TSTP Solution File: GRP175-4 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP175-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n032.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 12:25:07 EDT 2022
% Result : Unsatisfiable 0.50s 0.88s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP175-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : woody %s
% 0.12/0.31 % Computer : n032.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 600
% 0.12/0.31 % DateTime : Mon Jun 13 05:03:41 EDT 2022
% 0.12/0.31 % CPUTime :
% 0.50/0.88 ********************************************************************************
% 0.50/0.88 * W A L D M E I S T E R \| \ / \|/ *
% 0.50/0.88 * |/ | \/ | *
% 0.50/0.88 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.50/0.88 * A. Jaeger and B. Loechner | | *
% 0.50/0.88 * <waldmeister@informatik.uni-kl.de> | *
% 0.50/0.88 ********************************************************************************
% 0.50/0.88
% 0.50/0.88
% 0.50/0.88 Goals:
% 0.50/0.88 ------
% 0.50/0.88
% 0.50/0.88 ( 1) multiply(inverse(a),multiply(b,a)) ?=? least_upper_bound(identity,multiply(inverse(a),multiply(b,a)))
% 0.50/0.88
% 0.50/0.88 Detected structure: VerbandsgeordneteGruppe
% 0.50/0.88 ********************************************************************************
% 0.50/0.88 ****************************** COMPLETION - PROOF ******************************
% 0.50/0.88 ********************************************************************************
% 0.50/0.88
% 0.50/0.88 joined goal: 1 multiply(inverse(a),multiply(b,a)) ?= least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) to least_upper_bound(multiply(inverse(a),multiply(b,a)),identity)
% 0.50/0.88 goal joined
% 0.50/0.88 % SZS status Unsatisfiable
% 0.50/0.88 #START OF PROOF
% 0.50/0.88 % SZS output start CNFRefutation
% 0.50/0.88 cnf('0.1.0.0',axiom,
% 0.50/0.88 ( X1 = multiply(identity,X1) ),
% 0.50/0.88 file('/tmp/WALDMEISTER_30187_n032')).
% 0.50/0.88 cnf('0.1.1.0',plain,
% 0.50/0.88 ( X1 = multiply(identity,X1) ),
% 0.50/0.88 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.50/0.88 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.50/0.88 cnf('0.1.2.0',plain,
% 0.50/0.88 ( multiply(identity,X1) = X1 ),
% 0.50/0.88 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.50/0.88 [x,rule_1]).
% 0.50/0.88 cnf('0.5.0.0',axiom,
% 0.50/0.88 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.50/0.88 file('/tmp/WALDMEISTER_30187_n032')).
% 0.50/0.88 cnf('0.5.1.0',plain,
% 0.50/0.88 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.50/0.88 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.50/0.88 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.50/0.88 cnf('0.5.2.0',plain,
% 0.50/0.88 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 0.50/0.88 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.50/0.88 [x,rule_5]).
% 0.50/0.88 cnf('0.8.0.0',axiom,
% 0.50/0.88 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.50/0.88 file('/tmp/WALDMEISTER_30187_n032')).
% 0.50/0.88 cnf('0.8.1.0',plain,
% 0.50/0.88 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.50/0.88 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.50/0.88 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.50/0.88 cnf('0.8.2.0',plain,
% 0.50/0.88 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.50/0.88 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.50/0.88 [u,rule_8]).
% 0.50/0.88 cnf('0.10.0.0',axiom,
% 0.50/0.88 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.50/0.88 file('/tmp/WALDMEISTER_30187_n032')).
% 0.50/0.88 cnf('0.10.1.0',plain,
% 0.50/0.88 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.50/0.88 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.50/0.88 [weight('<9,0,0,[0,0,0,10]>')]).
% 0.50/0.88 cnf('0.10.2.0',plain,
% 0.50/0.88 ( multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)) ),
% 0.50/0.88 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.50/0.88 [u,rule_10]).
% 0.50/0.88 cnf('0.11.0.0',axiom,
% 0.50/0.88 ( multiply(inverse(X1),X1) = identity ),
% 0.50/0.88 file('/tmp/WALDMEISTER_30187_n032')).
