TSTP Solution File: SYO224^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO224^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 08:56:10 EDT 2024

% Result   : Theorem 47.09s 8.73s
% Output   : Refutation 47.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   38
%            Number of leaves      :   11
% Syntax   : Number of formulae    :  266 (   5 unt;  10 typ;   0 def)
%            Number of atoms       : 1077 ( 276 equ;   0 cnn)
%            Maximal formula atoms :    9 (   4 avg)
%            Number of connectives : 2127 ( 398   ~; 505   |;  84   &;1131   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   49 (  49   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :  247 ( 135   ^  86   !;  26   ?; 247   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cJ_type,type,
    cJ: $i ).

thf(cLIKE_type,type,
    cLIKE: $i > $i > $o ).

thf(cWRH_type,type,
    cWRH: $i > $o ).

thf(cW_type,type,
    cW: $i > $o ).

thf(cUNIQUE_type,type,
    cUNIQUE: $i > $o ).

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

thf(cP_type,type,
    cP: $i ).

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

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

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

thf(1,conjecture,
    ( ( ! [A: $i] :
          ( ( cUNIQUE @ A )
         => ! [B: $i] :
              ( ( ( cWRH @ B )
                & ( cW @ B ) )
             => ( A = B ) ) )
      & ( cUNIQUE @ cS )
      & ( cW @ cS )
      & ( cWRH @ cS ) )
   => ? [A: $i > $o] :
        ( ( ( A @ cP )
          = ( cLIKE @ cP @ cS ) )
        & ( ( A @ cJ )
          = ( ? [B: $i] :
                ( ( cUNIQUE @ B )
                & ( cW @ B )
                & ( cWRH @ B )
                & ( cLIKE @ cJ @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cLING1) ).

thf(2,negated_conjecture,
    ~ ( ( ! [A: $i] :
            ( ( cUNIQUE @ A )
           => ! [B: $i] :
                ( ( ( cWRH @ B )
                  & ( cW @ B ) )
               => ( A = B ) ) )
        & ( cUNIQUE @ cS )
        & ( cW @ cS )
        & ( cWRH @ cS ) )
     => ? [A: $i > $o] :
          ( ( ( A @ cP )
            = ( cLIKE @ cP @ cS ) )
          & ( ( A @ cJ )
            = ( ? [B: $i] :
                  ( ( cUNIQUE @ B )
                  & ( cW @ B )
                  & ( cWRH @ B )
                  & ( cLIKE @ cJ @ B ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ! [A: $i] :
            ( ( cUNIQUE @ A )
           => ! [B: $i] :
                ( ( ( cWRH @ B )
                  & ( cW @ B ) )
               => ( A = B ) ) )
        & ( cUNIQUE @ cS )
        & ( cW @ cS )
        & ( cWRH @ cS ) )
     => ? [A: $i > $o] :
          ( ( ( A @ cP )
            = ( cLIKE @ cP @ cS ) )
          & ( ( A @ cJ )
            = ( ? [B: $i] :
                  ( ( cUNIQUE @ B )
                  & ( cW @ B )
                  & ( cWRH @ B )
                  & ( cLIKE @ cJ @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    cWRH @ cS,
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [A: $i > $o] :
      ( ( ( A @ cP )
       != ( cLIKE @ cP @ cS ) )
      | ( ( A @ cJ )
       != ( ? [B: $i] :
              ( ( cUNIQUE @ B )
              & ( cW @ B )
              & ( cWRH @ B )
              & ( cLIKE @ cJ @ B ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [A: $i > $o] :
      ( ( ( A @ cP )
       != ( cLIKE @ cP @ cS ) )
      | ( ( A @ cJ )
       != ( ? [B: $i] :
              ( ( cUNIQUE @ B )
              & ( cW @ B )
              & ( cWRH @ B )
              & ( cLIKE @ cJ @ B ) ) ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(10,plain,
    ! [A: $i > $o] :
      ( ( ( A @ cP )
       != ( cLIKE @ cP @ cS ) )
      | ( ( A @ cJ )
       != ( ? [B: $i] :
              ( ( cUNIQUE @ B )
              & ( cW @ B )
              & ( cWRH @ B )
              & ( cLIKE @ cJ @ B ) ) ) ) ),
    inference(simp,[status(thm)],[9]) ).

thf(14,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ cP )
      | ~ ( cLIKE @ cP @ cS )
      | ( A @ cJ )
      | ? [B: $i] :
          ( ( cUNIQUE @ B )
          & ( cW @ B )
          & ( cWRH @ B )
          & ( cLIKE @ cJ @ B ) ) ),
    inference(bool_ext,[status(thm)],[10]) ).

thf(23,plain,
    ( ( cP != cP )
    | ~ ( cLIKE @ cP @ cS )
    | ( cP = cJ )
    | ? [A: $i] :
        ( ( cUNIQUE @ A )
        & ( cW @ A )
        & ( cWRH @ A )
        & ( cLIKE @ cJ @ A ) ) ),
    inference(replace_leibeq,[status(thm)],[14:[bind(A,$thf( (=) @ $i @ cP ))]]) ).

thf(26,plain,
    ( ( cP != cP )
    | ( cP = cJ )
    | ~ ( cLIKE @ cP @ cS )
    | ? [A: $i] :
        ( ( cUNIQUE @ A )
        & ( cW @ A )
        & ( cWRH @ A )
        & ( cLIKE @ cJ @ A ) ) ),
    inference(lifteq,[status(thm)],[23]) ).

thf(33,plain,
    ( ? [A: $i] :
        ( ( cUNIQUE @ A )
        & ( cW @ A )
        & ( cWRH @ A )
        & ( cLIKE @ cJ @ A ) )
    | ~ ( cLIKE @ cP @ cS )
    | ( cP = cJ ) ),
    inference(pattern_uni,[status(thm)],[26:[]]) ).

thf(37,plain,
    ( ( cP = cJ )
    | ~ ( cLIKE @ cP @ cS )
    | ( cW @ sk1 ) ),
    inference(cnf,[status(esa)],[33]) ).

thf(15,plain,
    ! [A: $i > $o] :
      ( ( A @ cP )
      | ( cLIKE @ cP @ cS )
      | ( A @ cJ )
      | ? [B: $i] :
          ( ( cUNIQUE @ B )
          & ( cW @ B )
          & ( cWRH @ B )
          & ( cLIKE @ cJ @ B ) ) ),
    inference(bool_ext,[status(thm)],[10]) ).

thf(49,plain,
    ! [A: $i > $o] :
      ( ( cUNIQUE @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( A @ cP ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(7370,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | $false
    | ( cLIKE @ cP @ cS )
    | $false ),
    inference(prim_subst,[status(thm)],[49:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).

thf(7595,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cP @ cS ) ),
    inference(simp,[status(thm)],[7370]) ).

