TSTP Solution File: GRP177-2 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP177-2 : 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 2.13s 2.56s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP177-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % 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 14:38:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.60/1.01 ********************************************************************************
% 0.60/1.01 * W A L D M E I S T E R \| \ / \|/ *
% 0.60/1.01 * |/ | \/ | *
% 0.60/1.01 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.60/1.01 * A. Jaeger and B. Loechner | | *
% 0.60/1.01 * <waldmeister@informatik.uni-kl.de> | *
% 0.60/1.01 ********************************************************************************
% 0.60/1.01
% 0.60/1.01
% 0.60/1.01 Goals:
% 0.60/1.01 ------
% 0.60/1.01
% 0.60/1.01 ( 1) 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))
% 0.60/1.01
% 0.60/1.01 Detected structure: VerbandsgeordneteGruppe
% 0.60/1.01 ********************************************************************************
% 0.60/1.01 ****************************** COMPLETION - PROOF ******************************
% 0.60/1.01 ********************************************************************************
% 0.60/1.01
% 2.13/2.56 joined goal: 1 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)) to greatest_lower_bound(a,multiply(b,c))
% 2.13/2.56 goal joined
% 2.13/2.56 % SZS status Unsatisfiable
% 2.13/2.56 #START OF PROOF
% 2.13/2.56 % SZS output start CNFRefutation
% 2.13/2.56 cnf('0.1.0.0',axiom,
% 2.13/2.56 ( X1 = multiply(identity,X1) ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026')).
% 2.13/2.56 cnf('0.1.1.0',plain,
% 2.13/2.56 ( X1 = multiply(identity,X1) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.1.0.0']),
% 2.13/2.56 [weight('<0,0,0,[0,0,0,1]>')]).
% 2.13/2.56 cnf('0.1.2.0',plain,
% 2.13/2.56 ( multiply(identity,X1) = X1 ),
% 2.13/2.56 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 2.13/2.56 [x,rule_1]).
% 2.13/2.56 cnf('0.2.0.0',axiom,
% 2.13/2.56 ( X1 = greatest_lower_bound(X1,X1) ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026')).
% 2.13/2.56 cnf('0.2.1.0',plain,
% 2.13/2.56 ( X1 = greatest_lower_bound(X1,X1) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.2.0.0']),
% 2.13/2.56 [weight('<1,0,0,[0,0,0,2]>')]).
% 2.13/2.56 cnf('0.2.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,X1) = X1 ),
% 2.13/2.56 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 2.13/2.56 [x,rule_2]).
% 2.13/2.56 cnf('0.6.0.0',axiom,
% 2.13/2.56 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026')).
% 2.13/2.56 cnf('0.6.1.0',plain,
% 2.13/2.56 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.6.0.0']),
% 2.13/2.56 [weight('<5,0,0,[0,0,0,6]>')]).
% 2.13/2.56 cnf('0.6.2.0',plain,
% 2.13/2.56 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 2.13/2.56 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 2.13/2.56 [x,rule_6]).
% 2.13/2.56 cnf('0.7.0.0',axiom,
% 2.13/2.56 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026')).
% 2.13/2.56 cnf('0.7.1.0',plain,
% 2.13/2.56 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.7.0.0']),
% 2.13/2.56 [weight('<6,0,0,[0,0,0,7]>')]).
% 2.13/2.56 cnf('0.7.2.0',plain,
% 2.13/2.56 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 2.13/2.56 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 2.13/2.56 [u,rule_7]).
% 2.13/2.56 cnf('0.9.0.0',axiom,
% 2.13/2.56 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026')).
% 2.13/2.56 cnf('0.9.1.0',plain,
% 2.13/2.56 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.9.0.0']),
% 2.13/2.56 [weight('<8,0,0,[0,0,0,9]>')]).
% 2.13/2.56 cnf('0.9.2.0',plain,
% 2.13/2.56 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 2.13/2.56 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 2.13/2.56 [u,rule_9]).
