TSTP Solution File: GRP190-2 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP190-2 : 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 12:25:19 EDT 2022
% Result : Unsatisfiable 0.65s 1.03s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP190-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.14 % Command : woody %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 15:58:06 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.65/1.01 ********************************************************************************
% 0.65/1.01 * W A L D M E I S T E R \| \ / \|/ *
% 0.65/1.01 * |/ | \/ | *
% 0.65/1.01 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.65/1.01 * A. Jaeger and B. Loechner | | *
% 0.65/1.01 * <waldmeister@informatik.uni-kl.de> | *
% 0.65/1.01 ********************************************************************************
% 0.65/1.01
% 0.65/1.01
% 0.65/1.01 Goals:
% 0.65/1.01 ------
% 0.65/1.01
% 0.65/1.01 ( 1) greatest_lower_bound(inverse(a),inverse(b)) ?=? inverse(a)
% 0.65/1.01
% 0.65/1.01 Detected structure: VerbandsgeordneteGruppe
% 0.65/1.01 ********************************************************************************
% 0.65/1.01 ****************************** COMPLETION - PROOF ******************************
% 0.65/1.01 ********************************************************************************
% 0.65/1.01
% 0.65/1.03 joined goal: 1 greatest_lower_bound(inverse(a),inverse(b)) ?= inverse(a) to inverse(a)
% 0.65/1.03 goal joined
% 0.65/1.03 % SZS status Unsatisfiable
% 0.65/1.03 #START OF PROOF
% 0.65/1.03 % SZS output start CNFRefutation
% 0.65/1.03 cnf('0.1.0.0',axiom,
% 0.65/1.03 ( X1 = multiply(identity,X1) ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026')).
% 0.65/1.03 cnf('0.1.1.0',plain,
% 0.65/1.03 ( X1 = multiply(identity,X1) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.65/1.03 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.65/1.03 cnf('0.1.2.0',plain,
% 0.65/1.03 ( multiply(identity,X1) = X1 ),
% 0.65/1.03 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_1]).
% 0.65/1.03 cnf('0.3.0.0',axiom,
% 0.65/1.03 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026')).
% 0.65/1.03 cnf('0.3.1.0',plain,
% 0.65/1.03 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.65/1.03 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.65/1.03 cnf('0.3.2.0',plain,
% 0.65/1.03 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 0.65/1.03 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_3]).
% 0.65/1.03 cnf('0.5.0.0',axiom,
% 0.65/1.03 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026')).
% 0.65/1.03 cnf('0.5.1.0',plain,
% 0.65/1.03 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.65/1.03 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.65/1.03 cnf('0.5.2.0',plain,
% 0.65/1.03 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 0.65/1.03 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_5]).
% 0.65/1.03 cnf('0.6.0.0',axiom,
% 0.65/1.03 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026')).
% 0.65/1.03 cnf('0.6.1.0',plain,
% 0.65/1.03 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.65/1.03 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.65/1.03 cnf('0.6.2.0',plain,
% 0.65/1.03 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.65/1.03 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_6]).
% 0.65/1.03 cnf('0.7.0.0',axiom,
% 0.65/1.03 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026')).
% 0.65/1.03 cnf('0.7.1.0',plain,
% 0.65/1.03 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.65/1.03 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.65/1.03 cnf('0.7.2.0',plain,
% 0.65/1.03 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.65/1.03 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.65/1.03 [u,rule_7]).
% 0.65/1.03 cnf('0.9.0.0',axiom,
% 0.65/1.03 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026')).
% 0.65/1.03 cnf('0.9.1.0',plain,
% 0.65/1.03 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.65/1.03 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.65/1.03 cnf('0.9.2.0',plain,
% 0.65/1.03 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.65/1.03 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.65/1.03 [u,rule_9]).
% 0.65/1.03 cnf('0.11.0.0',axiom,
% 0.65/1.03 ( multiply(inverse(X1),X1) = identity ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026')).