thf(8,plain,
    cW @ cS,
    inference(cnf,[status(esa)],[3]) ).

thf(20,plain,
    ! [A: $i > $o] :
      ( ~ ( cLIKE @ cP @ cS )
      | ( ( A @ cJ )
       != ( ? [B: $i] :
              ( ( cUNIQUE @ B )
              & ( cW @ B )
              & ( cWRH @ B )
              & ( cLIKE @ cJ @ B ) ) ) )
      | ( ( cW @ cS )
       != ( A @ cP ) ) ),
    inference(paramod_ordered,[status(thm)],[8,10]) ).

thf(28,plain,
    ( ~ ( cLIKE @ cP @ cS )
    | ( ( cW @ cS )
     != ( ? [A: $i] :
            ( ( cUNIQUE @ A )
            & ( cW @ A )
            & ( cWRH @ A )
            & ( cLIKE @ cJ @ A ) ) ) ) ),
    inference(pre_uni,[status(thm)],[20:[bind(A,$thf( ^ [B: $i] : ( cW @ cS ) ))]]) ).

thf(53,plain,
    ( ~ ( cLIKE @ cP @ cS )
    | ~ ? [A: $i] :
          ( ( cUNIQUE @ A )
          & ( cW @ A )
          & ( cWRH @ A )
          & ( cLIKE @ cJ @ A ) ) ),
    inference(rewrite,[status(thm)],[28,8]) ).

thf(54,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ~ ( cW @ A )
      | ~ ( cWRH @ A )
      | ~ ( cLIKE @ cJ @ A )
      | ~ ( cLIKE @ cP @ cS ) ),
    inference(cnf,[status(esa)],[53]) ).

thf(340,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ~ ( cW @ A )
      | ~ ( cLIKE @ cJ @ A )
      | ~ ( cLIKE @ cP @ cS )
      | ( ( cWRH @ cS )
       != ( cWRH @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5,54]) ).

thf(341,plain,
    ( ~ ( cUNIQUE @ cS )
    | ~ ( cW @ cS )
    | ~ ( cLIKE @ cJ @ cS )
    | ~ ( cLIKE @ cP @ cS ) ),
    inference(pattern_uni,[status(thm)],[340:[bind(A,$thf( cS ))]]) ).

thf(4,plain,
    cUNIQUE @ cS,
    inference(cnf,[status(esa)],[3]) ).

thf(395,plain,
    ( ~ $true
    | ~ $true
    | ~ ( cLIKE @ cJ @ cS )
    | ~ ( cLIKE @ cP @ cS ) ),
    inference(rewrite,[status(thm)],[341,4,8]) ).

thf(396,plain,
    ( ~ ( cLIKE @ cJ @ cS )
    | ~ ( cLIKE @ cP @ cS ) ),
    inference(simp,[status(thm)],[395]) ).

thf(425,plain,
    ( ~ ( cLIKE @ cJ @ cS )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cJ @ cS ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[396]) ).

thf(427,plain,
    ( ~ ( cLIKE @ cJ @ cS )
    | ( cP != cJ )
    | ( cS != cS ) ),
    inference(simp,[status(thm)],[425]) ).

thf(432,plain,
    ( ~ ( cLIKE @ cJ @ cS )
    | ( cP != cJ ) ),
    inference(simp,[status(thm)],[427]) ).

thf(7752,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cJ @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[7595,432]) ).

thf(7795,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ )
    | ( cP != cJ )
    | ( cS != cS ) ),
    inference(simp,[status(thm)],[7752]) ).

thf(7825,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ ) ),
    inference(simp,[status(thm)],[7795]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ~ ( cWRH @ B )
      | ~ ( cW @ B )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( cUNIQUE @ A )
      | ~ ( cWRH @ B )
      | ~ ( cW @ B ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(157,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( cUNIQUE @ A )
      | ~ ( cW @ B )
      | ( ( cWRH @ cS )
       != ( cWRH @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5,11]) ).

thf(158,plain,
    ! [A: $i] :
      ( ( A = cS )
      | ~ ( cUNIQUE @ A )
      | ~ ( cW @ cS ) ),
    inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( A )),bind(B,$thf( cS ))]]) ).

thf(2459,plain,
    ! [A: $i] :
      ( ( A = cS )
      | ~ ( cUNIQUE @ A )
      | ~ $true ),
    inference(rewrite,[status(thm)],[158,8]) ).

thf(2460,plain,
    ! [A: $i] :
      ( ( A = cS )
      | ~ ( cUNIQUE @ A ) ),
    inference(simp,[status(thm)],[2459]) ).

thf(46,plain,
    ! [A: $i > $o] :
      ( ( cLIKE @ cJ @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( A @ cP ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(4833,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | $false
    | ( cLIKE @ cP @ cS )
    | $false ),
    inference(prim_subst,[status(thm)],[46:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).

thf(5072,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cP @ cS ) ),
    inference(simp,[status(thm)],[4833]) ).

thf(5239,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cJ @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[5072,432]) ).

thf(5259,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ )
    | ( cP != cJ )
    | ( cS != cS ) ),
    inference(simp,[status(thm)],[5239]) ).

thf(5298,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ ) ),
    inference(simp,[status(thm)],[5259]) ).

thf(426,plain,
    ( ~ ( cLIKE @ cJ @ cS )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cJ @ cS ) ) ),
    inference(simp,[status(thm)],[425]) ).

thf(5333,plain,
    ( ( cP != cJ )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cJ @ cS ) )
    | ( ( cLIKE @ cJ
        @ ( sk3
          @ ^ [A: $i] : $false ) )
     != ( cLIKE @ cJ @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[5298,426]) ).

thf(5414,plain,
    ( ( cP != cJ )
    | ( cP != cJ )
    | ( cS != cS )
    | ( cJ != cJ )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != cS ) ),
    inference(simp,[status(thm)],[5333]) ).

thf(5447,plain,
    ( ( cP != cJ )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != cS ) ),
    inference(simp,[status(thm)],[5414]) ).

thf(5474,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( cP != cJ )
      | ( A
       != ( sk3
          @ ^ [B: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[2460,5447]) ).

thf(5475,plain,
    ( ~ ( cUNIQUE
        @ ( sk3
          @ ^ [A: $i] : $false ) )
    | ( cP != cJ ) ),
    inference(pattern_uni,[status(thm)],[5474:[bind(A,$thf( sk3 @ ^ [B: $i] : $false ))]]) ).

thf(7832,plain,
    ( ( cP != cJ )
    | ( ( cUNIQUE
        @ ( sk3
          @ ^ [A: $i] : $false ) )
     != ( cUNIQUE
        @ ( sk3
          @ ^ [A: $i] : $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7825,5475]) ).

