TSTP Solution File: GRP193-2 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP193-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n019.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 12:25:21 EDT 2022
% Result : Unsatisfiable 0.69s 1.09s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP193-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : woody %s
% 0.13/0.35 % Computer : n019.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 : Tue Jun 14 09:13:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.59/1.00 ********************************************************************************
% 0.59/1.00 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/1.00 * |/ | \/ | *
% 0.59/1.00 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/1.00 * A. Jaeger and B. Loechner | | *
% 0.59/1.00 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/1.00 ********************************************************************************
% 0.59/1.00
% 0.59/1.00
% 0.59/1.00 Goals:
% 0.59/1.00 ------
% 0.59/1.00
% 0.59/1.00 ( 1) greatest_lower_bound(a,multiply(b,c)) ?=? greatest_lower_bound(a,c)
% 0.59/1.00
% 0.59/1.00 Detected structure: VerbandsgeordneteGruppe
% 0.59/1.00 ********************************************************************************
% 0.59/1.00 ****************************** COMPLETION - PROOF ******************************
% 0.59/1.00 ********************************************************************************
% 0.59/1.00
% 0.69/1.09 joined goal: 1 greatest_lower_bound(a,multiply(b,c)) ?= greatest_lower_bound(a,c) to greatest_lower_bound(c,a)
% 0.69/1.09 goal joined
% 0.69/1.09 % SZS status Unsatisfiable
% 0.69/1.09 #START OF PROOF
% 0.69/1.09 % SZS output start CNFRefutation
% 0.69/1.09 cnf('0.2.0.0',axiom,
% 0.69/1.09 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019')).
% 0.69/1.09 cnf('0.2.1.0',plain,
% 0.69/1.09 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.69/1.09 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.69/1.09 cnf('0.2.2.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 0.69/1.09 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.69/1.09 [x,rule_2]).
% 0.69/1.09 cnf('0.3.0.0',axiom,
% 0.69/1.09 ( X1 = multiply(identity,X1) ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019')).
% 0.69/1.09 cnf('0.3.1.0',plain,
% 0.69/1.09 ( X1 = multiply(identity,X1) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.69/1.09 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.69/1.09 cnf('0.3.2.0',plain,
% 0.69/1.09 ( multiply(identity,X1) = X1 ),
% 0.69/1.09 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.69/1.09 [x,rule_3]).
% 0.69/1.09 cnf('0.5.0.0',axiom,
% 0.69/1.09 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019')).
% 0.69/1.09 cnf('0.5.1.0',plain,
% 0.69/1.09 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.69/1.09 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.69/1.09 cnf('0.5.2.0',plain,
% 0.69/1.09 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 0.69/1.09 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.69/1.09 [x,rule_5]).
% 0.69/1.09 cnf('0.6.0.0',axiom,
% 0.69/1.09 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019')).
% 0.69/1.09 cnf('0.6.1.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.69/1.09 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.69/1.09 cnf('0.6.2.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.69/1.09 inference(activate,[status(thm)],['0.6.1.0']),
% 0.69/1.09 [equation_1]).
% 0.69/1.09 cnf('0.7.0.0',axiom,
% 0.69/1.09 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019')).
% 0.69/1.09 cnf('0.7.1.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.69/1.09 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.69/1.09 cnf('0.7.2.0',plain,
% 0.69/1.09 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 0.69/1.09 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.69/1.09 [x,rule_6]).
% 0.69/1.09 cnf('0.8.0.0',axiom,
% 0.69/1.09 ( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)) ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019')).
% 0.69/1.09 cnf('0.8.1.0',plain,
% 0.69/1.09 ( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.69/1.09 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.69/1.09 cnf('0.8.1.1',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(a,multiply(b,c)) ),
% 0.69/1.09 inference(reduction,[status(thm)],['0.8.1.0','0.7.2.0',theory(equality)]),
% 0.69/1.09 [pos('L','L')]).
% 0.69/1.09 cnf('0.8.1.2',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(b,a),greatest_lower_bound(a,c)))) = greatest_lower_bound(a,multiply(b,c)) ),
% 0.69/1.09 inference(reduction,[status(thm)],['0.8.1.1','0.6.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2.2.1','L')]).
% 0.69/1.09 cnf('0.8.1.3',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(b,a),greatest_lower_bound(c,a)))) = greatest_lower_bound(a,multiply(b,c)) ),
% 0.69/1.09 inference(reduction,[status(thm)],['0.8.1.2','0.6.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2.2.2','L')]).
