TSTP Solution File: SEV248^5 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SEV248^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n025.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 15:59:51 EDT 2024

% Result   : Theorem 80.62s 13.57s
% Output   : Refutation 80.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   58
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   76 (  13 unt;   0 typ;   0 def)
%            Number of atoms       :  593 ( 566 equ;  73 cnn)
%            Maximal formula atoms :    7 (   7 avg)
%            Number of connectives :  555 (  74   ~; 258   |;   7   &; 216   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :  147 (  33   ^ 114   !;   0   ?; 147   :)

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

thf(sk1_type,type,
    sk1: a ).

thf(sk2_type,type,
    sk2: a ).

thf(sk3_type,type,
    sk3: a ).

thf(sk4_type,type,
    sk4: a ).

thf(sk5_type,type,
    sk5: a > $o ).

thf(sk6_type,type,
    sk6: ( a > $o ) > a ).

thf(sk7_type,type,
    sk7: a > ( a > $o ) > a ).

thf(1,conjecture,
    ! [A: a,B: a,C: a,D: a] :
      ( ( ! [E: a > $o] :
            ( ( ( E
                = ( (=) @ a @ A ) )
              | ! [F: a] :
                  ( ( E @ F )
                  = ( ( F = A )
                    | ( F = B ) ) ) )
            = ( ( E
                = ( (=) @ a @ C ) )
              | ! [F: a] :
                  ( ( E @ F )
                  = ( ( F = C )
                    | ( F = D ) ) ) ) ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM103_pme) ).

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

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

thf(4,plain,
    ( ( ! [A: a > $o] :
          ( ( ( A
              = ( (=) @ a @ sk1 ) )
            | ! [B: a] :
                ( ( A @ B )
                = ( ( B = sk1 )
                  | ( B = sk2 ) ) ) )
          = ( ( A
              = ( (=) @ a @ sk3 ) )
            | ! [B: a] :
                ( ( A @ B )
                = ( ( B = sk3 )
                  | ( B = sk4 ) ) ) ) ) )
   != ( ( sk1 = sk3 )
      & ( sk2 = sk4 ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ( sk1 = sk3 )
      & ( sk2 = sk4 ) )
   != ( ! [A: a > $o] :
          ( ( ( A
              = ( (=) @ a @ sk1 ) )
            | ! [B: a] :
                ( ( A @ B )
                = ( ( B = sk1 )
                  | ( B = sk2 ) ) ) )
          = ( ( A
              = ( (=) @ a @ sk3 ) )
            | ! [B: a] :
                ( ( A @ B )
                = ( ( B = sk3 )
                  | ( B = sk4 ) ) ) ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ( sk1 = sk3 )
      & ( sk2 = sk4 ) )
    | ! [A: a > $o] :
        ( ( ( A
            = ( (=) @ a @ sk1 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk1 )
                | ( B = sk2 ) ) ) )
        = ( ( A
            = ( (=) @ a @ sk3 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk3 )
                | ( B = sk4 ) ) ) ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(10,plain,
    ! [A: a > $o] :
      ( ( ( ( A
            = ( (=) @ a @ sk1 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk1 )
                | ( B = sk2 ) ) ) )
        = ( ( A
            = ( (=) @ a @ sk3 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk3 )
                | ( B = sk4 ) ) ) ) )
      | ( sk2 = sk4 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(12,plain,
    ! [A: a > $o] :
      ( ( ( ( A
            = ( (=) @ a @ sk3 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk3 )
                | ( B = sk4 ) ) ) )
        = ( ( A
            = ( (=) @ a @ sk1 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk1 )
                | ( B = sk2 ) ) ) ) )
      | ( sk4 = sk2 ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(15,plain,
    ! [A: a > $o] :
      ( ( sk4 = sk2 )
      | ( A
        = ( (=) @ a @ sk3 ) )
      | ! [B: a] :
          ( ( A @ B )
          = ( ( B = sk3 )
            | ( B = sk4 ) ) )
      | ~ ( ( A
            = ( (=) @ a @ sk1 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk1 )
                | ( B = sk2 ) ) ) ) ),
    inference(bool_ext,[status(thm)],[12]) ).

