TSTP Solution File: SEV119^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEV119^5 : 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 04:09:59 EDT 2024

% Result   : Theorem 130.13s 35.24s
% Output   : Refutation 130.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   82 (  25 unt;  27 typ;   0 def)
%            Number of atoms       :  365 (  39 equ;   0 cnn)
%            Maximal formula atoms :   14 (   6 avg)
%            Number of connectives : 1387 (  67   ~;  98   |; 102   &; 898   @)
%                                         (   0 <=>; 222  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  274 ( 274   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   30 (  28 usr;  18 con; 0-4 aty)
%            Number of variables   :  475 ( 140   ^ 335   !;   0   ?; 475   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

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

thf(sk2_type,type,
    sk2: a > a > $o ).

thf(sk3_type,type,
    sk3: a > a > $o ).

thf(sk6_type,type,
    sk6: a ).

thf(sk7_type,type,
    sk7: a ).

thf(sk8_type,type,
    sk8: a > a > $o ).

thf(sk11_type,type,
    sk11: a > a > $o ).

thf(sk14_type,type,
    sk14: a > a > $o ).

thf(sk17_type,type,
    sk17: a > a > $o ).

thf(sk18_type,type,
    sk18: a ).

thf(sk27_type,type,
    sk27: a ).

thf(sk28_type,type,
    sk28: a ).

thf(sk32_type,type,
    sk32: a ).

thf(sk33_type,type,
    sk33: a ).

thf(sk37_type,type,
    sk37: a ).

thf(sk38_type,type,
    sk38: a ).

thf(sk51_type,type,
    sk51: a > a > $o ).

thf(sk52_type,type,
    sk52: a > a > a > a > $o ).

thf(sk63_type,type,
    sk63: a > a > $o ).

thf(sk64_type,type,
    sk64: a > a > $o ).

thf(sk69_type,type,
    sk69: a ).

thf(sk70_type,type,
    sk70: a ).

thf(sk71_type,type,
    sk71: a ).

thf(sk72_type,type,
    sk72: a ).

thf(sk89_type,type,
    sk89: a ).

thf(sk90_type,type,
    sk90: a ).