% 0.65/1.03 cnf('0.11.1.0',plain,
% 0.65/1.03 ( multiply(inverse(X1),X1) = identity ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.65/1.03 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.65/1.03 cnf('0.11.2.0',plain,
% 0.65/1.03 ( multiply(inverse(X1),X1) = identity ),
% 0.65/1.03 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.65/1.03 [u,rule_11]).
% 0.65/1.03 cnf('0.12.0.0',axiom,
% 0.65/1.03 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026')).
% 0.65/1.03 cnf('0.12.1.0',plain,
% 0.65/1.03 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.65/1.03 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.65/1.03 cnf('0.12.2.0',plain,
% 0.65/1.03 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.65/1.03 inference(activate,[status(thm)],['0.12.1.0']),
% 0.65/1.03 [equation_1]).
% 0.65/1.03 cnf('0.13.0.0',axiom,
% 0.65/1.03 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026')).
% 0.65/1.03 cnf('0.13.1.0',plain,
% 0.65/1.03 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.65/1.03 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.65/1.03 cnf('0.13.2.0',plain,
% 0.65/1.03 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.65/1.03 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_12]).
% 0.65/1.03 cnf('0.14.0.0',axiom,
% 0.65/1.03 ( least_upper_bound(a,b) = a ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026')).
% 0.65/1.03 cnf('0.14.1.0',plain,
% 0.65/1.03 ( least_upper_bound(a,b) = a ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.65/1.03 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.65/1.03 cnf('0.14.1.1',plain,
% 0.65/1.03 ( least_upper_bound(b,a) = a ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.14.1.0','0.12.2.0',theory(equality)]),
% 0.65/1.03 [pos('L','L')]).
% 0.65/1.03 cnf('0.14.2.0',plain,
% 0.65/1.03 ( least_upper_bound(b,a) = a ),
% 0.65/1.03 inference(orient,[status(thm)],['0.14.1.1',theory(equality)]),
% 0.65/1.03 [u,rule_13]).
% 0.65/1.03 cnf('0.15.0.0',axiom,
% 0.65/1.03 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026')).
% 0.65/1.03 cnf('0.15.1.0',plain,
% 0.65/1.03 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.65/1.03 [weight('<14,0,0,[0,0,0,15]>')]).
% 0.65/1.03 cnf('0.15.2.0',plain,
% 0.65/1.03 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.65/1.03 inference(activate,[status(thm)],['0.15.1.0']),
% 0.65/1.03 [equation_2]).
% 0.65/1.03 cnf('0.17.0.0',plain,
% 0.65/1.03 ( b = greatest_lower_bound(b,a) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.5.2.0','0.14.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.17.1.0',plain,
% 0.65/1.03 ( b = greatest_lower_bound(b,a) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.65/1.03 [weight('<19,14,5,[0,0,0,2]>')]).
% 0.65/1.03 cnf('0.17.2.0',plain,
% 0.65/1.03 ( greatest_lower_bound(b,a) = b ),
% 0.65/1.03 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_15]).
% 0.65/1.03 cnf('0.19.0.0',plain,
% 0.65/1.03 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.3.2.0','0.15.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.19.1.0',plain,
% 0.65/1.03 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.65/1.03 [weight('<41,15,3,[0,0,0,2]>')]).
% 0.65/1.03 cnf('0.19.2.0',plain,
% 0.65/1.03 ( least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1 ),
% 0.65/1.03 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_17]).
% 0.65/1.03 cnf('0.21.0.0',plain,
% 0.65/1.03 ( least_upper_bound(b,least_upper_bound(a,X1)) = least_upper_bound(a,X1) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.13.2.0','0.14.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1','L')]).
% 0.65/1.03 cnf('0.21.1.0',plain,
% 0.65/1.03 ( least_upper_bound(b,least_upper_bound(a,X1)) = least_upper_bound(a,X1) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.65/1.03 [weight('<53,14,13,[0,0,0,1]>')]).
