TSTP Solution File: COL060-1 by Waldmeister---710

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Waldmeister---710
% Problem  : COL060-1 : TPTP v8.1.0. Released v1.0.0.
% 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 00:47:37 EDT 2022

% Result   : Unsatisfiable 0.58s 0.99s
% Output   : CNFRefutation 0.58s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : COL060-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13  % Command  : woody %s
% 0.13/0.34  % Computer : n022.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 09:27:07 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.58/0.98  ********************************************************************************
% 0.58/0.98  *                             W A L D M E I S T E R           \|  \ /      \|/ *
% 0.58/0.98  *                                                              |/  |    \/  |  *
% 0.58/0.98  *              (C) 1994-2010  A. Buch and Th. Hillenbrand,      \ /      \ /   *
% 0.58/0.98  *                             A. Jaeger and B. Loechner          |        |    *
% 0.58/0.98  *                             <waldmeister@informatik.uni-kl.de>          |    *
% 0.58/0.98  ********************************************************************************
% 0.58/0.98  
% 0.58/0.98  
% 0.58/0.98  Goals:
% 0.58/0.98  ------
% 0.58/0.98  
% 0.58/0.98  (   1)  true ?= false
% 0.58/0.98          using narrowing to prove apply(apply(apply(x1,f(x1)),g(x1)),h(x1)) ?= apply(g(x1),apply(f(x1),h(x1)))
% 0.58/0.98  
% 0.58/0.98  Detected structure: KombinatorlogikBT
% 0.58/0.98  ********************************************************************************
% 0.58/0.98  ****************************** COMPLETION - PROOF ******************************
% 0.58/0.98  ********************************************************************************
% 0.58/0.98  
% 0.58/0.99  joined goal:           1  apply(apply(apply(x1,f(x1)),g(x1)),h(x1)) ?= apply(g(x1),apply(f(x1),h(x1))) to false
% 0.58/0.99  goal joined
% 0.58/0.99  % SZS status Unsatisfiable
% 0.58/0.99  #START OF PROOF
% 0.58/0.99  % SZS output start CNFRefutation
% 0.58/0.99  cnf('0.1.0.0',axiom,
% 0.58/0.99      ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.58/0.99      file('/tmp/WALDMEISTER_23104_n022')).
% 0.58/0.99  cnf('0.1.1.0',plain,
% 0.58/0.99      ( apply(X1,X2) = apply(apply(t,X2),X1) ),
% 0.58/0.99      inference(weigh,[status(thm)],['0.1.0.0']),
% 0.58/0.99      [weight('<0,0,0,[0,0,0,1]>')]).
% 0.58/0.99  cnf('0.1.2.0',plain,
% 0.58/0.99      ( apply(apply(t,X1),X2) = apply(X2,X1) ),
% 0.58/0.99      inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.58/0.99      [x,rule_1]).
% 0.58/0.99  cnf('0.2.0.0',axiom,
% 0.58/0.99      ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.58/0.99      file('/tmp/WALDMEISTER_23104_n022')).
% 0.58/0.99  cnf('0.2.1.0',plain,
% 0.58/0.99      ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.58/0.99      inference(weigh,[status(thm)],['0.2.0.0']),
% 0.58/0.99      [weight('<1,0,0,[0,0,0,2]>')]).
% 0.58/0.99  cnf('0.2.2.0',plain,
% 0.58/0.99      ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.58/0.99      inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.58/0.99      [x,rule_2]).
% 0.58/0.99  cnf('0.3.0.0',axiom,
% 0.58/0.99      ( eq(X1,X1) = true ),
% 0.58/0.99      file('/tmp/WALDMEISTER_23104_n022')).
% 0.58/0.99  cnf('0.3.1.0',plain,
% 0.58/0.99      ( eq(X1,X1) = true ),
% 0.58/0.99      inference(weigh,[status(thm)],['0.3.0.0']),
% 0.58/0.99      [weight('<2,0,0,[0,0,0,3]>')]).
% 0.58/0.99  cnf('0.3.2.0',plain,
% 0.58/0.99      ( eq(X1,X1) = true ),
% 0.58/0.99      inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.58/0.99      [u,rule_3]).
% 0.58/0.99  cnf('0.4.0.0',axiom,
% 0.58/0.99      ( eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(g(X1),apply(f(X1),h(X1)))) = false ),
% 0.58/0.99      file('/tmp/WALDMEISTER_23104_n022')).
% 0.58/0.99  cnf('0.4.1.0',plain,
% 0.58/0.99      ( eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(g(X1),apply(f(X1),h(X1)))) = false ),
% 0.58/0.99      inference(weigh,[status(thm)],['0.4.0.0']),
% 0.58/0.99      [weight('<3,0,0,[0,0,0,4]>')]).
