TSTP Solution File: COL057-1 by Waldmeister---710

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Waldmeister---710
% Problem  : COL057-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : woody %s

% Computer : n025.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 00:47:36 EDT 2022

% Result   : Unsatisfiable 0.61s 1.02s
% Output   : CNFRefutation 0.61s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COL057-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : woody %s
% 0.13/0.34  % Computer : n025.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 09:44:43 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.61/1.01  ********************************************************************************
% 0.61/1.01  *                             W A L D M E I S T E R           \|  \ /      \|/ *
% 0.61/1.01  *                                                              |/  |    \/  |  *
% 0.61/1.01  *              (C) 1994-2010  A. Buch and Th. Hillenbrand,      \ /      \ /   *
% 0.61/1.01  *                             A. Jaeger and B. Loechner          |        |    *
% 0.61/1.01  *                             <waldmeister@informatik.uni-kl.de>          |    *
% 0.61/1.01  ********************************************************************************
% 0.61/1.01  
% 0.61/1.01  
% 0.61/1.01  Goals:
% 0.61/1.01  ------
% 0.61/1.01  
% 0.61/1.01  (   1)  true ?= false
% 0.61/1.01          using narrowing to prove x1 ?= apply(const1,x1)
% 0.61/1.01  
% 0.61/1.01  Detected structure: KombinatorlogikB
% 0.61/1.01  ********************************************************************************
% 0.61/1.01  ****************************** COMPLETION - PROOF ******************************
% 0.61/1.01  ********************************************************************************
% 0.61/1.01  
% 0.61/1.02  joined goal:           1  apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1))) to false
% 0.61/1.02  goal joined
% 0.61/1.02  % SZS status Unsatisfiable
% 0.61/1.02  #START OF PROOF
% 0.61/1.02  % SZS output start CNFRefutation
% 0.61/1.02  cnf('0.1.0.0',axiom,
% 0.61/1.02      ( X1 = apply(i,X1) ),
% 0.61/1.02      file('/tmp/WALDMEISTER_2285_n025')).
% 0.61/1.02  cnf('0.1.1.0',plain,
% 0.61/1.02      ( X1 = apply(i,X1) ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.1.0.0']),
% 0.61/1.02      [weight('<0,0,0,[0,0,0,1]>')]).
% 0.61/1.02  cnf('0.1.2.0',plain,
% 0.61/1.02      ( apply(i,X1) = X1 ),
% 0.61/1.02      inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.61/1.02      [x,rule_1]).
% 0.61/1.02  cnf('0.2.0.0',axiom,
% 0.61/1.02      ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.61/1.02      file('/tmp/WALDMEISTER_2285_n025')).
% 0.61/1.02  cnf('0.2.1.0',plain,
% 0.61/1.02      ( apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3) ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.2.0.0']),
% 0.61/1.02      [weight('<1,0,0,[0,0,0,2]>')]).
% 0.61/1.02  cnf('0.2.2.0',plain,
% 0.61/1.02      ( apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)) ),
% 0.61/1.02      inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.61/1.02      [x,rule_2]).
% 0.61/1.02  cnf('0.3.0.0',axiom,
% 0.61/1.02      ( apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2) ),
% 0.61/1.02      file('/tmp/WALDMEISTER_2285_n025')).
% 0.61/1.02  cnf('0.3.1.0',plain,
% 0.61/1.02      ( apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2) ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.3.0.0']),
% 0.61/1.02      [weight('<2,0,0,[0,0,0,3]>')]).
% 0.61/1.02  cnf('0.3.2.0',plain,
% 0.61/1.02      ( apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2) ),
% 0.61/1.02      inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
% 0.61/1.02      [x,rule_3]).
% 0.61/1.02  cnf('0.4.0.0',axiom,
% 0.61/1.02      ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.61/1.02      file('/tmp/WALDMEISTER_2285_n025')).
