TSTP Solution File: GRP193-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n011.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 12:25:20 EDT 2022
% Result : Unsatisfiable 0.68s 1.14s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 05:59:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.62/1.00 ********************************************************************************
% 0.62/1.00 * W A L D M E I S T E R \| \ / \|/ *
% 0.62/1.00 * |/ | \/ | *
% 0.62/1.00 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.62/1.00 * A. Jaeger and B. Loechner | | *
% 0.62/1.00 * <waldmeister@informatik.uni-kl.de> | *
% 0.62/1.00 ********************************************************************************
% 0.62/1.00
% 0.62/1.00
% 0.62/1.00 Goals:
% 0.62/1.00 ------
% 0.62/1.00
% 0.62/1.00 ( 1) greatest_lower_bound(a,multiply(b,c)) ?=? greatest_lower_bound(a,c)
% 0.62/1.00
% 0.62/1.00 Detected structure: VerbandsgeordneteGruppe
% 0.62/1.00 ********************************************************************************
% 0.62/1.00 ****************************** COMPLETION - PROOF ******************************
% 0.62/1.00 ********************************************************************************
% 0.62/1.00
% 0.68/1.14 joined goal: 1 greatest_lower_bound(a,multiply(b,c)) ?= greatest_lower_bound(a,c) to greatest_lower_bound(c,a)
% 0.68/1.14 goal joined
% 0.68/1.14 % SZS status Unsatisfiable
% 0.68/1.14 #START OF PROOF
% 0.68/1.14 % SZS output start CNFRefutation
% 0.68/1.14 cnf('0.1.0.0',axiom,
% 0.68/1.14 ( X1 = multiply(identity,X1) ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.1.1.0',plain,
% 0.68/1.14 ( X1 = multiply(identity,X1) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.68/1.14 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.68/1.14 cnf('0.1.2.0',plain,
% 0.68/1.14 ( multiply(identity,X1) = X1 ),
% 0.68/1.14 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.68/1.14 [x,rule_1]).
% 0.68/1.14 cnf('0.3.0.0',axiom,
% 0.68/1.14 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.3.1.0',plain,
% 0.68/1.14 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.68/1.14 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.68/1.14 cnf('0.3.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 0.68/1.14 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.68/1.14 [x,rule_3]).
% 0.68/1.14 cnf('0.6.0.0',axiom,
% 0.68/1.14 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.6.1.0',plain,
% 0.68/1.14 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.68/1.14 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.68/1.14 cnf('0.6.2.0',plain,
% 0.68/1.14 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.68/1.14 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.68/1.14 [x,rule_6]).
% 0.68/1.14 cnf('0.7.0.0',axiom,
% 0.68/1.14 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.7.1.0',plain,
% 0.68/1.14 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.68/1.14 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.68/1.14 cnf('0.7.2.0',plain,
% 0.68/1.14 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.68/1.14 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.68/1.14 [u,rule_7]).
% 0.68/1.14 cnf('0.9.0.0',axiom,
% 0.68/1.14 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.9.1.0',plain,
% 0.68/1.14 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.68/1.14 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.68/1.14 cnf('0.9.2.0',plain,
% 0.68/1.14 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.68/1.14 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.68/1.14 [u,rule_9]).
% 0.68/1.14 cnf('0.11.0.0',axiom,
% 0.68/1.14 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.11.1.0',plain,
% 0.68/1.14 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.68/1.14 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.68/1.14 cnf('0.11.2.0',plain,
% 0.68/1.14 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.68/1.14 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.68/1.14 [u,rule_11]).
% 0.68/1.14 cnf('0.12.0.0',axiom,
% 0.68/1.14 ( multiply(inverse(X1),X1) = identity ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.12.1.0',plain,
% 0.68/1.14 ( multiply(inverse(X1),X1) = identity ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.68/1.14 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.68/1.14 cnf('0.12.2.0',plain,
% 0.68/1.14 ( multiply(inverse(X1),X1) = identity ),
% 0.68/1.14 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.68/1.14 [u,rule_12]).
% 0.68/1.14 cnf('0.13.0.0',axiom,
% 0.68/1.14 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.13.1.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.68/1.14 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.68/1.14 cnf('0.13.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.68/1.14 inference(activate,[status(thm)],['0.13.1.0']),
% 0.68/1.14 [equation_1]).
% 0.68/1.14 cnf('0.14.0.0',axiom,
% 0.68/1.14 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.14.1.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.68/1.14 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.68/1.14 cnf('0.14.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 0.68/1.14 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.68/1.14 [x,rule_13]).
