TSTP Solution File: SEV190^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEV190^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 04:10:07 EDT 2024

% Result   : Theorem 111.61s 22.25s
% Output   : Refutation 112.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  271 (  71 unt;  11 typ;   1 def)
%            Number of atoms       : 1023 ( 433 equ;  76 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 4299 ( 486   ~; 393   |;  33   &;3368   @)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   8 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  133 ( 133   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :  775 ( 417   ^ 356   !;   2   ?; 775   :)

% Comments : 
%------------------------------------------------------------------------------
thf(iS_type,type,
    iS: $tType ).

thf(c0_type,type,
    c0: iS ).

thf(cJOIN_type,type,
    cJOIN: iS > iS > iS > $o ).

thf(cP_type,type,
    cP: iS > iS > iS ).

thf(cS_JOIN_CLOS_type,type,
    cS_JOIN_CLOS: iS > ( iS > iS > iS ) > ( iS > iS > iS > $o ) > $o ).

thf(cS_JOIN_CLOS_def,definition,
    ( cS_JOIN_CLOS
    = ( ^ [A: iS,B: iS > iS > iS,C: iS > iS > iS > $o] :
          ( ! [D: iS] : ( C @ D @ A @ D )
          & ! [D: iS] : ( C @ A @ D @ D )
          & ! [D: iS,E: iS,F: iS,G: iS,H: iS,I: iS] :
              ( ( ( C @ D @ E @ F )
                & ( C @ G @ H @ I ) )
             => ( C @ ( B @ D @ G ) @ ( B @ E @ H ) @ ( B @ F @ I ) ) ) ) ) ) ).

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

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

thf(sk3_type,type,
    sk3: iS ).

thf(sk4_type,type,
    sk4: iS > iS > iS ).

thf(sk5_type,type,
    sk5: iS > iS > iS ).

thf(sk7_type,type,
    sk7: iS ).

thf(1,conjecture,
    ( ( ! [A: iS,B: iS] :
          ( ( cP @ A @ B )
         != c0 )
      & ! [A: iS,B: iS,C: iS,D: iS] :
          ( ( ( cP @ A @ C )
            = ( cP @ B @ D ) )
         => ( ( A = B )
            & ( C = D ) ) )
      & ! [A: iS > $o] :
          ( ( ( A @ c0 )
            & ! [B: iS,C: iS] :
                ( ( ( A @ B )
                  & ( A @ C ) )
               => ( A @ ( cP @ B @ C ) ) ) )
         => ! [B: iS] : ( A @ B ) )
      & ( cS_JOIN_CLOS @ c0 @ cP @ cJOIN ) )
   => ! [A: iS] : ( cJOIN @ A @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM580_pme) ).

thf(2,negated_conjecture,
    ~ ( ( ! [A: iS,B: iS] :
            ( ( cP @ A @ B )
           != c0 )
        & ! [A: iS,B: iS,C: iS,D: iS] :
            ( ( ( cP @ A @ C )
              = ( cP @ B @ D ) )
           => ( ( A = B )
              & ( C = D ) ) )
        & ! [A: iS > $o] :
            ( ( ( A @ c0 )
              & ! [B: iS,C: iS] :
                  ( ( ( A @ B )
                    & ( A @ C ) )
                 => ( A @ ( cP @ B @ C ) ) ) )
           => ! [B: iS] : ( A @ B ) )
        & ( cS_JOIN_CLOS @ c0 @ cP @ cJOIN ) )
     => ! [A: iS] : ( cJOIN @ A @ A @ A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ! [A: iS,B: iS] :
            ( ( cP @ A @ B )
           != c0 )
        & ! [A: iS,B: iS,C: iS,D: iS] :
            ( ( ( cP @ A @ C )
              = ( cP @ B @ D ) )
           => ( ( A = B )
              & ( C = D ) ) )
        & ! [A: iS > $o] :
            ( ( ( A @ c0 )
              & ! [B: iS,C: iS] :
                  ( ( ( A @ B )
                    & ( A @ C ) )
                 => ( A @ ( cP @ B @ C ) ) ) )
           => ! [B: iS] : ( A @ B ) )
        & ! [A: iS] : ( cJOIN @ A @ c0 @ A )
        & ! [A: iS] : ( cJOIN @ c0 @ A @ A )
        & ! [A: iS,B: iS,C: iS,D: iS,E: iS,F: iS] :
            ( ( ( cJOIN @ A @ B @ C )
              & ( cJOIN @ D @ E @ F ) )
           => ( cJOIN @ ( cP @ A @ D ) @ ( cP @ B @ E ) @ ( cP @ C @ F ) ) ) )
     => ! [A: iS] : ( cJOIN @ A @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ( ( ~ ? [A: iS,B: iS] :
              ( ( cP @ A @ B )
              = c0 )
        & ! [A: iS,B: iS,C: iS,D: iS] :
            ( ( ( cP @ A @ C )
              = ( cP @ B @ D ) )
           => ( ( A = B )
              & ( C = D ) ) )
        & ! [A: iS > $o] :
            ( ( ( A @ c0 )
              & ! [B: iS,C: iS] :
                  ( ( ( A @ B )
                    & ( A @ C ) )
                 => ( A @ ( cP @ B @ C ) ) ) )
           => ! [B: iS] : ( A @ B ) )
        & ! [A: iS] : ( cJOIN @ A @ c0 @ A )
        & ! [A: iS] : ( cJOIN @ c0 @ A @ A )
        & ! [A: iS,B: iS,C: iS,D: iS,E: iS,F: iS] :
            ( ( ( cJOIN @ A @ B @ C )
              & ( cJOIN @ D @ E @ F ) )
           => ( cJOIN @ ( cP @ A @ D ) @ ( cP @ B @ E ) @ ( cP @ C @ F ) ) ) )
     => ! [A: iS] : ( cJOIN @ A @ A @ A ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(8,plain,
    ! [A: iS] : ( cJOIN @ c0 @ A @ A ),
    inference(cnf,[status(esa)],[4]) ).

thf(34,plain,
    ! [A: iS] : ( cJOIN @ c0 @ A @ A ),
    inference(simp,[status(thm)],[8]) ).

thf(5,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ( A @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(18,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ( A @ B ) ),
    inference(simp,[status(thm)],[5]) ).

thf(11,plain,
    ~ ( cJOIN @ sk3 @ sk3 @ sk3 ),
    inference(cnf,[status(esa)],[4]) ).

thf(42,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ( ( A @ B )
       != ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[18,11]) ).

thf(64,plain,
    ( ~ ( cJOIN @ c0 @ sk3 @ sk3 )
    | ~ ( cJOIN
        @ ( cP
          @ ( sk1
            @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
          @ ( sk2
            @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
        @ sk3
        @ sk3 ) ),
    inference(pre_uni,[status(thm)],[42:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).

thf(759,plain,
    ( ~ $true
    | ~ ( cJOIN
        @ ( cP
          @ ( sk1
            @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
          @ ( sk2
            @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
        @ sk3
        @ sk3 ) ),
    inference(rewrite,[status(thm)],[64,34]) ).

thf(760,plain,
    ~ ( cJOIN
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
      @ sk3
      @ sk3 ),
    inference(simp,[status(thm)],[759]) ).

thf(762,plain,
    ! [A: iS] :
      ( ( cJOIN @ c0 @ A @ A )
     != ( cJOIN
        @ ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) ) )
        @ sk3
        @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[34,760]) ).

thf(775,plain,
    ! [A: iS] :
      ( ( ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) ) )
       != c0 )
      | ( A != sk3 )
      | ( A != sk3 ) ),
    inference(simp,[status(thm)],[762]) ).

thf(785,plain,
    ( ( cP
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
   != c0 ),
    inference(simp,[status(thm)],[775]) ).

thf(7,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ ( sk1 @ A ) )
      | ( A @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(31,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ ( sk1 @ A ) )
      | ( A @ B ) ),
    inference(simp,[status(thm)],[7]) ).

thf(12,plain,
    ! [A: iS] : ( cJOIN @ A @ c0 @ A ),
    inference(cnf,[status(esa)],[4]) ).

thf(30,plain,
    ! [A: iS] : ( cJOIN @ A @ c0 @ A ),
    inference(simp,[status(thm)],[12]) ).

thf(47,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ( ( A @ B )
       != ( ~ ( A @ c0 ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[18]) ).

