TSTP Solution File: GRP178-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP178-1 : 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 12:25:08 EDT 2022
% Result : Unsatisfiable 0.61s 1.13s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP178-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : woody %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 07:40:20 EDT 2022
% 0.12/0.34 % 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
% 0.61/1.13 joined goal: 1 greatest_lower_bound(a,multiply(b,c)) ?= greatest_lower_bound(a,c) to greatest_lower_bound(c,a)
% 0.61/1.13 goal joined
% 0.61/1.13 % SZS status Unsatisfiable
% 0.61/1.13 #START OF PROOF
% 0.61/1.13 % SZS output start CNFRefutation
% 0.61/1.13 cnf('0.1.0.0',axiom,
% 0.61/1.13 ( X1 = multiply(identity,X1) ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.1.1.0',plain,
% 0.61/1.13 ( X1 = multiply(identity,X1) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.61/1.13 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.61/1.13 cnf('0.1.2.0',plain,
% 0.61/1.13 ( multiply(identity,X1) = X1 ),
% 0.61/1.13 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.61/1.13 [x,rule_1]).
% 0.61/1.13 cnf('0.5.0.0',axiom,
% 0.61/1.13 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.5.1.0',plain,
% 0.61/1.13 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.61/1.13 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.61/1.13 cnf('0.5.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 0.61/1.13 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.61/1.13 [x,rule_5]).
% 0.61/1.13 cnf('0.6.0.0',axiom,
% 0.61/1.13 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.6.1.0',plain,
% 0.61/1.13 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.61/1.13 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.61/1.13 cnf('0.6.2.0',plain,
% 0.61/1.13 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.61/1.13 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.61/1.13 [x,rule_6]).
% 0.61/1.13 cnf('0.8.0.0',axiom,
% 0.61/1.13 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.8.1.0',plain,
% 0.61/1.13 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.61/1.13 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.61/1.13 cnf('0.8.2.0',plain,
% 0.61/1.13 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.61/1.13 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.61/1.13 [u,rule_8]).
% 0.61/1.13 cnf('0.9.0.0',axiom,
% 0.61/1.13 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.9.1.0',plain,
% 0.61/1.13 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.61/1.13 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.61/1.13 cnf('0.9.2.0',plain,
% 0.61/1.13 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.13 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.61/1.13 [u,rule_9]).
% 0.61/1.13 cnf('0.10.0.0',axiom,
% 0.61/1.13 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.10.1.0',plain,
% 0.61/1.13 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.61/1.13 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.61/1.13 cnf('0.10.2.0',plain,
% 0.61/1.13 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.61/1.13 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.61/1.13 [u,rule_10]).
% 0.61/1.13 cnf('0.11.0.0',axiom,
% 0.61/1.13 ( multiply(inverse(X1),X1) = identity ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.11.1.0',plain,
% 0.61/1.13 ( multiply(inverse(X1),X1) = identity ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.61/1.13 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.61/1.13 cnf('0.11.2.0',plain,
% 0.61/1.13 ( multiply(inverse(X1),X1) = identity ),
% 0.61/1.13 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.61/1.13 [u,rule_11]).
% 0.61/1.13 cnf('0.12.0.0',axiom,
% 0.61/1.13 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.12.1.0',plain,
% 0.61/1.13 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.61/1.13 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.61/1.13 cnf('0.12.2.0',plain,
% 0.61/1.13 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.61/1.13 inference(activate,[status(thm)],['0.12.1.0']),
% 0.61/1.13 [equation_1]).
% 0.61/1.13 cnf('0.16.0.0',axiom,
% 0.61/1.13 ( least_upper_bound(identity,c) = c ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.16.1.0',plain,
% 0.61/1.13 ( least_upper_bound(identity,c) = c ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.61/1.13 [weight('<15,0,0,[0,0,0,16]>')]).
% 0.61/1.13 cnf('0.16.1.1',plain,
% 0.61/1.13 ( least_upper_bound(c,identity) = c ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.16.1.0','0.12.2.0',theory(equality)]),
% 0.61/1.13 [pos('L','L')]).
% 0.61/1.13 cnf('0.16.2.0',plain,
% 0.61/1.13 ( least_upper_bound(c,identity) = c ),
% 0.61/1.13 inference(orient,[status(thm)],['0.16.1.1',theory(equality)]),
% 0.61/1.13 [u,rule_15]).
% 0.61/1.13 cnf('0.17.0.0',axiom,
% 0.61/1.13 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.17.1.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.61/1.13 [weight('<16,0,0,[0,0,0,17]>')]).