% 0.68/1.14 cnf('0.15.0.0',axiom,
% 0.68/1.14 ( greatest_lower_bound(a,b) = identity ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.15.1.0',plain,
% 0.68/1.14 ( greatest_lower_bound(a,b) = identity ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.68/1.14 [weight('<14,0,0,[0,0,0,15]>')]).
% 0.68/1.14 cnf('0.15.1.1',plain,
% 0.68/1.14 ( greatest_lower_bound(b,a) = identity ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.15.1.0','0.13.2.0',theory(equality)]),
% 0.68/1.14 [pos('L','L')]).
% 0.68/1.14 cnf('0.15.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(b,a) = identity ),
% 0.68/1.14 inference(orient,[status(thm)],['0.15.1.1',theory(equality)]),
% 0.68/1.14 [u,rule_14]).
% 0.68/1.14 cnf('0.16.0.0',axiom,
% 0.68/1.14 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.16.1.0',plain,
% 0.68/1.14 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.68/1.14 [weight('<15,0,0,[0,0,0,16]>')]).
% 0.68/1.14 cnf('0.16.2.0',plain,
% 0.68/1.14 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.68/1.14 inference(activate,[status(thm)],['0.16.1.0']),
% 0.68/1.14 [equation_2]).
% 0.68/1.14 cnf('0.20.0.0',axiom,
% 0.68/1.14 ( least_upper_bound(identity,c) = c ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011')).
% 0.68/1.14 cnf('0.20.1.0',plain,
% 0.68/1.14 ( least_upper_bound(identity,c) = c ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.68/1.14 [weight('<19,0,0,[0,0,0,20]>')]).
% 0.68/1.14 cnf('0.20.1.1',plain,
% 0.68/1.14 ( least_upper_bound(c,identity) = c ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.20.1.0','0.16.2.0',theory(equality)]),
% 0.68/1.14 [pos('L','L')]).
% 0.68/1.14 cnf('0.20.2.0',plain,
% 0.68/1.14 ( least_upper_bound(c,identity) = c ),
% 0.68/1.14 inference(orient,[status(thm)],['0.20.1.1',theory(equality)]),
% 0.68/1.14 [u,rule_18]).
% 0.68/1.14 cnf('0.28.0.0',plain,
% 0.68/1.14 ( greatest_lower_bound(multiply(X1,b),multiply(X1,a)) = multiply(X1,identity) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.7.2.0','0.15.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.2','L')]).
% 0.68/1.14 cnf('0.28.1.0',plain,
% 0.68/1.14 ( greatest_lower_bound(multiply(X1,b),multiply(X1,a)) = multiply(X1,identity) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.28.0.0']),
% 0.68/1.14 [weight('<43,15,7,[0,0,0,2]>')]).
% 0.68/1.14 cnf('0.28.2.0',plain,
% 0.68/1.14 ( multiply(X1,identity) = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.68/1.14 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 0.68/1.14 [x,rule_26]).
% 0.68/1.14 cnf('0.38.0.0',plain,
% 0.68/1.14 ( least_upper_bound(multiply(c,X1),multiply(identity,X1)) = multiply(c,X1) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.11.2.0','0.20.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.1','L')]).
% 0.68/1.14 cnf('0.38.0.1',plain,
% 0.68/1.14 ( least_upper_bound(multiply(c,X1),X1) = multiply(c,X1) ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.38.0.0','0.1.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.2','L')]).
% 0.68/1.14 cnf('0.38.1.0',plain,
% 0.68/1.14 ( least_upper_bound(multiply(c,X1),X1) = multiply(c,X1) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.38.0.1']),
% 0.68/1.14 [weight('<53,20,11,[0,0,0,1]>')]).
% 0.68/1.14 cnf('0.38.1.1',plain,
% 0.68/1.14 ( least_upper_bound(X1,multiply(c,X1)) = multiply(c,X1) ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.38.1.0','0.16.2.0',theory(equality)]),
% 0.68/1.14 [pos('L','L')]).
% 0.68/1.14 cnf('0.38.2.0',plain,
% 0.68/1.14 ( least_upper_bound(X1,multiply(c,X1)) = multiply(c,X1) ),
% 0.68/1.14 inference(orient,[status(thm)],['0.38.1.1',theory(equality)]),
% 0.68/1.14 [u,rule_36]).
% 0.68/1.14 cnf('0.39.0.0',plain,
% 0.68/1.14 ( X1 = greatest_lower_bound(X1,multiply(c,X1)) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.3.2.0','0.38.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.2','L')]).
