TSTP Solution File: GRP186-3 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP186-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n019.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 12:25:15 EDT 2022
% Result : Unsatisfiable 0.59s 0.99s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP186-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : woody %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 04:08:40 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.59/0.99 ********************************************************************************
% 0.59/0.99 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/0.99 * |/ | \/ | *
% 0.59/0.99 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/0.99 * A. Jaeger and B. Loechner | | *
% 0.59/0.99 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/0.99 ********************************************************************************
% 0.59/0.99
% 0.59/0.99
% 0.59/0.99 Goals:
% 0.59/0.99 ------
% 0.59/0.99
% 0.59/0.99 ( 1) multiply(a,least_upper_bound(inverse(a),b)) ?=? least_upper_bound(multiply(a,b),identity)
% 0.59/0.99
% 0.59/0.99 Detected structure: VerbandsgeordneteGruppe
% 0.59/0.99 ********************************************************************************
% 0.59/0.99 ****************************** COMPLETION - PROOF ******************************
% 0.59/0.99 ********************************************************************************
% 0.59/0.99
% 0.59/0.99 joined goal: 1 multiply(a,least_upper_bound(inverse(a),b)) ?= least_upper_bound(multiply(a,b),identity) to least_upper_bound(identity,multiply(a,b))
% 0.59/0.99 goal joined
% 0.59/0.99 % SZS status Unsatisfiable
% 0.59/0.99 #START OF PROOF
% 0.59/0.99 % SZS output start CNFRefutation
% 0.59/0.99 cnf('0.1.0.0',axiom,
% 0.59/0.99 ( X1 = multiply(identity,X1) ),
% 0.59/0.99 file('/tmp/WALDMEISTER_27587_n019')).
% 0.59/0.99 cnf('0.1.1.0',plain,
% 0.59/0.99 ( X1 = multiply(identity,X1) ),
% 0.59/0.99 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.59/0.99 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.59/0.99 cnf('0.1.2.0',plain,
% 0.59/0.99 ( multiply(identity,X1) = X1 ),
% 0.59/0.99 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.59/0.99 [x,rule_1]).
% 0.59/0.99 cnf('0.6.0.0',axiom,
% 0.59/0.99 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.59/0.99 file('/tmp/WALDMEISTER_27587_n019')).
% 0.59/0.99 cnf('0.6.1.0',plain,
% 0.59/0.99 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.59/0.99 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.59/0.99 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.59/0.99 cnf('0.6.2.0',plain,
% 0.59/0.99 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.59/0.99 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.59/0.99 [x,rule_6]).
% 0.59/0.99 cnf('0.8.0.0',axiom,
% 0.59/0.99 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.59/0.99 file('/tmp/WALDMEISTER_27587_n019')).
% 0.59/0.99 cnf('0.8.1.0',plain,
% 0.59/0.99 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.59/0.99 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.59/0.99 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.59/0.99 cnf('0.8.2.0',plain,
% 0.59/0.99 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.59/0.99 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.59/0.99 [u,rule_8]).
% 0.59/0.99 cnf('0.11.0.0',axiom,
% 0.59/0.99 ( multiply(inverse(X1),X1) = identity ),
% 0.59/0.99 file('/tmp/WALDMEISTER_27587_n019')).
% 0.59/0.99 cnf('0.11.1.0',plain,
% 0.59/0.99 ( multiply(inverse(X1),X1) = identity ),
% 0.59/0.99 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.59/0.99 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.59/0.99 cnf('0.11.2.0',plain,
% 0.59/0.99 ( multiply(inverse(X1),X1) = identity ),
% 0.59/0.99 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.59/0.99 [u,rule_11]).
% 0.59/0.99 cnf('0.14.0.0',axiom,
% 0.59/0.99 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.59/0.99 file('/tmp/WALDMEISTER_27587_n019')).
% 0.59/0.99 cnf('0.14.1.0',plain,
% 0.59/0.99 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.59/0.99 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.59/0.99 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.59/0.99 cnf('0.14.2.0',plain,
% 0.59/0.99 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.59/0.99 inference(activate,[status(thm)],['0.14.1.0']),
% 0.59/0.99 [equation_2]).
% 0.59/0.99 cnf('0.22.0.0',plain,
% 0.59/0.99 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 0.59/0.99 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.1','L')]).
% 0.59/0.99 cnf('0.22.0.1',plain,
% 0.59/0.99 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.59/0.99 inference(reduction,[status(thm)],['0.22.0.0','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('R','L')]).
% 0.59/0.99 cnf('0.22.1.0',plain,
% 0.59/0.99 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.59/0.99 inference(weigh,[status(thm)],['0.22.0.1']),
% 0.59/0.99 [weight('<55,11,6,[0,0,0,1]>')]).
