%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL002-5 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n022.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 : Fri Jul 15 00:47:26 EDT 2022
% Result : Unsatisfiable 0.69s 1.05s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL002-5 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.06/0.12 % Command : woody %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue May 31 15:12:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.69/1.05 ********************************************************************************
% 0.69/1.05 * W A L D M E I S T E R \| \ / \|/ *
% 0.69/1.05 * |/ | \/ | *
% 0.69/1.05 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.69/1.05 * A. Jaeger and B. Loechner | | *
% 0.69/1.05 * <waldmeister@informatik.uni-kl.de> | *
% 0.69/1.05 ********************************************************************************
% 0.69/1.05
% 0.69/1.05
% 0.69/1.05 Goals:
% 0.69/1.05 ------
% 0.69/1.05
% 0.69/1.05 ( 1) apply(fixed_pt,weak_fixed_point(fixed_pt)) ?=? weak_fixed_point(fixed_pt)
% 0.69/1.05
% 0.69/1.05 Detected structure: KombinatorlogikB
% 0.69/1.05 ********************************************************************************
% 0.69/1.05 ****************************** COMPLETION - PROOF ******************************
% 0.69/1.05 ********************************************************************************
% 0.69/1.05
% 0.69/1.05 joined goal: 1 apply(fixed_pt,weak_fixed_point(fixed_pt)) ?= weak_fixed_point(fixed_pt) to apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))))
% 0.69/1.05 goal joined
% 0.69/1.05 % SZS status Unsatisfiable
% 0.69/1.05 #START OF PROOF
% 0.69/1.05 % SZS output start CNFRefutation
% 0.69/1.05 cnf('0.2.0.0',axiom,
% 0.69/1.05 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.69/1.05 file('/tmp/WALDMEISTER_16833_n022')).
% 0.69/1.05 cnf('0.2.1.0',plain,
% 0.69/1.05 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.69/1.05 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.69/1.05 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.69/1.05 cnf('0.2.2.0',plain,
% 0.69/1.05 ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.69/1.05 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.69/1.05 [x,rule_2]).
% 0.69/1.05 cnf('0.3.0.0',axiom,
% 0.69/1.05 ( apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2) ),
% 0.69/1.05 file('/tmp/WALDMEISTER_16833_n022')).
% 0.69/1.05 cnf('0.3.1.0',plain,
% 0.69/1.05 ( apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2) ),
% 0.69/1.05 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.69/1.05 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.69/1.05 cnf('0.3.2.0',plain,
% 0.69/1.05 ( apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2) ),
% 0.69/1.05 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.69/1.05 [x,rule_3]).
% 0.69/1.05 cnf('0.4.0.0',axiom,
% 0.69/1.05 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.69/1.05 file('/tmp/WALDMEISTER_16833_n022')).
% 0.69/1.05 cnf('0.4.1.0',plain,
% 0.69/1.05 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.69/1.05 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.69/1.05 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.69/1.05 cnf('0.4.2.0',plain,
% 0.69/1.05 ( apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)) ),
% 0.69/1.05 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.69/1.05 [x,rule_4]).
% 0.69/1.05 cnf('0.5.0.0',axiom,
% 0.69/1.05 ( apply(apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1)))),apply(s,apply(c,apply(b,X1)))) = weak_fixed_point(X1) ),
% 0.69/1.05 file('/tmp/WALDMEISTER_16833_n022')).
% 0.69/1.05 cnf('0.5.1.0',plain,
% 0.69/1.05 ( apply(apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1)))),apply(s,apply(c,apply(b,X1)))) = weak_fixed_point(X1) ),
% 0.69/1.05 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.69/1.05 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.69/1.05 cnf('0.5.2.0',plain,
% 0.69/1.05 ( weak_fixed_point(X1) = apply(apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1)))),apply(s,apply(c,apply(b,X1)))) ),
% 0.69/1.05 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.69/1.05 [x,rule_5]).