% 0.69/1.09 cnf('0.8.2.0',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(b,a),greatest_lower_bound(c,a)))) = greatest_lower_bound(a,multiply(b,c)) ),
% 0.69/1.09 inference(orient,[status(thm)],['0.8.1.3',theory(equality)]),
% 0.69/1.09 [u,rule_7]).
% 0.69/1.09 cnf('0.9.0.0',axiom,
% 0.69/1.09 ( greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2) ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019')).
% 0.69/1.09 cnf('0.9.1.0',plain,
% 0.69/1.09 ( greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.69/1.09 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.69/1.09 cnf('0.9.2.0',plain,
% 0.69/1.09 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.69/1.09 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.69/1.09 [x,rule_8]).
% 0.69/1.09 cnf('0.10.0.0',axiom,
% 0.69/1.09 ( greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)) ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019')).
% 0.69/1.09 cnf('0.10.1.0',plain,
% 0.69/1.09 ( greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.69/1.09 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.69/1.09 cnf('0.10.2.0',plain,
% 0.69/1.09 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.69/1.09 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.69/1.09 [x,rule_9]).
% 0.69/1.09 cnf('0.12.0.0',axiom,
% 0.69/1.09 ( greatest_lower_bound(identity,b) = identity ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019')).
% 0.69/1.09 cnf('0.12.1.0',plain,
% 0.69/1.09 ( greatest_lower_bound(identity,b) = identity ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.69/1.09 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.69/1.09 cnf('0.12.1.1',plain,
% 0.69/1.09 ( greatest_lower_bound(b,identity) = identity ),
% 0.69/1.09 inference(reduction,[status(thm)],['0.12.1.0','0.6.2.0',theory(equality)]),
% 0.69/1.09 [pos('L','L')]).
% 0.69/1.09 cnf('0.12.2.0',plain,
% 0.69/1.09 ( greatest_lower_bound(b,identity) = identity ),
% 0.69/1.09 inference(orient,[status(thm)],['0.12.1.1',theory(equality)]),
% 0.69/1.09 [u,rule_11]).
% 0.69/1.09 cnf('0.14.0.0',axiom,
% 0.69/1.09 ( greatest_lower_bound(a,b) = identity ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019')).
% 0.69/1.09 cnf('0.14.1.0',plain,
% 0.69/1.09 ( greatest_lower_bound(a,b) = identity ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.69/1.09 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.69/1.09 cnf('0.14.1.1',plain,
% 0.69/1.09 ( greatest_lower_bound(b,a) = identity ),
% 0.69/1.09 inference(reduction,[status(thm)],['0.14.1.0','0.6.2.0',theory(equality)]),
% 0.69/1.09 [pos('L','L')]).
% 0.69/1.09 cnf('0.14.2.0',plain,
% 0.69/1.09 ( greatest_lower_bound(b,a) = identity ),
% 0.69/1.09 inference(orient,[status(thm)],['0.14.1.1',theory(equality)]),
% 0.69/1.09 [u,rule_13]).
% 0.69/1.09 cnf('0.19.0.0',axiom,
% 0.69/1.09 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019')).
% 0.69/1.09 cnf('0.19.1.0',plain,
% 0.69/1.09 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.69/1.09 [weight('<18,0,0,[0,0,0,19]>')]).
% 0.69/1.09 cnf('0.19.2.0',plain,
% 0.69/1.09 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.69/1.09 inference(activate,[status(thm)],['0.19.1.0']),
% 0.69/1.09 [equation_2]).
% 0.69/1.09 cnf('0.27.0.0',plain,
% 0.69/1.09 ( greatest_lower_bound(multiply(b,X1),multiply(identity,X1)) = multiply(identity,X1) ),
% 0.69/1.09 inference(cp,[status(thm)],['0.9.2.0','0.12.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.1','L')]).
% 0.69/1.09 cnf('0.27.0.1',plain,
% 0.69/1.09 ( greatest_lower_bound(multiply(b,X1),X1) = multiply(identity,X1) ),
% 0.69/1.09 inference(reduction,[status(thm)],['0.27.0.0','0.3.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2','L')]).
% 0.69/1.09 cnf('0.27.0.2',plain,
% 0.69/1.09 ( greatest_lower_bound(multiply(b,X1),X1) = X1 ),
% 0.69/1.09 inference(reduction,[status(thm)],['0.27.0.1','0.3.2.0',theory(equality)]),
% 0.69/1.09 [pos('R','L')]).
