TSTP Solution File: GRP170-4 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP170-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n013.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 12:25:05 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
% 0.10/0.12 % Problem : GRP170-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : woody %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 21:54:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.62/1.04 ********************************************************************************
% 0.62/1.04 * W A L D M E I S T E R \| \ / \|/ *
% 0.62/1.04 * |/ | \/ | *
% 0.62/1.04 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.62/1.04 * A. Jaeger and B. Loechner | | *
% 0.62/1.04 * <waldmeister@informatik.uni-kl.de> | *
% 0.62/1.04 ********************************************************************************
% 0.62/1.04
% 0.62/1.04
% 0.62/1.04 Goals:
% 0.62/1.04 ------
% 0.62/1.04
% 0.62/1.04 ( 1) multiply(b,d) ?=? least_upper_bound(multiply(a,c),multiply(b,d))
% 0.62/1.04
% 0.62/1.04 Detected structure: VerbandsgeordneteGruppe
% 0.62/1.04 ********************************************************************************
% 0.62/1.04 ****************************** COMPLETION - PROOF ******************************
% 0.62/1.04 ********************************************************************************
% 0.62/1.04
% 0.62/1.04 joined goal: 1 multiply(b,d) ?= least_upper_bound(multiply(a,c),multiply(b,d)) to least_upper_bound(multiply(b,d),multiply(a,d))
% 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('0.5.0.0',axiom,
% 0.62/1.04 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_24265_n013')).
% 0.62/1.04 cnf('0.5.1.0',plain,
% 0.62/1.04 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.5.0.0']),
% 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 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = 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('0.7.0.0',axiom,
% 0.62/1.04 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_24265_n013')).
% 0.62/1.04 cnf('0.7.1.0',plain,
% 0.62/1.04 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,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 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_7]).
% 0.62/1.04 cnf('0.10.0.0',axiom,
% 0.62/1.04 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_24265_n013')).
% 0.62/1.04 cnf('0.10.1.0',plain,
% 0.62/1.04 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.62/1.04 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.62/1.04 cnf('0.10.2.0',plain,
% 0.62/1.04 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_10]).
% 0.62/1.04 cnf('0.12.0.0',axiom,
% 0.62/1.04 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_24265_n013')).
% 0.62/1.04 cnf('0.12.1.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.62/1.04 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.62/1.04 cnf('0.12.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.62/1.04 inference(activate,[status(thm)],['0.12.1.0']),
% 0.62/1.04 [equation_1]).
% 0.62/1.04 cnf('0.14.0.0',axiom,
% 0.62/1.04 ( greatest_lower_bound(c,d) = c ),
% 0.62/1.04 file('/tmp/WALDMEISTER_24265_n013')).
% 0.62/1.04 cnf('0.14.1.0',plain,
% 0.62/1.04 ( greatest_lower_bound(c,d) = c ),
% 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('0.14.1.1',plain,
% 0.62/1.04 ( greatest_lower_bound(d,c) = c ),
% 0.62/1.04 inference(reduction,[status(thm)],['0.14.1.0','0.12.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('0.14.2.0',plain,
% 0.62/1.04 ( greatest_lower_bound(d,c) = c ),
% 0.62/1.04 inference(orient,[status(thm)],['0.14.1.1',theory(equality)]),
% 0.62/1.04 [u,rule_13]).
% 0.62/1.04 cnf('0.15.0.0',axiom,
% 0.62/1.04 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_24265_n013')).
% 0.62/1.04 cnf('0.15.1.0',plain,
% 0.62/1.04 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.15.0.0']),
% 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(X1,X2) = least_upper_bound(X2,X1) ),
% 0.62/1.04 inference(activate,[status(thm)],['0.15.1.0']),
% 0.62/1.04 [equation_2]).
% 0.62/1.04 cnf('0.16.0.0',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_24265_n013')).
% 0.62/1.04 cnf('0.16.1.0',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)],['0.16.0.0']),
% 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(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.62/1.04 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.62/1.04 [x,rule_14]).
% 0.62/1.04 cnf('0.17.0.0',axiom,
% 0.62/1.04 ( least_upper_bound(a,b) = b ),
% 0.62/1.04 file('/tmp/WALDMEISTER_24265_n013')).
