TSTP Solution File: GRP186-2 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP186-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n023.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 12:25:14 EDT 2022
% Result : Unsatisfiable 0.87s 1.30s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP186-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 19:13:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.64/1.03 ********************************************************************************
% 0.64/1.03 * W A L D M E I S T E R \| \ / \|/ *
% 0.64/1.03 * |/ | \/ | *
% 0.64/1.03 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.64/1.03 * A. Jaeger and B. Loechner | | *
% 0.64/1.03 * <waldmeister@informatik.uni-kl.de> | *
% 0.64/1.03 ********************************************************************************
% 0.64/1.03
% 0.64/1.03
% 0.64/1.03 Goals:
% 0.64/1.03 ------
% 0.64/1.03
% 0.64/1.03 ( 1) multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) ?=? least_upper_bound(multiply(a,b),identity)
% 0.64/1.03
% 0.64/1.03 Detected structure: VerbandsgeordneteGruppe
% 0.64/1.03 ********************************************************************************
% 0.64/1.03 ****************************** COMPLETION - PROOF ******************************
% 0.64/1.03 ********************************************************************************
% 0.64/1.03
% 0.87/1.30 joined goal: 1 multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) ?= least_upper_bound(multiply(a,b),identity) to inverse(greatest_lower_bound(identity,inverse(multiply(a,b))))
% 0.87/1.30 goal joined
% 0.87/1.30 % SZS status Unsatisfiable
% 0.87/1.30 #START OF PROOF
% 0.87/1.30 % SZS output start CNFRefutation
% 0.87/1.30 cnf('0.1.0.0',axiom,
% 0.87/1.30 ( X1 = multiply(identity,X1) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.1.1.0',plain,
% 0.87/1.30 ( X1 = multiply(identity,X1) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.87/1.30 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.87/1.30 cnf('0.1.2.0',plain,
% 0.87/1.30 ( multiply(identity,X1) = X1 ),
% 0.87/1.30 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_1]).
% 0.87/1.30 cnf('0.3.0.0',axiom,
% 0.87/1.30 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.3.1.0',plain,
% 0.87/1.30 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.87/1.30 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.87/1.30 cnf('0.3.2.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 0.87/1.30 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_3]).
% 0.87/1.30 cnf('0.5.0.0',axiom,
% 0.87/1.30 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.5.1.0',plain,
% 0.87/1.30 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.87/1.30 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.87/1.30 cnf('0.5.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 0.87/1.30 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_5]).
% 0.87/1.30 cnf('0.6.0.0',axiom,
% 0.87/1.30 ( X1 = inverse(inverse(X1)) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.6.1.0',plain,
% 0.87/1.30 ( X1 = inverse(inverse(X1)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.87/1.30 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.87/1.30 cnf('0.6.2.0',plain,
% 0.87/1.30 ( inverse(inverse(X1)) = X1 ),
% 0.87/1.30 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_6]).
% 0.87/1.30 cnf('0.7.0.0',axiom,
% 0.87/1.30 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.7.1.0',plain,
% 0.87/1.30 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.87/1.30 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.87/1.30 cnf('0.7.2.0',plain,
% 0.87/1.30 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_7]).
% 0.87/1.30 cnf('0.9.0.0',axiom,
% 0.87/1.30 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.9.1.0',plain,
% 0.87/1.30 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.87/1.30 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.87/1.30 cnf('0.9.2.0',plain,
% 0.87/1.30 ( multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_9]).
% 0.87/1.30 cnf('0.10.0.0',axiom,
% 0.87/1.30 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.10.1.0',plain,
% 0.87/1.30 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.87/1.30 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.87/1.30 cnf('0.10.2.0',plain,
% 0.87/1.30 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_10]).
% 0.87/1.30 cnf('0.11.0.0',axiom,
% 0.87/1.30 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.11.1.0',plain,
% 0.87/1.30 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.87/1.30 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.87/1.30 cnf('0.11.2.0',plain,
% 0.87/1.30 ( multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_11]).
% 0.87/1.30 cnf('0.12.0.0',axiom,
% 0.87/1.30 ( multiply(inverse(X1),X1) = identity ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.12.1.0',plain,
% 0.87/1.30 ( multiply(inverse(X1),X1) = identity ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.87/1.30 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.87/1.30 cnf('0.12.2.0',plain,
% 0.87/1.30 ( multiply(inverse(X1),X1) = identity ),
% 0.87/1.30 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_12]).
% 0.87/1.30 cnf('0.13.0.0',axiom,
% 0.87/1.30 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.13.1.0',plain,
% 0.87/1.30 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.87/1.30 [weight('<12,0,0,[0,0,0,13]>')]).
