TSTP Solution File: COL006-5 by Waldmeister---710
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : COL006-5 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n024.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 00:47:28 EDT 2022
% Result : Unsatisfiable 0.59s 0.99s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL006-5 : TPTP v8.1.0. Released v2.1.0.
% 0.04/0.13 % Command : woody %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 08:56:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.59/0.99 ********************************************************************************
% 0.59/0.99 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/0.99 * |/ | \/ | *
% 0.59/0.99 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/0.99 * A. Jaeger and B. Loechner | | *
% 0.59/0.99 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/0.99 ********************************************************************************
% 0.59/0.99
% 0.59/0.99
% 0.59/0.99 Goals:
% 0.59/0.99 ------
% 0.59/0.99
% 0.59/0.99 ( 1) apply(strong_fixed_point,fixed_pt) ?=? apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
% 0.59/0.99
% 0.59/0.99 Detected structure: KombinatorlogikS
% 0.59/0.99 ********************************************************************************
% 0.59/0.99 ****************************** COMPLETION - PROOF ******************************
% 0.59/0.99 ********************************************************************************
% 0.59/0.99
% 0.59/0.99 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(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))))
% 0.59/0.99 goal joined
% 0.59/0.99 % SZS status Unsatisfiable
% 0.59/0.99 #START OF PROOF
% 0.59/0.99 % SZS output start CNFRefutation
% 0.59/0.99 cnf('0.1.0.0',axiom,
% 0.59/0.99 ( X1 = apply(apply(k,X1),X2) ),
% 0.59/0.99 file('/tmp/WALDMEISTER_21010_n024')).
% 0.59/0.99 cnf('0.1.1.0',plain,
% 0.59/0.99 ( X1 = apply(apply(k,X1),X2) ),
% 0.59/0.99 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.59/0.99 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.59/0.99 cnf('0.1.2.0',plain,
% 0.59/0.99 ( apply(apply(k,X1),X2) = X1 ),
% 0.59/0.99 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.59/0.99 [x,rule_1]).
% 0.59/0.99 cnf('0.2.0.0',axiom,
% 0.59/0.99 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.59/0.99 file('/tmp/WALDMEISTER_21010_n024')).
% 0.59/0.99 cnf('0.2.1.0',plain,
% 0.59/0.99 ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.59/0.99 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.59/0.99 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.59/0.99 cnf('0.2.2.0',plain,
% 0.59/0.99 ( apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)) ),
% 0.59/0.99 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.59/0.99 [x,rule_2]).
% 0.59/0.99 cnf('0.3.0.0',axiom,
% 0.59/0.99 ( apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))) = strong_fixed_point ),
% 0.59/0.99 file('/tmp/WALDMEISTER_21010_n024')).
% 0.59/0.99 cnf('0.3.1.0',plain,
% 0.59/0.99 ( apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))) = strong_fixed_point ),
% 0.59/0.99 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.59/0.99 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.59/0.99 cnf('0.3.2.0',plain,
% 0.59/0.99 ( strong_fixed_point = apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))) ),
% 0.59/0.99 inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.59/0.99 [x,rule_3]).
% 0.59/0.99 cnf('1.0.0.0',conjecture,
% 0.59/0.99 ( apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
% 0.59/0.99 file('/tmp/WALDMEISTER_21010_n024',conjecture_1)).
% 0.59/0.99 cnf('1.0.0.1',plain,
% 0.59/0.99 ( apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.0','0.3.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.1','L')]).
% 0.59/0.99 cnf('1.0.0.2',plain,
% 0.59/0.99 ( apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),fixed_pt) = apply(fixed_pt,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),fixed_pt)) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.1','0.3.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2.1','L')]).
% 0.59/0.99 cnf('1.0.0.3',plain,
% 0.59/0.99 ( apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),fixed_pt) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),fixed_pt))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.2','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2','L')]).
% 0.59/0.99 cnf('1.0.0.4',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),fixed_pt)) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),fixed_pt))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.3','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('L','L')]).
% 0.59/0.99 cnf('1.0.0.5',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),fixed_pt)) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(apply(apply(s,apply(k,s)),k),fixed_pt)))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.4','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2.2','L')]).
% 0.59/0.99 cnf('1.0.0.6',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(apply(apply(s,apply(k,s)),k),fixed_pt))) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(apply(apply(s,apply(k,s)),k),fixed_pt)))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.5','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.2','L')]).
% 0.59/0.99 cnf('1.0.0.7',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(apply(apply(s,apply(k,s)),k),fixed_pt))) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.6','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2.2.2','L')]).
% 0.59/0.99 cnf('1.0.0.8',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)))) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.7','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.2.2','L')]).
% 0.59/0.99 cnf('1.0.0.9',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)))) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(s,apply(k,fixed_pt))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.8','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2.2.2.1','L')]).
% 0.59/0.99 cnf('1.0.0.10',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(s,apply(k,fixed_pt)))) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(s,apply(k,fixed_pt))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.9','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.2.2.1','L')]).
% 0.59/0.99 cnf('1.0.0.11',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(k,apply(apply(s,s),apply(s,k))),fixed_pt),apply(s,apply(k,fixed_pt)))) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.10','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2.2.1','L')]).