% 0.61/1.02  cnf('0.4.1.0',plain,
% 0.61/1.02      ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.4.0.0']),
% 0.61/1.02      [weight('<3,0,0,[0,0,0,4]>')]).
% 0.61/1.02  cnf('0.4.2.0',plain,
% 0.61/1.02      ( apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2) ),
% 0.61/1.02      inference(activate,[status(thm)],['0.4.1.0']),
% 0.61/1.02      [equation_1]).
% 0.61/1.02  cnf('0.5.0.0',axiom,
% 0.61/1.02      ( eq(X1,X1) = true ),
% 0.61/1.02      file('/tmp/WALDMEISTER_2285_n025')).
% 0.61/1.02  cnf('0.5.1.0',plain,
% 0.61/1.02      ( eq(X1,X1) = true ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.5.0.0']),
% 0.61/1.02      [weight('<4,0,0,[0,0,0,5]>')]).
% 0.61/1.02  cnf('0.5.2.0',plain,
% 0.61/1.02      ( eq(X1,X1) = true ),
% 0.61/1.02      inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.61/1.02      [u,rule_4]).
% 0.61/1.02  cnf('0.6.0.0',axiom,
% 0.61/1.02      ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.61/1.02      file('/tmp/WALDMEISTER_2285_n025')).
% 0.61/1.02  cnf('0.6.1.0',plain,
% 0.61/1.02      ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.6.0.0']),
% 0.61/1.02      [weight('<5,0,0,[0,0,0,6]>')]).
% 0.61/1.02  cnf('0.6.2.0',plain,
% 0.61/1.02      ( eq(apply(X1,f(X1)),apply(f(X1),apply(X1,f(X1)))) = false ),
% 0.61/1.02      inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.61/1.02      [u,rule_5]).
% 0.61/1.02  cnf('0.8.0.0',plain,
% 0.61/1.02      ( apply(apply(apply(s,i),X1),X2) = apply(X2,apply(X1,X2)) ),
% 0.61/1.02      inference(cp,[status(thm)],['0.4.2.0','0.1.2.0',theory(equality)]),
% 0.61/1.02      [pos('L.1','L')]).
% 0.61/1.02  cnf('0.8.1.0',plain,
% 0.61/1.02      ( apply(apply(apply(s,i),X1),X2) = apply(X2,apply(X1,X2)) ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.8.0.0']),
% 0.61/1.02      [weight('<12,4,1,[1,0,0,1]>')]).
% 0.61/1.02  cnf('0.8.2.0',plain,
% 0.61/1.02      ( apply(apply(apply(s,i),X1),X2) = apply(X2,apply(X1,X2)) ),
% 0.61/1.02      inference(activate,[status(thm)],['0.8.1.0']),
% 0.61/1.02      [equation_2]).
% 0.61/1.02  cnf('0.9.0.0',plain,
% 0.61/1.02      ( false = eq(apply(X1,f(X1)),apply(apply(apply(s,i),X1),f(X1))) ),
% 0.61/1.02      inference(cp,[status(thm)],['0.6.2.0','0.8.2.0',theory(equality)]),
% 0.61/1.02      [pos('L.2','R')]).
% 0.61/1.02  cnf('0.9.1.0',plain,
% 0.61/1.02      ( false = eq(apply(X1,f(X1)),apply(apply(apply(s,i),X1),f(X1))) ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.9.0.0']),
% 0.61/1.02      [weight('<72,8,6,[0,1,0,5]>')]).
% 0.61/1.02  cnf('0.9.2.0',plain,
% 0.61/1.02      ( eq(apply(X1,f(X1)),apply(apply(apply(s,i),X1),f(X1))) = false ),
% 0.61/1.02      inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.61/1.02      [x,rule_7]).
% 0.61/1.02  cnf('0.10.0.0',plain,
% 0.61/1.02      ( apply(apply(apply(s,i),i),X1) = apply(X1,X1) ),
% 0.61/1.02      inference(cp,[status(thm)],['0.8.2.0','0.1.2.0',theory(equality)]),
% 0.61/1.02      [pos('R.2','L')]).