% 0.87/1.30 cnf('0.13.2.0',plain,
% 0.87/1.30 ( multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)) ),
% 0.87/1.30 inference(activate,[status(thm)],['0.13.1.0']),
% 0.87/1.30 [equation_1]).
% 0.87/1.30 cnf('0.14.0.0',axiom,
% 0.87/1.30 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.14.1.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.87/1.30 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.87/1.30 cnf('0.14.2.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.87/1.30 inference(activate,[status(thm)],['0.14.1.0']),
% 0.87/1.30 [equation_2]).
% 0.87/1.30 cnf('0.15.0.0',axiom,
% 0.87/1.30 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.15.1.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.87/1.30 [weight('<14,0,0,[0,0,0,15]>')]).
% 0.87/1.30 cnf('0.15.2.0',plain,
% 0.87/1.30 ( least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_13]).
% 0.87/1.30 cnf('0.16.0.0',axiom,
% 0.87/1.30 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.16.1.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.87/1.30 [weight('<15,0,0,[0,0,0,16]>')]).
% 0.87/1.30 cnf('0.16.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.87/1.30 inference(activate,[status(thm)],['0.16.1.0']),
% 0.87/1.30 [equation_3]).
% 0.87/1.30 cnf('0.17.0.0',axiom,
% 0.87/1.30 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.17.1.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.87/1.30 [weight('<16,0,0,[0,0,0,17]>')]).
% 0.87/1.30 cnf('0.17.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_14]).
% 0.87/1.30 cnf('0.18.0.0',axiom,
% 0.87/1.30 ( inverse(identity) = identity ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023')).
% 0.87/1.30 cnf('0.18.1.0',plain,
% 0.87/1.30 ( inverse(identity) = identity ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.18.0.0']),
% 0.87/1.30 [weight('<17,0,0,[0,0,0,18]>')]).
% 0.87/1.30 cnf('0.18.2.0',plain,
% 0.87/1.30 ( inverse(identity) = identity ),
% 0.87/1.30 inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_15]).
% 0.87/1.30 cnf('0.19.0.0',plain,
% 0.87/1.30 ( inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.13.2.0','0.18.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','L')]).
% 0.87/1.30 cnf('0.19.0.1',plain,
% 0.87/1.30 ( inverse(multiply(X1,identity)) = inverse(X1) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.19.0.0','0.1.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.19.1.0',plain,
% 0.87/1.30 ( multiply(X1,identity) = X1 ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.19.0.1']),
% 0.87/1.30 [weight('<19,18,13,[0,0,0,1]>')]).
% 0.87/1.30 cnf('0.19.2.0',plain,
% 0.87/1.30 ( multiply(X1,identity) = X1 ),
% 0.87/1.30 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_16]).
% 0.87/1.30 cnf('0.21.0.0',plain,
% 0.87/1.30 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.5.2.0','0.14.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2','L')]).
% 0.87/1.30 cnf('0.21.1.0',plain,
% 0.87/1.30 ( X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.87/1.30 [weight('<41,14,5,[0,0,0,2]>')]).
% 0.87/1.30 cnf('0.21.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1 ),
% 0.87/1.30 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_18]).
% 0.87/1.30 cnf('0.22.0.0',plain,
% 0.87/1.30 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.3.2.0','0.16.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2','L')]).
% 0.87/1.30 cnf('0.22.1.0',plain,
% 0.87/1.30 ( X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.22.0.0']),
% 0.87/1.30 [weight('<41,16,3,[0,0,0,2]>')]).
% 0.87/1.30 cnf('0.22.2.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1 ),
% 0.87/1.30 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_19]).
% 0.87/1.30 cnf('0.27.0.0',plain,
% 0.87/1.30 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.7.2.0','0.12.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','L')]).
% 0.87/1.30 cnf('0.27.0.1',plain,
% 0.87/1.30 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.27.0.0','0.1.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.27.1.0',plain,
% 0.87/1.30 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.27.0.1']),
% 0.87/1.30 [weight('<55,12,7,[0,0,0,1]>')]).
% 0.87/1.30 cnf('0.27.2.0',plain,
% 0.87/1.30 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.87/1.30 inference(orient,[status(thm)],['0.27.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_24]).
% 0.87/1.30 cnf('0.29.0.0',plain,
% 0.87/1.30 ( inverse(X1) = multiply(inverse(inverse(X2)),inverse(multiply(X1,X2))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.27.2.0','0.13.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2','L')]).
% 0.87/1.30 cnf('0.29.0.1',plain,
% 0.87/1.30 ( inverse(X1) = multiply(X2,inverse(multiply(X1,X2))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.29.0.0','0.6.2.0',theory(equality)]),
% 0.87/1.30 [pos('R.1','L')]).