thf(79,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ( ( A @ B )
       != ( ~ ( A @ c0 ) ) ) ),
    inference(simp,[status(thm)],[47]) ).

thf(41,plain,
    ! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ~ ( C @ c0 )
      | ( C @ D )
      | ( ( A @ B )
       != ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[18,18]) ).

thf(68,plain,
    ! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ~ ( C @ c0 )
      | ( C @ D )
      | ( ( A @ B )
       != ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
    inference(pre_uni,[status(thm)],[41:[]]) ).

thf(69,plain,
    ! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
      ( ( C @ D )
      | ~ ( C @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ~ ( A @ c0 )
      | ( ( A @ B )
       != ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
    inference(pre_uni,[status(thm)],[68:[]]) ).

thf(9,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ ( sk2 @ A ) )
      | ( A @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(26,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ ( sk2 @ A ) )
      | ( A @ B ) ),
    inference(simp,[status(thm)],[9]) ).

thf(347,plain,
    ! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ B )
      | ( C @ ( sk2 @ C ) )
      | ( C @ D )
      | ( ( A @ ( sk2 @ A ) )
       != ( C @ c0 ) ) ),
    inference(paramod_ordered,[status(thm)],[26,26]) ).

thf(360,plain,
    ! [C: iS,B: iS > $o,A: iS] :
      ( ( c0 != c0 )
      | ( c0 = A )
      | ( B @ ( sk2 @ B ) )
      | ( B @ C )
      | ( ( c0
          = ( sk2 @ ( (=) @ iS @ c0 ) ) )
       != ( B @ c0 ) ) ),
    inference(replace_leibeq,[status(thm)],[347:[bind(A,$thf( (=) @ iS @ c0 ))]]) ).

thf(371,plain,
    ! [C: iS,B: iS > $o,A: iS] :
      ( ( c0 != c0 )
      | ( c0 = A )
      | ( B @ ( sk2 @ B ) )
      | ( B @ C )
      | ( ( c0
          = ( sk2 @ ( (=) @ iS @ c0 ) ) )
       != ( B @ c0 ) ) ),
    inference(lifteq,[status(thm)],[360]) ).

thf(382,plain,
    ! [B: iS,A: iS] :
      ( ( c0
        = ( sk2 @ ( (=) @ iS @ B ) ) )
      | ( c0
        = ( sk2
          @ ( (=) @ iS
            @ ( sk2
              @ ^ [C: iS] :
                  ( c0
                  = ( sk2 @ ( (=) @ iS @ C ) ) ) ) ) ) )
      | ( c0 = A ) ),
    inference(pre_uni,[status(thm)],[371:[bind(A,$thf( A )),bind(B,$thf( ^ [D: iS] : ( c0 = ( sk2 @ ( (=) @ iS @ D ) ) ) )),bind(C,$thf( C ))]]) ).

thf(448,plain,
    ! [B: iS,A: iS] :
      ( ( ( sk2 @ ( (=) @ iS @ B ) )
        = c0 )
      | ( ( sk2
          @ ( (=) @ iS
            @ ( sk2
              @ ^ [C: iS] :
                  ( c0
                  = ( sk2 @ ( (=) @ iS @ C ) ) ) ) ) )
        = c0 )
      | ( c0 = A ) ),
    inference(lifteq,[status(thm)],[382]) ).

thf(449,plain,
    ! [B: iS,A: iS] :
      ( ( ( sk2 @ ( (=) @ iS @ B ) )
        = c0 )
      | ( ( sk2
          @ ( (=) @ iS
            @ ( sk2
              @ ^ [C: iS] :
                  ( c0
                  = ( sk2 @ ( (=) @ iS @ C ) ) ) ) ) )
        = c0 )
      | ( c0 = A ) ),
    inference(simp,[status(thm)],[448]) ).

thf(5706,plain,
    ! [B: iS,A: iS] :
      ( ( ( sk2 @ ( (=) @ iS @ B ) )
        = c0 )
      | ( c0 = A )
      | ( ( sk2
          @ ( (=) @ iS
            @ ( sk2
              @ ^ [C: iS] :
                  ( c0
                  = ( sk2 @ ( (=) @ iS @ C ) ) ) ) ) )
       != ( sk2 @ ( (=) @ iS @ B ) ) )
      | ( c0 != c0 ) ),
    inference(eqfactor_ordered,[status(thm)],[449]) ).

thf(5794,plain,
    ! [A: iS] :
      ( ( ( sk2
          @ ( (=) @ iS
            @ ( sk2
              @ ^ [B: iS] :
                  ( c0
                  = ( sk2 @ ( (=) @ iS @ B ) ) ) ) ) )
        = c0 )
      | ( c0 = A ) ),
    inference(pattern_uni,[status(thm)],[5706:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ^ [C: iS] : ( c0 = ( sk2 @ ( (=) @ iS @ C ) ) ) ))]]) ).

thf(6818,plain,
    ! [A: iS] :
      ( ( ( sk2
          @ ( (=) @ iS
            @ ( sk2
              @ ^ [B: iS] :
                  ( c0
                  = ( sk2 @ ( (=) @ iS @ B ) ) ) ) ) )
        = c0 )
      | ( A
       != ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5794,785]) ).

thf(6819,plain,
    ( ( sk2
      @ ( (=) @ iS
        @ ( sk2
          @ ^ [A: iS] :
              ( c0
              = ( sk2 @ ( (=) @ iS @ A ) ) ) ) ) )
    = c0 ),
    inference(pattern_uni,[status(thm)],[6818:[bind(A,$thf( cP @ ( sk1 @ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) ) @ ( sk2 @ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) ) ))]]) ).

thf(43,plain,
    ! [C: iS,B: iS > $o,A: iS] :
      ( ~ ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) )
      | ( B @ C )
      | ( ( cJOIN @ A @ c0 @ A )
       != ( B @ c0 ) ) ),
    inference(paramod_ordered,[status(thm)],[30,18]) ).

thf(74,plain,
    ! [C: iS > iS,B: iS > iS,A: iS] :
      ( ~ ( cJOIN
          @ ( B
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) )
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) )
          @ ( C
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) ) )
      | ( cJOIN @ ( B @ A ) @ A @ ( C @ A ) )
      | ( ( B @ c0 )
       != ( C @ c0 ) ) ),
    inference(pre_uni,[status(thm)],[43:[bind(A,$thf( D @ c0 )),bind(B,$thf( ^ [F: iS] : ( cJOIN @ ( D @ F ) @ F @ ( F @ F ) ) )),bind(C,$thf( C ))]]) ).

thf(76,plain,
    ! [C: iS > iS,B: iS > iS,A: iS] :
      ( ( cJOIN @ ( B @ A ) @ A @ ( C @ A ) )
      | ~ ( cJOIN
          @ ( B
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) )
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) )
          @ ( C
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) ) )
      | ( ( B @ c0 )
       != ( C @ c0 ) ) ),
    inference(pre_uni,[status(thm)],[74:[]]) ).

thf(86,plain,
    ! [C: iS > iS,B: iS > iS,A: iS] :
      ( ( cJOIN @ ( B @ A ) @ A @ ( C @ A ) )
      | ~ ( cJOIN
          @ ( B
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) )
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) )
          @ ( C
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) ) )
      | ( ( B @ c0 )
       != ( C @ c0 ) ) ),
    inference(simp,[status(thm)],[76]) ).

thf(6226,plain,
    ! [C: iS > iS,B: iS > iS,A: iS] :
      ( ~ ( cJOIN
          @ ( B
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) )
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) )
          @ ( C
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) ) )
      | ( ( B @ c0 )
       != ( C @ c0 ) )
      | ( ( cJOIN @ ( B @ A ) @ A @ ( C @ A ) )
       != ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[86,11]) ).

thf(6525,plain,
    ( ~ ( cJOIN
        @ ( cP
          @ ( sk1
            @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
          @ ( sk2
            @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
        @ ( cP
          @ ( sk1
            @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
          @ ( sk2
            @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
        @ ( cP
          @ ( sk1
            @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
          @ ( sk2
            @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) )
    | ( c0 != c0 ) ),
    inference(pre_uni,[status(thm)],[6226:[bind(A,$thf( sk3 )),bind(B,$thf( ^ [D: iS] : D )),bind(C,$thf( ^ [D: iS] : D ))]]) ).

thf(6527,plain,
    ~ ( cJOIN
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[6525:[]]) ).