% 0.58/0.99  cnf('0.4.2.0',plain,
% 0.58/0.99      ( eq(apply(apply(apply(X1,f(X1)),g(X1)),h(X1)),apply(g(X1),apply(f(X1),h(X1)))) = false ),
% 0.58/0.99      inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.58/0.99      [u,rule_4]).
% 0.58/0.99  cnf('0.9.0.0',plain,
% 0.58/0.99      ( false = eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))),apply(g(apply(apply(b,X1),X2)),apply(f(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))))) ),
% 0.58/0.99      inference(cp,[status(thm)],['0.4.2.0','0.2.2.0',theory(equality)]),
% 0.58/0.99      [pos('L.1.1.1','L')]).
% 0.58/0.99  cnf('0.9.1.0',plain,
% 0.58/0.99      ( false = eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))),apply(g(apply(apply(b,X1),X2)),apply(f(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))))) ),
% 0.58/0.99      inference(weigh,[status(thm)],['0.9.0.0']),
% 0.58/0.99      [weight('<44,4,2,[1,0,0,3]>')]).
% 0.58/0.99  cnf('0.9.2.0',plain,
% 0.58/0.99      ( eq(apply(apply(apply(X1,apply(X2,f(apply(apply(b,X1),X2)))),g(apply(apply(b,X1),X2))),h(apply(apply(b,X1),X2))),apply(g(apply(apply(b,X1),X2)),apply(f(apply(apply(b,X1),X2)),h(apply(apply(b,X1),X2))))) = false ),
% 0.58/0.99      inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.58/0.99      [x,rule_9]).
% 0.58/0.99  cnf('0.17.0.0',plain,
% 0.58/0.99      ( false = eq(apply(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),g(apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,apply(t,X2)),X1))),apply(g(apply(apply(b,apply(t,X2)),X1)),apply(f(apply(apply(b,apply(t,X2)),X1)),h(apply(apply(b,apply(t,X2)),X1))))) ),
% 0.58/0.99      inference(cp,[status(thm)],['0.9.2.0','0.1.2.0',theory(equality)]),
% 0.58/0.99      [pos('L.1.1.1','L')]).
% 0.58/0.99  cnf('0.17.1.0',plain,
% 0.58/0.99      ( false = eq(apply(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),g(apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,apply(t,X2)),X1))),apply(g(apply(apply(b,apply(t,X2)),X1)),apply(f(apply(apply(b,apply(t,X2)),X1)),h(apply(apply(b,apply(t,X2)),X1))))) ),
% 0.58/0.99      inference(weigh,[status(thm)],['0.17.0.0']),
% 0.58/0.99      [weight('<56,9,1,[1,0,0,3]>')]).
% 0.58/0.99  cnf('0.17.2.0',plain,
% 0.58/0.99      ( eq(apply(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),X1))),X2),g(apply(apply(b,apply(t,X2)),X1))),h(apply(apply(b,apply(t,X2)),X1))),apply(g(apply(apply(b,apply(t,X2)),X1)),apply(f(apply(apply(b,apply(t,X2)),X1)),h(apply(apply(b,apply(t,X2)),X1))))) = false ),
% 0.58/0.99      inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.58/0.99      [x,rule_17]).
% 0.58/0.99  cnf('0.55.0.0',plain,
% 0.58/0.99      ( false = eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),apply(g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))))) ),
% 0.58/0.99      inference(cp,[status(thm)],['0.17.2.0','0.2.2.0',theory(equality)]),
% 0.58/0.99      [pos('L.1.1.1.1','L')]).
% 0.58/0.99  cnf('0.55.1.0',plain,
% 0.58/0.99      ( false = eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),apply(g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))))) ),
% 0.58/0.99      inference(weigh,[status(thm)],['0.55.0.0']),
% 0.58/0.99      [weight('<82,17,2,[1,0,0,4]>')]).
% 0.58/0.99  cnf('0.55.2.0',plain,
% 0.58/0.99      ( eq(apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))))),X3),g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))),apply(g(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),apply(f(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2))),h(apply(apply(b,apply(t,X3)),apply(apply(b,X1),X2)))))) = false ),
% 0.58/0.99      inference(orient,[status(thm)],['0.55.1.0',theory(equality)]),
% 0.58/0.99      [x,rule_55]).
% 0.58/0.99  cnf('0.56.0.0',plain,
% 0.58/0.99      ( false = eq(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),apply(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))))) ),
% 0.58/0.99      inference(cp,[status(thm)],['0.55.2.0','0.2.2.0',theory(equality)]),
% 0.58/0.99      [pos('L.1.1','L')]).
% 0.58/0.99  cnf('0.56.1.0',plain,
% 0.58/0.99      ( false = eq(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),apply(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))))) ),
% 0.58/0.99      inference(weigh,[status(thm)],['0.56.0.0']),
% 0.58/0.99      [weight('<80,55,2,[1,0,0,2]>')]).
