TSTP Solution File: SEV052^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEV052^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 04:10:50 EDT 2024

% Result   : Theorem 3.84s 2.49s
% Output   : Refutation 4.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   21 (   5 unt;   4 typ;   0 def)
%            Number of atoms       :  123 (  54 equ;  32 cnn)
%            Maximal formula atoms :    6 (   7 avg)
%            Number of connectives :  172 (  18   ~;  18   |;   9   &; 124   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   92 (  92   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   42 (  24   ^  15   !;   3   ?;  42   :)

% 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(sk3_type,type,
    sk3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(sk4_type,type,
    sk4: ( ( $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 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120B_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 ) ) ),
    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 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    ! [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( A
        @ ^ [B: $i] : $true
        @ ^ [B: $i] : $false )
      | ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
      | ( A @ ( sk3 @ A ) @ ( sk4 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ( ( ( ^ [A: $i] : $true )
      = ( ^ [A: $i] : $false ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
      = ( sk4 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(replace_andrewseq,[status(thm)],[5:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).

thf(14,plain,
    ( ( ( ^ [A: $i] : $false )
      = ( ^ [A: $i] : $true ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
      = ( sk3 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(15,plain,
    ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
    = ( sk3 @ ( (=) @ ( $i > $o ) ) ) ),
    inference(simp,[status(thm)],[14]) ).

thf(6,plain,
    ! [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( A
        @ ^ [B: $i] : $true
        @ ^ [B: $i] : $false )
      | ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
      | ( A @ ( sk2 @ A ) @ ( sk3 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ( ( ( ^ [A: $i] : $true )
      = ( ^ [A: $i] : $false ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
      = ( sk3 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(replace_andrewseq,[status(thm)],[6:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).

thf(10,plain,
    ( ( ( ^ [A: $i] : $false )
      = ( ^ [A: $i] : $true ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
      = ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(11,plain,
    ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
    = ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
    inference(simp,[status(thm)],[10]) ).

thf(18,plain,
    ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
    = ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
    inference(rewrite,[status(thm)],[15,11]) ).

thf(4,plain,
    ! [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( A
        @ ^ [B: $i] : $true
        @ ^ [B: $i] : $false )
      | ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
      | ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ( ( ( ^ [A: $i] : $true )
      = ( ^ [A: $i] : $false ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
     != ( sk4 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(replace_andrewseq,[status(thm)],[4:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).

thf(12,plain,
    ( ( ( ^ [A: $i] : $false )
      = ( ^ [A: $i] : $true ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
     != ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(13,plain,
    ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
   != ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
    inference(simp,[status(thm)],[12]) ).

thf(19,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[18,13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEV052^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n019.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 19:14:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.18/1.14  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.64/1.33  % [INFO] 	 Parsing done (180ms). 
% 1.64/1.34  % [INFO] 	 Running in sequential loop mode. 
% 2.30/1.79  % [INFO] 	 nitpick registered as external prover. 
% 2.30/1.80  % [INFO] 	 Scanning for conjecture ... 
% 2.39/1.90  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.54/1.94  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.54/1.95  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.54/1.95  % [INFO] 	 Type checking passed. 
% 2.54/1.95  % [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 ... 
% 3.59/2.48  % [INFO] 	 Killing All external provers ... 
% 3.84/2.49  % Time passed: 1937ms (effective reasoning time: 1132ms)
% 3.84/2.49  % 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)>
% 3.84/2.49  % Axioms used in derivation (0): 
% 3.84/2.49  % No. of inferences in proof: 17
% 3.84/2.49  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1937 ms resp. 1132 ms w/o parsing
% 4.08/2.64  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.08/2.64  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------