TSTP Solution File: GRP178-2 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP178-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n032.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 12:25:08 EDT 2022
% Result : Unsatisfiable 0.47s 0.93s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP178-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.10 % Command : woody %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Mon Jun 13 08:11:11 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.42/0.84 ********************************************************************************
% 0.42/0.84 * W A L D M E I S T E R \| \ / \|/ *
% 0.42/0.84 * |/ | \/ | *
% 0.42/0.84 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.42/0.84 * A. Jaeger and B. Loechner | | *
% 0.42/0.84 * <waldmeister@informatik.uni-kl.de> | *
% 0.42/0.84 ********************************************************************************
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 Goals:
% 0.42/0.84 ------
% 0.42/0.84
% 0.42/0.84 ( 1) greatest_lower_bound(a,multiply(b,c)) ?=? greatest_lower_bound(a,c)
% 0.42/0.84
% 0.42/0.84 Detected structure: VerbandsgeordneteGruppe
% 0.42/0.84 ********************************************************************************
% 0.42/0.84 ****************************** COMPLETION - PROOF ******************************
% 0.42/0.84 ********************************************************************************
% 0.42/0.84
% 0.47/0.93 joined goal: 1 greatest_lower_bound(a,multiply(b,c)) ?= greatest_lower_bound(a,c) to greatest_lower_bound(c,a)
% 0.47/0.93 goal joined
% 0.47/0.93 % SZS status Unsatisfiable
% 0.47/0.93 #START OF PROOF
% 0.47/0.93 % SZS output start CNFRefutation
% 0.47/0.93 cnf('0.1.0.0',axiom,
% 0.47/0.93 ( X1 = multiply(identity,X1) ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.1.1.0',plain,
% 0.47/0.93 ( X1 = multiply(identity,X1) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.47/0.93 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.47/0.93 cnf('0.1.2.0',plain,
% 0.47/0.93 ( multiply(identity,X1) = X1 ),
% 0.47/0.93 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_1]).
% 0.47/0.93 cnf('0.3.0.0',axiom,
% 0.47/0.93 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.3.1.0',plain,
% 0.47/0.93 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.47/0.93 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.47/0.93 cnf('0.3.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 0.47/0.93 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_3]).
% 0.47/0.93 cnf('0.5.0.0',axiom,
% 0.47/0.93 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.5.1.0',plain,
% 0.47/0.93 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.47/0.93 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.47/0.93 cnf('0.5.2.0',plain,
% 0.47/0.93 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 0.47/0.93 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_5]).
% 0.47/0.93 cnf('0.6.0.0',axiom,
% 0.47/0.93 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.6.1.0',plain,
% 0.47/0.93 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.47/0.93 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.47/0.93 cnf('0.6.2.0',plain,
% 0.47/0.93 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.47/0.93 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_6]).
% 0.47/0.93 cnf('0.7.0.0',axiom,
% 0.47/0.93 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.7.1.0',plain,
% 0.47/0.93 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.47/0.93 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.47/0.93 cnf('0.7.2.0',plain,
% 0.47/0.93 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.47/0.93 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.47/0.93 [u,rule_7]).
% 0.47/0.93 cnf('0.9.0.0',axiom,
% 0.47/0.93 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.9.1.0',plain,
% 0.47/0.93 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.47/0.93 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.47/0.93 cnf('0.9.2.0',plain,
% 0.47/0.93 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.47/0.93 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.47/0.93 [u,rule_9]).
% 0.47/0.93 cnf('0.11.0.0',axiom,
% 0.47/0.93 ( multiply(inverse(X1),X1) = identity ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.11.1.0',plain,
% 0.47/0.93 ( multiply(inverse(X1),X1) = identity ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.47/0.93 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.47/0.93 cnf('0.11.2.0',plain,
% 0.47/0.93 ( multiply(inverse(X1),X1) = identity ),
% 0.47/0.93 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.47/0.93 [u,rule_11]).
% 0.47/0.93 cnf('0.12.0.0',axiom,
% 0.47/0.93 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.12.1.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.47/0.93 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.47/0.93 cnf('0.12.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.47/0.93 inference(activate,[status(thm)],['0.12.1.0']),
% 0.47/0.93 [equation_1]).
