TSTP Solution File: GRP114-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP114-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n028.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 12:24:29 EDT 2022
% Result : Unsatisfiable 0.72s 1.08s
% Output : CNFRefutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP114-1 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 01:46:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.59/0.98 ********************************************************************************
% 0.59/0.98 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/0.98 * |/ | \/ | *
% 0.59/0.98 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/0.98 * A. Jaeger and B. Loechner | | *
% 0.59/0.98 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/0.98 ********************************************************************************
% 0.59/0.98
% 0.59/0.98
% 0.59/0.98 Goals:
% 0.59/0.98 ------
% 0.59/0.98
% 0.59/0.98 ( 1) multiply(positive_part(a),negative_part(a)) ?=? a
% 0.59/0.98
% 0.59/0.98 Detected structure: Gruppe
% 0.59/0.98 ********************************************************************************
% 0.59/0.98 ****************************** COMPLETION - PROOF ******************************
% 0.59/0.98 ********************************************************************************
% 0.59/0.98
% 0.72/1.08 joined goal: 1 multiply(positive_part(a),negative_part(a)) ?= a to a
% 0.72/1.08 goal joined
% 0.72/1.08 % SZS status Unsatisfiable
% 0.72/1.08 #START OF PROOF
% 0.72/1.08 % SZS output start CNFRefutation
% 0.72/1.08 cnf('0.1.0.0',axiom,
% 0.72/1.08 ( X1 = multiply(identity,X1) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.1.1.0',plain,
% 0.72/1.08 ( X1 = multiply(identity,X1) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.72/1.08 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.72/1.08 cnf('0.1.2.0',plain,
% 0.72/1.08 ( multiply(identity,X1) = X1 ),
% 0.72/1.08 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_1]).
% 0.72/1.08 cnf('0.3.0.0',axiom,
% 0.72/1.08 ( X1 = union(intersection(X2,X1),X1) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.3.1.0',plain,
% 0.72/1.08 ( X1 = union(intersection(X2,X1),X1) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.72/1.08 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.72/1.08 cnf('0.3.2.0',plain,
% 0.72/1.08 ( union(intersection(X1,X2),X2) = X2 ),
% 0.72/1.08 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_3]).
% 0.72/1.08 cnf('0.5.0.0',axiom,
% 0.72/1.08 ( X1 = intersection(union(X2,X1),X1) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.5.1.0',plain,
% 0.72/1.08 ( X1 = intersection(union(X2,X1),X1) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.72/1.08 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.72/1.08 cnf('0.5.2.0',plain,
% 0.72/1.08 ( intersection(union(X1,X2),X2) = X2 ),
% 0.72/1.08 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_5]).
% 0.72/1.08 cnf('0.6.0.0',axiom,
% 0.72/1.08 ( X1 = inverse(inverse(X1)) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.6.1.0',plain,
% 0.72/1.08 ( X1 = inverse(inverse(X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.72/1.08 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.72/1.08 cnf('0.6.2.0',plain,
% 0.72/1.08 ( inverse(inverse(X1)) = X1 ),
% 0.72/1.08 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_6]).
% 0.72/1.08 cnf('0.7.0.0',axiom,
% 0.72/1.08 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.7.1.0',plain,
% 0.72/1.08 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.72/1.08 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.72/1.08 cnf('0.7.2.0',plain,
% 0.72/1.08 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_7]).
% 0.72/1.08 cnf('0.8.0.0',axiom,
% 0.72/1.08 ( multiply(X1,union(X2,X3)) = union(multiply(X1,X2),multiply(X1,X3)) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.8.1.0',plain,
% 0.72/1.08 ( multiply(X1,union(X2,X3)) = union(multiply(X1,X2),multiply(X1,X3)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.72/1.08 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.72/1.08 cnf('0.8.2.0',plain,
% 0.72/1.08 ( union(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,union(X2,X3)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_8]).
% 0.72/1.08 cnf('0.9.0.0',axiom,
% 0.72/1.08 ( multiply(X1,intersection(X2,X3)) = intersection(multiply(X1,X2),multiply(X1,X3)) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.9.1.0',plain,
% 0.72/1.08 ( multiply(X1,intersection(X2,X3)) = intersection(multiply(X1,X2),multiply(X1,X3)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.72/1.08 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.72/1.08 cnf('0.9.2.0',plain,
% 0.72/1.08 ( intersection(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,intersection(X2,X3)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_9]).
% 0.72/1.08 cnf('0.10.0.0',axiom,
% 0.72/1.08 ( multiply(union(X1,X2),X3) = union(multiply(X1,X3),multiply(X2,X3)) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.10.1.0',plain,
% 0.72/1.08 ( multiply(union(X1,X2),X3) = union(multiply(X1,X3),multiply(X2,X3)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.72/1.08 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.72/1.08 cnf('0.10.2.0',plain,
% 0.72/1.08 ( union(multiply(X1,X2),multiply(X3,X2)) = multiply(union(X1,X3),X2) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_10]).
% 0.72/1.08 cnf('0.11.0.0',axiom,
% 0.72/1.08 ( multiply(intersection(X1,X2),X3) = intersection(multiply(X1,X3),multiply(X2,X3)) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.11.1.0',plain,
% 0.72/1.08 ( multiply(intersection(X1,X2),X3) = intersection(multiply(X1,X3),multiply(X2,X3)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.72/1.08 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.72/1.08 cnf('0.11.2.0',plain,
% 0.72/1.08 ( intersection(multiply(X1,X2),multiply(X3,X2)) = multiply(intersection(X1,X3),X2) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_11]).