% 0.87/1.30 cnf('0.29.1.0',plain,
% 0.87/1.30 ( inverse(X1) = multiply(X2,inverse(multiply(X1,X2))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.29.0.1']),
% 0.87/1.30 [weight('<62,27,13,[1,0,0,3]>')]).
% 0.87/1.30 cnf('0.29.2.0',plain,
% 0.87/1.30 ( multiply(X1,inverse(multiply(X2,X1))) = inverse(X2) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_26]).
% 0.87/1.30 cnf('0.46.0.0',plain,
% 0.87/1.30 ( multiply(X1,X2) = inverse(multiply(inverse(X2),inverse(X1))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.6.2.0','0.13.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','R')]).
% 0.87/1.30 cnf('0.46.1.0',plain,
% 0.87/1.30 ( multiply(X1,X2) = inverse(multiply(inverse(X2),inverse(X1))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.46.0.0']),
% 0.87/1.30 [weight('<99,13,6,[0,1,0,1]>')]).
% 0.87/1.30 cnf('0.46.2.0',plain,
% 0.87/1.30 ( multiply(X1,X2) = inverse(multiply(inverse(X2),inverse(X1))) ),
% 0.87/1.30 inference(activate,[status(thm)],['0.46.1.0']),
% 0.87/1.30 [equation_4]).
% 0.87/1.30 cnf('0.47.0.0',plain,
% 0.87/1.30 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.13.2.0','0.6.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','L')]).
% 0.87/1.30 cnf('0.47.1.0',plain,
% 0.87/1.30 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.47.0.0']),
% 0.87/1.30 [weight('<99,13,6,[1,0,0,1]>')]).
% 0.87/1.30 cnf('0.47.2.0',plain,
% 0.87/1.30 ( inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)) ),
% 0.87/1.30 inference(activate,[status(thm)],['0.47.1.0']),
% 0.87/1.30 [equation_5]).
% 0.87/1.30 cnf('0.65.0.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X2,X1),X3) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.17.2.0','0.16.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','L')]).
% 0.87/1.30 cnf('0.65.0.1',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X3)) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.65.0.0','0.17.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.65.1.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X3)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.65.0.1']),
% 0.87/1.30 [weight('<120,17,16,[1,0,0,1]>')]).
% 0.87/1.30 cnf('0.65.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X3)) ),
% 0.87/1.30 inference(activate,[status(thm)],['0.65.1.0']),
% 0.87/1.30 [equation_10]).
% 0.87/1.30 cnf('0.69.0.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,X2) = greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,least_upper_bound(X2,X3))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.5.2.0','0.15.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2','L')]).
% 0.87/1.30 cnf('0.69.1.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,X2) = greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,least_upper_bound(X2,X3))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.69.0.0']),
% 0.87/1.30 [weight('<129,15,5,[0,0,0,2]>')]).
% 0.87/1.30 cnf('0.69.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,least_upper_bound(X2,X3))) = least_upper_bound(X1,X2) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_57]).
% 0.87/1.30 cnf('0.137.0.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(X1,X2)) = multiply(X3,inverse(least_upper_bound(multiply(X1,X3),multiply(X2,X3)))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.29.2.0','0.10.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1','L')]).
% 0.87/1.30 cnf('0.137.1.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(X1,X2)) = multiply(X3,inverse(least_upper_bound(multiply(X1,X3),multiply(X2,X3)))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.137.0.0']),
% 0.87/1.30 [weight('<164,29,10,[1,0,0,3]>')]).
% 0.87/1.30 cnf('0.137.2.0',plain,
% 0.87/1.30 ( multiply(X1,inverse(least_upper_bound(multiply(X2,X1),multiply(X3,X1)))) = inverse(least_upper_bound(X2,X3)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.137.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_125]).
% 0.87/1.30 cnf('0.138.0.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,X1)) = multiply(X2,inverse(least_upper_bound(X2,multiply(X1,X2)))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.137.2.0','0.1.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1.1','L')]).
% 0.87/1.30 cnf('0.138.1.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,X1)) = multiply(X2,inverse(least_upper_bound(X2,multiply(X1,X2)))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.138.0.0']),
% 0.87/1.30 [weight('<116,137,1,[1,0,0,4]>')]).
% 0.87/1.30 cnf('0.138.2.0',plain,
% 0.87/1.30 ( multiply(X1,inverse(least_upper_bound(X1,multiply(X2,X1)))) = inverse(least_upper_bound(identity,X2)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.138.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_126]).
% 0.87/1.30 cnf('0.139.0.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(X1,identity))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.138.2.0','0.12.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1.2','L')]).
% 0.87/1.30 cnf('0.139.1.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(X1,identity))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.139.0.0']),
% 0.87/1.30 [weight('<83,138,12,[1,0,0,5]>')]).