% 0.47/0.93 cnf('0.13.0.0',axiom,
% 0.47/0.93 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.13.1.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.47/0.93 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.47/0.93 cnf('0.13.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 0.47/0.93 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_12]).
% 0.47/0.93 cnf('0.16.0.0',axiom,
% 0.47/0.93 ( greatest_lower_bound(identity,c) = identity ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.16.1.0',plain,
% 0.47/0.93 ( greatest_lower_bound(identity,c) = identity ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.47/0.93 [weight('<15,0,0,[0,0,0,16]>')]).
% 0.47/0.93 cnf('0.16.1.1',plain,
% 0.47/0.93 ( greatest_lower_bound(c,identity) = identity ),
% 0.47/0.93 inference(reduction,[status(thm)],['0.16.1.0','0.12.2.0',theory(equality)]),
% 0.47/0.93 [pos('L','L')]).
% 0.47/0.93 cnf('0.16.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(c,identity) = identity ),
% 0.47/0.93 inference(orient,[status(thm)],['0.16.1.1',theory(equality)]),
% 0.47/0.93 [u,rule_15]).
% 0.47/0.93 cnf('0.17.0.0',axiom,
% 0.47/0.93 ( greatest_lower_bound(a,b) = identity ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.17.1.0',plain,
% 0.47/0.93 ( greatest_lower_bound(a,b) = identity ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.47/0.93 [weight('<16,0,0,[0,0,0,17]>')]).
% 0.47/0.93 cnf('0.17.1.1',plain,
% 0.47/0.93 ( greatest_lower_bound(b,a) = identity ),
% 0.47/0.93 inference(reduction,[status(thm)],['0.17.1.0','0.12.2.0',theory(equality)]),
% 0.47/0.93 [pos('L','L')]).
% 0.47/0.93 cnf('0.17.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(b,a) = identity ),
% 0.47/0.93 inference(orient,[status(thm)],['0.17.1.1',theory(equality)]),
% 0.47/0.93 [u,rule_16]).
% 0.47/0.93 cnf('0.18.0.0',axiom,
% 0.47/0.93 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032')).
% 0.47/0.93 cnf('0.18.1.0',plain,
% 0.47/0.93 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.47/0.93 [weight('<17,0,0,[0,0,0,18]>')]).
% 0.47/0.93 cnf('0.18.2.0',plain,
% 0.47/0.93 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.47/0.93 inference(activate,[status(thm)],['0.18.1.0']),
% 0.47/0.93 [equation_2]).
% 0.47/0.93 cnf('0.24.0.0',plain,
% 0.47/0.93 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.5.2.0','0.12.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.2','L')]).
% 0.47/0.93 cnf('0.24.1.0',plain,
% 0.47/0.93 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.24.0.0']),
% 0.47/0.93 [weight('<41,12,5,[0,0,0,2]>')]).
% 0.47/0.93 cnf('0.24.2.0',plain,
% 0.47/0.93 ( least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1 ),
% 0.47/0.93 inference(orient,[status(thm)],['0.24.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_22]).
% 0.47/0.93 cnf('0.30.0.0',plain,
% 0.47/0.93 ( greatest_lower_bound(multiply(X1,b),multiply(X1,a)) = multiply(X1,identity) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.7.2.0','0.17.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.2','L')]).
% 0.47/0.93 cnf('0.30.1.0',plain,
% 0.47/0.93 ( greatest_lower_bound(multiply(X1,b),multiply(X1,a)) = multiply(X1,identity) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.30.0.0']),
% 0.47/0.93 [weight('<43,17,7,[0,0,0,2]>')]).
% 0.47/0.93 cnf('0.30.2.0',plain,
% 0.47/0.93 ( multiply(X1,identity) = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.47/0.93 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_28]).
% 0.47/0.93 cnf('0.50.0.0',plain,
% 0.47/0.93 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.1','L')]).
% 0.47/0.93 cnf('0.50.0.1',plain,
% 0.47/0.93 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.47/0.93 inference(reduction,[status(thm)],['0.50.0.0','0.1.2.0',theory(equality)]),
% 0.47/0.93 [pos('R','L')]).