% 0.50/0.88 cnf('0.11.1.0',plain,
% 0.50/0.88 ( multiply(inverse(X1),X1) = identity ),
% 0.50/0.88 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.50/0.88 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.50/0.88 cnf('0.11.2.0',plain,
% 0.50/0.88 ( multiply(inverse(X1),X1) = identity ),
% 0.50/0.88 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.50/0.88 [u,rule_11]).
% 0.50/0.88 cnf('0.12.0.0',axiom,
% 0.50/0.88 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.50/0.88 file('/tmp/WALDMEISTER_30187_n032')).
% 0.50/0.88 cnf('0.12.1.0',plain,
% 0.50/0.88 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.50/0.88 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.50/0.88 [weight('<11,0,0,[0,0,0,12]>')]).
% 0.50/0.88 cnf('0.12.2.0',plain,
% 0.50/0.88 ( greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1) ),
% 0.50/0.88 inference(activate,[status(thm)],['0.12.1.0']),
% 0.50/0.88 [equation_1]).
% 0.50/0.88 cnf('0.14.0.0',axiom,
% 0.50/0.88 ( greatest_lower_bound(identity,b) = identity ),
% 0.50/0.88 file('/tmp/WALDMEISTER_30187_n032')).
% 0.50/0.88 cnf('0.14.1.0',plain,
% 0.50/0.88 ( greatest_lower_bound(identity,b) = identity ),
% 0.50/0.88 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.50/0.88 [weight('<13,0,0,[0,0,0,14]>')]).
% 0.50/0.88 cnf('0.14.1.1',plain,
% 0.50/0.88 ( greatest_lower_bound(b,identity) = identity ),
% 0.50/0.88 inference(reduction,[status(thm)],['0.14.1.0','0.12.2.0',theory(equality)]),
% 0.50/0.88 [pos('L','L')]).
% 0.50/0.88 cnf('0.14.2.0',plain,
% 0.50/0.88 ( greatest_lower_bound(b,identity) = identity ),
% 0.50/0.88 inference(orient,[status(thm)],['0.14.1.1',theory(equality)]),
% 0.50/0.88 [u,rule_13]).
% 0.50/0.88 cnf('0.15.0.0',axiom,
% 0.50/0.88 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.50/0.88 file('/tmp/WALDMEISTER_30187_n032')).
% 0.50/0.88 cnf('0.15.1.0',plain,
% 0.50/0.88 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.50/0.88 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.50/0.88 [weight('<14,0,0,[0,0,0,15]>')]).
% 0.50/0.88 cnf('0.15.2.0',plain,
% 0.50/0.88 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.50/0.88 inference(activate,[status(thm)],['0.15.1.0']),
% 0.50/0.88 [equation_2]).
% 0.50/0.88 cnf('0.17.0.0',plain,
% 0.50/0.88 ( b = least_upper_bound(b,identity) ),
% 0.50/0.88 inference(cp,[status(thm)],['0.5.2.0','0.14.2.0',theory(equality)]),
% 0.50/0.88 [pos('L.2','L')]).
% 0.50/0.88 cnf('0.17.1.0',plain,
% 0.50/0.88 ( b = least_upper_bound(b,identity) ),
% 0.50/0.88 inference(weigh,[status(thm)],['0.17.0.0']),
% 0.50/0.88 [weight('<19,14,5,[0,0,0,2]>')]).
% 0.50/0.88 cnf('0.17.2.0',plain,
% 0.50/0.88 ( least_upper_bound(b,identity) = b ),
% 0.50/0.88 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.50/0.88 [x,rule_15]).
% 0.50/0.88 cnf('1.0.0.0',conjecture,
% 0.50/0.88 ( multiply(inverse(a),multiply(b,a)) = least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) ),
% 0.50/0.88 file('/tmp/WALDMEISTER_30187_n032',conjecture_1)).
% 0.50/0.88 cnf('1.0.0.1',plain,
% 0.50/0.88 ( multiply(inverse(a),multiply(b,a)) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) ),
% 0.50/0.88 inference(reduction,[status(thm)],['1.0.0.0','0.15.2.0',theory(equality)]),
% 0.50/0.88 [pos('R','L')]).
% 0.50/0.88 cnf('1.0.0.2',plain,
% 0.50/0.88 ( multiply(inverse(a),multiply(least_upper_bound(b,identity),a)) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) ),
% 0.50/0.88 inference(reduction,[status(thm)],['1.0.0.1','0.17.2.0',theory(equality)]),
% 0.50/0.88 [pos('L.2.1','R')]).