thf(7833,plain,
    cP != cJ,
    inference(pattern_uni,[status(thm)],[7832:[]]) ).

thf(7926,plain,
    ( ~ ( cLIKE @ cP @ cS )
    | ( cW @ sk1 ) ),
    inference(simplifyReflect,[status(thm)],[37,7833]) ).

thf(38,plain,
    ( ( cP = cJ )
    | ~ ( cLIKE @ cP @ cS )
    | ( cUNIQUE @ sk1 ) ),
    inference(cnf,[status(esa)],[33]) ).

thf(7927,plain,
    ( ~ ( cLIKE @ cP @ cS )
    | ( cUNIQUE @ sk1 ) ),
    inference(simplifyReflect,[status(thm)],[38,7833]) ).

thf(8688,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cUNIQUE @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[7595,7927]) ).

thf(8689,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cUNIQUE @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[8688:[]]) ).

thf(8990,plain,
    ! [A: $i] :
      ( ( cUNIQUE @ sk1 )
      | ( A = cS )
      | ( ( cUNIQUE
          @ ( sk3
            @ ^ [B: $i] : $false ) )
       != ( cUNIQUE @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8689,2460]) ).

thf(8991,plain,
    ( ( cUNIQUE @ sk1 )
    | ( ( sk3
        @ ^ [A: $i] : $false )
      = cS ) ),
    inference(pattern_uni,[status(thm)],[8990:[bind(A,$thf( sk3 @ ^ [B: $i] : $false ))]]) ).

thf(9010,plain,
    ( ( cUNIQUE @ sk1 )
    | ( ( cUNIQUE
        @ ( sk3
          @ ^ [A: $i] : $false ) )
     != ( cUNIQUE @ sk1 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[8689]) ).

thf(9025,plain,
    ( ( cUNIQUE @ sk1 )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != sk1 ) ),
    inference(simp,[status(thm)],[9010]) ).

thf(10155,plain,
    ( ( cUNIQUE @ sk1 )
    | ( sk1 != cS )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != ( sk3
        @ ^ [A: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[8991,9025]) ).

thf(10156,plain,
    ( ( cUNIQUE @ sk1 )
    | ( sk1 != cS ) ),
    inference(pattern_uni,[status(thm)],[10155:[]]) ).

thf(7930,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( cS != cJ )
      | ( A != cP ) ),
    inference(paramod_ordered,[status(thm)],[2460,7833]) ).

thf(7931,plain,
    ( ~ ( cUNIQUE @ cP )
    | ( cS != cJ ) ),
    inference(pattern_uni,[status(thm)],[7930:[bind(A,$thf( cP ))]]) ).

thf(7944,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ~ ( cUNIQUE @ cP )
      | ( A != cJ )
      | ( cS != cS ) ),
    inference(paramod_ordered,[status(thm)],[2460,7931]) ).

thf(7945,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ~ ( cUNIQUE @ cP )
      | ( A != cJ ) ),
    inference(pattern_uni,[status(thm)],[7944:[]]) ).

thf(7977,plain,
    ( ~ ( cUNIQUE @ cJ )
    | ~ ( cUNIQUE @ cP ) ),
    inference(simp,[status(thm)],[7945]) ).

thf(10244,plain,
    ( ( sk1 != cS )
    | ~ ( cUNIQUE @ cP )
    | ( ( cUNIQUE @ sk1 )
     != ( cUNIQUE @ cJ ) ) ),
    inference(paramod_ordered,[status(thm)],[10156,7977]) ).

thf(10298,plain,
    ( ( sk1 != cS )
    | ~ ( cUNIQUE @ cP )
    | ( sk1 != cJ ) ),
    inference(simp,[status(thm)],[10244]) ).

thf(8630,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cW @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[7595,7926]) ).

thf(8631,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cW @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[8630:[]]) ).

thf(8929,plain,
    ! [A: $i] :
      ( ( cW @ sk1 )
      | ( A = cS )
      | ( ( cUNIQUE
          @ ( sk3
            @ ^ [B: $i] : $false ) )
       != ( cUNIQUE @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8631,2460]) ).

thf(8930,plain,
    ( ( cW @ sk1 )
    | ( ( sk3
        @ ^ [A: $i] : $false )
      = cS ) ),
    inference(pattern_uni,[status(thm)],[8929:[bind(A,$thf( sk3 @ ^ [B: $i] : $false ))]]) ).

thf(48,plain,
    ! [A: $i > $o] :
      ( ( cW @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( A @ cP ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(6226,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | $false
    | ( cLIKE @ cP @ cS )
    | $false ),
    inference(prim_subst,[status(thm)],[48:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).

thf(6428,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cP @ cS ) ),
    inference(simp,[status(thm)],[6226]) ).

thf(6530,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cW @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[6428,37]) ).

thf(6531,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cW @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[6530:[]]) ).

thf(6577,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cJ @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[6428,432]) ).

thf(6600,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ )
    | ( cP != cJ )
    | ( cS != cS ) ),
    inference(simp,[status(thm)],[6577]) ).

thf(6635,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ ) ),
    inference(simp,[status(thm)],[6600]) ).

thf(6915,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cW @ sk1 )
    | ( cP != cP ) ),
    inference(paramod_ordered,[status(thm)],[6531,6635]) ).

thf(6916,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cW @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[6915:[]]) ).

thf(7101,plain,
    ( ( cW @ sk1 )
    | ( ( cW
        @ ( sk3
          @ ^ [A: $i] : $false ) )
     != ( cW @ sk1 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[6916]) ).

thf(7118,plain,
    ( ( cW @ sk1 )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != sk1 ) ),
    inference(simp,[status(thm)],[7101]) ).

thf(9197,plain,
    ( ( cW @ sk1 )
    | ( sk1 != cS )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != ( sk3
        @ ^ [A: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[8930,7118]) ).

thf(9198,plain,
    ( ( cW @ sk1 )
    | ( sk1 != cS ) ),
    inference(pattern_uni,[status(thm)],[9197:[]]) ).

thf(9242,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( cW @ sk1 )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[2460,9198]) ).

thf(9243,plain,
    ( ~ ( cUNIQUE @ sk1 )
    | ( cW @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[9242:[bind(A,$thf( sk1 ))]]) ).

thf(36,plain,
    ( ( cP = cJ )
    | ~ ( cLIKE @ cP @ cS )
    | ( cWRH @ sk1 ) ),
    inference(cnf,[status(esa)],[33]) ).

thf(7929,plain,
    ( ~ ( cLIKE @ cP @ cS )
    | ( cWRH @ sk1 ) ),
    inference(simplifyReflect,[status(thm)],[36,7833]) ).

thf(8745,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cWRH @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[7595,7929]) ).

thf(8746,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cWRH @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[8745:[]]) ).

