TSTP Solution File: COL003-14 by Waldmeister---710
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- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL003-14 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n029.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 0.57s 0.98s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL003-14 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n029.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 : Tue May 31 09:57:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.98 ********************************************************************************
% 0.57/0.98 * W A L D M E I S T E R \| \ / \|/ *
% 0.57/0.98 * |/ | \/ | *
% 0.57/0.98 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.57/0.98 * A. Jaeger and B. Loechner | | *
% 0.57/0.98 * <waldmeister@informatik.uni-kl.de> | *
% 0.57/0.98 ********************************************************************************
% 0.57/0.98
% 0.57/0.98
% 0.57/0.98 Goals:
% 0.57/0.98 ------
% 0.57/0.98
% 0.57/0.98 ( 1) apply(strong_fixed_point,fixed_pt) ?=? apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
% 0.57/0.98
% 0.57/0.98 Detected structure: KombinatorlogikB
% 0.57/0.98 ********************************************************************************
% 0.57/0.98 ****************************** COMPLETION - PROOF ******************************
% 0.57/0.98 ********************************************************************************
% 0.57/0.98
% 0.57/0.98 joined goal: 1 apply(strong_fixed_point,fixed_pt) ?= apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) to apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))))
% 0.57/0.98 goal joined
% 0.57/0.98 % SZS status Unsatisfiable
% 0.57/0.98 #START OF PROOF
% 0.57/0.98 % SZS output start CNFRefutation
% 0.57/0.98 cnf('0.1.0.0',axiom,
% 0.57/0.98 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.57/0.98 file('/tmp/WALDMEISTER_25816_n029')).
% 0.57/0.98 cnf('0.1.1.0',plain,
% 0.57/0.98 ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.57/0.98 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.57/0.98 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.57/0.98 cnf('0.1.2.0',plain,
% 0.57/0.98 ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.57/0.98 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.57/0.98 [x,rule_1]).
% 0.57/0.98 cnf('0.2.0.0',axiom,
% 0.57/0.98 ( apply(apply(X1,X2),X2) = apply(apply(w,X1),X2) ),
% 0.57/0.98 file('/tmp/WALDMEISTER_25816_n029')).
% 0.57/0.98 cnf('0.2.1.0',plain,
% 0.57/0.98 ( apply(apply(X1,X2),X2) = apply(apply(w,X1),X2) ),
% 0.57/0.98 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.57/0.98 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.57/0.98 cnf('0.2.2.0',plain,
% 0.57/0.98 ( apply(apply(w,X1),X2) = apply(apply(X1,X2),X2) ),
% 0.57/0.98 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.57/0.98 [x,rule_2]).
% 0.57/0.98 cnf('0.3.0.0',axiom,
% 0.57/0.98 ( apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b) = strong_fixed_point ),
% 0.57/0.98 file('/tmp/WALDMEISTER_25816_n029')).
% 0.57/0.98 cnf('0.3.1.0',plain,
% 0.57/0.98 ( apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b) = strong_fixed_point ),
% 0.57/0.98 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.57/0.98 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.57/0.98 cnf('0.3.2.0',plain,
% 0.57/0.98 ( strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b) ),
% 0.57/0.98 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.57/0.98 [x,rule_3]).
% 0.57/0.98 cnf('1.0.0.0',conjecture,
% 0.57/0.98 ( apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
% 0.57/0.98 file('/tmp/WALDMEISTER_25816_n029',conjecture_1)).
% 0.57/0.98 cnf('1.0.0.1',plain,
% 0.57/0.98 ( apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.0','0.3.2.0',theory(equality)]),
% 0.57/0.98 [pos('L.1','L')]).
% 0.57/0.98 cnf('1.0.0.2',plain,
% 0.57/0.98 ( apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) = apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt)) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.1','0.3.2.0',theory(equality)]),
% 0.57/0.98 [pos('R.2.1','L')]).
% 0.57/0.98 cnf('1.0.0.3',plain,
% 0.57/0.98 ( apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) = apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.2','0.1.2.0',theory(equality)]),
% 0.57/0.98 [pos('R.2','L')]).
% 0.57/0.98 cnf('1.0.0.4',plain,
% 0.57/0.98 ( apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) = apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.3','0.1.2.0',theory(equality)]),
% 0.57/0.98 [pos('L','L')]).
% 0.57/0.98 cnf('1.0.0.5',plain,
% 0.57/0.98 ( apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) = apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt)))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.4','0.1.2.0',theory(equality)]),
% 0.57/0.98 [pos('R.2','L')]).
