TSTP Solution File: SEV087^5 by Leo-III---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV087^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n024.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 Jun 24 15:58:10 EDT 2024

% Result   : Theorem 3.82s 2.20s
% Output   : Refutation 3.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    1
% Syntax   : Number of formulae    :    8 (   1 unt;   0 typ;   0 def)
%            Number of atoms       :   64 (  29 equ;  16 cnn)
%            Maximal formula atoms :    8 (   8 avg)
%            Number of connectives :  131 (  12   ~;  10   |;  15   &;  88   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   50 (  50   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   34 (  12   ^  19   !;   3   ?;  34   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sk1_type,type,
    sk1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(sk2_type,type,
    sk2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(sk4_type,type,
    sk4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(sk5_type,type,
    sk5: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(sk6_type,type,
    sk6: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(1,conjecture,
    ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ~ ( A
          @ ^ [B: $i] : $true
          @ ^ [B: $i] : $false )
      & ! [B: $i > $o] : ( A @ B @ B )
      & ! [B: $i > $o,C: $i > $o,D: $i > $o] :
          ( ( ( A @ B @ C )
            & ( A @ C @ D ) )
         => ( A @ B @ D ) )
      & ! [B: $i > $o,C: $i > $o] :
          ( ( ( A @ B @ C )
            & ( A @ C @ B ) )
         => ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120H_pme) ).

thf(2,negated_conjecture,
    ~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ~ ( A
            @ ^ [B: $i] : $true
            @ ^ [B: $i] : $false )
        & ! [B: $i > $o] : ( A @ B @ B )
        & ! [B: $i > $o,C: $i > $o,D: $i > $o] :
            ( ( ( A @ B @ C )
              & ( A @ C @ D ) )
           => ( A @ B @ D ) )
        & ! [B: $i > $o,C: $i > $o] :
            ( ( ( A @ B @ C )
              & ( A @ C @ B ) )
           => ( B = C ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ~ ( A
            @ ^ [B: $i] : $true
            @ ^ [B: $i] : $false )
        & ! [B: $i > $o] : ( A @ B @ B )
        & ! [B: $i > $o,C: $i > $o,D: $i > $o] :
            ( ( ( A @ B @ C )
              & ( A @ C @ D ) )
           => ( A @ B @ D ) )
        & ! [B: $i > $o,C: $i > $o] :
            ( ( ( A @ B @ C )
              & ( A @ C @ B ) )
           => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,plain,
    ! [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( A
        @ ^ [B: $i] : $true
        @ ^ [B: $i] : $false )
      | ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
      | ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
      | ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ( ( ( ^ [A: $i] : $true )
      = ( ^ [A: $i] : $false ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
     != ( sk4 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(replace_andrewseq,[status(thm)],[10:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).

thf(23,plain,
    ( ( ( ^ [A: $i] : $false )
      = ( ^ [A: $i] : $true ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
     != ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(24,plain,
    ( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
     != ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(simp,[status(thm)],[23]) ).

thf(54,plain,
    $false,
    inference(e,[status(thm)],[3,24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : SEV087^5 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.09  % Command  : run_Leo-III %s %d THM
% 0.08/0.29  % Computer : n024.cluster.edu
% 0.08/0.29  % Model    : x86_64 x86_64
% 0.08/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29  % Memory   : 8042.1875MB
% 0.08/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29  % CPULimit : 300
% 0.08/0.29  % WCLimit  : 300
% 0.08/0.29  % DateTime : Fri Jun 21 19:17:40 EDT 2024
% 0.08/0.29  % CPUTime  : 
% 1.11/0.97  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.35/1.09  % [INFO] 	 Parsing done (114ms). 
% 1.35/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.76/1.36  % [INFO] 	 eprover registered as external prover. 
% 1.76/1.36  % [INFO] 	 Scanning for conjecture ... 
% 2.03/1.44  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.08/1.48  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.08/1.48  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.08/1.48  % [INFO] 	 Type checking passed. 
% 2.08/1.48  % [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 ... 
% 3.82/2.19  % External prover 'e' found a proof!
% 3.82/2.20  % [INFO] 	 Killing All external provers ... 
% 3.82/2.20  % Time passed: 1671ms (effective reasoning time: 1097ms)
% 3.82/2.20  % 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)>
% 3.82/2.20  % Axioms used in derivation (0): 
% 3.82/2.20  % No. of inferences in proof: 8
% 3.82/2.20  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1671 ms resp. 1097 ms w/o parsing
% 3.82/2.24  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.82/2.24  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------