thf(49,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ~ ( B @ c0 )
      | ~ ~ ( B
            @ ( cP
              @ ( sk1
                @ ^ [C: iS] :
                    ~ ( B @ C ) )
              @ ( sk2
                @ ^ [C: iS] :
                    ~ ( B @ C ) ) ) )
      | ~ ( B @ A ) ),
    inference(prim_subst,[status(thm)],[18:[bind(A,$thf( ^ [D: iS] : ~ ( C @ D ) ))]]) ).

thf(87,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ A )
      | ( B
        @ ( cP
          @ ( sk1
            @ ^ [C: iS] :
                ~ ( B @ C ) )
          @ ( sk2
            @ ^ [C: iS] :
                ~ ( B @ C ) ) ) )
      | ( B @ c0 ) ),
    inference(cnf,[status(esa)],[49]) ).

thf(88,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ A )
      | ( B
        @ ( cP
          @ ( sk1
            @ ^ [C: iS] :
                ~ ( B @ C ) )
          @ ( sk2
            @ ^ [C: iS] :
                ~ ( B @ C ) ) ) )
      | ( B @ c0 ) ),
    inference(simp,[status(thm)],[87]) ).

thf(353,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ~ ( B @ c0 )
      | ~ ( B
          @ ( sk2
            @ ^ [C: iS] :
                ~ ( B @ C ) ) )
      | ~ ( B @ A ) ),
    inference(prim_subst,[status(thm)],[26:[bind(A,$thf( ^ [D: iS] : ~ ( C @ D ) ))]]) ).

thf(434,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ A )
      | ~ ( B
          @ ( sk2
            @ ^ [C: iS] :
                ~ ( B @ C ) ) )
      | ( B @ c0 ) ),
    inference(cnf,[status(esa)],[353]) ).

thf(435,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ A )
      | ~ ( B
          @ ( sk2
            @ ^ [C: iS] :
                ~ ( B @ C ) ) )
      | ( B @ c0 ) ),
    inference(simp,[status(thm)],[434]) ).

thf(850,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ A )
      | ( B @ c0 )
      | ~ ( B
          @ ( sk2
            @ ^ [C: iS] :
                ~ ( B @ C ) ) )
      | ~ ( B @ A ) ),
    inference(eqfactor_ordered,[status(thm)],[435]) ).

thf(871,plain,
    ! [A: iS] :
      ( ( A != A )
      | ( A = c0 )
      | ( A
       != ( sk2
          @ ^ [B: iS] : ( A != B ) ) )
      | ( A != A ) ),
    inference(replace_leibeq,[status(thm)],[850:[bind(A,$thf( A )),bind(B,$thf( (=) @ iS @ A ))]]) ).

thf(886,plain,
    ! [A: iS] :
      ( ( A != A )
      | ( A = c0 )
      | ( A
       != ( sk2
          @ ^ [B: iS] : ( A != B ) ) )
      | ( A != A ) ),
    inference(lifteq,[status(thm)],[871]) ).

thf(994,plain,
    ! [A: iS] :
      ( ( A = c0 )
      | ( A
       != ( sk2
          @ ^ [B: iS] : ( A != B ) ) ) ),
    inference(simp,[status(thm)],[886]) ).

thf(6720,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ ( sk2 @ A ) )
      | ( ( A @ B )
       != ( cJOIN
          @ ( cP
            @ ( sk1
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
            @ ( sk2
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
          @ ( cP
            @ ( sk1
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
            @ ( sk2
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
          @ ( cP
            @ ( sk1
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
            @ ( sk2
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[26,6527]) ).

thf(6737,plain,
    ( ~ ( cJOIN @ c0 @ c0 @ c0 )
    | ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
    inference(pre_uni,[status(thm)],[6720:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ C @ C ) )),bind(B,$thf( cP @ ( sk1 @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) @ ( sk2 @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ))]]) ).

thf(17,plain,
    ! [A: iS] :
      ( ( c0 != c0 )
      | ( c0
        = ( sk1 @ ( (=) @ iS @ c0 ) ) )
      | ( c0 = A ) ),
    inference(replace_leibeq,[status(thm)],[7:[bind(A,$thf( (=) @ iS @ c0 ))]]) ).

thf(28,plain,
    ! [A: iS] :
      ( ( c0 != c0 )
      | ( ( sk1 @ ( (=) @ iS @ c0 ) )
        = c0 )
      | ( c0 = A ) ),
    inference(lifteq,[status(thm)],[17]) ).

thf(29,plain,
    ! [A: iS] :
      ( ( ( sk1 @ ( (=) @ iS @ c0 ) )
        = c0 )
      | ( c0 = A ) ),
    inference(simp,[status(thm)],[28]) ).

thf(6,plain,
    ! [B: iS,A: iS] :
      ( ( cP @ A @ B )
     != c0 ),
    inference(cnf,[status(esa)],[4]) ).

thf(25,plain,
    ! [B: iS,A: iS] :
      ( ( cP @ A @ B )
     != c0 ),
    inference(lifteq,[status(thm)],[6]) ).

thf(110,plain,
    ! [C: iS,B: iS,A: iS] :
      ( ( ( sk1 @ ( (=) @ iS @ c0 ) )
        = c0 )
      | ( A
       != ( cP @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[29,25]) ).

thf(111,plain,
    ( ( sk1 @ ( (=) @ iS @ c0 ) )
    = c0 ),
    inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( cP @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).

thf(44,plain,
    ! [C: iS,B: iS > $o,A: iS] :
      ( ~ ( B @ c0 )
      | ( B @ C )
      | ( ( cJOIN @ A @ c0 @ A )
       != ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,18]) ).

thf(80,plain,
    ! [C: iS > iS,B: iS > iS,A: iS] :
      ( ~ ( cJOIN @ ( B @ c0 ) @ c0 @ ( C @ c0 ) )
      | ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
      | ( ( B
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
       != ( C
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) ) ),
    inference(pre_uni,[status(thm)],[44:[bind(A,$thf( D @ ( cP @ ( sk1 @ ^ [F: iS] : ( cJOIN @ ( D @ F ) @ c0 @ ( F @ F ) ) ) @ ( sk2 @ ^ [F: iS] : ( cJOIN @ ( D @ F ) @ c0 @ ( F @ F ) ) ) ) )),bind(B,$thf( ^ [F: iS] : ( cJOIN @ ( D @ F ) @ c0 @ ( F @ F ) ) )),bind(C,$thf( C ))]]) ).

thf(81,plain,
    ! [C: iS > iS,B: iS > iS,A: iS] :
      ( ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
      | ~ ( cJOIN @ ( B @ c0 ) @ c0 @ ( C @ c0 ) )
      | ( ( B
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
       != ( C
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) ) ),
    inference(pre_uni,[status(thm)],[80:[]]) ).

thf(89,plain,
    ! [C: iS > iS,B: iS > iS,A: iS] :
      ( ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
      | ~ ( cJOIN @ ( B @ c0 ) @ c0 @ ( C @ c0 ) )
      | ( ( B
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
       != ( C
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) ) ),
    inference(simp,[status(thm)],[81]) ).

thf(8238,plain,
    ! [C: iS > iS,B: iS > iS,A: iS] :
      ( ( cJOIN @ ( B @ A ) @ c0 @ c0 )
      | ~ ( cJOIN @ ( B @ c0 ) @ c0 @ ( C @ c0 ) )
      | ( ( B
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
       != ( C
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) )
      | ( ( sk1 @ ( (=) @ iS @ c0 ) )
       != ( C @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[111,89]) ).

thf(8339,plain,
    ! [A: iS > iS] :
      ( ( cJOIN @ ( A @ ( sk1 @ ( (=) @ iS @ c0 ) ) ) @ c0 @ c0 )
      | ~ ( cJOIN @ ( A @ c0 ) @ c0 @ c0 )
      | ( ( A
          @ ( cP
            @ ( sk1
              @ ^ [B: iS] : ( cJOIN @ ( A @ B ) @ c0 @ B ) )
            @ ( sk2
              @ ^ [B: iS] : ( cJOIN @ ( A @ B ) @ c0 @ B ) ) ) )
       != ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ ( A @ B ) @ c0 @ B ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ ( A @ B ) @ c0 @ B ) ) ) ) ),
    inference(pre_uni,[status(thm)],[8238:[bind(A,$thf( sk1 @ ( (=) @ iS @ c0 ) )),bind(B,$thf( B )),bind(C,$thf( ^ [D: iS] : D ))]]) ).