% 0.65/1.03 cnf('0.21.2.0',plain,
% 0.65/1.03 ( least_upper_bound(b,least_upper_bound(a,X1)) = least_upper_bound(a,X1) ),
% 0.65/1.03 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.65/1.03 [u,rule_19]).
% 0.65/1.03 cnf('0.22.0.0',plain,
% 0.65/1.03 ( b = greatest_lower_bound(b,least_upper_bound(a,X1)) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.5.2.0','0.21.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.22.1.0',plain,
% 0.65/1.03 ( b = greatest_lower_bound(b,least_upper_bound(a,X1)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.22.0.0']),
% 0.65/1.03 [weight('<41,21,5,[0,0,0,2]>')]).
% 0.65/1.03 cnf('0.22.2.0',plain,
% 0.65/1.03 ( greatest_lower_bound(b,least_upper_bound(a,X1)) = b ),
% 0.65/1.03 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_20]).
% 0.65/1.03 cnf('0.28.0.0',plain,
% 0.65/1.03 ( least_upper_bound(a,X1) = least_upper_bound(least_upper_bound(a,X1),b) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.19.2.0','0.22.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.28.0.1',plain,
% 0.65/1.03 ( least_upper_bound(a,X1) = least_upper_bound(a,least_upper_bound(X1,b)) ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.28.0.0','0.13.2.0',theory(equality)]),
% 0.65/1.03 [pos('R','L')]).
% 0.65/1.03 cnf('0.28.1.0',plain,
% 0.65/1.03 ( least_upper_bound(a,X1) = least_upper_bound(a,least_upper_bound(X1,b)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.28.0.1']),
% 0.65/1.03 [weight('<53,22,19,[0,0,0,2]>')]).
% 0.65/1.03 cnf('0.28.2.0',plain,
% 0.65/1.03 ( least_upper_bound(a,least_upper_bound(X1,b)) = least_upper_bound(a,X1) ),
% 0.65/1.03 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_26]).
% 0.65/1.03 cnf('0.30.0.0',plain,
% 0.65/1.03 ( least_upper_bound(a,X1) = least_upper_bound(a,least_upper_bound(b,X1)) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.28.2.0','0.12.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.30.1.0',plain,
% 0.65/1.03 ( least_upper_bound(a,X1) = least_upper_bound(a,least_upper_bound(b,X1)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.30.0.0']),
% 0.65/1.03 [weight('<53,28,12,[1,0,0,2]>')]).
% 0.65/1.03 cnf('0.30.2.0',plain,
% 0.65/1.03 ( least_upper_bound(a,least_upper_bound(b,X1)) = least_upper_bound(a,X1) ),
% 0.65/1.03 inference(orient,[status(thm)],['0.30.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_28]).
% 0.65/1.03 cnf('0.31.0.0',plain,
% 0.65/1.03 ( least_upper_bound(a,greatest_lower_bound(b,X1)) = least_upper_bound(a,b) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.30.2.0','0.3.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.31.1.0',plain,
% 0.65/1.03 ( least_upper_bound(a,greatest_lower_bound(b,X1)) = least_upper_bound(a,b) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.31.0.0']),
% 0.65/1.03 [weight('<53,30,3,[1,0,0,2]>')]).
% 0.65/1.03 cnf('0.31.1.1',plain,
% 0.65/1.03 ( least_upper_bound(a,greatest_lower_bound(b,X1)) = least_upper_bound(b,a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.31.1.0','0.12.2.0',theory(equality)]),
% 0.65/1.03 [pos('R','L')]).
% 0.65/1.03 cnf('0.31.1.2',plain,
% 0.65/1.03 ( least_upper_bound(a,greatest_lower_bound(b,X1)) = a ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.31.1.1','0.14.2.0',theory(equality)]),
% 0.65/1.03 [pos('R','L')]).
% 0.65/1.03 cnf('0.31.2.0',plain,
% 0.65/1.03 ( least_upper_bound(a,greatest_lower_bound(b,X1)) = a ),
% 0.65/1.03 inference(orient,[status(thm)],['0.31.1.2',theory(equality)]),
% 0.65/1.03 [u,rule_29]).
