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Leo-III---1.8.0.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV226+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:58:28 AM UTC 2026

% Result   : Theorem 13.55s 5.71s
% Output   : Refutation 14.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   19 (  12 unt;   0 typ;   2 def)
%            Number of atoms       :  484 ( 427 equ;   0 cnn)
%            Maximal formula atoms :   81 (  25 avg)
%            Number of connectives :  884 ( 237   ~;  42   |; 402   &; 184   @)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   47 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;  12 con; 0-3 aty)
%            Number of variables   :   25 (   0   ^;  23   !;   0   ?;  25   :)
%                                         (   0  !>;   0  ?*;   0  @-;   2  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(leq_decl,type,
    leq: $i > $i > $o ).

thf(n0_decl,type,
    n0: $i ).

thf(n5_decl,type,
    n5: $i ).

thf(a_select3_decl,type,
    a_select3: $i > $i > $i > $i ).

thf(q_ds1_filter_decl,type,
    q_ds1_filter: $i ).

thf(n2_decl,type,
    n2: $i ).

thf(r_ds1_filter_decl,type,
    r_ds1_filter: $i ).

thf(n3_decl,type,
    n3: $i ).

thf(n4_decl,type,
    n4: $i ).

thf(n1_decl,type,
    n1: $i ).

thf(a_select2_decl,type,
    a_select2: $i > $i > $i ).

thf(xinit_noise_decl,type,
    xinit_noise: $i ).

thf(sk1_decl,type,
    sk1: $i ).

thf(sk2_decl,type,
    sk2: $i ).

thf(sk1_def,definition,
    ( sk1
    = ( @+[A: $i] :
          ~ ! [B: $i] :
              ( ( ( n5 @ ( B @ leq ) )
                & ( n5 @ ( A @ leq ) )
                & ( B @ ( n0 @ leq ) )
                & ( A @ ( n0 @ leq ) ) )
             => ( ( ( n2 = B )
                  & ( n2 = A )
                  & ( n1 = B )
                  & ( n1 = A )
                  & ~ ( ( n5 = B )
                      & ( n5 = A ) )
                  & ~ ( ( n5 = A )
                      & ( n4 = B ) )
                  & ~ ( ( n5 = B )
                      & ( n4 = A ) )
                  & ~ ( ( n4 = B )
                      & ( n4 = A ) )
                  & ~ ( ( n5 = A )
                      & ( n3 = B ) )
                  & ~ ( ( n4 = A )
                      & ( n3 = B ) )
                  & ~ ( ( n5 = B )
                      & ( n3 = A ) )
                  & ~ ( ( n4 = B )
                      & ( n3 = A ) )
                  & ~ ( ( n3 = B )
                      & ( n3 = A ) )
                  & ~ ( ( n5 = A )
                      & ( n2 = B ) )
                  & ~ ( ( n4 = A )
                      & ( n2 = B ) )
                  & ~ ( ( n3 = A )
                      & ( n2 = B ) )
                  & ~ ( ( n5 = B )
                      & ( n2 = A ) )
                  & ~ ( ( n4 = B )
                      & ( n2 = A ) )
                  & ~ ( ( n3 = B )
                      & ( n2 = A ) )
                  & ~ ( ( n2 = B )
                      & ( n2 = A ) )
                  & ~ ( ( n5 = A )
                      & ( n1 = B ) )
                  & ~ ( ( n4 = A )
                      & ( n1 = B ) )
                  & ~ ( ( n3 = A )
                      & ( n1 = B ) )
                  & ~ ( ( n2 = A )
                      & ( n1 = B ) )
                  & ~ ( ( n5 = B )
                      & ( n1 = A ) )
                  & ~ ( ( n4 = B )
                      & ( n1 = A ) )
                  & ~ ( ( n3 = B )
                      & ( n1 = A ) )
                  & ~ ( ( n2 = B )
                      & ( n1 = A ) )
                  & ~ ( ( n5 = A )
                      & ( n0 = B ) )
                  & ~ ( ( n4 = A )
                      & ( n0 = B ) )
                  & ~ ( ( n3 = A )
                      & ( n0 = B ) )
                  & ~ ( ( n2 = A )
                      & ( n0 = B ) )
                  & ~ ( ( n5 = B )
                      & ( n0 = A ) )
                  & ~ ( ( n4 = B )
                      & ( n0 = A ) )
                  & ~ ( ( n3 = B )
                      & ( n0 = A ) ) )
               => ( ( n1 @ ( xinit_noise @ a_select2 ) )
                  = ( n2 @ ( xinit_noise @ a_select2 ) ) ) ) ) ) ) ).