thf(1,conjecture,
    ! [A: ( a > a > $o ) > $o,B: a > a > $o,C: a > a > $o] :
      ( ( ^ [D: a,E: a] :
          ! [F: a > a > $o] :
            ( ( ! [G: a,H: a] :
                  ( ( ( B @ G @ H )
                    | ( C @ G @ H ) )
                 => ( F @ G @ H ) )
              & ( A @ F ) )
           => ( F @ D @ E ) ) )
      = ( ^ [D: a,E: a] :
          ! [F: a > a > $o] :
            ( ( ! [G: a,H: a] :
                  ( ( ! [I: a > a > $o] :
                        ( ( ! [J: a,K: a] :
                              ( ( B @ J @ K )
                             => ( I @ J @ K ) )
                          & ( A @ I ) )
                       => ( I @ G @ H ) )
                    | ! [I: a > a > $o] :
                        ( ( ! [J: a,K: a] :
                              ( ( C @ J @ K )
                             => ( I @ J @ K ) )
                          & ( A @ I ) )
                       => ( I @ G @ H ) ) )
                 => ( F @ G @ H ) )
              & ( A @ F ) )
           => ( F @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM252_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: ( a > a > $o ) > $o,B: a > a > $o,C: a > a > $o] :
        ( ( ^ [D: a,E: a] :
            ! [F: a > a > $o] :
              ( ( ! [G: a,H: a] :
                    ( ( ( B @ G @ H )
                      | ( C @ G @ H ) )
                   => ( F @ G @ H ) )
                & ( A @ F ) )
             => ( F @ D @ E ) ) )
        = ( ^ [D: a,E: a] :
            ! [F: a > a > $o] :
              ( ( ! [G: a,H: a] :
                    ( ( ! [I: a > a > $o] :
                          ( ( ! [J: a,K: a] :
                                ( ( B @ J @ K )
                               => ( I @ J @ K ) )
                            & ( A @ I ) )
                         => ( I @ G @ H ) )
                      | ! [I: a > a > $o] :
                          ( ( ! [J: a,K: a] :
                                ( ( C @ J @ K )
                               => ( I @ J @ K ) )
                            & ( A @ I ) )
                         => ( I @ G @ H ) ) )
                   => ( F @ G @ H ) )
                & ( A @ F ) )
             => ( F @ D @ E ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: ( a > a > $o ) > $o,B: a > a > $o,C: a > a > $o] :
        ( ( ^ [D: a,E: a] :
            ! [F: a > a > $o] :
              ( ( ! [G: a,H: a] :
                    ( ( ( B @ G @ H )
                      | ( C @ G @ H ) )
                   => ( F @ G @ H ) )
                & ( A @ F ) )
             => ( F @ D @ E ) ) )
        = ( ^ [D: a,E: a] :
            ! [F: a > a > $o] :
              ( ( ! [G: a,H: a] :
                    ( ( ! [I: a > a > $o] :
                          ( ( ! [J: a,K: a] :
                                ( ( B @ J @ K )
                               => ( I @ J @ K ) )
                            & ( A @ I ) )
                         => ( I @ G @ H ) )
                      | ! [I: a > a > $o] :
                          ( ( ! [J: a,K: a] :
                                ( ( C @ J @ K )
                               => ( I @ J @ K ) )
                            & ( A @ I ) )
                         => ( I @ G @ H ) ) )
                   => ( F @ G @ H ) )
                & ( A @ F ) )
             => ( F @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ^ [A: a,B: a] :
        ! [C: a > a > $o] :
          ( ( ! [D: a,E: a] :
                ( ( ( sk2 @ D @ E )
                  | ( sk3 @ D @ E ) )
               => ( C @ D @ E ) )
            & ( sk1 @ C ) )
         => ( C @ A @ B ) ) )
   != ( ^ [A: a,B: a] :
        ! [C: a > a > $o] :
          ( ( ! [D: a,E: a] :
                ( ( ! [F: a > a > $o] :
                      ( ( ! [G: a,H: a] :
                            ( ( sk2 @ G @ H )
                           => ( F @ G @ H ) )
                        & ( sk1 @ F ) )
                     => ( F @ D @ E ) )
                  | ! [F: a > a > $o] :
                      ( ( ! [G: a,H: a] :
                            ( ( sk3 @ G @ H )
                           => ( F @ G @ H ) )
                        & ( sk1 @ F ) )
                     => ( F @ D @ E ) ) )
               => ( C @ D @ E ) )
            & ( sk1 @ C ) )
         => ( C @ A @ B ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ^ [A: a,B: a] :
        ! [C: a > a > $o] :
          ( ( ! [D: a,E: a] :
                ( ( ( sk2 @ D @ E )
                  | ( sk3 @ D @ E ) )
               => ( C @ D @ E ) )
            & ( sk1 @ C ) )
         => ( C @ A @ B ) ) )
   != ( ^ [A: a,B: a] :
        ! [C: a > a > $o] :
          ( ( ! [D: a,E: a] :
                ( ( ! [F: a > a > $o] :
                      ( ( ! [G: a,H: a] :
                            ( ( sk2 @ G @ H )
                           => ( F @ G @ H ) )
                        & ( sk1 @ F ) )
                     => ( F @ D @ E ) )
                  | ! [F: a > a > $o] :
                      ( ( ! [G: a,H: a] :
                            ( ( sk3 @ G @ H )
                           => ( F @ G @ H ) )
                        & ( sk1 @ F ) )
                     => ( F @ D @ E ) ) )
               => ( C @ D @ E ) )
            & ( sk1 @ C ) )
         => ( C @ A @ B ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ^ [A: a,B: a,C: a > a > $o] :
          ( ( ! [D: a,E: a] :
                ( ( ( sk2 @ D @ E )
                  | ( sk3 @ D @ E ) )
               => ( C @ D @ E ) )
            & ( sk1 @ C ) )
         => ( C @ A @ B ) ) )
   != ( ^ [A: a,B: a,C: a > a > $o] :
          ( ( ! [D: a,E: a] :
                ( ( ! [F: a > a > $o] :
                      ( ( ! [G: a,H: a] :
                            ( ( sk2 @ G @ H )
                           => ( F @ G @ H ) )
                        & ( sk1 @ F ) )
                     => ( F @ D @ E ) )
                  | ! [F: a > a > $o] :
                      ( ( ! [G: a,H: a] :
                            ( ( sk3 @ G @ H )
                           => ( F @ G @ H ) )
                        & ( sk1 @ F ) )
                     => ( F @ D @ E ) ) )
               => ( C @ D @ E ) )
            & ( sk1 @ C ) )
         => ( C @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ( ^ [A: a,B: a,C: a > a > $o] :
            ( ! [D: a,E: a] :
                ( ( ( sk2 @ D @ E )
                  | ( sk3 @ D @ E ) )
               => ( C @ D @ E ) )
            & ( sk1 @ C ) ) )
     != ( ^ [A: a,B: a,C: a > a > $o] :
            ( ! [D: a,E: a] :
                ( ( ! [F: a > a > $o] :
                      ( ( ! [G: a,H: a] :
                            ( ( sk2 @ G @ H )
                           => ( F @ G @ H ) )
                        & ( sk1 @ F ) )
                     => ( F @ D @ E ) )
                  | ! [F: a > a > $o] :
                      ( ( ! [G: a,H: a] :
                            ( ( sk3 @ G @ H )
                           => ( F @ G @ H ) )
                        & ( sk1 @ F ) )
                     => ( F @ D @ E ) ) )
               => ( C @ D @ E ) )
            & ( sk1 @ C ) ) ) )
    | ( ( ^ [A: a,B: a,C: a > a > $o] : ( C @ A @ B ) )
     != ( ^ [A: a,B: a,C: a > a > $o] : ( C @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[6]) ).