thf(8342,plain,
    ( ~ ( cJOIN @ c0 @ c0 @ c0 )
    | ( cJOIN @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ c0 @ c0 ) ),
    inference(pre_uni,[status(thm)],[8339:[bind(A,$thf( ^ [B: iS] : B ))]]) ).

thf(9255,plain,
    ( ~ $true
    | ( cJOIN @ c0 @ c0 @ c0 ) ),
    inference(rewrite,[status(thm)],[8342,34,111]) ).

thf(9256,plain,
    cJOIN @ c0 @ c0 @ c0,
    inference(simp,[status(thm)],[9255]) ).

thf(13211,plain,
    ( ~ $true
    | ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
    inference(rewrite,[status(thm)],[6737,9256]) ).

thf(13212,plain,
    ( cJOIN
    @ ( sk2
      @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
    @ ( sk2
      @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
    @ ( sk2
      @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ),
    inference(simp,[status(thm)],[13211]) ).

thf(14,plain,
    ! [D: iS,C: iS,B: iS,A: iS] :
      ( ( ( cP @ A @ C )
       != ( cP @ B @ D ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(22,plain,
    ! [D: iS,C: iS,B: iS,A: iS] :
      ( ( ( cP @ A @ C )
       != ( cP @ B @ D ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(23,plain,
    ! [D: iS,C: iS,B: iS,A: iS] :
      ( ( ( cP @ A @ C )
       != ( cP @ B @ D ) )
      | ( A = B ) ),
    inference(simp,[status(thm)],[22]) ).

thf(24,plain,
    ! [B: iS,A: iS] :
      ( ( sk5 @ A @ ( cP @ B @ A ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(cP),[sk5])]) ).

thf(343,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ ( sk2 @ A ) )
      | ( ( A @ B )
       != ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[26,11]) ).

thf(387,plain,
    ( ~ ( cJOIN @ c0 @ sk3 @ sk3 )
    | ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
      @ sk3
      @ sk3 ) ),
    inference(pre_uni,[status(thm)],[343:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).

thf(1086,plain,
    ( ~ $true
    | ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
      @ sk3
      @ sk3 ) ),
    inference(rewrite,[status(thm)],[387,34]) ).

thf(1087,plain,
    ( cJOIN
    @ ( sk2
      @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
    @ sk3
    @ sk3 ),
    inference(simp,[status(thm)],[1086]) ).

thf(10,plain,
    ! [D: iS,C: iS,B: iS,A: iS] :
      ( ( ( cP @ A @ C )
       != ( cP @ B @ D ) )
      | ( C = D ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(19,plain,
    ! [D: iS,C: iS,B: iS,A: iS] :
      ( ( ( cP @ A @ C )
       != ( cP @ B @ D ) )
      | ( C = D ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(20,plain,
    ! [D: iS,C: iS,B: iS,A: iS] :
      ( ( ( cP @ A @ C )
       != ( cP @ B @ D ) )
      | ( C = D ) ),
    inference(simp,[status(thm)],[19]) ).

thf(562,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ ( sk1 @ A ) )
      | ( ( A @ B )
       != ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[31,11]) ).

thf(657,plain,
    ( ~ ( cJOIN @ c0 @ sk3 @ sk3 )
    | ( cJOIN
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
      @ sk3
      @ sk3 ) ),
    inference(pre_uni,[status(thm)],[562:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).

thf(4387,plain,
    ( ~ $true
    | ( cJOIN
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
      @ sk3
      @ sk3 ) ),
    inference(rewrite,[status(thm)],[657,34]) ).

thf(4388,plain,
    ( cJOIN
    @ ( sk1
      @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
    @ sk3
    @ sk3 ),
    inference(simp,[status(thm)],[4387]) ).

thf(4399,plain,
    ( ( cJOIN
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
      @ sk3
      @ sk3 )
   != ( cJOIN
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
      @ sk3
      @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[4388,760]) ).

thf(4447,plain,
    ( ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
     != ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
    | ( sk3 != sk3 )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[4399]) ).

thf(4471,plain,
    ( ( cP
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
   != ( sk1
      @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) ),
    inference(simp,[status(thm)],[4447]) ).

thf(40,plain,
    ! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
      | ( C @ D )
      | ( ( A @ B )
       != ( C @ c0 ) ) ),
    inference(paramod_ordered,[status(thm)],[18,18]) ).

thf(77,plain,
    ! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
      | ( C @ D )
      | ( ( A @ B )
       != ( C @ c0 ) ) ),
    inference(pre_uni,[status(thm)],[40:[]]) ).

thf(78,plain,
    ! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
      ( ( C @ D )
      | ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ~ ( A @ c0 )
      | ( ( A @ B )
       != ( C @ c0 ) ) ),
    inference(pre_uni,[status(thm)],[77:[]]) ).

thf(16,plain,
    ! [A: iS] :
      ( ( c0 != c0 )
      | ( c0
        = ( sk2 @ ( (=) @ iS @ c0 ) ) )
      | ( c0 = A ) ),
    inference(replace_leibeq,[status(thm)],[9:[bind(A,$thf( (=) @ iS @ c0 ))]]) ).

thf(32,plain,
    ! [A: iS] :
      ( ( c0 != c0 )
      | ( ( sk2 @ ( (=) @ iS @ c0 ) )
        = c0 )
      | ( c0 = A ) ),
    inference(lifteq,[status(thm)],[16]) ).

thf(33,plain,
    ! [A: iS] :
      ( ( ( sk2 @ ( (=) @ iS @ c0 ) )
        = c0 )
      | ( c0 = A ) ),
    inference(simp,[status(thm)],[32]) ).

thf(63,plain,
    ( ~ ( cJOIN @ sk3 @ c0 @ sk3 )
    | ~ ( cJOIN @ sk3
        @ ( cP
          @ ( sk1
            @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
          @ ( sk2
            @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
        @ sk3 ) ),
    inference(pre_uni,[status(thm)],[42:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).

thf(103,plain,
    ( ~ $true
    | ~ ( cJOIN @ sk3
        @ ( cP
          @ ( sk1
            @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
          @ ( sk2
            @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
        @ sk3 ) ),
    inference(rewrite,[status(thm)],[63,30]) ).

thf(104,plain,
    ~ ( cJOIN @ sk3
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
      @ sk3 ),
    inference(simp,[status(thm)],[103]) ).

thf(106,plain,
    ! [A: iS] :
      ( ( cJOIN @ A @ c0 @ A )
     != ( cJOIN @ sk3
        @ ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) )
        @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[30,104]) ).

thf(108,plain,
    ! [A: iS] :
      ( ( A != sk3 )
      | ( ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) )
       != c0 )
      | ( A != sk3 ) ),
    inference(simp,[status(thm)],[106]) ).

thf(109,plain,
    ( ( cP
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
   != c0 ),
    inference(simp,[status(thm)],[108]) ).

thf(210,plain,
    ! [A: iS] :
      ( ( ( sk2 @ ( (=) @ iS @ c0 ) )
        = c0 )
      | ( A
       != ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[33,109]) ).

thf(211,plain,
    ( ( sk2 @ ( (=) @ iS @ c0 ) )
    = c0 ),
    inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( cP @ ( sk1 @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) @ ( sk2 @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) ))]]) ).

thf(564,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ ( sk1 @ A ) )
      | ( ( A @ B )
       != ( cJOIN @ sk3
          @ ( cP
            @ ( sk1
              @ ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) )
            @ ( sk2
              @ ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) ) )
          @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[31,104]) ).

thf(637,plain,
    ( ~ ( cJOIN @ sk3 @ c0 @ sk3 )
    | ( cJOIN @ sk3
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
      @ sk3 ) ),
    inference(pre_uni,[status(thm)],[564:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) )),bind(B,$thf( cP @ ( sk1 @ ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) ) @ ( sk2 @ ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) ) ))]]) ).

thf(1841,plain,
    ( ~ $true
    | ( cJOIN @ sk3
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
      @ sk3 ) ),
    inference(rewrite,[status(thm)],[637,30]) ).

thf(1842,plain,
    ( cJOIN @ sk3
    @ ( sk1
      @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
    @ sk3 ),
    inference(simp,[status(thm)],[1841]) ).

