%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : GRP166-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n027.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 12:25:02 EDT 2022
% Result : Unsatisfiable 0.62s 1.00s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP166-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n027.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 19:34:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.62/0.98 ********************************************************************************
% 0.62/0.98 * W A L D M E I S T E R \| \ / \|/ *
% 0.62/0.98 * |/ | \/ | *
% 0.62/0.98 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.62/0.98 * A. Jaeger and B. Loechner | | *
% 0.62/0.98 * <waldmeister@informatik.uni-kl.de> | *
% 0.62/0.98 ********************************************************************************
% 0.62/0.98
% 0.62/0.98
% 0.62/0.98 Goals:
% 0.62/0.98 ------
% 0.62/0.98
% 0.62/0.98 ( 1) greatest_lower_bound(a,multiply(a,b)) ?=? a
% 0.62/0.98
% 0.62/0.98 Detected structure: VerbandsgeordneteGruppe
% 0.62/0.98 ********************************************************************************
% 0.62/0.98 ****************************** COMPLETION - PROOF ******************************
% 0.62/0.98 ********************************************************************************
% 0.62/0.98
% 0.62/1.00 joined goal: 1 greatest_lower_bound(a,multiply(a,b)) ?= a to a
% 0.62/1.00 goal joined
% 0.62/1.00 % SZS status Unsatisfiable
% 0.62/1.00 #START OF PROOF
% 0.62/1.00 % SZS output start CNFRefutation
% 0.62/1.00 cnf('0.1.0.0',axiom,
% 0.62/1.00 ( X1 = multiply(identity,X1) ),
% 0.62/1.00 file('/tmp/WALDMEISTER_27862_n027')).
% 0.62/1.00 cnf('0.1.1.0',plain,
% 0.62/1.00 ( X1 = multiply(identity,X1) ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.62/1.00 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.62/1.00 cnf('0.1.2.0',plain,
% 0.62/1.00 ( multiply(identity,X1) = X1 ),
% 0.62/1.00 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.62/1.00 [x,rule_1]).
% 0.62/1.00 cnf('0.3.0.0',axiom,
% 0.62/1.00 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.62/1.00 file('/tmp/WALDMEISTER_27862_n027')).
% 0.62/1.00 cnf('0.3.1.0',plain,
% 0.62/1.00 ( X1 = greatest_lower_bound(X1,least_upper_bound(X1,X2)) ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.62/1.00 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.62/1.00 cnf('0.3.2.0',plain,
% 0.62/1.00 ( greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1 ),
% 0.62/1.00 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.62/1.00 [x,rule_3]).
% 0.62/1.00 cnf('0.5.0.0',axiom,
% 0.62/1.00 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.62/1.00 file('/tmp/WALDMEISTER_27862_n027')).
% 0.62/1.00 cnf('0.5.1.0',plain,
% 0.62/1.00 ( X1 = least_upper_bound(X1,greatest_lower_bound(X1,X2)) ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.62/1.00 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.62/1.00 cnf('0.5.2.0',plain,
% 0.62/1.00 ( least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1 ),
% 0.62/1.00 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.62/1.00 [x,rule_5]).
% 0.62/1.00 cnf('0.6.0.0',axiom,
% 0.62/1.00 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.62/1.00 file('/tmp/WALDMEISTER_27862_n027')).
% 0.62/1.00 cnf('0.6.1.0',plain,
% 0.62/1.00 ( multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3) ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.62/1.00 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.62/1.00 cnf('0.6.2.0',plain,
% 0.62/1.00 ( multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)) ),
% 0.62/1.00 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.62/1.00 [x,rule_6]).
% 0.62/1.00 cnf('0.8.0.0',axiom,
% 0.62/1.00 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.62/1.00 file('/tmp/WALDMEISTER_27862_n027')).
% 0.62/1.00 cnf('0.8.1.0',plain,
% 0.62/1.00 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.62/1.00 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.62/1.00 cnf('0.8.2.0',plain,
% 0.62/1.00 ( multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)) ),
% 0.62/1.00 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.62/1.00 [u,rule_8]).
