TSTP Solution File: GRP185-1 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP185-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n025.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 12:25:13 EDT 2022
% Result : Unsatisfiable 0.56s 1.00s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP185-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.12 % Command : woody %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 08:23:39 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.56/0.98 ********************************************************************************
% 0.56/0.98 * W A L D M E I S T E R \| \ / \|/ *
% 0.56/0.98 * |/ | \/ | *
% 0.56/0.98 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.56/0.98 * A. Jaeger and B. Loechner | | *
% 0.56/0.98 * <waldmeister@informatik.uni-kl.de> | *
% 0.56/0.98 ********************************************************************************
% 0.56/0.98
% 0.56/0.98
% 0.56/0.98 Goals:
% 0.56/0.98 ------
% 0.56/0.98
% 0.56/0.98 ( 1) multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ?=? least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))
% 0.56/0.98
% 0.56/0.98 Detected structure: VerbandsgeordneteGruppe
% 0.56/0.98 ********************************************************************************
% 0.56/0.98 ****************************** COMPLETION - PROOF ******************************
% 0.56/0.98 ********************************************************************************
% 0.56/0.98
% 0.56/1.00 joined goal: 1 multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ?= least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) to least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b))))
% 0.56/1.00 goal joined
% 0.56/1.00 % SZS status Unsatisfiable
% 0.56/1.00 #START OF PROOF
% 0.56/1.00 % SZS output start CNFRefutation
% 0.56/1.00 cnf('0.1.0.0',axiom,
% 0.56/1.00 ( X1 = multiply(identity,X1) ),
% 0.56/1.00 file('/tmp/WALDMEISTER_13966_n025')).
% 0.56/1.00 cnf('0.1.1.0',plain,
% 0.56/1.00 ( X1 = multiply(identity,X1) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.56/1.00 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.56/1.00 cnf('0.1.2.0',plain,
% 0.56/1.00 ( multiply(identity,X1) = X1 ),
% 0.56/1.00 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_1]).
% 0.56/1.00 cnf('0.3.0.0',axiom,
% 0.56/1.00 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.56/1.00 file('/tmp/WALDMEISTER_13966_n025')).
% 0.56/1.00 cnf('0.3.1.0',plain,
% 0.56/1.00 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.56/1.00 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.56/1.00 cnf('0.3.2.0',plain,
% 0.56/1.00 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 0.56/1.00 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_3]).
% 0.56/1.00 cnf('0.5.0.0',axiom,
% 0.56/1.00 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.56/1.00 file('/tmp/WALDMEISTER_13966_n025')).
% 0.56/1.00 cnf('0.5.1.0',plain,
% 0.56/1.00 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.56/1.00 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.56/1.00 cnf('0.5.2.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 0.56/1.00 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_5]).
% 0.56/1.00 cnf('0.6.0.0',axiom,
% 0.56/1.00 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.56/1.00 file('/tmp/WALDMEISTER_13966_n025')).
% 0.56/1.00 cnf('0.6.1.0',plain,
% 0.56/1.00 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.56/1.00 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.56/1.00 cnf('0.6.2.0',plain,
% 0.56/1.00 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.56/1.00 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_6]).
% 0.56/1.00 cnf('0.8.0.0',axiom,
% 0.56/1.00 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.56/1.00 file('/tmp/WALDMEISTER_13966_n025')).
% 0.56/1.00 cnf('0.8.1.0',plain,
% 0.56/1.00 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.56/1.00 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.56/1.00 cnf('0.8.2.0',plain,
% 0.56/1.00 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.56/1.00 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.56/1.00 [u,rule_8]).
% 0.56/1.00 cnf('0.10.0.0',axiom,
% 0.56/1.00 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.56/1.00 file('/tmp/WALDMEISTER_13966_n025')).
% 0.56/1.00 cnf('0.10.1.0',plain,
% 0.56/1.00 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.56/1.00 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.56/1.00 cnf('0.10.2.0',plain,
% 0.56/1.00 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.56/1.00 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.56/1.00 [u,rule_10]).
% 0.56/1.00 cnf('0.11.0.0',axiom,
% 0.56/1.00 ( multiply(inverse(X1),X1) = identity ),
% 0.56/1.00 file('/tmp/WALDMEISTER_13966_n025')).
% 0.56/1.00 cnf('0.11.1.0',plain,
% 0.56/1.00 ( multiply(inverse(X1),X1) = identity ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.56/1.00 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.56/1.00 cnf('0.11.2.0',plain,
% 0.56/1.00 ( multiply(inverse(X1),X1) = identity ),
% 0.56/1.00 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.56/1.00 [u,rule_11]).
% 0.56/1.00 cnf('0.12.0.0',axiom,
% 0.56/1.00 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.56/1.00 file('/tmp/WALDMEISTER_13966_n025')).