% 0.72/1.08 cnf('0.12.0.0',axiom,
% 0.72/1.08 ( multiply(inverse(X1),X1) = identity ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.12.1.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),X1) = identity ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.72/1.08 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.72/1.08 cnf('0.12.2.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),X1) = identity ),
% 0.72/1.08 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_12]).
% 0.72/1.08 cnf('0.13.0.0',axiom,
% 0.72/1.08 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.13.1.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.72/1.08 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.72/1.08 cnf('0.13.2.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_13]).
% 0.72/1.08 cnf('0.14.0.0',axiom,
% 0.72/1.08 ( union(X1,X2) = union(X2,X1) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.14.1.0',plain,
% 0.72/1.08 ( union(X1,X2) = union(X2,X1) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.72/1.08 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.72/1.08 cnf('0.14.2.0',plain,
% 0.72/1.08 ( union(X1,X2) = union(X2,X1) ),
% 0.72/1.08 inference(activate,[status(thm)],['0.14.1.0']),
% 0.72/1.08 [equation_1]).
% 0.72/1.08 cnf('0.15.0.0',axiom,
% 0.72/1.08 ( union(X1,union(X2,X3)) = union(union(X1,X2),X3) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.15.1.0',plain,
% 0.72/1.08 ( union(X1,union(X2,X3)) = union(union(X1,X2),X3) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.72/1.08 [weight('<14,0,0,[0,0,0,15]>')]).
% 0.72/1.08 cnf('0.15.2.0',plain,
% 0.72/1.08 ( union(union(X1,X2),X3) = union(X1,union(X2,X3)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_14]).
% 0.72/1.08 cnf('0.16.0.0',axiom,
% 0.72/1.08 ( union(X1,identity) = positive_part(X1) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.16.1.0',plain,
% 0.72/1.08 ( union(X1,identity) = positive_part(X1) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.72/1.08 [weight('<15,0,0,[0,0,0,16]>')]).
% 0.72/1.08 cnf('0.16.2.0',plain,
% 0.72/1.08 ( union(X1,identity) = positive_part(X1) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_15]).
% 0.72/1.08 cnf('0.17.0.0',axiom,
% 0.72/1.08 ( intersection(X1,X2) = intersection(X2,X1) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.17.1.0',plain,
% 0.72/1.08 ( intersection(X1,X2) = intersection(X2,X1) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.72/1.08 [weight('<16,0,0,[0,0,0,17]>')]).
% 0.72/1.08 cnf('0.17.2.0',plain,
% 0.72/1.08 ( intersection(X1,X2) = intersection(X2,X1) ),
% 0.72/1.08 inference(activate,[status(thm)],['0.17.1.0']),
% 0.72/1.08 [equation_2]).
% 0.72/1.08 cnf('0.18.0.0',axiom,
% 0.72/1.08 ( intersection(X1,intersection(X2,X3)) = intersection(intersection(X1,X2),X3) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.18.1.0',plain,
% 0.72/1.08 ( intersection(X1,intersection(X2,X3)) = intersection(intersection(X1,X2),X3) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.72/1.08 [weight('<17,0,0,[0,0,0,18]>')]).
% 0.72/1.08 cnf('0.18.2.0',plain,
% 0.72/1.08 ( intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_16]).
% 0.72/1.08 cnf('0.19.0.0',axiom,
% 0.72/1.08 ( intersection(X1,identity) = negative_part(X1) ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.19.1.0',plain,
% 0.72/1.08 ( intersection(X1,identity) = negative_part(X1) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.72/1.08 [weight('<18,0,0,[0,0,0,19]>')]).
% 0.72/1.08 cnf('0.19.2.0',plain,
% 0.72/1.08 ( intersection(X1,identity) = negative_part(X1) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_17]).
% 0.72/1.08 cnf('0.20.0.0',axiom,
% 0.72/1.08 ( inverse(identity) = identity ),
% 0.72/1.08 file('/tmp/WALDMEISTER_20573_n028')).
% 0.72/1.08 cnf('0.20.1.0',plain,
% 0.72/1.08 ( inverse(identity) = identity ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.72/1.08 [weight('<19,0,0,[0,0,0,20]>')]).
% 0.72/1.08 cnf('0.20.2.0',plain,
% 0.72/1.08 ( inverse(identity) = identity ),
% 0.72/1.08 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_18]).
% 0.72/1.08 cnf('0.23.0.0',plain,
% 0.72/1.08 ( positive_part(X1) = union(identity,X1) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.16.2.0','0.14.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.23.1.0',plain,
% 0.72/1.08 ( positive_part(X1) = union(identity,X1) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.72/1.08 [weight('<3,16,14,[1,0,0,0]>')]).
% 0.72/1.08 cnf('0.23.2.0',plain,
% 0.72/1.08 ( union(identity,X1) = positive_part(X1) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_21]).