% 0.58/0.99  cnf('0.56.2.0',plain,
% 0.58/0.99      ( eq(apply(apply(apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(X2,g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))),apply(g(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),apply(f(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1))),h(apply(apply(b,apply(t,X2)),apply(apply(b,b),X1)))))) = false ),
% 0.58/0.99      inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 0.58/0.99      [x,rule_56]).
% 0.58/0.99  cnf('0.57.0.0',plain,
% 0.58/0.99      ( false = eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),apply(g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))))) ),
% 0.58/0.99      inference(cp,[status(thm)],['0.56.2.0','0.1.2.0',theory(equality)]),
% 0.58/0.99      [pos('L.1.1','L')]).
% 0.58/0.99  cnf('0.57.1.0',plain,
% 0.58/0.99      ( false = eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),apply(g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))))) ),
% 0.58/0.99      inference(weigh,[status(thm)],['0.57.0.0']),
% 0.58/0.99      [weight('<78,56,1,[1,0,0,2]>')]).
% 0.58/0.99  cnf('0.57.2.0',plain,
% 0.58/0.99      ( eq(apply(apply(apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))),apply(g(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),t)))))) = false ),
% 0.58/0.99      inference(orient,[status(thm)],['0.57.1.0',theory(equality)]),
% 0.58/0.99      [x,rule_57]).
% 0.58/0.99  cnf('0.58.0.0',plain,
% 0.58/0.99      ( false = eq(apply(g(apply(apply(b,apply(t,b)),apply(apply(b,b),t))),apply(f(apply(apply(b,apply(t,b)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,b)),apply(apply(b,b),t))))),apply(g(apply(apply(b,apply(t,b)),apply(apply(b,b),t))),apply(f(apply(apply(b,apply(t,b)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,b)),apply(apply(b,b),t)))))) ),
% 0.58/0.99      inference(cp,[status(thm)],['0.57.2.0','0.2.2.0',theory(equality)]),
% 0.58/0.99      [pos('L.1','L')]).
% 0.58/0.99  cnf('0.58.0.1',plain,
% 0.58/0.99      ( false = true ),
% 0.58/0.99      inference(reduction,[status(thm)],['0.58.0.0','0.3.2.0',theory(equality)]),
% 0.58/0.99      [pos('R','L')]).
% 0.58/0.99  cnf('0.58.1.0',plain,
% 0.58/0.99      ( false = true ),
% 0.58/0.99      inference(weigh,[status(thm)],['0.58.0.1']),
% 0.58/0.99      [weight('<5,57,2,[1,0,0,1]>')]).
% 0.58/0.99  cnf('0.58.2.0',plain,
% 0.58/0.99      ( true = false ),
% 0.58/0.99      inference(orient,[status(thm)],['0.58.1.0',theory(equality)]),
% 0.58/0.99      [x,rule_58]).
% 0.58/0.99  cnf('1.0.0.0',conjecture,
% 0.58/0.99      ( true = false ),
% 0.58/0.99      file('/tmp/WALDMEISTER_23104_n022',conjecture_1)).
% 0.58/0.99  cnf('1.0.0.1',plain,
% 0.58/0.99      ( false = false ),
% 0.58/0.99      inference(reduction,[status(thm)],['1.0.0.0','0.58.2.0',theory(equality)]),
% 0.58/0.99      [pos('L','L')]).
% 0.58/0.99  cnf('1.0.0.2',plain,
% 0.58/0.99      ( $true ),
% 0.58/0.99      inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.58/0.99      [conjecture_1]).
% 0.58/0.99  
% 0.58/0.99  Proved Goals:
% 0.58/0.99  No.  1: true ?= false, current false ?= false
% 0.58/0.99          using narrowing to prove apply(apply(apply(x1,f(x1)),g(x1)),h(x1)) ?= apply(g(x1),apply(f(x1),h(x1)))
% 0.58/0.99  
% 0.58/0.99  1 goal was specified, which was proved.
% 0.58/0.99  % SZS output end CNFRefutation
% 0.58/0.99  #END OF PROOF
% 0.58/0.99  
% 0.58/0.99  Problem         WALDMEISTER_23104_n022 
% 0.58/0.99  CPs.gen                  115 
% 0.58/0.99  CPs.reexp                  0 
% 0.58/0.99  Select                    72 
% 0.58/0.99  R                         58 
% 0.58/0.99  E                          0 
% 0.58/0.99  vsize                   6.4M 
% 0.58/0.99  rss                     3.5M 
% 0.58/0.99  process.time          0.007s 
% 0.58/0.99  wallclock.time        0.007s 
% 0.58/0.99  status                     S
% 0.58/0.99  
% 0.58/0.99  
% 0.58/0.99  Waldmeister states: Goal proved.
% 0.58/0.99  % SZS status Unsatisfiable
%------------------------------------------------------------------------------