% 0.50/0.88 cnf('1.0.0.3',plain,
% 0.50/0.88 ( multiply(inverse(a),multiply(least_upper_bound(identity,b),a)) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) ),
% 0.50/0.88 inference(reduction,[status(thm)],['1.0.0.2','0.15.2.0',theory(equality)]),
% 0.50/0.88 [pos('L.2.1','L')]).
% 0.50/0.88 cnf('1.0.0.4',plain,
% 0.50/0.88 ( multiply(inverse(a),least_upper_bound(multiply(identity,a),multiply(b,a))) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) ),
% 0.50/0.88 inference(reduction,[status(thm)],['1.0.0.3','0.10.2.0',theory(equality)]),
% 0.50/0.88 [pos('L.2','L')]).
% 0.50/0.88 cnf('1.0.0.5',plain,
% 0.50/0.88 ( multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) ),
% 0.50/0.88 inference(reduction,[status(thm)],['1.0.0.4','0.1.2.0',theory(equality)]),
% 0.50/0.88 [pos('L.2.1','L')]).
% 0.50/0.88 cnf('1.0.0.6',plain,
% 0.50/0.88 ( multiply(inverse(a),least_upper_bound(multiply(b,a),a)) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) ),
% 0.50/0.88 inference(reduction,[status(thm)],['1.0.0.5','0.15.2.0',theory(equality)]),
% 0.50/0.88 [pos('L.2','L')]).
% 0.50/0.88 cnf('1.0.0.7',plain,
% 0.50/0.88 ( least_upper_bound(multiply(inverse(a),multiply(b,a)),multiply(inverse(a),a)) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) ),
% 0.50/0.88 inference(reduction,[status(thm)],['1.0.0.6','0.8.2.0',theory(equality)]),
% 0.50/0.88 [pos('L','L')]).
% 0.50/0.88 cnf('1.0.0.8',plain,
% 0.50/0.88 ( least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) ),
% 0.50/0.88 inference(reduction,[status(thm)],['1.0.0.7','0.11.2.0',theory(equality)]),
% 0.50/0.88 [pos('L.2','L')]).
% 0.50/0.88 cnf('1.0.0.9',plain,
% 0.50/0.88 ( $true ),
% 0.50/0.88 inference(trivial,[status(thm)],['1.0.0.8',theory(equality)]),
% 0.50/0.88 [conjecture_1]).
% 0.50/0.88
% 0.50/0.88 Proved Goals:
% 0.50/0.88 No. 1: multiply(inverse(a),multiply(b,a)) ?= least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) joined, current: least_upper_bound(multiply(inverse(a),multiply(b,a)),identity) = least_upper_bound(multiply(inverse(a),multiply(b,a)),identity)
% 0.50/0.88 1 goal was specified, which was proved.
% 0.50/0.88 % SZS output end CNFRefutation
% 0.50/0.88 #END OF PROOF
% 0.50/0.88
% 0.50/0.88 Problem WALDMEISTER_30187_n032
% 0.50/0.88 CPs.gen 63
% 0.50/0.88 CPs.reexp 0
% 0.50/0.88 Select 17
% 0.50/0.88 R 15
% 0.50/0.88 E 2
% 0.50/0.88 vsize 6.5M
% 0.50/0.88 rss 3.7M
% 0.50/0.88 process.time 0.002s
% 0.50/0.88 wallclock.time 0.003s
% 0.50/0.88 status S
% 0.50/0.88
% 0.50/0.88
% 0.50/0.88 Waldmeister states: Goal proved.
% 0.50/0.88 % SZS status Unsatisfiable
% 0.50/0.88
% 0.50/0.88 Problem WALDMEISTER_30187_n032
% 0.50/0.88 CPs.gen 0
% 0.50/0.88 CPs.reexp 0
% 0.50/0.88 Select 0
% 0.50/0.88 R 0
% 0.50/0.88 E 0
% 0.50/0.88 vsize 6.0M
% 0.50/0.88 rss 3.2M
% 0.50/0.88 process.time 0.001s
% 0.50/0.88 wallclock.time 0.003s
% 0.50/0.88 status S
%------------------------------------------------------------------------------