TSTP Solution File: COL037-1 by Waldmeister---710

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Waldmeister---710
% Problem  : COL037-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : woody %s

% Computer : n017.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 00:47:32 EDT 2022

% Result   : Unsatisfiable 0.61s 1.03s
% Output   : CNFRefutation 0.61s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : COL037-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : woody %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue May 31 06:59:41 EDT 2022
% 0.12/0.33  % 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)  true ?= false
% 0.57/0.98          using narrowing to prove x1 ?= apply(const1,x1)
% 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  
% 0.61/1.03  joined goal:           1  apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1))) to false
% 0.61/1.03  goal joined
% 0.61/1.03  % SZS status Unsatisfiable
% 0.61/1.03  #START OF PROOF
% 0.61/1.03  % SZS output start CNFRefutation
% 0.61/1.03  cnf('0.1.0.0',axiom,
% 0.61/1.03      ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.61/1.03      file('/tmp/WALDMEISTER_18610_n017')).
% 0.61/1.03  cnf('0.1.1.0',plain,
% 0.61/1.03      ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.1.0.0']),
% 0.61/1.03      [weight('<0,0,0,[0,0,0,1]>')]).
% 0.61/1.03  cnf('0.1.2.0',plain,
% 0.61/1.03      ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.61/1.03      inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.61/1.03      [x,rule_1]).
% 0.61/1.03  cnf('0.2.0.0',axiom,
% 0.61/1.03      ( apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2) ),
% 0.61/1.03      file('/tmp/WALDMEISTER_18610_n017')).
% 0.61/1.03  cnf('0.2.1.0',plain,
% 0.61/1.03      ( apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2) ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.2.0.0']),
% 0.61/1.03      [weight('<1,0,0,[0,0,0,2]>')]).
% 0.61/1.03  cnf('0.2.2.0',plain,
% 0.61/1.03      ( apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2) ),
% 0.61/1.03      inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.61/1.03      [x,rule_2]).
% 0.61/1.03  cnf('0.3.0.0',axiom,
% 0.61/1.03      ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.61/1.03      file('/tmp/WALDMEISTER_18610_n017')).
% 0.61/1.03  cnf('0.3.1.0',plain,
% 0.61/1.03      ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.3.0.0']),
% 0.61/1.03      [weight('<2,0,0,[0,0,0,3]>')]).
% 0.61/1.03  cnf('0.3.2.0',plain,
% 0.61/1.03      ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.61/1.03      inference(activate,[status(thm)],['0.3.1.0']),
% 0.61/1.03      [equation_1]).
% 0.61/1.03  cnf('0.4.0.0',axiom,
% 0.61/1.03      ( eq(X1,X1) = true ),
% 0.61/1.03      file('/tmp/WALDMEISTER_18610_n017')).
% 0.61/1.03  cnf('0.4.1.0',plain,
% 0.61/1.03      ( eq(X1,X1) = true ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.4.0.0']),
% 0.61/1.03      [weight('<3,0,0,[0,0,0,4]>')]).
% 0.61/1.03  cnf('0.4.2.0',plain,
% 0.61/1.03      ( eq(X1,X1) = true ),
% 0.61/1.03      inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.61/1.03      [u,rule_3]).
% 0.61/1.03  cnf('0.5.0.0',axiom,
% 0.61/1.03      ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.61/1.03      file('/tmp/WALDMEISTER_18610_n017')).
% 0.61/1.03  cnf('0.5.1.0',plain,
% 0.61/1.03      ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.5.0.0']),
% 0.61/1.03      [weight('<4,0,0,[0,0,0,5]>')]).
% 0.61/1.03  cnf('0.5.2.0',plain,
% 0.61/1.03      ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.61/1.03      inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.61/1.03      [u,rule_4]).
% 0.61/1.03  cnf('0.6.0.0',plain,
% 0.61/1.03      ( apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(s,b),X2),X1),X3) ),
% 0.61/1.03      inference(cp,[status(thm)],['0.1.2.0','0.3.2.0',theory(equality)]),
% 0.61/1.03      [pos('L.1','L')]).
% 0.61/1.03  cnf('0.6.1.0',plain,
% 0.61/1.03      ( apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(s,b),X2),X1),X3) ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.6.0.0']),
% 0.61/1.03      [weight('<16,3,1,[0,0,0,1]>')]).