% 0.69/1.09 cnf('0.27.1.0',plain,
% 0.69/1.09 ( greatest_lower_bound(multiply(b,X1),X1) = X1 ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.27.0.2']),
% 0.69/1.09 [weight('<41,12,9,[0,0,0,1]>')]).
% 0.69/1.09 cnf('0.27.1.1',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,multiply(b,X1)) = X1 ),
% 0.69/1.09 inference(reduction,[status(thm)],['0.27.1.0','0.6.2.0',theory(equality)]),
% 0.69/1.09 [pos('L','L')]).
% 0.69/1.09 cnf('0.27.2.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,multiply(b,X1)) = X1 ),
% 0.69/1.09 inference(orient,[status(thm)],['0.27.1.1',theory(equality)]),
% 0.69/1.09 [u,rule_25]).
% 0.69/1.09 cnf('0.29.0.0',plain,
% 0.69/1.09 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 0.69/1.09 inference(cp,[status(thm)],['0.2.2.0','0.19.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2','L')]).
% 0.69/1.09 cnf('0.29.1.0',plain,
% 0.69/1.09 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.29.0.0']),
% 0.69/1.09 [weight('<41,19,2,[0,0,0,2]>')]).
% 0.69/1.09 cnf('0.29.2.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1 ),
% 0.69/1.09 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.69/1.09 [x,rule_27]).
% 0.69/1.09 cnf('0.46.0.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(greatest_lower_bound(X1,X2),X1) ),
% 0.69/1.09 inference(cp,[status(thm)],['0.29.2.0','0.5.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2','L')]).
% 0.69/1.09 cnf('0.46.0.1',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.69/1.09 inference(reduction,[status(thm)],['0.46.0.0','0.7.2.0',theory(equality)]),
% 0.69/1.09 [pos('R','L')]).
% 0.69/1.09 cnf('0.46.1.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.46.0.1']),
% 0.69/1.09 [weight('<53,29,5,[1,0,0,2]>')]).
% 0.69/1.09 cnf('0.46.2.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2) ),
% 0.69/1.09 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 0.69/1.09 [x,rule_44]).
% 0.69/1.09 cnf('0.133.0.0',plain,
% 0.69/1.09 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = multiply(identity,X1) ),
% 0.69/1.09 inference(cp,[status(thm)],['0.9.2.0','0.14.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.1','L')]).
% 0.69/1.09 cnf('0.133.0.1',plain,
% 0.69/1.09 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.69/1.09 inference(reduction,[status(thm)],['0.133.0.0','0.3.2.0',theory(equality)]),
% 0.69/1.09 [pos('R','L')]).
% 0.69/1.09 cnf('0.133.1.0',plain,
% 0.69/1.09 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.133.0.1']),
% 0.69/1.09 [weight('<71,14,9,[0,0,0,1]>')]).
% 0.69/1.09 cnf('0.133.2.0',plain,
% 0.69/1.09 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.69/1.09 inference(orient,[status(thm)],['0.133.1.0',theory(equality)]),
% 0.69/1.09 [u,rule_131]).
% 0.69/1.09 cnf('0.474.0.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(b,X1),X2)) = greatest_lower_bound(X1,X2) ),
% 0.69/1.09 inference(cp,[status(thm)],['0.7.2.0','0.27.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.1','L')]).
% 0.69/1.09 cnf('0.474.1.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(b,X1),X2)) = greatest_lower_bound(X1,X2) ),
% 0.69/1.09 inference(weigh,[status(thm)],['0.474.0.0']),
% 0.69/1.09 [weight('<87,27,7,[0,0,0,1]>')]).
% 0.69/1.09 cnf('0.474.2.0',plain,
% 0.69/1.09 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(b,X1),X2)) = greatest_lower_bound(X1,X2) ),
% 0.69/1.09 inference(orient,[status(thm)],['0.474.1.0',theory(equality)]),
% 0.69/1.09 [u,rule_470]).
% 0.69/1.09 cnf('1.0.0.0',conjecture,
% 0.69/1.09 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
% 0.69/1.09 file('/tmp/WALDMEISTER_19382_n019',conjecture_1)).
% 0.69/1.09 cnf('1.0.0.1',plain,
% 0.69/1.09 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.0','0.6.2.0',theory(equality)]),
% 0.69/1.09 [pos('R','L')]).
