TSTP Solution File: GRP185-4 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP185-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n004.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 12:25:14 EDT 2022
% Result : Unsatisfiable 0.59s 0.98s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP185-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 13:33:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.56/0.97 ********************************************************************************
% 0.56/0.97 * W A L D M E I S T E R \| \ / \|/ *
% 0.56/0.97 * |/ | \/ | *
% 0.56/0.97 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.56/0.97 * A. Jaeger and B. Loechner | | *
% 0.56/0.97 * <waldmeister@informatik.uni-kl.de> | *
% 0.56/0.97 ********************************************************************************
% 0.56/0.97
% 0.56/0.97
% 0.56/0.97 Goals:
% 0.56/0.97 ------
% 0.56/0.97
% 0.56/0.97 ( 1) greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ?=? least_upper_bound(multiply(a,b),identity)
% 0.56/0.97
% 0.56/0.97 Detected structure: VerbandsgeordneteGruppe
% 0.56/0.97 ********************************************************************************
% 0.56/0.97 ****************************** COMPLETION - PROOF ******************************
% 0.56/0.97 ********************************************************************************
% 0.56/0.97
% 0.59/0.98 joined goal: 1 greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ?= least_upper_bound(multiply(a,b),identity) to least_upper_bound(identity,multiply(a,b))
% 0.59/0.98 goal joined
% 0.59/0.98 % SZS status Unsatisfiable
% 0.59/0.98 #START OF PROOF
% 0.59/0.98 % SZS output start CNFRefutation
% 0.59/0.98 cnf('0.1.0.0',axiom,
% 0.59/0.98 ( X1 = multiply(identity,X1) ),
% 0.59/0.98 file('/tmp/WALDMEISTER_27235_n004')).
% 0.59/0.98 cnf('0.1.1.0',plain,
% 0.59/0.98 ( X1 = multiply(identity,X1) ),
% 0.59/0.98 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.59/0.98 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.59/0.98 cnf('0.1.2.0',plain,
% 0.59/0.98 ( multiply(identity,X1) = X1 ),
% 0.59/0.98 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.59/0.98 [x,rule_1]).
% 0.59/0.98 cnf('0.3.0.0',axiom,
% 0.59/0.98 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.59/0.98 file('/tmp/WALDMEISTER_27235_n004')).
% 0.59/0.98 cnf('0.3.1.0',plain,
% 0.59/0.98 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.59/0.98 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.59/0.98 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.59/0.98 cnf('0.3.2.0',plain,
% 0.59/0.98 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 0.59/0.98 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.59/0.98 [x,rule_3]).
% 0.59/0.98 cnf('0.9.0.0',axiom,
% 0.59/0.98 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.59/0.98 file('/tmp/WALDMEISTER_27235_n004')).
% 0.59/0.98 cnf('0.9.1.0',plain,
% 0.59/0.98 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.59/0.98 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.59/0.98 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.59/0.98 cnf('0.9.2.0',plain,
% 0.59/0.98 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.59/0.98 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.59/0.98 [u,rule_9]).
% 0.59/0.98 cnf('0.11.0.0',axiom,
% 0.59/0.98 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.59/0.98 file('/tmp/WALDMEISTER_27235_n004')).
% 0.59/0.98 cnf('0.11.1.0',plain,
% 0.59/0.98 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.59/0.98 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.59/0.98 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.59/0.98 cnf('0.11.2.0',plain,
% 0.59/0.98 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.59/0.98 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.59/0.98 [u,rule_11]).
% 0.59/0.98 cnf('0.16.0.0',axiom,
% 0.59/0.98 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.59/0.98 file('/tmp/WALDMEISTER_27235_n004')).
% 0.59/0.98 cnf('0.16.1.0',plain,
% 0.59/0.98 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.59/0.98 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.59/0.98 [weight('<15,0,0,[0,0,0,16]>')]).
% 0.59/0.98 cnf('0.16.2.0',plain,
% 0.59/0.98 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.59/0.98 inference(activate,[status(thm)],['0.16.1.0']),
% 0.59/0.98 [equation_3]).
% 0.59/0.98 cnf('0.17.0.0',axiom,
% 0.59/0.98 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.59/0.98 file('/tmp/WALDMEISTER_27235_n004')).
% 0.59/0.98 cnf('0.17.1.0',plain,
% 0.59/0.98 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.59/0.98 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.59/0.98 [weight('<16,0,0,[0,0,0,17]>')]).
% 0.59/0.98 cnf('0.17.2.0',plain,
% 0.59/0.98 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.59/0.98 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.59/0.98 [x,rule_14]).
% 0.59/0.98 cnf('1.0.0.0',conjecture,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) = least_upper_bound(multiply(a,b),identity) ),
% 0.59/0.98 file('/tmp/WALDMEISTER_27235_n004',conjecture_1)).
% 0.59/0.98 cnf('1.0.0.1',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(multiply(least_upper_bound(a,identity),b),multiply(least_upper_bound(a,identity),identity))) = least_upper_bound(multiply(a,b),identity) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.0','0.9.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2','L')]).
% 0.59/0.98 cnf('1.0.0.2',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(least_upper_bound(multiply(a,b),multiply(identity,b)),multiply(least_upper_bound(a,identity),identity))) = least_upper_bound(multiply(a,b),identity) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.1','0.11.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.1','L')]).
% 0.59/0.98 cnf('1.0.0.3',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(least_upper_bound(multiply(a,b),multiply(identity,b)),multiply(least_upper_bound(a,identity),identity))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.2','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('R','L')]).
% 0.59/0.98 cnf('1.0.0.4',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(multiply(a,b),identity),least_upper_bound(least_upper_bound(multiply(identity,b),multiply(a,b)),multiply(least_upper_bound(a,identity),identity))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.3','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.1','L')]).
