TSTP Solution File: GRP177-2 by Waldmeister---710

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------