% 0.72/1.08 cnf('0.24.0.0',plain,
% 0.72/1.08 ( negative_part(X1) = intersection(identity,X1) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.19.2.0','0.17.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.24.1.0',plain,
% 0.72/1.08 ( negative_part(X1) = intersection(identity,X1) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.24.0.0']),
% 0.72/1.08 [weight('<3,19,17,[1,0,0,0]>')]).
% 0.72/1.08 cnf('0.24.2.0',plain,
% 0.72/1.08 ( intersection(identity,X1) = negative_part(X1) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_22]).
% 0.72/1.08 cnf('0.25.0.0',plain,
% 0.72/1.08 ( inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.13.2.0','0.20.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.25.0.1',plain,
% 0.72/1.08 ( inverse(multiply(X1,identity)) = inverse(X1) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.25.0.0','0.1.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.25.1.0',plain,
% 0.72/1.08 ( multiply(X1,identity) = X1 ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.25.0.1']),
% 0.72/1.08 [weight('<3,20,13,[0,0,0,1]>')]).
% 0.72/1.08 cnf('0.25.2.0',plain,
% 0.72/1.08 ( multiply(X1,identity) = X1 ),
% 0.72/1.08 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_23]).
% 0.72/1.08 cnf('0.26.0.0',plain,
% 0.72/1.08 ( identity = multiply(X1,inverse(X1)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.12.2.0','0.6.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.26.1.0',plain,
% 0.72/1.08 ( identity = multiply(X1,inverse(X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.26.0.0']),
% 0.72/1.08 [weight('<4,12,6,[1,0,0,1]>')]).
% 0.72/1.08 cnf('0.26.2.0',plain,
% 0.72/1.08 ( multiply(X1,inverse(X1)) = identity ),
% 0.72/1.08 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_24]).
% 0.72/1.08 cnf('0.27.0.0',plain,
% 0.72/1.08 ( positive_part(union(X1,X2)) = union(X1,union(X2,identity)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.16.2.0','0.15.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.27.0.1',plain,
% 0.72/1.08 ( positive_part(union(X1,X2)) = union(X1,positive_part(X2)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.27.0.0','0.16.2.0',theory(equality)]),
% 0.72/1.08 [pos('R.2','L')]).
% 0.72/1.08 cnf('0.27.1.0',plain,
% 0.72/1.08 ( positive_part(union(X1,X2)) = union(X1,positive_part(X2)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.27.0.1']),
% 0.72/1.08 [weight('<4,16,15,[1,0,0,0]>')]).
% 0.72/1.08 cnf('0.27.2.0',plain,
% 0.72/1.08 ( positive_part(union(X1,X2)) = union(X1,positive_part(X2)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_25]).
% 0.72/1.08 cnf('0.31.0.0',plain,
% 0.72/1.08 ( union(identity,union(X1,X2)) = union(positive_part(X1),X2) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.15.2.0','0.23.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.31.0.1',plain,
% 0.72/1.08 ( positive_part(union(X1,X2)) = union(positive_part(X1),X2) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.31.0.0','0.23.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.31.1.0',plain,
% 0.72/1.08 ( positive_part(union(X1,X2)) = union(positive_part(X1),X2) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.31.0.1']),
% 0.72/1.08 [weight('<4,23,15,[0,0,0,1]>')]).
% 0.72/1.08 cnf('0.31.1.1',plain,
% 0.72/1.08 ( union(X1,positive_part(X2)) = union(positive_part(X1),X2) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.31.1.0','0.27.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.31.2.0',plain,
% 0.72/1.08 ( union(positive_part(X1),X2) = union(X1,positive_part(X2)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.31.1.1',theory(equality)]),
% 0.72/1.08 [x,rule_29]).
% 0.72/1.08 cnf('0.35.0.0',plain,
% 0.72/1.08 ( union(intersection(X1,X2),X2) = X2 ),
% 0.72/1.08 inference(interreduction_right,[status(thm)],['0.3.2.0'])).
% 0.72/1.08 cnf('0.35.1.0',plain,
% 0.72/1.08 ( union(intersection(X1,X2),X2) = X2 ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.35.0.0']),
% 0.72/1.08 [weight('<5,3,14,[0,0,0,0]>')]).
% 0.72/1.08 cnf('0.35.1.1',plain,
% 0.72/1.08 ( union(X2,intersection(X1,X2)) = X2 ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.35.1.0','0.14.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.35.2.0',plain,
% 0.72/1.08 ( union(X1,intersection(X2,X1)) = X1 ),
% 0.72/1.08 inference(orient,[status(thm)],['0.35.1.1',theory(equality)]),
% 0.72/1.08 [u,rule_33]).
% 0.72/1.08 cnf('0.36.0.0',plain,
% 0.72/1.08 ( identity = union(identity,negative_part(X1)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.35.2.0','0.19.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.36.0.1',plain,
% 0.72/1.08 ( identity = positive_part(negative_part(X1)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.36.0.0','0.23.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.36.1.0',plain,
% 0.72/1.08 ( identity = positive_part(negative_part(X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.36.0.1']),
% 0.72/1.08 [weight('<3,35,19,[1,0,0,2]>')]).
% 0.72/1.08 cnf('0.36.2.0',plain,
% 0.72/1.08 ( positive_part(negative_part(X1)) = identity ),
% 0.72/1.08 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_34]).
