TSTP Solution File: SYO170^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO170^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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  : 300s
% DateTime : Tue May 21 08:59:28 EDT 2024

% Result   : Theorem 72.58s 11.80s
% Output   : Refutation 72.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   52 (  22 unt;   5 typ;   0 def)
%            Number of atoms       :  187 (  42 equ;   0 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  519 (  34   ~;  28   |;  16   &; 429   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   6 con; 0-3 aty)
%            Number of variables   :  142 (   0   ^ 142   !;   0   ?; 142   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ab_type,type,
    ab: $i ).

thf(a_type,type,
    a: $i ).

thf(b_type,type,
    b: $i ).

thf(cP_type,type,
    cP: $i > $i > $i > $o ).

thf(e_type,type,
    e: $i ).

thf(1,conjecture,
    ( ( ! [A: $i] : ( cP @ e @ A @ A )
      & ! [A: $i] : ( cP @ A @ e @ A )
      & ! [A: $i] : ( cP @ A @ A @ e )
      & ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
          ( ( ( cP @ A @ B @ D )
            & ( cP @ B @ C @ E ) )
         => ( ( cP @ D @ C @ F )
            = ( cP @ A @ E @ F ) ) ) )
   => ( ( cP @ a @ b @ ab )
     => ( cP @ b @ a @ ab ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM105) ).

thf(2,negated_conjecture,
    ~ ( ( ! [A: $i] : ( cP @ e @ A @ A )
        & ! [A: $i] : ( cP @ A @ e @ A )
        & ! [A: $i] : ( cP @ A @ A @ e )
        & ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
            ( ( ( cP @ A @ B @ D )
              & ( cP @ B @ C @ E ) )
           => ( ( cP @ D @ C @ F )
              = ( cP @ A @ E @ F ) ) ) )
     => ( ( cP @ a @ b @ ab )
       => ( cP @ b @ a @ ab ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ! [A: $i] : ( cP @ e @ A @ A )
        & ! [A: $i] : ( cP @ A @ e @ A )
        & ! [A: $i] : ( cP @ A @ A @ e )
        & ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
            ( ( ( cP @ A @ B @ D )
              & ( cP @ B @ C @ E ) )
           => ( ( cP @ D @ C @ F )
              = ( cP @ A @ E @ F ) ) ) )
     => ( ( cP @ a @ b @ ab )
       => ( cP @ b @ a @ ab ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ( ( ! [A: $i] : ( cP @ e @ A @ A )
        & ! [A: $i] : ( cP @ A @ e @ A )
        & ! [A: $i] : ( cP @ A @ A @ e )
        & ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
            ( ( ( cP @ A @ B @ D )
              & ( cP @ B @ C @ E ) )
           => ! [F: $i] :
                ( ( cP @ D @ C @ F )
                = ( cP @ A @ E @ F ) ) ) )
     => ( ( cP @ a @ b @ ab )
       => ( cP @ b @ a @ ab ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(8,plain,
    ~ ( cP @ b @ a @ ab ),
    inference(cnf,[status(esa)],[4]) ).

thf(9,plain,
    ! [A: $i] : ( cP @ A @ A @ e ),
    inference(cnf,[status(esa)],[4]) ).

thf(13,plain,
    ! [A: $i] : ( cP @ A @ A @ e ),
    inference(simp,[status(thm)],[9]) ).

thf(6,plain,
    cP @ a @ b @ ab,
    inference(cnf,[status(esa)],[4]) ).

thf(5,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( cP @ A @ B @ D )
      | ~ ( cP @ B @ C @ E )
      | ( ( cP @ D @ C @ F )
        = ( cP @ A @ E @ F ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ D @ C @ F )
        = ( cP @ A @ E @ F ) )
      | ~ ( cP @ A @ B @ D )
      | ~ ( cP @ B @ C @ E ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(12,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ D @ C @ F )
        = ( cP @ A @ E @ F ) )
      | ~ ( cP @ A @ B @ D )
      | ~ ( cP @ B @ C @ E ) ),
    inference(simp,[status(thm)],[11]) ).

