TSTP Solution File: GRP169-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP169-1 : 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 12:25:04 EDT 2022
% Result : Unsatisfiable 0.66s 1.03s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP169-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.11 % Command : woody %s
% 0.12/0.31 % Computer : n026.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 600
% 0.12/0.31 % DateTime : Mon Jun 13 15:45:51 EDT 2022
% 0.12/0.31 % CPUTime :
% 0.63/1.01 ********************************************************************************
% 0.63/1.01 * W A L D M E I S T E R \| \ / \|/ *
% 0.63/1.01 * |/ | \/ | *
% 0.63/1.01 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.63/1.01 * A. Jaeger and B. Loechner | | *
% 0.63/1.01 * <waldmeister@informatik.uni-kl.de> | *
% 0.63/1.01 ********************************************************************************
% 0.63/1.01
% 0.63/1.01
% 0.63/1.01 Goals:
% 0.63/1.01 ------
% 0.63/1.01
% 0.63/1.01 ( 1) least_upper_bound(a,b) ?=? a
% 0.63/1.01
% 0.63/1.01 Detected structure: VerbandsgeordneteGruppe
% 0.63/1.01 ********************************************************************************
% 0.63/1.01 ****************************** COMPLETION - PROOF ******************************
% 0.63/1.01 ********************************************************************************
% 0.63/1.01
% 0.66/1.03 joined goal: 1 least_upper_bound(a,b) ?= a to a
% 0.66/1.03 goal joined
% 0.66/1.03 % SZS status Unsatisfiable
% 0.66/1.03 #START OF PROOF
% 0.66/1.03 % SZS output start CNFRefutation
% 0.66/1.03 cnf('0.1.0.0',axiom,
% 0.66/1.03 ( X1 = multiply(identity,X1) ),
% 0.66/1.03 file('/tmp/WALDMEISTER_4973_n026')).
% 0.66/1.03 cnf('0.1.1.0',plain,
% 0.66/1.03 ( X1 = multiply(identity,X1) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.66/1.03 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.66/1.03 cnf('0.1.2.0',plain,
% 0.66/1.03 ( multiply(identity,X1) = X1 ),
% 0.66/1.03 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.66/1.03 [x,rule_1]).
% 0.66/1.03 cnf('0.6.0.0',axiom,
% 0.66/1.03 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.66/1.03 file('/tmp/WALDMEISTER_4973_n026')).
% 0.66/1.03 cnf('0.6.1.0',plain,
% 0.66/1.03 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.66/1.03 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.66/1.03 cnf('0.6.2.0',plain,
% 0.66/1.03 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.66/1.03 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.66/1.03 [x,rule_6]).
% 0.66/1.03 cnf('0.7.0.0',axiom,
% 0.66/1.03 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.66/1.03 file('/tmp/WALDMEISTER_4973_n026')).
% 0.66/1.03 cnf('0.7.1.0',plain,
% 0.66/1.03 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.66/1.03 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.66/1.03 cnf('0.7.2.0',plain,
% 0.66/1.03 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.66/1.03 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.66/1.03 [u,rule_7]).
% 0.66/1.03 cnf('0.9.0.0',axiom,
% 0.66/1.03 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.66/1.03 file('/tmp/WALDMEISTER_4973_n026')).
% 0.66/1.03 cnf('0.9.1.0',plain,
% 0.66/1.03 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.66/1.03 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.66/1.03 cnf('0.9.2.0',plain,
% 0.66/1.03 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.66/1.03 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.66/1.03 [u,rule_9]).
% 0.66/1.03 cnf('0.11.0.0',axiom,
% 0.66/1.03 ( multiply(inverse(X1),X1) = identity ),
% 0.66/1.03 file('/tmp/WALDMEISTER_4973_n026')).
% 0.66/1.03 cnf('0.11.1.0',plain,
% 0.66/1.03 ( multiply(inverse(X1),X1) = identity ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.66/1.03 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.66/1.03 cnf('0.11.2.0',plain,
% 0.66/1.03 ( multiply(inverse(X1),X1) = identity ),
% 0.66/1.03 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.66/1.03 [u,rule_11]).
% 0.66/1.03 cnf('0.12.0.0',axiom,
% 0.66/1.03 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.66/1.03 file('/tmp/WALDMEISTER_4973_n026')).