% 0.61/1.13 cnf('0.17.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.61/1.13 inference(activate,[status(thm)],['0.17.1.0']),
% 0.61/1.13 [equation_2]).
% 0.61/1.13 cnf('0.18.0.0',axiom,
% 0.61/1.13 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.18.1.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.61/1.13 [weight('<17,0,0,[0,0,0,18]>')]).
% 0.61/1.13 cnf('0.18.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 0.61/1.13 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 0.61/1.13 [x,rule_16]).
% 0.61/1.13 cnf('0.19.0.0',axiom,
% 0.61/1.13 ( greatest_lower_bound(a,b) = identity ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026')).
% 0.61/1.13 cnf('0.19.1.0',plain,
% 0.61/1.13 ( greatest_lower_bound(a,b) = identity ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.61/1.13 [weight('<18,0,0,[0,0,0,19]>')]).
% 0.61/1.13 cnf('0.19.1.1',plain,
% 0.61/1.13 ( greatest_lower_bound(b,a) = identity ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.19.1.0','0.17.2.0',theory(equality)]),
% 0.61/1.13 [pos('L','L')]).
% 0.61/1.13 cnf('0.19.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(b,a) = identity ),
% 0.61/1.13 inference(orient,[status(thm)],['0.19.1.1',theory(equality)]),
% 0.61/1.13 [u,rule_17]).
% 0.61/1.13 cnf('0.27.0.0',plain,
% 0.61/1.13 ( greatest_lower_bound(multiply(X1,b),multiply(X1,a)) = multiply(X1,identity) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.8.2.0','0.19.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.2','L')]).
% 0.61/1.13 cnf('0.27.1.0',plain,
% 0.61/1.13 ( greatest_lower_bound(multiply(X1,b),multiply(X1,a)) = multiply(X1,identity) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.27.0.0']),
% 0.61/1.13 [weight('<43,19,8,[0,0,0,2]>')]).
% 0.61/1.13 cnf('0.27.2.0',plain,
% 0.61/1.13 ( multiply(X1,identity) = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.61/1.13 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 0.61/1.13 [x,rule_25]).
% 0.61/1.13 cnf('0.36.0.0',plain,
% 0.61/1.13 ( least_upper_bound(multiply(c,X1),multiply(identity,X1)) = multiply(c,X1) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.9.2.0','0.16.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.1','L')]).
% 0.61/1.13 cnf('0.36.0.1',plain,
% 0.61/1.13 ( least_upper_bound(multiply(c,X1),X1) = multiply(c,X1) ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.36.0.0','0.1.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.2','L')]).
% 0.61/1.13 cnf('0.36.1.0',plain,
% 0.61/1.13 ( least_upper_bound(multiply(c,X1),X1) = multiply(c,X1) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.36.0.1']),
% 0.61/1.13 [weight('<53,16,9,[0,0,0,1]>')]).
% 0.61/1.13 cnf('0.36.1.1',plain,
% 0.61/1.13 ( least_upper_bound(X1,multiply(c,X1)) = multiply(c,X1) ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.36.1.0','0.12.2.0',theory(equality)]),
% 0.61/1.13 [pos('L','L')]).
% 0.61/1.13 cnf('0.36.2.0',plain,
% 0.61/1.13 ( least_upper_bound(X1,multiply(c,X1)) = multiply(c,X1) ),
% 0.61/1.13 inference(orient,[status(thm)],['0.36.1.1',theory(equality)]),
% 0.61/1.13 [u,rule_34]).
% 0.61/1.13 cnf('0.37.0.0',plain,
% 0.61/1.13 ( X1 = greatest_lower_bound(X1,multiply(c,X1)) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.5.2.0','0.36.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.2','L')]).
% 0.61/1.13 cnf('0.37.1.0',plain,
% 0.61/1.13 ( X1 = greatest_lower_bound(X1,multiply(c,X1)) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.37.0.0']),
% 0.61/1.13 [weight('<41,36,5,[0,0,0,2]>')]).
% 0.61/1.13 cnf('0.37.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,multiply(c,X1)) = X1 ),
% 0.61/1.13 inference(orient,[status(thm)],['0.37.1.0',theory(equality)]),
% 0.61/1.13 [x,rule_35]).
% 0.61/1.13 cnf('0.48.0.0',plain,
% 0.61/1.13 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.1','L')]).