% 0.68/1.14 cnf('0.39.1.0',plain,
% 0.68/1.14 ( X1 = greatest_lower_bound(X1,multiply(c,X1)) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.39.0.0']),
% 0.68/1.14 [weight('<41,38,3,[0,0,0,2]>')]).
% 0.68/1.14 cnf('0.39.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,multiply(c,X1)) = X1 ),
% 0.68/1.14 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.68/1.14 [x,rule_37]).
% 0.68/1.14 cnf('0.49.0.0',plain,
% 0.68/1.14 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.6.2.0','0.12.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.1','L')]).
% 0.68/1.14 cnf('0.49.0.1',plain,
% 0.68/1.14 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.49.0.0','0.1.2.0',theory(equality)]),
% 0.68/1.14 [pos('R','L')]).
% 0.68/1.14 cnf('0.49.1.0',plain,
% 0.68/1.14 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.49.0.1']),
% 0.68/1.14 [weight('<55,12,6,[0,0,0,1]>')]).
% 0.68/1.14 cnf('0.49.2.0',plain,
% 0.68/1.14 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.68/1.14 inference(orient,[status(thm)],['0.49.1.0',theory(equality)]),
% 0.68/1.14 [u,rule_47]).
% 0.68/1.14 cnf('0.50.0.0',plain,
% 0.68/1.14 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.49.2.0','0.49.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.2','L')]).
% 0.68/1.14 cnf('0.50.1.0',plain,
% 0.68/1.14 ( X1 = inverse(inverse(X1)) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.50.0.0']),
% 0.68/1.14 [weight('<19,49,49,[0,0,0,3]>')]).
% 0.68/1.14 cnf('0.50.2.0',plain,
% 0.68/1.14 ( inverse(inverse(X1)) = X1 ),
% 0.68/1.14 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 0.68/1.14 [x,rule_48]).
% 0.68/1.14 cnf('0.78.0.0',plain,
% 0.68/1.14 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.49.2.0','0.50.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.1','L')]).
% 0.68/1.14 cnf('0.78.1.0',plain,
% 0.68/1.14 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.78.0.0']),
% 0.68/1.14 [weight('<55,50,49,[0,0,0,1]>')]).
% 0.68/1.14 cnf('0.78.2.0',plain,
% 0.68/1.14 ( multiply(X1,multiply(inverse(X1),X2)) = X2 ),
% 0.68/1.14 inference(orient,[status(thm)],['0.78.1.0',theory(equality)]),
% 0.68/1.14 [x,rule_76]).
% 0.68/1.14 cnf('0.131.0.0',plain,
% 0.68/1.14 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = multiply(identity,X1) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.9.2.0','0.15.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.1','L')]).
% 0.68/1.14 cnf('0.131.0.1',plain,
% 0.68/1.14 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.131.0.0','0.1.2.0',theory(equality)]),
% 0.68/1.14 [pos('R','L')]).
% 0.68/1.14 cnf('0.131.1.0',plain,
% 0.68/1.14 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.131.0.1']),
% 0.68/1.14 [weight('<71,15,9,[0,0,0,1]>')]).
% 0.68/1.14 cnf('0.131.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.68/1.14 inference(orient,[status(thm)],['0.131.1.0',theory(equality)]),
% 0.68/1.14 [u,rule_129]).
% 0.68/1.14 cnf('0.253.0.0',plain,
% 0.68/1.14 ( X1 = multiply(X1,identity) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.78.2.0','0.12.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.2','L')]).
% 0.68/1.14 cnf('0.253.0.1',plain,
% 0.68/1.14 ( X1 = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.253.0.0','0.28.2.0',theory(equality)]),
% 0.68/1.14 [pos('R','L')]).
% 0.68/1.14 cnf('0.253.1.0',plain,
% 0.68/1.14 ( X1 = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.253.0.1']),
% 0.68/1.14 [weight('<71,78,12,[1,0,0,2]>')]).
% 0.68/1.14 cnf('0.253.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(multiply(X1,b),multiply(X1,a)) = X1 ),
% 0.68/1.14 inference(orient,[status(thm)],['0.253.1.0',theory(equality)]),
% 0.68/1.14 [x,rule_251]).
% 0.68/1.14 cnf('0.254.0.0',plain,
% 0.68/1.14 ( multiply(X1,identity) = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.68/1.14 inference(interreduction_right,[status(thm)],['0.28.2.0'])).
% 0.68/1.14 cnf('0.254.0.1',plain,
% 0.68/1.14 ( multiply(X1,identity) = X1 ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.254.0.0','0.253.2.0',theory(equality)]),
% 0.68/1.14 [pos('R','L')]).