thf(25,plain,
    ! [B: a,A: a > $o] :
      ( ( ( A @ ( sk7 @ B @ A ) )
       != ( ( ( sk7 @ B @ A )
            = sk1 )
          | ( ( sk7 @ B @ A )
            = sk2 ) ) )
      | ( A
        = ( (=) @ a @ sk3 ) )
      | ( ( A @ B )
        = ( ( B = sk3 )
          | ( B = sk4 ) ) )
      | ( sk4 = sk2 ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(27,plain,
    ! [B: a,A: a > $o] :
      ( ( ( A @ ( sk7 @ B @ A ) )
       != ( ( ( sk7 @ B @ A )
            = sk1 )
          | ( ( sk7 @ B @ A )
            = sk2 ) ) )
      | ( A
        = ( (=) @ a @ sk3 ) )
      | ( ( A @ B )
        = ( ( B = sk3 )
          | ( B = sk4 ) ) )
      | ( sk4 = sk2 ) ),
    inference(lifteq,[status(thm)],[25]) ).

thf(1432,plain,
    ! [A: a] :
      ( ( sk4 = sk2 )
      | ( ( ( A = sk3 )
          | ( A = sk4 ) )
        = ( ( A = sk1 )
          | ( A = sk2 ) ) )
      | ( ( ^ [B: a] :
              ( ( B = sk1 )
              | ( B = sk2 ) ) )
        = ( (=) @ a @ sk3 ) ) ),
    inference(pre_uni,[status(thm)],[27:[bind(A,$thf( ^ [C: a] : ( ( C = sk1 ) | ( C = sk2 ) ) )),bind(B,$thf( B ))]]) ).

thf(1631,plain,
    ! [A: a] :
      ( ( sk4 = sk2 )
      | ( ( ( A = sk3 )
          | ( A = sk4 ) )
        = ( ( A = sk1 )
          | ( A = sk2 ) ) )
      | ( ( ^ [B: a] :
              ( ( B = sk1 )
              | ( B = sk2 ) ) )
        = ( (=) @ a @ sk3 ) ) ),
    inference(simp,[status(thm)],[1432]) ).

thf(11,plain,
    ! [A: a > $o] :
      ( ( ( ( A
            = ( (=) @ a @ sk1 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk1 )
                | ( B = sk2 ) ) ) )
        = ( ( A
            = ( (=) @ a @ sk3 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk3 )
                | ( B = sk4 ) ) ) ) )
      | ( sk1 = sk3 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(13,plain,
    ! [A: a > $o] :
      ( ( ( ( A
            = ( (=) @ a @ sk3 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk3 )
                | ( B = sk4 ) ) ) )
        = ( ( A
            = ( (=) @ a @ sk1 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk1 )
                | ( B = sk2 ) ) ) ) )
      | ( sk3 = sk1 ) ),
    inference(lifteq,[status(thm)],[11]) ).

thf(30,plain,
    ! [A: a > $o] :
      ( ( sk3 = sk1 )
      | ~ ( ( A
            = ( (=) @ a @ sk3 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk3 )
                | ( B = sk4 ) ) ) )
      | ( A
        = ( (=) @ a @ sk1 ) )
      | ! [B: a] :
          ( ( A @ B )
          = ( ( B = sk1 )
            | ( B = sk2 ) ) ) ),
    inference(bool_ext,[status(thm)],[13]) ).

thf(48,plain,
    ! [B: a,A: a > $o] :
      ( ( A
        = ( (=) @ a @ sk1 ) )
      | ( ( A @ B )
        = ( ( B = sk1 )
          | ( B = sk2 ) ) )
      | ( A
       != ( (=) @ a @ sk3 ) )
      | ( sk3 = sk1 ) ),
    inference(cnf,[status(esa)],[30]) ).