% 0.61/1.13 cnf('0.48.0.1',plain,
% 0.61/1.13 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.48.0.0','0.1.2.0',theory(equality)]),
% 0.61/1.13 [pos('R','L')]).
% 0.61/1.13 cnf('0.48.1.0',plain,
% 0.61/1.13 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.48.0.1']),
% 0.61/1.13 [weight('<55,11,6,[0,0,0,1]>')]).
% 0.61/1.13 cnf('0.48.2.0',plain,
% 0.61/1.13 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.61/1.13 inference(orient,[status(thm)],['0.48.1.0',theory(equality)]),
% 0.61/1.13 [u,rule_46]).
% 0.61/1.13 cnf('0.49.0.0',plain,
% 0.61/1.13 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.48.2.0','0.48.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.2','L')]).
% 0.61/1.13 cnf('0.49.1.0',plain,
% 0.61/1.13 ( X1 = inverse(inverse(X1)) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.49.0.0']),
% 0.61/1.13 [weight('<19,48,48,[0,0,0,3]>')]).
% 0.61/1.13 cnf('0.49.2.0',plain,
% 0.61/1.13 ( inverse(inverse(X1)) = X1 ),
% 0.61/1.13 inference(orient,[status(thm)],['0.49.1.0',theory(equality)]),
% 0.61/1.13 [x,rule_47]).
% 0.61/1.13 cnf('0.77.0.0',plain,
% 0.61/1.13 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.48.2.0','0.49.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.1','L')]).
% 0.61/1.13 cnf('0.77.1.0',plain,
% 0.61/1.13 ( X1 = multiply(X2,multiply(inverse(X2),X1)) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.77.0.0']),
% 0.61/1.13 [weight('<55,49,48,[0,0,0,1]>')]).
% 0.61/1.13 cnf('0.77.2.0',plain,
% 0.61/1.13 ( multiply(X1,multiply(inverse(X1),X2)) = X2 ),
% 0.61/1.13 inference(orient,[status(thm)],['0.77.1.0',theory(equality)]),
% 0.61/1.13 [x,rule_75]).
% 0.61/1.13 cnf('0.130.0.0',plain,
% 0.61/1.13 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = multiply(identity,X1) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.10.2.0','0.19.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.1','L')]).
% 0.61/1.13 cnf('0.130.0.1',plain,
% 0.61/1.13 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.130.0.0','0.1.2.0',theory(equality)]),
% 0.61/1.13 [pos('R','L')]).
% 0.61/1.13 cnf('0.130.1.0',plain,
% 0.61/1.13 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.130.0.1']),
% 0.61/1.13 [weight('<71,19,10,[0,0,0,1]>')]).
% 0.61/1.13 cnf('0.130.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(multiply(b,X1),multiply(a,X1)) = X1 ),
% 0.61/1.13 inference(orient,[status(thm)],['0.130.1.0',theory(equality)]),
% 0.61/1.13 [u,rule_128]).
% 0.61/1.13 cnf('0.222.0.0',plain,
% 0.61/1.13 ( X1 = multiply(X1,identity) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.77.2.0','0.11.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.2','L')]).
% 0.61/1.13 cnf('0.222.0.1',plain,
% 0.61/1.13 ( X1 = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.222.0.0','0.27.2.0',theory(equality)]),
% 0.61/1.13 [pos('R','L')]).
% 0.61/1.13 cnf('0.222.1.0',plain,
% 0.61/1.13 ( X1 = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.222.0.1']),
% 0.61/1.13 [weight('<71,77,11,[1,0,0,2]>')]).
% 0.61/1.13 cnf('0.222.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(multiply(X1,b),multiply(X1,a)) = X1 ),
% 0.61/1.13 inference(orient,[status(thm)],['0.222.1.0',theory(equality)]),
% 0.61/1.13 [x,rule_220]).
% 0.61/1.13 cnf('0.223.0.0',plain,
% 0.61/1.13 ( multiply(X1,identity) = greatest_lower_bound(multiply(X1,b),multiply(X1,a)) ),
% 0.61/1.13 inference(interreduction_right,[status(thm)],['0.27.2.0'])).
% 0.61/1.13 cnf('0.223.0.1',plain,
% 0.61/1.13 ( multiply(X1,identity) = X1 ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.223.0.0','0.222.2.0',theory(equality)]),
% 0.61/1.13 [pos('R','L')]).
% 0.61/1.13 cnf('0.223.1.0',plain,
% 0.61/1.13 ( multiply(X1,identity) = X1 ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.223.0.1']),
% 0.61/1.13 [weight('<19,27,222,[0,0,0,0]>')]).
