X1 = multiply(X1,negative_part(positive_part(a))) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.70.0.1']),
% 0.62/1.04 [weight('<41,67,56,[0,0,0,3]>')]).
% 0.62/1.04 cnf('0.70.2.0',plain,
% 0.62/1.04 ( multiply(X1,negative_part(positive_part(a))) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.70.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_64]).
% 0.62/1.04 cnf('0.71.0.0',plain,
% 0.62/1.04 ( positive_part(negative_part(X1)) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.70.2.0','0.40.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.71.1.0',plain,
% 0.62/1.04 ( positive_part(negative_part(X1)) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.71.0.0']),
% 0.62/1.04 [weight('<27,70,40,[1,0,0,0]>')]).
% 0.62/1.04 cnf('0.71.2.0',plain,
% 0.62/1.04 ( positive_part(negative_part(X1)) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.71.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_65]).
% 0.62/1.04 cnf('0.74.0.0',plain,
% 0.62/1.04 ( positive_part(negative_part(a)) = negative_part(positive_part(X1)) ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.66.2.0'])).
% 0.62/1.04 cnf('0.74.0.1',plain,
% 0.62/1.04 ( negative_part(positive_part(a)) = negative_part(positive_part(X1)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.74.0.0','0.71.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.74.1.0',plain,
% 0.62/1.04 ( negative_part(positive_part(a)) = negative_part(positive_part(X1)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.74.0.1']),
% 0.62/1.04 [weight('<48,66,71,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.74.2.0',plain,
% 0.62/1.04 ( negative_part(positive_part(a)) = negative_part(positive_part(X1)) ),
% 0.62/1.04 inference(activate,[status(thm)],['0.74.1.0']),
% 0.62/1.04 [equation_7]).
% 0.62/1.04 cnf('0.74.2.1',plain,
% 0.62/1.04 ( negative_part(positive_part(a)) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(instr,[status(thm)],['0.74.2.0',theory(equality)])).
% 0.62/1.04 cnf('0.76.0.0',plain,
% 0.62/1.04 ( negative_part(positive_part(X1)) = negative_part(positive_part(X2)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.74.2.0','0.74.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.76.1.0',plain,
% 0.62/1.04 ( negative_part(positive_part(X1)) = negative_part(positive_part(X2)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.76.0.0']),
% 0.62/1.04 [weight('<48,74,74,[1,0,0,0]>')]).
% 0.62/1.04 cnf('0.76.2.0',plain,
% 0.62/1.04 ( negative_part(positive_part(X1)) = negative_part(positive_part(X2)) ),
% 0.62/1.04 inference(activate,[status(thm)],['0.76.1.0']),
% 0.62/1.04 [equation_8]).
% 0.62/1.04 cnf('0.76.2.1',plain,
% 0.62/1.04 ( negative_part(positive_part(X1)) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(instr,[status(thm)],['0.76.2.0',theory(equality)])).
% 0.62/1.04 cnf('0.76.2.2',plain,
% 0.62/1.04 ( negative_part(positive_part(a)) = negative_part(positive_part(X1)) ),
% 0.62/1.04 inference(instl,[status(thm)],['0.76.2.0',theory(equality)])).
% 0.62/1.04 cnf('0.77.0.0',plain,
% 0.62/1.04 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.56.2.0','0.57.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.77.1.0',plain,
% 0.62/1.04 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.77.0.0']),
% 0.62/1.04 [weight('<55,57,56,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.77.2.0',plain,
% 0.62/1.04 ( multiply(X1,multiply(inverse(X1),X2)) = X2 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.77.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_69]).
% 0.62/1.04 cnf('0.79.0.0',plain,
% 0.62/1.04 ( positive_part(X1) = least_upper_bound(positive_part(X1),negative_part(positive_part(X2))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.34.2.0','0.76.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.79.0.1',plain,
% 0.62/1.04 ( positive_part(X1) = positive_part(least_upper_bound(X1,negative_part(positive_part(X2)))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.79.0.0','0.43.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.79.1.0',plain,
% 0.62/1.04 ( positive_part(X1) = positive_part(least_upper_bound(X1,negative_part(positive_part(X2)))) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.79.0.1']),
% 0.62/1.04 [weight('<62,76,34,[0,0,0,2]>')]).
% 0.62/1.04 cnf('0.79.2.0',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(X1,negative_part(positive_part(X2)))) = positive_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.79.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_71]).
% 0.62/1.04 cnf('0.81.0.0',plain,
% 0.62/1.04 ( multiply(negative_part(X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)) ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.51.2.0'])).
