TSTP Solution File: GRP001^5 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : GRP001^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 : Mon May 20 21:02:53 EDT 2024

% Result   : Theorem 30.50s 5.66s
% Output   : Refutation 30.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   40 (  24 unt;   4 typ;   0 def)
%            Number of atoms       :   59 (  58 equ;   0 cnn)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  278 (  23   ~;  11   |;   9   &; 232   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :   84 (   0   ^  84   !;   0   ?;  84   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cP_type,type,
    cP: $i > $i > $i ).

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

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $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] :
          ( ( cP @ ( cP @ A @ B ) @ C )
          = ( cP @ A @ ( cP @ B @ C ) ) ) )
   => ! [A: $i,B: $i] :
        ( ( cP @ A @ B )
        = ( cP @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_COMM2) ).

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] :
            ( ( cP @ ( cP @ A @ B ) @ C )
            = ( cP @ A @ ( cP @ B @ C ) ) ) )
     => ! [A: $i,B: $i] :
          ( ( cP @ A @ B )
          = ( cP @ B @ A ) ) ),
    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] :
            ( ( cP @ ( cP @ A @ B ) @ C )
            = ( cP @ A @ ( cP @ B @ C ) ) ) )
     => ! [A: $i,B: $i] :
          ( ( cP @ A @ B )
          = ( cP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    ! [A: $i] :
      ( ( cP @ A @ A )
      = e ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ! [A: $i] :
      ( ( cP @ A @ A )
      = e ),
    inference(lifteq,[status(thm)],[6]) ).

thf(11,plain,
    ! [A: $i] :
      ( ( cP @ A @ A )
      = e ),
    inference(simp,[status(thm)],[10]) ).

thf(8,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( cP @ ( cP @ A @ B ) @ C )
      = ( cP @ A @ ( cP @ B @ C ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( cP @ ( cP @ A @ B ) @ C )
      = ( cP @ A @ ( cP @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( cP @ ( cP @ A @ B ) @ C )
      = ( cP @ A @ ( cP @ B @ C ) ) ),
    inference(simp,[status(thm)],[14]) ).

thf(65,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ e @ D )
        = ( cP @ B @ ( cP @ C @ D ) ) )
      | ( ( cP @ A @ A )
       != ( cP @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[11,15]) ).

thf(66,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ e @ B )
      = ( cP @ A @ ( cP @ A @ B ) ) ),
    inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(76,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ e @ B )
      = ( cP @ A @ ( cP @ A @ B ) ) ),
    inference(simp,[status(thm)],[66]) ).

thf(5,plain,
    ! [A: $i] :
      ( ( cP @ e @ A )
      = A ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [A: $i] :
      ( ( cP @ e @ A )
      = A ),
    inference(lifteq,[status(thm)],[5]) ).

thf(165,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ A @ ( cP @ A @ B ) )
      = B ),
    inference(rewrite,[status(thm)],[76,9]) ).

thf(4,plain,
    ( ( cP @ sk1 @ sk2 )
   != ( cP @ sk2 @ sk1 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(16,plain,
    ( ( cP @ sk2 @ sk1 )
   != ( cP @ sk1 @ sk2 ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(69,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( cP @ A @ ( cP @ B @ C ) )
       != ( cP @ sk1 @ sk2 ) )
      | ( ( cP @ ( cP @ A @ B ) @ C )
       != ( cP @ sk2 @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[15,16]) ).

thf(70,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != sk1 )
      | ( ( cP @ B @ C )
       != sk2 )
      | ( ( cP @ ( cP @ A @ B ) @ C )
       != ( cP @ sk2 @ sk1 ) ) ),
    inference(simp,[status(thm)],[69]) ).

thf(78,plain,
    ! [B: $i,A: $i] :
      ( ( ( cP @ A @ B )
       != sk2 )
      | ( ( cP @ ( cP @ sk1 @ A ) @ B )
       != ( cP @ sk2 @ sk1 ) ) ),
    inference(simp,[status(thm)],[70]) ).

thf(586,plain,
    ! [B: $i,A: $i] :
      ( ( ( cP @ A @ B )
       != sk2 )
      | ( ( cP @ sk1 @ ( cP @ A @ B ) )
       != ( cP @ sk2 @ sk1 ) ) ),
    inference(rewrite,[status(thm)],[78,15]) ).

thf(599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ C @ D )
       != sk2 )
      | ( B
       != ( cP @ sk2 @ sk1 ) )
      | ( ( cP @ A @ ( cP @ A @ B ) )
       != ( cP @ sk1 @ ( cP @ C @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[165,586]) ).

thf(600,plain,
    ! [A: $i] :
      ( ( ( cP @ sk1 @ A )
       != sk2 )
      | ( A
       != ( cP @ sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[599:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( B ))]]) ).

thf(702,plain,
    ( ( cP @ sk1 @ ( cP @ sk2 @ sk1 ) )
   != sk2 ),
    inference(simp,[status(thm)],[600]) ).

thf(63,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ B @ ( cP @ C @ D ) )
        = e )
      | ( ( cP @ A @ A )
       != ( cP @ ( cP @ B @ C ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[11,15]) ).

thf(64,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ A @ ( cP @ B @ ( cP @ A @ B ) ) )
      = e ),
    inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( cP @ G @ H )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( cP @ G @ H ))]]) ).

thf(75,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ A @ ( cP @ B @ ( cP @ A @ B ) ) )
      = e ),
    inference(simp,[status(thm)],[64]) ).

thf(190,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( cP @ C @ e )
        = D )
      | ( ( cP @ A @ ( cP @ B @ ( cP @ A @ B ) ) )
       != ( cP @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[75,165]) ).

thf(191,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ A @ e )
      = ( cP @ B @ ( cP @ A @ B ) ) ),
    inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( cP @ H @ ( cP @ G @ H ) ))]]) ).

thf(222,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ A @ e )
      = ( cP @ B @ ( cP @ A @ B ) ) ),
    inference(simp,[status(thm)],[191]) ).

thf(7,plain,
    ! [A: $i] :
      ( ( cP @ A @ e )
      = A ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [A: $i] :
      ( ( cP @ A @ e )
      = A ),
    inference(lifteq,[status(thm)],[7]) ).

thf(13,plain,
    ! [A: $i] :
      ( ( cP @ A @ e )
      = A ),
    inference(simp,[status(thm)],[12]) ).

thf(8881,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ B @ ( cP @ A @ B ) )
      = A ),
    inference(rewrite,[status(thm)],[222,13]) ).

thf(8883,plain,
    sk2 != sk2,
    inference(rewrite,[status(thm)],[702,8881]) ).

thf(8884,plain,
    $false,
    inference(simp,[status(thm)],[8883]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP001^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n010.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sun May 19 05:47:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.96/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.21/0.97  % [INFO] 	 Parsing done (102ms). 
% 1.21/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.63/1.19  % [INFO] 	 nitpick registered as external prover. 
% 1.63/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.84/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.84/1.27  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.84/1.27  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.84/1.27  % [INFO] 	 Type checking passed. 
% 1.84/1.28  % [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 ... 
% 30.50/5.66  % [INFO] 	 Killing All external provers ... 
% 30.50/5.66  % Time passed: 5127ms (effective reasoning time: 4674ms)
% 30.50/5.66  % 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)>
% 30.50/5.66  % Axioms used in derivation (0): 
% 30.50/5.66  % No. of inferences in proof: 36
% 30.50/5.66  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5127 ms resp. 4674 ms w/o parsing
% 30.50/5.69  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.50/5.69  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------