% 0.87/1.30 cnf('0.139.2.0',plain,
% 0.87/1.30 ( multiply(X1,inverse(least_upper_bound(X1,identity))) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.139.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_127]).
% 0.87/1.30 cnf('0.140.0.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(identity,X1))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.139.2.0','0.14.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1','L')]).
% 0.87/1.30 cnf('0.140.1.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(identity,X1))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.140.0.0']),
% 0.87/1.30 [weight('<83,139,14,[1,0,0,3]>')]).
% 0.87/1.30 cnf('0.140.2.0',plain,
% 0.87/1.30 ( multiply(X1,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,inverse(X1))) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.140.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_128]).
% 0.87/1.30 cnf('0.141.0.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1)))) = multiply(greatest_lower_bound(identity,X1),inverse(identity)) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.140.2.0','0.3.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1','L')]).
% 0.87/1.30 cnf('0.141.0.1',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1)))) = greatest_lower_bound(multiply(identity,inverse(identity)),multiply(X1,inverse(identity))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.141.0.0','0.11.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.141.0.2',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1)))) = greatest_lower_bound(inverse(identity),multiply(X1,inverse(identity))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.141.0.1','0.1.2.0',theory(equality)]),
% 0.87/1.30 [pos('R.1','L')]).
% 0.87/1.30 cnf('0.141.0.3',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1)))) = greatest_lower_bound(identity,multiply(X1,inverse(identity))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.141.0.2','0.18.2.0',theory(equality)]),
% 0.87/1.30 [pos('R.1','L')]).
% 0.87/1.30 cnf('0.141.0.4',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1)))) = greatest_lower_bound(identity,multiply(X1,identity)) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.141.0.3','0.18.2.0',theory(equality)]),
% 0.87/1.30 [pos('R.2.2','L')]).
% 0.87/1.30 cnf('0.141.0.5',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1)))) = greatest_lower_bound(identity,X1) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.141.0.4','0.19.2.0',theory(equality)]),
% 0.87/1.30 [pos('R.2','L')]).
% 0.87/1.30 cnf('0.141.1.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1)))) = greatest_lower_bound(identity,X1) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.141.0.5']),
% 0.87/1.30 [weight('<87,140,3,[1,0,0,3]>')]).
% 0.87/1.30 cnf('0.141.2.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1)))) = greatest_lower_bound(identity,X1) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.141.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_129]).
% 0.87/1.30 cnf('0.142.0.0',plain,
% 0.87/1.30 ( least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,X1)) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.6.2.0','0.141.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','L')]).
% 0.87/1.30 cnf('0.142.1.0',plain,
% 0.87/1.30 ( least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,X1)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.142.0.0']),
% 0.87/1.30 [weight('<76,141,6,[0,0,0,1]>')]).
% 0.87/1.30 cnf('0.142.2.0',plain,
% 0.87/1.30 ( least_upper_bound(identity,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,X1)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.142.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_130]).
% 0.87/1.30 cnf('0.143.0.0',plain,
% 0.87/1.30 ( identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.5.2.0','0.142.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2','L')]).
% 0.87/1.30 cnf('0.143.1.0',plain,
% 0.87/1.30 ( identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.143.0.0']),
% 0.87/1.30 [weight('<55,142,5,[0,0,0,2]>')]).
% 0.87/1.30 cnf('0.143.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) = identity ),
% 0.87/1.30 inference(orient,[status(thm)],['0.143.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_131]).
% 0.87/1.30 cnf('0.148.0.0',plain,
% 0.87/1.30 ( greatest_lower_bound(multiply(identity,X1),multiply(inverse(greatest_lower_bound(identity,X2)),X1)) = multiply(identity,X1) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.11.2.0','0.143.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','L')]).
% 0.87/1.30 cnf('0.148.0.1',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),X1)) = multiply(identity,X1) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.148.0.0','0.1.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','L')]).
% 0.87/1.30 cnf('0.148.0.2',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),X1)) = X1 ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.148.0.1','0.1.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.148.1.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),X1)) = X1 ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.148.0.2']),
% 0.87/1.30 [weight('<89,143,11,[0,0,0,1]>')]).
% 0.87/1.30 cnf('0.148.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,multiply(inverse(greatest_lower_bound(identity,X2)),X1)) = X1 ),
% 0.87/1.30 inference(orient,[status(thm)],['0.148.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_136]).
% 0.87/1.30 cnf('0.168.0.0',plain,
% 0.87/1.30 ( inverse(X1) = greatest_lower_bound(inverse(X1),inverse(multiply(X1,inverse(inverse(greatest_lower_bound(identity,X2)))))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.148.2.0','0.47.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2','R')]).
