TSTP Solution File: GRP185-2 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP185-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n029.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 0.57s 1.00s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP185-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : woody %s
% 0.12/0.33 % Computer : n029.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
% 0.12/0.34 % DateTime : Mon Jun 13 07:28:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.57/0.98 ********************************************************************************
% 0.57/0.98 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.98 * |/ | \/ | *
% 0.57/0.98 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.98 * A. Jaeger and B. Loechner | | *
% 0.57/0.98 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.98 ********************************************************************************
% 0.57/0.98
% 0.57/0.98
% 0.57/0.98 Goals:
% 0.57/0.98 ------
% 0.57/0.98
% 0.57/0.98 ( 1) multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ?=? least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))
% 0.57/0.98
% 0.57/0.98 Detected structure: VerbandsgeordneteGruppe
% 0.57/0.98 ********************************************************************************
% 0.57/0.98 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.98 ********************************************************************************
% 0.57/0.98
% 0.57/1.00 joined goal: 1 multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ?= least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) to least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b))))
% 0.57/1.00 goal joined
% 0.57/1.00 % SZS status Unsatisfiable
% 0.57/1.00 #START OF PROOF
% 0.57/1.00 % SZS output start CNFRefutation
% 0.57/1.00 cnf('0.1.0.0',axiom,
% 0.57/1.00 ( X1 = multiply(identity,X1) ),
% 0.57/1.00 file('/tmp/WALDMEISTER_31228_n029')).
% 0.57/1.00 cnf('0.1.1.0',plain,
% 0.57/1.00 ( X1 = multiply(identity,X1) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.57/1.00 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.57/1.00 cnf('0.1.2.0',plain,
% 0.57/1.00 ( multiply(identity,X1) = X1 ),
% 0.57/1.00 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.57/1.00 [x,rule_1]).
% 0.57/1.00 cnf('0.3.0.0',axiom,
% 0.57/1.00 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.57/1.00 file('/tmp/WALDMEISTER_31228_n029')).
% 0.57/1.00 cnf('0.3.1.0',plain,
% 0.57/1.00 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.57/1.00 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.57/1.00 cnf('0.3.2.0',plain,
% 0.57/1.00 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 0.57/1.00 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.57/1.00 [x,rule_3]).
% 0.57/1.00 cnf('0.5.0.0',axiom,
% 0.57/1.00 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.57/1.00 file('/tmp/WALDMEISTER_31228_n029')).
% 0.57/1.00 cnf('0.5.1.0',plain,
% 0.57/1.00 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.57/1.00 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.57/1.00 cnf('0.5.2.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 0.57/1.00 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.57/1.00 [x,rule_5]).
% 0.57/1.00 cnf('0.9.0.0',axiom,
% 0.57/1.00 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.57/1.00 file('/tmp/WALDMEISTER_31228_n029')).
% 0.57/1.00 cnf('0.9.1.0',plain,
% 0.57/1.00 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.57/1.00 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.57/1.00 cnf('0.9.2.0',plain,
% 0.57/1.00 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.57/1.00 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.57/1.00 [u,rule_9]).
% 0.57/1.00 cnf('0.11.0.0',axiom,
% 0.57/1.00 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.57/1.00 file('/tmp/WALDMEISTER_31228_n029')).
% 0.57/1.00 cnf('0.11.1.0',plain,
% 0.57/1.00 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.57/1.00 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.57/1.00 cnf('0.11.2.0',plain,
% 0.57/1.00 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.57/1.00 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.57/1.00 [u,rule_11]).
% 0.57/1.00 cnf('0.13.0.0',axiom,
% 0.57/1.00 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.57/1.00 file('/tmp/WALDMEISTER_31228_n029')).
% 0.57/1.00 cnf('0.13.1.0',plain,
% 0.57/1.00 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.57/1.00 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.57/1.00 cnf('0.13.2.0',plain,
% 0.57/1.00 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.57/1.00 inference(activate,[status(thm)],['0.13.1.0']),
% 0.57/1.00 [equation_1]).
% 0.57/1.00 cnf('0.14.0.0',axiom,
% 0.57/1.00 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.57/1.00 file('/tmp/WALDMEISTER_31228_n029')).