thf(171,plain,
    ( ~ ( cJOIN @ sk3
        @ ( cP @ c0
          @ ( sk2
            @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
        @ sk3 )
    | ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[111,104]) ).

thf(173,plain,
    ( ~ ( cJOIN @ sk3
        @ ( cP @ c0
          @ ( sk2
            @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
        @ sk3 )
    | ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[171]) ).

thf(317,plain,
    ( ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
    | ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[211,173]) ).

thf(322,plain,
    ( ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
    | ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[317]) ).

thf(327,plain,
    ( ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
    | ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[322]) ).

thf(524,plain,
    ( ( ( cJOIN @ sk3 @ sk7 @ sk3 )
     != ( c0 = sk7 ) )
    | ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ),
    inference(func_ext,[status(esa)],[327]) ).

thf(4248,plain,
    ( ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
    | ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
    | ( c0 != sk7 ) ),
    inference(bool_ext,[status(thm)],[524]) ).

thf(4308,plain,
    ( ( sk7 != c0 )
    | ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
    | ~ ( cJOIN @ sk3 @ sk7 @ sk3 ) ),
    inference(lifteq,[status(thm)],[4248]) ).

thf(4489,plain,
    ! [A: iS] :
      ( ( sk7 != c0 )
      | ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
      | ( ( cJOIN @ A @ c0 @ A )
       != ( cJOIN @ sk3 @ sk7 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[30,4308]) ).

thf(4586,plain,
    ! [A: iS] :
      ( ( sk7 != c0 )
      | ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
      | ( A != sk3 )
      | ( sk7 != c0 )
      | ( A != sk3 ) ),
    inference(simp,[status(thm)],[4489]) ).

thf(4639,plain,
    ( ( sk7 != c0 )
    | ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ),
    inference(simp,[status(thm)],[4586]) ).

thf(4657,plain,
    ( ( sk7 != c0 )
    | ( ( cJOIN @ sk3
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
        @ sk3 )
     != ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[1842,4639]) ).

thf(4687,plain,
    ( ( sk7 != c0 )
    | ( sk3 != sk3 )
    | ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( cP @ c0 @ c0 ) )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[4657]) ).

thf(4724,plain,
    ( ( sk7 != c0 )
    | ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( cP @ c0 @ c0 ) ) ),
    inference(simp,[status(thm)],[4687]) ).

thf(386,plain,
    ( ~ ( cJOIN @ sk3 @ c0 @ sk3 )
    | ( cJOIN @ sk3
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
      @ sk3 ) ),
    inference(pre_uni,[status(thm)],[343:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).

thf(793,plain,
    ( ~ $true
    | ( cJOIN @ sk3
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
      @ sk3 ) ),
    inference(rewrite,[status(thm)],[386,30]) ).

thf(794,plain,
    ( cJOIN @ sk3
    @ ( sk2
      @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
    @ sk3 ),
    inference(simp,[status(thm)],[793]) ).

thf(803,plain,
    ( ( cJOIN @ sk3
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
      @ sk3 )
   != ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[794,11]) ).

thf(814,plain,
    ( ( sk3 != sk3 )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != sk3 )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[803]) ).

thf(821,plain,
    ( ( sk2
      @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
   != sk3 ),
    inference(simp,[status(thm)],[814]) ).

thf(1864,plain,
    ( ( cJOIN @ sk3
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
      @ sk3 )
   != ( cJOIN @ sk3
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
      @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[1842,104]) ).

thf(1883,plain,
    ( ( sk3 != sk3 )
    | ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
     != ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[1864]) ).

thf(1896,plain,
    ( ( cP
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
   != ( sk1
      @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) ),
    inference(simp,[status(thm)],[1883]) ).

thf(13227,plain,
    ( ( cJOIN
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) )
   != ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13212,6527]) ).

thf(13304,plain,
    ( ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
    | ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
    | ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
    inference(simp,[status(thm)],[13227]) ).

thf(13340,plain,
    ( ( cP
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
   != ( sk2
      @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ),
    inference(simp,[status(thm)],[13304]) ).

thf(13349,plain,
    ( ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ c0 )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[211,13340]) ).

thf(13352,plain,
    ( ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ c0 )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[13349]) ).

thf(73,plain,
    ! [C: iS > iS,B: iS > iS,A: iS] :
      ( ~ ( cJOIN
          @ ( B
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
          @ c0
          @ ( C
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) )
      | ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
      | ( ( B @ c0 )
       != ( C @ c0 ) ) ),
    inference(pre_uni,[status(thm)],[43:[bind(A,$thf( D @ c0 )),bind(B,$thf( ^ [F: iS] : ( cJOIN @ ( D @ F ) @ c0 @ ( F @ F ) ) )),bind(C,$thf( C ))]]) ).

thf(75,plain,
    ! [C: iS > iS,B: iS > iS,A: iS] :
      ( ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
      | ~ ( cJOIN
          @ ( B
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
          @ c0
          @ ( C
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) )
      | ( ( B @ c0 )
       != ( C @ c0 ) ) ),
    inference(pre_uni,[status(thm)],[73:[]]) ).

thf(85,plain,
    ! [C: iS > iS,B: iS > iS,A: iS] :
      ( ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
      | ~ ( cJOIN
          @ ( B
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
          @ c0
          @ ( C
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) )
      | ( ( B @ c0 )
       != ( C @ c0 ) ) ),
    inference(simp,[status(thm)],[75]) ).

thf(6675,plain,
    ! [A: iS] :
      ( ( cJOIN @ c0 @ A @ A )
     != ( cJOIN
        @ ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) )
        @ ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) )
        @ ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[34,6527]) ).

thf(6747,plain,
    ! [A: iS] :
      ( ( ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) )
       != c0 )
      | ( A
       != ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) ) )
      | ( A
       != ( cP
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) ) ) ),
    inference(simp,[status(thm)],[6675]) ).

thf(6773,plain,
    ( ( cP
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
   != c0 ),
    inference(simp,[status(thm)],[6747]) ).

thf(21,plain,
    ! [B: iS,A: iS] :
      ( ( sk4 @ A @ ( cP @ A @ B ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(cP),[sk4])]) ).

thf(65,plain,
    ( ~ ( cJOIN @ c0 @ c0 @ sk3 )
    | ~ ( cJOIN
        @ ( cP
          @ ( sk1
            @ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
          @ ( sk2
            @ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) ) )
        @ ( cP
          @ ( sk1
            @ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
          @ ( sk2
            @ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) ) )
        @ sk3 ) ),
    inference(pre_uni,[status(thm)],[42:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).

thf(53,plain,
    ! [C: iS > $o,B: iS > $o,A: iS] :
      ( ~ ( ( B @ c0 )
          | ( C @ c0 ) )
      | ~ ( ( B
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] :
                    ( ( B @ D )
                    | ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] :
                    ( ( B @ D )
                    | ( C @ D ) ) ) ) )
          | ( C
            @ ( cP
              @ ( sk1
                @ ^ [D: iS] :
                    ( ( B @ D )
                    | ( C @ D ) ) )
              @ ( sk2
                @ ^ [D: iS] :
                    ( ( B @ D )
                    | ( C @ D ) ) ) ) ) )
      | ( B @ A )
      | ( C @ A ) ),
    inference(prim_subst,[status(thm)],[18:[bind(A,$thf( ^ [E: iS] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).

thf(93,plain,
    ! [C: iS > $o,B: iS > $o,A: iS] :
      ( ( B @ A )
      | ( C @ A )
      | ~ ( C
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) ) ) )
      | ~ ( C @ c0 ) ),
    inference(cnf,[status(esa)],[53]) ).

thf(97,plain,
    ! [C: iS > $o,B: iS > $o,A: iS] :
      ( ( B @ A )
      | ( C @ A )
      | ~ ( C
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) ) ) )
      | ~ ( C @ c0 ) ),
    inference(simp,[status(thm)],[93]) ).

thf(15663,plain,
    ( ( ( cP @ c0 @ c0 )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[111,13352]) ).

thf(15664,plain,
    ( ( ( cP @ c0 @ c0 )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[15663]) ).

thf(15665,plain,
    ( ( ( cP @ c0 @ c0 )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[15664]) ).

thf(6677,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ ( sk1 @ A ) )
      | ( ( A @ B )
       != ( cJOIN
          @ ( cP
            @ ( sk1
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
            @ ( sk2
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
          @ ( cP
            @ ( sk1
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
            @ ( sk2
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
          @ ( cP
            @ ( sk1
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
            @ ( sk2
              @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[31,6527]) ).