thf(50,plain,
    ! [B: a,A: a > $o] :
      ( ( A
        = ( (=) @ a @ sk1 ) )
      | ( ( A @ B )
        = ( ( B = sk1 )
          | ( B = sk2 ) ) )
      | ( A
       != ( (=) @ a @ sk3 ) )
      | ( sk3 = sk1 ) ),
    inference(lifteq,[status(thm)],[48]) ).

thf(51,plain,
    ! [A: a] :
      ( ( ( (=) @ a @ sk3 )
        = ( (=) @ a @ sk1 ) )
      | ( ( ( A = sk1 )
          | ( A = sk2 ) )
        = ( sk3 = A ) )
      | ( sk3 = sk1 ) ),
    inference(simp,[status(thm)],[50]) ).

thf(3215,plain,
    ! [A: a] :
      ( ( ( (=) @ a @ sk3 )
        = ( (=) @ a @ sk1 ) )
      | ( sk3 = sk1 )
      | ~ ( ( A = sk1 )
          | ( A = sk2 ) )
      | ( sk3 = A ) ),
    inference(bool_ext,[status(thm)],[51]) ).

thf(3430,plain,
    ! [A: a] :
      ( ( sk3 = A )
      | ( ( (=) @ a @ sk3 )
        = ( (=) @ a @ sk1 ) )
      | ( sk3 = sk1 )
      | ~ ( ( A = sk1 )
          | ( A = sk2 ) ) ),
    inference(lifteq,[status(thm)],[3215]) ).

thf(3492,plain,
    ! [A: a] :
      ( ( A != sk1 )
      | ( sk3 = sk1 )
      | ( ( (=) @ a @ sk3 )
        = ( (=) @ a @ sk1 ) )
      | ( sk3 = A ) ),
    inference(cnf,[status(esa)],[3430]) ).

thf(3495,plain,
    ! [A: a] :
      ( ( A != sk1 )
      | ( sk3 = sk1 )
      | ( ( (=) @ a @ sk3 )
        = ( (=) @ a @ sk1 ) )
      | ( sk3 = A ) ),
    inference(lifteq,[status(thm)],[3492]) ).

thf(3496,plain,
    ( ( sk3 = sk1 )
    | ( ( (=) @ a @ sk3 )
      = ( (=) @ a @ sk1 ) ) ),
    inference(simp,[status(thm)],[3495]) ).

thf(3585,plain,
    ! [A: a] :
      ( ( ( sk3 = A )
        = ( sk1 = A ) )
      | ( sk3 = sk1 ) ),
    inference(func_ext,[status(esa)],[3496]) ).

thf(3837,plain,
    ! [A: a] :
      ( ( sk3 = sk1 )
      | ( sk3 != A )
      | ( sk1 = A ) ),
    inference(bool_ext,[status(thm)],[3585]) ).

thf(4017,plain,
    ! [A: a] :
      ( ( sk3 != A )
      | ( sk1 = A )
      | ( sk3 = sk1 ) ),
    inference(lifteq,[status(thm)],[3837]) ).

thf(4053,plain,
    sk3 = sk1,
    inference(simp,[status(thm)],[4017]) ).

thf(14,plain,
    ! [A: a > $o] :
      ( ( sk4 = sk2 )
      | ~ ( ( A
            = ( (=) @ a @ sk3 ) )
          | ! [B: a] :
              ( ( A @ B )
              = ( ( B = sk3 )
                | ( B = sk4 ) ) ) )
      | ( A
        = ( (=) @ a @ sk1 ) )
      | ! [B: a] :
          ( ( A @ B )
          = ( ( B = sk1 )
            | ( B = sk2 ) ) ) ),
    inference(bool_ext,[status(thm)],[12]) ).

