TSTP Solution File: NUN025^3 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : NUN025^3 : TPTP v8.2.0. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.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 02:16:09 EDT 2024

% Result   : Theorem 5.76s 2.63s
% Output   : Refutation 5.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   60 (  18 unt;   4 typ;   0 def)
%            Number of atoms       :  266 ( 236 equ;   0 cnn)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  782 (  94   ~;  55   |;  68   &; 541   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-3 aty)
%            Number of variables   :  160 (   0   ^ 142   !;  18   ?; 160   :)

% Comments : 
%------------------------------------------------------------------------------
thf(zero_type,type,
    zero: $i ).

thf(s_type,type,
    s: $i > $i ).

thf(ite_type,type,
    ite: $o > $i > $i > $i ).

thf(h_type,type,
    h: $i > $i ).

thf(1,conjecture,
    ( ( ! [A: $o,B: $i,C: $i] :
          ( A
         => ( ( ite @ A @ B @ C )
            = B ) )
      & ! [A: $o,B: $i,C: $i] :
          ( ~ A
         => ( ( ite @ A @ B @ C )
            = C ) )
      & ! [A: $i] :
          ( ( s @ A )
         != zero )
      & ! [A: $i] :
          ( ( s @ A )
         != A )
      & ! [A: $i] :
          ( ( h @ A )
          = ( ite @ ( A = zero ) @ ( s @ zero )
            @ ( ite
              @ ( A
                = ( s @ zero ) )
              @ zero
              @ ( s @ zero ) ) ) ) )
   => ? [A: $i > $i] :
        ( ( ( A @ zero )
          = ( s @ zero ) )
        & ( ( A @ ( s @ zero ) )
          = zero )
        & ( ( A @ ( s @ ( s @ zero ) ) )
          = ( s @ zero ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n10) ).

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

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

thf(4,plain,
    ~ ( ( ! [A: $i,B: $i] :
            ( $true
           => ( ( ite @ $true @ A @ B )
              = A ) )
        & ! [A: $i,B: $i] :
            ( ~ $true
           => ( ( ite @ $true @ A @ B )
              = B ) )
        & ! [A: $i] :
            ( ( s @ A )
           != zero )
        & ! [A: $i] :
            ( ( s @ A )
           != A )
        & ! [A: $i] :
            ( ( h @ A )
            = ( ite @ ( A = zero ) @ ( s @ zero )
              @ ( ite
                @ ( A
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) ) ) )
     => ? [A: $i > $i] :
          ( ( ( A @ zero )
            = ( s @ zero ) )
          & ( ( A @ ( s @ zero ) )
            = zero )
          & ( ( A @ ( s @ ( s @ zero ) ) )
            = ( s @ zero ) ) ) ),
    inference(instance,[status(thm)],[3]) ).

thf(5,plain,
    ~ ( ( ! [A: $i,B: $i] :
            ( ( ite @ $true @ A @ B )
            = A )
        & ! [A: $i] :
            ( ( s @ A )
           != zero )
        & ! [A: $i] :
            ( ( s @ A )
           != A )
        & ! [A: $i] :
            ( ( h @ A )
            = ( ite @ ( A = zero ) @ ( s @ zero )
              @ ( ite
                @ ( A
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) ) ) )
     => ? [A: $i > $i] :
          ( ( ( A @ zero )
            = ( s @ zero ) )
          & ( ( A @ ( s @ zero ) )
            = zero )
          & ( ( A @ ( s @ ( s @ zero ) ) )
            = ( s @ zero ) ) ) ),
    inference(simp,[status(thm)],[4]) ).

thf(12,plain,
    ~ ( ( ! [A: $i,B: $i] :
            ( ( ite @ $true @ A @ B )
            = A )
        & ~ ? [A: $i] :
              ( ( s @ A )
              = zero )
        & ~ ? [A: $i] :
              ( ( s @ A )
              = A )
        & ! [A: $i] :
            ( ( h @ A )
            = ( ite @ ( A = zero ) @ ( s @ zero )
              @ ( ite
                @ ( A
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) ) ) )
     => ? [A: $i > $i] :
          ( ( ( A @ zero )
            = ( s @ zero ) )
          & ( ( A @ ( s @ zero ) )
            = zero )
          & ( ( A @ ( s @ ( s @ zero ) ) )
            = ( s @ zero ) ) ) ),
    inference(miniscope,[status(thm)],[5]) ).

