TSTP Solution File: GRP185-3 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP185-3 : 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 12:25:13 EDT 2022
% Result : Unsatisfiable 0.64s 1.03s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP185-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.13 % Command : woody %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 06:20:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.64/1.02 ********************************************************************************
% 0.64/1.02 * W A L D M E I S T E R \| \ / \|/ *
% 0.64/1.02 * |/ | \/ | *
% 0.64/1.02 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.64/1.02 * A. Jaeger and B. Loechner | | *
% 0.64/1.02 * <waldmeister@informatik.uni-kl.de> | *
% 0.64/1.02 ********************************************************************************
% 0.64/1.02
% 0.64/1.02
% 0.64/1.02 Goals:
% 0.64/1.02 ------
% 0.64/1.02
% 0.64/1.02 ( 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)
% 0.64/1.02
% 0.64/1.02 Detected structure: VerbandsgeordneteGruppe
% 0.64/1.02 ********************************************************************************
% 0.64/1.02 ****************************** COMPLETION - PROOF ******************************
% 0.64/1.02 ********************************************************************************
% 0.64/1.02
% 0.64/1.03 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))
% 0.64/1.03 goal joined
% 0.64/1.03 % SZS status Unsatisfiable
% 0.64/1.03 #START OF PROOF
% 0.64/1.03 % SZS output start CNFRefutation
% 0.64/1.03 cnf('0.1.0.0',axiom,
% 0.64/1.03 ( X1 = multiply(identity,X1) ),
% 0.64/1.03 file('/tmp/WALDMEISTER_3115_n026')).
% 0.64/1.03 cnf('0.1.1.0',plain,
% 0.64/1.03 ( X1 = multiply(identity,X1) ),
% 0.64/1.03 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.64/1.03 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.64/1.03 cnf('0.1.2.0',plain,
% 0.64/1.03 ( multiply(identity,X1) = X1 ),
% 0.64/1.03 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.64/1.03 [x,rule_1]).
% 0.64/1.03 cnf('0.3.0.0',axiom,
% 0.64/1.03 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.64/1.03 file('/tmp/WALDMEISTER_3115_n026')).
% 0.64/1.03 cnf('0.3.1.0',plain,
% 0.64/1.03 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.64/1.03 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.64/1.03 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.64/1.03 cnf('0.3.2.0',plain,
% 0.64/1.03 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 0.64/1.03 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.64/1.03 [x,rule_3]).
% 0.64/1.03 cnf('0.8.0.0',axiom,
% 0.64/1.03 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.64/1.03 file('/tmp/WALDMEISTER_3115_n026')).
% 0.64/1.03 cnf('0.8.1.0',plain,
% 0.64/1.03 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.64/1.03 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.64/1.03 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.64/1.03 cnf('0.8.2.0',plain,
% 0.64/1.03 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.64/1.03 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.64/1.03 [u,rule_8]).
% 0.64/1.03 cnf('0.10.0.0',axiom,
% 0.64/1.03 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.64/1.03 file('/tmp/WALDMEISTER_3115_n026')).
% 0.64/1.03 cnf('0.10.1.0',plain,
% 0.64/1.03 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.64/1.03 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.64/1.03 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.64/1.03 cnf('0.10.2.0',plain,
% 0.64/1.03 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.64/1.03 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.64/1.03 [u,rule_10]).
% 0.64/1.03 cnf('0.14.0.0',axiom,
% 0.64/1.03 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.64/1.03 file('/tmp/WALDMEISTER_3115_n026')).
% 0.64/1.03 cnf('0.14.1.0',plain,
% 0.64/1.03 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.64/1.03 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.64/1.03 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.64/1.03 cnf('0.14.2.0',plain,
% 0.64/1.03 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.64/1.03 inference(activate,[status(thm)],['0.14.1.0']),
% 0.64/1.03 [equation_2]).
% 0.64/1.03 cnf('0.15.0.0',axiom,
% 0.64/1.03 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.64/1.03 file('/tmp/WALDMEISTER_3115_n026')).
% 0.64/1.03 cnf('0.15.1.0',plain,
% 0.64/1.03 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.64/1.03 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.64/1.03 [weight('<14,0,0,[0,0,0,15]>')]).
% 0.64/1.03 cnf('0.15.2.0',plain,
% 0.64/1.03 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.64/1.03 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.64/1.03 [x,rule_13]).
% 0.64/1.03 cnf('1.0.0.0',conjecture,
% 0.64/1.03 ( 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) ),
% 0.64/1.03 file('/tmp/WALDMEISTER_3115_n026',conjecture_1)).