% 0.87/1.30 cnf('0.168.0.1',plain,
% 0.87/1.30 ( inverse(X1) = greatest_lower_bound(inverse(X1),inverse(multiply(X1,greatest_lower_bound(identity,X2)))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.168.0.0','0.6.2.0',theory(equality)]),
% 0.87/1.30 [pos('R.2.1.2','L')]).
% 0.87/1.30 cnf('0.168.0.2',plain,
% 0.87/1.30 ( inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(multiply(X1,identity),multiply(X1,X2)))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.168.0.1','0.9.2.0',theory(equality)]),
% 0.87/1.30 [pos('R.2.1','L')]).
% 0.87/1.30 cnf('0.168.0.3',plain,
% 0.87/1.30 ( inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,multiply(X1,X2)))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.168.0.2','0.19.2.0',theory(equality)]),
% 0.87/1.30 [pos('R.2.1.1','L')]).
% 0.87/1.30 cnf('0.168.1.0',plain,
% 0.87/1.30 ( inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,multiply(X1,X2)))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.168.0.3']),
% 0.87/1.30 [weight('<119,148,47,[1,0,1,2]>')]).
% 0.87/1.30 cnf('0.168.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,multiply(X1,X2)))) = inverse(X1) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.168.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_156]).
% 0.87/1.30 cnf('0.170.0.0',plain,
% 0.87/1.30 ( inverse(inverse(X1)) = greatest_lower_bound(inverse(inverse(X1)),inverse(greatest_lower_bound(inverse(X1),X2))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.168.2.0','0.27.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1.2','L')]).
% 0.87/1.30 cnf('0.170.0.1',plain,
% 0.87/1.30 ( X1 = greatest_lower_bound(inverse(inverse(X1)),inverse(greatest_lower_bound(inverse(X1),X2))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.170.0.0','0.6.2.0',theory(equality)]),
% 0.87/1.30 [pos('L','L')]).
% 0.87/1.30 cnf('0.170.0.2',plain,
% 0.87/1.30 ( X1 = greatest_lower_bound(X1,inverse(greatest_lower_bound(inverse(X1),X2))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.170.0.1','0.6.2.0',theory(equality)]),
% 0.87/1.30 [pos('R.1','L')]).
% 0.87/1.30 cnf('0.170.1.0',plain,
% 0.87/1.30 ( X1 = greatest_lower_bound(X1,inverse(greatest_lower_bound(inverse(X1),X2))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.170.0.2']),
% 0.87/1.30 [weight('<71,168,27,[1,0,0,6]>')]).
% 0.87/1.30 cnf('0.170.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,inverse(greatest_lower_bound(inverse(X1),X2))) = X1 ),
% 0.87/1.30 inference(orient,[status(thm)],['0.170.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_158]).
% 0.87/1.30 cnf('0.171.0.0',plain,
% 0.87/1.30 ( X1 = greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.170.2.0','0.16.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1','L')]).
% 0.87/1.30 cnf('0.171.1.0',plain,
% 0.87/1.30 ( X1 = greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.171.0.0']),
% 0.87/1.30 [weight('<71,170,16,[1,0,0,3]>')]).
% 0.87/1.30 cnf('0.171.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = X1 ),
% 0.87/1.30 inference(orient,[status(thm)],['0.171.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_159]).
% 0.87/1.30 cnf('0.174.0.0',plain,
% 0.87/1.30 ( inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.171.2.0','0.6.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1.2','L')]).
% 0.87/1.30 cnf('0.174.1.0',plain,
% 0.87/1.30 ( inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.174.0.0']),
% 0.87/1.30 [weight('<79,171,6,[1,0,0,5]>')]).
% 0.87/1.30 cnf('0.174.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) = inverse(X1) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.174.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_162]).
% 0.87/1.30 cnf('0.176.0.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(least_upper_bound(X1,X2)),inverse(X1)) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.174.2.0','0.5.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1','L')]).
% 0.87/1.30 cnf('0.176.1.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(least_upper_bound(X1,X2)),inverse(X1)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.176.0.0']),
% 0.87/1.30 [weight('<95,174,5,[1,0,0,4]>')]).
% 0.87/1.30 cnf('0.176.1.1',plain,
% 0.87/1.30 ( inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.176.1.0','0.16.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.176.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(least_upper_bound(X1,X2)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.176.1.1',theory(equality)]),
% 0.87/1.30 [x,rule_164]).
% 0.87/1.30 cnf('0.177.0.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.176.2.0','0.18.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','L')]).
% 0.87/1.30 cnf('0.177.1.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.177.0.0']),
% 0.87/1.30 [weight('<76,176,18,[1,0,0,1]>')]).
% 0.87/1.30 cnf('0.177.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.177.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_165]).
% 0.87/1.30 cnf('0.178.0.0',plain,
% 0.87/1.30 ( identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.3.2.0','0.177.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2','L')]).