% 0.59/0.98 cnf('1.0.0.5',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(identity,b),multiply(a,b)),multiply(least_upper_bound(a,identity),identity))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.4','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.1','L')]).
% 0.59/0.98 cnf('1.0.0.6',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(identity,b),least_upper_bound(multiply(a,b),multiply(least_upper_bound(a,identity),identity)))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.5','0.17.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2','L')]).
% 0.59/0.98 cnf('1.0.0.7',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(identity,b),least_upper_bound(multiply(least_upper_bound(a,identity),identity),multiply(a,b)))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.6','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.2','L')]).
% 0.59/0.98 cnf('1.0.0.8',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(identity,b),least_upper_bound(multiply(least_upper_bound(identity,a),identity),multiply(a,b)))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.7','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.2.1.1','L')]).
% 0.59/0.98 cnf('1.0.0.9',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(least_upper_bound(identity,a),identity),multiply(a,b)),multiply(identity,b))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.8','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2','L')]).
% 0.59/0.98 cnf('1.0.0.10',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,b),multiply(least_upper_bound(identity,a),identity)),multiply(identity,b))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.9','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.1','L')]).
% 0.59/0.98 cnf('1.0.0.11',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,b),least_upper_bound(multiply(least_upper_bound(identity,a),identity),multiply(identity,b)))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.10','0.17.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2','L')]).
% 0.59/0.98 cnf('1.0.0.12',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(least_upper_bound(identity,a),identity),multiply(identity,b)),multiply(a,b))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.11','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2','L')]).
% 0.59/0.98 cnf('1.0.0.13',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(least_upper_bound(a,identity),identity),multiply(identity,b)),multiply(a,b))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.12','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.1.1.1','L')]).
% 0.59/0.98 cnf('1.0.0.14',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(identity,b),multiply(least_upper_bound(a,identity),identity)),multiply(a,b))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.13','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.1','L')]).
% 0.59/0.98 cnf('1.0.0.15',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(identity,b),least_upper_bound(multiply(a,identity),multiply(identity,identity))),multiply(a,b))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.14','0.11.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.1.2','L')]).
% 0.59/0.98 cnf('1.0.0.16',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(identity,b),least_upper_bound(multiply(a,identity),identity)),multiply(a,b))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.15','0.1.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.1.2.2','L')]).
% 0.59/0.98 cnf('1.0.0.17',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(identity,b),least_upper_bound(least_upper_bound(multiply(a,identity),identity),multiply(a,b)))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.16','0.17.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2','L')]).
% 0.59/0.98 cnf('1.0.0.18',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(least_upper_bound(multiply(a,identity),identity),multiply(a,b)),multiply(identity,b))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.17','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2','L')]).
% 0.59/0.98 cnf('1.0.0.19',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(least_upper_bound(multiply(a,identity),identity),multiply(a,b)),b)) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.18','0.1.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.2','L')]).
% 0.59/0.98 cnf('1.0.0.20',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(multiply(a,identity),least_upper_bound(identity,multiply(a,b))),b)) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.19','0.17.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.1','L')]).
% 0.59/0.98 cnf('1.0.0.21',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(a,identity)),b)) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.20','0.16.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2.1','L')]).
% 0.59/0.98 cnf('1.0.0.22',plain,
% 0.59/0.98 ( greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(multiply(a,identity),b))) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.21','0.17.2.0',theory(equality)]),
% 0.59/0.98 [pos('L.2','L')]).
% 0.59/0.98 cnf('1.0.0.23',plain,
% 0.59/0.98 ( least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(a,b)) ),
% 0.59/0.98 inference(reduction,[status(thm)],['1.0.0.22','0.3.2.0',theory(equality)]),
% 0.59/0.98 [pos('L','L')]).
% 0.59/0.98 cnf('1.0.0.24',plain,
% 0.59/0.98 ( $true ),
% 0.59/0.98 inference(trivial,[status(thm)],['1.0.0.23',theory(equality)]),
% 0.59/0.98 [conjecture_1]).
% 0.59/0.98
% 0.59/0.98 Proved Goals:
% 0.59/0.98 No. 1: greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ?= least_upper_bound(multiply(a,b),identity) joined, current: least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(a,b))
% 0.59/0.98 1 goal was specified, which was proved.
% 0.59/0.98 % SZS output end CNFRefutation
% 0.59/0.98 #END OF PROOF
% 0.59/0.98
% 0.59/0.98 Problem WALDMEISTER_27235_n004
% 0.59/0.98 CPs.gen 67
% 0.59/0.98 CPs.reexp 0
% 0.59/0.98 Select 17
% 0.59/0.98 R 14
% 0.59/0.98 E 3
% 0.59/0.98 vsize 6.6M
% 0.59/0.98 rss 3.8M
% 0.59/0.98 process.time 0.012s
% 0.59/0.98 wallclock.time 0.013s
% 0.59/0.98 status S
% 0.59/0.98
% 0.59/0.98
% 0.59/0.98 Waldmeister states: Goal proved.
% 0.59/0.98 % SZS status Unsatisfiable
% 0.59/0.98
% 0.59/0.98 Problem WALDMEISTER_27235_n004
% 0.59/0.98 CPs.gen 0
% 0.59/0.98 CPs.reexp 0
% 0.59/0.98 Select 0
% 0.59/0.98 R 0
% 0.59/0.98 E 0
% 0.59/0.98 vsize 6.0M
% 0.59/0.98 rss 3.2M
% 0.59/0.98 process.time 0.001s
% 0.59/0.98 wallclock.time 0.012s
% 0.59/0.98 status S
%------------------------------------------------------------------------------