% 2.13/2.56 cnf('0.11.0.0',axiom,
% 2.13/2.56 ( multiply(inverse(X1),X1) = identity ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026')).
% 2.13/2.56 cnf('0.11.1.0',plain,
% 2.13/2.56 ( multiply(inverse(X1),X1) = identity ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.11.0.0']),
% 2.13/2.56 [weight('<10,0,0,[0,0,0,11]>')]).
% 2.13/2.56 cnf('0.11.2.0',plain,
% 2.13/2.56 ( multiply(inverse(X1),X1) = identity ),
% 2.13/2.56 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 2.13/2.56 [u,rule_11]).
% 2.13/2.56 cnf('0.12.0.0',axiom,
% 2.13/2.56 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026')).
% 2.13/2.56 cnf('0.12.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.12.0.0']),
% 2.13/2.56 [weight('<11,0,0,[0,0,0,12]>')]).
% 2.13/2.56 cnf('0.12.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 2.13/2.56 inference(activate,[status(thm)],['0.12.1.0']),
% 2.13/2.56 [equation_1]).
% 2.13/2.56 cnf('0.13.0.0',axiom,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026')).
% 2.13/2.56 cnf('0.13.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.13.0.0']),
% 2.13/2.56 [weight('<12,0,0,[0,0,0,13]>')]).
% 2.13/2.56 cnf('0.13.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 2.13/2.56 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 2.13/2.56 [x,rule_12]).
% 2.13/2.56 cnf('0.14.0.0',axiom,
% 2.13/2.56 ( greatest_lower_bound(identity,a) = identity ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026')).
% 2.13/2.56 cnf('0.14.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(identity,a) = identity ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.14.0.0']),
% 2.13/2.56 [weight('<13,0,0,[0,0,0,14]>')]).
% 2.13/2.56 cnf('0.14.1.1',plain,
% 2.13/2.56 ( greatest_lower_bound(a,identity) = identity ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.14.1.0','0.12.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('0.14.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(a,identity) = identity ),
% 2.13/2.56 inference(orient,[status(thm)],['0.14.1.1',theory(equality)]),
% 2.13/2.56 [u,rule_13]).
% 2.13/2.56 cnf('0.15.0.0',axiom,
% 2.13/2.56 ( greatest_lower_bound(identity,b) = identity ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026')).
% 2.13/2.56 cnf('0.15.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(identity,b) = identity ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.15.0.0']),
% 2.13/2.56 [weight('<14,0,0,[0,0,0,15]>')]).
% 2.13/2.56 cnf('0.15.1.1',plain,
% 2.13/2.56 ( greatest_lower_bound(b,identity) = identity ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.15.1.0','0.12.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('0.15.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(b,identity) = identity ),
% 2.13/2.56 inference(orient,[status(thm)],['0.15.1.1',theory(equality)]),
% 2.13/2.56 [u,rule_14]).
% 2.13/2.56 cnf('0.16.0.0',axiom,
% 2.13/2.56 ( greatest_lower_bound(identity,c) = identity ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026')).
% 2.13/2.56 cnf('0.16.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(identity,c) = identity ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.16.0.0']),
% 2.13/2.56 [weight('<15,0,0,[0,0,0,16]>')]).
% 2.13/2.56 cnf('0.16.1.1',plain,
% 2.13/2.56 ( greatest_lower_bound(c,identity) = identity ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.16.1.0','0.12.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('0.16.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(c,identity) = identity ),
% 2.13/2.56 inference(orient,[status(thm)],['0.16.1.1',theory(equality)]),
% 2.13/2.56 [u,rule_15]).
% 2.13/2.56 cnf('0.23.0.0',plain,
% 2.13/2.56 ( greatest_lower_bound(multiply(a,X1),multiply(identity,X1)) = multiply(identity,X1) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.9.2.0','0.14.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.1','L')]).
% 2.13/2.56 cnf('0.23.0.1',plain,
% 2.13/2.56 ( greatest_lower_bound(multiply(a,X1),X1) = multiply(identity,X1) ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.23.0.0','0.1.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','L')]).