thf(14,plain,
    ! [A: $i] :
      ( ( h @ A )
      = ( ite @ ( A = zero ) @ ( s @ zero )
        @ ( ite
          @ ( A
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(38,plain,
    ! [A: $i] :
      ( ( ite @ ( A = zero ) @ ( s @ zero )
        @ ( ite
          @ ( A
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) )
      = ( h @ A ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(39,plain,
    ! [A: $i] :
      ( ( ite @ ( A = zero ) @ ( s @ zero )
        @ ( ite
          @ ( A
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) )
      = ( h @ A ) ),
    inference(simp,[status(thm)],[38]) ).

thf(10,plain,
    ~ ( ( ! [A: $i,B: $i] :
            ( $false
           => ( ( ite @ $false @ A @ B )
              = A ) )
        & ! [A: $i,B: $i] :
            ( ~ $false
           => ( ( ite @ $false @ A @ B )
              = B ) )
        & ! [A: $i] :
            ( ( s @ A )
           != zero )
        & ! [A: $i] :
            ( ( s @ A )
           != A )
        & ! [A: $i] :
            ( ( h @ A )
            = ( ite @ ( A = zero ) @ ( s @ zero )
              @ ( ite
                @ ( A
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) ) ) )
     => ? [A: $i > $i] :
          ( ( ( A @ zero )
            = ( s @ zero ) )
          & ( ( A @ ( s @ zero ) )
            = zero )
          & ( ( A @ ( s @ ( s @ zero ) ) )
            = ( s @ zero ) ) ) ),
    inference(instance,[status(thm)],[3]) ).

thf(11,plain,
    ~ ( ( ! [A: $i,B: $i] :
            ( ( ite @ $false @ A @ B )
            = B )
        & ! [A: $i] :
            ( ( s @ A )
           != zero )
        & ! [A: $i] :
            ( ( s @ A )
           != A )
        & ! [A: $i] :
            ( ( h @ A )
            = ( ite @ ( A = zero ) @ ( s @ zero )
              @ ( ite
                @ ( A
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) ) ) )
     => ? [A: $i > $i] :
          ( ( ( A @ zero )
            = ( s @ zero ) )
          & ( ( A @ ( s @ zero ) )
            = zero )
          & ( ( A @ ( s @ ( s @ zero ) ) )
            = ( s @ zero ) ) ) ),
    inference(simp,[status(thm)],[10]) ).

thf(30,plain,
    ~ ( ( ! [A: $i,B: $i] :
            ( ( ite @ $false @ A @ B )
            = B )
        & ~ ? [A: $i] :
              ( ( s @ A )
              = zero )
        & ~ ? [A: $i] :
              ( ( s @ A )
              = A )
        & ! [A: $i] :
            ( ( h @ A )
            = ( ite @ ( A = zero ) @ ( s @ zero )
              @ ( ite
                @ ( A
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) ) ) )
     => ? [A: $i > $i] :
          ( ( ( A @ zero )
            = ( s @ zero ) )
          & ( ( A @ ( s @ zero ) )
            = zero )
          & ( ( A @ ( s @ ( s @ zero ) ) )
            = ( s @ zero ) ) ) ),
    inference(miniscope,[status(thm)],[11]) ).

thf(34,plain,
    ! [B: $i,A: $i] :
      ( ( ite @ $false @ A @ B )
      = B ),
    inference(cnf,[status(esa)],[30]) ).

thf(61,plain,
    ! [B: $i,A: $i] :
      ( ( ite @ $false @ A @ B )
      = B ),
    inference(lifteq,[status(thm)],[34]) ).

thf(73,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( h @ A )
        = C )
      | ( ( ite @ ( A = zero ) @ ( s @ zero )
          @ ( ite
            @ ( A
              = ( s @ zero ) )
            @ zero
            @ ( s @ zero ) ) )
       != ( ite @ $false @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[39,61]) ).

thf(77,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( h @ A )
        = C )
      | ( A = zero )
      | ( ( s @ zero )
       != B )
      | ( ( ite
          @ ( A
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) )
       != C ) ),
    inference(simp,[status(thm)],[73]) ).