% 0.72/1.08 cnf('0.38.0.0',plain,
% 0.72/1.08 ( intersection(union(X1,X2),X2) = X2 ),
% 0.72/1.08 inference(interreduction_right,[status(thm)],['0.5.2.0'])).
% 0.72/1.08 cnf('0.38.1.0',plain,
% 0.72/1.08 ( intersection(union(X1,X2),X2) = X2 ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.38.0.0']),
% 0.72/1.08 [weight('<5,5,17,[0,0,0,0]>')]).
% 0.72/1.08 cnf('0.38.1.1',plain,
% 0.72/1.08 ( intersection(X2,union(X1,X2)) = X2 ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.38.1.0','0.17.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.38.2.0',plain,
% 0.72/1.08 ( intersection(X1,union(X2,X1)) = X1 ),
% 0.72/1.08 inference(orient,[status(thm)],['0.38.1.1',theory(equality)]),
% 0.72/1.08 [u,rule_36]).
% 0.72/1.08 cnf('0.39.0.0',plain,
% 0.72/1.08 ( identity = intersection(identity,positive_part(X1)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.38.2.0','0.16.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.39.0.1',plain,
% 0.72/1.08 ( identity = negative_part(positive_part(X1)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.39.0.0','0.24.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.39.1.0',plain,
% 0.72/1.08 ( identity = negative_part(positive_part(X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.39.0.1']),
% 0.72/1.08 [weight('<3,38,16,[1,0,0,2]>')]).
% 0.72/1.08 cnf('0.39.2.0',plain,
% 0.72/1.08 ( negative_part(positive_part(X1)) = identity ),
% 0.72/1.08 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_37]).
% 0.72/1.08 cnf('0.40.0.0',plain,
% 0.72/1.08 ( X1 = intersection(X1,positive_part(X1)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.38.2.0','0.23.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.40.1.0',plain,
% 0.72/1.08 ( X1 = intersection(X1,positive_part(X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.40.0.0']),
% 0.72/1.08 [weight('<4,38,23,[1,0,0,2]>')]).
% 0.72/1.08 cnf('0.40.2.0',plain,
% 0.72/1.08 ( intersection(X1,positive_part(X1)) = X1 ),
% 0.72/1.08 inference(orient,[status(thm)],['0.40.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_38]).
% 0.72/1.08 cnf('0.41.0.0',plain,
% 0.72/1.08 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.13.2.0','0.6.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.41.1.0',plain,
% 0.72/1.08 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.41.0.0']),
% 0.72/1.08 [weight('<5,13,6,[1,0,0,1]>')]).
% 0.72/1.08 cnf('0.41.2.0',plain,
% 0.72/1.08 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.41.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_39]).
% 0.72/1.08 cnf('0.42.0.0',plain,
% 0.72/1.08 ( inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.13.2.0','0.6.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.42.1.0',plain,
% 0.72/1.08 ( inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.42.0.0']),
% 0.72/1.08 [weight('<5,13,6,[1,0,0,3]>')]).
% 0.72/1.08 cnf('0.42.2.0',plain,
% 0.72/1.08 ( inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.42.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_40]).
% 0.72/1.08 cnf('0.45.0.0',plain,
% 0.72/1.08 ( multiply(X1,union(identity,X2)) = union(X1,multiply(X1,X2)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.8.2.0','0.25.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.45.0.1',plain,
% 0.72/1.08 ( multiply(X1,positive_part(X2)) = union(X1,multiply(X1,X2)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.45.0.0','0.23.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.45.1.0',plain,
% 0.72/1.08 ( multiply(X1,positive_part(X2)) = union(X1,multiply(X1,X2)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.45.0.1']),
% 0.72/1.08 [weight('<5,25,8,[0,0,0,1]>')]).
% 0.72/1.08 cnf('0.45.2.0',plain,
% 0.72/1.08 ( union(X1,multiply(X1,X2)) = multiply(X1,positive_part(X2)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_43]).
% 0.72/1.08 cnf('0.47.0.0',plain,
% 0.72/1.08 ( multiply(X1,intersection(identity,X2)) = intersection(X1,multiply(X1,X2)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.9.2.0','0.25.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.47.0.1',plain,
% 0.72/1.08 ( multiply(X1,negative_part(X2)) = intersection(X1,multiply(X1,X2)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.47.0.0','0.24.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.47.1.0',plain,
% 0.72/1.08 ( multiply(X1,negative_part(X2)) = intersection(X1,multiply(X1,X2)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.47.0.1']),
% 0.72/1.08 [weight('<5,25,9,[0,0,0,1]>')]).
% 0.72/1.08 cnf('0.47.2.0',plain,
% 0.72/1.08 ( intersection(X1,multiply(X1,X2)) = multiply(X1,negative_part(X2)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_45]).
% 0.72/1.08 cnf('0.48.0.0',plain,
% 0.72/1.08 ( multiply(multiply(X1,X2),negative_part(X2)) = multiply(intersection(X1,multiply(X1,X2)),X2) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.47.2.0','0.11.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.48.0.1',plain,
% 0.72/1.08 ( multiply(X1,multiply(X2,negative_part(X2))) = multiply(intersection(X1,multiply(X1,X2)),X2) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.48.0.0','0.7.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.48.0.2',plain,
% 0.72/1.08 ( multiply(X1,multiply(X2,negative_part(X2))) = multiply(multiply(X1,negative_part(X2)),X2) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.48.0.1','0.47.2.0',theory(equality)]),
% 0.72/1.08 [pos('R.1','L')]).