% 0.61/1.13 cnf('0.223.2.0',plain,
% 0.61/1.13 ( multiply(X1,identity) = X1 ),
% 0.61/1.13 inference(orient,[status(thm)],['0.223.1.0',theory(equality)]),
% 0.61/1.13 [u,rule_221]).
% 0.61/1.13 cnf('0.324.0.0',plain,
% 0.61/1.13 ( multiply(inverse(c),X1) = greatest_lower_bound(multiply(inverse(c),X1),X1) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.37.2.0','0.77.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.2','L')]).
% 0.61/1.13 cnf('0.324.1.0',plain,
% 0.61/1.13 ( multiply(inverse(c),X1) = greatest_lower_bound(multiply(inverse(c),X1),X1) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.324.0.0']),
% 0.61/1.13 [weight('<76,77,37,[0,0,0,2]>')]).
% 0.61/1.13 cnf('0.324.1.1',plain,
% 0.61/1.13 ( multiply(inverse(c),X1) = greatest_lower_bound(X1,multiply(inverse(c),X1)) ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.324.1.0','0.17.2.0',theory(equality)]),
% 0.61/1.13 [pos('R','L')]).
% 0.61/1.13 cnf('0.324.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,multiply(inverse(c),X1)) = multiply(inverse(c),X1) ),
% 0.61/1.13 inference(orient,[status(thm)],['0.324.1.1',theory(equality)]),
% 0.61/1.13 [x,rule_322]).
% 0.61/1.13 cnf('0.325.0.0',plain,
% 0.61/1.13 ( multiply(inverse(c),c) = greatest_lower_bound(c,identity) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.324.2.0','0.11.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.2','L')]).
% 0.61/1.13 cnf('0.325.0.1',plain,
% 0.61/1.13 ( identity = greatest_lower_bound(c,identity) ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.325.0.0','0.11.2.0',theory(equality)]),
% 0.61/1.13 [pos('L','L')]).
% 0.61/1.13 cnf('0.325.1.0',plain,
% 0.61/1.13 ( identity = greatest_lower_bound(c,identity) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.325.0.1']),
% 0.61/1.13 [weight('<19,324,11,[1,0,0,2]>')]).
% 0.61/1.13 cnf('0.325.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(c,identity) = identity ),
% 0.61/1.13 inference(orient,[status(thm)],['0.325.1.0',theory(equality)]),
% 0.61/1.13 [x,rule_323]).
% 0.61/1.13 cnf('0.326.0.0',plain,
% 0.61/1.13 ( greatest_lower_bound(multiply(X1,c),multiply(X1,identity)) = multiply(X1,identity) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.8.2.0','0.325.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.2','L')]).
% 0.61/1.13 cnf('0.326.0.1',plain,
% 0.61/1.13 ( greatest_lower_bound(multiply(X1,c),X1) = multiply(X1,identity) ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.326.0.0','0.223.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.2','L')]).
% 0.61/1.13 cnf('0.326.0.2',plain,
% 0.61/1.13 ( greatest_lower_bound(multiply(X1,c),X1) = X1 ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.326.0.1','0.223.2.0',theory(equality)]),
% 0.61/1.13 [pos('R','L')]).
% 0.61/1.13 cnf('0.326.1.0',plain,
% 0.61/1.13 ( greatest_lower_bound(multiply(X1,c),X1) = X1 ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.326.0.2']),
% 0.61/1.13 [weight('<41,325,8,[0,0,0,2]>')]).
% 0.61/1.13 cnf('0.326.1.1',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,multiply(X1,c)) = X1 ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.326.1.0','0.17.2.0',theory(equality)]),
% 0.61/1.13 [pos('L','L')]).
% 0.61/1.13 cnf('0.326.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,multiply(X1,c)) = X1 ),
% 0.61/1.13 inference(orient,[status(thm)],['0.326.1.1',theory(equality)]),
% 0.61/1.13 [u,rule_324]).
% 0.61/1.13 cnf('0.481.0.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,c),X2)) = greatest_lower_bound(X1,X2) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.18.2.0','0.326.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.1','L')]).
% 0.61/1.13 cnf('0.481.1.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,c),X2)) = greatest_lower_bound(X1,X2) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.481.0.0']),
% 0.61/1.13 [weight('<87,326,18,[0,0,0,1]>')]).
% 0.61/1.13 cnf('0.481.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,c),X2)) = greatest_lower_bound(X1,X2) ),
% 0.61/1.13 inference(orient,[status(thm)],['0.481.1.0',theory(equality)]),
% 0.61/1.13 [u,rule_477]).