% 0.62/1.00 cnf('0.11.0.0',axiom,
% 0.62/1.00 ( multiply(inverse(X1),X1) = identity ),
% 0.62/1.00 file('/tmp/WALDMEISTER_27862_n027')).
% 0.62/1.00 cnf('0.11.1.0',plain,
% 0.62/1.00 ( multiply(inverse(X1),X1) = identity ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.62/1.00 [weight('<10,0,0,[0,0,0,11]>')]).
% 0.62/1.00 cnf('0.11.2.0',plain,
% 0.62/1.00 ( multiply(inverse(X1),X1) = identity ),
% 0.62/1.00 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.62/1.00 [u,rule_11]).
% 0.62/1.00 cnf('0.15.0.0',axiom,
% 0.62/1.00 ( greatest_lower_bound(b,identity) = identity ),
% 0.62/1.00 file('/tmp/WALDMEISTER_27862_n027')).
% 0.62/1.00 cnf('0.15.1.0',plain,
% 0.62/1.00 ( greatest_lower_bound(b,identity) = identity ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.62/1.00 [weight('<14,0,0,[0,0,0,15]>')]).
% 0.62/1.00 cnf('0.15.2.0',plain,
% 0.62/1.00 ( greatest_lower_bound(b,identity) = identity ),
% 0.62/1.00 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.62/1.00 [u,rule_14]).
% 0.62/1.00 cnf('0.16.0.0',axiom,
% 0.62/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.62/1.00 file('/tmp/WALDMEISTER_27862_n027')).
% 0.62/1.00 cnf('0.16.1.0',plain,
% 0.62/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.16.0.0']),
% 0.62/1.00 [weight('<15,0,0,[0,0,0,16]>')]).
% 0.62/1.00 cnf('0.16.2.0',plain,
% 0.62/1.00 ( least_upper_bound(X1,X2) = least_upper_bound(X2,X1) ),
% 0.62/1.00 inference(activate,[status(thm)],['0.16.1.0']),
% 0.62/1.00 [equation_2]).
% 0.62/1.00 cnf('0.19.0.0',plain,
% 0.62/1.00 ( b = least_upper_bound(b,identity) ),
% 0.62/1.00 inference(cp,[status(thm)],['0.5.2.0','0.15.2.0',theory(equality)]),
% 0.62/1.00 [pos('L.2','L')]).
% 0.62/1.00 cnf('0.19.1.0',plain,
% 0.62/1.00 ( b = least_upper_bound(b,identity) ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.62/1.00 [weight('<19,15,5,[0,0,0,2]>')]).
% 0.62/1.00 cnf('0.19.2.0',plain,
% 0.62/1.00 ( least_upper_bound(b,identity) = b ),
% 0.62/1.00 inference(orient,[status(thm)],['0.19.1.0',theory(equality)]),
% 0.62/1.00 [x,rule_17]).
% 0.62/1.00 cnf('0.56.0.0',plain,
% 0.62/1.00 ( multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2) ),
% 0.62/1.00 inference(cp,[status(thm)],['0.6.2.0','0.11.2.0',theory(equality)]),
% 0.62/1.00 [pos('L.1','L')]).
% 0.62/1.00 cnf('0.56.0.1',plain,
% 0.62/1.00 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.62/1.00 inference(reduction,[status(thm)],['0.56.0.0','0.1.2.0',theory(equality)]),
% 0.62/1.00 [pos('R','L')]).
% 0.62/1.00 cnf('0.56.1.0',plain,
% 0.62/1.00 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.56.0.1']),
% 0.62/1.00 [weight('<55,11,6,[0,0,0,1]>')]).
% 0.62/1.00 cnf('0.56.2.0',plain,
% 0.62/1.00 ( multiply(inverse(X1),multiply(X1,X2)) = X2 ),
% 0.62/1.00 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 0.62/1.00 [u,rule_54]).