% 0.72/1.08 cnf('0.48.0.3',plain,
% 0.72/1.08 ( multiply(X1,multiply(X2,negative_part(X2))) = multiply(X1,multiply(negative_part(X2),X2)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.48.0.2','0.7.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.48.1.0',plain,
% 0.72/1.08 ( multiply(X2,negative_part(X2)) = multiply(negative_part(X2),X2) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.48.0.3']),
% 0.72/1.08 [weight('<4,47,11,[1,0,0,0]>')]).
% 0.72/1.08 cnf('0.48.2.0',plain,
% 0.72/1.08 ( multiply(negative_part(X1),X1) = multiply(X1,negative_part(X1)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_46]).
% 0.72/1.08 cnf('0.51.0.0',plain,
% 0.72/1.08 ( union(negative_part(X1),positive_part(X2)) = union(identity,X2) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.31.2.0','0.36.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.51.0.1',plain,
% 0.72/1.08 ( union(negative_part(X1),positive_part(X2)) = positive_part(X2) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.51.0.0','0.23.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.51.1.0',plain,
% 0.72/1.08 ( union(negative_part(X1),positive_part(X2)) = positive_part(X2) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.51.0.1']),
% 0.72/1.08 [weight('<5,36,31,[0,0,0,1]>')]).
% 0.72/1.08 cnf('0.51.2.0',plain,
% 0.72/1.08 ( union(negative_part(X1),positive_part(X2)) = positive_part(X2) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.51.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_49]).
% 0.72/1.08 cnf('0.57.0.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),positive_part(X1)) = union(inverse(X1),identity) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.45.2.0','0.12.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.57.0.1',plain,
% 0.72/1.08 ( multiply(inverse(X1),positive_part(X1)) = positive_part(inverse(X1)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.57.0.0','0.16.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.57.1.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),positive_part(X1)) = positive_part(inverse(X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.57.0.1']),
% 0.72/1.08 [weight('<5,45,12,[1,0,0,2]>')]).
% 0.72/1.08 cnf('0.57.2.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),positive_part(X1)) = positive_part(inverse(X1)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_55]).
% 0.72/1.08 cnf('0.62.0.0',plain,
% 0.72/1.08 ( multiply(union(identity,X1),X2) = union(X2,multiply(X1,X2)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.10.2.0','0.1.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.62.1.0',plain,
% 0.72/1.08 ( multiply(union(identity,X1),X2) = union(X2,multiply(X1,X2)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.62.0.0']),
% 0.72/1.08 [weight('<?,10,1,[1,0,0,1]>')]).
% 0.72/1.08 cnf('0.62.1.1',plain,
% 0.72/1.08 ( multiply(positive_part(X1),X2) = union(X2,multiply(X1,X2)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.62.1.0','0.23.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.62.2.0',plain,
% 0.72/1.08 ( union(X1,multiply(X2,X1)) = multiply(positive_part(X2),X1) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.62.1.1',theory(equality)]),
% 0.72/1.08 [x,rule_60]).
% 0.72/1.08 cnf('0.64.0.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),negative_part(X1)) = intersection(inverse(X1),identity) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.47.2.0','0.12.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.64.0.1',plain,
% 0.72/1.08 ( multiply(inverse(X1),negative_part(X1)) = negative_part(inverse(X1)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.64.0.0','0.19.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.64.1.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),negative_part(X1)) = negative_part(inverse(X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.64.0.1']),
% 0.72/1.08 [weight('<5,47,12,[1,0,0,2]>')]).
% 0.72/1.08 cnf('0.64.2.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),negative_part(X1)) = negative_part(inverse(X1)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.64.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_62]).
% 0.72/1.08 cnf('0.66.0.0',plain,
% 0.72/1.08 ( multiply(inverse(positive_part(X1)),X1) = inverse(positive_part(inverse(X1))) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.42.2.0','0.57.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.66.1.0',plain,
% 0.72/1.08 ( multiply(inverse(positive_part(X1)),X1) = inverse(positive_part(inverse(X1))) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.66.0.0']),
% 0.72/1.08 [weight('<5,57,42,[0,0,0,1]>')]).
% 0.72/1.08 cnf('0.66.2.0',plain,
% 0.72/1.08 ( multiply(inverse(positive_part(X1)),X1) = inverse(positive_part(inverse(X1))) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.66.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_64]).
% 0.72/1.08 cnf('0.67.0.0',plain,
% 0.72/1.08 ( multiply(positive_part(inverse(X1)),X1) = union(X1,identity) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.62.2.0','0.12.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.67.0.1',plain,
% 0.72/1.08 ( multiply(positive_part(inverse(X1)),X1) = positive_part(X1) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.67.0.0','0.16.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.67.1.0',plain,
% 0.72/1.08 ( multiply(positive_part(inverse(X1)),X1) = positive_part(X1) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.67.0.1']),
% 0.72/1.08 [weight('<5,62,12,[1,0,0,2]>')]).
% 0.72/1.08 cnf('0.67.2.0',plain,
% 0.72/1.08 ( multiply(positive_part(inverse(X1)),X1) = positive_part(X1) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.67.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_65]).