% 0.61/1.03  cnf('0.6.2.0',plain,
% 0.61/1.03      ( apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(s,b),X2),X1),X3) ),
% 0.61/1.03      inference(activate,[status(thm)],['0.6.1.0']),
% 0.61/1.03      [equation_2]).
% 0.61/1.03  cnf('0.10.0.0',plain,
% 0.61/1.03      ( apply(apply(X1,X2),apply(X3,X1)) = apply(apply(apply(apply(s,c),X3),X1),X2) ),
% 0.61/1.03      inference(cp,[status(thm)],['0.2.2.0','0.3.2.0',theory(equality)]),
% 0.61/1.03      [pos('L.1','L')]).
% 0.61/1.03  cnf('0.10.1.0',plain,
% 0.61/1.03      ( apply(apply(X1,X2),apply(X3,X1)) = apply(apply(apply(apply(s,c),X3),X1),X2) ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.10.0.0']),
% 0.61/1.03      [weight('<16,3,2,[0,0,0,1]>')]).
% 0.61/1.03  cnf('0.10.2.0',plain,
% 0.61/1.03      ( apply(apply(X1,X2),apply(X3,X1)) = apply(apply(apply(apply(s,c),X3),X1),X2) ),
% 0.61/1.03      inference(activate,[status(thm)],['0.10.1.0']),
% 0.61/1.03      [equation_4]).
% 0.61/1.03  cnf('0.11.0.0',plain,
% 0.61/1.03      ( false = eq(apply(apply(apply(apply(s,c),X1),X2),f(apply(apply(apply(s,c),X1),X2))),apply(f(apply(apply(apply(s,c),X1),X2)),apply(apply(X2,f(apply(apply(apply(s,c),X1),X2))),apply(X1,X2)))) ),
% 0.61/1.03      inference(cp,[status(thm)],['0.5.2.0','0.10.2.0',theory(equality)]),
% 0.61/1.03      [pos('L.2.2','R')]).
% 0.61/1.03  cnf('0.11.1.0',plain,
% 0.61/1.03      ( false = eq(apply(apply(apply(apply(s,c),X1),X2),f(apply(apply(apply(s,c),X1),X2))),apply(f(apply(apply(apply(s,c),X1),X2)),apply(apply(X2,f(apply(apply(apply(s,c),X1),X2))),apply(X1,X2)))) ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.11.0.0']),
% 0.61/1.03      [weight('<546,10,5,[0,1,0,8]>')]).
% 0.61/1.03  cnf('0.11.1.1',plain,
% 0.61/1.03      ( false = eq(apply(apply(apply(apply(s,c),X1),X2),f(apply(apply(apply(s,c),X1),X2))),apply(apply(apply(apply(s,b),X2),f(apply(apply(apply(s,c),X1),X2))),apply(X1,X2))) ),
% 0.61/1.03      inference(reduction,[status(thm)],['0.11.1.0','0.6.2.0',theory(equality)]),
% 0.61/1.03      [pos('R.2','L')]).
% 0.61/1.03  cnf('0.11.2.0',plain,
% 0.61/1.03      ( eq(apply(apply(apply(apply(s,c),X1),X2),f(apply(apply(apply(s,c),X1),X2))),apply(apply(apply(apply(s,b),X2),f(apply(apply(apply(s,c),X1),X2))),apply(X1,X2))) = false ),
% 0.61/1.03      inference(orient,[status(thm)],['0.11.1.1',theory(equality)]),
% 0.61/1.03      [x,rule_7]).
% 0.61/1.03  cnf('0.12.0.0',plain,
% 0.61/1.03      ( apply(apply(apply(s,apply(c,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X3) ),
% 0.61/1.03      inference(cp,[status(thm)],['0.3.2.0','0.2.2.0',theory(equality)]),
% 0.61/1.03      [pos('L','L')]).
% 0.61/1.03  cnf('0.12.1.0',plain,
% 0.61/1.03      ( apply(apply(apply(s,apply(c,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X3) ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.12.0.0']),
% 0.61/1.03      [weight('<16,3,2,[1,0,0,0]>')]).