% 0.69/1.09 cnf('1.0.0.2',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(b,a),greatest_lower_bound(c,a)))) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.1','0.8.2.0',theory(equality)]),
% 0.69/1.09 [pos('L','R')]).
% 0.69/1.09 cnf('1.0.0.3',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(multiply(greatest_lower_bound(b,a),greatest_lower_bound(c,a)),multiply(b,c))) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.2','0.6.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2','L')]).
% 0.69/1.09 cnf('1.0.0.4',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(multiply(greatest_lower_bound(b,a),c),multiply(greatest_lower_bound(b,a),a)),multiply(b,c))) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.3','0.10.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2.1','L')]).
% 0.69/1.09 cnf('1.0.0.5',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(multiply(greatest_lower_bound(b,a),c),greatest_lower_bound(multiply(greatest_lower_bound(b,a),a),multiply(b,c)))) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.4','0.7.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2','L')]).
% 0.69/1.09 cnf('1.0.0.6',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(multiply(b,c),multiply(a,c)),greatest_lower_bound(multiply(greatest_lower_bound(b,a),a),multiply(b,c)))) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.5','0.9.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2.1','L')]).
% 0.69/1.09 cnf('1.0.0.7',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(multiply(greatest_lower_bound(b,a),a),multiply(b,c)))) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.6','0.133.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2.1','L')]).
% 0.69/1.09 cnf('1.0.0.8',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(b,a),a)))) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.7','0.6.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2.2','L')]).
% 0.69/1.09 cnf('1.0.0.9',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(c,multiply(greatest_lower_bound(b,a),a))) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.8','0.474.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2','L')]).
% 0.69/1.09 cnf('1.0.0.10',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(multiply(b,a),multiply(a,a)))) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.9','0.9.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2.2','L')]).
% 0.69/1.09 cnf('1.0.0.11',plain,
% 0.69/1.09 ( greatest_lower_bound(a,greatest_lower_bound(c,a)) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.10','0.133.2.0',theory(equality)]),
% 0.69/1.09 [pos('L.2.2','L')]).
% 0.69/1.09 cnf('1.0.0.12',plain,
% 0.69/1.09 ( greatest_lower_bound(a,c) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.11','0.46.2.0',theory(equality)]),
% 0.69/1.09 [pos('L','L')]).
% 0.69/1.09 cnf('1.0.0.13',plain,
% 0.69/1.09 ( greatest_lower_bound(c,a) = greatest_lower_bound(c,a) ),
% 0.69/1.09 inference(reduction,[status(thm)],['1.0.0.12','0.6.2.0',theory(equality)]),
% 0.69/1.09 [pos('L','L')]).
% 0.69/1.09 cnf('1.0.0.14',plain,
% 0.69/1.09 ( $true ),
% 0.69/1.09 inference(trivial,[status(thm)],['1.0.0.13',theory(equality)]),
% 0.69/1.09 [conjecture_1]).
% 0.69/1.09
% 0.69/1.09 Proved Goals:
% 0.69/1.09 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)
% 0.69/1.09 1 goal was specified, which was proved.
% 0.69/1.09 % SZS output end CNFRefutation
% 0.69/1.09 #END OF PROOF
% 0.69/1.09
% 0.69/1.09 Problem WALDMEISTER_19382_n019
% 0.69/1.09 CPs.gen 12988
% 0.69/1.09 CPs.reexp 0
% 0.69/1.09 Select 1809
% 0.69/1.09 R 470
% 0.69/1.09 E 4
% 0.69/1.09 vsize 7.1M
% 0.69/1.09 rss 4.4M
% 0.69/1.09 process.time 0.089s
% 0.69/1.09 wallclock.time 0.093s
% 0.69/1.09 status S
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Waldmeister states: Goal proved.
% 0.69/1.09 % SZS status Unsatisfiable
% 0.69/1.09
% 0.69/1.09 Problem WALDMEISTER_19382_n019
% 0.69/1.09 CPs.gen 558
% 0.69/1.09 CPs.reexp 0
% 0.69/1.09 Select 115
% 0.69/1.09 R 54
% 0.69/1.09 E 2
% 0.69/1.09 vsize 6.5M
% 0.69/1.09 rss 3.8M
% 0.69/1.09 process.time 0.004s
% 0.69/1.09 wallclock.time 0.092s
% 0.69/1.09 status S
%------------------------------------------------------------------------------