% 0.72/1.08 cnf('0.68.0.0',plain,
% 0.72/1.08 ( multiply(positive_part(X1),inverse(X1)) = union(inverse(X1),identity) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.62.2.0','0.26.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.68.0.1',plain,
% 0.72/1.08 ( multiply(positive_part(X1),inverse(X1)) = positive_part(inverse(X1)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.68.0.0','0.16.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.68.1.0',plain,
% 0.72/1.08 ( multiply(positive_part(X1),inverse(X1)) = positive_part(inverse(X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.68.0.1']),
% 0.72/1.08 [weight('<5,62,26,[1,0,0,2]>')]).
% 0.72/1.08 cnf('0.68.2.0',plain,
% 0.72/1.08 ( multiply(positive_part(X1),inverse(X1)) = positive_part(inverse(X1)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.68.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_66]).
% 0.72/1.08 cnf('0.71.0.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.7.2.0','0.12.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.71.0.1',plain,
% 0.72/1.08 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.71.0.0','0.1.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.71.1.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.71.0.1']),
% 0.72/1.08 [weight('<6,12,7,[0,0,0,1]>')]).
% 0.72/1.08 cnf('0.71.2.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.72/1.08 inference(orient,[status(thm)],['0.71.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_69]).
% 0.72/1.08 cnf('0.74.0.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),intersection(X1,X2)) = intersection(identity,multiply(inverse(X1),X2)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.9.2.0','0.12.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.74.1.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),intersection(X1,X2)) = intersection(identity,multiply(inverse(X1),X2)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.74.0.0']),
% 0.72/1.08 [weight('<6,12,9,[0,0,0,1]>')]).
% 0.72/1.08 cnf('0.74.1.1',plain,
% 0.72/1.08 ( multiply(inverse(X1),intersection(X1,X2)) = negative_part(multiply(inverse(X1),X2)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.74.1.0','0.24.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.74.2.0',plain,
% 0.72/1.08 ( multiply(inverse(X1),intersection(X1,X2)) = negative_part(multiply(inverse(X1),X2)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.74.1.1',theory(equality)]),
% 0.72/1.08 [u,rule_72]).
% 0.72/1.08 cnf('0.125.0.0',plain,
% 0.72/1.08 ( multiply(positive_part(inverse(X1)),negative_part(X1)) = union(negative_part(X1),negative_part(inverse(X1))) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.62.2.0','0.64.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.125.1.0',plain,
% 0.72/1.08 ( multiply(positive_part(inverse(X1)),negative_part(X1)) = union(negative_part(X1),negative_part(inverse(X1))) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.125.0.0']),
% 0.72/1.08 [weight('<6,64,62,[0,0,0,2]>')]).
% 0.72/1.08 cnf('0.125.2.0',plain,
% 0.72/1.08 ( multiply(positive_part(inverse(X1)),negative_part(X1)) = union(negative_part(X1),negative_part(inverse(X1))) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.125.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_123]).
% 0.72/1.08 cnf('0.128.0.0',plain,
% 0.72/1.08 ( multiply(positive_part(inverse(X1)),negative_part(X1)) = intersection(positive_part(inverse(X1)),positive_part(X1)) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.47.2.0','0.67.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.128.1.0',plain,
% 0.72/1.08 ( multiply(positive_part(inverse(X1)),negative_part(X1)) = intersection(positive_part(inverse(X1)),positive_part(X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.128.0.0']),
% 0.72/1.08 [weight('<6,67,47,[0,0,0,2]>')]).
% 0.72/1.08 cnf('0.128.1.1',plain,
% 0.72/1.08 ( union(negative_part(X1),negative_part(inverse(X1))) = intersection(positive_part(inverse(X1)),positive_part(X1)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.128.1.0','0.125.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.128.1.2',plain,
% 0.72/1.08 ( union(negative_part(X1),negative_part(inverse(X1))) = intersection(positive_part(X1),positive_part(inverse(X1))) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.128.1.1','0.17.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.128.2.0',plain,
% 0.72/1.08 ( union(negative_part(X1),negative_part(inverse(X1))) = intersection(positive_part(X1),positive_part(inverse(X1))) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.128.1.2',theory(equality)]),
% 0.72/1.08 [u,rule_126]).
% 0.72/1.08 cnf('0.185.0.0',plain,
% 0.72/1.08 ( multiply(negative_part(X1),positive_part(X1)) = union(negative_part(X1),multiply(X1,negative_part(X1))) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.45.2.0','0.48.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.185.1.0',plain,
% 0.72/1.08 ( multiply(negative_part(X1),positive_part(X1)) = union(negative_part(X1),multiply(X1,negative_part(X1))) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.185.0.0']),
% 0.72/1.08 [weight('<7,48,45,[0,0,0,2]>')]).
% 0.72/1.08 cnf('0.185.1.1',plain,
% 0.72/1.08 ( multiply(negative_part(X1),positive_part(X1)) = multiply(positive_part(X1),negative_part(X1)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.185.1.0','0.62.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.185.2.0',plain,
% 0.72/1.08 ( multiply(positive_part(X1),negative_part(X1)) = multiply(negative_part(X1),positive_part(X1)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.185.1.1',theory(equality)]),
% 0.72/1.08 [x,rule_183]).