% 0.59/0.99 cnf('1.0.0.12',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.11','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.2.1','L')]).
% 0.59/0.99 cnf('1.0.0.13',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.12','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2.2','L')]).
% 0.59/0.99 cnf('1.0.0.14',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.13','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.2','L')]).
% 0.59/0.99 cnf('1.0.0.15',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),fixed_pt),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.14','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2.1','L')]).
% 0.59/0.99 cnf('1.0.0.16',plain,
% 0.59/0.99 ( apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.15','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.1','L')]).
% 0.59/0.99 cnf('1.0.0.17',plain,
% 0.59/0.99 ( apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.16','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2','L')]).
% 0.59/0.99 cnf('1.0.0.18',plain,
% 0.59/0.99 ( apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) = apply(fixed_pt,apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.17','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('L','L')]).
% 0.59/0.99 cnf('1.0.0.19',plain,
% 0.59/0.99 ( apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) = apply(fixed_pt,apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.18','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2.2','L')]).
% 0.59/0.99 cnf('1.0.0.20',plain,
% 0.59/0.99 ( apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))))) = apply(fixed_pt,apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.19','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.2','L')]).
% 0.59/0.99 cnf('1.0.0.21',plain,
% 0.59/0.99 ( apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))))) = apply(fixed_pt,apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.20','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2.2','L')]).
% 0.59/0.99 cnf('1.0.0.22',plain,
% 0.59/0.99 ( apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.21','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.2','L')]).
% 0.59/0.99 cnf('1.0.0.23',plain,
% 0.59/0.99 ( apply(apply(apply(apply(s,k),k),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.22','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2.1','L')]).
% 0.59/0.99 cnf('1.0.0.24',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.23','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.1','L')]).
% 0.59/0.99 cnf('1.0.0.25',plain,
% 0.59/0.99 ( apply(apply(apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.24','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('R.2.1','L')]).
% 0.59/0.99 cnf('1.0.0.26',plain,
% 0.59/0.99 ( apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.25','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.1','L')]).
% 0.59/0.99 cnf('1.0.0.27',plain,
% 0.59/0.99 ( apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(apply(s,k),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) = apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.26','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('L','L')]).
% 0.59/0.99 cnf('1.0.0.28',plain,
% 0.59/0.99 ( apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(k,apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))))) = apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.27','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.2','L')]).
% 0.59/0.99 cnf('1.0.0.29',plain,
% 0.59/0.99 ( apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))) = apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.28','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.2','L')]).
% 0.59/0.99 cnf('1.0.0.30',plain,
% 0.59/0.99 ( apply(apply(apply(k,fixed_pt),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))),apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) = apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.29','0.2.2.0',theory(equality)]),
% 0.59/0.99 [pos('L','L')]).
% 0.59/0.99 cnf('1.0.0.31',plain,
% 0.59/0.99 ( apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) = apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) ),
% 0.59/0.99 inference(reduction,[status(thm)],['1.0.0.30','0.1.2.0',theory(equality)]),
% 0.59/0.99 [pos('L.1','L')]).
% 0.59/0.99 cnf('1.0.0.32',plain,
% 0.59/0.99 ( $true ),
% 0.59/0.99 inference(trivial,[status(thm)],['1.0.0.31',theory(equality)]),
% 0.59/0.99 [conjecture_1]).
% 0.59/0.99
% 0.59/0.99 Proved Goals:
% 0.59/0.99 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(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))))) = apply(fixed_pt,apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt)))),apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),apply(s,apply(k,fixed_pt))))))
% 0.59/0.99 1 goal was specified, which was proved.
% 0.59/0.99 % SZS output end CNFRefutation
% 0.59/0.99 #END OF PROOF
% 0.59/0.99
% 0.59/0.99 Problem WALDMEISTER_21010_n024
% 0.59/0.99 CPs.gen 0
% 0.59/0.99 CPs.reexp 0
% 0.59/0.99 Select 3
% 0.59/0.99 R 3
% 0.59/0.99 E 0
% 0.59/0.99 vsize 6.5M
% 0.59/0.99 rss 3.6M
% 0.59/0.99 process.time 0.003s
% 0.59/0.99 wallclock.time 0.003s
% 0.59/0.99 status S
% 0.59/0.99
% 0.59/0.99
% 0.59/0.99 Waldmeister states: Goal proved.
% 0.59/0.99 % SZS status Unsatisfiable
% 0.59/0.99
% 0.59/0.99 Problem WALDMEISTER_21010_n024
% 0.59/0.99 CPs.gen 0
% 0.59/0.99 CPs.reexp 0
% 0.59/0.99 Select 0
% 0.59/0.99 R 0
% 0.59/0.99 E 0
% 0.59/0.99 vsize 6.0M
% 0.59/0.99 rss 3.2M
% 0.59/0.99 process.time 0.001s
% 0.59/0.99 wallclock.time 0.003s
% 0.59/0.99 status S
%------------------------------------------------------------------------------