% 0.62/1.04 cnf('0.81.0.1',plain,
% 0.62/1.04 ( multiply(negative_part(X1),X2) = inverse(least_upper_bound(inverse(X2),inverse(multiply(X1,X2)))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.81.0.0','0.65.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.81.1.0',plain,
% 0.62/1.04 ( multiply(negative_part(X1),X2) = inverse(least_upper_bound(inverse(X2),inverse(multiply(X1,X2)))) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.81.0.1']),
% 0.62/1.04 [weight('<64,51,65,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.81.2.0',plain,
% 0.62/1.04 ( multiply(negative_part(X1),X2) = inverse(least_upper_bound(inverse(X2),inverse(multiply(X1,X2)))) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.81.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_73]).
% 0.62/1.04 cnf('0.82.0.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,least_upper_bound(negative_part(X1),X2)) = least_upper_bound(X1,X2) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.15.2.0','0.34.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.82.1.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,least_upper_bound(negative_part(X1),X2)) = least_upper_bound(X1,X2) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.82.0.0']),
% 0.62/1.04 [weight('<69,34,15,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.82.2.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,least_upper_bound(negative_part(X1),X2)) = least_upper_bound(X1,X2) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.82.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_74]).
% 0.62/1.04 cnf('0.91.0.0',plain,
% 0.62/1.04 ( multiply(X1,multiply(inverse(X1),X2)) = multiply(negative_part(positive_part(a)),X2) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.19.2.0','0.68.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.91.1.0',plain,
% 0.62/1.04 ( multiply(X1,multiply(inverse(X1),X2)) = multiply(negative_part(positive_part(a)),X2) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.91.0.0']),
% 0.62/1.04 [weight('<83,68,19,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.91.1.1',plain,
% 0.62/1.04 ( X2 = multiply(negative_part(positive_part(a)),X2) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.91.1.0','0.77.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.91.1.2',plain,
% 0.62/1.04 ( X2 = inverse(least_upper_bound(inverse(X2),inverse(multiply(positive_part(a),X2)))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.91.1.1','0.81.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.91.2.0',plain,
% 0.62/1.04 ( inverse(least_upper_bound(inverse(X1),inverse(multiply(positive_part(a),X1)))) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.91.1.2',theory(equality)]),
% 0.62/1.04 [x,rule_83]).
% 0.62/1.04 cnf('0.97.0.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 0.62/1.04 inference(interreduction_right,[status(thm)],['0.4.2.0'])).
% 0.62/1.04 cnf('0.97.0.1',plain,
% 0.62/1.04 ( least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),inverse(X2)))) = X1 ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.97.0.0','0.65.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.97.1.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),inverse(X2)))) = X1 ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.97.0.1']),
% 0.62/1.04 [weight('<89,4,65,[0,0,0,0]>')]).
% 0.62/1.04 cnf('0.97.2.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),inverse(X2)))) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.97.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_89]).
% 0.62/1.04 cnf('0.98.0.0',plain,
% 0.62/1.04 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.97.2.0','0.57.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2.1.2','L')]).
% 0.62/1.04 cnf('0.98.1.0',plain,
% 0.62/1.04 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.98.0.0']),
% 0.62/1.04 [weight('<71,97,57,[1,0,0,6]>')]).
% 0.62/1.04 cnf('0.98.2.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.98.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_90]).
% 0.62/1.04 cnf('0.99.0.0',plain,
% 0.62/1.04 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.98.2.0','0.14.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2.1','L')]).
% 0.62/1.04 cnf('0.99.1.0',plain,
% 0.62/1.04 ( X1 = least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.99.0.0']),
% 0.62/1.04 [weight('<71,98,14,[1,0,0,3]>')]).
% 0.62/1.04 cnf('0.99.2.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.99.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_91]).
% 0.62/1.04 cnf('0.100.0.0',plain,
% 0.62/1.04 ( multiply(positive_part(a),X1) = least_upper_bound(multiply(positive_part(a),X1),X1) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.99.2.0','0.91.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.100.1.0',plain,
% 0.62/1.04 ( multiply(positive_part(a),X1) = least_upper_bound(multiply(positive_part(a),X1),X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.100.0.0']),
% 0.62/1.04 [weight('<76,99,91,[1,0,0,2]>')]).
% 0.62/1.04 cnf('0.100.1.1',plain,
% 0.62/1.04 ( multiply(positive_part(a),X1) = least_upper_bound(X1,multiply(positive_part(a),X1)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.100.1.0','0.14.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.100.2.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,multiply(positive_part(a),X1)) = multiply(positive_part(a),X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.100.1.1',theory(equality)]),
% 0.62/1.04 [x,rule_92]).