% 0.47/0.93 cnf('0.50.1.0',plain,
% 0.47/0.93 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.50.0.1']),
% 0.47/0.93 [weight('<55,11,6,[0,0,0,1]>')]).
% 0.47/0.93 cnf('0.50.2.0',plain,
% 0.47/0.93 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.47/0.93 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 0.47/0.93 [u,rule_48]).
% 0.47/0.93 cnf('0.51.0.0',plain,
% 0.47/0.93 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.50.2.0','0.50.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.2','L')]).
% 0.47/0.93 cnf('0.51.1.0',plain,
% 0.47/0.93 ( X1 = inverse(inverse(X1)) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.51.0.0']),
% 0.47/0.93 [weight('<19,50,50,[0,0,0,3]>')]).
% 0.47/0.93 cnf('0.51.2.0',plain,
% 0.47/0.93 ( inverse(inverse(X1)) = X1 ),
% 0.47/0.93 inference(orient,[status(thm)],['0.51.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_49]).
% 0.47/0.93 cnf('0.79.0.0',plain,
% 0.47/0.93 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.50.2.0','0.51.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.1','L')]).
% 0.47/0.93 cnf('0.79.1.0',plain,
% 0.47/0.93 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.79.0.0']),
% 0.47/0.93 [weight('<55,51,50,[0,0,0,1]>')]).
% 0.47/0.93 cnf('0.79.2.0',plain,
% 0.47/0.93 ( multiply(X1,multiply(inverse(X1),X2)) = X2 ),
% 0.47/0.93 inference(orient,[status(thm)],['0.79.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_77]).
% 0.47/0.93 cnf('0.132.0.0',plain,
% 0.47/0.93 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = multiply(identity,X1) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.9.2.0','0.17.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.1','L')]).
% 0.47/0.93 cnf('0.132.0.1',plain,
% 0.47/0.93 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.47/0.93 inference(reduction,[status(thm)],['0.132.0.0','0.1.2.0',theory(equality)]),
% 0.47/0.93 [pos('R','L')]).
% 0.47/0.93 cnf('0.132.1.0',plain,
% 0.47/0.93 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.132.0.1']),
% 0.47/0.93 [weight('<71,17,9,[0,0,0,1]>')]).
% 0.47/0.93 cnf('0.132.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.47/0.93 inference(orient,[status(thm)],['0.132.1.0',theory(equality)]),
% 0.47/0.93 [u,rule_130]).
% 0.47/0.93 cnf('0.256.0.0',plain,
% 0.47/0.93 ( X1 = multiply(X1,identity) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.79.2.0','0.11.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.2','L')]).
% 0.47/0.93 cnf('0.256.0.1',plain,
% 0.47/0.93 ( X1 = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.47/0.93 inference(reduction,[status(thm)],['0.256.0.0','0.30.2.0',theory(equality)]),
% 0.47/0.93 [pos('R','L')]).
% 0.47/0.93 cnf('0.256.1.0',plain,
% 0.47/0.93 ( X1 = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.256.0.1']),
% 0.47/0.93 [weight('<71,79,11,[1,0,0,2]>')]).
% 0.47/0.93 cnf('0.256.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(multiply(X1,b),multiply(X1,a)) = X1 ),
% 0.47/0.93 inference(orient,[status(thm)],['0.256.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_254]).
% 0.47/0.93 cnf('0.257.0.0',plain,
% 0.47/0.93 ( multiply(X1,identity) = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.47/0.93 inference(interreduction_right,[status(thm)],['0.30.2.0'])).
% 0.47/0.93 cnf('0.257.0.1',plain,
% 0.47/0.93 ( multiply(X1,identity) = X1 ),
% 0.47/0.93 inference(reduction,[status(thm)],['0.257.0.0','0.256.2.0',theory(equality)]),
% 0.47/0.93 [pos('R','L')]).
% 0.47/0.93 cnf('0.257.1.0',plain,
% 0.47/0.93 ( multiply(X1,identity) = X1 ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.257.0.1']),
% 0.47/0.93 [weight('<19,30,256,[0,0,0,0]>')]).