thf(47,plain,
    ! [A: $i > $o] :
      ( ( cWRH @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( A @ cP ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(82,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | $false
    | ( cLIKE @ cP @ cS )
    | $false ),
    inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).

thf(110,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cP @ cS ) ),
    inference(simp,[status(thm)],[82]) ).

thf(139,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cWRH @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[110,36]) ).

thf(140,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cWRH @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[139:[]]) ).

thf(494,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cJ @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[110,432]) ).

thf(514,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ )
    | ( cP != cJ )
    | ( cS != cS ) ),
    inference(simp,[status(thm)],[494]) ).

thf(517,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP != cJ ) ),
    inference(simp,[status(thm)],[514]) ).

thf(528,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cWRH @ sk1 )
    | ( cP != cP ) ),
    inference(paramod_ordered,[status(thm)],[140,517]) ).

thf(529,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cWRH @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[528:[]]) ).

thf(628,plain,
    ( ( cWRH @ sk1 )
    | ( ( cWRH
        @ ( sk3
          @ ^ [A: $i] : $false ) )
     != ( cWRH @ sk1 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[529]) ).

thf(630,plain,
    ( ( cWRH @ sk1 )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != sk1 ) ),
    inference(simp,[status(thm)],[628]) ).

thf(2579,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( cWRH @ sk1 )
      | ( sk1 != cS )
      | ( A
       != ( sk3
          @ ^ [B: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[2460,630]) ).

thf(2580,plain,
    ( ~ ( cUNIQUE
        @ ( sk3
          @ ^ [A: $i] : $false ) )
    | ( cWRH @ sk1 )
    | ( sk1 != cS ) ),
    inference(pattern_uni,[status(thm)],[2579:[bind(A,$thf( sk3 @ ^ [B: $i] : $false ))]]) ).

thf(9049,plain,
    ( ( cWRH @ sk1 )
    | ( sk1 != cS )
    | ( ( cUNIQUE
        @ ( sk3
          @ ^ [A: $i] : $false ) )
     != ( cUNIQUE
        @ ( sk3
          @ ^ [A: $i] : $false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8746,2580]) ).

thf(9050,plain,
    ( ( cWRH @ sk1 )
    | ( sk1 != cS ) ),
    inference(pattern_uni,[status(thm)],[9049:[]]) ).

thf(35,plain,
    ( ( cP = cJ )
    | ~ ( cLIKE @ cP @ cS )
    | ( cLIKE @ cJ @ sk1 ) ),
    inference(cnf,[status(esa)],[33]) ).

thf(7928,plain,
    ( ~ ( cLIKE @ cP @ cS )
    | ( cLIKE @ cJ @ sk1 ) ),
    inference(simplifyReflect,[status(thm)],[35,7833]) ).

thf(11509,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cJ @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[7595,7928]) ).

thf(11510,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cJ @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[11509:[]]) ).

thf(7687,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ~ ( cLIKE @ cJ @ cS )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[7595,396]) ).

thf(7688,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ~ ( cLIKE @ cJ @ cS ) ),
    inference(pattern_uni,[status(thm)],[7687:[]]) ).

thf(12481,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( ( cLIKE @ cJ @ sk1 )
     != ( cLIKE @ cJ @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[11510,7688]) ).

thf(12539,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cJ != cJ )
    | ( sk1 != cS ) ),
    inference(simp,[status(thm)],[12481]) ).

thf(12568,plain,
    ( ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( sk1 != cS ) ),
    inference(simp,[status(thm)],[12539]) ).

thf(12591,plain,
    ! [A: $i] :
      ( ( sk1 != cS )
      | ( A = cS )
      | ( ( cUNIQUE
          @ ( sk3
            @ ^ [B: $i] : $false ) )
       != ( cUNIQUE @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[12568,2460]) ).

thf(12592,plain,
    ( ( sk1 != cS )
    | ( ( sk3
        @ ^ [A: $i] : $false )
      = cS ) ),
    inference(pattern_uni,[status(thm)],[12591:[bind(A,$thf( sk3 @ ^ [B: $i] : $false ))]]) ).

thf(12698,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( ( sk3
          @ ^ [B: $i] : $false )
        = cS )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[2460,12592]) ).

thf(12699,plain,
    ( ~ ( cUNIQUE @ sk1 )
    | ( ( sk3
        @ ^ [A: $i] : $false )
      = cS ) ),
    inference(pattern_uni,[status(thm)],[12698:[bind(A,$thf( sk1 ))]]) ).

thf(70,plain,
    ! [A: $i > $o] :
      ( ( cWRH @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( ( A @ cP )
       != ( A @ cJ ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[47]) ).

thf(87,plain,
    ! [A: $i > $o] :
      ( ( cWRH @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( ( A @ cP )
       != ( A @ cJ ) ) ),
    inference(pre_uni,[status(thm)],[70:[]]) ).

thf(88,plain,
    ! [A: $i > $o] :
      ( ( cLIKE @ cP @ cS )
      | ( A @ cJ )
      | ( cWRH @ ( sk3 @ A ) )
      | ( ( A @ cP )
       != ( A @ cJ ) ) ),
    inference(pre_uni,[status(thm)],[87:[]]) ).

thf(8144,plain,
    ( ~ ( cUNIQUE @ cJ )
    | ( ( cUNIQUE @ cP )
     != ( cUNIQUE @ cJ ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[7977]) ).

thf(8166,plain,
    ( ~ ( cUNIQUE @ cJ )
    | ( ( cUNIQUE @ cP )
     != ( cUNIQUE @ cJ ) ) ),
    inference(simp,[status(thm)],[8144]) ).

thf(10288,plain,
    ( ( sk1 != cS )
    | ~ ( cUNIQUE @ cJ )
    | ( ( cUNIQUE @ sk1 )
     != ( cUNIQUE @ cP ) ) ),
    inference(paramod_ordered,[status(thm)],[10156,8166]) ).

thf(10293,plain,
    ( ( sk1 != cS )
    | ~ ( cUNIQUE @ cJ )
    | ( sk1 != cP ) ),
    inference(simp,[status(thm)],[10288]) ).

thf(11644,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ~ ( cUNIQUE @ cJ )
      | ( sk1 != cP )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[2460,10293]) ).

thf(11645,plain,
    ( ~ ( cUNIQUE @ sk1 )
    | ~ ( cUNIQUE @ cJ )
    | ( sk1 != cP ) ),
    inference(pattern_uni,[status(thm)],[11644:[bind(A,$thf( sk1 ))]]) ).

thf(2490,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ~ ( cLIKE @ cJ @ cS )
      | ~ ( cLIKE @ cS @ cS )
      | ( A != cP ) ),
    inference(paramod_ordered,[status(thm)],[2460,396]) ).