% 0.61/1.02  cnf('0.10.1.0',plain,
% 0.61/1.02      ( apply(apply(apply(s,i),i),X1) = apply(X1,X1) ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.10.0.0']),
% 0.61/1.02      [weight('<10,8,1,[1,1,0,2]>')]).
% 0.61/1.02  cnf('0.10.2.0',plain,
% 0.61/1.02      ( apply(apply(apply(s,i),i),X1) = apply(X1,X1) ),
% 0.61/1.02      inference(activate,[status(thm)],['0.10.1.0']),
% 0.61/1.02      [equation_3]).
% 0.61/1.02  cnf('0.11.0.0',plain,
% 0.61/1.02      ( false = eq(apply(apply(X1,f(apply(apply(c,X1),X2))),X2),apply(apply(apply(s,i),apply(apply(c,X1),X2)),f(apply(apply(c,X1),X2)))) ),
% 0.61/1.02      inference(cp,[status(thm)],['0.9.2.0','0.3.2.0',theory(equality)]),
% 0.61/1.02      [pos('L.1','L')]).
% 0.61/1.02  cnf('0.11.1.0',plain,
% 0.61/1.02      ( false = eq(apply(apply(X1,f(apply(apply(c,X1),X2))),X2),apply(apply(apply(s,i),apply(apply(c,X1),X2)),f(apply(apply(c,X1),X2)))) ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.11.0.0']),
% 0.61/1.02      [weight('<364,9,3,[1,0,0,1]>')]).
% 0.61/1.02  cnf('0.11.2.0',plain,
% 0.61/1.02      ( eq(apply(apply(X1,f(apply(apply(c,X1),X2))),X2),apply(apply(apply(s,i),apply(apply(c,X1),X2)),f(apply(apply(c,X1),X2)))) = false ),
% 0.61/1.02      inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.61/1.02      [x,rule_8]).
% 0.61/1.02  cnf('0.13.0.0',plain,
% 0.61/1.02      ( false = eq(apply(apply(X1,X2),f(apply(apply(c,apply(c,X1)),X2))),apply(apply(apply(s,i),apply(apply(c,apply(c,X1)),X2)),f(apply(apply(c,apply(c,X1)),X2)))) ),
% 0.61/1.02      inference(cp,[status(thm)],['0.11.2.0','0.3.2.0',theory(equality)]),
% 0.61/1.02      [pos('L.1','L')]).
% 0.61/1.02  cnf('0.13.1.0',plain,
% 0.61/1.02      ( false = eq(apply(apply(X1,X2),f(apply(apply(c,apply(c,X1)),X2))),apply(apply(apply(s,i),apply(apply(c,apply(c,X1)),X2)),f(apply(apply(c,apply(c,X1)),X2)))) ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.13.0.0']),
% 0.61/1.02      [weight('<256,11,3,[1,0,0,1]>')]).
% 0.61/1.02  cnf('0.13.2.0',plain,
% 0.61/1.02      ( eq(apply(apply(X1,X2),f(apply(apply(c,apply(c,X1)),X2))),apply(apply(apply(s,i),apply(apply(c,apply(c,X1)),X2)),f(apply(apply(c,apply(c,X1)),X2)))) = false ),
% 0.61/1.02      inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.61/1.02      [x,rule_9]).
% 0.61/1.02  cnf('0.15.0.0',plain,
% 0.61/1.02      ( false = eq(apply(apply(X1,apply(c,apply(c,X1))),f(apply(apply(c,apply(c,X1)),apply(c,apply(c,X1))))),apply(apply(apply(s,i),apply(apply(apply(s,i),i),apply(c,apply(c,X1)))),f(apply(apply(c,apply(c,X1)),apply(c,apply(c,X1)))))) ),
% 0.61/1.02      inference(cp,[status(thm)],['0.13.2.0','0.10.2.0',theory(equality)]),
% 0.61/1.02      [pos('L.2.1.2','R')]).