% 0.66/1.03 cnf('0.12.1.0',plain,
% 0.66/1.03 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.66/1.03 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.66/1.03 cnf('0.12.2.0',plain,
% 0.66/1.03 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.66/1.03 inference(activate,[status(thm)],['0.12.1.0']),
% 0.66/1.03 [equation_1]).
% 0.66/1.03 cnf('0.14.0.0',axiom,
% 0.66/1.03 ( least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
% 0.66/1.03 file('/tmp/WALDMEISTER_4973_n026')).
% 0.66/1.03 cnf('0.14.1.0',plain,
% 0.66/1.03 ( least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.66/1.03 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.66/1.03 cnf('0.14.2.0',plain,
% 0.66/1.03 ( least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
% 0.66/1.03 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.66/1.03 [u,rule_13]).
% 0.66/1.03 cnf('0.24.0.0',plain,
% 0.66/1.03 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.1','L')]).
% 0.66/1.03 cnf('0.24.0.1',plain,
% 0.66/1.03 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.24.0.0','0.1.2.0',theory(equality)]),
% 0.66/1.03 [pos('R','L')]).
% 0.66/1.03 cnf('0.24.1.0',plain,
% 0.66/1.03 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.24.0.1']),
% 0.66/1.03 [weight('<55,11,6,[0,0,0,1]>')]).
% 0.66/1.03 cnf('0.24.2.0',plain,
% 0.66/1.03 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.66/1.03 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 0.66/1.03 [u,rule_22]).
% 0.66/1.03 cnf('0.25.0.0',plain,
% 0.66/1.03 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.24.2.0','0.24.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.2','L')]).
% 0.66/1.03 cnf('0.25.1.0',plain,
% 0.66/1.03 ( X1 = inverse(inverse(X1)) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.66/1.03 [weight('<19,24,24,[0,0,0,3]>')]).
% 0.66/1.03 cnf('0.25.2.0',plain,
% 0.66/1.03 ( inverse(inverse(X1)) = X1 ),
% 0.66/1.03 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.66/1.03 [x,rule_23]).
% 0.66/1.03 cnf('0.27.0.0',plain,
% 0.66/1.03 ( identity = multiply(X1,inverse(X1)) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.11.2.0','0.25.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.1','L')]).
% 0.66/1.03 cnf('0.27.1.0',plain,
% 0.66/1.03 ( identity = multiply(X1,inverse(X1)) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.27.0.0']),
% 0.66/1.03 [weight('<29,25,11,[0,0,0,1]>')]).
% 0.66/1.03 cnf('0.27.2.0',plain,
% 0.66/1.03 ( multiply(X1,inverse(X1)) = identity ),
% 0.66/1.03 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 0.66/1.03 [x,rule_25]).
% 0.66/1.03 cnf('0.29.0.0',plain,
% 0.66/1.03 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.24.2.0','0.27.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.2','L')]).
% 0.66/1.03 cnf('0.29.1.0',plain,
% 0.66/1.03 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.29.0.0']),
% 0.66/1.03 [weight('<34,27,24,[0,0,0,3]>')]).
% 0.66/1.03 cnf('0.29.2.0',plain,
% 0.66/1.03 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 0.66/1.03 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.66/1.03 [x,rule_27]).
% 0.66/1.03 cnf('0.30.0.0',plain,
% 0.66/1.03 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.29.2.0','0.25.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.1','L')]).
% 0.66/1.03 cnf('0.30.0.1',plain,
% 0.66/1.03 ( X1 = multiply(X1,identity) ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.30.0.0','0.25.2.0',theory(equality)]),
% 0.66/1.03 [pos('L','L')]).
% 0.66/1.03 cnf('0.30.1.0',plain,
% 0.66/1.03 ( X1 = multiply(X1,identity) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.30.0.1']),
% 0.66/1.03 [weight('<19,29,25,[1,0,0,1]>')]).
% 0.66/1.03 cnf('0.30.2.0',plain,
% 0.66/1.03 ( multiply(X1,identity) = X1 ),
% 0.66/1.03 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 0.66/1.03 [x,rule_28]).
% 0.66/1.03 cnf('0.31.0.0',plain,
% 0.66/1.03 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.24.2.0','0.25.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.1','L')]).