thf(2491,plain,
    ( ~ ( cUNIQUE @ cP )
    | ~ ( cLIKE @ cJ @ cS )
    | ~ ( cLIKE @ cS @ cS ) ),
    inference(pattern_uni,[status(thm)],[2490:[bind(A,$thf( cP ))]]) ).

thf(42,plain,
    ! [A: $i > $o] :
      ( ( cLIKE @ cJ @ ( sk2 @ A ) )
      | ( A @ cJ )
      | ~ ( cLIKE @ cP @ cS )
      | ~ ( A @ cP ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(7959,plain,
    ( ( cS != cJ )
    | ( ( cUNIQUE @ cP )
     != ( cUNIQUE @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[4,7931]) ).

thf(7974,plain,
    ( ( cS != cJ )
    | ( cP != cS ) ),
    inference(simp,[status(thm)],[7959]) ).

thf(7986,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( A != cJ )
      | ( cP != cS )
      | ( cS != cS ) ),
    inference(paramod_ordered,[status(thm)],[2460,7974]) ).

thf(7987,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( A != cJ )
      | ( cP != cS ) ),
    inference(pattern_uni,[status(thm)],[7986:[]]) ).

thf(7996,plain,
    ( ~ ( cUNIQUE @ cJ )
    | ( cP != cS ) ),
    inference(simp,[status(thm)],[7987]) ).

thf(10289,plain,
    ( ( sk1 != cS )
    | ( cP != cS )
    | ( ( cUNIQUE @ sk1 )
     != ( cUNIQUE @ cJ ) ) ),
    inference(paramod_ordered,[status(thm)],[10156,7996]) ).

thf(10290,plain,
    ( ( sk1 != cS )
    | ( cP != cS )
    | ( sk1 != cJ ) ),
    inference(simp,[status(thm)],[10289]) ).

thf(11612,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( cP != cS )
      | ( sk1 != cJ )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[2460,10290]) ).

thf(11613,plain,
    ( ~ ( cUNIQUE @ sk1 )
    | ( cP != cS )
    | ( sk1 != cJ ) ),
    inference(pattern_uni,[status(thm)],[11612:[bind(A,$thf( sk1 ))]]) ).

thf(9055,plain,
    ! [A: $i] :
      ( ( cWRH @ sk1 )
      | ( A = cS )
      | ( ( cUNIQUE
          @ ( sk3
            @ ^ [B: $i] : $false ) )
       != ( cUNIQUE @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8746,2460]) ).

thf(9056,plain,
    ( ( cWRH @ sk1 )
    | ( ( sk3
        @ ^ [A: $i] : $false )
      = cS ) ),
    inference(pattern_uni,[status(thm)],[9055:[bind(A,$thf( sk3 @ ^ [B: $i] : $false ))]]) ).

thf(8747,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cWRH @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[5072,7929]) ).

thf(8748,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cWRH @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[8747:[]]) ).

thf(11511,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cJ @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[5072,7928]) ).

thf(11512,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cJ @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[11511:[]]) ).

thf(16478,plain,
    ( ( cLIKE @ cJ @ sk1 )
    | ( ( cLIKE @ cJ
        @ ( sk3
          @ ^ [A: $i] : $false ) )
     != ( cLIKE @ cJ @ sk1 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[11512]) ).

thf(16526,plain,
    ( ( cLIKE @ cJ @ sk1 )
    | ( cJ != cJ )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != sk1 ) ),
    inference(simp,[status(thm)],[16478]) ).

thf(16544,plain,
    ( ( cLIKE @ cJ @ sk1 )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != sk1 ) ),
    inference(simp,[status(thm)],[16526]) ).

thf(60,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( cWRH @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( A @ cP )
      | ~ ( B @ cP )
      | ( ( B @ cJ )
       != ( ? [C: $i] :
              ( ( cUNIQUE @ C )
              & ( cW @ C )
              & ( cWRH @ C )
              & ( cLIKE @ cJ @ C ) ) ) )
      | ( ( cLIKE @ cP @ cS )
       != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[47,10]) ).

thf(61,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( cWRH @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( A @ cP )
      | ~ ( B @ cP )
      | ( ( B @ cJ )
       != ( ? [C: $i] :
              ( ( cUNIQUE @ C )
              & ( cW @ C )
              & ( cWRH @ C )
              & ( cLIKE @ cJ @ C ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[60:[]]) ).

thf(7932,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ~ ( cWRH @ B )
      | ~ ( cW @ B )
      | ( B != cJ )
      | ( A != cP ) ),
    inference(paramod_ordered,[status(thm)],[11,7833]) ).

thf(7933,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ cP )
      | ~ ( cWRH @ A )
      | ~ ( cW @ A )
      | ( A != cJ ) ),
    inference(pattern_uni,[status(thm)],[7932:[bind(A,$thf( cP ))]]) ).

thf(7936,plain,
    ( ~ ( cUNIQUE @ cP )
    | ~ ( cWRH @ cJ )
    | ~ ( cW @ cJ ) ),
    inference(simp,[status(thm)],[7933]) ).

thf(8690,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cUNIQUE @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[5072,7927]) ).

thf(8691,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cUNIQUE @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[8690:[]]) ).

thf(11142,plain,
    ( ( cWRH @ sk1 )
    | ( cLIKE @ cJ @ cS )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != ( sk3
        @ ^ [A: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[9056,8748]) ).

thf(11143,plain,
    ( ( cWRH @ sk1 )
    | ( cLIKE @ cJ @ cS ) ),
    inference(pattern_uni,[status(thm)],[11142:[]]) ).

thf(9024,plain,
    ( ( cUNIQUE @ sk1 )
    | ( ( cUNIQUE
        @ ( sk3
          @ ^ [A: $i] : $false ) )
     != ( cUNIQUE @ sk1 ) ) ),
    inference(simp,[status(thm)],[9010]) ).

thf(11667,plain,
    ( ( sk1 != cS )
    | ( sk1 != cP )
    | ( ( cUNIQUE @ sk1 )
     != ( cUNIQUE @ cJ ) ) ),
    inference(paramod_ordered,[status(thm)],[10156,10293]) ).

thf(11677,plain,
    ( ( sk1 != cS )
    | ( sk1 != cP )
    | ( sk1 != cJ ) ),
    inference(simp,[status(thm)],[11667]) ).

thf(7934,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ~ ( cWRH @ B )
      | ~ ( cW @ B )
      | ( A != cJ )
      | ( B != cP ) ),
    inference(paramod_ordered,[status(thm)],[11,7833]) ).

thf(7935,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ~ ( cWRH @ cP )
      | ~ ( cW @ cP )
      | ( A != cJ ) ),
    inference(pattern_uni,[status(thm)],[7934:[bind(A,$thf( A )),bind(B,$thf( cP ))]]) ).