% 0.56/1.00 cnf('0.12.1.0',plain,
% 0.56/1.00 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.56/1.00 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.56/1.00 cnf('0.12.2.0',plain,
% 0.56/1.00 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.56/1.00 inference(activate,[status(thm)],['0.12.1.0']),
% 0.56/1.00 [equation_1]).
% 0.56/1.00 cnf('0.14.0.0',axiom,
% 0.56/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.56/1.00 file('/tmp/WALDMEISTER_13966_n025')).
% 0.56/1.00 cnf('0.14.1.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.56/1.00 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.56/1.00 cnf('0.14.2.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.56/1.00 inference(activate,[status(thm)],['0.14.1.0']),
% 0.56/1.00 [equation_2]).
% 0.56/1.00 cnf('0.15.0.0',axiom,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.56/1.00 file('/tmp/WALDMEISTER_13966_n025')).
% 0.56/1.00 cnf('0.15.1.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.56/1.00 [weight('<14,0,0,[0,0,0,15]>')]).
% 0.56/1.00 cnf('0.15.2.0',plain,
% 0.56/1.00 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.56/1.00 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_13]).
% 0.56/1.00 cnf('0.16.0.0',plain,
% 0.56/1.00 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.56/1.00 inference(cp,[status(thm)],['0.5.2.0','0.12.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.2','L')]).
% 0.56/1.00 cnf('0.16.1.0',plain,
% 0.56/1.00 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.56/1.00 [weight('<41,12,5,[0,0,0,2]>')]).
% 0.56/1.00 cnf('0.16.2.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1 ),
% 0.56/1.00 inference(orient,[status(thm)],['0.16.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_14]).
% 0.56/1.00 cnf('0.20.0.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(least_upper_bound(X1,X2),X1) ),
% 0.56/1.00 inference(cp,[status(thm)],['0.16.2.0','0.3.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.2','L')]).
% 0.56/1.00 cnf('0.20.0.1',plain,
% 0.56/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)) ),
% 0.56/1.00 inference(reduction,[status(thm)],['0.20.0.0','0.15.2.0',theory(equality)]),
% 0.56/1.00 [pos('R','L')]).
% 0.56/1.00 cnf('0.20.1.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.20.0.1']),
% 0.56/1.00 [weight('<53,16,3,[1,0,0,2]>')]).
% 0.56/1.00 cnf('0.20.2.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2) ),
% 0.56/1.00 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_18]).
% 0.56/1.00 cnf('0.22.0.0',plain,
% 0.56/1.00 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 0.56/1.00 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.1','L')]).
% 0.56/1.00 cnf('0.22.0.1',plain,
% 0.56/1.00 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.56/1.00 inference(reduction,[status(thm)],['0.22.0.0','0.1.2.0',theory(equality)]),
% 0.56/1.00 [pos('R','L')]).
% 0.56/1.00 cnf('0.22.1.0',plain,
% 0.56/1.00 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.22.0.1']),
% 0.56/1.00 [weight('<55,11,6,[0,0,0,1]>')]).
% 0.56/1.00 cnf('0.22.2.0',plain,
% 0.56/1.00 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.56/1.00 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.56/1.00 [u,rule_20]).
% 0.56/1.00 cnf('0.23.0.0',plain,
% 0.56/1.00 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 0.56/1.00 inference(cp,[status(thm)],['0.22.2.0','0.22.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.2','L')]).
% 0.56/1.00 cnf('0.23.1.0',plain,
% 0.56/1.00 ( X1 = inverse(inverse(X1)) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.56/1.00 [weight('<19,22,22,[0,0,0,3]>')]).
% 0.56/1.00 cnf('0.23.2.0',plain,
% 0.56/1.00 ( inverse(inverse(X1)) = X1 ),
% 0.56/1.00 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_21]).
% 0.56/1.00 cnf('0.25.0.0',plain,
% 0.56/1.00 ( identity = multiply(X1,inverse(X1)) ),
% 0.56/1.00 inference(cp,[status(thm)],['0.11.2.0','0.23.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.1','L')]).
% 0.56/1.00 cnf('0.25.1.0',plain,
% 0.56/1.00 ( identity = multiply(X1,inverse(X1)) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.56/1.00 [weight('<29,23,11,[0,0,0,1]>')]).
% 0.56/1.00 cnf('0.25.2.0',plain,
% 0.56/1.00 ( multiply(X1,inverse(X1)) = identity ),
% 0.56/1.00 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_23]).
% 0.56/1.00 cnf('0.27.0.0',plain,
% 0.56/1.00 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 0.56/1.00 inference(cp,[status(thm)],['0.22.2.0','0.25.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.2','L')]).
% 0.56/1.00 cnf('0.27.1.0',plain,
% 0.56/1.00 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.27.0.0']),
% 0.56/1.00 [weight('<34,25,22,[0,0,0,3]>')]).