% 0.72/1.08 cnf('0.231.0.0',plain,
% 0.72/1.08 ( X1 = multiply(inverse(inverse(positive_part(X1))),inverse(positive_part(inverse(X1)))) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.71.2.0','0.66.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.231.0.1',plain,
% 0.72/1.08 ( X1 = inverse(multiply(positive_part(inverse(X1)),inverse(positive_part(X1)))) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.231.0.0','0.13.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.231.0.2',plain,
% 0.72/1.08 ( X1 = multiply(positive_part(X1),inverse(positive_part(inverse(X1)))) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.231.0.1','0.41.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.231.1.0',plain,
% 0.72/1.08 ( X1 = multiply(positive_part(X1),inverse(positive_part(inverse(X1)))) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.231.0.2']),
% 0.72/1.08 [weight('<7,71,66,[1,0,0,3]>')]).
% 0.72/1.08 cnf('0.231.2.0',plain,
% 0.72/1.08 ( multiply(positive_part(X1),inverse(positive_part(inverse(X1)))) = X1 ),
% 0.72/1.08 inference(orient,[status(thm)],['0.231.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_229]).
% 0.72/1.08 cnf('0.235.0.0',plain,
% 0.72/1.08 ( inverse(X1) = multiply(inverse(positive_part(X1)),positive_part(inverse(X1))) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.71.2.0','0.68.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.235.1.0',plain,
% 0.72/1.08 ( inverse(X1) = multiply(inverse(positive_part(X1)),positive_part(inverse(X1))) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.235.0.0']),
% 0.72/1.08 [weight('<7,71,68,[1,0,0,3]>')]).
% 0.72/1.08 cnf('0.235.2.0',plain,
% 0.72/1.08 ( multiply(inverse(positive_part(X1)),positive_part(inverse(X1))) = inverse(X1) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.235.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_233]).
% 0.72/1.08 cnf('0.326.0.0',plain,
% 0.72/1.08 ( union(negative_part(X1),positive_part(negative_part(inverse(X1)))) = positive_part(intersection(positive_part(X1),positive_part(inverse(X1)))) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.27.2.0','0.128.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.326.0.1',plain,
% 0.72/1.08 ( positive_part(negative_part(inverse(X1))) = positive_part(intersection(positive_part(X1),positive_part(inverse(X1)))) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.326.0.0','0.51.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.326.0.2',plain,
% 0.72/1.08 ( identity = positive_part(intersection(positive_part(X1),positive_part(inverse(X1)))) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.326.0.1','0.36.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.326.1.0',plain,
% 0.72/1.08 ( identity = positive_part(intersection(positive_part(X1),positive_part(inverse(X1)))) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.326.0.2']),
% 0.72/1.08 [weight('<7,128,27,[0,0,0,1]>')]).
% 0.72/1.08 cnf('0.326.2.0',plain,
% 0.72/1.08 ( positive_part(intersection(positive_part(X1),positive_part(inverse(X1)))) = identity ),
% 0.72/1.08 inference(orient,[status(thm)],['0.326.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_324]).
% 0.72/1.08 cnf('0.327.0.0',plain,
% 0.72/1.08 ( intersection(positive_part(X1),positive_part(inverse(X1))) = intersection(intersection(positive_part(X1),positive_part(inverse(X1))),identity) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.40.2.0','0.326.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.327.0.1',plain,
% 0.72/1.08 ( intersection(positive_part(X1),positive_part(inverse(X1))) = intersection(positive_part(X1),intersection(positive_part(inverse(X1)),identity)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.327.0.0','0.18.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.327.0.2',plain,
% 0.72/1.08 ( intersection(positive_part(X1),positive_part(inverse(X1))) = intersection(positive_part(X1),negative_part(positive_part(inverse(X1)))) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.327.0.1','0.19.2.0',theory(equality)]),
% 0.72/1.08 [pos('R.2','L')]).
% 0.72/1.08 cnf('0.327.0.3',plain,
% 0.72/1.08 ( intersection(positive_part(X1),positive_part(inverse(X1))) = intersection(positive_part(X1),identity) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.327.0.2','0.39.2.0',theory(equality)]),
% 0.72/1.08 [pos('R.2','L')]).
% 0.72/1.08 cnf('0.327.0.4',plain,
% 0.72/1.08 ( intersection(positive_part(X1),positive_part(inverse(X1))) = negative_part(positive_part(X1)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.327.0.3','0.19.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.327.0.5',plain,
% 0.72/1.08 ( intersection(positive_part(X1),positive_part(inverse(X1))) = identity ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.327.0.4','0.39.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.327.1.0',plain,
% 0.72/1.08 ( intersection(positive_part(X1),positive_part(inverse(X1))) = identity ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.327.0.5']),
% 0.72/1.08 [weight('<6,326,40,[0,0,0,2]>')]).
% 0.72/1.08 cnf('0.327.2.0',plain,
% 0.72/1.08 ( intersection(positive_part(X1),positive_part(inverse(X1))) = identity ),
% 0.72/1.08 inference(orient,[status(thm)],['0.327.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_325]).