thf(10,plain,
    ( ( ^ [A: a,B: a,C: a > a > $o] :
          ( ! [D: a,E: a] :
              ( ( ( sk2 @ D @ E )
                | ( sk3 @ D @ E ) )
             => ( C @ D @ E ) )
          & ( sk1 @ C ) ) )
   != ( ^ [A: a,B: a,C: a > a > $o] :
          ( ! [D: a,E: a] :
              ( ( ! [F: a > a > $o] :
                    ( ( ! [G: a,H: a] :
                          ( ( sk2 @ G @ H )
                         => ( F @ G @ H ) )
                      & ( sk1 @ F ) )
                   => ( F @ D @ E ) )
                | ! [F: a > a > $o] :
                    ( ( ! [G: a,H: a] :
                          ( ( sk3 @ G @ H )
                         => ( F @ G @ H ) )
                      & ( sk1 @ F ) )
                   => ( F @ D @ E ) ) )
             => ( C @ D @ E ) )
          & ( sk1 @ C ) ) ) ),
    inference(simp,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ( ^ [A: a,B: a,C: a > a > $o] :
          ! [D: a,E: a] :
            ( ( ( sk2 @ D @ E )
              | ( sk3 @ D @ E ) )
           => ( C @ D @ E ) ) )
     != ( ^ [A: a,B: a,C: a > a > $o] :
          ! [D: a,E: a] :
            ( ( ! [F: a > a > $o] :
                  ( ( ! [G: a,H: a] :
                        ( ( sk2 @ G @ H )
                       => ( F @ G @ H ) )
                    & ( sk1 @ F ) )
                 => ( F @ D @ E ) )
              | ! [F: a > a > $o] :
                  ( ( ! [G: a,H: a] :
                        ( ( sk3 @ G @ H )
                       => ( F @ G @ H ) )
                    & ( sk1 @ F ) )
                 => ( F @ D @ E ) ) )
           => ( C @ D @ E ) ) ) )
    | ( ( ^ [A: a,B: a] : sk1 )
     != ( ^ [A: a,B: a] : sk1 ) ) ),
    inference(simp,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ^ [A: a,B: a,C: a > a > $o] :
        ! [D: a,E: a] :
          ( ( ( sk2 @ D @ E )
            | ( sk3 @ D @ E ) )
         => ( C @ D @ E ) ) )
   != ( ^ [A: a,B: a,C: a > a > $o] :
        ! [D: a,E: a] :
          ( ( ! [F: a > a > $o] :
                ( ( ! [G: a,H: a] :
                      ( ( sk2 @ G @ H )
                     => ( F @ G @ H ) )
                  & ( sk1 @ F ) )
               => ( F @ D @ E ) )
            | ! [F: a > a > $o] :
                ( ( ! [G: a,H: a] :
                      ( ( sk3 @ G @ H )
                     => ( F @ G @ H ) )
                  & ( sk1 @ F ) )
               => ( F @ D @ E ) ) )
         => ( C @ D @ E ) ) ) ),
    inference(simp,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ^ [A: a,B: a,C: a > a > $o,D: a] :
        ! [E: a] :
          ( ( ( sk2 @ D @ E )
            | ( sk3 @ D @ E ) )
         => ( C @ D @ E ) ) )
   != ( ^ [A: a,B: a,C: a > a > $o,D: a] :
        ! [E: a] :
          ( ( ! [F: a > a > $o] :
                ( ( ! [G: a,H: a] :
                      ( ( sk2 @ G @ H )
                     => ( F @ G @ H ) )
                  & ( sk1 @ F ) )
               => ( F @ D @ E ) )
            | ! [F: a > a > $o] :
                ( ( ! [G: a,H: a] :
                      ( ( sk3 @ G @ H )
                     => ( F @ G @ H ) )
                  & ( sk1 @ F ) )
               => ( F @ D @ E ) ) )
         => ( C @ D @ E ) ) ) ),
    inference(simp,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
          ( ( ( sk2 @ D @ E )
            | ( sk3 @ D @ E ) )
         => ( C @ D @ E ) ) )
   != ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
          ( ( ! [F: a > a > $o] :
                ( ( ! [G: a,H: a] :
                      ( ( sk2 @ G @ H )
                     => ( F @ G @ H ) )
                  & ( sk1 @ F ) )
               => ( F @ D @ E ) )
            | ! [F: a > a > $o] :
                ( ( ! [G: a,H: a] :
                      ( ( sk3 @ G @ H )
                     => ( F @ G @ H ) )
                  & ( sk1 @ F ) )
               => ( F @ D @ E ) ) )
         => ( C @ D @ E ) ) ) ),
    inference(simp,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
            ( ( sk2 @ D @ E )
            | ( sk3 @ D @ E ) ) )
     != ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
            ( ! [F: a > a > $o] :
                ( ( ! [G: a,H: a] :
                      ( ( sk2 @ G @ H )
                     => ( F @ G @ H ) )
                  & ( sk1 @ F ) )
               => ( F @ D @ E ) )
            | ! [F: a > a > $o] :
                ( ( ! [G: a,H: a] :
                      ( ( sk3 @ G @ H )
                     => ( F @ G @ H ) )
                  & ( sk1 @ F ) )
               => ( F @ D @ E ) ) ) ) )
    | ( ( ^ [A: a,B: a,C: a > a > $o] : C )
     != ( ^ [A: a,B: a,C: a > a > $o] : C ) ) ),
    inference(simp,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
          ( ( sk2 @ D @ E )
          | ( sk3 @ D @ E ) ) )
   != ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
          ( ! [F: a > a > $o] :
              ( ( ! [G: a,H: a] :
                    ( ( sk2 @ G @ H )
                   => ( F @ G @ H ) )
                & ( sk1 @ F ) )
             => ( F @ D @ E ) )
          | ! [F: a > a > $o] :
              ( ( ! [G: a,H: a] :
                    ( ( sk3 @ G @ H )
                   => ( F @ G @ H ) )
                & ( sk1 @ F ) )
             => ( F @ D @ E ) ) ) ) ),
    inference(simp,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ( sk2 @ sk27 @ sk28 )
      | ( sk3 @ sk27 @ sk28 ) )
   != ( ! [A: a > a > $o] :
          ( ( ! [B: a,C: a] :
                ( ( sk2 @ B @ C )
               => ( A @ B @ C ) )
            & ( sk1 @ A ) )
         => ( A @ sk27 @ sk28 ) )
      | ! [A: a > a > $o] :
          ( ( ! [B: a,C: a] :
                ( ( sk3 @ B @ C )
               => ( A @ B @ C ) )
            & ( sk1 @ A ) )
         => ( A @ sk27 @ sk28 ) ) ) ),
    inference(func_ext,[status(esa)],[20]) ).