% 0.65/1.03 cnf('0.33.0.0',plain,
% 0.65/1.03 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1','L')]).
% 0.65/1.03 cnf('0.33.0.1',plain,
% 0.65/1.03 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.33.0.0','0.1.2.0',theory(equality)]),
% 0.65/1.03 [pos('R','L')]).
% 0.65/1.03 cnf('0.33.1.0',plain,
% 0.65/1.03 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.33.0.1']),
% 0.65/1.03 [weight('<55,11,6,[0,0,0,1]>')]).
% 0.65/1.03 cnf('0.33.2.0',plain,
% 0.65/1.03 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.65/1.03 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 0.65/1.03 [u,rule_31]).
% 0.65/1.03 cnf('0.34.0.0',plain,
% 0.65/1.03 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.33.2.0','0.33.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.34.1.0',plain,
% 0.65/1.03 ( X1 = inverse(inverse(X1)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.34.0.0']),
% 0.65/1.03 [weight('<19,33,33,[0,0,0,3]>')]).
% 0.65/1.03 cnf('0.34.2.0',plain,
% 0.65/1.03 ( inverse(inverse(X1)) = X1 ),
% 0.65/1.03 inference(orient,[status(thm)],['0.34.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_32]).
% 0.65/1.03 cnf('0.36.0.0',plain,
% 0.65/1.03 ( identity = multiply(X1,inverse(X1)) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.11.2.0','0.34.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1','L')]).
% 0.65/1.03 cnf('0.36.1.0',plain,
% 0.65/1.03 ( identity = multiply(X1,inverse(X1)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.36.0.0']),
% 0.65/1.03 [weight('<29,34,11,[0,0,0,1]>')]).
% 0.65/1.03 cnf('0.36.2.0',plain,
% 0.65/1.03 ( multiply(X1,inverse(X1)) = identity ),
% 0.65/1.03 inference(orient,[status(thm)],['0.36.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_34]).
% 0.65/1.03 cnf('0.38.0.0',plain,
% 0.65/1.03 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.33.2.0','0.36.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.38.1.0',plain,
% 0.65/1.03 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.38.0.0']),
% 0.65/1.03 [weight('<34,36,33,[0,0,0,3]>')]).
% 0.65/1.03 cnf('0.38.2.0',plain,
% 0.65/1.03 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 0.65/1.03 inference(orient,[status(thm)],['0.38.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_36]).
% 0.65/1.03 cnf('0.39.0.0',plain,
% 0.65/1.03 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.38.2.0','0.34.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1','L')]).
% 0.65/1.03 cnf('0.39.0.1',plain,
% 0.65/1.03 ( X1 = multiply(X1,identity) ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.39.0.0','0.34.2.0',theory(equality)]),
% 0.65/1.03 [pos('L','L')]).
% 0.65/1.03 cnf('0.39.1.0',plain,
% 0.65/1.03 ( X1 = multiply(X1,identity) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.39.0.1']),
% 0.65/1.03 [weight('<19,38,34,[1,0,0,1]>')]).
% 0.65/1.03 cnf('0.39.2.0',plain,
% 0.65/1.03 ( multiply(X1,identity) = X1 ),
% 0.65/1.03 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_37]).
% 0.65/1.03 cnf('0.49.0.0',plain,
% 0.65/1.03 ( least_upper_bound(a,X1) = least_upper_bound(b,least_upper_bound(X1,a)) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.21.2.0','0.12.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.49.1.0',plain,
% 0.65/1.03 ( least_upper_bound(a,X1) = least_upper_bound(b,least_upper_bound(X1,a)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.49.0.0']),
% 0.65/1.03 [weight('<80,21,12,[1,0,0,2]>')]).