% 2.13/2.56 cnf('0.23.0.2',plain,
% 2.13/2.56 ( greatest_lower_bound(multiply(a,X1),X1) = X1 ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.23.0.1','0.1.2.0',theory(equality)]),
% 2.13/2.56 [pos('R','L')]).
% 2.13/2.56 cnf('0.23.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(multiply(a,X1),X1) = X1 ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.23.0.2']),
% 2.13/2.56 [weight('<41,14,9,[0,0,0,1]>')]).
% 2.13/2.56 cnf('0.23.1.1',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,multiply(a,X1)) = X1 ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.23.1.0','0.12.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('0.23.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,multiply(a,X1)) = X1 ),
% 2.13/2.56 inference(orient,[status(thm)],['0.23.1.1',theory(equality)]),
% 2.13/2.56 [u,rule_21]).
% 2.13/2.56 cnf('0.24.0.0',plain,
% 2.13/2.56 ( greatest_lower_bound(multiply(b,X1),multiply(identity,X1)) = multiply(identity,X1) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.9.2.0','0.15.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.1','L')]).
% 2.13/2.56 cnf('0.24.0.1',plain,
% 2.13/2.56 ( greatest_lower_bound(multiply(b,X1),X1) = multiply(identity,X1) ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.24.0.0','0.1.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','L')]).
% 2.13/2.56 cnf('0.24.0.2',plain,
% 2.13/2.56 ( greatest_lower_bound(multiply(b,X1),X1) = X1 ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.24.0.1','0.1.2.0',theory(equality)]),
% 2.13/2.56 [pos('R','L')]).
% 2.13/2.56 cnf('0.24.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(multiply(b,X1),X1) = X1 ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.24.0.2']),
% 2.13/2.56 [weight('<41,15,9,[0,0,0,1]>')]).
% 2.13/2.56 cnf('0.24.1.1',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,multiply(b,X1)) = X1 ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.24.1.0','0.12.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('0.24.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,multiply(b,X1)) = X1 ),
% 2.13/2.56 inference(orient,[status(thm)],['0.24.1.1',theory(equality)]),
% 2.13/2.56 [u,rule_22]).
% 2.13/2.56 cnf('0.27.0.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.13.2.0','0.2.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.1','L')]).
% 2.13/2.56 cnf('0.27.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.27.0.0']),
% 2.13/2.56 [weight('<53,13,2,[1,0,0,1]>')]).
% 2.13/2.56 cnf('0.27.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 2.13/2.56 [u,rule_25]).
% 2.13/2.56 cnf('0.79.0.0',plain,
% 2.13/2.56 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.1','L')]).
% 2.13/2.56 cnf('0.79.0.1',plain,
% 2.13/2.56 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.79.0.0','0.1.2.0',theory(equality)]),
% 2.13/2.56 [pos('R','L')]).
% 2.13/2.56 cnf('0.79.1.0',plain,
% 2.13/2.56 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.79.0.1']),
% 2.13/2.56 [weight('<55,11,6,[0,0,0,1]>')]).
% 2.13/2.56 cnf('0.79.2.0',plain,
% 2.13/2.56 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 2.13/2.56 inference(orient,[status(thm)],['0.79.1.0',theory(equality)]),
% 2.13/2.56 [u,rule_77]).
% 2.13/2.56 cnf('0.80.0.0',plain,
% 2.13/2.56 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.79.2.0','0.79.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','L')]).
% 2.13/2.56 cnf('0.80.1.0',plain,
% 2.13/2.56 ( X1 = inverse(inverse(X1)) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.80.0.0']),
% 2.13/2.56 [weight('<19,79,79,[0,0,0,3]>')]).
% 2.13/2.56 cnf('0.80.2.0',plain,
% 2.13/2.56 ( inverse(inverse(X1)) = X1 ),
% 2.13/2.56 inference(orient,[status(thm)],['0.80.1.0',theory(equality)]),
% 2.13/2.56 [x,rule_78]).