thf(21,plain,
    ! [B: a,A: a > $o] :
      ( ( A
        = ( (=) @ a @ sk1 ) )
      | ( ( A @ B )
        = ( ( B = sk1 )
          | ( B = sk2 ) ) )
      | ( ( A @ ( sk6 @ A ) )
       != ( ( ( sk6 @ A )
            = sk3 )
          | ( ( sk6 @ A )
            = sk4 ) ) )
      | ( sk4 = sk2 ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(24,plain,
    ! [B: a,A: a > $o] :
      ( ( A
        = ( (=) @ a @ sk1 ) )
      | ( ( A @ B )
        = ( ( B = sk1 )
          | ( B = sk2 ) ) )
      | ( ( A @ ( sk6 @ A ) )
       != ( ( ( sk6 @ A )
            = sk3 )
          | ( ( sk6 @ A )
            = sk4 ) ) )
      | ( sk4 = sk2 ) ),
    inference(lifteq,[status(thm)],[21]) ).

thf(556,plain,
    ! [A: a] :
      ( ( sk4 = sk2 )
      | ( ( ( A = sk3 )
          | ( A = sk4 ) )
        = ( ( A = sk1 )
          | ( A = sk2 ) ) )
      | ( ( ^ [B: a] :
              ( ( B = sk3 )
              | ( B = sk4 ) ) )
        = ( (=) @ a @ sk1 ) ) ),
    inference(pre_uni,[status(thm)],[24:[bind(A,$thf( ^ [C: a] : ( ( C = sk3 ) | ( C = sk4 ) ) )),bind(B,$thf( B ))]]) ).

thf(866,plain,
    ! [A: a] :
      ( ( sk4 = sk2 )
      | ( ( ( A = sk3 )
          | ( A = sk4 ) )
        = ( ( A = sk1 )
          | ( A = sk2 ) ) )
      | ( ( ^ [B: a] :
              ( ( B = sk3 )
              | ( B = sk4 ) ) )
        = ( (=) @ a @ sk1 ) ) ),
    inference(simp,[status(thm)],[556]) ).

thf(5085,plain,
    ! [A: a] :
      ( ( sk4 = sk2 )
      | ( ( ( A = sk1 )
          | ( A = sk4 ) )
        = ( ( A = sk1 )
          | ( A = sk2 ) ) )
      | ( ( ^ [B: a] :
              ( ( B = sk1 )
              | ( B = sk4 ) ) )
        = ( (=) @ a @ sk1 ) ) ),
    inference(rewrite,[status(thm)],[866,4053]) ).

thf(6,plain,
    ( ~ ( ( sk1 = sk3 )
        & ( sk2 = sk4 ) )
    | ~ ! [A: a > $o] :
          ( ( ( A
              = ( (=) @ a @ sk1 ) )
            | ! [B: a] :
                ( ( A @ B )
                = ( ( B = sk1 )
                  | ( B = sk2 ) ) ) )
          = ( ( A
              = ( (=) @ a @ sk3 ) )
            | ! [B: a] :
                ( ( A @ B )
                = ( ( B = sk3 )
                  | ( B = sk4 ) ) ) ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ( ( sk5
          = ( (=) @ a @ sk1 ) )
        | ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk2 ) ) ) )
     != ( ( sk5
          = ( (=) @ a @ sk3 ) )
        | ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk3 )
              | ( A = sk4 ) ) ) ) )
    | ( sk1 != sk3 )
    | ( sk2 != sk4 ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(9,plain,
    ( ( ( ( sk5
          = ( (=) @ a @ sk3 ) )
        | ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk3 )
              | ( A = sk4 ) ) ) )
     != ( ( sk5
          = ( (=) @ a @ sk1 ) )
        | ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk2 ) ) ) ) )
    | ( sk3 != sk1 )
    | ( sk4 != sk2 ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(4135,plain,
    ( ( ( ( sk5
          = ( (=) @ a @ sk1 ) )
        | ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk4 ) ) ) )
     != ( ( sk5
          = ( (=) @ a @ sk1 ) )
        | ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk2 ) ) ) ) )
    | ( sk1 != sk1 )
    | ( sk4 != sk2 ) ),
    inference(rewrite,[status(thm)],[9,4053]) ).