% 0.57/0.98 cnf('1.0.0.6',plain,
% 0.57/0.98 ( apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt)))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.5','0.1.2.0',theory(equality)]),
% 0.57/0.98 [pos('L','L')]).
% 0.57/0.98 cnf('1.0.0.7',plain,
% 0.57/0.98 ( apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) = apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.6','0.1.2.0',theory(equality)]),
% 0.57/0.98 [pos('R.2.2','L')]).
% 0.57/0.98 cnf('1.0.0.8',plain,
% 0.57/0.98 ( apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))) = apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.7','0.1.2.0',theory(equality)]),
% 0.57/0.98 [pos('L.2','L')]).
% 0.57/0.98 cnf('1.0.0.9',plain,
% 0.57/0.98 ( apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))) = apply(fixed_pt,apply(apply(w,apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.8','0.2.2.0',theory(equality)]),
% 0.57/0.98 [pos('R.2','L')]).
% 0.57/0.98 cnf('1.0.0.10',plain,
% 0.57/0.98 ( apply(apply(w,apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(fixed_pt,apply(apply(w,apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.9','0.2.2.0',theory(equality)]),
% 0.57/0.98 [pos('L','L')]).
% 0.57/0.98 cnf('1.0.0.11',plain,
% 0.57/0.98 ( apply(apply(w,apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.10','0.2.2.0',theory(equality)]),
% 0.57/0.98 [pos('R.2','L')]).
% 0.57/0.98 cnf('1.0.0.12',plain,
% 0.57/0.98 ( apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.11','0.2.2.0',theory(equality)]),
% 0.57/0.98 [pos('L','L')]).
% 0.57/0.98 cnf('1.0.0.13',plain,
% 0.57/0.98 ( apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.12','0.2.2.0',theory(equality)]),
% 0.57/0.98 [pos('L.1','L')]).
% 0.57/0.98 cnf('1.0.0.14',plain,
% 0.57/0.98 ( apply(apply(apply(b,fixed_pt),apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt))))),apply(w,apply(b,apply(b,fixed_pt)))) = apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.13','0.1.2.0',theory(equality)]),
% 0.57/0.98 [pos('L.1','L')]).
% 0.57/0.98 cnf('1.0.0.15',plain,
% 0.57/0.98 ( apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))) ),
% 0.57/0.98 inference(reduction,[status(thm)],['1.0.0.14','0.1.2.0',theory(equality)]),
% 0.57/0.98 [pos('L','L')]).
% 0.57/0.98 cnf('1.0.0.16',plain,
% 0.57/0.98 ( $true ),
% 0.57/0.98 inference(trivial,[status(thm)],['1.0.0.15',theory(equality)]),
% 0.57/0.98 [conjecture_1]).
% 0.57/0.98
% 0.57/0.98 Proved Goals:
% 0.57/0.98 No. 1: apply(strong_fixed_point,fixed_pt) ?= apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) joined, current: apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))))
% 0.57/0.98 1 goal was specified, which was proved.
% 0.57/0.98 % SZS output end CNFRefutation
% 0.57/0.98 #END OF PROOF
% 0.57/0.98
% 0.57/0.98 Problem WALDMEISTER_25816_n029
% 0.57/0.98 CPs.gen 0
% 0.57/0.98 CPs.reexp 0
% 0.57/0.98 Select 3
% 0.57/0.98 R 3
% 0.57/0.98 E 0
% 0.57/0.98 vsize 6.5M
% 0.57/0.98 rss 3.7M
% 0.57/0.98 process.time 0.002s
% 0.57/0.98 wallclock.time 0.003s
% 0.57/0.98 status S
% 0.57/0.98
% 0.57/0.98
% 0.57/0.98 Waldmeister states: Goal proved.
% 0.57/0.98 % SZS status Unsatisfiable
% 0.57/0.98
% 0.57/0.98 Problem WALDMEISTER_25816_n029
% 0.57/0.98 CPs.gen 0
% 0.57/0.98 CPs.reexp 0
% 0.57/0.98 Select 0
% 0.57/0.98 R 0
% 0.57/0.98 E 0
% 0.57/0.98 vsize 6.0M
% 0.57/0.98 rss 3.2M
% 0.57/0.98 process.time 0.001s
% 0.57/0.98 wallclock.time 0.002s
% 0.57/0.98 status S
%------------------------------------------------------------------------------