% 0.62/1.04 cnf('0.17.1.0',plain,
% 0.62/1.04 ( least_upper_bound(a,b) = b ),
% 0.62/1.04 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.62/1.04 [weight('<16,0,0,[0,0,0,17]>')]).
% 0.62/1.04 cnf('0.17.2.0',plain,
% 0.62/1.04 ( least_upper_bound(a,b) = b ),
% 0.62/1.04 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.62/1.04 [u,rule_15]).
% 0.62/1.04 cnf('1.0.0.0',conjecture,
% 0.62/1.04 ( multiply(b,d) = least_upper_bound(multiply(a,c),multiply(b,d)) ),
% 0.62/1.04 file('/tmp/WALDMEISTER_24265_n013',conjecture_1)).
% 0.62/1.04 cnf('1.0.0.1',plain,
% 0.62/1.04 ( multiply(b,d) = least_upper_bound(multiply(a,greatest_lower_bound(d,c)),multiply(b,d)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.0','0.14.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.1.2','R')]).
% 0.62/1.04 cnf('1.0.0.2',plain,
% 0.62/1.04 ( multiply(b,d) = least_upper_bound(multiply(a,greatest_lower_bound(c,d)),multiply(b,d)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.1','0.12.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.1.2','L')]).
% 0.62/1.04 cnf('1.0.0.3',plain,
% 0.62/1.04 ( multiply(b,d) = least_upper_bound(greatest_lower_bound(multiply(a,c),multiply(a,d)),multiply(b,d)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.2','0.7.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.1','L')]).
% 0.62/1.04 cnf('1.0.0.4',plain,
% 0.62/1.04 ( multiply(b,d) = least_upper_bound(multiply(b,d),greatest_lower_bound(multiply(a,c),multiply(a,d))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.3','0.15.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('1.0.0.5',plain,
% 0.62/1.04 ( multiply(least_upper_bound(a,b),d) = least_upper_bound(multiply(b,d),greatest_lower_bound(multiply(a,c),multiply(a,d))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.4','0.17.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','R')]).
% 0.62/1.04 cnf('1.0.0.6',plain,
% 0.62/1.04 ( multiply(least_upper_bound(a,b),d) = least_upper_bound(multiply(least_upper_bound(a,b),d),greatest_lower_bound(multiply(a,c),multiply(a,d))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.5','0.17.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.1.1','R')]).
% 0.62/1.04 cnf('1.0.0.7',plain,
% 0.62/1.04 ( multiply(least_upper_bound(a,b),d) = least_upper_bound(multiply(least_upper_bound(b,a),d),greatest_lower_bound(multiply(a,c),multiply(a,d))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.6','0.15.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.1.1','L')]).
% 0.62/1.04 cnf('1.0.0.8',plain,
% 0.62/1.04 ( multiply(least_upper_bound(b,a),d) = least_upper_bound(multiply(least_upper_bound(b,a),d),greatest_lower_bound(multiply(a,c),multiply(a,d))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.7','0.15.2.0',theory(equality)]),
% 0.62/1.04 [pos('L.1','L')]).
% 0.62/1.04 cnf('1.0.0.9',plain,
% 0.62/1.04 ( multiply(least_upper_bound(b,a),d) = least_upper_bound(multiply(least_upper_bound(b,a),d),greatest_lower_bound(multiply(a,d),multiply(a,c))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.8','0.12.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2','L')]).
% 0.62/1.04 cnf('1.0.0.10',plain,
% 0.62/1.04 ( least_upper_bound(multiply(b,d),multiply(a,d)) = least_upper_bound(multiply(least_upper_bound(b,a),d),greatest_lower_bound(multiply(a,d),multiply(a,c))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.9','0.10.2.0',theory(equality)]),
% 0.62/1.04 [pos('L','L')]).