thf(7937,plain,
    ( ~ ( cUNIQUE @ cJ )
    | ~ ( cWRH @ cP )
    | ~ ( cW @ cP ) ),
    inference(simp,[status(thm)],[7935]) ).

thf(932,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cUNIQUE @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[110,38]) ).

thf(933,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cUNIQUE @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[932:[]]) ).

thf(1057,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cUNIQUE @ sk1 )
    | ( cP != cP ) ),
    inference(paramod_ordered,[status(thm)],[933,517]) ).

thf(1058,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cUNIQUE @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[1057:[]]) ).

thf(2615,plain,
    ! [A: $i] :
      ( ( cWRH
        @ ( sk3
          @ ^ [B: $i] : $false ) )
      | ( A = cS )
      | ( ( cUNIQUE @ sk1 )
       != ( cUNIQUE @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1058,2460]) ).

thf(2616,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( sk1 = cS ) ),
    inference(pattern_uni,[status(thm)],[2615:[bind(A,$thf( sk1 ))]]) ).

thf(564,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cLIKE @ cJ @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[110,35]) ).

thf(565,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cLIKE @ cJ @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[564:[]]) ).

thf(1482,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cJ @ sk1 )
    | ( cP != cP ) ),
    inference(paramod_ordered,[status(thm)],[565,517]) ).

thf(1483,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cJ @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[1482:[]]) ).

thf(400,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ~ ( cLIKE @ cJ @ cS )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[110,396]) ).

thf(401,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ~ ( cLIKE @ cJ @ cS ) ),
    inference(pattern_uni,[status(thm)],[400:[]]) ).

thf(1561,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( ( cLIKE @ cJ @ sk1 )
     != ( cLIKE @ cJ @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[1483,401]) ).

thf(1576,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cJ != cJ )
    | ( sk1 != cS ) ),
    inference(simp,[status(thm)],[1561]) ).

thf(1593,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( sk1 != cS ) ),
    inference(simp,[status(thm)],[1576]) ).

thf(3153,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( sk1 != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[2616,1593]) ).

thf(3154,plain,
    ( cWRH
    @ ( sk3
      @ ^ [A: $i] : $false ) ),
    inference(pattern_uni,[status(thm)],[3153:[]]) ).

thf(67,plain,
    ! [A: $i > $o] :
      ( ( A @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( A @ cP )
      | ( ( cWRH @ ( sk3 @ A ) )
       != ( A @ cJ ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[47]) ).

thf(97,plain,
    ! [A: $i > $o] :
      ( ( A @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( A @ cP )
      | ( ( cWRH @ ( sk3 @ A ) )
       != ( A @ cJ ) ) ),
    inference(simp,[status(thm)],[67]) ).

thf(77,plain,
    ( ( cWRH @ ( sk3 @ cUNIQUE ) )
    | ( cUNIQUE @ cJ )
    | ( cLIKE @ cP @ cS )
    | ( cUNIQUE @ cP ) ),
    inference(prim_subst,[status(thm)],[47:[bind(A,$thf( cUNIQUE ))]]) ).

thf(59,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( cWRH @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( A @ cP )
      | ~ ( cLIKE @ cP @ cS )
      | ( ( B @ cJ )
       != ( ? [C: $i] :
              ( ( cUNIQUE @ C )
              & ( cW @ C )
              & ( cWRH @ C )
              & ( cLIKE @ cJ @ C ) ) ) )
      | ( ( cLIKE @ cP @ cS )
       != ( B @ cP ) ) ),
    inference(paramod_ordered,[status(thm)],[47,10]) ).

thf(96,plain,
    ! [A: $i > $o] :
      ( ( cWRH @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( A @ cP )
      | ~ ( cLIKE @ cP @ cS )
      | ( ( cLIKE @ cJ @ cS )
       != ( ? [B: $i] :
              ( ( cUNIQUE @ B )
              & ( cW @ B )
              & ( cWRH @ B )
              & ( cLIKE @ cJ @ B ) ) ) ) ),
    inference(pre_uni,[status(thm)],[59:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( cLIKE @ C @ cS ) ))]]) ).

thf(10256,plain,
    ( ( sk1 != cS )
    | ( cS != cJ )
    | ( ( cUNIQUE @ sk1 )
     != ( cUNIQUE @ cP ) ) ),
    inference(paramod_ordered,[status(thm)],[10156,7931]) ).

thf(10302,plain,
    ( ( sk1 != cS )
    | ( cS != cJ )
    | ( sk1 != cP ) ),
    inference(simp,[status(thm)],[10256]) ).

thf(2565,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( cWRH @ A )
      | ( cS != cS ) ),
    inference(paramod_ordered,[status(thm)],[2460,5]) ).

thf(2566,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( cWRH @ A ) ),
    inference(pattern_uni,[status(thm)],[2565:[]]) ).

thf(9111,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( cWRH @ sk1 )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[2460,9050]) ).

thf(9112,plain,
    ( ~ ( cUNIQUE @ sk1 )
    | ( cWRH @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[9111:[bind(A,$thf( sk1 ))]]) ).

thf(73,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( cWRH
        @ ( sk3
          @ ^ [C: $i] :
              ( ( A @ C )
              | ( B @ C ) ) ) )
      | ( A @ cJ )
      | ( B @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( A @ cP )
      | ( B @ cP ) ),
    inference(prim_subst,[status(thm)],[47:[bind(A,$thf( ^ [D: $i] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).

thf(104,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( A @ cP )
      | ( B @ cP )
      | ( cLIKE @ cP @ cS )
      | ( A @ cJ )
      | ( B @ cJ )
      | ( cWRH
        @ ( sk3
          @ ^ [C: $i] :
              ( ( A @ C )
              | ( B @ C ) ) ) ) ),
    inference(cnf,[status(esa)],[73]) ).

thf(105,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( A @ cP )
      | ( B @ cP )
      | ( cLIKE @ cP @ cS )
      | ( A @ cJ )
      | ( B @ cJ )
      | ( cWRH
        @ ( sk3
          @ ^ [C: $i] :
              ( ( A @ C )
              | ( B @ C ) ) ) ) ),
    inference(simp,[status(thm)],[104]) ).

thf(12595,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( cUNIQUE
        @ ( sk3
          @ ^ [B: $i] : $false ) )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[2460,12568]) ).

thf(12596,plain,
    ( ~ ( cUNIQUE @ sk1 )
    | ( cUNIQUE
      @ ( sk3
        @ ^ [A: $i] : $false ) ) ),
    inference(pattern_uni,[status(thm)],[12595:[bind(A,$thf( sk1 ))]]) ).