% 0.56/1.00 cnf('0.27.2.0',plain,
% 0.56/1.00 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 0.56/1.00 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_25]).
% 0.56/1.00 cnf('0.28.0.0',plain,
% 0.56/1.00 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 0.56/1.00 inference(cp,[status(thm)],['0.27.2.0','0.23.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.1','L')]).
% 0.56/1.00 cnf('0.28.0.1',plain,
% 0.56/1.00 ( X1 = multiply(X1,identity) ),
% 0.56/1.00 inference(reduction,[status(thm)],['0.28.0.0','0.23.2.0',theory(equality)]),
% 0.56/1.00 [pos('L','L')]).
% 0.56/1.00 cnf('0.28.1.0',plain,
% 0.56/1.00 ( X1 = multiply(X1,identity) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.28.0.1']),
% 0.56/1.00 [weight('<19,27,23,[1,0,0,1]>')]).
% 0.56/1.00 cnf('0.28.2.0',plain,
% 0.56/1.00 ( multiply(X1,identity) = X1 ),
% 0.56/1.00 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_26]).
% 0.56/1.00 cnf('0.52.0.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(least_upper_bound(X2,X1),X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.56/1.00 inference(cp,[status(thm)],['0.15.2.0','0.20.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.1','L')]).
% 0.56/1.00 cnf('0.52.0.1',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.56/1.00 inference(reduction,[status(thm)],['0.52.0.0','0.15.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.2','L')]).
% 0.56/1.00 cnf('0.52.0.2',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.56/1.00 inference(reduction,[status(thm)],['0.52.0.1','0.15.2.0',theory(equality)]),
% 0.56/1.00 [pos('R','L')]).
% 0.56/1.00 cnf('0.52.1.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.52.0.2']),
% 0.56/1.00 [weight('<103,20,15,[0,0,0,1]>')]).
% 0.56/1.00 cnf('0.52.2.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.56/1.00 inference(orient,[status(thm)],['0.52.1.0',theory(equality)]),
% 0.56/1.00 [u,rule_46]).
% 0.56/1.00 cnf('0.53.0.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) ),
% 0.56/1.00 inference(cp,[status(thm)],['0.20.2.0','0.15.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.2','L')]).
% 0.56/1.00 cnf('0.53.1.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.53.0.0']),
% 0.56/1.00 [weight('<103,20,15,[1,0,0,2]>')]).
% 0.56/1.00 cnf('0.53.2.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.56/1.00 inference(orient,[status(thm)],['0.53.1.0',theory(equality)]),
% 0.56/1.00 [x,rule_47]).
% 0.56/1.00 cnf('0.65.0.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)) ),
% 0.56/1.00 inference(cp,[status(thm)],['0.15.2.0','0.14.2.0',theory(equality)]),
% 0.56/1.00 [pos('L','L')]).
% 0.56/1.00 cnf('0.65.1.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)) ),
% 0.56/1.00 inference(weigh,[status(thm)],['0.65.0.0']),
% 0.56/1.00 [weight('<120,15,14,[1,0,0,0]>')]).
% 0.56/1.00 cnf('0.65.2.0',plain,
% 0.56/1.00 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)) ),
% 0.56/1.00 inference(activate,[status(thm)],['0.65.1.0']),
% 0.56/1.00 [equation_9]).
% 0.56/1.00 cnf('1.0.0.0',conjecture,
% 0.56/1.00 ( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.56/1.00 file('/tmp/WALDMEISTER_13966_n025',conjecture_1)).
% 0.56/1.00 cnf('1.0.0.1',plain,
% 0.56/1.00 ( least_upper_bound(multiply(a,least_upper_bound(b,identity)),multiply(identity,least_upper_bound(b,identity))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.0','0.10.2.0',theory(equality)]),
% 0.56/1.00 [pos('L','L')]).
% 0.56/1.00 cnf('1.0.0.2',plain,
% 0.56/1.00 ( least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,identity)),multiply(identity,least_upper_bound(b,identity))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.1','0.8.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.1','L')]).
% 0.56/1.00 cnf('1.0.0.3',plain,
% 0.56/1.00 ( least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),multiply(identity,least_upper_bound(b,identity)))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.2','0.15.2.0',theory(equality)]),
% 0.56/1.00 [pos('L','L')]).
% 0.56/1.00 cnf('1.0.0.4',plain,
% 0.56/1.00 ( least_upper_bound(multiply(a,b),least_upper_bound(a,multiply(identity,least_upper_bound(b,identity)))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.3','0.28.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.2.1','L')]).
% 0.56/1.00 cnf('1.0.0.5',plain,
% 0.56/1.00 ( least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.4','0.1.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.2.2','L')]).
