TSTP Solution File: SEU894^5 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU894^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 03:44:10 EDT 2024

% Result   : Theorem 3.18s 1.69s
% Output   : Refutation 3.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   16 (   9 unt;   2 typ;   0 def)
%            Number of atoms       :   27 (  26 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  105 (  10   ~;   1   |;  12   &;  66   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   29 (  29   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   51 (  12   ^  28   !;  11   ?;  51   :)

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

thf(sk3_type,type,
    sk3: ( $i > $i ) > $i ).

thf(1,conjecture,
    ! [A: $i > $i] :
    ? [B: $i > $i] :
      ( ( ! [C: ( $i > $i ) > $o] :
            ( ( ( C @ A )
              & ! [D: $i > $i] :
                  ( ( C @ D )
                 => ( C
                    @ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
           => ( C @ B ) )
        & ? [C: $i] :
            ( ( ( B @ C )
              = C )
            & ! [D: $i] :
                ( ( ( B @ D )
                  = D )
               => ( C = D ) ) ) )
     => ? [C: $i] :
          ( ( A @ C )
          = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM15_0_pme) ).

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

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

thf(4,plain,
    ~ ! [A: $i > $i] :
        ( ( ! [B: $i > $i,C: ( $i > $i ) > $o] :
              ( ( ( C @ A )
                & ! [D: $i > $i] :
                    ( ( C @ D )
                   => ( C
                      @ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
             => ( C @ B ) )
          & ! [B: $i > $i] :
            ? [C: $i] :
              ( ( ( B @ C )
                = C )
              & ! [D: $i] :
                  ( ( ( B @ D )
                    = D )
                 => ( C = D ) ) ) )
       => ? [B: $i] :
            ( ( A @ B )
            = B ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(7,plain,
    ! [A: $i > $i] :
      ( ( A @ ( sk3 @ A ) )
      = ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(16,plain,
    ! [A: $i > $i] :
      ( ( A @ ( sk3 @ A ) )
      = ( sk3 @ A ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(17,plain,
    ! [A: $i > $i] :
      ( ( A @ ( sk3 @ A ) )
      = ( sk3 @ A ) ),
    inference(simp,[status(thm)],[16]) ).

thf(5,plain,
    ! [A: $i] :
      ( ( sk1 @ A )
     != A ),
    inference(cnf,[status(esa)],[4]) ).

thf(12,plain,
    ! [A: $i] :
      ( ( sk1 @ A )
     != A ),
    inference(lifteq,[status(thm)],[5]) ).

thf(13,plain,
    ! [A: $i] :
      ( ( sk1 @ A )
     != A ),
    inference(simp,[status(thm)],[12]) ).

thf(22,plain,
    ! [A: $i] :
      ( ( sk3
        @ ^ [B: $i] : ( sk1 @ A ) )
     != ( sk3
        @ ^ [B: $i] : A ) ),
    inference(rewrite,[status(thm)],[13,17]) ).

thf(30,plain,
    ! [B: $i,A: $i > $i] :
      ( ( ( sk3
          @ ^ [C: $i] : ( sk3 @ A ) )
       != ( sk3
          @ ^ [C: $i] : B ) )
      | ( ( A @ ( sk3 @ A ) )
       != ( sk1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[17,22]) ).

thf(32,plain,
    ! [A: $i > $i] :
      ( ( sk3
        @ ^ [B: $i] :
            ( A
            @ ( sk3
              @ ^ [C: $i] : ( sk1 @ ( A @ C ) ) ) ) )
     != ( sk3
        @ ^ [B: $i] :
            ( sk3
            @ ^ [C: $i] : ( sk1 @ ( A @ C ) ) ) ) ),
    inference(pre_uni,[status(thm)],[30:[bind(A,$thf( ^ [D: $i] : ( sk1 @ ( C @ D ) ) )),bind(B,$thf( C @ ( sk3 @ ^ [D: $i] : ( sk1 @ ( C @ D ) ) ) ))]]) ).

thf(33,plain,
    $false,
    inference(pre_uni,[status(thm)],[32:[bind(A,$thf( ^ [B: $i] : B ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU894^5 : TPTP v8.2.0. Released v4.0.0.
% 0.16/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n018.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 17:50:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.95/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/0.94  % [INFO] 	 Parsing done (101ms). 
% 1.23/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.58/1.17  % [INFO] 	 nitpick registered as external prover. 
% 1.58/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.70/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.88/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.88/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.88/1.25  % [INFO] 	 Type checking passed. 
% 1.95/1.25  % [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 ... 
% 3.18/1.68  % [INFO] 	 Killing All external provers ... 
% 3.18/1.69  % Time passed: 1154ms (effective reasoning time: 733ms)
% 3.18/1.69  % 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)>
% 3.18/1.69  % Axioms used in derivation (0): 
% 3.18/1.69  % No. of inferences in proof: 14
% 3.18/1.69  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1154 ms resp. 733 ms w/o parsing
% 3.18/1.72  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.18/1.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------