thf(45,plain,
    ! [A: $i > $o] :
      ( ( cUNIQUE @ ( sk2 @ A ) )
      | ( A @ cJ )
      | ~ ( cLIKE @ cP @ cS )
      | ~ ( A @ cP ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(13,plain,
    ! [A: $i > $o] :
      ( ( A @ cP )
      | ( cLIKE @ cP @ cS )
      | ~ ( A @ cJ )
      | ~ ? [B: $i] :
            ( ( cUNIQUE @ B )
            & ( cW @ B )
            & ( cWRH @ B )
            & ( cLIKE @ cJ @ B ) ) ),
    inference(bool_ext,[status(thm)],[10]) ).

thf(24,plain,
    ( ( cJ = cP )
    | ( cLIKE @ cP @ cS )
    | ( cJ != cJ )
    | ~ ? [A: $i] :
          ( ( cUNIQUE @ A )
          & ( cW @ A )
          & ( cWRH @ A )
          & ( cLIKE @ cJ @ A ) ) ),
    inference(replace_leibeq,[status(thm)],[13:[bind(A,$thf( (=) @ $i @ cJ ))]]) ).

thf(25,plain,
    ( ( cP = cJ )
    | ( cJ != cJ )
    | ( cLIKE @ cP @ cS )
    | ~ ? [A: $i] :
          ( ( cUNIQUE @ A )
          & ( cW @ A )
          & ( cWRH @ A )
          & ( cLIKE @ cJ @ A ) ) ),
    inference(lifteq,[status(thm)],[24]) ).

thf(27,plain,
    ( ~ ? [A: $i] :
          ( ( cUNIQUE @ A )
          & ( cW @ A )
          & ( cWRH @ A )
          & ( cLIKE @ cJ @ A ) )
    | ( cLIKE @ cP @ cS )
    | ( cP = cJ ) ),
    inference(pattern_uni,[status(thm)],[25:[]]) ).

thf(50,plain,
    ! [A: $i] :
      ( ( cP = cJ )
      | ( cLIKE @ cP @ cS )
      | ~ ( cUNIQUE @ A )
      | ~ ( cW @ A )
      | ~ ( cWRH @ A )
      | ~ ( cLIKE @ cJ @ A ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(8217,plain,
    ! [A: $i] :
      ( ( cLIKE @ cP @ cS )
      | ~ ( cUNIQUE @ A )
      | ~ ( cW @ A )
      | ~ ( cWRH @ A )
      | ~ ( cLIKE @ cJ @ A ) ),
    inference(simplifyReflect,[status(thm)],[50,7833]) ).

thf(44,plain,
    ! [A: $i > $o] :
      ( ( cW @ ( sk2 @ A ) )
      | ( A @ cJ )
      | ~ ( cLIKE @ cP @ cS )
      | ~ ( A @ cP ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(5202,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cW @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[5072,37]) ).

thf(5203,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cW @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[5202:[]]) ).

thf(5626,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cW @ sk1 )
    | ( cP != cP ) ),
    inference(paramod_ordered,[status(thm)],[5203,5298]) ).

thf(5627,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cW @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[5626:[]]) ).

thf(69,plain,
    ! [A: $i > $o] :
      ( ( cWRH @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( ( A @ cP )
       != ( cWRH @ ( sk3 @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[47]) ).

thf(86,plain,
    ! [A: $i > $o] :
      ( ( cWRH @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( ( A @ cP )
       != ( cWRH @ ( sk3 @ A ) ) ) ),
    inference(simp,[status(thm)],[69]) ).

thf(10627,plain,
    ( ( cUNIQUE @ sk1 )
    | ( cLIKE @ cJ @ cS )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != ( sk3
        @ ^ [A: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[8991,8691]) ).

thf(10628,plain,
    ( ( cUNIQUE @ sk1 )
    | ( cLIKE @ cJ @ cS ) ),
    inference(pattern_uni,[status(thm)],[10627:[]]) ).

thf(2646,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( cW @ A )
      | ( cS != cS ) ),
    inference(paramod_ordered,[status(thm)],[2460,8]) ).

thf(2647,plain,
    ! [A: $i] :
      ( ~ ( cUNIQUE @ A )
      | ( cW @ A ) ),
    inference(pattern_uni,[status(thm)],[2646:[]]) ).

thf(8493,plain,
    ( ~ ( cWRH @ cJ )
    | ~ ( cW @ cJ )
    | ( ( cUNIQUE @ cP )
     != ( cUNIQUE @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[4,7936]) ).

thf(8529,plain,
    ( ~ ( cWRH @ cJ )
    | ~ ( cW @ cJ )
    | ( cP != cS ) ),
    inference(simp,[status(thm)],[8493]) ).

thf(80,plain,
    ( ( cWRH @ ( sk3 @ cWRH ) )
    | ( cWRH @ cJ )
    | ( cLIKE @ cP @ cS )
    | ( cWRH @ cP ) ),
    inference(prim_subst,[status(thm)],[47:[bind(A,$thf( cWRH ))]]) ).

thf(9201,plain,
    ( ( cW @ sk1 )
    | ( cLIKE @ cJ @ cS )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != ( sk3
        @ ^ [A: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[8930,5627]) ).

thf(9202,plain,
    ( ( cW @ sk1 )
    | ( cLIKE @ cJ @ cS ) ),
    inference(pattern_uni,[status(thm)],[9201:[]]) ).

thf(6536,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cUNIQUE @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[6428,38]) ).

thf(6537,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cP = cJ )
    | ( cUNIQUE @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[6536:[]]) ).

thf(8001,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cUNIQUE @ sk1 ) ),
    inference(simplifyReflect,[status(thm)],[6537,7833]) ).

thf(8017,plain,
    ! [A: $i] :
      ( ( cW
        @ ( sk3
          @ ^ [B: $i] : $false ) )
      | ( A = cS )
      | ( ( cUNIQUE @ sk1 )
       != ( cUNIQUE @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8001,2460]) ).

thf(8018,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( sk1 = cS ) ),
    inference(pattern_uni,[status(thm)],[8017:[bind(A,$thf( sk1 ))]]) ).

thf(11487,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cJ @ sk1 )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[6428,7928]) ).

thf(11488,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cLIKE @ cJ @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[11487:[]]) ).

thf(6513,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ~ ( cLIKE @ cJ @ cS )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[6428,396]) ).

thf(6514,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ~ ( cLIKE @ cJ @ cS ) ),
    inference(pattern_uni,[status(thm)],[6513:[]]) ).

thf(11973,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( ( cLIKE @ cJ @ sk1 )
     != ( cLIKE @ cJ @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[11488,6514]) ).

thf(12030,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( cJ != cJ )
    | ( sk1 != cS ) ),
    inference(simp,[status(thm)],[11973]) ).

thf(12074,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( sk1 != cS ) ),
    inference(simp,[status(thm)],[12030]) ).