% 0.62/1.04 cnf('1.0.0.11',plain,
% 0.62/1.04 ( least_upper_bound(multiply(b,d),multiply(a,d)) = least_upper_bound(greatest_lower_bound(multiply(a,d),multiply(a,c)),multiply(least_upper_bound(b,a),d)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.10','0.15.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('1.0.0.12',plain,
% 0.62/1.04 ( least_upper_bound(multiply(b,d),multiply(a,d)) = least_upper_bound(greatest_lower_bound(multiply(a,d),multiply(a,c)),least_upper_bound(multiply(b,d),multiply(a,d))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.11','0.10.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2','L')]).
% 0.62/1.04 cnf('1.0.0.13',plain,
% 0.62/1.04 ( least_upper_bound(multiply(b,d),multiply(a,d)) = least_upper_bound(greatest_lower_bound(multiply(a,d),multiply(a,c)),least_upper_bound(multiply(a,d),multiply(b,d))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.12','0.15.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2','L')]).
% 0.62/1.04 cnf('1.0.0.14',plain,
% 0.62/1.04 ( least_upper_bound(multiply(b,d),multiply(a,d)) = least_upper_bound(least_upper_bound(multiply(a,d),multiply(b,d)),greatest_lower_bound(multiply(a,d),multiply(a,c))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.13','0.15.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('1.0.0.15',plain,
% 0.62/1.04 ( least_upper_bound(multiply(b,d),multiply(a,d)) = least_upper_bound(multiply(a,d),least_upper_bound(multiply(b,d),greatest_lower_bound(multiply(a,d),multiply(a,c)))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.14','0.16.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('1.0.0.16',plain,
% 0.62/1.04 ( least_upper_bound(multiply(b,d),multiply(a,d)) = least_upper_bound(least_upper_bound(multiply(b,d),greatest_lower_bound(multiply(a,d),multiply(a,c))),multiply(a,d)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.15','0.15.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('1.0.0.17',plain,
% 0.62/1.04 ( least_upper_bound(multiply(b,d),multiply(a,d)) = least_upper_bound(multiply(b,d),least_upper_bound(greatest_lower_bound(multiply(a,d),multiply(a,c)),multiply(a,d))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.16','0.16.2.0',theory(equality)]),
% 0.62/1.04 [pos('R','L')]).
% 0.62/1.04 cnf('1.0.0.18',plain,
% 0.62/1.04 ( least_upper_bound(multiply(b,d),multiply(a,d)) = least_upper_bound(multiply(b,d),least_upper_bound(multiply(a,d),greatest_lower_bound(multiply(a,d),multiply(a,c)))) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.17','0.15.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2','L')]).
% 0.62/1.04 cnf('1.0.0.19',plain,
% 0.62/1.04 ( least_upper_bound(multiply(b,d),multiply(a,d)) = least_upper_bound(multiply(b,d),multiply(a,d)) ),
% 0.62/1.04 inference(reduction,[status(thm)],['1.0.0.18','0.5.2.0',theory(equality)]),
% 0.62/1.04 [pos('R.2','L')]).
% 0.62/1.04 cnf('1.0.0.20',plain,
% 0.62/1.04 ( $true ),
% 0.62/1.04 inference(trivial,[status(thm)],['1.0.0.19',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(b,d) ?= least_upper_bound(multiply(a,c),multiply(b,d)) joined, current: least_upper_bound(multiply(b,d),multiply(a,d)) = least_upper_bound(multiply(b,d),multiply(a,d))
% 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_24265_n013
% 0.62/1.04 CPs.gen 63
% 0.62/1.04 CPs.reexp 0
% 0.62/1.04 Select 17
% 0.62/1.04 R 15
% 0.62/1.04 E 2
% 0.62/1.04 vsize 6.6M
% 0.62/1.04 rss 3.7M
% 0.62/1.04 process.time 0.003s
% 0.62/1.04 wallclock.time 0.004s
% 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_24265_n013
% 0.62/1.04 CPs.gen 0
% 0.62/1.04 CPs.reexp 0
% 0.62/1.04 Select 0
% 0.62/1.04 R 0
% 0.62/1.04 E 0
% 0.62/1.04 vsize 6.0M
% 0.62/1.04 rss 3.3M
% 0.62/1.04 process.time 0.001s
% 0.62/1.04 wallclock.time 0.003s
% 0.62/1.04 status S
%------------------------------------------------------------------------------