% 0.61/1.13 cnf('0.526.0.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,c))) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.481.2.0','0.17.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.2','L')]).
% 0.61/1.13 cnf('0.526.1.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,c))) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.526.0.0']),
% 0.61/1.13 [weight('<87,481,17,[1,0,0,2]>')]).
% 0.61/1.13 cnf('0.526.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,c))) = greatest_lower_bound(X1,X2) ),
% 0.61/1.13 inference(orient,[status(thm)],['0.526.1.0',theory(equality)]),
% 0.61/1.13 [x,rule_522]).
% 0.61/1.13 cnf('0.527.0.0',plain,
% 0.61/1.13 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
% 0.61/1.13 inference(cp,[status(thm)],['0.526.2.0','0.130.2.0',theory(equality)]),
% 0.61/1.13 [pos('L.2','L')]).
% 0.61/1.13 cnf('0.527.1.0',plain,
% 0.61/1.13 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
% 0.61/1.13 inference(weigh,[status(thm)],['0.527.0.0']),
% 0.61/1.13 [weight('<53,526,130,[1,0,0,2]>')]).
% 0.61/1.13 cnf('0.527.1.1',plain,
% 0.61/1.13 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(c,a) ),
% 0.61/1.13 inference(reduction,[status(thm)],['0.527.1.0','0.17.2.0',theory(equality)]),
% 0.61/1.13 [pos('R','L')]).
% 0.61/1.13 cnf('0.527.2.0',plain,
% 0.61/1.13 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(c,a) ),
% 0.61/1.13 inference(orient,[status(thm)],['0.527.1.1',theory(equality)]),
% 0.61/1.13 [u,rule_523]).
% 0.61/1.13 cnf('1.0.0.0',conjecture,
% 0.61/1.13 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c) ),
% 0.61/1.13 file('/tmp/WALDMEISTER_882_n026',conjecture_1)).
% 0.61/1.13 cnf('1.0.0.1',plain,
% 0.61/1.13 ( greatest_lower_bound(c,a) = greatest_lower_bound(a,c) ),
% 0.61/1.13 inference(reduction,[status(thm)],['1.0.0.0','0.527.2.0',theory(equality)]),
% 0.61/1.13 [pos('L','L')]).
% 0.61/1.13 cnf('1.0.0.2',plain,
% 0.61/1.13 ( greatest_lower_bound(c,a) = greatest_lower_bound(c,a) ),
% 0.61/1.13 inference(reduction,[status(thm)],['1.0.0.1','0.17.2.0',theory(equality)]),
% 0.61/1.13 [pos('R','L')]).
% 0.61/1.13 cnf('1.0.0.3',plain,
% 0.61/1.13 ( $true ),
% 0.61/1.13 inference(trivial,[status(thm)],['1.0.0.2',theory(equality)]),
% 0.61/1.13 [conjecture_1]).
% 0.61/1.13
% 0.61/1.13 Proved Goals:
% 0.61/1.13 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)
% 0.61/1.13 1 goal was specified, which was proved.
% 0.61/1.13 % SZS output end CNFRefutation
% 0.61/1.13 #END OF PROOF
% 0.61/1.13
% 0.61/1.13 Problem WALDMEISTER_882_n026
% 0.61/1.13 CPs.gen 22134
% 0.61/1.13 CPs.reexp 0
% 0.61/1.13 Select 3024
% 0.61/1.13 R 523
% 0.61/1.13 E 4
% 0.61/1.13 vsize 7.2M
% 0.61/1.13 rss 4.4M
% 0.61/1.13 process.time 0.128s
% 0.61/1.13 wallclock.time 0.134s
% 0.61/1.13 status S
% 0.61/1.13
% 0.61/1.13
% 0.61/1.13 Waldmeister states: Goal proved.
% 0.61/1.13 % SZS status Unsatisfiable
% 0.61/1.13
% 0.61/1.13 Problem WALDMEISTER_882_n026
% 0.61/1.13 CPs.gen 1006
% 0.61/1.13 CPs.reexp 0
% 0.61/1.13 Select 230
% 0.61/1.13 R 91
% 0.61/1.13 E 2
% 0.61/1.13 vsize 6.5M
% 0.61/1.13 rss 3.8M
% 0.61/1.13 process.time 0.007s
% 0.61/1.13 wallclock.time 0.134s
% 0.61/1.13 status S
%------------------------------------------------------------------------------