thf(103,plain,
    ( ~ ( ( sk2 @ sk27 @ sk28 )
        | ( sk3 @ sk27 @ sk28 ) )
    | ~ ( ! [A: a > a > $o] :
            ( ( ! [B: a,C: a] :
                  ( ( sk2 @ B @ C )
                 => ( A @ B @ C ) )
              & ( sk1 @ A ) )
           => ( A @ sk27 @ sk28 ) )
        | ! [A: a > a > $o] :
            ( ( ! [B: a,C: a] :
                  ( ( sk3 @ B @ C )
                 => ( A @ B @ C ) )
              & ( sk1 @ A ) )
           => ( A @ sk27 @ sk28 ) ) ) ),
    inference(bool_ext,[status(thm)],[22]) ).

thf(106,plain,
    ( ( sk1 @ sk63 )
    | ~ ( sk2 @ sk27 @ sk28 ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(21,plain,
    ( ( ( ^ [A: a,B: a,C: a > a > $o] : sk2 )
     != ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
          ! [F: a > a > $o] :
            ( ( ! [G: a,H: a] :
                  ( ( sk2 @ G @ H )
                 => ( F @ G @ H ) )
              & ( sk1 @ F ) )
           => ( F @ D @ E ) ) ) )
    | ( ( ^ [A: a,B: a,C: a > a > $o] : sk3 )
     != ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
          ! [F: a > a > $o] :
            ( ( ! [G: a,H: a] :
                  ( ( sk3 @ G @ H )
                 => ( F @ G @ H ) )
              & ( sk1 @ F ) )
           => ( F @ D @ E ) ) ) ) ),
    inference(simp,[status(thm)],[20]) ).