thf(sk2_def,definition,
    ( sk2
    = ( @+[A: $i] :
          ~ ( ( ( n5 @ ( A @ leq ) )
              & ( n5 @ ( sk1 @ leq ) )
              & ( A @ ( n0 @ leq ) )
              & ( sk1 @ ( n0 @ leq ) ) )
           => ( ( ( n2 = A )
                & ( n2 = sk1 )
                & ( n1 = A )
                & ( n1 = sk1 )
                & ~ ( ( n5 = A )
                    & ( n5 = sk1 ) )
                & ~ ( ( n5 = sk1 )
                    & ( n4 = A ) )
                & ~ ( ( n5 = A )
                    & ( n4 = sk1 ) )
                & ~ ( ( n4 = A )
                    & ( n4 = sk1 ) )
                & ~ ( ( n5 = sk1 )
                    & ( n3 = A ) )
                & ~ ( ( n4 = sk1 )
                    & ( n3 = A ) )
                & ~ ( ( n5 = A )
                    & ( n3 = sk1 ) )
                & ~ ( ( n4 = A )
                    & ( n3 = sk1 ) )
                & ~ ( ( n3 = A )
                    & ( n3 = sk1 ) )
                & ~ ( ( n5 = sk1 )
                    & ( n2 = A ) )
                & ~ ( ( n4 = sk1 )
                    & ( n2 = A ) )
                & ~ ( ( n3 = sk1 )
                    & ( n2 = A ) )
                & ~ ( ( n5 = A )
                    & ( n2 = sk1 ) )
                & ~ ( ( n4 = A )
                    & ( n2 = sk1 ) )
                & ~ ( ( n3 = A )
                    & ( n2 = sk1 ) )
                & ~ ( ( n2 = A )
                    & ( n2 = sk1 ) )
                & ~ ( ( n5 = sk1 )
                    & ( n1 = A ) )
                & ~ ( ( n4 = sk1 )
                    & ( n1 = A ) )
                & ~ ( ( n3 = sk1 )
                    & ( n1 = A ) )
                & ~ ( ( n2 = sk1 )
                    & ( n1 = A ) )
                & ~ ( ( n5 = A )
                    & ( n1 = sk1 ) )
                & ~ ( ( n4 = A )
                    & ( n1 = sk1 ) )
                & ~ ( ( n3 = A )
                    & ( n1 = sk1 ) )
                & ~ ( ( n2 = A )
                    & ( n1 = sk1 ) )
                & ~ ( ( n5 = sk1 )
                    & ( n0 = A ) )
                & ~ ( ( n4 = sk1 )
                    & ( n0 = A ) )
                & ~ ( ( n3 = sk1 )
                    & ( n0 = A ) )
                & ~ ( ( n2 = sk1 )
                    & ( n0 = A ) )
                & ~ ( ( n5 = A )
                    & ( n0 = sk1 ) )
                & ~ ( ( n4 = A )
                    & ( n0 = sk1 ) )
                & ~ ( ( n3 = A )
                    & ( n0 = sk1 ) ) )
             => ( ( n1 @ ( xinit_noise @ a_select2 ) )
                = ( n2 @ ( xinit_noise @ a_select2 ) ) ) ) ) ) ) ).

thf(1,conjecture,
    ( ( ! [A: $i,B: $i] :
          ( ( ( n2 @ ( B @ leq ) )
            & ( n2 @ ( A @ leq ) )
            & ( B @ ( n0 @ leq ) )
            & ( A @ ( n0 @ leq ) ) )
         => ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
            = ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
      & ! [A: $i,B: $i] :
          ( ( ( n5 @ ( B @ leq ) )
            & ( n5 @ ( A @ leq ) )
            & ( B @ ( n0 @ leq ) )
            & ( A @ ( n0 @ leq ) ) )
         => ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
            = ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) ) )
   => ! [A: $i,B: $i] :
        ( ( ( n5 @ ( B @ leq ) )
          & ( n5 @ ( A @ leq ) )
          & ( B @ ( n0 @ leq ) )
          & ( A @ ( n0 @ leq ) ) )
       => ( ( ( n2 = B )
            & ( n2 = A )
            & ( n1 = B )
            & ( n1 = A )
            & ~ ( ( n5 = B )
                & ( n5 = A ) )
            & ~ ( ( n5 = A )
                & ( n4 = B ) )
            & ~ ( ( n5 = B )
                & ( n4 = A ) )
            & ~ ( ( n4 = B )
                & ( n4 = A ) )
            & ~ ( ( n5 = A )
                & ( n3 = B ) )
            & ~ ( ( n4 = A )
                & ( n3 = B ) )
            & ~ ( ( n5 = B )
                & ( n3 = A ) )
            & ~ ( ( n4 = B )
                & ( n3 = A ) )
            & ~ ( ( n3 = B )
                & ( n3 = A ) )
            & ~ ( ( n5 = A )
                & ( n2 = B ) )
            & ~ ( ( n4 = A )
                & ( n2 = B ) )
            & ~ ( ( n3 = A )
                & ( n2 = B ) )
            & ~ ( ( n5 = B )
                & ( n2 = A ) )
            & ~ ( ( n4 = B )
                & ( n2 = A ) )
            & ~ ( ( n3 = B )
                & ( n2 = A ) )
            & ~ ( ( n2 = B )
                & ( n2 = A ) )
            & ~ ( ( n5 = A )
                & ( n1 = B ) )
            & ~ ( ( n4 = A )
                & ( n1 = B ) )
            & ~ ( ( n3 = A )
                & ( n1 = B ) )
            & ~ ( ( n2 = A )
                & ( n1 = B ) )
            & ~ ( ( n5 = B )
                & ( n1 = A ) )
            & ~ ( ( n4 = B )
                & ( n1 = A ) )
            & ~ ( ( n3 = B )
                & ( n1 = A ) )
            & ~ ( ( n2 = B )
                & ( n1 = A ) )
            & ~ ( ( n5 = A )
                & ( n0 = B ) )
            & ~ ( ( n4 = A )
                & ( n0 = B ) )
            & ~ ( ( n3 = A )
                & ( n0 = B ) )
            & ~ ( ( n2 = A )
                & ( n0 = B ) )
            & ~ ( ( n5 = B )
                & ( n0 = A ) )
            & ~ ( ( n4 = B )
                & ( n0 = A ) )
            & ~ ( ( n3 = B )
                & ( n0 = A ) ) )
         => ( ( n1 @ ( xinit_noise @ a_select2 ) )
            = ( n2 @ ( xinit_noise @ a_select2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0601) ).