thf(80,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = zero )
      | ( ( h @ A )
        = C )
      | ( ( s @ zero )
       != B )
      | ( ( ite
          @ ( A
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) )
       != C ) ),
    inference(lifteq,[status(thm)],[77]) ).

thf(81,plain,
    ! [A: $i] :
      ( ( A = zero )
      | ( ( ite
          @ ( A
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) )
        = ( h @ A ) ) ),
    inference(simp,[status(thm)],[80]) ).

thf(257,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = zero )
      | ( ( h @ A )
        = C )
      | ( ( ite
          @ ( A
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) )
       != ( ite @ $false @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[81,61]) ).

thf(268,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = zero )
      | ( ( h @ A )
        = C )
      | ( A
        = ( s @ zero ) )
      | ( zero != B )
      | ( ( s @ zero )
       != C ) ),
    inference(simp,[status(thm)],[257]) ).

thf(285,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( s @ zero ) )
      | ( A = zero )
      | ( ( h @ A )
        = C )
      | ( zero != B )
      | ( ( s @ zero )
       != C ) ),
    inference(lifteq,[status(thm)],[268]) ).

thf(286,plain,
    ! [A: $i] :
      ( ( A
        = ( s @ zero ) )
      | ( A = zero )
      | ( ( h @ A )
        = ( s @ zero ) ) ),
    inference(simp,[status(thm)],[285]) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ( ite @ $true @ A @ B )
      = A ),
    inference(cnf,[status(esa)],[12]) ).

thf(66,plain,
    ! [B: $i,A: $i] :
      ( ( ite @ $true @ A @ B )
      = A ),
    inference(lifteq,[status(thm)],[16]) ).

thf(91,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( h @ C ) )
      | ( ( ite @ $true @ A @ B )
       != ( ite @ ( C = zero ) @ ( s @ zero )
          @ ( ite
            @ ( C
              = ( s @ zero ) )
            @ zero
            @ ( s @ zero ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[66,39]) ).

thf(96,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( h @ C ) )
      | ( C != zero )
      | ( A
       != ( s @ zero ) )
      | ( B
       != ( ite
          @ ( C
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) ) ),
    inference(simp,[status(thm)],[91]) ).

thf(98,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C != zero )
      | ( A
        = ( h @ C ) )
      | ( A
       != ( s @ zero ) )
      | ( B
       != ( ite
          @ ( C
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) ) ),
    inference(lifteq,[status(thm)],[96]) ).

thf(99,plain,
    ( ( h @ zero )
    = ( s @ zero ) ),
    inference(simp,[status(thm)],[98]) ).

thf(35,plain,
    ! [A: $i > $i] :
      ( ( ( A @ zero )
       != ( s @ zero ) )
      | ( ( A @ ( s @ zero ) )
       != zero )
      | ( ( A @ ( s @ ( s @ zero ) ) )
       != ( s @ zero ) ) ),
    inference(cnf,[status(esa)],[30]) ).

thf(42,plain,
    ! [A: $i > $i] :
      ( ( ( A @ zero )
       != ( s @ zero ) )
      | ( ( A @ ( s @ zero ) )
       != zero )
      | ( ( A @ ( s @ ( s @ zero ) ) )
       != ( s @ zero ) ) ),
    inference(lifteq,[status(thm)],[35]) ).

thf(43,plain,
    ! [A: $i > $i] :
      ( ( ( A @ zero )
       != ( s @ zero ) )
      | ( ( A @ ( s @ zero ) )
       != zero )
      | ( ( A @ ( s @ ( s @ zero ) ) )
       != ( s @ zero ) ) ),
    inference(simp,[status(thm)],[42]) ).

thf(117,plain,
    ! [A: $i > $i] :
      ( ( ( A @ ( s @ zero ) )
       != zero )
      | ( ( A @ ( s @ ( s @ zero ) ) )
       != ( s @ zero ) )
      | ( ( h @ zero )
       != ( A @ zero ) ) ),
    inference(paramod_ordered,[status(thm)],[99,43]) ).

thf(127,plain,
    ( ( ( h @ ( s @ zero ) )
     != zero )
    | ( ( h @ ( s @ ( s @ zero ) ) )
     != ( s @ zero ) ) ),
    inference(pre_uni,[status(thm)],[117:[bind(A,$thf( h ))]]) ).