% 0.61/1.02  cnf('0.15.1.0',plain,
% 0.61/1.02      ( false = eq(apply(apply(X1,apply(c,apply(c,X1))),f(apply(apply(c,apply(c,X1)),apply(c,apply(c,X1))))),apply(apply(apply(s,i),apply(apply(apply(s,i),i),apply(c,apply(c,X1)))),f(apply(apply(c,apply(c,X1)),apply(c,apply(c,X1)))))) ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.15.0.0']),
% 0.61/1.02      [weight('<240,13,10,[1,0,1,18]>')]).
% 0.61/1.02  cnf('0.15.1.1',plain,
% 0.61/1.02      ( false = eq(apply(apply(X1,apply(c,apply(c,X1))),f(apply(apply(apply(s,c),c),apply(c,X1)))),apply(apply(apply(s,i),apply(apply(apply(s,i),i),apply(c,apply(c,X1)))),f(apply(apply(c,apply(c,X1)),apply(c,apply(c,X1)))))) ),
% 0.61/1.02      inference(reduction,[status(thm)],['0.15.1.0','0.4.2.0',theory(equality)]),
% 0.61/1.02      [pos('R.1.2.1','L')]).
% 0.61/1.02  cnf('0.15.1.2',plain,
% 0.61/1.02      ( false = eq(apply(apply(X1,apply(c,apply(c,X1))),f(apply(apply(apply(s,c),c),apply(c,X1)))),apply(apply(apply(s,i),apply(apply(apply(s,i),i),apply(c,apply(c,X1)))),f(apply(apply(apply(s,c),c),apply(c,X1))))) ),
% 0.61/1.02      inference(reduction,[status(thm)],['0.15.1.1','0.4.2.0',theory(equality)]),
% 0.61/1.02      [pos('R.2.2.1','L')]).
% 0.61/1.02  cnf('0.15.2.0',plain,
% 0.61/1.02      ( eq(apply(apply(X1,apply(c,apply(c,X1))),f(apply(apply(apply(s,c),c),apply(c,X1)))),apply(apply(apply(s,i),apply(apply(apply(s,i),i),apply(c,apply(c,X1)))),f(apply(apply(apply(s,c),c),apply(c,X1))))) = false ),
% 0.61/1.02      inference(orient,[status(thm)],['0.15.1.2',theory(equality)]),
% 0.61/1.02      [x,rule_10]).
% 0.61/1.02  cnf('0.17.0.0',plain,
% 0.61/1.02      ( false = eq(apply(apply(X1,apply(X2,apply(c,apply(c,apply(apply(b,X1),X2))))),f(apply(apply(apply(s,c),c),apply(c,apply(apply(b,X1),X2))))),apply(apply(apply(s,i),apply(apply(apply(s,i),i),apply(c,apply(c,apply(apply(b,X1),X2))))),f(apply(apply(apply(s,c),c),apply(c,apply(apply(b,X1),X2)))))) ),
% 0.61/1.02      inference(cp,[status(thm)],['0.15.2.0','0.2.2.0',theory(equality)]),
% 0.61/1.02      [pos('L.1.1','L')]).
% 0.61/1.02  cnf('0.17.1.0',plain,
% 0.61/1.02      ( false = eq(apply(apply(X1,apply(X2,apply(c,apply(c,apply(apply(b,X1),X2))))),f(apply(apply(apply(s,c),c),apply(c,apply(apply(b,X1),X2))))),apply(apply(apply(s,i),apply(apply(apply(s,i),i),apply(c,apply(c,apply(apply(b,X1),X2))))),f(apply(apply(apply(s,c),c),apply(c,apply(apply(b,X1),X2)))))) ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.17.0.0']),
% 0.61/1.02      [weight('<0,15,2,[1,0,0,2]>')]).