% 0.66/1.03 cnf('0.31.1.0',plain,
% 0.66/1.03 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.31.0.0']),
% 0.66/1.03 [weight('<55,25,24,[0,0,0,1]>')]).
% 0.66/1.03 cnf('0.31.2.0',plain,
% 0.66/1.03 ( multiply(X1,multiply(inverse(X1),X2)) = X2 ),
% 0.66/1.03 inference(orient,[status(thm)],['0.31.1.0',theory(equality)]),
% 0.66/1.03 [x,rule_29]).
% 0.66/1.03 cnf('0.52.0.0',plain,
% 0.66/1.03 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.27.2.0','0.6.2.0',theory(equality)]),
% 0.66/1.03 [pos('L','L')]).
% 0.66/1.03 cnf('0.52.1.0',plain,
% 0.66/1.03 ( identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.52.0.0']),
% 0.66/1.03 [weight('<89,27,6,[1,0,0,0]>')]).
% 0.66/1.03 cnf('0.52.2.0',plain,
% 0.66/1.03 ( multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity ),
% 0.66/1.03 inference(orient,[status(thm)],['0.52.1.0',theory(equality)]),
% 0.66/1.03 [x,rule_50]).
% 0.66/1.03 cnf('0.53.0.0',plain,
% 0.66/1.03 ( multiply(X1,inverse(multiply(X2,X1))) = multiply(inverse(X2),identity) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.24.2.0','0.52.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.2','L')]).
% 0.66/1.03 cnf('0.53.0.1',plain,
% 0.66/1.03 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.53.0.0','0.30.2.0',theory(equality)]),
% 0.66/1.03 [pos('R','L')]).
% 0.66/1.03 cnf('0.53.1.0',plain,
% 0.66/1.03 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.53.0.1']),
% 0.66/1.03 [weight('<62,52,24,[0,0,0,3]>')]).
% 0.66/1.03 cnf('0.53.2.0',plain,
% 0.66/1.03 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 0.66/1.03 inference(orient,[status(thm)],['0.53.1.0',theory(equality)]),
% 0.66/1.03 [u,rule_51]).
% 0.66/1.03 cnf('0.60.0.0',plain,
% 0.66/1.03 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.24.2.0','0.53.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.2','L')]).
% 0.66/1.03 cnf('0.60.1.0',plain,
% 0.66/1.03 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.60.0.0']),
% 0.66/1.03 [weight('<99,53,24,[0,0,0,3]>')]).
% 0.66/1.03 cnf('0.60.2.0',plain,
% 0.66/1.03 ( inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)) ),
% 0.66/1.03 inference(activate,[status(thm)],['0.60.1.0']),
% 0.66/1.03 [equation_3]).
% 0.66/1.03 cnf('0.61.0.0',plain,
% 0.66/1.03 ( multiply(inverse(X1),multiply(inverse(X2),X3)) = multiply(inverse(multiply(X2,X1)),X3) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.6.2.0','0.60.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.1','R')]).
% 0.66/1.03 cnf('0.61.1.0',plain,
% 0.66/1.03 ( multiply(inverse(X1),multiply(inverse(X2),X3)) = multiply(inverse(multiply(X2,X1)),X3) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.61.0.0']),
% 0.66/1.03 [weight('<97,60,6,[0,1,0,1]>')]).
% 0.66/1.03 cnf('0.61.2.0',plain,
% 0.66/1.03 ( multiply(inverse(multiply(X1,X2)),X3) = multiply(inverse(X2),multiply(inverse(X1),X3)) ),
% 0.66/1.03 inference(orient,[status(thm)],['0.61.1.0',theory(equality)]),
% 0.66/1.03 [x,rule_58]).
% 0.66/1.03 cnf('0.62.0.0',plain,
% 0.66/1.03 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.31.2.0','0.53.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.2','L')]).
% 0.66/1.03 cnf('0.62.1.0',plain,
% 0.66/1.03 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.62.0.0']),
% 0.66/1.03 [weight('<99,53,31,[0,0,0,2]>')]).
% 0.66/1.03 cnf('0.62.2.0',plain,
% 0.66/1.03 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.66/1.03 inference(activate,[status(thm)],['0.62.1.0']),
% 0.66/1.03 [equation_4]).