% 0.57/1.00 cnf('0.14.1.0',plain,
% 0.57/1.00 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.57/1.00 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.57/1.00 cnf('0.14.2.0',plain,
% 0.57/1.00 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.57/1.00 inference(activate,[status(thm)],['0.14.1.0']),
% 0.57/1.00 [equation_2]).
% 0.57/1.00 cnf('0.16.0.0',axiom,
% 0.57/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.57/1.00 file('/tmp/WALDMEISTER_31228_n029')).
% 0.57/1.00 cnf('0.16.1.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.57/1.00 [weight('<15,0,0,[0,0,0,16]>')]).
% 0.57/1.00 cnf('0.16.2.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.57/1.00 inference(activate,[status(thm)],['0.16.1.0']),
% 0.57/1.00 [equation_3]).
% 0.57/1.00 cnf('0.17.0.0',axiom,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.57/1.00 file('/tmp/WALDMEISTER_31228_n029')).
% 0.57/1.00 cnf('0.17.1.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.57/1.00 [weight('<16,0,0,[0,0,0,17]>')]).
% 0.57/1.00 cnf('0.17.2.0',plain,
% 0.57/1.00 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.57/1.00 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.57/1.00 [x,rule_14]).
% 0.57/1.00 cnf('0.18.0.0',axiom,
% 0.57/1.00 ( inverse(identity) = identity ),
% 0.57/1.00 file('/tmp/WALDMEISTER_31228_n029')).
% 0.57/1.00 cnf('0.18.1.0',plain,
% 0.57/1.00 ( inverse(identity) = identity ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.57/1.00 [weight('<17,0,0,[0,0,0,18]>')]).
% 0.57/1.00 cnf('0.18.2.0',plain,
% 0.57/1.00 ( inverse(identity) = identity ),
% 0.57/1.00 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 0.57/1.00 [u,rule_15]).
% 0.57/1.00 cnf('0.19.0.0',plain,
% 0.57/1.00 ( inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)) ),
% 0.57/1.00 inference(cp,[status(thm)],['0.13.2.0','0.18.2.0',theory(equality)]),
% 0.57/1.00 [pos('L.1','L')]).
% 0.57/1.00 cnf('0.19.0.1',plain,
% 0.57/1.00 ( inverse(multiply(X1,identity)) = inverse(X1) ),
% 0.57/1.00 inference(reduction,[status(thm)],['0.19.0.0','0.1.2.0',theory(equality)]),
% 0.57/1.00 [pos('R','L')]).
% 0.57/1.00 cnf('0.19.1.0',plain,
% 0.57/1.00 ( multiply(X1,identity) = X1 ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.19.0.1']),
% 0.57/1.00 [weight('<19,18,13,[0,0,0,1]>')]).
% 0.57/1.00 cnf('0.19.2.0',plain,
% 0.57/1.00 ( multiply(X1,identity) = X1 ),
% 0.57/1.00 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.57/1.00 [u,rule_16]).
% 0.57/1.00 cnf('0.21.0.0',plain,
% 0.57/1.00 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.57/1.00 inference(cp,[status(thm)],['0.5.2.0','0.14.2.0',theory(equality)]),
% 0.57/1.00 [pos('L.2','L')]).
% 0.57/1.00 cnf('0.21.1.0',plain,
% 0.57/1.00 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.57/1.00 [weight('<41,14,5,[0,0,0,2]>')]).
% 0.57/1.00 cnf('0.21.2.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1 ),
% 0.57/1.00 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.57/1.00 [x,rule_18]).
% 0.57/1.00 cnf('0.25.0.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(least_upper_bound(X1,X2),X1) ),
% 0.57/1.00 inference(cp,[status(thm)],['0.21.2.0','0.3.2.0',theory(equality)]),
% 0.57/1.00 [pos('L.2','L')]).
% 0.57/1.00 cnf('0.25.0.1',plain,
% 0.57/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)) ),
% 0.57/1.00 inference(reduction,[status(thm)],['0.25.0.0','0.17.2.0',theory(equality)]),
% 0.57/1.00 [pos('R','L')]).
% 0.57/1.00 cnf('0.25.1.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.25.0.1']),
% 0.57/1.00 [weight('<53,21,3,[1,0,0,2]>')]).
% 0.57/1.00 cnf('0.25.2.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2) ),
% 0.57/1.00 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.57/1.00 [x,rule_22]).