% 0.47/0.93 cnf('0.257.2.0',plain,
% 0.47/0.93 ( multiply(X1,identity) = X1 ),
% 0.47/0.93 inference(orient,[status(thm)],['0.257.1.0',theory(equality)]),
% 0.47/0.93 [u,rule_255]).
% 0.47/0.93 cnf('0.416.0.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.13.2.0','0.3.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.1','L')]).
% 0.47/0.93 cnf('0.416.1.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.416.0.0']),
% 0.47/0.93 [weight('<87,13,3,[1,0,0,1]>')]).
% 0.47/0.93 cnf('0.416.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3) ),
% 0.47/0.93 inference(orient,[status(thm)],['0.416.1.0',theory(equality)]),
% 0.47/0.93 [u,rule_412]).
% 0.47/0.93 cnf('0.417.0.0',plain,
% 0.47/0.93 ( greatest_lower_bound(multiply(X1,c),multiply(X1,identity)) = multiply(X1,identity) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.7.2.0','0.16.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.2','L')]).
% 0.47/0.93 cnf('0.417.1.0',plain,
% 0.47/0.93 ( greatest_lower_bound(multiply(X1,c),multiply(X1,identity)) = multiply(X1,identity) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.417.0.0']),
% 0.47/0.93 [weight('<87,16,7,[0,0,0,2]>')]).
% 0.47/0.93 cnf('0.417.1.1',plain,
% 0.47/0.93 ( greatest_lower_bound(multiply(X1,c),X1) = multiply(X1,identity) ),
% 0.47/0.93 inference(reduction,[status(thm)],['0.417.1.0','0.257.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.2','L')]).
% 0.47/0.93 cnf('0.417.1.2',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,multiply(X1,c)) = multiply(X1,identity) ),
% 0.47/0.93 inference(reduction,[status(thm)],['0.417.1.1','0.12.2.0',theory(equality)]),
% 0.47/0.93 [pos('L','L')]).
% 0.47/0.93 cnf('0.417.1.3',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,multiply(X1,c)) = X1 ),
% 0.47/0.93 inference(reduction,[status(thm)],['0.417.1.2','0.257.2.0',theory(equality)]),
% 0.47/0.93 [pos('R','L')]).
% 0.47/0.93 cnf('0.417.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,multiply(X1,c)) = X1 ),
% 0.47/0.93 inference(orient,[status(thm)],['0.417.1.3',theory(equality)]),
% 0.47/0.93 [u,rule_413]).
% 0.47/0.93 cnf('0.418.0.0',plain,
% 0.47/0.93 ( multiply(X1,c) = least_upper_bound(multiply(X1,c),X1) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.24.2.0','0.417.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.2','L')]).
% 0.47/0.93 cnf('0.418.1.0',plain,
% 0.47/0.93 ( multiply(X1,c) = least_upper_bound(multiply(X1,c),X1) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.418.0.0']),
% 0.47/0.93 [weight('<53,417,24,[0,0,0,2]>')]).
% 0.47/0.93 cnf('0.418.1.1',plain,
% 0.47/0.93 ( multiply(X1,c) = least_upper_bound(X1,multiply(X1,c)) ),
% 0.47/0.93 inference(reduction,[status(thm)],['0.418.1.0','0.18.2.0',theory(equality)]),
% 0.47/0.93 [pos('R','L')]).
% 0.47/0.93 cnf('0.418.2.0',plain,
% 0.47/0.93 ( least_upper_bound(X1,multiply(X1,c)) = multiply(X1,c) ),
% 0.47/0.93 inference(orient,[status(thm)],['0.418.1.1',theory(equality)]),
% 0.47/0.93 [x,rule_414]).
% 0.47/0.93 cnf('0.511.0.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,X3))) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.416.2.0','0.12.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.2','L')]).
% 0.47/0.93 cnf('0.511.1.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,X3))) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.511.0.0']),
% 0.47/0.93 [weight('<87,416,12,[1,0,0,2]>')]).
% 0.47/0.93 cnf('0.511.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,X3))) = greatest_lower_bound(X1,X2) ),
% 0.47/0.93 inference(orient,[status(thm)],['0.511.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_507]).
% 0.47/0.93 cnf('0.555.0.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,c))) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.511.2.0','0.418.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.2.2','L')]).