% 0.66/1.03 cnf('0.118.0.0',plain,
% 0.66/1.03 ( least_upper_bound(multiply(X1,inverse(a)),multiply(X1,inverse(b))) = multiply(X1,inverse(b)) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.7.2.0','0.14.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.2','L')]).
% 0.66/1.03 cnf('0.118.1.0',plain,
% 0.66/1.03 ( least_upper_bound(multiply(X1,inverse(a)),multiply(X1,inverse(b))) = multiply(X1,inverse(b)) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.118.0.0']),
% 0.66/1.03 [weight('<139,14,7,[0,0,0,2]>')]).
% 0.66/1.03 cnf('0.118.2.0',plain,
% 0.66/1.03 ( least_upper_bound(multiply(X1,inverse(a)),multiply(X1,inverse(b))) = multiply(X1,inverse(b)) ),
% 0.66/1.03 inference(orient,[status(thm)],['0.118.1.0',theory(equality)]),
% 0.66/1.03 [u,rule_106]).
% 0.66/1.03 cnf('0.119.0.0',plain,
% 0.66/1.03 ( multiply(inverse(inverse(b)),inverse(b)) = least_upper_bound(multiply(inverse(inverse(b)),inverse(a)),identity) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.118.2.0','0.11.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.2','L')]).
% 0.66/1.03 cnf('0.119.0.1',plain,
% 0.66/1.03 ( identity = least_upper_bound(multiply(inverse(inverse(b)),inverse(a)),identity) ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.119.0.0','0.11.2.0',theory(equality)]),
% 0.66/1.03 [pos('L','L')]).
% 0.66/1.03 cnf('0.119.0.2',plain,
% 0.66/1.03 ( identity = least_upper_bound(multiply(b,inverse(a)),identity) ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.119.0.1','0.25.2.0',theory(equality)]),
% 0.66/1.03 [pos('R.1.1','L')]).
% 0.66/1.03 cnf('0.119.1.0',plain,
% 0.66/1.03 ( identity = least_upper_bound(multiply(b,inverse(a)),identity) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.119.0.2']),
% 0.66/1.03 [weight('<55,118,11,[1,0,0,5]>')]).
% 0.66/1.03 cnf('0.119.1.1',plain,
% 0.66/1.03 ( identity = least_upper_bound(identity,multiply(b,inverse(a))) ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.119.1.0','0.12.2.0',theory(equality)]),
% 0.66/1.03 [pos('R','L')]).
% 0.66/1.03 cnf('0.119.1.2',plain,
% 0.66/1.03 ( identity = least_upper_bound(identity,inverse(multiply(a,inverse(b)))) ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.119.1.1','0.62.2.0',theory(equality)]),
% 0.66/1.03 [pos('R.2','R')]).
% 0.66/1.03 cnf('0.119.2.0',plain,
% 0.66/1.03 ( least_upper_bound(identity,inverse(multiply(a,inverse(b)))) = identity ),
% 0.66/1.03 inference(orient,[status(thm)],['0.119.1.2',theory(equality)]),
% 0.66/1.03 [x,rule_107]).
% 0.66/1.03 cnf('0.122.0.0',plain,
% 0.66/1.03 ( least_upper_bound(multiply(identity,X1),multiply(inverse(multiply(a,inverse(b))),X1)) = multiply(identity,X1) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.9.2.0','0.119.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.1','L')]).
% 0.66/1.03 cnf('0.122.0.1',plain,
% 0.66/1.03 ( least_upper_bound(X1,multiply(inverse(multiply(a,inverse(b))),X1)) = multiply(identity,X1) ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.122.0.0','0.1.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.1','L')]).
% 0.66/1.03 cnf('0.122.0.2',plain,
% 0.66/1.03 ( least_upper_bound(X1,multiply(inverse(inverse(b)),multiply(inverse(a),X1))) = multiply(identity,X1) ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.122.0.1','0.61.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.2','L')]).
% 0.66/1.03 cnf('0.122.0.3',plain,
% 0.66/1.03 ( least_upper_bound(X1,multiply(b,multiply(inverse(a),X1))) = multiply(identity,X1) ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.122.0.2','0.25.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.2.1','L')]).
% 0.66/1.03 cnf('0.122.0.4',plain,
% 0.66/1.03 ( least_upper_bound(X1,multiply(b,multiply(inverse(a),X1))) = X1 ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.122.0.3','0.1.2.0',theory(equality)]),
% 0.66/1.03 [pos('R','L')]).