thf(45,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ D @ C @ F )
        = ( cP @ A @ E @ F ) )
      | ~ ( cP @ A @ B @ D )
      | ( ( cP @ a @ b @ ab )
       != ( cP @ B @ C @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[6,12]) ).

thf(46,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( cP @ B @ b @ C )
        = ( cP @ A @ ab @ C ) )
      | ~ ( cP @ A @ a @ B ) ),
    inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( b )),bind(D,$thf( D )),bind(E,$thf( ab ))]]) ).

thf(68,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( cP @ B @ b @ C )
        = ( cP @ A @ ab @ C ) )
      | ~ ( cP @ A @ a @ B ) ),
    inference(simp,[status(thm)],[46]) ).

thf(4814,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ C @ b @ D )
        = ( cP @ B @ ab @ D ) )
      | ( ( cP @ A @ A @ e )
       != ( cP @ B @ a @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[13,68]) ).

thf(4815,plain,
    ! [A: $i] :
      ( ( cP @ e @ b @ A )
      = ( cP @ a @ ab @ A ) ),
    inference(pattern_uni,[status(thm)],[4814:[bind(A,$thf( a )),bind(B,$thf( a )),bind(C,$thf( e ))]]) ).

thf(5224,plain,
    ! [A: $i] :
      ( ( cP @ e @ b @ A )
      = ( cP @ a @ ab @ A ) ),
    inference(simp,[status(thm)],[4815]) ).

thf(10,plain,
    ! [A: $i] : ( cP @ e @ A @ A ),
    inference(cnf,[status(esa)],[4]) ).

thf(5530,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ a @ ab @ A )
      | ( ( cP @ e @ b @ A )
       != ( cP @ e @ B @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5224,10]) ).

thf(5531,plain,
    cP @ a @ ab @ b,
    inference(pattern_uni,[status(thm)],[5530:[bind(A,$thf( b )),bind(B,$thf( b ))]]) ).

thf(43,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ D @ C @ F )
        = ( cP @ A @ E @ F ) )
      | ~ ( cP @ B @ C @ E )
      | ( ( cP @ a @ b @ ab )
       != ( cP @ A @ B @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[6,12]) ).

thf(44,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( cP @ ab @ A @ C )
        = ( cP @ a @ B @ C ) )
      | ~ ( cP @ b @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( a )),bind(B,$thf( b )),bind(C,$thf( C )),bind(D,$thf( ab ))]]) ).

thf(67,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( cP @ ab @ A @ C )
        = ( cP @ a @ B @ C ) )
      | ~ ( cP @ b @ A @ B ) ),
    inference(simp,[status(thm)],[44]) ).

thf(259,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ ab @ B @ D )
        = ( cP @ a @ C @ D ) )
      | ( ( cP @ A @ A @ e )
       != ( cP @ b @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[13,67]) ).

thf(260,plain,
    ! [A: $i] :
      ( ( cP @ a @ e @ A )
      = ( cP @ ab @ b @ A ) ),
    inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( b )),bind(B,$thf( b )),bind(C,$thf( e ))]]) ).

thf(305,plain,
    ! [A: $i] :
      ( ( cP @ a @ e @ A )
      = ( cP @ ab @ b @ A ) ),
    inference(simp,[status(thm)],[260]) ).

thf(7,plain,
    ! [A: $i] : ( cP @ A @ e @ A ),
    inference(cnf,[status(esa)],[4]) ).

thf(14,plain,
    ! [A: $i] : ( cP @ A @ e @ A ),
    inference(simp,[status(thm)],[7]) ).

thf(348,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ ab @ b @ A )
      | ( ( cP @ a @ e @ A )
       != ( cP @ B @ e @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[305,14]) ).

thf(349,plain,
    cP @ ab @ b @ a,
    inference(pattern_uni,[status(thm)],[348:[bind(A,$thf( a )),bind(B,$thf( a ))]]) ).

thf(84,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ E @ D @ G )
        = ( cP @ B @ F @ G ) )
      | ~ ( cP @ C @ D @ F )
      | ( ( cP @ A @ A @ e )
       != ( cP @ B @ C @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[13,12]) ).