% 0.62/1.04 cnf('0.103.0.0',plain,
% 0.62/1.04 ( multiply(positive_part(a),inverse(positive_part(a))) = least_upper_bound(inverse(positive_part(a)),negative_part(positive_part(a))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.100.2.0','0.68.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.103.0.1',plain,
% 0.62/1.04 ( negative_part(positive_part(a)) = least_upper_bound(inverse(positive_part(a)),negative_part(positive_part(a))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.103.0.0','0.68.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.103.0.2',plain,
% 0.62/1.04 ( negative_part(positive_part(a)) = least_upper_bound(negative_part(inverse(a)),negative_part(positive_part(a))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.103.0.1','0.61.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.1','L')]).
% 0.62/1.04 cnf('0.103.1.0',plain,
% 0.62/1.04 ( negative_part(positive_part(a)) = least_upper_bound(negative_part(inverse(a)),negative_part(positive_part(a))) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.103.0.2']),
% 0.62/1.04 [weight('<87,100,68,[1,0,0,2]>')]).
% 0.62/1.04 cnf('0.103.1.1',plain,
% 0.62/1.04 ( negative_part(positive_part(a)) = least_upper_bound(negative_part(positive_part(a)),negative_part(inverse(a))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.103.1.0','0.14.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.103.2.0',plain,
% 0.62/1.04 ( least_upper_bound(negative_part(positive_part(a)),negative_part(inverse(a))) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.103.1.1',theory(equality)]),
% 0.62/1.04 [x,rule_95]).
% 0.62/1.04 cnf('0.105.0.0',plain,
% 0.62/1.04 ( negative_part(positive_part(a)) = least_upper_bound(negative_part(positive_part(X1)),negative_part(inverse(a))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.103.2.0','0.76.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.105.1.0',plain,
% 0.62/1.04 ( negative_part(positive_part(a)) = least_upper_bound(negative_part(positive_part(X1)),negative_part(inverse(a))) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.105.0.0']),
% 0.62/1.04 [weight('<87,103,76,[1,0,0,1]>')]).
% 0.62/1.04 cnf('0.105.2.0',plain,
% 0.62/1.04 ( least_upper_bound(negative_part(positive_part(X1)),negative_part(inverse(a))) = negative_part(positive_part(a)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.105.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_97]).
% 0.62/1.04 cnf('0.106.0.0',plain,
% 0.62/1.04 ( least_upper_bound(positive_part(X1),negative_part(inverse(a))) = least_upper_bound(positive_part(X1),negative_part(positive_part(a))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.82.2.0','0.105.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2','L')]).
% 0.62/1.04 cnf('0.106.0.1',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(X1,negative_part(inverse(a)))) = least_upper_bound(positive_part(X1),negative_part(positive_part(a))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.106.0.0','0.43.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.106.0.2',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(X1,negative_part(inverse(a)))) = positive_part(least_upper_bound(X1,negative_part(positive_part(a)))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.106.0.1','0.43.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.106.0.3',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(X1,negative_part(inverse(a)))) = positive_part(X1) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.106.0.2','0.79.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.106.1.0',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(X1,negative_part(inverse(a)))) = positive_part(X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.106.0.3']),
% 0.62/1.04 [weight('<62,105,82,[0,0,0,2]>')]).
% 0.62/1.04 cnf('0.106.2.0',plain,
% 0.62/1.04 ( positive_part(least_upper_bound(X1,negative_part(inverse(a)))) = positive_part(X1) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.106.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_98]).
% 0.62/1.04 cnf('0.110.0.0',plain,
% 0.62/1.04 ( negative_part(inverse(least_upper_bound(X1,negative_part(inverse(a))))) = inverse(positive_part(X1)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.61.2.0','0.106.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('0.110.0.1',plain,
% 0.62/1.04 ( negative_part(inverse(least_upper_bound(X1,negative_part(inverse(a))))) = negative_part(inverse(X1)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.110.0.0','0.61.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('0.110.1.0',plain,
% 0.62/1.04 ( negative_part(inverse(least_upper_bound(X1,negative_part(inverse(a))))) = negative_part(inverse(X1)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.110.0.1']),
% 0.62/1.04 [weight('<87,106,61,[0,0,0,1]>')]).
% 0.62/1.04 cnf('0.110.2.0',plain,
% 0.62/1.04 ( negative_part(inverse(least_upper_bound(X1,negative_part(inverse(a))))) = negative_part(inverse(X1)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.110.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_102]).
% 0.62/1.04 cnf('0.116.0.0',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(X2),multiply(negative_part(inverse(X2)),X1)) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.77.2.0','0.61.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2.1','L')]).
% 0.62/1.04 cnf('0.116.1.0',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(X2),multiply(negative_part(inverse(X2)),X1)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.116.0.0']),
% 0.62/1.04 [weight('<89,77,61,[1,0,0,3]>')]).