% 0.87/1.30 cnf('0.178.1.0',plain,
% 0.87/1.30 ( identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.178.0.0']),
% 0.87/1.30 [weight('<55,177,3,[0,0,0,2]>')]).
% 0.87/1.30 cnf('0.178.2.0',plain,
% 0.87/1.30 ( least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) = identity ),
% 0.87/1.30 inference(orient,[status(thm)],['0.178.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_166]).
% 0.87/1.30 cnf('0.179.0.0',plain,
% 0.87/1.30 ( identity = least_upper_bound(identity,inverse(least_upper_bound(X1,identity))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.178.2.0','0.14.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1','L')]).
% 0.87/1.30 cnf('0.179.1.0',plain,
% 0.87/1.30 ( identity = least_upper_bound(identity,inverse(least_upper_bound(X1,identity))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.179.0.0']),
% 0.87/1.30 [weight('<55,178,14,[1,0,0,3]>')]).
% 0.87/1.30 cnf('0.179.2.0',plain,
% 0.87/1.30 ( least_upper_bound(identity,inverse(least_upper_bound(X1,identity))) = identity ),
% 0.87/1.30 inference(orient,[status(thm)],['0.179.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_167]).
% 0.87/1.30 cnf('0.180.0.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(X1,identity)) = greatest_lower_bound(inverse(least_upper_bound(X1,identity)),identity) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.21.2.0','0.179.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2','L')]).
% 0.87/1.30 cnf('0.180.1.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(X1,identity)) = greatest_lower_bound(inverse(least_upper_bound(X1,identity)),identity) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.180.0.0']),
% 0.87/1.30 [weight('<76,179,21,[0,0,0,2]>')]).
% 0.87/1.30 cnf('0.180.1.1',plain,
% 0.87/1.30 ( inverse(least_upper_bound(X1,identity)) = greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.180.1.0','0.16.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.180.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) = inverse(least_upper_bound(X1,identity)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.180.1.1',theory(equality)]),
% 0.87/1.30 [x,rule_168]).
% 0.87/1.30 cnf('0.198.0.0',plain,
% 0.87/1.30 ( inverse(greatest_lower_bound(X1,inverse(X2))) = least_upper_bound(inverse(greatest_lower_bound(X1,inverse(X2))),X2) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.22.2.0','0.171.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2','L')]).
% 0.87/1.30 cnf('0.198.1.0',plain,
% 0.87/1.30 ( inverse(greatest_lower_bound(X1,inverse(X2))) = least_upper_bound(inverse(greatest_lower_bound(X1,inverse(X2))),X2) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.198.0.0']),
% 0.87/1.30 [weight('<103,171,22,[0,0,0,2]>')]).
% 0.87/1.30 cnf('0.198.1.1',plain,
% 0.87/1.30 ( inverse(greatest_lower_bound(X1,inverse(X2))) = least_upper_bound(X2,inverse(greatest_lower_bound(X1,inverse(X2)))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.198.1.0','0.14.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.198.2.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = inverse(greatest_lower_bound(X2,inverse(X1))) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.198.1.1',theory(equality)]),
% 0.87/1.30 [x,rule_186]).
% 0.87/1.30 cnf('0.322.0.0',plain,
% 0.87/1.30 ( greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(least_upper_bound(X2,identity)))) = greatest_lower_bound(X1,inverse(least_upper_bound(X2,identity))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.65.2.0','0.180.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2','L')]).
% 0.87/1.30 cnf('0.322.1.0',plain,
% 0.87/1.30 ( greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(least_upper_bound(X2,identity)))) = greatest_lower_bound(X1,inverse(least_upper_bound(X2,identity))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.322.0.0']),
% 0.87/1.30 [weight('<134,180,65,[0,0,0,2]>')]).
% 0.87/1.30 cnf('0.322.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(least_upper_bound(X2,identity)))) = greatest_lower_bound(X1,inverse(least_upper_bound(X2,identity))) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.322.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_310]).
% 0.87/1.30 cnf('0.409.0.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,identity) = greatest_lower_bound(least_upper_bound(X1,identity),least_upper_bound(X1,inverse(greatest_lower_bound(identity,X2)))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.69.2.0','0.142.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.2','L')]).
% 0.87/1.30 cnf('0.409.1.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,identity) = greatest_lower_bound(least_upper_bound(X1,identity),least_upper_bound(X1,inverse(greatest_lower_bound(identity,X2)))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.409.0.0']),
% 0.87/1.30 [weight('<153,142,69,[0,0,0,6]>')]).
% 0.87/1.30 cnf('0.409.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(least_upper_bound(X1,identity),least_upper_bound(X1,inverse(greatest_lower_bound(identity,X2)))) = least_upper_bound(X1,identity) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.409.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_397]).