thf(9,plain,
    ( ( ( ! [A: a,B: a] :
            ( ( ( sk2 @ A @ B )
              | ( sk3 @ A @ B ) )
           => ( sk8 @ A @ B ) )
        & ( sk1 @ sk8 ) )
     => ( sk8 @ sk6 @ sk7 ) )
   != ( ( ! [A: a,B: a] :
            ( ( ! [C: a > a > $o] :
                  ( ( ! [D: a,E: a] :
                        ( ( sk2 @ D @ E )
                       => ( C @ D @ E ) )
                    & ( sk1 @ C ) )
                 => ( C @ A @ B ) )
              | ! [C: a > a > $o] :
                  ( ( ! [D: a,E: a] :
                        ( ( sk3 @ D @ E )
                       => ( C @ D @ E ) )
                    & ( sk1 @ C ) )
                 => ( C @ A @ B ) ) )
           => ( sk8 @ A @ B ) )
        & ( sk1 @ sk8 ) )
     => ( sk8 @ sk6 @ sk7 ) ) ),
    inference(func_ext,[status(esa)],[6]) ).

thf(157,plain,
    ( ~ ( ( ! [A: a,B: a] :
              ( ( ( sk2 @ A @ B )
                | ( sk3 @ A @ B ) )
             => ( sk8 @ A @ B ) )
          & ( sk1 @ sk8 ) )
       => ( sk8 @ sk6 @ sk7 ) )
    | ~ ( ( ! [A: a,B: a] :
              ( ( ! [C: a > a > $o] :
                    ( ( ! [D: a,E: a] :
                          ( ( sk2 @ D @ E )
                         => ( C @ D @ E ) )
                      & ( sk1 @ C ) )
                   => ( C @ A @ B ) )
                | ! [C: a > a > $o] :
                    ( ( ! [D: a,E: a] :
                          ( ( sk3 @ D @ E )
                         => ( C @ D @ E ) )
                      & ( sk1 @ C ) )
                   => ( C @ A @ B ) ) )
             => ( sk8 @ A @ B ) )
          & ( sk1 @ sk8 ) )
       => ( sk8 @ sk6 @ sk7 ) ) ),
    inference(bool_ext,[status(thm)],[9]) ).

thf(197,plain,
    ( ~ ( sk8 @ sk6 @ sk7 )
    | ~ ( sk8 @ sk6 @ sk7 ) ),
    inference(cnf,[status(esa)],[157]) ).

thf(229,plain,
    ~ ( sk8 @ sk6 @ sk7 ),
    inference(simp,[status(thm)],[197]) ).

thf(17,plain,
    ( ( ! [A: a] :
          ( ( ( sk2 @ sk18 @ A )
            | ( sk3 @ sk18 @ A ) )
         => ( sk17 @ sk18 @ A ) ) )
   != ( ! [A: a] :
          ( ( ! [B: a > a > $o] :
                ( ( ! [C: a,D: a] :
                      ( ( sk2 @ C @ D )
                     => ( B @ C @ D ) )
                  & ( sk1 @ B ) )
               => ( B @ sk18 @ A ) )
            | ! [B: a > a > $o] :
                ( ( ! [C: a,D: a] :
                      ( ( sk3 @ C @ D )
                     => ( B @ C @ D ) )
                  & ( sk1 @ B ) )
               => ( B @ sk18 @ A ) ) )
         => ( sk17 @ sk18 @ A ) ) ) ),
    inference(func_ext,[status(esa)],[14]) ).

thf(108,plain,
    ( ~ ( sk63 @ sk27 @ sk28 )
    | ~ ( sk3 @ sk27 @ sk28 ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(15,plain,
    ( ( ! [A: a,B: a] :
          ( ( ( sk2 @ A @ B )
            | ( sk3 @ A @ B ) )
         => ( sk14 @ A @ B ) ) )
   != ( ! [A: a,B: a] :
          ( ( ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk2 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) )
            | ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk3 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) ) )
         => ( sk14 @ A @ B ) ) ) ),
    inference(func_ext,[status(esa)],[13]) ).

thf(123,plain,
    ( ( ^ [A: a] :
        ! [B: a] :
          ( ( ( sk2 @ A @ B )
            | ( sk3 @ A @ B ) )
         => ( sk14 @ A @ B ) ) )
   != ( ^ [A: a] :
        ! [B: a] :
          ( ( ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk2 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) )
            | ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk3 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) ) )
         => ( sk14 @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[15]) ).

thf(150,plain,
    ( ( ^ [A: a,B: a] :
          ( ( ( sk2 @ A @ B )
            | ( sk3 @ A @ B ) )
         => ( sk14 @ A @ B ) ) )
   != ( ^ [A: a,B: a] :
          ( ( ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk2 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) )
            | ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk3 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) ) )
         => ( sk14 @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[123]) ).