% 2.13/2.56 cnf('0.82.0.0',plain,
% 2.13/2.56 ( identity = multiply(X1,inverse(X1)) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.11.2.0','0.80.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.1','L')]).
% 2.13/2.56 cnf('0.82.1.0',plain,
% 2.13/2.56 ( identity = multiply(X1,inverse(X1)) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.82.0.0']),
% 2.13/2.56 [weight('<29,80,11,[0,0,0,1]>')]).
% 2.13/2.56 cnf('0.82.2.0',plain,
% 2.13/2.56 ( multiply(X1,inverse(X1)) = identity ),
% 2.13/2.56 inference(orient,[status(thm)],['0.82.1.0',theory(equality)]),
% 2.13/2.56 [x,rule_80]).
% 2.13/2.56 cnf('0.99.0.0',plain,
% 2.13/2.56 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.79.2.0','0.82.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','L')]).
% 2.13/2.56 cnf('0.99.1.0',plain,
% 2.13/2.56 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.99.0.0']),
% 2.13/2.56 [weight('<34,82,79,[0,0,0,3]>')]).
% 2.13/2.56 cnf('0.99.2.0',plain,
% 2.13/2.56 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 2.13/2.56 inference(orient,[status(thm)],['0.99.1.0',theory(equality)]),
% 2.13/2.56 [x,rule_97]).
% 2.13/2.56 cnf('0.100.0.0',plain,
% 2.13/2.56 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.99.2.0','0.80.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.1','L')]).
% 2.13/2.56 cnf('0.100.0.1',plain,
% 2.13/2.56 ( X1 = multiply(X1,identity) ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.100.0.0','0.80.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('0.100.1.0',plain,
% 2.13/2.56 ( X1 = multiply(X1,identity) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.100.0.1']),
% 2.13/2.56 [weight('<19,99,80,[1,0,0,1]>')]).
% 2.13/2.56 cnf('0.100.2.0',plain,
% 2.13/2.56 ( multiply(X1,identity) = X1 ),
% 2.13/2.56 inference(orient,[status(thm)],['0.100.1.0',theory(equality)]),
% 2.13/2.56 [x,rule_98]).
% 2.13/2.56 cnf('0.474.0.0',plain,
% 2.13/2.56 ( greatest_lower_bound(multiply(X1,c),multiply(X1,identity)) = multiply(X1,identity) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.7.2.0','0.16.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','L')]).
% 2.13/2.56 cnf('0.474.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(multiply(X1,c),multiply(X1,identity)) = multiply(X1,identity) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.474.0.0']),
% 2.13/2.56 [weight('<87,16,7,[0,0,0,2]>')]).
% 2.13/2.56 cnf('0.474.1.1',plain,
% 2.13/2.56 ( greatest_lower_bound(multiply(X1,c),X1) = multiply(X1,identity) ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.474.1.0','0.100.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','L')]).
% 2.13/2.56 cnf('0.474.1.2',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,multiply(X1,c)) = multiply(X1,identity) ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.474.1.1','0.12.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('0.474.1.3',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,multiply(X1,c)) = X1 ),
% 2.13/2.56 inference(reduction,[status(thm)],['0.474.1.2','0.100.2.0',theory(equality)]),
% 2.13/2.56 [pos('R','L')]).
% 2.13/2.56 cnf('0.474.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,multiply(X1,c)) = X1 ),
% 2.13/2.56 inference(orient,[status(thm)],['0.474.1.3',theory(equality)]),
% 2.13/2.56 [u,rule_469]).
% 2.13/2.56 cnf('0.528.0.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(a,X1),X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.13.2.0','0.23.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.1','L')]).
% 2.13/2.56 cnf('0.528.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(a,X1),X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.528.0.0']),
% 2.13/2.56 [weight('<87,23,13,[0,0,0,1]>')]).
% 2.13/2.56 cnf('0.528.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(a,X1),X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(orient,[status(thm)],['0.528.1.0',theory(equality)]),
% 2.13/2.56 [u,rule_523]).