% 0.87/1.30 cnf('0.410.0.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,identity) = greatest_lower_bound(least_upper_bound(X1,identity),inverse(greatest_lower_bound(identity,inverse(X1)))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.409.2.0','0.198.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2','L')]).
% 0.87/1.30 cnf('0.410.1.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,identity) = greatest_lower_bound(least_upper_bound(X1,identity),inverse(greatest_lower_bound(identity,inverse(X1)))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.410.0.0']),
% 0.87/1.30 [weight('<129,409,198,[1,0,0,4]>')]).
% 0.87/1.30 cnf('0.410.1.1',plain,
% 0.87/1.30 ( least_upper_bound(X1,identity) = greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X1))),least_upper_bound(X1,identity)) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.410.1.0','0.16.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.410.2.0',plain,
% 0.87/1.30 ( greatest_lower_bound(inverse(greatest_lower_bound(identity,inverse(X1))),least_upper_bound(X1,identity)) = least_upper_bound(X1,identity) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.410.1.1',theory(equality)]),
% 0.87/1.30 [x,rule_398]).
% 0.87/1.30 cnf('0.411.0.0',plain,
% 0.87/1.30 ( greatest_lower_bound(identity,inverse(X1)) = greatest_lower_bound(greatest_lower_bound(identity,inverse(X1)),inverse(least_upper_bound(X1,identity))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.170.2.0','0.410.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1','L')]).
% 0.87/1.30 cnf('0.411.0.1',plain,
% 0.87/1.30 ( greatest_lower_bound(identity,inverse(X1)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,identity)))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.411.0.0','0.17.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.411.0.2',plain,
% 0.87/1.30 ( greatest_lower_bound(identity,inverse(X1)) = greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,identity))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.411.0.1','0.322.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.411.0.3',plain,
% 0.87/1.30 ( greatest_lower_bound(identity,inverse(X1)) = inverse(least_upper_bound(X1,identity)) ),
% 0.87/1.30 inference(reduction,[status(thm)],['0.411.0.2','0.176.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('0.411.1.0',plain,
% 0.87/1.30 ( greatest_lower_bound(identity,inverse(X1)) = inverse(least_upper_bound(X1,identity)) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.411.0.3']),
% 0.87/1.30 [weight('<44,410,170,[0,0,0,3]>')]).
% 0.87/1.30 cnf('0.411.2.0',plain,
% 0.87/1.30 ( inverse(least_upper_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.411.1.0',theory(equality)]),
% 0.87/1.30 [x,rule_399]).
% 0.87/1.30 cnf('0.413.0.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,identity) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 0.87/1.30 inference(cp,[status(thm)],['0.6.2.0','0.411.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','L')]).
% 0.87/1.30 cnf('0.413.1.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,identity) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 0.87/1.30 inference(weigh,[status(thm)],['0.413.0.0']),
% 0.87/1.30 [weight('<35,411,6,[0,0,0,1]>')]).
% 0.87/1.30 cnf('0.413.2.0',plain,
% 0.87/1.30 ( least_upper_bound(X1,identity) = inverse(greatest_lower_bound(identity,inverse(X1))) ),
% 0.87/1.30 inference(orient,[status(thm)],['0.413.1.0',theory(equality)]),
% 0.87/1.30 [u,rule_401]).
% 0.87/1.30 cnf('1.0.0.0',conjecture,
% 0.87/1.30 ( multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) = least_upper_bound(multiply(a,b),identity) ),
% 0.87/1.30 file('/tmp/WALDMEISTER_2454_n023',conjecture_1)).
% 0.87/1.30 cnf('1.0.0.1',plain,
% 0.87/1.30 ( multiply(a,inverse(greatest_lower_bound(inverse(b),a))) = least_upper_bound(multiply(a,b),identity) ),
% 0.87/1.30 inference(reduction,[status(thm)],['1.0.0.0','0.16.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.2.1','L')]).
% 0.87/1.30 cnf('1.0.0.2',plain,
% 0.87/1.30 ( inverse(multiply(greatest_lower_bound(inverse(b),a),inverse(a))) = least_upper_bound(multiply(a,b),identity) ),
% 0.87/1.30 inference(reduction,[status(thm)],['1.0.0.1','0.47.2.0',theory(equality)]),
% 0.87/1.30 [pos('L','R')]).
% 0.87/1.30 cnf('1.0.0.3',plain,
% 0.87/1.30 ( inverse(greatest_lower_bound(multiply(inverse(b),inverse(a)),multiply(a,inverse(a)))) = least_upper_bound(multiply(a,b),identity) ),
% 0.87/1.30 inference(reduction,[status(thm)],['1.0.0.2','0.11.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','L')]).