thf(4136,plain,
    ( ( ( ( sk5
          = ( (=) @ a @ sk1 ) )
        | ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk4 ) ) ) )
     != ( ( sk5
          = ( (=) @ a @ sk1 ) )
        | ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk2 ) ) ) ) )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[4135]) ).

thf(4193,plain,
    ( ( ( sk5
        = ( (=) @ a @ sk1 ) )
     != ( sk5
        = ( (=) @ a @ sk1 ) ) )
    | ( ( ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk4 ) ) ) )
     != ( ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk2 ) ) ) ) )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[4136]) ).

thf(4196,plain,
    ( ( ( ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk4 ) ) ) )
     != ( ! [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk2 ) ) ) ) )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[4193]) ).

thf(4209,plain,
    ( ( ( ^ [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk4 ) ) ) )
     != ( ^ [A: a] :
            ( ( sk5 @ A )
            = ( ( A = sk1 )
              | ( A = sk2 ) ) ) ) )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[4196]) ).

thf(4258,plain,
    ( ( sk5 != sk5 )
    | ( ( ^ [A: a] :
            ( ( A = sk1 )
            | ( A = sk4 ) ) )
     != ( ^ [A: a] :
            ( ( A = sk1 )
            | ( A = sk2 ) ) ) )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[4209]) ).

thf(4260,plain,
    ( ( ( ^ [A: a] :
            ( ( A = sk1 )
            | ( A = sk4 ) ) )
     != ( ^ [A: a] :
            ( ( A = sk1 )
            | ( A = sk2 ) ) ) )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[4258]) ).

thf(4261,plain,
    ( ( ( ^ [A: a] : ( A = sk1 ) )
     != ( ^ [A: a] : ( A = sk1 ) ) )
    | ( ( ^ [A: a] : ( A = sk4 ) )
     != ( ^ [A: a] : ( A = sk2 ) ) )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[4260]) ).

thf(4263,plain,
    ( ( ( ^ [A: a] : ( A = sk4 ) )
     != ( ^ [A: a] : ( A = sk2 ) ) )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[4261]) ).

thf(4264,plain,
    ( ( ( ^ [A: a] : A )
     != ( ^ [A: a] : A ) )
    | ( ( ^ [A: a] : sk4 )
     != ( ^ [A: a] : sk2 ) )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[4263]) ).

thf(4266,plain,
    ( ( ( ^ [A: a] : sk4 )
     != ( ^ [A: a] : sk2 ) )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[4264]) ).

thf(4267,plain,
    ( ( sk4 != sk2 )
    | ( sk4 != sk2 ) ),
    inference(func_ext,[status(esa)],[4266]) ).

thf(4268,plain,
    sk4 != sk2,
    inference(simp,[status(thm)],[4267]) ).

thf(5086,plain,
    ! [A: a] :
      ( ( ( ( A = sk1 )
          | ( A = sk4 ) )
        = ( ( A = sk1 )
          | ( A = sk2 ) ) )
      | ( ( ^ [B: a] :
              ( ( B = sk1 )
              | ( B = sk4 ) ) )
        = ( (=) @ a @ sk1 ) ) ),
    inference(simplifyReflect,[status(thm)],[5085,4268]) ).

thf(5087,plain,
    ! [B: a,A: a] :
      ( ( ( ( B = sk1 )
          | ( B = sk4 ) )
        = ( sk1 = B ) )
      | ( ( ( A = sk1 )
          | ( A = sk4 ) )
        = ( ( A = sk1 )
          | ( A = sk2 ) ) ) ),
    inference(func_ext,[status(esa)],[5086]) ).