% 2.13/2.56 cnf('0.529.0.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(b,X1),X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.13.2.0','0.24.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.1','L')]).
% 2.13/2.56 cnf('0.529.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(b,X1),X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.529.0.0']),
% 2.13/2.56 [weight('<87,24,13,[0,0,0,1]>')]).
% 2.13/2.56 cnf('0.529.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(b,X1),X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(orient,[status(thm)],['0.529.1.0',theory(equality)]),
% 2.13/2.56 [u,rule_524]).
% 2.13/2.56 cnf('0.608.0.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,c),X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.13.2.0','0.474.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.1','L')]).
% 2.13/2.56 cnf('0.608.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,c),X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.608.0.0']),
% 2.13/2.56 [weight('<87,474,13,[0,0,0,1]>')]).
% 2.13/2.56 cnf('0.608.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,c),X2)) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(orient,[status(thm)],['0.608.1.0',theory(equality)]),
% 2.13/2.56 [u,rule_603]).
% 2.13/2.56 cnf('0.610.0.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(a,X1))) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.528.2.0','0.12.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','L')]).
% 2.13/2.56 cnf('0.610.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(a,X1))) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.610.0.0']),
% 2.13/2.56 [weight('<87,528,12,[1,0,0,2]>')]).
% 2.13/2.56 cnf('0.610.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(a,X1))) = greatest_lower_bound(X1,X2) ),
% 2.13/2.56 inference(orient,[status(thm)],['0.610.1.0',theory(equality)]),
% 2.13/2.56 [x,rule_605]).
% 2.13/2.56 cnf('0.1417.0.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X3,X1)) ),
% 2.13/2.56 inference(cp,[status(thm)],['0.12.2.0','0.13.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('0.1417.1.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X3,X1)) ),
% 2.13/2.56 inference(weigh,[status(thm)],['0.1417.0.0']),
% 2.13/2.56 [weight('<?,13,12,[0,0,0,0]>')]).
% 2.13/2.56 cnf('0.1417.2.0',plain,
% 2.13/2.56 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X3,X1)) ),
% 2.13/2.56 inference(activate,[status(thm)],['0.1417.1.0']),
% 2.13/2.56 [equation_6]).
% 2.13/2.56 cnf('1.0.0.0',conjecture,
% 2.13/2.56 ( 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)) ),
% 2.13/2.56 file('/tmp/WALDMEISTER_19189_n026',conjecture_1)).
% 2.13/2.56 cnf('1.0.0.1',plain,
% 2.13/2.56 ( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(multiply(greatest_lower_bound(a,b),a),multiply(greatest_lower_bound(a,b),c))) = greatest_lower_bound(a,multiply(b,c)) ),
% 2.13/2.56 inference(reduction,[status(thm)],['1.0.0.0','0.7.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','L')]).
% 2.13/2.56 cnf('1.0.0.2',plain,
% 2.13/2.56 ( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(multiply(greatest_lower_bound(a,b),a),greatest_lower_bound(multiply(a,c),multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)) ),
% 2.13/2.56 inference(reduction,[status(thm)],['1.0.0.1','0.9.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2.2','L')]).
% 2.13/2.56 cnf('1.0.0.3',plain,
% 2.13/2.56 ( greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),greatest_lower_bound(greatest_lower_bound(multiply(a,a),multiply(b,a)),greatest_lower_bound(multiply(a,c),multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)) ),
% 2.13/2.56 inference(reduction,[status(thm)],['1.0.0.2','0.9.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2.1','L')]).
% 2.13/2.56 cnf('1.0.0.4',plain,
% 2.13/2.56 ( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(greatest_lower_bound(multiply(a,a),multiply(b,a)),greatest_lower_bound(multiply(a,c),multiply(b,c))))) = greatest_lower_bound(a,multiply(b,c)) ),
% 2.13/2.56 inference(reduction,[status(thm)],['1.0.0.3','0.13.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('1.0.0.5',plain,
% 2.13/2.56 ( greatest_lower_bound(a,greatest_lower_bound(greatest_lower_bound(multiply(a,c),multiply(b,c)),greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,a),multiply(b,a))))) = greatest_lower_bound(a,multiply(b,c)) ),
% 2.13/2.56 inference(reduction,[status(thm)],['1.0.0.4','0.1417.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','R')]).