% 0.62/1.00 cnf('0.57.0.0',plain,
% 0.62/1.00 ( multiply(X1,X2) = multiply(inverse(inverse(X1)),X2) ),
% 0.62/1.00 inference(cp,[status(thm)],['0.56.2.0','0.56.2.0',theory(equality)]),
% 0.62/1.00 [pos('L.2','L')]).
% 0.62/1.00 cnf('0.57.1.0',plain,
% 0.62/1.00 ( X1 = inverse(inverse(X1)) ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.57.0.0']),
% 0.62/1.00 [weight('<19,56,56,[0,0,0,3]>')]).
% 0.62/1.00 cnf('0.57.2.0',plain,
% 0.62/1.00 ( inverse(inverse(X1)) = X1 ),
% 0.62/1.00 inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 0.62/1.00 [x,rule_55]).
% 0.62/1.00 cnf('0.59.0.0',plain,
% 0.62/1.00 ( identity = multiply(X1,inverse(X1)) ),
% 0.62/1.00 inference(cp,[status(thm)],['0.11.2.0','0.57.2.0',theory(equality)]),
% 0.62/1.00 [pos('L.1','L')]).
% 0.62/1.00 cnf('0.59.1.0',plain,
% 0.62/1.00 ( identity = multiply(X1,inverse(X1)) ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.59.0.0']),
% 0.62/1.00 [weight('<29,57,11,[0,0,0,1]>')]).
% 0.62/1.00 cnf('0.59.2.0',plain,
% 0.62/1.00 ( multiply(X1,inverse(X1)) = identity ),
% 0.62/1.00 inference(orient,[status(thm)],['0.59.1.0',theory(equality)]),
% 0.62/1.00 [x,rule_57]).
% 0.62/1.00 cnf('0.69.0.0',plain,
% 0.62/1.00 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 0.62/1.00 inference(cp,[status(thm)],['0.56.2.0','0.59.2.0',theory(equality)]),
% 0.62/1.00 [pos('L.2','L')]).
% 0.62/1.00 cnf('0.69.1.0',plain,
% 0.62/1.00 ( inverse(X1) = multiply(inverse(X1),identity) ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.69.0.0']),
% 0.62/1.00 [weight('<34,59,56,[0,0,0,3]>')]).
% 0.62/1.00 cnf('0.69.2.0',plain,
% 0.62/1.00 ( multiply(inverse(X1),identity) = inverse(X1) ),
% 0.62/1.00 inference(orient,[status(thm)],['0.69.1.0',theory(equality)]),
% 0.62/1.00 [x,rule_67]).
% 0.62/1.00 cnf('0.70.0.0',plain,
% 0.62/1.00 ( inverse(inverse(X1)) = multiply(X1,identity) ),
% 0.62/1.00 inference(cp,[status(thm)],['0.69.2.0','0.57.2.0',theory(equality)]),
% 0.62/1.00 [pos('L.1','L')]).
% 0.62/1.00 cnf('0.70.0.1',plain,
% 0.62/1.00 ( X1 = multiply(X1,identity) ),
% 0.62/1.00 inference(reduction,[status(thm)],['0.70.0.0','0.57.2.0',theory(equality)]),
% 0.62/1.00 [pos('L','L')]).
% 0.62/1.00 cnf('0.70.1.0',plain,
% 0.62/1.00 ( X1 = multiply(X1,identity) ),
% 0.62/1.00 inference(weigh,[status(thm)],['0.70.0.1']),
% 0.62/1.00 [weight('<19,69,57,[1,0,0,1]>')]).
% 0.62/1.00 cnf('0.70.2.0',plain,
% 0.62/1.00 ( multiply(X1,identity) = X1 ),
% 0.62/1.00 inference(orient,[status(thm)],['0.70.1.0',theory(equality)]),
% 0.62/1.00 [x,rule_68]).