% 0.68/1.14 cnf('0.254.1.0',plain,
% 0.68/1.14 ( multiply(X1,identity) = X1 ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.254.0.1']),
% 0.68/1.14 [weight('<19,28,253,[0,0,0,0]>')]).
% 0.68/1.14 cnf('0.254.2.0',plain,
% 0.68/1.14 ( multiply(X1,identity) = X1 ),
% 0.68/1.14 inference(orient,[status(thm)],['0.254.1.0',theory(equality)]),
% 0.68/1.14 [u,rule_252]).
% 0.68/1.14 cnf('0.355.0.0',plain,
% 0.68/1.14 ( multiply(inverse(c),X1) = greatest_lower_bound(multiply(inverse(c),X1),X1) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.39.2.0','0.78.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.2','L')]).
% 0.68/1.14 cnf('0.355.1.0',plain,
% 0.68/1.14 ( multiply(inverse(c),X1) = greatest_lower_bound(multiply(inverse(c),X1),X1) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.355.0.0']),
% 0.68/1.14 [weight('<76,78,39,[0,0,0,2]>')]).
% 0.68/1.14 cnf('0.355.1.1',plain,
% 0.68/1.14 ( multiply(inverse(c),X1) = greatest_lower_bound(X1,multiply(inverse(c),X1)) ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.355.1.0','0.13.2.0',theory(equality)]),
% 0.68/1.14 [pos('R','L')]).
% 0.68/1.14 cnf('0.355.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,multiply(inverse(c),X1)) = multiply(inverse(c),X1) ),
% 0.68/1.14 inference(orient,[status(thm)],['0.355.1.1',theory(equality)]),
% 0.68/1.14 [x,rule_353]).
% 0.68/1.14 cnf('0.356.0.0',plain,
% 0.68/1.14 ( multiply(inverse(c),c) = greatest_lower_bound(c,identity) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.355.2.0','0.12.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.2','L')]).
% 0.68/1.14 cnf('0.356.0.1',plain,
% 0.68/1.14 ( identity = greatest_lower_bound(c,identity) ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.356.0.0','0.12.2.0',theory(equality)]),
% 0.68/1.14 [pos('L','L')]).
% 0.68/1.14 cnf('0.356.1.0',plain,
% 0.68/1.14 ( identity = greatest_lower_bound(c,identity) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.356.0.1']),
% 0.68/1.14 [weight('<19,355,12,[1,0,0,2]>')]).
% 0.68/1.14 cnf('0.356.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(c,identity) = identity ),
% 0.68/1.14 inference(orient,[status(thm)],['0.356.1.0',theory(equality)]),
% 0.68/1.14 [x,rule_354]).
% 0.68/1.14 cnf('0.357.0.0',plain,
% 0.68/1.14 ( greatest_lower_bound(multiply(X1,c),multiply(X1,identity)) = multiply(X1,identity) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.7.2.0','0.356.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.2','L')]).
% 0.68/1.14 cnf('0.357.0.1',plain,
% 0.68/1.14 ( greatest_lower_bound(multiply(X1,c),X1) = multiply(X1,identity) ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.357.0.0','0.254.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.2','L')]).
% 0.68/1.14 cnf('0.357.0.2',plain,
% 0.68/1.14 ( greatest_lower_bound(multiply(X1,c),X1) = X1 ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.357.0.1','0.254.2.0',theory(equality)]),
% 0.68/1.14 [pos('R','L')]).
% 0.68/1.14 cnf('0.357.1.0',plain,
% 0.68/1.14 ( greatest_lower_bound(multiply(X1,c),X1) = X1 ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.357.0.2']),
% 0.68/1.14 [weight('<41,356,7,[0,0,0,2]>')]).
% 0.68/1.14 cnf('0.357.1.1',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,multiply(X1,c)) = X1 ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.357.1.0','0.13.2.0',theory(equality)]),
% 0.68/1.14 [pos('L','L')]).
% 0.68/1.14 cnf('0.357.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,multiply(X1,c)) = X1 ),
% 0.68/1.14 inference(orient,[status(thm)],['0.357.1.1',theory(equality)]),
% 0.68/1.14 [u,rule_355]).
% 0.68/1.14 cnf('0.512.0.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,c),X2)) = greatest_lower_bound(X1,X2) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.14.2.0','0.357.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.1','L')]).
% 0.68/1.14 cnf('0.512.1.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,c),X2)) = greatest_lower_bound(X1,X2) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.512.0.0']),
% 0.68/1.14 [weight('<87,357,14,[0,0,0,1]>')]).
% 0.68/1.14 cnf('0.512.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,c),X2)) = greatest_lower_bound(X1,X2) ),
% 0.68/1.14 inference(orient,[status(thm)],['0.512.1.0',theory(equality)]),
% 0.68/1.14 [u,rule_508]).