thf(6753,plain,
    ( ~ ( cJOIN @ c0 @ c0 @ c0 )
    | ( cJOIN
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
    inference(pre_uni,[status(thm)],[6677:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ C @ C ) )),bind(B,$thf( cP @ ( sk1 @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) @ ( sk2 @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ))]]) ).

thf(16523,plain,
    ( ~ $true
    | ( cJOIN
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
    inference(rewrite,[status(thm)],[6753,9256]) ).

thf(16524,plain,
    ( cJOIN
    @ ( sk1
      @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
    @ ( sk1
      @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
    @ ( sk1
      @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ),
    inference(simp,[status(thm)],[16523]) ).

thf(16534,plain,
    ( ( cJOIN
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) )
   != ( cJOIN
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[16524,6527]) ).

thf(16624,plain,
    ( ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
     != ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
    | ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
     != ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
    | ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
     != ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
    inference(simp,[status(thm)],[16534]) ).

thf(16652,plain,
    ( ( cP
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
   != ( sk1
      @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ),
    inference(simp,[status(thm)],[16624]) ).

thf(587,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ~ ( B @ c0 )
      | ~ ( B
          @ ( sk1
            @ ^ [C: iS] :
                ~ ( B @ C ) ) )
      | ~ ( B @ A ) ),
    inference(prim_subst,[status(thm)],[31:[bind(A,$thf( ^ [D: iS] : ~ ( C @ D ) ))]]) ).

thf(717,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ A )
      | ~ ( B
          @ ( sk1
            @ ^ [C: iS] :
                ~ ( B @ C ) ) )
      | ( B @ c0 ) ),
    inference(cnf,[status(esa)],[587]) ).

thf(718,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ A )
      | ~ ( B
          @ ( sk1
            @ ^ [C: iS] :
                ~ ( B @ C ) ) )
      | ( B @ c0 ) ),
    inference(simp,[status(thm)],[717]) ).

thf(1163,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ~ ( B @ A )
      | ~ ~ ( B
            @ ( sk1
              @ ^ [C: iS] :
                  ~ ~ ( B @ C ) ) )
      | ~ ( B @ c0 ) ),
    inference(prim_subst,[status(thm)],[718:[bind(A,$thf( A )),bind(B,$thf( ^ [D: iS] : ~ ( C @ D ) ))]]) ).

thf(1258,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ c0 )
      | ( B
        @ ( sk1
          @ ^ [C: iS] :
              ~ ~ ( B @ C ) ) )
      | ( B @ A ) ),
    inference(cnf,[status(esa)],[1163]) ).

thf(1259,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ c0 )
      | ( B @ ( sk1 @ B ) )
      | ( B @ A ) ),
    inference(simp,[status(thm)],[1258]) ).

thf(854,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ~ ( B @ A )
      | ~ ~ ( B
            @ ( sk2
              @ ^ [C: iS] :
                  ~ ~ ( B @ C ) ) )
      | ~ ( B @ c0 ) ),
    inference(prim_subst,[status(thm)],[435:[bind(A,$thf( A )),bind(B,$thf( ^ [D: iS] : ~ ( C @ D ) ))]]) ).

thf(983,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ c0 )
      | ( B
        @ ( sk2
          @ ^ [C: iS] :
              ~ ~ ( B @ C ) ) )
      | ( B @ A ) ),
    inference(cnf,[status(esa)],[854]) ).

thf(984,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ c0 )
      | ( B @ ( sk2 @ B ) )
      | ( B @ A ) ),
    inference(simp,[status(thm)],[983]) ).

thf(9278,plain,
    ! [B: iS > $o,A: iS] :
      ( ( B @ ( sk2 @ B ) )
      | ( B @ A )
      | ( ( cJOIN @ c0 @ c0 @ c0 )
       != ( B @ c0 ) ) ),
    inference(paramod_ordered,[status(thm)],[9256,984]) ).

thf(9373,plain,
    ! [A: iS] :
      ( ( cJOIN
        @ ( sk2
          @ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) )
        @ c0
        @ c0 )
      | ( cJOIN @ A @ c0 @ c0 ) ),
    inference(pre_uni,[status(thm)],[9278:[bind(A,$thf( A )),bind(B,$thf( ^ [C: iS] : ( cJOIN @ C @ c0 @ c0 ) ))]]) ).

thf(15126,plain,
    ! [A: iS] :
      ( ( cJOIN
        @ ( sk2
          @ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) )
        @ c0
        @ c0 )
      | ( ( cJOIN @ A @ c0 @ c0 )
       != ( cJOIN
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) )
          @ c0
          @ c0 ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[9373]) ).

thf(15248,plain,
    ( cJOIN
    @ ( sk2
      @ ^ [A: iS] : ( cJOIN @ A @ c0 @ c0 ) )
    @ c0
    @ c0 ),
    inference(pattern_uni,[status(thm)],[15126:[bind(A,$thf( sk2 @ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) ))]]) ).

thf(4516,plain,
    ( ( sk7 != c0 )
    | ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
    | ( ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
     != ( cJOIN @ sk3 @ sk7 @ sk3 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[4308]) ).

thf(4607,plain,
    ( ( sk7 != c0 )
    | ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
    | ( sk3 != sk3 )
    | ( ( cP @ c0 @ c0 )
     != sk7 )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[4516]) ).

thf(4645,plain,
    ( ( sk7 != c0 )
    | ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
    | ( ( cP @ c0 @ c0 )
     != sk7 ) ),
    inference(simp,[status(thm)],[4607]) ).

thf(6030,plain,
    ! [A: iS] :
      ( ( sk7 != c0 )
      | ( ( cP @ c0 @ c0 )
       != sk7 )
      | ( ( cJOIN @ A @ c0 @ A )
       != ( cJOIN @ sk3 @ sk7 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[30,4645]) ).

thf(6077,plain,
    ! [A: iS] :
      ( ( sk7 != c0 )
      | ( ( cP @ c0 @ c0 )
       != sk7 )
      | ( A != sk3 )
      | ( sk7 != c0 )
      | ( A != sk3 ) ),
    inference(simp,[status(thm)],[6030]) ).

thf(6116,plain,
    ( ( sk7 != c0 )
    | ( ( cP @ c0 @ c0 )
     != sk7 ) ),
    inference(simp,[status(thm)],[6077]) ).

thf(92,plain,
    ! [C: iS > $o,B: iS > $o,A: iS] :
      ( ( B @ A )
      | ( C @ A )
      | ~ ( B
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) ) ) )
      | ~ ( B @ c0 ) ),
    inference(cnf,[status(esa)],[53]) ).

thf(96,plain,
    ! [C: iS > $o,B: iS > $o,A: iS] :
      ( ( B @ A )
      | ( C @ A )
      | ~ ( B
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) ) ) )
      | ~ ( B @ c0 ) ),
    inference(simp,[status(thm)],[92]) ).

thf(57,plain,
    ! [B: iS,A: iS] :
      ( ( c0 != c0 )
      | ( c0 = B )
      | ( ( cJOIN @ A @ c0 @ A )
       != ( c0
          = ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
    inference(replace_leibeq,[status(thm)],[44:[bind(A,$thf( A )),bind(B,$thf( (=) @ iS @ c0 ))]]) ).

thf(59,plain,
    ! [B: iS,A: iS] :
      ( ( c0 != c0 )
      | ( c0 = B )
      | ( ( cJOIN @ A @ c0 @ A )
       != ( c0
          = ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
    inference(lifteq,[status(thm)],[57]) ).

thf(100,plain,
    ! [B: iS,A: iS] :
      ( ( c0 = B )
      | ( ( cJOIN @ A @ c0 @ A )
       != ( c0
          = ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
    inference(simp,[status(thm)],[59]) ).

thf(13603,plain,
    ! [B: iS,A: iS] :
      ( ( c0 = B )
      | ( ( cJOIN @ A @ c0 @ A )
       != ( c0
          = ( cP @ c0 @ c0 ) ) ) ),
    inference(rewrite,[status(thm)],[100,211,111]) ).

thf(13606,plain,
    ! [B: iS,A: iS] :
      ( ( ( cJOIN @ A @ c0 @ A )
       != ( c0
          = ( cP @ c0 @ c0 ) ) )
      | ( B
       != ( cP
          @ ( sk1
            @ ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) )
          @ ( sk2
            @ ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13603,785]) ).