% 0.61/1.02  cnf('0.17.2.0',plain,
% 0.61/1.02      ( eq(apply(apply(X1,apply(X2,apply(c,apply(c,apply(apply(b,X1),X2))))),f(apply(apply(apply(s,c),c),apply(c,apply(apply(b,X1),X2))))),apply(apply(apply(s,i),apply(apply(apply(s,i),i),apply(c,apply(c,apply(apply(b,X1),X2))))),f(apply(apply(apply(s,c),c),apply(c,apply(apply(b,X1),X2)))))) = false ),
% 0.61/1.02      inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.61/1.02      [x,rule_11]).
% 0.61/1.02  cnf('0.18.0.0',plain,
% 0.61/1.02      ( false = true ),
% 0.61/1.02      inference(cp,[status(thm)],['0.17.2.0','0.5.2.0',theory(equality)]),
% 0.61/1.02      [pos('L','L')]).
% 0.61/1.02  cnf('0.18.1.0',plain,
% 0.61/1.02      ( false = true ),
% 0.61/1.02      inference(weigh,[status(thm)],['0.18.0.0']),
% 0.61/1.02      [weight('<2,17,5,[1,0,0,0]>')]).
% 0.61/1.02  cnf('0.18.2.0',plain,
% 0.61/1.02      ( true = false ),
% 0.61/1.02      inference(orient,[status(thm)],['0.18.1.0',theory(equality)]),
% 0.61/1.02      [x,rule_12]).
% 0.61/1.02  cnf('1.0.0.0',conjecture,
% 0.61/1.02      ( true = false ),
% 0.61/1.02      file('/tmp/WALDMEISTER_2285_n025',conjecture_1)).
% 0.61/1.02  cnf('1.0.0.1',plain,
% 0.61/1.02      ( false = false ),
% 0.61/1.02      inference(reduction,[status(thm)],['1.0.0.0','0.18.2.0',theory(equality)]),
% 0.61/1.02      [pos('L','L')]).
% 0.61/1.02  cnf('1.0.0.2',plain,
% 0.61/1.02      ( $true ),
% 0.61/1.02      inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
% 0.61/1.02      [conjecture_1]).
% 0.61/1.02  
% 0.61/1.02  Proved Goals:
% 0.61/1.02  No.  1: true ?= false, current false ?= false
% 0.61/1.02          using narrowing to prove apply(x1,f(x1)) ?= apply(f(x1),apply(x1,f(x1)))
% 0.61/1.02  
% 0.61/1.02  1 goal was specified, which was proved.
% 0.61/1.02  % SZS output end CNFRefutation
% 0.61/1.02  #END OF PROOF
% 0.61/1.02  
% 0.61/1.02  Problem         WALDMEISTER_2285_n025 
% 0.61/1.02  CPs.gen                  276 
% 0.61/1.02  CPs.reexp                  0 
% 0.61/1.02  Select                    28 
% 0.61/1.02  R                         12 
% 0.61/1.02  E                          6 
% 0.61/1.02  vsize                   6.5M 
% 0.61/1.02  rss                     3.7M 
% 0.61/1.02  process.time          0.006s 
% 0.61/1.02  wallclock.time        0.007s 
% 0.61/1.02  status                     S
% 0.61/1.02  
% 0.61/1.02  
% 0.61/1.02  Waldmeister states: Goal proved.
% 0.61/1.02  % SZS status Unsatisfiable
% 0.61/1.02  
% 0.61/1.02  Problem         WALDMEISTER_2285_n025 
% 0.61/1.02  CPs.gen                    0 
% 0.61/1.02  CPs.reexp                  0 
% 0.61/1.02  Select                     0 
% 0.61/1.02  R                          0 
% 0.61/1.02  E                          0 
% 0.61/1.02  vsize                   6.0M 
% 0.61/1.02  rss                     3.2M 
% 0.61/1.02  process.time          0.001s 
% 0.61/1.02  wallclock.time        0.006s 
% 0.61/1.02  status                     S
%------------------------------------------------------------------------------