thf(12087,plain,
    ( ( cW
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ( sk1 != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[8018,12074]) ).

thf(12088,plain,
    ( cW
    @ ( sk3
      @ ^ [A: $i] : $false ) ),
    inference(pattern_uni,[status(thm)],[12087:[]]) ).

thf(95,plain,
    ! [A: $i > $o] :
      ( ( cWRH @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( A @ cP )
      | ~ ( cLIKE @ cP @ cS )
      | ( ( cLIKE @ cP @ cS )
       != ( ? [B: $i] :
              ( ( cUNIQUE @ B )
              & ( cW @ B )
              & ( cWRH @ B )
              & ( cLIKE @ cJ @ B ) ) ) ) ),
    inference(pre_uni,[status(thm)],[59:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( cLIKE @ cP @ cS ) ))]]) ).

thf(43,plain,
    ! [A: $i > $o] :
      ( ( cWRH @ ( sk2 @ A ) )
      | ( A @ cJ )
      | ~ ( cLIKE @ cP @ cS )
      | ~ ( A @ cP ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(72,plain,
    ! [A: $i > $o] :
      ( ( cWRH @ ( sk3 @ A ) )
      | ( A @ cJ )
      | ( cLIKE @ cP @ cS )
      | ( ( A @ cP )
       != ( cLIKE @ cP @ cS ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[47]) ).

thf(99,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : ( cLIKE @ A @ cS ) ) )
    | ( cLIKE @ cJ @ cS )
    | ( cLIKE @ cP @ cS ) ),
    inference(pre_uni,[status(thm)],[72:[bind(A,$thf( ^ [B: $i] : ( cLIKE @ B @ cS ) ))]]) ).

thf(16613,plain,
    ( ( sk1 != cS )
    | ( cLIKE @ cJ @ sk1 )
    | ( ( sk3
        @ ^ [A: $i] : $false )
     != ( sk3
        @ ^ [A: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[12592,16544]) ).

thf(16614,plain,
    ( ( sk1 != cS )
    | ( cLIKE @ cJ @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[16613:[]]) ).

thf(98,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : ( cLIKE @ cP @ cS ) ) )
    | ( cLIKE @ cP @ cS )
    | ( cLIKE @ cP @ cS ) ),
    inference(pre_uni,[status(thm)],[72:[bind(A,$thf( ^ [B: $i] : ( cLIKE @ cP @ cS ) ))]]) ).

thf(119,plain,
    ( ( cWRH
      @ ( sk3
        @ ^ [A: $i] : ( cLIKE @ cP @ cS ) ) )
    | ( cLIKE @ cP @ cS ) ),
    inference(simp,[status(thm)],[98]) ).

thf(79,plain,
    ( ( cWRH @ ( sk3 @ cW ) )
    | ( cW @ cJ )
    | ( cLIKE @ cP @ cS )
    | ( cW @ cP ) ),
    inference(prim_subst,[status(thm)],[47:[bind(A,$thf( cW ))]]) ).

thf(3943,plain,
    ( ~ ( cLIKE @ cJ @ cS )
    | ~ ( cLIKE @ cS @ cS )
    | ( ( cUNIQUE @ cP )
     != ( cUNIQUE @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[4,2491]) ).

thf(4007,plain,
    ( ~ ( cLIKE @ cJ @ cS )
    | ~ ( cLIKE @ cS @ cS )
    | ( cP != cS ) ),
    inference(simp,[status(thm)],[3943]) ).

thf(8859,plain,
    ( ~ ( cWRH @ cP )
    | ~ ( cW @ cP )
    | ( ( cUNIQUE @ cS )
     != ( cUNIQUE @ cJ ) ) ),
    inference(paramod_ordered,[status(thm)],[4,7937]) ).

thf(8869,plain,
    ( ~ ( cWRH @ cP )
    | ~ ( cW @ cP )
    | ( cS != cJ ) ),
    inference(simp,[status(thm)],[8859]) ).

thf(9395,plain,
    ( ( ( cUNIQUE @ cP )
     != ( cUNIQUE @ cJ ) )
    | ( ( cUNIQUE @ cS )
     != ( cUNIQUE @ cJ ) ) ),
    inference(paramod_ordered,[status(thm)],[4,8166]) ).

thf(9414,plain,
    ( ( ( cUNIQUE @ cP )
     != ( cUNIQUE @ cJ ) )
    | ( cS != cJ ) ),
    inference(simp,[status(thm)],[9395]) ).

thf(5175,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ~ ( cLIKE @ cJ @ cS )
    | ( ( cLIKE @ cP @ cS )
     != ( cLIKE @ cP @ cS ) ) ),
    inference(paramod_ordered,[status(thm)],[5072,396]) ).

thf(5176,plain,
    ( ( cLIKE @ cJ
      @ ( sk3
        @ ^ [A: $i] : $false ) )
    | ~ ( cLIKE @ cJ @ cS ) ),
    inference(pattern_uni,[status(thm)],[5175:[]]) ).

thf(17456,plain,
    $false,
    inference(e,[status(thm)],[5,7926,10298,9243,9050,8991,8930,12699,88,10,12568,11645,2491,42,11613,9056,8748,11512,11510,46,16544,7931,61,7936,396,8691,11143,7688,9024,11677,7937,630,3154,8746,7977,97,2460,8631,77,96,7927,10302,2566,9112,105,12596,45,7118,8217,7833,44,9025,5627,12592,54,49,86,10628,2647,7928,8529,7929,3,80,8689,426,9202,48,10290,12088,95,10293,11,7595,43,99,10156,7974,8166,7996,16614,8,119,5072,4,79,4007,8869,9414,5176,9198,47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SYO224^5 : TPTP v8.2.0. Released v4.0.0.
% 0.17/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n026.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Mon May 20 09:20:09 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 0.96/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.21/1.03  % [INFO] 	 Parsing done (109ms). 
% 1.21/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.78/1.26  % [INFO] 	 eprover registered as external prover. 
% 1.78/1.27  % [INFO] 	 cvc4 registered as external prover. 
% 1.78/1.27  % [INFO] 	 Scanning for conjecture ... 
% 1.93/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.93/1.35  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.93/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.03/1.36  % [INFO] 	 Type checking passed. 
% 2.03/1.36  % [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 ... 
% 47.09/8.73  % External prover 'e' found a proof!
% 47.09/8.73  % [INFO] 	 Killing All external provers ... 
% 47.09/8.73  % Time passed: 8177ms (effective reasoning time: 7685ms)
% 47.09/8.73  % 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)>
% 47.09/8.73  % Axioms used in derivation (0): 
% 47.09/8.73  % No. of inferences in proof: 256
% 47.09/8.73  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8177 ms resp. 7685 ms w/o parsing
% 47.09/8.84  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 47.09/8.84  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------