% 0.66/1.03 cnf('0.122.1.0',plain,
% 0.66/1.03 ( least_upper_bound(X1,multiply(b,multiply(inverse(a),X1))) = X1 ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.122.0.4']),
% 0.66/1.03 [weight('<89,119,9,[0,0,0,1]>')]).
% 0.66/1.03 cnf('0.122.2.0',plain,
% 0.66/1.03 ( least_upper_bound(X1,multiply(b,multiply(inverse(a),X1))) = X1 ),
% 0.66/1.03 inference(orient,[status(thm)],['0.122.1.0',theory(equality)]),
% 0.66/1.03 [u,rule_110]).
% 0.66/1.03 cnf('0.123.0.0',plain,
% 0.66/1.03 ( a = least_upper_bound(a,multiply(b,identity)) ),
% 0.66/1.03 inference(cp,[status(thm)],['0.122.2.0','0.11.2.0',theory(equality)]),
% 0.66/1.03 [pos('L.2.2','L')]).
% 0.66/1.03 cnf('0.123.0.1',plain,
% 0.66/1.03 ( a = least_upper_bound(a,b) ),
% 0.66/1.03 inference(reduction,[status(thm)],['0.123.0.0','0.30.2.0',theory(equality)]),
% 0.66/1.03 [pos('R.2','L')]).
% 0.66/1.03 cnf('0.123.1.0',plain,
% 0.66/1.03 ( a = least_upper_bound(a,b) ),
% 0.66/1.03 inference(weigh,[status(thm)],['0.123.0.1']),
% 0.66/1.03 [weight('<19,122,11,[1,0,0,4]>')]).
% 0.66/1.03 cnf('0.123.2.0',plain,
% 0.66/1.03 ( least_upper_bound(a,b) = a ),
% 0.66/1.03 inference(orient,[status(thm)],['0.123.1.0',theory(equality)]),
% 0.66/1.03 [x,rule_111]).
% 0.66/1.03 cnf('1.0.0.0',conjecture,
% 0.66/1.03 ( least_upper_bound(a,b) = a ),
% 0.66/1.03 file('/tmp/WALDMEISTER_4973_n026',conjecture_1)).
% 0.66/1.03 cnf('1.0.0.1',plain,
% 0.66/1.03 ( a = a ),
% 0.66/1.03 inference(reduction,[status(thm)],['1.0.0.0','0.123.2.0',theory(equality)]),
% 0.66/1.03 [pos('L','L')]).
% 0.66/1.03 cnf('1.0.0.2',plain,
% 0.66/1.03 ( $true ),
% 0.66/1.03 inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.66/1.03 [conjecture_1]).
% 0.66/1.03
% 0.66/1.03 Proved Goals:
% 0.66/1.03 No. 1: least_upper_bound(a,b) ?= a joined, current: a = a
% 0.66/1.03 1 goal was specified, which was proved.
% 0.66/1.03 % SZS output end CNFRefutation
% 0.66/1.03 #END OF PROOF
% 0.66/1.03
% 0.66/1.03 Problem WALDMEISTER_4973_n026
% 0.66/1.03 CPs.gen 5078
% 0.66/1.03 CPs.reexp 0
% 0.66/1.03 Select 554
% 0.66/1.03 R 111
% 0.66/1.03 E 12
% 0.66/1.03 vsize 6.5M
% 0.66/1.03 rss 3.7M
% 0.66/1.03 process.time 0.024s
% 0.66/1.03 wallclock.time 0.026s
% 0.66/1.03 status S
% 0.66/1.03
% 0.66/1.03
% 0.66/1.03 Waldmeister states: Goal proved.
% 0.66/1.03 % SZS status Unsatisfiable
% 0.66/1.03
% 0.66/1.03 Problem WALDMEISTER_4973_n026
% 0.66/1.03 CPs.gen 141
% 0.66/1.03 CPs.reexp 0
% 0.66/1.03 Select 22
% 0.66/1.03 R 20
% 0.66/1.03 E 2
% 0.66/1.03 vsize 6.5M
% 0.66/1.03 rss 3.7M
% 0.66/1.03 process.time 0.002s
% 0.66/1.03 wallclock.time 0.025s
% 0.66/1.03 status S
%------------------------------------------------------------------------------