% 0.65/1.03 cnf('0.49.2.0',plain,
% 0.65/1.03 ( least_upper_bound(a,X1) = least_upper_bound(b,least_upper_bound(X1,a)) ),
% 0.65/1.03 inference(activate,[status(thm)],['0.49.1.0']),
% 0.65/1.03 [equation_3]).
% 0.65/1.03 cnf('0.50.0.0',plain,
% 0.65/1.03 ( least_upper_bound(b,least_upper_bound(X1,a)) = least_upper_bound(X1,a) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.49.2.0','0.12.2.0',theory(equality)]),
% 0.65/1.03 [pos('L','L')]).
% 0.65/1.03 cnf('0.50.1.0',plain,
% 0.65/1.03 ( least_upper_bound(b,least_upper_bound(X1,a)) = least_upper_bound(X1,a) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.50.0.0']),
% 0.65/1.03 [weight('<53,49,12,[1,0,0,0]>')]).
% 0.65/1.03 cnf('0.50.2.0',plain,
% 0.65/1.03 ( least_upper_bound(b,least_upper_bound(X1,a)) = least_upper_bound(X1,a) ),
% 0.65/1.03 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 0.65/1.03 [u,rule_47]).
% 0.65/1.03 cnf('0.52.0.0',plain,
% 0.65/1.03 ( least_upper_bound(multiply(X1,b),multiply(X1,a)) = multiply(X1,a) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.7.2.0','0.14.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.52.1.0',plain,
% 0.65/1.03 ( least_upper_bound(multiply(X1,b),multiply(X1,a)) = multiply(X1,a) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.52.0.0']),
% 0.65/1.03 [weight('<87,14,7,[0,0,0,2]>')]).
% 0.65/1.03 cnf('0.52.2.0',plain,
% 0.65/1.03 ( least_upper_bound(multiply(X1,b),multiply(X1,a)) = multiply(X1,a) ),
% 0.65/1.03 inference(orient,[status(thm)],['0.52.1.0',theory(equality)]),
% 0.65/1.03 [u,rule_49]).
% 0.65/1.03 cnf('0.53.0.0',plain,
% 0.65/1.03 ( multiply(inverse(a),a) = least_upper_bound(multiply(inverse(a),b),identity) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.52.2.0','0.11.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.53.0.1',plain,
% 0.65/1.03 ( identity = least_upper_bound(multiply(inverse(a),b),identity) ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.53.0.0','0.11.2.0',theory(equality)]),
% 0.65/1.03 [pos('L','L')]).
% 0.65/1.03 cnf('0.53.1.0',plain,
% 0.65/1.03 ( identity = least_upper_bound(multiply(inverse(a),b),identity) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.53.0.1']),
% 0.65/1.03 [weight('<55,52,11,[1,0,0,4]>')]).
% 0.65/1.03 cnf('0.53.1.1',plain,
% 0.65/1.03 ( identity = least_upper_bound(identity,multiply(inverse(a),b)) ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.53.1.0','0.12.2.0',theory(equality)]),
% 0.65/1.03 [pos('R','L')]).
% 0.65/1.03 cnf('0.53.2.0',plain,
% 0.65/1.03 ( least_upper_bound(identity,multiply(inverse(a),b)) = identity ),
% 0.65/1.03 inference(orient,[status(thm)],['0.53.1.1',theory(equality)]),
% 0.65/1.03 [x,rule_50]).
% 0.65/1.03 cnf('0.99.0.0',plain,
% 0.65/1.03 ( least_upper_bound(multiply(identity,X1),multiply(multiply(inverse(a),b),X1)) = multiply(identity,X1) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.9.2.0','0.53.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1','L')]).
% 0.65/1.03 cnf('0.99.0.1',plain,
% 0.65/1.03 ( least_upper_bound(X1,multiply(multiply(inverse(a),b),X1)) = multiply(identity,X1) ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.99.0.0','0.1.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1','L')]).