thf(5106,plain,
    ! [B: a,A: a] :
      ( ~ ( ( B = sk1 )
          | ( B = sk4 ) )
      | ( sk1 = B )
      | ~ ( ( A = sk1 )
          | ( A = sk4 ) )
      | ( A = sk1 )
      | ( A = sk2 ) ),
    inference(bool_ext,[status(thm)],[5087]) ).

thf(5145,plain,
    ! [B: a,A: a] :
      ( ( sk1 = B )
      | ~ ( ( B = sk1 )
          | ( B = sk4 ) )
      | ~ ( ( A = sk1 )
          | ( A = sk4 ) )
      | ( A = sk1 )
      | ( A = sk2 ) ),
    inference(lifteq,[status(thm)],[5106]) ).

thf(5212,plain,
    ! [B: a,A: a] :
      ( ( A = sk1 )
      | ( A = sk2 )
      | ( A != sk4 )
      | ( B != sk4 )
      | ( sk1 = B ) ),
    inference(cnf,[status(esa)],[5145]) ).

thf(5218,plain,
    ! [B: a,A: a] :
      ( ( A = sk1 )
      | ( A = sk2 )
      | ( A != sk4 )
      | ( B != sk4 )
      | ( sk1 = B ) ),
    inference(lifteq,[status(thm)],[5212]) ).

thf(5219,plain,
    ( ( sk4 = sk1 )
    | ( sk4 = sk2 )
    | ( sk4 = sk1 ) ),
    inference(simp,[status(thm)],[5218]) ).

thf(5285,plain,
    ( ( sk4 = sk1 )
    | ( sk4 = sk2 ) ),
    inference(simp,[status(thm)],[5219]) ).

thf(5286,plain,
    sk4 = sk1,
    inference(simplifyReflect,[status(thm)],[5285,4268]) ).

thf(5758,plain,
    ! [A: a] :
      ( ( sk2 = sk1 )
      | ( ( ( A = sk1 )
          | ( A = sk2 ) )
        = ( ( A = sk1 )
          | ( A = sk1 ) ) )
      | ( ( ^ [B: a] :
              ( ( B = sk1 )
              | ( B = sk2 ) ) )
        = ( (=) @ a @ sk1 ) ) ),
    inference(rewrite,[status(thm)],[1631,4053,5286]) ).

thf(5759,plain,
    ! [A: a] :
      ( ( sk2 = sk1 )
      | ( ( ( A = sk1 )
          | ( A = sk2 ) )
        = ( A = sk1 ) )
      | ( ( ^ [B: a] :
              ( ( B = sk1 )
              | ( B = sk2 ) ) )
        = ( (=) @ a @ sk1 ) ) ),
    inference(simp,[status(thm)],[5758]) ).

thf(5289,plain,
    sk2 != sk1,
    inference(rewrite,[status(thm)],[4268,5286]) ).

thf(5760,plain,
    ! [A: a] :
      ( ( ( ( A = sk1 )
          | ( A = sk2 ) )
        = ( A = sk1 ) )
      | ( ( ^ [B: a] :
              ( ( B = sk1 )
              | ( B = sk2 ) ) )
        = ( (=) @ a @ sk1 ) ) ),
    inference(simplifyReflect,[status(thm)],[5759,5289]) ).

thf(5762,plain,
    ! [A: a] :
      ( ( ( ^ [B: a] :
              ( ( B = sk1 )
              | ( B = sk2 ) ) )
        = ( (=) @ a @ sk1 ) )
      | ~ ( ( A = sk1 )
          | ( A = sk2 ) )
      | ( A = sk1 ) ),
    inference(bool_ext,[status(thm)],[5760]) ).