thf(90,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( ite @ ( C = zero ) @ ( s @ zero ) @ A )
        = ( h @ C ) )
      | ( ( ite @ $true @ A @ B )
       != ( ite
          @ ( C
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) ) ),
    inference(paramod_ordered,[status(thm)],[66,39]) ).

thf(97,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( ite @ ( C = zero ) @ ( s @ zero ) @ A )
        = ( h @ C ) )
      | ( C
       != ( s @ zero ) )
      | ( A != zero )
      | ( B
       != ( s @ zero ) ) ),
    inference(simp,[status(thm)],[90]) ).

thf(100,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
       != ( s @ zero ) )
      | ( ( ite @ ( C = zero ) @ ( s @ zero ) @ A )
        = ( h @ C ) )
      | ( A != zero )
      | ( B
       != ( s @ zero ) ) ),
    inference(lifteq,[status(thm)],[97]) ).

thf(101,plain,
    ( ( ite
      @ ( ( s @ zero )
        = zero )
      @ ( s @ zero )
      @ zero )
    = ( h @ ( s @ zero ) ) ),
    inference(simp,[status(thm)],[100]) ).

thf(144,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( h @ ( s @ zero ) ) )
      | ( ( ite @ $false @ A @ B )
       != ( ite
          @ ( ( s @ zero )
            = zero )
          @ ( s @ zero )
          @ zero ) ) ),
    inference(paramod_ordered,[status(thm)],[61,101]) ).

thf(154,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( h @ ( s @ zero ) ) )
      | ( ( s @ zero )
        = zero )
      | ( A
       != ( s @ zero ) )
      | ( B != zero ) ),
    inference(simp,[status(thm)],[144]) ).

thf(166,plain,
    ! [B: $i,A: $i] :
      ( ( ( s @ zero )
        = zero )
      | ( B
        = ( h @ ( s @ zero ) ) )
      | ( A
       != ( s @ zero ) )
      | ( B != zero ) ),
    inference(lifteq,[status(thm)],[154]) ).

thf(167,plain,
    ( ( ( s @ zero )
      = zero )
    | ( ( h @ ( s @ zero ) )
      = zero ) ),
    inference(simp,[status(thm)],[166]) ).

thf(6,plain,
    ~ ( ( ! [A: $i,B: $i] :
            ( $true
           => ( ( ite @ $true @ A @ B )
              = A ) )
        & ! [A: $i,B: $i] :
            ( ~ $false
           => ( ( ite @ $false @ A @ B )
              = B ) )
        & ! [A: $i] :
            ( ( s @ A )
           != zero )
        & ! [A: $i] :
            ( ( s @ A )
           != A )
        & ! [A: $i] :
            ( ( h @ A )
            = ( ite @ ( A = zero ) @ ( s @ zero )
              @ ( ite
                @ ( A
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) ) ) )
     => ? [A: $i > $i] :
          ( ( ( A @ zero )
            = ( s @ zero ) )
          & ( ( A @ ( s @ zero ) )
            = zero )
          & ( ( A @ ( s @ ( s @ zero ) ) )
            = ( s @ zero ) ) ) ),
    inference(instance,[status(thm)],[3]) ).

thf(7,plain,
    ~ ( ( ! [A: $i,B: $i] :
            ( ( ite @ $true @ A @ B )
            = A )
        & ! [A: $i,B: $i] :
            ( ( ite @ $false @ A @ B )
            = B )
        & ! [A: $i] :
            ( ( s @ A )
           != zero )
        & ! [A: $i] :
            ( ( s @ A )
           != A )
        & ! [A: $i] :
            ( ( h @ A )
            = ( ite @ ( A = zero ) @ ( s @ zero )
              @ ( ite
                @ ( A
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) ) ) )
     => ? [A: $i > $i] :
          ( ( ( A @ zero )
            = ( s @ zero ) )
          & ( ( A @ ( s @ zero ) )
            = zero )
          & ( ( A @ ( s @ ( s @ zero ) ) )
            = ( s @ zero ) ) ) ),
    inference(simp,[status(thm)],[6]) ).