% 0.59/0.99 cnf('0.22.2.0',plain,
% 0.59/0.99 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.59/0.99 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.59/0.99 [u,rule_20]).
% 0.59/0.99 cnf('0.23.0.0',plain,
% 0.59/0.99 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 0.59/0.99 inference(cp,[status(thm)],['0.22.2.0','0.22.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.2','L')]).
% 0.59/0.99 cnf('0.23.1.0',plain,
% 0.59/0.99 ( X1 = inverse(inverse(X1)) ),
% 0.59/0.99 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.59/0.99 [weight('<19,22,22,[0,0,0,3]>')]).
% 0.59/0.99 cnf('0.23.2.0',plain,
% 0.59/0.99 ( inverse(inverse(X1)) = X1 ),
% 0.59/0.99 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.59/0.99 [x,rule_21]).
% 0.59/0.99 cnf('0.25.0.0',plain,
% 0.59/0.99 ( identity = multiply(X1,inverse(X1)) ),
% 0.59/0.99 inference(cp,[status(thm)],['0.11.2.0','0.23.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.1','L')]).
% 0.59/0.99 cnf('0.25.1.0',plain,
% 0.59/0.99 ( identity = multiply(X1,inverse(X1)) ),
% 0.59/0.99 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.59/0.99 [weight('<29,23,11,[0,0,0,1]>')]).
% 0.59/0.99 cnf('0.25.2.0',plain,
% 0.59/0.99 ( multiply(X1,inverse(X1)) = identity ),
% 0.59/0.99 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.59/0.99 [x,rule_23]).
% 0.59/0.99 cnf('1.0.0.0',conjecture,
% 0.59/0.99 ( multiply(a,least_upper_bound(inverse(a),b)) = least_upper_bound(multiply(a,b),identity) ),
% 0.59/0.99 file('/tmp/WALDMEISTER_27587_n019',conjecture_1)).
% 0.59/0.99 cnf('1.0.0.1',plain,
% 0.59/0.99 ( least_upper_bound(multiply(a,inverse(a)),multiply(a,b)) = least_upper_bound(multiply(a,b),identity) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.0','0.8.2.0',theory(equality)]),
% 0.59/0.99 [pos('L','L')]).
% 0.59/0.99 cnf('1.0.0.2',plain,
% 0.59/0.99 ( least_upper_bound(multiply(a,inverse(a)),multiply(a,b)) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.1','0.14.2.0',theory(equality)]),
% 0.59/0.99 [pos('R','L')]).
% 0.59/0.99 cnf('1.0.0.3',plain,
% 0.59/0.99 ( least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.2','0.25.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.1','L')]).
% 0.59/0.99 cnf('1.0.0.4',plain,
% 0.59/0.99 ( $true ),
% 0.59/0.99 inference(trivial,[status(thm)],['1.0.0.3',theory(equality)]),
% 0.59/0.99 [conjecture_1]).
% 0.59/0.99
% 0.59/0.99 Proved Goals:
% 0.59/0.99 No. 1: multiply(a,least_upper_bound(inverse(a),b)) ?= least_upper_bound(multiply(a,b),identity) joined, current: least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(a,b))
% 0.59/0.99 1 goal was specified, which was proved.
% 0.59/0.99 % SZS output end CNFRefutation
% 0.59/0.99 #END OF PROOF
% 0.59/0.99
% 0.59/0.99 Problem WALDMEISTER_27587_n019
% 0.59/0.99 CPs.gen 153
% 0.59/0.99 CPs.reexp 0
% 0.59/0.99 Select 27
% 0.59/0.99 R 23
% 0.59/0.99 E 2
% 0.59/0.99 vsize 6.5M
% 0.59/0.99 rss 3.7M
% 0.59/0.99 process.time 0.003s
% 0.59/0.99 wallclock.time 0.004s
% 0.59/0.99 status S
% 0.59/0.99
% 0.59/0.99
% 0.59/0.99 Waldmeister states: Goal proved.
% 0.59/0.99 % SZS status Unsatisfiable
% 0.59/0.99
% 0.59/0.99 Problem WALDMEISTER_27587_n019
% 0.59/0.99 CPs.gen 0
% 0.59/0.99 CPs.reexp 0
% 0.59/0.99 Select 0
% 0.59/0.99 R 0
% 0.59/0.99 E 0
% 0.59/0.99 vsize 6.0M
% 0.59/0.99 rss 3.2M
% 0.59/0.99 process.time 0.001s
% 0.59/0.99 wallclock.time 0.003s
% 0.59/0.99 status S
%------------------------------------------------------------------------------