% 0.69/1.05 cnf('1.0.0.0',conjecture,
% 0.69/1.05 ( apply(fixed_pt,weak_fixed_point(fixed_pt)) = weak_fixed_point(fixed_pt) ),
% 0.69/1.05 file('/tmp/WALDMEISTER_16833_n022',conjecture_1)).
% 0.69/1.05 cnf('1.0.0.1',plain,
% 0.69/1.05 ( apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) = weak_fixed_point(fixed_pt) ),
% 0.69/1.05 inference(reduction,[status(thm)],['1.0.0.0','0.5.2.0',theory(equality)]),
% 0.69/1.05 [pos('L.2','L')]).
% 0.69/1.05 cnf('1.0.0.2',plain,
% 0.69/1.05 ( apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) = apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))) ),
% 0.69/1.05 inference(reduction,[status(thm)],['1.0.0.1','0.5.2.0',theory(equality)]),
% 0.69/1.05 [pos('R','L')]).
% 0.69/1.05 cnf('1.0.0.3',plain,
% 0.69/1.05 ( apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) = apply(apply(apply(c,apply(b,fixed_pt)),apply(s,apply(c,apply(b,fixed_pt)))),apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))) ),
% 0.69/1.05 inference(reduction,[status(thm)],['1.0.0.2','0.4.2.0',theory(equality)]),
% 0.69/1.05 [pos('R','L')]).
% 0.69/1.05 cnf('1.0.0.4',plain,
% 0.69/1.05 ( apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) = apply(apply(apply(b,fixed_pt),apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))),apply(s,apply(c,apply(b,fixed_pt)))) ),
% 0.69/1.05 inference(reduction,[status(thm)],['1.0.0.3','0.3.2.0',theory(equality)]),
% 0.69/1.05 [pos('R','L')]).
% 0.69/1.05 cnf('1.0.0.5',plain,
% 0.69/1.05 ( apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) ),
% 0.69/1.05 inference(reduction,[status(thm)],['1.0.0.4','0.2.2.0',theory(equality)]),
% 0.69/1.05 [pos('R','L')]).
% 0.69/1.05 cnf('1.0.0.6',plain,
% 0.69/1.05 ( $true ),
% 0.69/1.05 inference(trivial,[status(thm)],['1.0.0.5',theory(equality)]),
% 0.69/1.05 [conjecture_1]).
% 0.69/1.05
% 0.69/1.05 Proved Goals:
% 0.69/1.05 No. 1: apply(fixed_pt,weak_fixed_point(fixed_pt)) ?= weak_fixed_point(fixed_pt) joined, current: apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))))
% 0.69/1.05 1 goal was specified, which was proved.
% 0.69/1.05 % SZS output end CNFRefutation
% 0.69/1.05 #END OF PROOF
% 0.69/1.05
% 0.69/1.05 Problem WALDMEISTER_16833_n022
% 0.69/1.05 CPs.gen 0
% 0.69/1.05 CPs.reexp 0
% 0.69/1.05 Select 5
% 0.69/1.05 R 5
% 0.69/1.05 E 0
% 0.69/1.05 vsize 6.5M
% 0.69/1.05 rss 3.7M
% 0.69/1.05 process.time 0.002s
% 0.69/1.05 wallclock.time 0.003s
% 0.69/1.05 status S
% 0.69/1.05
% 0.69/1.05
% 0.69/1.05 Waldmeister states: Goal proved.
% 0.69/1.05 % SZS status Unsatisfiable
% 0.69/1.05
% 0.69/1.05 Problem WALDMEISTER_16833_n022
% 0.69/1.05 CPs.gen 0
% 0.69/1.05 CPs.reexp 0
% 0.69/1.05 Select 0
% 0.69/1.05 R 0
% 0.69/1.05 E 0
% 0.69/1.05 vsize 6.0M
% 0.69/1.05 rss 3.2M
% 0.69/1.05 process.time 0.001s
% 0.69/1.05 wallclock.time 0.002s
% 0.69/1.05 status S
%------------------------------------------------------------------------------