thf(13607,plain,
    ! [A: iS] :
      ( ( cJOIN @ A @ c0 @ A )
     != ( c0
        = ( cP @ c0 @ c0 ) ) ),
    inference(pattern_uni,[status(thm)],[13606:[bind(A,$thf( A )),bind(B,$thf( cP @ ( sk1 @ ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) ) @ ( sk2 @ ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) ) ))]]) ).

thf(9258,plain,
    ! [B: iS > $o,A: iS] :
      ( ( B @ ( sk1 @ B ) )
      | ( B @ A )
      | ( ( cJOIN @ c0 @ c0 @ c0 )
       != ( B @ c0 ) ) ),
    inference(paramod_ordered,[status(thm)],[9256,1259]) ).

thf(9408,plain,
    ! [A: iS] :
      ( ( cJOIN @ c0
        @ ( sk1
          @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
        @ c0 )
      | ( cJOIN @ c0 @ A @ c0 ) ),
    inference(pre_uni,[status(thm)],[9258:[bind(A,$thf( A )),bind(B,$thf( ^ [C: iS] : ( cJOIN @ c0 @ C @ c0 ) ))]]) ).

thf(15991,plain,
    ! [A: iS] :
      ( ( cJOIN @ c0
        @ ( sk1
          @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
        @ c0 )
      | ( ( cJOIN @ c0 @ A @ c0 )
       != ( cJOIN @ c0
          @ ( sk1
            @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
          @ c0 ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[9408]) ).

thf(16115,plain,
    ( cJOIN @ c0
    @ ( sk1
      @ ^ [A: iS] : ( cJOIN @ c0 @ A @ c0 ) )
    @ c0 ),
    inference(pattern_uni,[status(thm)],[15991:[bind(A,$thf( sk1 @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) ))]]) ).

thf(1845,plain,
    ( ( cJOIN @ sk3
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
      @ sk3 )
   != ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[1842,11]) ).

thf(1882,plain,
    ( ( sk3 != sk3 )
    | ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != sk3 )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[1845]) ).

thf(1895,plain,
    ( ( sk1
      @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
   != sk3 ),
    inference(simp,[status(thm)],[1882]) ).

thf(13261,plain,
    ( ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
   != ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[13212,11]) ).

thf(13319,plain,
    ( ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != sk3 )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != sk3 )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != sk3 ) ),
    inference(simp,[status(thm)],[13261]) ).

thf(13326,plain,
    ( ( sk2
      @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
   != sk3 ),
    inference(simp,[status(thm)],[13319]) ).

thf(804,plain,
    ( ( cJOIN @ sk3
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
      @ sk3 )
   != ( cJOIN @ sk3
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
      @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[794,104]) ).

thf(812,plain,
    ( ( sk3 != sk3 )
    | ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[804]) ).

thf(819,plain,
    ( ( cP
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
   != ( sk2
      @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) ),
    inference(simp,[status(thm)],[812]) ).

thf(1091,plain,
    ( ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
      @ sk3
      @ sk3 )
   != ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[1087,11]) ).

thf(1112,plain,
    ( ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
     != sk3 )
    | ( sk3 != sk3 )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[1091]) ).

thf(1124,plain,
    ( ( sk2
      @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
   != sk3 ),
    inference(simp,[status(thm)],[1112]) ).

thf(13,plain,
    ! [F: iS,E: iS,D: iS,C: iS,B: iS,A: iS] :
      ( ~ ( cJOIN @ A @ B @ C )
      | ~ ( cJOIN @ D @ E @ F )
      | ( cJOIN @ ( cP @ A @ D ) @ ( cP @ B @ E ) @ ( cP @ C @ F ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(27,plain,
    ! [F: iS,E: iS,D: iS,C: iS,B: iS,A: iS] :
      ( ~ ( cJOIN @ A @ B @ C )
      | ~ ( cJOIN @ D @ E @ F )
      | ( cJOIN @ ( cP @ A @ D ) @ ( cP @ B @ E ) @ ( cP @ C @ F ) ) ),
    inference(simp,[status(thm)],[13]) ).

thf(45,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ B )
      | ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
       != ( A @ c0 ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[18]) ).

thf(70,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ( A @ B )
      | ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
       != ( A @ c0 ) ) ),
    inference(pre_uni,[status(thm)],[45:[]]) ).

thf(71,plain,
    ! [B: iS,A: iS > $o] :
      ( ( A @ B )
      | ~ ( A @ c0 )
      | ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
       != ( A @ c0 ) ) ),
    inference(pre_uni,[status(thm)],[70:[]]) ).

thf(1161,plain,
    ! [B: iS > $o,A: iS] :
      ( ~ ( B @ A )
      | ( B @ c0 )
      | ~ ( B
          @ ( sk1
            @ ^ [C: iS] :
                ~ ( B @ C ) ) )
      | ~ ( B @ A ) ),
    inference(eqfactor_ordered,[status(thm)],[718]) ).

thf(1173,plain,
    ! [A: iS] :
      ( ( A != A )
      | ( A = c0 )
      | ( A
       != ( sk1
          @ ^ [B: iS] : ( A != B ) ) )
      | ( A != A ) ),
    inference(replace_leibeq,[status(thm)],[1161:[bind(A,$thf( A )),bind(B,$thf( (=) @ iS @ A ))]]) ).

thf(1188,plain,
    ! [A: iS] :
      ( ( A != A )
      | ( A = c0 )
      | ( A
       != ( sk1
          @ ^ [B: iS] : ( A != B ) ) )
      | ( A != A ) ),
    inference(lifteq,[status(thm)],[1173]) ).

thf(1271,plain,
    ! [A: iS] :
      ( ( A = c0 )
      | ( A
       != ( sk1
          @ ^ [B: iS] : ( A != B ) ) ) ),
    inference(simp,[status(thm)],[1188]) ).

thf(16589,plain,
    ( ( cJOIN
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ c0 )
    | ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[111,16524]) ).

thf(16632,plain,
    ( ( cJOIN
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ c0 )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[16589]) ).

thf(1863,plain,
    ( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( cJOIN @ sk3
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
        @ sk3 )
     != ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[1842,327]) ).

thf(1879,plain,
    ( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( (=) @ iS @ c0 ) )
    | ( sk3 != sk3 )
    | ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( cP @ c0 @ c0 ) )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[1863]) ).

thf(1894,plain,
    ( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( cP @ c0 @ c0 ) ) ),
    inference(simp,[status(thm)],[1879]) ).

thf(13234,plain,
    ( ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ c0 )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[211,13212]) ).

thf(13303,plain,
    ( ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ c0 )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[13234]) ).

thf(13375,plain,
    ( ( cJOIN @ c0
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ c0 )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[211,13303]) ).

thf(13455,plain,
    ( ( cJOIN @ c0
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ c0 )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[13375]) ).

thf(13467,plain,
    ( ( cJOIN @ c0
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ c0 )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[13455]) ).

thf(13376,plain,
    ( ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ c0
      @ c0 )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[211,13303]) ).

thf(13450,plain,
    ( ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ c0
      @ c0 )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[13376]) ).

thf(13464,plain,
    ( ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ c0
      @ c0 )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[13450]) ).

thf(37,plain,
    ! [A: iS] :
      ( ( cJOIN @ A @ c0 @ A )
     != ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[30,11]) ).

thf(38,plain,
    ! [A: iS] :
      ( ( A != sk3 )
      | ( sk3 != c0 )
      | ( A != sk3 ) ),
    inference(simp,[status(thm)],[37]) ).

thf(39,plain,
    sk3 != c0,
    inference(simp,[status(thm)],[38]) ).

thf(94,plain,
    ! [C: iS > $o,B: iS > $o,A: iS] :
      ( ( B @ A )
      | ( C @ A )
      | ~ ( C
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) ) ) )
      | ~ ( B @ c0 ) ),
    inference(cnf,[status(esa)],[53]) ).

thf(98,plain,
    ! [C: iS > $o,B: iS > $o,A: iS] :
      ( ( B @ A )
      | ( C @ A )
      | ~ ( C
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) ) ) )
      | ~ ( B @ c0 ) ),
    inference(simp,[status(thm)],[94]) ).