% 0.56/1.00 cnf('1.0.0.6',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(least_upper_bound(b,identity),multiply(a,b))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.5','0.65.2.0',theory(equality)]),
% 0.56/1.00 [pos('L','R')]).
% 0.56/1.00 cnf('1.0.0.7',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.6','0.15.2.0',theory(equality)]),
% 0.56/1.00 [pos('L.2','L')]).
% 0.56/1.00 cnf('1.0.0.8',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.7','0.15.2.0',theory(equality)]),
% 0.56/1.00 [pos('R','L')]).
% 0.56/1.00 cnf('1.0.0.9',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,least_upper_bound(b,identity)),multiply(identity,least_upper_bound(b,identity))))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.8','0.10.2.0',theory(equality)]),
% 0.56/1.00 [pos('R.2.2','L')]).
% 0.56/1.00 cnf('1.0.0.10',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,identity)),multiply(identity,least_upper_bound(b,identity))))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.9','0.8.2.0',theory(equality)]),
% 0.56/1.00 [pos('R.2.2.1','L')]).
% 0.56/1.00 cnf('1.0.0.11',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),multiply(identity,least_upper_bound(b,identity)))))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.10','0.15.2.0',theory(equality)]),
% 0.56/1.00 [pos('R.2.2','L')]).
% 0.56/1.00 cnf('1.0.0.12',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,identity),multiply(identity,least_upper_bound(b,identity))))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.11','0.52.2.0',theory(equality)]),
% 0.56/1.00 [pos('R','L')]).
% 0.56/1.00 cnf('1.0.0.13',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,multiply(identity,least_upper_bound(b,identity))))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.12','0.28.2.0',theory(equality)]),
% 0.56/1.00 [pos('R.2.2.1','L')]).
% 0.56/1.00 cnf('1.0.0.14',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,least_upper_bound(b,identity)))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.13','0.1.2.0',theory(equality)]),
% 0.56/1.00 [pos('R.2.2.2','L')]).
% 0.56/1.00 cnf('1.0.0.15',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,b))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.14','0.53.2.0',theory(equality)]),
% 0.56/1.00 [pos('R.2','L')]).
% 0.56/1.00 cnf('1.0.0.16',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.15','0.65.2.0',theory(equality)]),
% 0.56/1.00 [pos('R.2','R')]).
% 0.56/1.00 cnf('1.0.0.17',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(a,least_upper_bound(least_upper_bound(b,identity),multiply(a,b))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.16','0.65.2.0',theory(equality)]),
% 0.56/1.00 [pos('R','R')]).
% 0.56/1.00 cnf('1.0.0.18',plain,
% 0.56/1.00 ( least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) ),
% 0.56/1.00 inference(reduction,[status(thm)],['1.0.0.17','0.15.2.0',theory(equality)]),
% 0.56/1.00 [pos('R.2','L')]).
% 0.56/1.00 cnf('1.0.0.19',plain,
% 0.56/1.00 ( $true ),
% 0.56/1.00 inference(trivial,[status(thm)],['1.0.0.18',theory(equality)]),
% 0.56/1.00 [conjecture_1]).
% 0.56/1.00
% 0.56/1.00 Proved Goals:
% 0.56/1.00 No. 1: multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) ?= least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) joined, current: least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b)))) = least_upper_bound(a,least_upper_bound(b,least_upper_bound(identity,multiply(a,b))))
% 0.56/1.00 1 goal was specified, which was proved.
% 0.56/1.00 % SZS output end CNFRefutation
% 0.56/1.00 #END OF PROOF
% 0.56/1.00
% 0.56/1.00 Problem WALDMEISTER_13966_n025
% 0.56/1.00 CPs.gen 1587
% 0.56/1.00 CPs.reexp 0
% 0.56/1.00 Select 170
% 0.56/1.00 R 56
% 0.56/1.00 E 9
% 0.56/1.00 vsize 7.0M
% 0.56/1.00 rss 4.1M
% 0.56/1.00 process.time 0.024s
% 0.56/1.00 wallclock.time 0.025s
% 0.56/1.00 status S
% 0.56/1.00
% 0.56/1.00
% 0.56/1.00 Waldmeister states: Goal proved.
% 0.56/1.00 % SZS status Unsatisfiable
% 0.56/1.00
% 0.56/1.00 Problem WALDMEISTER_13966_n025
% 0.56/1.00 CPs.gen 0
% 0.56/1.00 CPs.reexp 0
% 0.56/1.00 Select 0
% 0.56/1.00 R 0
% 0.56/1.00 E 0
% 0.56/1.00 vsize 6.0M
% 0.56/1.00 rss 3.2M
% 0.56/1.00 process.time 0.001s
% 0.56/1.00 wallclock.time 0.024s
% 0.56/1.00 status S
%------------------------------------------------------------------------------