thf(107,plain,
    ( ~ ( sk63 @ sk27 @ sk28 )
    | ~ ( sk2 @ sk27 @ sk28 ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(209,plain,
    ( ( sk1 @ sk8 )
    | ( sk1 @ sk8 ) ),
    inference(cnf,[status(esa)],[157]) ).

thf(227,plain,
    sk1 @ sk8,
    inference(simp,[status(thm)],[209]) ).

thf(151,plain,
    ( ( ( ^ [A: a,B: a] :
            ( ( sk2 @ A @ B )
            | ( sk3 @ A @ B ) ) )
     != ( ^ [A: a,B: a] :
            ( ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk2 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) )
            | ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk3 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) ) ) ) )
    | ( sk14 != sk14 ) ),
    inference(simp,[status(thm)],[150]) ).

thf(152,plain,
    ( ( ^ [A: a,B: a] :
          ( ( sk2 @ A @ B )
          | ( sk3 @ A @ B ) ) )
   != ( ^ [A: a,B: a] :
          ( ! [C: a > a > $o] :
              ( ( ! [D: a,E: a] :
                    ( ( sk2 @ D @ E )
                   => ( C @ D @ E ) )
                & ( sk1 @ C ) )
             => ( C @ A @ B ) )
          | ! [C: a > a > $o] :
              ( ( ! [D: a,E: a] :
                    ( ( sk3 @ D @ E )
                   => ( C @ D @ E ) )
                & ( sk1 @ C ) )
             => ( C @ A @ B ) ) ) ) ),
    inference(simp,[status(thm)],[151]) ).

thf(116,plain,
    ( ( sk1 @ sk64 )
    | ~ ( sk3 @ sk27 @ sk28 ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(257,plain,
    ( ~ ! [A: a] :
          ( ( ( sk2 @ sk18 @ A )
            | ( sk3 @ sk18 @ A ) )
         => ( sk17 @ sk18 @ A ) )
    | ~ ! [A: a] :
          ( ( ! [B: a > a > $o] :
                ( ( ! [C: a,D: a] :
                      ( ( sk2 @ C @ D )
                     => ( B @ C @ D ) )
                  & ( sk1 @ B ) )
               => ( B @ sk18 @ A ) )
            | ! [B: a > a > $o] :
                ( ( ! [C: a,D: a] :
                      ( ( sk3 @ C @ D )
                     => ( B @ C @ D ) )
                  & ( sk1 @ B ) )
               => ( B @ sk18 @ A ) ) )
         => ( sk17 @ sk18 @ A ) ) ),
    inference(bool_ext,[status(thm)],[17]) ).

thf(265,plain,
    ( ~ ( sk17 @ sk18 @ sk90 )
    | ~ ( sk17 @ sk18 @ sk89 ) ),
    inference(cnf,[status(esa)],[257]) ).

thf(109,plain,
    ( ~ ( sk64 @ sk27 @ sk28 )
    | ~ ( sk2 @ sk27 @ sk28 ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(256,plain,
    ( ( ^ [A: a] :
          ( ( ( sk2 @ sk18 @ A )
            | ( sk3 @ sk18 @ A ) )
         => ( sk17 @ sk18 @ A ) ) )
   != ( ^ [A: a] :
          ( ( ! [B: a > a > $o] :
                ( ( ! [C: a,D: a] :
                      ( ( sk2 @ C @ D )
                     => ( B @ C @ D ) )
                  & ( sk1 @ B ) )
               => ( B @ sk18 @ A ) )
            | ! [B: a > a > $o] :
                ( ( ! [C: a,D: a] :
                      ( ( sk3 @ C @ D )
                     => ( B @ C @ D ) )
                  & ( sk1 @ B ) )
               => ( B @ sk18 @ A ) ) )
         => ( sk17 @ sk18 @ A ) ) ) ),
    inference(simp,[status(thm)],[17]) ).

thf(124,plain,
    ( ~ ! [A: a,B: a] :
          ( ( ( sk2 @ A @ B )
            | ( sk3 @ A @ B ) )
         => ( sk14 @ A @ B ) )
    | ~ ! [A: a,B: a] :
          ( ( ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk2 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) )
            | ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk3 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) ) )
         => ( sk14 @ A @ B ) ) ),
    inference(bool_ext,[status(thm)],[15]) ).

thf(128,plain,
    ( ~ ( sk14 @ sk71 @ sk72 )
    | ~ ( sk14 @ sk69 @ sk70 ) ),
    inference(cnf,[status(esa)],[124]) ).