% 0.57/1.00 cnf('0.49.0.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(least_upper_bound(X2,X1),X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.57/1.00 inference(cp,[status(thm)],['0.17.2.0','0.25.2.0',theory(equality)]),
% 0.57/1.00 [pos('L.1','L')]).
% 0.57/1.00 cnf('0.49.0.1',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.57/1.00 inference(reduction,[status(thm)],['0.49.0.0','0.17.2.0',theory(equality)]),
% 0.57/1.00 [pos('L.2','L')]).
% 0.57/1.00 cnf('0.49.0.2',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.57/1.00 inference(reduction,[status(thm)],['0.49.0.1','0.17.2.0',theory(equality)]),
% 0.57/1.00 [pos('R','L')]).
% 0.57/1.00 cnf('0.49.1.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.49.0.2']),
% 0.57/1.00 [weight('<103,25,17,[0,0,0,1]>')]).
% 0.57/1.00 cnf('0.49.2.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.57/1.00 inference(orient,[status(thm)],['0.49.1.0',theory(equality)]),
% 0.57/1.00 [u,rule_43]).
% 0.57/1.00 cnf('0.50.0.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) ),
% 0.57/1.00 inference(cp,[status(thm)],['0.25.2.0','0.17.2.0',theory(equality)]),
% 0.57/1.00 [pos('L.2','L')]).
% 0.57/1.00 cnf('0.50.1.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.50.0.0']),
% 0.57/1.00 [weight('<103,25,17,[1,0,0,2]>')]).
% 0.57/1.00 cnf('0.50.2.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.57/1.00 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 0.57/1.00 [x,rule_44]).
% 0.57/1.00 cnf('0.62.0.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)) ),
% 0.57/1.00 inference(cp,[status(thm)],['0.17.2.0','0.16.2.0',theory(equality)]),
% 0.57/1.00 [pos('L','L')]).
% 0.57/1.00 cnf('0.62.1.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)) ),
% 0.57/1.00 inference(weigh,[status(thm)],['0.62.0.0']),
% 0.57/1.00 [weight('<120,17,16,[1,0,0,0]>')]).
% 0.57/1.00 cnf('0.62.2.0',plain,
% 0.57/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)) ),
% 0.57/1.00 inference(activate,[status(thm)],['0.62.1.0']),
% 0.57/1.00 [equation_9]).
% 0.57/1.00 cnf('1.0.0.0',conjecture,
% 0.57/1.00 ( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.57/1.00 file('/tmp/WALDMEISTER_31228_n029',conjecture_1)).
% 0.57/1.00 cnf('1.0.0.1',plain,
% 0.57/1.00 ( least_upper_bound(multiply(a,least_upper_bound(b,identity)),multiply(identity,least_upper_bound(b,identity))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.0','0.11.2.0',theory(equality)]),
% 0.57/1.00 [pos('L','L')]).
% 0.57/1.00 cnf('1.0.0.2',plain,
% 0.57/1.00 ( least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,identity)),multiply(identity,least_upper_bound(b,identity))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.1','0.9.2.0',theory(equality)]),
% 0.57/1.00 [pos('L.1','L')]).
% 0.57/1.00 cnf('1.0.0.3',plain,
% 0.57/1.00 ( least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),multiply(identity,least_upper_bound(b,identity)))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.2','0.17.2.0',theory(equality)]),
% 0.57/1.00 [pos('L','L')]).
% 0.57/1.00 cnf('1.0.0.4',plain,
% 0.57/1.00 ( least_upper_bound(multiply(a,b),least_upper_bound(a,multiply(identity,least_upper_bound(b,identity)))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.3','0.19.2.0',theory(equality)]),
% 0.57/1.00 [pos('L.2.1','L')]).
% 0.57/1.00 cnf('1.0.0.5',plain,
% 0.57/1.00 ( least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.4','0.1.2.0',theory(equality)]),
% 0.57/1.00 [pos('L.2.2','L')]).
% 0.57/1.00 cnf('1.0.0.6',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(least_upper_bound(b,identity),multiply(a,b))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.5','0.62.2.0',theory(equality)]),
% 0.57/1.00 [pos('L','R')]).
% 0.57/1.00 cnf('1.0.0.7',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.6','0.17.2.0',theory(equality)]),
% 0.57/1.00 [pos('L.2','L')]).