thf(18,plain,
    ~ ( ( ! [A: $i,B: $i] :
            ( ( ite @ $true @ A @ B )
            = A )
        & ! [A: $i,B: $i] :
            ( ( ite @ $false @ A @ B )
            = B )
        & ~ ? [A: $i] :
              ( ( s @ A )
              = zero )
        & ~ ? [A: $i] :
              ( ( s @ A )
              = A )
        & ! [A: $i] :
            ( ( h @ A )
            = ( ite @ ( A = zero ) @ ( s @ zero )
              @ ( ite
                @ ( A
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) ) ) )
     => ? [A: $i > $i] :
          ( ( ( A @ zero )
            = ( s @ zero ) )
          & ( ( A @ ( s @ zero ) )
            = zero )
          & ( ( A @ ( s @ ( s @ zero ) ) )
            = ( s @ zero ) ) ) ),
    inference(miniscope,[status(thm)],[7]) ).

thf(19,plain,
    ! [A: $i] :
      ( ( s @ A )
     != zero ),
    inference(cnf,[status(esa)],[18]) ).

thf(44,plain,
    ! [A: $i] :
      ( ( s @ A )
     != zero ),
    inference(lifteq,[status(thm)],[19]) ).

thf(45,plain,
    ! [A: $i] :
      ( ( s @ A )
     != zero ),
    inference(simp,[status(thm)],[44]) ).

thf(195,plain,
    ( ( h @ ( s @ zero ) )
    = zero ),
    inference(simplifyReflect,[status(thm)],[167,45]) ).

thf(197,plain,
    ( ( zero != zero )
    | ( ( h @ ( s @ ( s @ zero ) ) )
     != ( s @ zero ) ) ),
    inference(rewrite,[status(thm)],[127,195]) ).

thf(198,plain,
    ( ( h @ ( s @ ( s @ zero ) ) )
   != ( s @ zero ) ),
    inference(simp,[status(thm)],[197]) ).

thf(352,plain,
    ! [A: $i] :
      ( ( A
        = ( s @ zero ) )
      | ( A = zero )
      | ( ( h @ A )
       != ( h @ ( s @ ( s @ zero ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[286,198]) ).

thf(353,plain,
    ( ( ( s @ ( s @ zero ) )
      = ( s @ zero ) )
    | ( ( s @ ( s @ zero ) )
      = zero ) ),
    inference(pattern_uni,[status(thm)],[352:[bind(A,$thf( s @ ( s @ zero ) ))]]) ).

thf(24,plain,
    ! [A: $i] :
      ( ( s @ A )
     != A ),
    inference(cnf,[status(esa)],[18]) ).

thf(36,plain,
    ! [A: $i] :
      ( ( s @ A )
     != A ),
    inference(lifteq,[status(thm)],[24]) ).

thf(37,plain,
    ! [A: $i] :
      ( ( s @ A )
     != A ),
    inference(simp,[status(thm)],[36]) ).

thf(363,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[353,37,45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : NUN025^3 : TPTP v8.2.0. Released v6.4.0.
% 0.16/0.16  % Command  : run_Leo-III %s %d
% 0.18/0.38  % Computer : n015.cluster.edu
% 0.18/0.38  % Model    : x86_64 x86_64
% 0.18/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38  % Memory   : 8042.1875MB
% 0.18/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38  % CPULimit : 300
% 0.18/0.38  % WCLimit  : 300
% 0.18/0.38  % DateTime : Sat May 18 15:05:09 EDT 2024
% 0.18/0.38  % CPUTime  : 
% 1.05/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.36/1.08  % [INFO] 	 Parsing done (146ms). 
% 1.36/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.35  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.35  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.36  % [INFO] 	 Scanning for conjecture ... 
% 2.06/1.47  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.06/1.51  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.06/1.51  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.06/1.51  % [INFO] 	 Type checking passed. 
% 2.06/1.52  % [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 ... 
% 5.76/2.63  % [INFO] 	 Killing All external provers ... 
% 5.76/2.63  % Time passed: 2071ms (effective reasoning time: 1531ms)
% 5.76/2.63  % 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)>
% 5.76/2.63  % Axioms used in derivation (0): 
% 5.76/2.63  % No. of inferences in proof: 56
% 5.76/2.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2071 ms resp. 1531 ms w/o parsing
% 5.76/2.69  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.76/2.69  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------