TSTP Solution File: SEV289^5 by Leo-III---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV289^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% 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 : Mon Jun 24 15:58:42 EDT 2024

% Result   : Theorem 3.40s 1.76s
% Output   : Refutation 3.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    6 (   3 unt;   0 typ;   2 def)
%            Number of atoms       :   17 (   6 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   61 (   8   ~;   0   |;  11   &;  33   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  31   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   27 (  12   ^   9   !;   6   ?;  27   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cNAT_type,type,
    cNAT: ( ( $i > $o ) > $o ) > $o ).

thf(cNAT_def,definition,
    ( cNAT
    = ( ^ [A: ( $i > $o ) > $o] :
        ! [B: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( B @ cZERO )
            & ! [C: ( $i > $o ) > $o] :
                ( ( B @ C )
               => ( B @ ( cSUCC @ C ) ) ) )
         => ( B @ A ) ) ) ) ).

thf(cSUCC_type,type,
    cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).

thf(cSUCC_def,definition,
    ( cSUCC
    = ( ^ [A: ( $i > $o ) > $o,B: $i > $o] :
        ? [C: $i] :
          ( ( B @ C )
          & ( A
            @ ^ [D: $i] :
                ( ( D != C )
                & ( B @ D ) ) ) ) ) ) ).

thf(1,conjecture,
    ! [A: ( $i > $o ) > $o] :
      ( ( cNAT @ A )
     => ( cNAT @ ( cSUCC @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTTTP6101) ).

thf(2,negated_conjecture,
    ~ ! [A: ( $i > $o ) > $o] :
        ( ( cNAT @ A )
       => ( cNAT @ ( cSUCC @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SEV289^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.08/0.13  % Command  : run_Leo-III %s %d THM
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Jun 21 19:38:55 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.95/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.19/0.96  % [INFO] 	 Parsing done (99ms). 
% 1.19/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.47/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.47/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.70/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.84/1.24  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.84/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.84/1.24  % [INFO] 	 Type checking passed. 
% 1.84/1.24  % [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 ... 
% 3.40/1.75  % External prover 'e' found a proof!
% 3.40/1.75  % [INFO] 	 Killing All external provers ... 
% 3.40/1.75  % Time passed: 1220ms (effective reasoning time: 783ms)
% 3.40/1.75  % 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)>
% 3.40/1.76  % Axioms used in derivation (0): 
% 3.40/1.76  % No. of inferences in proof: 4
% 3.40/1.76  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1220 ms resp. 783 ms w/o parsing
% 3.68/1.78  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.68/1.78  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------