% 0.57/1.00 cnf('1.0.0.8',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.7','0.17.2.0',theory(equality)]),
% 0.57/1.00 [pos('R','L')]).
% 0.57/1.00 cnf('1.0.0.9',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,least_upper_bound(b,identity)),multiply(identity,least_upper_bound(b,identity))))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.8','0.11.2.0',theory(equality)]),
% 0.57/1.00 [pos('R.2.2','L')]).
% 0.57/1.00 cnf('1.0.0.10',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,identity)),multiply(identity,least_upper_bound(b,identity))))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.9','0.9.2.0',theory(equality)]),
% 0.57/1.00 [pos('R.2.2.1','L')]).
% 0.57/1.00 cnf('1.0.0.11',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),multiply(identity,least_upper_bound(b,identity)))))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.10','0.17.2.0',theory(equality)]),
% 0.57/1.00 [pos('R.2.2','L')]).
% 0.57/1.00 cnf('1.0.0.12',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,identity),multiply(identity,least_upper_bound(b,identity))))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.11','0.49.2.0',theory(equality)]),
% 0.57/1.00 [pos('R','L')]).
% 0.57/1.00 cnf('1.0.0.13',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,multiply(identity,least_upper_bound(b,identity))))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.12','0.19.2.0',theory(equality)]),
% 0.57/1.00 [pos('R.2.2.1','L')]).
% 0.57/1.00 cnf('1.0.0.14',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,least_upper_bound(b,identity)))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.13','0.1.2.0',theory(equality)]),
% 0.57/1.00 [pos('R.2.2.2','L')]).
% 0.57/1.00 cnf('1.0.0.15',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,b))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.14','0.50.2.0',theory(equality)]),
% 0.57/1.00 [pos('R.2','L')]).
% 0.57/1.00 cnf('1.0.0.16',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.15','0.62.2.0',theory(equality)]),
% 0.57/1.00 [pos('R.2','R')]).
% 0.57/1.00 cnf('1.0.0.17',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(a,least_upper_bound(least_upper_bound(b,identity),multiply(a,b))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.16','0.62.2.0',theory(equality)]),
% 0.57/1.00 [pos('R','R')]).
% 0.57/1.00 cnf('1.0.0.18',plain,
% 0.57/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) ),
% 0.57/1.00 inference(reduction,[status(thm)],['1.0.0.17','0.17.2.0',theory(equality)]),
% 0.57/1.00 [pos('R.2','L')]).
% 0.57/1.00 cnf('1.0.0.19',plain,
% 0.57/1.00 ( $true ),
% 0.57/1.00 inference(trivial,[status(thm)],['1.0.0.18',theory(equality)]),
% 0.57/1.00 [conjecture_1]).
% 0.57/1.00
% 0.57/1.00 Proved Goals:
% 0.57/1.00 No. 1: multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ?= least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) joined, current: least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b))))
% 0.57/1.00 1 goal was specified, which was proved.
% 0.57/1.00 % SZS output end CNFRefutation
% 0.57/1.00 #END OF PROOF
% 0.57/1.00
% 0.57/1.00 Problem WALDMEISTER_31228_n029
% 0.57/1.00 CPs.gen 1540
% 0.57/1.00 CPs.reexp 0
% 0.57/1.00 Select 169
% 0.57/1.00 R 53
% 0.57/1.00 E 9
% 0.57/1.00 vsize 7.0M
% 0.57/1.00 rss 4.1M
% 0.57/1.00 process.time 0.024s
% 0.57/1.00 wallclock.time 0.025s
% 0.57/1.00 status S
% 0.57/1.00
% 0.57/1.00
% 0.57/1.00 Waldmeister states: Goal proved.
% 0.57/1.00 % SZS status Unsatisfiable
% 0.57/1.00
% 0.57/1.00 Problem WALDMEISTER_31228_n029
% 0.57/1.00 CPs.gen 0
% 0.57/1.00 CPs.reexp 0
% 0.57/1.00 Select 0
% 0.57/1.00 R 0
% 0.57/1.00 E 0
% 0.57/1.00 vsize 6.0M
% 0.57/1.00 rss 3.2M
% 0.57/1.00 process.time 0.001s
% 0.57/1.00 wallclock.time 0.024s
% 0.57/1.00 status S
%------------------------------------------------------------------------------