% 0.64/1.03 cnf('1.0.0.1',plain,
% 0.64/1.03 ( 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) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.0','0.8.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2','L')]).
% 0.64/1.03 cnf('1.0.0.2',plain,
% 0.64/1.03 ( 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) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.1','0.10.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.1','L')]).
% 0.64/1.03 cnf('1.0.0.3',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.2','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('R','L')]).
% 0.64/1.03 cnf('1.0.0.4',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.3','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.1','L')]).
% 0.64/1.03 cnf('1.0.0.5',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.4','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.1','L')]).
% 0.64/1.03 cnf('1.0.0.6',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.5','0.15.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2','L')]).
% 0.64/1.03 cnf('1.0.0.7',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.6','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.2','L')]).
% 0.64/1.03 cnf('1.0.0.8',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.7','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.2.1.1','L')]).
% 0.64/1.03 cnf('1.0.0.9',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.8','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2','L')]).
% 0.64/1.03 cnf('1.0.0.10',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.9','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.1','L')]).
% 0.64/1.03 cnf('1.0.0.11',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.10','0.15.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2','L')]).
% 0.64/1.03 cnf('1.0.0.12',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.11','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2','L')]).
% 0.64/1.03 cnf('1.0.0.13',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.12','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.1.1.1','L')]).
% 0.64/1.03 cnf('1.0.0.14',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.13','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.1','L')]).
% 0.64/1.03 cnf('1.0.0.15',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.14','0.10.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.1.2','L')]).
% 0.64/1.03 cnf('1.0.0.16',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.15','0.1.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.1.2.2','L')]).
% 0.64/1.03 cnf('1.0.0.17',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.16','0.15.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2','L')]).
% 0.64/1.03 cnf('1.0.0.18',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.17','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2','L')]).
% 0.64/1.03 cnf('1.0.0.19',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.18','0.1.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.2','L')]).
% 0.64/1.03 cnf('1.0.0.20',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.19','0.15.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.1','L')]).
% 0.64/1.03 cnf('1.0.0.21',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.20','0.14.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2.1','L')]).
% 0.64/1.03 cnf('1.0.0.22',plain,
% 0.64/1.03 ( 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)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.21','0.15.2.0',theory(equality)]),
% 0.64/1.03 [pos('L.2','L')]).
% 0.64/1.03 cnf('1.0.0.23',plain,
% 0.64/1.03 ( least_upper_bound(identity,multiply(a,b)) = least_upper_bound(identity,multiply(a,b)) ),
% 0.64/1.03 inference(reduction,[status(thm)],['1.0.0.22','0.3.2.0',theory(equality)]),
% 0.64/1.03 [pos('L','L')]).
% 0.64/1.03 cnf('1.0.0.24',plain,
% 0.64/1.03 ( $true ),
% 0.64/1.03 inference(trivial,[status(thm)],['1.0.0.23',theory(equality)]),
% 0.64/1.03 [conjecture_1]).
% 0.64/1.03
% 0.64/1.03 Proved Goals:
% 0.64/1.03 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))
% 0.64/1.03 1 goal was specified, which was proved.
% 0.64/1.03 % SZS output end CNFRefutation
% 0.64/1.03 #END OF PROOF
% 0.64/1.03
% 0.64/1.03 Problem WALDMEISTER_3115_n026
% 0.64/1.03 CPs.gen 49
% 0.64/1.03 CPs.reexp 0
% 0.64/1.03 Select 15
% 0.64/1.03 R 13
% 0.64/1.03 E 2
% 0.64/1.03 vsize 6.6M
% 0.64/1.03 rss 3.8M
% 0.64/1.03 process.time 0.012s
% 0.64/1.03 wallclock.time 0.013s
% 0.64/1.03 status S
% 0.64/1.03
% 0.64/1.03
% 0.64/1.03 Waldmeister states: Goal proved.
% 0.64/1.03 % SZS status Unsatisfiable
% 0.64/1.03
% 0.64/1.03 Problem WALDMEISTER_3115_n026
% 0.64/1.03 CPs.gen 0
% 0.64/1.03 CPs.reexp 0
% 0.64/1.03 Select 0
% 0.64/1.03 R 0
% 0.64/1.03 E 0
% 0.64/1.03 vsize 6.0M
% 0.64/1.03 rss 3.2M
% 0.64/1.03 process.time 0.001s
% 0.64/1.03 wallclock.time 0.012s
% 0.64/1.03 status S
%------------------------------------------------------------------------------