% 0.65/1.03 cnf('0.99.0.2',plain,
% 0.65/1.03 ( least_upper_bound(X1,multiply(inverse(a),multiply(b,X1))) = multiply(identity,X1) ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.99.0.1','0.6.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('0.99.0.3',plain,
% 0.65/1.03 ( least_upper_bound(X1,multiply(inverse(a),multiply(b,X1))) = X1 ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.99.0.2','0.1.2.0',theory(equality)]),
% 0.65/1.03 [pos('R','L')]).
% 0.65/1.03 cnf('0.99.1.0',plain,
% 0.65/1.03 ( least_upper_bound(X1,multiply(inverse(a),multiply(b,X1))) = X1 ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.99.0.3']),
% 0.65/1.03 [weight('<89,53,9,[0,0,0,1]>')]).
% 0.65/1.03 cnf('0.99.2.0',plain,
% 0.65/1.03 ( least_upper_bound(X1,multiply(inverse(a),multiply(b,X1))) = X1 ),
% 0.65/1.03 inference(orient,[status(thm)],['0.99.1.0',theory(equality)]),
% 0.65/1.03 [u,rule_96]).
% 0.65/1.03 cnf('0.100.0.0',plain,
% 0.65/1.03 ( inverse(b) = least_upper_bound(inverse(b),multiply(inverse(a),identity)) ),
% 0.65/1.03 inference(cp,[status(thm)],['0.99.2.0','0.36.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2.2','L')]).
% 0.65/1.03 cnf('0.100.0.1',plain,
% 0.65/1.03 ( inverse(b) = least_upper_bound(inverse(b),inverse(a)) ),
% 0.65/1.03 inference(reduction,[status(thm)],['0.100.0.0','0.39.2.0',theory(equality)]),
% 0.65/1.03 [pos('R.2','L')]).
% 0.65/1.03 cnf('0.100.1.0',plain,
% 0.65/1.03 ( inverse(b) = least_upper_bound(inverse(b),inverse(a)) ),
% 0.65/1.03 inference(weigh,[status(thm)],['0.100.0.1']),
% 0.65/1.03 [weight('<47,99,36,[1,0,0,5]>')]).
% 0.65/1.03 cnf('0.100.2.0',plain,
% 0.65/1.03 ( least_upper_bound(inverse(b),inverse(a)) = inverse(b) ),
% 0.65/1.03 inference(orient,[status(thm)],['0.100.1.0',theory(equality)]),
% 0.65/1.03 [x,rule_97]).
% 0.65/1.03 cnf('1.0.0.0',conjecture,
% 0.65/1.03 ( greatest_lower_bound(inverse(a),inverse(b)) = inverse(a) ),
% 0.65/1.03 file('/tmp/WALDMEISTER_14589_n026',conjecture_1)).
% 0.65/1.03 cnf('1.0.0.1',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(b,a)),inverse(b)) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.0','0.14.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1','R')]).
% 0.65/1.03 cnf('1.0.0.2',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(a,b)),inverse(b)) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.1','0.12.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1','L')]).
% 0.65/1.03 cnf('1.0.0.3',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(a,greatest_lower_bound(b,a))),inverse(b)) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.2','0.17.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1.2','R')]).
% 0.65/1.03 cnf('1.0.0.4',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(a,greatest_lower_bound(a,b))),inverse(b)) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.3','0.15.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1.2','L')]).
% 0.65/1.03 cnf('1.0.0.5',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,b),a))),inverse(b)) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.4','0.49.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1','L')]).
% 0.65/1.03 cnf('1.0.0.6',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(least_upper_bound(greatest_lower_bound(a,b),a),b)),inverse(b)) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.5','0.12.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1','L')]).
% 0.65/1.03 cnf('1.0.0.7',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(greatest_lower_bound(a,b),least_upper_bound(a,b))),inverse(b)) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.6','0.13.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1','L')]).
% 0.65/1.03 cnf('1.0.0.8',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(greatest_lower_bound(a,b),least_upper_bound(b,least_upper_bound(b,a)))),inverse(b)) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.7','0.49.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1.2','L')]).