thf(105,plain,
    ( ( sk1 @ sk64 )
    | ~ ( sk2 @ sk27 @ sk28 ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(359,plain,
    ( ( ( ^ [A: a] :
            ( ( sk2 @ sk18 @ A )
            | ( sk3 @ sk18 @ A ) ) )
     != ( ^ [A: a] :
            ( ! [B: a > a > $o] :
                ( ( ! [C: a,D: a] :
                      ( ( sk2 @ C @ D )
                     => ( B @ C @ D ) )
                  & ( sk1 @ B ) )
               => ( B @ sk18 @ A ) )
            | ! [B: a > a > $o] :
                ( ( ! [C: a,D: a] :
                      ( ( sk3 @ C @ D )
                     => ( B @ C @ D ) )
                  & ( sk1 @ B ) )
               => ( B @ sk18 @ A ) ) ) ) )
    | ( ( sk17 @ sk18 )
     != ( sk17 @ sk18 ) ) ),
    inference(simp,[status(thm)],[256]) ).

thf(360,plain,
    ( ( ^ [A: a] :
          ( ( sk2 @ sk18 @ A )
          | ( sk3 @ sk18 @ A ) ) )
   != ( ^ [A: a] :
          ( ! [B: a > a > $o] :
              ( ( ! [C: a,D: a] :
                    ( ( sk2 @ C @ D )
                   => ( B @ C @ D ) )
                & ( sk1 @ B ) )
             => ( B @ sk18 @ A ) )
          | ! [B: a > a > $o] :
              ( ( ! [C: a,D: a] :
                    ( ( sk3 @ C @ D )
                   => ( B @ C @ D ) )
                & ( sk1 @ B ) )
             => ( B @ sk18 @ A ) ) ) ) ),
    inference(simp,[status(thm)],[359]) ).

thf(12,plain,
    ( ( ! [A: a,B: a] :
          ( ( ( sk2 @ A @ B )
            | ( sk3 @ A @ B ) )
         => ( sk11 @ A @ B ) )
      & ( sk1 @ sk11 ) )
   != ( ! [A: a,B: a] :
          ( ( ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk2 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) )
            | ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk3 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) ) )
         => ( sk11 @ A @ B ) )
      & ( sk1 @ sk11 ) ) ),
    inference(func_ext,[status(esa)],[10]) ).

thf(284,plain,
    ( ( ( ! [A: a,B: a] :
            ( ( ( sk2 @ A @ B )
              | ( sk3 @ A @ B ) )
           => ( sk11 @ A @ B ) ) )
     != ( ! [A: a,B: a] :
            ( ( ! [C: a > a > $o] :
                  ( ( ! [D: a,E: a] :
                        ( ( sk2 @ D @ E )
                       => ( C @ D @ E ) )
                    & ( sk1 @ C ) )
                 => ( C @ A @ B ) )
              | ! [C: a > a > $o] :
                  ( ( ! [D: a,E: a] :
                        ( ( sk3 @ D @ E )
                       => ( C @ D @ E ) )
                    & ( sk1 @ C ) )
                 => ( C @ A @ B ) ) )
           => ( sk11 @ A @ B ) ) ) )
    | ( ( sk1 @ sk11 )
     != ( sk1 @ sk11 ) ) ),
    inference(simp,[status(thm)],[12]) ).

thf(311,plain,
    ( ( ! [A: a,B: a] :
          ( ( ( sk2 @ A @ B )
            | ( sk3 @ A @ B ) )
         => ( sk11 @ A @ B ) ) )
   != ( ! [A: a,B: a] :
          ( ( ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk2 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) )
            | ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk3 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) ) )
         => ( sk11 @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[284]) ).

thf(7,plain,
    ( ( ! [A: a > a > $o] :
          ( ( ! [B: a,C: a] :
                ( ( ( sk2 @ B @ C )
                  | ( sk3 @ B @ C ) )
               => ( A @ B @ C ) )
            & ( sk1 @ A ) )
         => ( A @ sk4 @ sk5 ) ) )
   != ( ! [A: a > a > $o] :
          ( ( ! [B: a,C: a] :
                ( ( ! [D: a > a > $o] :
                      ( ( ! [E: a,F: a] :
                            ( ( sk2 @ E @ F )
                           => ( D @ E @ F ) )
                        & ( sk1 @ D ) )
                     => ( D @ B @ C ) )
                  | ! [D: a > a > $o] :
                      ( ( ! [E: a,F: a] :
                            ( ( sk3 @ E @ F )
                           => ( D @ E @ F ) )
                        & ( sk1 @ D ) )
                     => ( D @ B @ C ) ) )
               => ( A @ B @ C ) )
            & ( sk1 @ A ) )
         => ( A @ sk4 @ sk5 ) ) ) ),
    inference(func_ext,[status(esa)],[5]) ).