% 0.68/1.14 cnf('0.557.0.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,c))) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.512.2.0','0.13.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.2','L')]).
% 0.68/1.14 cnf('0.557.1.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,c))) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.557.0.0']),
% 0.68/1.14 [weight('<87,512,13,[1,0,0,2]>')]).
% 0.68/1.14 cnf('0.557.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,c))) = greatest_lower_bound(X1,X2) ),
% 0.68/1.14 inference(orient,[status(thm)],['0.557.1.0',theory(equality)]),
% 0.68/1.14 [x,rule_553]).
% 0.68/1.14 cnf('0.558.0.0',plain,
% 0.68/1.14 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
% 0.68/1.14 inference(cp,[status(thm)],['0.557.2.0','0.131.2.0',theory(equality)]),
% 0.68/1.14 [pos('L.2','L')]).
% 0.68/1.14 cnf('0.558.1.0',plain,
% 0.68/1.14 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
% 0.68/1.14 inference(weigh,[status(thm)],['0.558.0.0']),
% 0.68/1.14 [weight('<53,557,131,[1,0,0,2]>')]).
% 0.68/1.14 cnf('0.558.1.1',plain,
% 0.68/1.14 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(c,a) ),
% 0.68/1.14 inference(reduction,[status(thm)],['0.558.1.0','0.13.2.0',theory(equality)]),
% 0.68/1.14 [pos('R','L')]).
% 0.68/1.14 cnf('0.558.2.0',plain,
% 0.68/1.14 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(c,a) ),
% 0.68/1.14 inference(orient,[status(thm)],['0.558.1.1',theory(equality)]),
% 0.68/1.14 [u,rule_554]).
% 0.68/1.14 cnf('1.0.0.0',conjecture,
% 0.68/1.14 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
% 0.68/1.14 file('/tmp/WALDMEISTER_8791_n011',conjecture_1)).
% 0.68/1.14 cnf('1.0.0.1',plain,
% 0.68/1.14 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(c,a) ),
% 0.68/1.14 inference(reduction,[status(thm)],['1.0.0.0','0.13.2.0',theory(equality)]),
% 0.68/1.14 [pos('R','L')]).
% 0.68/1.14 cnf('1.0.0.2',plain,
% 0.68/1.14 ( greatest_lower_bound(c,a) = greatest_lower_bound(c,a) ),
% 0.68/1.14 inference(reduction,[status(thm)],['1.0.0.1','0.558.2.0',theory(equality)]),
% 0.68/1.14 [pos('L','L')]).
% 0.68/1.14 cnf('1.0.0.3',plain,
% 0.68/1.14 ( $true ),
% 0.68/1.14 inference(trivial,[status(thm)],['1.0.0.2',theory(equality)]),
% 0.68/1.14 [conjecture_1]).
% 0.68/1.14
% 0.68/1.14 Proved Goals:
% 0.68/1.14 No. 1: greatest_lower_bound(a,multiply(b,c)) ?= greatest_lower_bound(a,c) joined, current: greatest_lower_bound(c,a) = greatest_lower_bound(c,a)
% 0.68/1.14 1 goal was specified, which was proved.
% 0.68/1.14 % SZS output end CNFRefutation
% 0.68/1.14 #END OF PROOF
% 0.68/1.14
% 0.68/1.14 Problem WALDMEISTER_8791_n011
% 0.68/1.14 CPs.gen 23960
% 0.68/1.14 CPs.reexp 0
% 0.68/1.14 Select 3122
% 0.68/1.14 R 554
% 0.68/1.14 E 4
% 0.68/1.14 vsize 6.8M
% 0.68/1.14 rss 4.1M
% 0.68/1.14 process.time 0.132s
% 0.68/1.14 wallclock.time 0.139s
% 0.68/1.14 status S
% 0.68/1.14
% 0.68/1.14
% 0.68/1.14 Waldmeister states: Goal proved.
% 0.68/1.14 % SZS status Unsatisfiable
% 0.68/1.14
% 0.68/1.14 Problem WALDMEISTER_8791_n011
% 0.68/1.14 CPs.gen 1031
% 0.68/1.14 CPs.reexp 0
% 0.68/1.14 Select 230
% 0.68/1.14 R 94
% 0.68/1.14 E 2
% 0.68/1.14 vsize 6.5M
% 0.68/1.14 rss 3.8M
% 0.68/1.14 process.time 0.007s
% 0.68/1.14 wallclock.time 0.138s
% 0.68/1.14 status S
%------------------------------------------------------------------------------