% 0.62/1.04 cnf('0.116.1.1',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(X2),inverse(least_upper_bound(inverse(X1),inverse(multiply(inverse(X2),X1))))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.116.1.0','0.81.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2','L')]).
% 0.62/1.04 cnf('0.116.2.0',plain,
% 0.62/1.04 ( multiply(positive_part(X1),inverse(least_upper_bound(inverse(X2),inverse(multiply(inverse(X1),X2))))) = X2 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.116.1.1',theory(equality)]),
% 0.62/1.04 [x,rule_108]).
% 0.62/1.04 cnf('0.117.0.0',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(X1),inverse(least_upper_bound(inverse(X1),inverse(negative_part(positive_part(a)))))) ),
% 0.62/1.04 inference(cp,[status(thm)],['0.116.2.0','0.67.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.2.1.2.1','L')]).
% 0.62/1.04 cnf('0.117.0.1',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(X1),inverse(least_upper_bound(inverse(X1),positive_part(inverse(positive_part(a)))))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.117.0.0','0.63.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2.1.2','L')]).
% 0.62/1.04 cnf('0.117.0.2',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(X1),inverse(positive_part(least_upper_bound(inverse(X1),inverse(positive_part(a)))))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.117.0.1','0.41.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2.1','L')]).
% 0.62/1.04 cnf('0.117.0.3',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(X1),negative_part(inverse(least_upper_bound(inverse(X1),inverse(positive_part(a)))))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.117.0.2','0.61.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2','L')]).
% 0.62/1.04 cnf('0.117.0.4',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(X1),negative_part(inverse(least_upper_bound(inverse(X1),negative_part(inverse(a)))))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.117.0.3','0.61.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2.1.1.2','L')]).
% 0.62/1.04 cnf('0.117.0.5',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(X1),negative_part(inverse(inverse(X1)))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.117.0.4','0.110.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2','L')]).
% 0.62/1.04 cnf('0.117.0.6',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(X1),negative_part(X1)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.117.0.5','0.57.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2.1','L')]).
% 0.62/1.04 cnf('0.117.1.0',plain,
% 0.62/1.04 ( X1 = multiply(positive_part(X1),negative_part(X1)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.117.0.6']),
% 0.62/1.04 [weight('<41,116,67,[1,0,0,8]>')]).
% 0.62/1.04 cnf('0.117.2.0',plain,
% 0.62/1.04 ( multiply(positive_part(X1),negative_part(X1)) = X1 ),
% 0.62/1.04 inference(orient,[status(thm)],['0.117.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_109]).
% 0.62/1.04 cnf('1.0.0.0',conjecture,
% 0.62/1.04 ( multiply(positive_part(a),negative_part(a)) = a ),
% 0.62/1.04 file('/tmp/WALDMEISTER_14927_n026',conjecture_1)).
% 0.62/1.04 cnf('1.0.0.1',plain,
% 0.62/1.04 ( a = a ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.0','0.117.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('1.0.0.2',plain,
% 0.62/1.04 ( $true ),
% 0.62/1.04 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.62/1.04 [conjecture_1]).
% 0.62/1.04
% 0.62/1.04 Proved Goals:
% 0.62/1.04 No. 1: multiply(positive_part(a),negative_part(a)) ?= a joined, current: a = a
% 0.62/1.04 1 goal was specified, which was proved.
% 0.62/1.04 % SZS output end CNFRefutation
% 0.62/1.04 #END OF PROOF
% 0.62/1.04
% 0.62/1.04 Problem WALDMEISTER_14927_n026
% 0.62/1.04 CPs.gen 1463
% 0.62/1.04 CPs.reexp 0
% 0.62/1.04 Select 220
% 0.62/1.04 R 109
% 0.62/1.04 E 8
% 0.62/1.04 vsize 6.6M
% 0.62/1.04 rss 3.7M
% 0.62/1.04 process.time 0.012s
% 0.62/1.04 wallclock.time 0.013s
% 0.62/1.04 status S
% 0.62/1.04
% 0.62/1.04
% 0.62/1.04 Waldmeister states: Goal proved.
% 0.62/1.04 % SZS status Unsatisfiable
% 0.62/1.04
% 0.62/1.04 Problem WALDMEISTER_14927_n026
% 0.62/1.04 CPs.gen 44
% 0.62/1.04 CPs.reexp 0
% 0.62/1.04 Select 10
% 0.62/1.04 R 9
% 0.62/1.04 E 1
% 0.62/1.04 vsize 6.5M
% 0.62/1.04 rss 3.8M
% 0.62/1.04 process.time 0.002s
% 0.62/1.04 wallclock.time 0.012s
% 0.62/1.04 status S
%------------------------------------------------------------------------------