TSTP Solution File: NUM812^5 by Leo-III-SAT---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : NUM812^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% 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 13:06:28 EDT 2024

% Result   : Theorem 41.47s 7.57s
% Output   : Refutation 41.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   22 (   8 unt;   0 typ;   1 def)
%            Number of atoms       :   45 (  38 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  131 (  40   ~;  25   |;   2   &;  57   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   5 usr;   6 con; 0-2 aty)
%            Number of variables   :   41 (   9   ^  29   !;   3   ?;  41   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c0_type,type,
    c0: $i ).

thf(cS_type,type,
    cS: $i > $i ).

thf(cIND_type,type,
    cIND: $o ).

thf(cIND_def,definition,
    ( cIND
    = ( ! [A: $i > $o] :
          ( ( ( A @ c0 )
            & ! [B: $i] :
                ( ( A @ B )
               => ( A @ ( cS @ B ) ) ) )
         => ! [B: $i] : ( A @ B ) ) ) ) ).

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

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

thf(1,conjecture,
    ( cIND
   => ! [A: $i] :
        ( ( A = c0 )
        | ? [B: $i] :
            ( A
            = ( cS @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM578) ).

thf(2,negated_conjecture,
    ~ ( cIND
     => ! [A: $i] :
          ( ( A = c0 )
          | ? [B: $i] :
              ( A
              = ( cS @ B ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i > $o] :
          ( ( ( A @ c0 )
            & ! [B: $i] :
                ( ( A @ B )
               => ( A @ ( cS @ B ) ) ) )
         => ! [B: $i] : ( A @ B ) )
     => ! [A: $i] :
          ( ( A = c0 )
          | ? [B: $i] :
              ( A
              = ( cS @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cS @ ( sk1 @ A ) ) )
      | ( A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(35,plain,
    ! [B: $i > $o,A: $i] :
      ( ~ ~ ( B @ c0 )
      | ~ ~ ( B
            @ ( cS
              @ ( sk1
                @ ^ [C: $i] :
                    ~ ( B @ C ) ) ) )
      | ~ ( B @ A ) ),
    inference(prim_subst,[status(thm)],[6:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).

thf(59,plain,
    ! [B: $i > $o,A: $i] :
      ( ~ ( B @ A )
      | ( B
        @ ( cS
          @ ( sk1
            @ ^ [C: $i] :
                ~ ( B @ C ) ) ) )
      | ( B @ c0 ) ),
    inference(cnf,[status(esa)],[35]) ).

thf(60,plain,
    ! [B: $i > $o,A: $i] :
      ( ~ ( B @ A )
      | ( B
        @ ( cS
          @ ( sk1
            @ ^ [C: $i] :
                ~ ( B @ C ) ) ) )
      | ( B @ c0 ) ),
    inference(simp,[status(thm)],[59]) ).

thf(3087,plain,
    ! [B: $i > $o,A: $i] :
      ( ~ ( B @ A )
      | ( B @ c0 )
      | ( ( B
          @ ( cS
            @ ( sk1
              @ ^ [C: $i] :
                  ~ ( B @ C ) ) ) )
       != ( ~ ( B @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[60]) ).

thf(3108,plain,
    ! [A: $i] :
      ( ( A != A )
      | ( A = c0 )
      | ( ( A
          = ( cS
            @ ( sk1
              @ ^ [B: $i] : ( A != B ) ) ) )
       != ( A != A ) )
      | ~ $true ),
    inference(replace_leibeq,[status(thm)],[3087:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ A ))]]) ).

thf(3127,plain,
    ! [A: $i] :
      ( ( A != A )
      | ( A = c0 )
      | ( ( A
          = ( cS
            @ ( sk1
              @ ^ [B: $i] : ( A != B ) ) ) )
       != ( A != A ) )
      | ~ $true ),
    inference(lifteq,[status(thm)],[3108]) ).

thf(3224,plain,
    ! [A: $i] :
      ( ( A = c0 )
      | ( A
        = ( cS
          @ ( sk1
            @ ^ [B: $i] : ( A != B ) ) ) ) ),
    inference(simp,[status(thm)],[3127]) ).

thf(4741,plain,
    ! [A: $i] :
      ( ( A
        = ( cS
          @ ( sk1
            @ ^ [B: $i] : ( A != B ) ) ) )
      | ( A = c0 ) ),
    inference(lifteq,[status(thm)],[3224]) ).

thf(4,plain,
    ! [A: $i] :
      ( sk2
     != ( cS @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(15,plain,
    ! [A: $i] :
      ( ( cS @ A )
     != sk2 ),
    inference(lifteq,[status(thm)],[4]) ).

thf(16,plain,
    ! [A: $i] :
      ( ( cS @ A )
     != sk2 ),
    inference(simp,[status(thm)],[15]) ).

thf(4833,plain,
    ! [B: $i,A: $i] :
      ( ( A = c0 )
      | ( A != sk2 )
      | ( ( cS
          @ ( sk1
            @ ^ [C: $i] : ( A != C ) ) )
       != ( cS @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4741,16]) ).

thf(4834,plain,
    ! [A: $i] :
      ( ( A = c0 )
      | ( A != sk2 ) ),
    inference(pattern_uni,[status(thm)],[4833:[bind(A,$thf( A )),bind(B,$thf( sk1 @ ^ [C: $i] : ( A != C ) ))]]) ).

thf(4985,plain,
    sk2 = c0,
    inference(simp,[status(thm)],[4834]) ).

thf(5,plain,
    sk2 != c0,
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    sk2 != c0,
    inference(lifteq,[status(thm)],[5]) ).

thf(4988,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[4985,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : NUM812^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.00/0.10  % Command  : run_Leo-III %s %d SAT
% 0.09/0.30  % Computer : n024.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Sun Jun 23 04:03:25 EDT 2024
% 0.09/0.31  % CPUTime  : 
% 1.00/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.25/1.15  % [INFO] 	 Parsing done (161ms). 
% 1.25/1.16  % [INFO] 	 Running in sequential loop mode. 
% 1.93/1.54  % [INFO] 	 nitpick registered as external prover. 
% 1.93/1.55  % [INFO] 	 Scanning for conjecture ... 
% 2.11/1.64  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.11/1.68  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.11/1.68  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.11/1.68  % [INFO] 	 Type checking passed. 
% 2.11/1.69  % [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 ... 
% 41.47/7.56  % [INFO] 	 Killing All external provers ... 
% 41.47/7.57  % Time passed: 7073ms (effective reasoning time: 6389ms)
% 41.47/7.57  % 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)>
% 41.47/7.57  % Axioms used in derivation (0): 
% 41.47/7.57  % No. of inferences in proof: 21
% 41.47/7.57  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7073 ms resp. 6389 ms w/o parsing
% 41.47/7.67  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 41.47/7.67  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------