thf(85,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ e @ B @ D )
        = ( cP @ A @ C @ D ) )
      | ~ ( cP @ A @ B @ C ) ),
    inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( e ))]]) ).

thf(96,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ e @ B @ D )
        = ( cP @ A @ C @ D ) )
      | ~ ( cP @ A @ B @ C ) ),
    inference(simp,[status(thm)],[85]) ).

thf(19489,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ e @ B @ D )
        = ( cP @ A @ C @ D ) )
      | ( ( cP @ ab @ b @ a )
       != ( cP @ A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[349,96]) ).

thf(19490,plain,
    ! [A: $i] :
      ( ( cP @ e @ b @ A )
      = ( cP @ ab @ a @ A ) ),
    inference(pattern_uni,[status(thm)],[19489:[bind(A,$thf( ab )),bind(B,$thf( b )),bind(C,$thf( a ))]]) ).

thf(20003,plain,
    ! [A: $i] :
      ( ( cP @ e @ b @ A )
      = ( cP @ ab @ a @ A ) ),
    inference(simp,[status(thm)],[19490]) ).

thf(20336,plain,
    ! [A: $i] :
      ( ( cP @ a @ ab @ A )
      = ( cP @ ab @ a @ A ) ),
    inference(rewrite,[status(thm)],[20003,5224]) ).

thf(20340,plain,
    cP @ ab @ a @ b,
    inference(rewrite,[status(thm)],[5531,20336]) ).

thf(86,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ E @ D @ G )
        = ( cP @ B @ F @ G ) )
      | ~ ( cP @ B @ C @ E )
      | ( ( cP @ A @ A @ e )
       != ( cP @ C @ D @ F ) ) ),
    inference(paramod_ordered,[status(thm)],[13,12]) ).

thf(87,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ C @ A @ D )
        = ( cP @ B @ e @ D ) )
      | ~ ( cP @ B @ A @ C ) ),
    inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( E )),bind(F,$thf( e ))]]) ).

thf(97,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ C @ A @ D )
        = ( cP @ B @ e @ D ) )
      | ~ ( cP @ B @ A @ C ) ),
    inference(simp,[status(thm)],[87]) ).

thf(21393,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ C @ A @ D )
        = ( cP @ B @ e @ D ) )
      | ( ( cP @ ab @ a @ b )
       != ( cP @ B @ A @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[20340,97]) ).

thf(21394,plain,
    ! [A: $i] :
      ( ( cP @ b @ a @ A )
      = ( cP @ ab @ e @ A ) ),
    inference(pattern_uni,[status(thm)],[21393:[bind(A,$thf( a )),bind(B,$thf( ab )),bind(C,$thf( b ))]]) ).

thf(22228,plain,
    ! [A: $i] :
      ( ( cP @ b @ a @ A )
      = ( cP @ ab @ e @ A ) ),
    inference(simp,[status(thm)],[21394]) ).

thf(24503,plain,
    ~ ( cP @ ab @ e @ ab ),
    inference(rewrite,[status(thm)],[8,22228]) ).

thf(25024,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[24503,14]) ).

thf(25025,plain,
    $false,
    inference(simp,[status(thm)],[25024]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : SYO170^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n006.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Mon May 20 09:52:39 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.82/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.03/0.92  % [INFO] 	 Parsing done (103ms). 
% 1.14/0.93  % [INFO] 	 Running in sequential loop mode. 
% 1.42/1.15  % [INFO] 	 nitpick registered as external prover. 
% 1.42/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.65/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.74/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.74/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.74/1.25  % [INFO] 	 Type checking passed. 
% 1.74/1.26  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 72.58/11.79  % [INFO] 	 Killing All external provers ... 
% 72.58/11.79  % Time passed: 11300ms (effective reasoning time: 10854ms)
% 72.58/11.79  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 72.58/11.79  % Axioms used in derivation (0): 
% 72.58/11.79  % No. of inferences in proof: 47
% 72.58/11.80  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11300 ms resp. 10854 ms w/o parsing
% 72.58/11.83  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 72.58/11.83  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------