thf(54,plain,
    ( ~ ! [A: a > a > $o] :
          ( ( ! [B: a,C: a] :
                ( ( ( sk2 @ B @ C )
                  | ( sk3 @ B @ C ) )
               => ( A @ B @ C ) )
            & ( sk1 @ A ) )
         => ( A @ sk4 @ sk5 ) )
    | ~ ! [A: a > a > $o] :
          ( ( ! [B: a,C: a] :
                ( ( ! [D: a > a > $o] :
                      ( ( ! [E: a,F: a] :
                            ( ( sk2 @ E @ F )
                           => ( D @ E @ F ) )
                        & ( sk1 @ D ) )
                     => ( D @ B @ C ) )
                  | ! [D: a > a > $o] :
                      ( ( ! [E: a,F: a] :
                            ( ( sk3 @ E @ F )
                           => ( D @ E @ F ) )
                        & ( sk1 @ D ) )
                     => ( D @ B @ C ) ) )
               => ( A @ B @ C ) )
            & ( sk1 @ A ) )
         => ( A @ sk4 @ sk5 ) ) ),
    inference(bool_ext,[status(thm)],[7]) ).

thf(81,plain,
    ! [B: a,A: a] :
      ( ( sk1 @ ( sk52 @ B @ A ) )
      | ( sk1 @ sk51 ) ),
    inference(cnf,[status(esa)],[54]) ).

thf(112,plain,
    ( ~ ( sk64 @ sk27 @ sk28 )
    | ~ ( sk3 @ sk27 @ sk28 ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(286,plain,
    ( ( ! [A: a,B: a] :
          ( ( ( sk2 @ A @ B )
            | ( sk3 @ A @ B ) )
         => ( sk11 @ A @ B ) )
      & ( sk1 @ sk11 ) )
    | ( ! [A: a,B: a] :
          ( ( ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk2 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) )
            | ! [C: a > a > $o] :
                ( ( ! [D: a,E: a] :
                      ( ( sk3 @ D @ E )
                     => ( C @ D @ E ) )
                  & ( sk1 @ C ) )
               => ( C @ A @ B ) ) )
         => ( sk11 @ A @ B ) )
      & ( sk1 @ sk11 ) ) ),
    inference(bool_ext,[status(thm)],[12]) ).

thf(332,plain,
    ( ( sk1 @ sk11 )
    | ( sk1 @ sk11 ) ),
    inference(cnf,[status(esa)],[286]) ).

thf(355,plain,
    sk1 @ sk11,
    inference(simp,[status(thm)],[332]) ).

thf(114,plain,
    ( ( sk1 @ sk63 )
    | ~ ( sk3 @ sk27 @ sk28 ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(23,plain,
    ( ( ( sk2 @ sk32 @ sk33 )
     != ( ! [A: a > a > $o] :
            ( ( ! [B: a,C: a] :
                  ( ( sk2 @ B @ C )
                 => ( A @ B @ C ) )
              & ( sk1 @ A ) )
           => ( A @ sk32 @ sk33 ) ) ) )
    | ( ( sk3 @ sk37 @ sk38 )
     != ( ! [A: a > a > $o] :
            ( ( ! [B: a,C: a] :
                  ( ( sk3 @ B @ C )
                 => ( A @ B @ C ) )
              & ( sk1 @ A ) )
           => ( A @ sk37 @ sk38 ) ) ) ) ),
    inference(func_ext,[status(esa)],[21]) ).

thf(2396,plain,
    $false,
    inference(cvc4,[status(thm)],[5,10,14,106,6,21,229,13,17,22,108,3,150,16,107,15,227,20,152,116,265,109,256,128,105,360,311,81,7,112,123,355,114,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV119^5 : TPTP v8.2.0. Released v4.0.0.
% 0.15/0.15  % 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
% 0.23/0.37  % CPULimit : 300
% 0.23/0.37  % WCLimit  : 300
% 0.23/0.37  % DateTime : Sun May 19 18:42:39 EDT 2024
% 0.23/0.37  % CPUTime  : 
% 0.94/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.97  % [INFO] 	 Parsing done (103ms). 
% 1.30/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.62/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.91/1.28  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.91/1.28  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.91/1.28  % [INFO] 	 Type checking passed. 
% 1.91/1.29  % [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 ... 
% 130.13/35.24  % External prover 'cvc4' found a proof!
% 130.13/35.24  % [INFO] 	 Killing All external provers ... 
% 130.13/35.24  % Time passed: 34714ms (effective reasoning time: 34258ms)
% 130.13/35.24  % 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)>
% 130.13/35.24  % Axioms used in derivation (0): 
% 130.13/35.24  % No. of inferences in proof: 55
% 130.13/35.24  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 34714 ms resp. 34258 ms w/o parsing
% 130.13/35.29  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 130.13/35.30  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------