% 0.65/1.03 cnf('1.0.0.9',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(greatest_lower_bound(a,b),least_upper_bound(b,least_upper_bound(b,a)))),least_upper_bound(inverse(b),inverse(a))) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.8','0.100.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','R')]).
% 0.65/1.03 cnf('1.0.0.10',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(greatest_lower_bound(a,b),least_upper_bound(b,least_upper_bound(b,a)))),least_upper_bound(inverse(a),inverse(b))) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.9','0.12.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.2','L')]).
% 0.65/1.03 cnf('1.0.0.11',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(greatest_lower_bound(b,a),least_upper_bound(b,least_upper_bound(b,a)))),least_upper_bound(inverse(a),inverse(b))) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.10','0.15.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1.1','L')]).
% 0.65/1.03 cnf('1.0.0.12',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(greatest_lower_bound(b,a),least_upper_bound(b,a))),least_upper_bound(inverse(a),inverse(b))) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.11','0.50.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1.2','L')]).
% 0.65/1.03 cnf('1.0.0.13',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(greatest_lower_bound(b,a),a)),least_upper_bound(inverse(a),inverse(b))) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.12','0.14.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1.2','L')]).
% 0.65/1.03 cnf('1.0.0.14',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(least_upper_bound(a,greatest_lower_bound(b,a))),least_upper_bound(inverse(a),inverse(b))) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.13','0.12.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1','L')]).
% 0.65/1.03 cnf('1.0.0.15',plain,
% 0.65/1.03 ( greatest_lower_bound(inverse(a),least_upper_bound(inverse(a),inverse(b))) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.14','0.31.2.0',theory(equality)]),
% 0.65/1.03 [pos('L.1.1','L')]).
% 0.65/1.03 cnf('1.0.0.16',plain,
% 0.65/1.03 ( inverse(a) = inverse(a) ),
% 0.65/1.03 inference(reduction,[status(thm)],['1.0.0.15','0.5.2.0',theory(equality)]),
% 0.65/1.03 [pos('L','L')]).
% 0.65/1.03 cnf('1.0.0.17',plain,
% 0.65/1.03 ( $true ),
% 0.65/1.03 inference(trivial,[status(thm)],['1.0.0.16',theory(equality)]),
% 0.65/1.03 [conjecture_1]).
% 0.65/1.03
% 0.65/1.03 Proved Goals:
% 0.65/1.03 No. 1: greatest_lower_bound(inverse(a),inverse(b)) ?= inverse(a) joined, current: inverse(a) = inverse(a)
% 0.65/1.03 1 goal was specified, which was proved.
% 0.65/1.03 % SZS output end CNFRefutation
% 0.65/1.03 #END OF PROOF
% 0.65/1.03
% 0.65/1.03 Problem WALDMEISTER_14589_n026
% 0.65/1.03 CPs.gen 2400
% 0.65/1.03 CPs.reexp 0
% 0.65/1.03 Select 266
% 0.65/1.03 R 97
% 0.65/1.03 E 3
% 0.65/1.03 vsize 6.5M
% 0.65/1.03 rss 3.7M
% 0.65/1.03 process.time 0.021s
% 0.65/1.03 wallclock.time 0.023s
% 0.65/1.03 status S
% 0.65/1.03
% 0.65/1.03
% 0.65/1.03 Waldmeister states: Goal proved.
% 0.65/1.03 % SZS status Unsatisfiable
% 0.65/1.03
% 0.65/1.03 Problem WALDMEISTER_14589_n026
% 0.65/1.03 CPs.gen 32
% 0.65/1.03 CPs.reexp 0
% 0.65/1.03 Select 10
% 0.65/1.03 R 10
% 0.65/1.03 E 0
% 0.65/1.03 vsize 6.5M
% 0.65/1.03 rss 3.7M
% 0.65/1.03 process.time 0.002s
% 0.65/1.03 wallclock.time 0.022s
% 0.65/1.03 status S
%------------------------------------------------------------------------------