thf(5766,plain,
    ! [A: a] :
      ( ( A = sk1 )
      | ( ( ^ [B: a] :
              ( ( B = sk1 )
              | ( B = sk2 ) ) )
        = ( (=) @ a @ sk1 ) )
      | ~ ( ( A = sk1 )
          | ( A = sk2 ) ) ),
    inference(lifteq,[status(thm)],[5762]) ).

thf(5768,plain,
    ! [A: a] :
      ( ( A != sk2 )
      | ( ( ^ [B: a] :
              ( ( B = sk1 )
              | ( B = sk2 ) ) )
        = ( (=) @ a @ sk1 ) )
      | ( A = sk1 ) ),
    inference(cnf,[status(esa)],[5766]) ).

thf(5770,plain,
    ! [A: a] :
      ( ( A != sk2 )
      | ( ( ^ [B: a] :
              ( ( B = sk1 )
              | ( B = sk2 ) ) )
        = ( (=) @ a @ sk1 ) )
      | ( A = sk1 ) ),
    inference(lifteq,[status(thm)],[5768]) ).

thf(5771,plain,
    ( ( ( ^ [A: a] :
            ( ( A = sk1 )
            | ( A = sk2 ) ) )
      = ( (=) @ a @ sk1 ) )
    | ( sk2 = sk1 ) ),
    inference(simp,[status(thm)],[5770]) ).

thf(5777,plain,
    ( ( ^ [A: a] :
          ( ( A = sk1 )
          | ( A = sk2 ) ) )
    = ( (=) @ a @ sk1 ) ),
    inference(simplifyReflect,[status(thm)],[5771,5289]) ).

thf(5778,plain,
    ! [A: a] :
      ( ( ( A = sk1 )
        | ( A = sk2 ) )
      = ( sk1 = A ) ),
    inference(func_ext,[status(esa)],[5777]) ).

thf(5784,plain,
    ! [A: a] :
      ( ~ ( ( A = sk1 )
          | ( A = sk2 ) )
      | ( sk1 = A ) ),
    inference(bool_ext,[status(thm)],[5778]) ).

thf(5798,plain,
    ! [A: a] :
      ( ( sk1 = A )
      | ~ ( ( A = sk1 )
          | ( A = sk2 ) ) ),
    inference(lifteq,[status(thm)],[5784]) ).

thf(5810,plain,
    ! [A: a] :
      ( ( A != sk2 )
      | ( sk1 = A ) ),
    inference(cnf,[status(esa)],[5798]) ).

thf(5812,plain,
    ! [A: a] :
      ( ( A != sk2 )
      | ( sk1 = A ) ),
    inference(lifteq,[status(thm)],[5810]) ).

thf(5813,plain,
    sk2 = sk1,
    inference(simp,[status(thm)],[5812]) ).

thf(5830,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[5813,5289]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEV248^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.11  % Command  : run_Leo-III %s %d SAT
% 0.10/0.31  % Computer : n025.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Fri Jun 21 18:44:10 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.99/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.26/1.11  % [INFO] 	 Parsing done (154ms). 
% 1.26/1.12  % [INFO] 	 Running in sequential loop mode. 
% 1.85/1.48  % [INFO] 	 nitpick registered as external prover. 
% 1.85/1.48  % [INFO] 	 Scanning for conjecture ... 
% 2.04/1.57  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.04/1.61  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.04/1.61  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.04/1.62  % [INFO] 	 Type checking passed. 
% 2.04/1.62  % [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 ... 
% 80.62/13.55  % [INFO] 	 Killing All external provers ... 
% 80.62/13.57  % Time passed: 13067ms (effective reasoning time: 12426ms)
% 80.62/13.57  % 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)>
% 80.62/13.57  % Axioms used in derivation (0): 
% 80.62/13.57  % No. of inferences in proof: 76
% 80.62/13.57  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 13067 ms resp. 12426 ms w/o parsing
% 80.75/13.64  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 80.75/13.64  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------