% 0.62/1.00 cnf('1.0.0.0',conjecture,
% 0.62/1.00 ( greatest_lower_bound(a,multiply(a,b)) = a ),
% 0.62/1.00 file('/tmp/WALDMEISTER_27862_n027',conjecture_1)).
% 0.62/1.00 cnf('1.0.0.1',plain,
% 0.62/1.00 ( greatest_lower_bound(a,multiply(a,least_upper_bound(b,identity))) = a ),
% 0.62/1.00 inference(reduction,[status(thm)],['1.0.0.0','0.19.2.0',theory(equality)]),
% 0.62/1.00 [pos('L.2.2','R')]).
% 0.62/1.00 cnf('1.0.0.2',plain,
% 0.62/1.00 ( greatest_lower_bound(a,least_upper_bound(multiply(a,b),multiply(a,identity))) = a ),
% 0.62/1.00 inference(reduction,[status(thm)],['1.0.0.1','0.8.2.0',theory(equality)]),
% 0.62/1.00 [pos('L.2','L')]).
% 0.62/1.00 cnf('1.0.0.3',plain,
% 0.62/1.00 ( greatest_lower_bound(a,least_upper_bound(multiply(a,b),a)) = a ),
% 0.62/1.00 inference(reduction,[status(thm)],['1.0.0.2','0.70.2.0',theory(equality)]),
% 0.62/1.00 [pos('L.2.2','L')]).
% 0.62/1.00 cnf('1.0.0.4',plain,
% 0.62/1.00 ( greatest_lower_bound(a,least_upper_bound(a,multiply(a,b))) = a ),
% 0.62/1.00 inference(reduction,[status(thm)],['1.0.0.3','0.16.2.0',theory(equality)]),
% 0.62/1.00 [pos('L.2','L')]).
% 0.62/1.00 cnf('1.0.0.5',plain,
% 0.62/1.00 ( a = a ),
% 0.62/1.00 inference(reduction,[status(thm)],['1.0.0.4','0.3.2.0',theory(equality)]),
% 0.62/1.00 [pos('L','L')]).
% 0.62/1.00 cnf('1.0.0.6',plain,
% 0.62/1.00 ( $true ),
% 0.62/1.00 inference(trivial,[status(thm)],['1.0.0.5',theory(equality)]),
% 0.62/1.00 [conjecture_1]).
% 0.62/1.00
% 0.62/1.00 Proved Goals:
% 0.62/1.00 No. 1: greatest_lower_bound(a,multiply(a,b)) ?= a joined, current: a = a
% 0.62/1.00 1 goal was specified, which was proved.
% 0.62/1.00 % SZS output end CNFRefutation
% 0.62/1.00 #END OF PROOF
% 0.62/1.00
% 0.62/1.00 Problem WALDMEISTER_27862_n027
% 0.62/1.00 CPs.gen 708
% 0.62/1.00 CPs.reexp 0
% 0.62/1.00 Select 122
% 0.62/1.00 R 68
% 0.62/1.00 E 2
% 0.62/1.00 vsize 7.0M
% 0.62/1.00 rss 4.1M
% 0.62/1.00 process.time 0.021s
% 0.62/1.00 wallclock.time 0.022s
% 0.62/1.00 status S
% 0.62/1.00
% 0.62/1.00
% 0.62/1.00 Waldmeister states: Goal proved.
% 0.62/1.00 % SZS status Unsatisfiable
% 0.62/1.00
% 0.62/1.00 Problem WALDMEISTER_27862_n027
% 0.62/1.00 CPs.gen 0
% 0.62/1.00 CPs.reexp 0
% 0.62/1.00 Select 0
% 0.62/1.00 R 0
% 0.62/1.00 E 0
% 0.62/1.00 vsize 6.0M
% 0.62/1.00 rss 3.2M
% 0.62/1.00 process.time 0.001s
% 0.62/1.00 wallclock.time 0.021s
% 0.62/1.00 status S
%------------------------------------------------------------------------------