% 0.72/1.08 cnf('0.328.0.0',plain,
% 0.72/1.08 ( negative_part(multiply(inverse(positive_part(X1)),positive_part(inverse(X1)))) = multiply(inverse(positive_part(X1)),identity) ),
% 0.72/1.08 inference(cp,[status(thm)],['0.74.2.0','0.327.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.328.0.1',plain,
% 0.72/1.08 ( negative_part(inverse(X1)) = multiply(inverse(positive_part(X1)),identity) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.328.0.0','0.235.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.1','L')]).
% 0.72/1.08 cnf('0.328.0.2',plain,
% 0.72/1.08 ( negative_part(inverse(X1)) = inverse(positive_part(X1)) ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.328.0.1','0.25.2.0',theory(equality)]),
% 0.72/1.08 [pos('R','L')]).
% 0.72/1.08 cnf('0.328.1.0',plain,
% 0.72/1.08 ( negative_part(inverse(X1)) = inverse(positive_part(X1)) ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.328.0.2']),
% 0.72/1.08 [weight('<3,327,74,[0,0,0,3]>')]).
% 0.72/1.08 cnf('0.328.2.0',plain,
% 0.72/1.08 ( inverse(positive_part(X1)) = negative_part(inverse(X1)) ),
% 0.72/1.08 inference(orient,[status(thm)],['0.328.1.0',theory(equality)]),
% 0.72/1.08 [x,rule_326]).
% 0.72/1.08 cnf('0.333.0.0',plain,
% 0.72/1.08 ( multiply(positive_part(X1),inverse(positive_part(inverse(X1)))) = X1 ),
% 0.72/1.08 inference(interreduction_right,[status(thm)],['0.231.2.0'])).
% 0.72/1.08 cnf('0.333.0.1',plain,
% 0.72/1.08 ( multiply(positive_part(X1),negative_part(inverse(inverse(X1)))) = X1 ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.333.0.0','0.328.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2','L')]).
% 0.72/1.08 cnf('0.333.0.2',plain,
% 0.72/1.08 ( multiply(positive_part(X1),negative_part(X1)) = X1 ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.333.0.1','0.6.2.0',theory(equality)]),
% 0.72/1.08 [pos('L.2.1','L')]).
% 0.72/1.08 cnf('0.333.0.3',plain,
% 0.72/1.08 ( multiply(negative_part(X1),positive_part(X1)) = X1 ),
% 0.72/1.08 inference(reduction,[status(thm)],['0.333.0.2','0.185.2.0',theory(equality)]),
% 0.72/1.08 [pos('L','L')]).
% 0.72/1.08 cnf('0.333.1.0',plain,
% 0.72/1.08 ( multiply(negative_part(X1),positive_part(X1)) = X1 ),
% 0.72/1.08 inference(weigh,[status(thm)],['0.333.0.3']),
% 0.72/1.08 [weight('<5,231,328,[0,0,0,0]>')]).
% 0.72/1.08 cnf('0.333.2.0',plain,
% 0.72/1.08 ( multiply(negative_part(X1),positive_part(X1)) = X1 ),
% 0.72/1.08 inference(orient,[status(thm)],['0.333.1.0',theory(equality)]),
% 0.72/1.08 [u,rule_331]).
% 0.72/1.08 cnf('1.0.0.0',conjecture,
% 0.72/1.08 ( multiply(positive_part(a),negative_part(a)) = a ),
% 0.72/1.09 file('/tmp/WALDMEISTER_20573_n028',conjecture_1)).
% 0.72/1.09 cnf('1.0.0.1',plain,
% 0.72/1.09 ( multiply(negative_part(a),positive_part(a)) = a ),
% 0.72/1.09 inference(reduction,[status(thm)],['1.0.0.0','0.185.2.0',theory(equality)]),
% 0.72/1.09 [pos('L','L')]).
% 0.72/1.09 cnf('1.0.0.2',plain,
% 0.72/1.09 ( a = a ),
% 0.72/1.09 inference(reduction,[status(thm)],['1.0.0.1','0.333.2.0',theory(equality)]),
% 0.72/1.09 [pos('L','L')]).
% 0.72/1.09 cnf('1.0.0.3',plain,
% 0.72/1.09 ( $true ),
% 0.72/1.09 inference(trivial,[status(thm)],['1.0.0.2',theory(equality)]),
% 0.72/1.09 [conjecture_1]).
% 0.72/1.09
% 0.72/1.09 Proved Goals:
% 0.72/1.09 No. 1: multiply(positive_part(a),negative_part(a)) ?= a joined, current: a = a
% 0.72/1.09 1 goal was specified, which was proved.
% 0.72/1.09 % SZS output end CNFRefutation
% 0.72/1.09 #END OF PROOF
% 0.72/1.09
% 0.72/1.09 Problem WALDMEISTER_20573_n028
% 0.72/1.09 CPs.gen 24197
% 0.72/1.09 CPs.reexp 0
% 0.72/1.09 Select 931
% 0.72/1.09 R 331
% 0.72/1.09 E 2
% 0.72/1.09 vsize 6.5M
% 0.72/1.09 rss 3.8M
% 0.72/1.09 process.time 0.101s
% 0.72/1.09 wallclock.time 0.101s
% 0.72/1.09 status S
% 0.72/1.09
% 0.72/1.09
% 0.72/1.09 Waldmeister states: Goal proved.
% 0.72/1.09 % SZS status Unsatisfiable
%------------------------------------------------------------------------------