% 0.47/0.93 cnf('0.555.1.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,c))) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.555.0.0']),
% 0.47/0.93 [weight('<87,511,418,[1,0,0,4]>')]).
% 0.47/0.93 cnf('0.555.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,c))) = greatest_lower_bound(X1,X2) ),
% 0.47/0.93 inference(orient,[status(thm)],['0.555.1.0',theory(equality)]),
% 0.47/0.93 [x,rule_551]).
% 0.47/0.93 cnf('0.556.0.0',plain,
% 0.47/0.93 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
% 0.47/0.93 inference(cp,[status(thm)],['0.555.2.0','0.132.2.0',theory(equality)]),
% 0.47/0.93 [pos('L.2','L')]).
% 0.47/0.93 cnf('0.556.1.0',plain,
% 0.47/0.93 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
% 0.47/0.93 inference(weigh,[status(thm)],['0.556.0.0']),
% 0.47/0.93 [weight('<53,555,132,[1,0,0,2]>')]).
% 0.47/0.93 cnf('0.556.1.1',plain,
% 0.47/0.93 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(c,a) ),
% 0.47/0.93 inference(reduction,[status(thm)],['0.556.1.0','0.12.2.0',theory(equality)]),
% 0.47/0.93 [pos('R','L')]).
% 0.47/0.93 cnf('0.556.2.0',plain,
% 0.47/0.93 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(c,a) ),
% 0.47/0.93 inference(orient,[status(thm)],['0.556.1.1',theory(equality)]),
% 0.47/0.93 [u,rule_552]).
% 0.47/0.93 cnf('1.0.0.0',conjecture,
% 0.47/0.93 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
% 0.47/0.93 file('/tmp/WALDMEISTER_21421_n032',conjecture_1)).
% 0.47/0.93 cnf('1.0.0.1',plain,
% 0.47/0.93 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(c,a) ),
% 0.47/0.93 inference(reduction,[status(thm)],['1.0.0.0','0.12.2.0',theory(equality)]),
% 0.47/0.93 [pos('R','L')]).
% 0.47/0.93 cnf('1.0.0.2',plain,
% 0.47/0.93 ( greatest_lower_bound(c,a) = greatest_lower_bound(c,a) ),
% 0.47/0.93 inference(reduction,[status(thm)],['1.0.0.1','0.556.2.0',theory(equality)]),
% 0.47/0.93 [pos('L','L')]).
% 0.47/0.93 cnf('1.0.0.3',plain,
% 0.47/0.93 ( $true ),
% 0.47/0.93 inference(trivial,[status(thm)],['1.0.0.2',theory(equality)]),
% 0.47/0.93 [conjecture_1]).
% 0.47/0.93
% 0.47/0.93 Proved Goals:
% 0.47/0.93 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)
% 0.47/0.93 1 goal was specified, which was proved.
% 0.47/0.93 % SZS output end CNFRefutation
% 0.47/0.93 #END OF PROOF
% 0.47/0.93
% 0.47/0.93 Problem WALDMEISTER_21421_n032
% 0.47/0.93 CPs.gen 24103
% 0.47/0.93 CPs.reexp 0
% 0.47/0.93 Select 3078
% 0.47/0.93 R 552
% 0.47/0.93 E 4
% 0.47/0.93 vsize 6.8M
% 0.47/0.93 rss 4.1M
% 0.47/0.93 process.time 0.088s
% 0.47/0.93 wallclock.time 0.094s
% 0.47/0.93 status S
% 0.47/0.93
% 0.47/0.93
% 0.47/0.93 Waldmeister states: Goal proved.
% 0.47/0.93 % SZS status Unsatisfiable
% 0.47/0.93
% 0.47/0.93 Problem WALDMEISTER_21421_n032
% 0.47/0.93 CPs.gen 1015
% 0.47/0.93 CPs.reexp 0
% 0.47/0.93 Select 230
% 0.47/0.93 R 92
% 0.47/0.93 E 2
% 0.47/0.93 vsize 6.5M
% 0.47/0.93 rss 3.8M
% 0.47/0.93 process.time 0.006s
% 0.47/0.93 wallclock.time 0.094s
% 0.47/0.93 status S
%------------------------------------------------------------------------------