thf(9372,plain,
    ! [A: iS] :
      ( ( cJOIN @ c0
        @ ( sk2
          @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
        @ c0 )
      | ( cJOIN @ c0 @ A @ c0 ) ),
    inference(pre_uni,[status(thm)],[9278:[bind(A,$thf( A )),bind(B,$thf( ^ [C: iS] : ( cJOIN @ c0 @ C @ c0 ) ))]]) ).

thf(11978,plain,
    ! [A: iS] :
      ( ( cJOIN @ c0
        @ ( sk2
          @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
        @ c0 )
      | ( ( cJOIN @ c0 @ A @ c0 )
       != ( cJOIN @ c0
          @ ( sk2
            @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
          @ c0 ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[9372]) ).

thf(12135,plain,
    ( cJOIN @ c0
    @ ( sk2
      @ ^ [A: iS] : ( cJOIN @ c0 @ A @ c0 ) )
    @ c0 ),
    inference(pattern_uni,[status(thm)],[11978:[bind(A,$thf( sk2 @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) ))]]) ).

thf(807,plain,
    ( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( cJOIN @ sk3
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
        @ sk3 )
     != ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[794,327]) ).

thf(815,plain,
    ( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( (=) @ iS @ c0 ) )
    | ( sk3 != sk3 )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( cP @ c0 @ c0 ) )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[807]) ).

thf(823,plain,
    ( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( (=) @ iS @ c0 ) )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( cP @ c0 @ c0 ) ) ),
    inference(simp,[status(thm)],[815]) ).

thf(14905,plain,
    ! [B: iS,A: iS] :
      ( ( c0
       != ( cP @ c0 @ c0 ) )
      | ( ( cJOIN @ c0 @ A @ A )
       != ( cJOIN @ B @ c0 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[34,13607]) ).

thf(14906,plain,
    ( c0
   != ( cP @ c0 @ c0 ) ),
    inference(pattern_uni,[status(thm)],[14905:[bind(A,$thf( c0 )),bind(B,$thf( c0 ))]]) ).

thf(14934,plain,
    ( ( cP @ c0 @ c0 )
   != c0 ),
    inference(lifteq,[status(thm)],[14906]) ).

thf(91,plain,
    ! [C: iS > $o,B: iS > $o,A: iS] :
      ( ( B @ A )
      | ( C @ A )
      | ~ ( B
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) ) ) )
      | ~ ( C @ c0 ) ),
    inference(cnf,[status(esa)],[53]) ).

thf(95,plain,
    ! [C: iS > $o,B: iS > $o,A: iS] :
      ( ( B @ A )
      | ( C @ A )
      | ~ ( B
          @ ( cP
            @ ( sk1
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) )
            @ ( sk2
              @ ^ [D: iS] :
                  ( ( B @ D )
                  | ( C @ D ) ) ) ) )
      | ~ ( C @ c0 ) ),
    inference(simp,[status(thm)],[91]) ).

thf(4419,plain,
    ( ( cJOIN
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
      @ sk3
      @ sk3 )
   != ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[4388,11]) ).

thf(4445,plain,
    ( ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
     != sk3 )
    | ( sk3 != sk3 )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[4419]) ).

thf(4469,plain,
    ( ( sk1
      @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
   != sk3 ),
    inference(simp,[status(thm)],[4445]) ).

thf(48,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ( ( A @ B )
       != ( ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[18]) ).

thf(72,plain,
    ! [B: iS,A: iS > $o] :
      ( ~ ( A @ c0 )
      | ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
      | ( ( A @ B )
       != ( ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ) ) ),
    inference(simp,[status(thm)],[48]) ).

thf(1088,plain,
    ( ( cJOIN
      @ ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
      @ sk3
      @ sk3 )
   != ( cJOIN
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
      @ sk3
      @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[1087,760]) ).

thf(1115,plain,
    ( ( ( cP
        @ ( sk1
          @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
    | ( sk3 != sk3 )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[1088]) ).

thf(1126,plain,
    ( ( cP
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
      @ ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
   != ( sk2
      @ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) ),
    inference(simp,[status(thm)],[1115]) ).

thf(4660,plain,
    ( ( sk7 != c0 )
    | ( ( cJOIN @ sk3
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
        @ sk3 )
     != ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[794,4639]) ).

thf(4685,plain,
    ( ( sk7 != c0 )
    | ( sk3 != sk3 )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( cP @ c0 @ c0 ) )
    | ( sk3 != sk3 ) ),
    inference(simp,[status(thm)],[4660]) ).

thf(4723,plain,
    ( ( sk7 != c0 )
    | ( ( sk2
        @ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
     != ( cP @ c0 @ c0 ) ) ),
    inference(simp,[status(thm)],[4685]) ).

thf(50,plain,
    ! [D: iS > iS,C: iS > iS,B: iS > iS,A: iS] :
      ( ~ ( cJOIN @ ( B @ c0 ) @ ( C @ c0 ) @ ( D @ c0 ) )
      | ~ ( cJOIN
          @ ( B
            @ ( cP
              @ ( sk1
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
              @ ( sk2
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) )
          @ ( C
            @ ( cP
              @ ( sk1
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
              @ ( sk2
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) )
          @ ( D
            @ ( cP
              @ ( sk1
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
              @ ( sk2
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) ) )
      | ( cJOIN @ ( B @ A ) @ ( C @ A ) @ ( D @ A ) ) ),
    inference(prim_subst,[status(thm)],[18:[bind(A,$thf( ^ [F: iS] : ( cJOIN @ ( C @ F ) @ ( D @ F ) @ ( E @ F ) ) ))]]) ).

thf(90,plain,
    ! [D: iS > iS,C: iS > iS,B: iS > iS,A: iS] :
      ( ~ ( cJOIN @ ( B @ c0 ) @ ( C @ c0 ) @ ( D @ c0 ) )
      | ~ ( cJOIN
          @ ( B
            @ ( cP
              @ ( sk1
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
              @ ( sk2
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) )
          @ ( C
            @ ( cP
              @ ( sk1
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
              @ ( sk2
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) )
          @ ( D
            @ ( cP
              @ ( sk1
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
              @ ( sk2
                @ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) ) )
      | ( cJOIN @ ( B @ A ) @ ( C @ A ) @ ( D @ A ) ) ),
    inference(simp,[status(thm)],[50]) ).

thf(16575,plain,
    ( ( cJOIN
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
      @ ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
   != ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[16524,11]) ).

thf(16634,plain,
    ( ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != sk3 )
    | ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != sk3 )
    | ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != sk3 ) ),
    inference(simp,[status(thm)],[16575]) ).

thf(16659,plain,
    ( ( sk1
      @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
   != sk3 ),
    inference(simp,[status(thm)],[16634]) ).

thf(13350,plain,
    ( ( ( cP @ c0
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
    | ( ( sk1
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[111,13340]) ).

thf(13353,plain,
    ( ( ( cP @ c0
        @ ( sk2
          @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
     != ( sk2
        @ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
    | ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
     != ( (=) @ iS @ c0 ) ) ),
    inference(simp,[status(thm)],[13350]) ).

thf(21443,plain,
    $false,
    inference(cvc4,[status(thm)],[785,31,30,79,69,760,6819,6527,88,994,13212,24,25,1087,20,4471,78,211,4724,821,1896,89,13352,85,6773,21,65,435,97,15665,16652,1259,15248,109,6116,96,1842,16524,13607,13340,984,173,16115,1895,794,9256,13326,718,13603,34,819,1124,27,71,1271,86,16632,1894,13467,13464,39,98,4388,12135,3,823,14934,18,95,327,4469,11,72,4639,524,1126,104,13303,26,23,4723,90,111,16659,13353]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEV190^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n022.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 18:49:54 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.94/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.13/0.97  % [INFO] 	 Parsing done (106ms). 
% 1.13/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.62/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.62/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 1.62/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.96/1.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.96/1.29  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.96/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.96/1.30  % [INFO] 	 Type checking passed. 
% 1.96/1.30  % [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 ... 
% 111.61/22.24  % External prover 'cvc4' found a proof!
% 111.61/22.24  % [INFO] 	 Killing All external provers ... 
% 111.61/22.24  % Time passed: 21720ms (effective reasoning time: 21257ms)
% 111.61/22.24  % 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)>
% 111.61/22.25  % Axioms used in derivation (0): 
% 111.61/22.25  % No. of inferences in proof: 259
% 111.61/22.25  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21720 ms resp. 21257 ms w/o parsing
% 112.05/22.36  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 112.05/22.37  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------