% 2.13/2.56 cnf('1.0.0.6',plain,
% 2.13/2.56 ( greatest_lower_bound(a,greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,a),multiply(b,a)))))) = greatest_lower_bound(a,multiply(b,c)) ),
% 2.13/2.56 inference(reduction,[status(thm)],['1.0.0.5','0.13.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','L')]).
% 2.13/2.56 cnf('1.0.0.7',plain,
% 2.13/2.56 ( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,a),multiply(b,a))))) = greatest_lower_bound(a,multiply(b,c)) ),
% 2.13/2.56 inference(reduction,[status(thm)],['1.0.0.6','0.608.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('1.0.0.8',plain,
% 2.13/2.56 ( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,a),multiply(b,a)))) = greatest_lower_bound(a,multiply(b,c)) ),
% 2.13/2.56 inference(reduction,[status(thm)],['1.0.0.7','0.27.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','L')]).
% 2.13/2.56 cnf('1.0.0.9',plain,
% 2.13/2.56 ( greatest_lower_bound(a,greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(b,c),multiply(a,a)))) = greatest_lower_bound(a,multiply(b,c)) ),
% 2.13/2.56 inference(reduction,[status(thm)],['1.0.0.8','0.1417.2.0',theory(equality)]),
% 2.13/2.56 [pos('L.2','R')]).
% 2.13/2.56 cnf('1.0.0.10',plain,
% 2.13/2.56 ( greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(a,a))) = greatest_lower_bound(a,multiply(b,c)) ),
% 2.13/2.56 inference(reduction,[status(thm)],['1.0.0.9','0.529.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('1.0.0.11',plain,
% 2.13/2.56 ( greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,multiply(b,c)) ),
% 2.13/2.56 inference(reduction,[status(thm)],['1.0.0.10','0.610.2.0',theory(equality)]),
% 2.13/2.56 [pos('L','L')]).
% 2.13/2.56 cnf('1.0.0.12',plain,
% 2.13/2.56 ( $true ),
% 2.13/2.56 inference(trivial,[status(thm)],['1.0.0.11',theory(equality)]),
% 2.13/2.56 [conjecture_1]).
% 2.13/2.56
% 2.13/2.56 Proved Goals:
% 2.13/2.56 No. 1: 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)) joined, current: greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,multiply(b,c))
% 2.13/2.56 1 goal was specified, which was proved.
% 2.13/2.56 % SZS output end CNFRefutation
% 2.13/2.56 #END OF PROOF
% 2.13/2.56
% 2.13/2.56 Problem WALDMEISTER_19189_n026
% 2.13/2.56 CPs.gen 147836
% 2.13/2.56 CPs.reexp 0
% 2.13/2.56 Select 17002
% 2.13/2.56 R 1411
% 2.13/2.56 E 6
% 2.13/2.56 vsize 7.5M
% 2.13/2.56 rss 4.8M
% 2.13/2.56 process.time 0.458s
% 2.13/2.56 wallclock.time 1.548s
% 2.13/2.56 status S
% 2.13/2.56
% 2.13/2.56
% 2.13/2.56 Waldmeister states: Goal proved.
% 2.13/2.56 % SZS status Unsatisfiable
% 2.13/2.56
% 2.13/2.56 Problem WALDMEISTER_19189_n026
% 2.13/2.56 CPs.gen 437464
% 2.13/2.56 CPs.reexp 0
% 2.13/2.56 Select 44895
% 2.13/2.56 R 2103
% 2.13/2.56 E 8
% 2.13/2.56 vsize 9.3M
% 2.13/2.56 rss 4.9M
% 2.13/2.56 process.time 1.092s
% 2.13/2.56 wallclock.time 1.547s
% 2.13/2.56 status S
%------------------------------------------------------------------------------