% 0.87/1.30 cnf('1.0.0.4',plain,
% 0.87/1.30 ( inverse(greatest_lower_bound(multiply(inverse(b),inverse(a)),inverse(multiply(a,inverse(a))))) = least_upper_bound(multiply(a,b),identity) ),
% 0.87/1.30 inference(reduction,[status(thm)],['1.0.0.3','0.47.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1.2','R')]).
% 0.87/1.30 cnf('1.0.0.5',plain,
% 0.87/1.30 ( inverse(greatest_lower_bound(multiply(inverse(b),inverse(a)),inverse(inverse(multiply(inverse(inverse(a)),inverse(a)))))) = least_upper_bound(multiply(a,b),identity) ),
% 0.87/1.30 inference(reduction,[status(thm)],['1.0.0.4','0.46.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1.2.1','L')]).
% 0.87/1.30 cnf('1.0.0.6',plain,
% 0.87/1.30 ( inverse(greatest_lower_bound(inverse(multiply(a,b)),inverse(inverse(multiply(inverse(inverse(a)),inverse(a)))))) = least_upper_bound(multiply(a,b),identity) ),
% 0.87/1.30 inference(reduction,[status(thm)],['1.0.0.5','0.13.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1.1','L')]).
% 0.87/1.30 cnf('1.0.0.7',plain,
% 0.87/1.30 ( inverse(greatest_lower_bound(inverse(inverse(multiply(inverse(inverse(a)),inverse(a)))),inverse(multiply(a,b)))) = least_upper_bound(multiply(a,b),identity) ),
% 0.87/1.30 inference(reduction,[status(thm)],['1.0.0.6','0.16.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1','L')]).
% 0.87/1.30 cnf('1.0.0.8',plain,
% 0.87/1.30 ( inverse(greatest_lower_bound(multiply(inverse(inverse(a)),inverse(a)),inverse(multiply(a,b)))) = least_upper_bound(multiply(a,b),identity) ),
% 0.87/1.30 inference(reduction,[status(thm)],['1.0.0.7','0.6.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1.1','L')]).
% 0.87/1.30 cnf('1.0.0.9',plain,
% 0.87/1.30 ( inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) = least_upper_bound(multiply(a,b),identity) ),
% 0.87/1.30 inference(reduction,[status(thm)],['1.0.0.8','0.12.2.0',theory(equality)]),
% 0.87/1.30 [pos('L.1.1','L')]).
% 0.87/1.30 cnf('1.0.0.10',plain,
% 0.87/1.30 ( inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) = inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) ),
% 0.87/1.30 inference(reduction,[status(thm)],['1.0.0.9','0.413.2.0',theory(equality)]),
% 0.87/1.30 [pos('R','L')]).
% 0.87/1.30 cnf('1.0.0.11',plain,
% 0.87/1.30 ( $true ),
% 0.87/1.30 inference(trivial,[status(thm)],['1.0.0.10',theory(equality)]),
% 0.87/1.30 [conjecture_1]).
% 0.87/1.30
% 0.87/1.30 Proved Goals:
% 0.87/1.30 No. 1: multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) ?= least_upper_bound(multiply(a,b),identity) joined, current: inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))) = inverse(greatest_lower_bound(identity,inverse(multiply(a,b))))
% 0.87/1.30 1 goal was specified, which was proved.
% 0.87/1.30 % SZS output end CNFRefutation
% 0.87/1.30 #END OF PROOF
% 0.87/1.30
% 0.87/1.30 Problem WALDMEISTER_2454_n023
% 0.87/1.30 CPs.gen 55672
% 0.87/1.30 CPs.reexp 0
% 0.87/1.30 Select 5588
% 0.87/1.30 R 401
% 0.87/1.30 E 12
% 0.87/1.30 vsize 7.1M
% 0.87/1.30 rss 4.4M
% 0.87/1.30 process.time 0.222s
% 0.87/1.30 wallclock.time 0.271s
% 0.87/1.30 status S
% 0.87/1.30
% 0.87/1.30
% 0.87/1.30 Waldmeister states: Goal proved.
% 0.87/1.30 % SZS status Unsatisfiable
% 0.87/1.30
% 0.87/1.30 Problem WALDMEISTER_2454_n023
% 0.87/1.30 CPs.gen 9322
% 0.87/1.30 CPs.reexp 0
% 0.87/1.30 Select 551
% 0.87/1.30 R 179
% 0.87/1.30 E 2
% 0.87/1.30 vsize 6.5M
% 0.87/1.30 rss 3.7M
% 0.87/1.30 process.time 0.049s
% 0.87/1.30 wallclock.time 0.270s
% 0.87/1.30 status S
%------------------------------------------------------------------------------