% 0.61/1.03  cnf('0.12.2.0',plain,
% 0.61/1.03      ( apply(apply(apply(s,apply(c,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X3) ),
% 0.61/1.03      inference(activate,[status(thm)],['0.12.1.0']),
% 0.61/1.03      [equation_5]).
% 0.61/1.03  cnf('0.13.0.0',plain,
% 0.61/1.03      ( false = eq(apply(apply(apply(c,X1),apply(X2,X1)),f(apply(apply(apply(s,c),X2),X1))),apply(apply(apply(apply(s,b),X1),f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1))) ),
% 0.61/1.03      inference(cp,[status(thm)],['0.11.2.0','0.3.2.0',theory(equality)]),
% 0.61/1.03      [pos('L.1.1','R')]).
% 0.61/1.03  cnf('0.13.0.1',plain,
% 0.61/1.03      ( false = eq(apply(apply(X1,f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1)),apply(apply(apply(apply(s,b),X1),f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1))) ),
% 0.61/1.03      inference(reduction,[status(thm)],['0.13.0.0','0.2.2.0',theory(equality)]),
% 0.61/1.03      [pos('R.1','L')]).
% 0.61/1.03  cnf('0.13.1.0',plain,
% 0.61/1.03      ( false = eq(apply(apply(X1,f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1)),apply(apply(apply(apply(s,b),X1),f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1))) ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.13.0.1']),
% 0.61/1.03      [weight('<320,11,3,[1,0,1,2]>')]).
% 0.61/1.03  cnf('0.13.2.0',plain,
% 0.61/1.03      ( eq(apply(apply(X1,f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1)),apply(apply(apply(apply(s,b),X1),f(apply(apply(apply(s,c),X2),X1))),apply(X2,X1))) = false ),
% 0.61/1.03      inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.61/1.03      [x,rule_8]).
% 0.61/1.03  cnf('0.24.0.0',plain,
% 0.61/1.03      ( apply(apply(apply(s,apply(c,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X3)) ),
% 0.61/1.03      inference(cp,[status(thm)],['0.12.2.0','0.1.2.0',theory(equality)]),
% 0.61/1.03      [pos('R','L')]).
% 0.61/1.03  cnf('0.24.1.0',plain,
% 0.61/1.03      ( apply(apply(apply(s,apply(c,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X3)) ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.24.0.0']),
% 0.61/1.03      [weight('<18,12,1,[1,1,0,0]>')]).
% 0.61/1.03  cnf('0.24.2.0',plain,
% 0.61/1.03      ( apply(apply(apply(s,apply(c,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X3)) ),
% 0.61/1.03      inference(activate,[status(thm)],['0.24.1.0']),
% 0.61/1.03      [equation_10]).
% 0.61/1.03  cnf('0.25.0.0',plain,
% 0.61/1.03      ( false = eq(apply(apply(apply(apply(X1,X2),X2),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(X3,apply(apply(X1,X2),X2))),apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),X1),X2),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(X3,apply(apply(X1,X2),X2)))) ),
% 0.61/1.03      inference(cp,[status(thm)],['0.13.2.0','0.24.2.0',theory(equality)]),
% 0.61/1.03      [pos('L.2.1.1','R')]).
% 0.61/1.03  cnf('0.25.1.0',plain,
% 0.61/1.03      ( false = eq(apply(apply(apply(apply(X1,X2),X2),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(X3,apply(apply(X1,X2),X2))),apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),X1),X2),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(X3,apply(apply(X1,X2),X2)))) ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.25.0.0']),
% 0.61/1.03      [weight('<0,24,13,[0,1,0,17]>')]).
% 0.61/1.03  cnf('0.25.1.1',plain,
% 0.61/1.03      ( false = eq(apply(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),X1),X2),f(apply(apply(apply(s,c),X3),apply(apply(X1,X2),X2)))),apply(X3,apply(apply(X1,X2),X2)))) ),
% 0.61/1.03      inference(reduction,[status(thm)],['0.25.1.0','0.10.2.0',theory(equality)]),
% 0.61/1.03      [pos('R.1','L')]).
% 0.61/1.03  cnf('0.25.2.0',plain,
% 0.61/1.03      ( eq(apply(apply(apply(apply(s,c),X1),apply(apply(X2,X3),X3)),f(apply(apply(apply(s,c),X1),apply(apply(X2,X3),X3)))),apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),X2),X3),f(apply(apply(apply(s,c),X1),apply(apply(X2,X3),X3)))),apply(X1,apply(apply(X2,X3),X3)))) = false ),
% 0.61/1.03      inference(orient,[status(thm)],['0.25.1.1',theory(equality)]),
% 0.61/1.03      [x,rule_15]).
% 0.61/1.03  cnf('0.26.0.0',plain,
% 0.61/1.03      ( false = eq(apply(apply(apply(apply(s,c),X1),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),f(apply(apply(apply(s,c),X1),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))))),apply(apply(apply(apply(s,c),X1),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),f(apply(apply(apply(s,c),X1),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b))))))))) ),
% 0.61/1.03      inference(cp,[status(thm)],['0.25.2.0','0.10.2.0',theory(equality)]),
% 0.61/1.03      [pos('L.2','L')]).
% 0.61/1.03  cnf('0.26.0.1',plain,
% 0.61/1.03      ( false = true ),
% 0.61/1.03      inference(reduction,[status(thm)],['0.26.0.0','0.4.2.0',theory(equality)]),
% 0.61/1.03      [pos('R','L')]).
% 0.61/1.03  cnf('0.26.1.0',plain,
% 0.61/1.03      ( false = true ),
% 0.61/1.03      inference(weigh,[status(thm)],['0.26.0.1']),
% 0.61/1.03      [weight('<2,25,10,[1,0,0,25]>')]).
% 0.61/1.03  cnf('0.26.2.0',plain,
% 0.61/1.03      ( true = false ),
% 0.61/1.03      inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 0.61/1.03      [x,rule_16]).
% 0.61/1.03  cnf('1.0.0.0',conjecture,
% 0.61/1.03      ( true = false ),
% 0.61/1.03      file('/tmp/WALDMEISTER_18610_n017',conjecture_1)).
% 0.61/1.03  cnf('1.0.0.1',plain,
% 0.61/1.03      ( false = false ),
% 0.61/1.03      inference(reduction,[status(thm)],['1.0.0.0','0.26.2.0',theory(equality)]),
% 0.61/1.03      [pos('L','L')]).
% 0.61/1.03  cnf('1.0.0.2',plain,
% 0.61/1.03      ( $true ),
% 0.61/1.03      inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.61/1.03      [conjecture_1]).
% 0.61/1.03  
% 0.61/1.03  Proved Goals:
% 0.61/1.03  No.  1: true ?= false, current false ?= false
% 0.61/1.03          using narrowing to prove apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1)))
% 0.61/1.03  
% 0.61/1.03  1 goal was specified, which was proved.
% 0.61/1.03  % SZS output end CNFRefutation
% 0.61/1.03  #END OF PROOF
% 0.61/1.03  
% 0.61/1.03  Problem         WALDMEISTER_18610_n017 
% 0.61/1.03  CPs.gen                 2059 
% 0.61/1.03  CPs.reexp                  0 
% 0.61/1.03  Select                    32 
% 0.61/1.03  R                         16 
% 0.61/1.03  E                         10 
% 0.61/1.03  vsize                   6.5M 
% 0.61/1.03  rss                     3.6M 
% 0.61/1.03  process.time          0.046s 
% 0.61/1.03  wallclock.time        0.047s 
% 0.61/1.03  status                     S
% 0.61/1.03  
% 0.61/1.03  
% 0.61/1.03  Waldmeister states: Goal proved.
% 0.61/1.03  % SZS status Unsatisfiable
% 0.61/1.03  
% 0.61/1.03  Problem         WALDMEISTER_18610_n017 
% 0.61/1.03  CPs.gen                    0 
% 0.61/1.03  CPs.reexp                  0 
% 0.61/1.03  Select                     0 
% 0.61/1.03  R                          0 
% 0.61/1.03  E                          0 
% 0.61/1.03  vsize                   6.0M 
% 0.61/1.03  rss                     3.2M 
% 0.61/1.03  process.time          0.001s 
% 0.61/1.03  wallclock.time        0.046s 
% 0.61/1.03  status                     S
%------------------------------------------------------------------------------