thf(2,negated_conjecture,
    ~ ( ( ! [A: $i,B: $i] :
            ( ( ( n2 @ ( B @ leq ) )
              & ( n2 @ ( A @ leq ) )
              & ( B @ ( n0 @ leq ) )
              & ( A @ ( n0 @ leq ) ) )
           => ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
              = ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
        & ! [A: $i,B: $i] :
            ( ( ( n5 @ ( B @ leq ) )
              & ( n5 @ ( A @ leq ) )
              & ( B @ ( n0 @ leq ) )
              & ( A @ ( n0 @ leq ) ) )
           => ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
              = ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) ) )
     => ! [A: $i,B: $i] :
          ( ( ( n5 @ ( B @ leq ) )
            & ( n5 @ ( A @ leq ) )
            & ( B @ ( n0 @ leq ) )
            & ( A @ ( n0 @ leq ) ) )
         => ( ( ( n2 = B )
              & ( n2 = A )
              & ( n1 = B )
              & ( n1 = A )
              & ~ ( ( n5 = B )
                  & ( n5 = A ) )
              & ~ ( ( n5 = A )
                  & ( n4 = B ) )
              & ~ ( ( n5 = B )
                  & ( n4 = A ) )
              & ~ ( ( n4 = B )
                  & ( n4 = A ) )
              & ~ ( ( n5 = A )
                  & ( n3 = B ) )
              & ~ ( ( n4 = A )
                  & ( n3 = B ) )
              & ~ ( ( n5 = B )
                  & ( n3 = A ) )
              & ~ ( ( n4 = B )
                  & ( n3 = A ) )
              & ~ ( ( n3 = B )
                  & ( n3 = A ) )
              & ~ ( ( n5 = A )
                  & ( n2 = B ) )
              & ~ ( ( n4 = A )
                  & ( n2 = B ) )
              & ~ ( ( n3 = A )
                  & ( n2 = B ) )
              & ~ ( ( n5 = B )
                  & ( n2 = A ) )
              & ~ ( ( n4 = B )
                  & ( n2 = A ) )
              & ~ ( ( n3 = B )
                  & ( n2 = A ) )
              & ~ ( ( n2 = B )
                  & ( n2 = A ) )
              & ~ ( ( n5 = A )
                  & ( n1 = B ) )
              & ~ ( ( n4 = A )
                  & ( n1 = B ) )
              & ~ ( ( n3 = A )
                  & ( n1 = B ) )
              & ~ ( ( n2 = A )
                  & ( n1 = B ) )
              & ~ ( ( n5 = B )
                  & ( n1 = A ) )
              & ~ ( ( n4 = B )
                  & ( n1 = A ) )
              & ~ ( ( n3 = B )
                  & ( n1 = A ) )
              & ~ ( ( n2 = B )
                  & ( n1 = A ) )
              & ~ ( ( n5 = A )
                  & ( n0 = B ) )
              & ~ ( ( n4 = A )
                  & ( n0 = B ) )
              & ~ ( ( n3 = A )
                  & ( n0 = B ) )
              & ~ ( ( n2 = A )
                  & ( n0 = B ) )
              & ~ ( ( n5 = B )
                  & ( n0 = A ) )
              & ~ ( ( n4 = B )
                  & ( n0 = A ) )
              & ~ ( ( n3 = B )
                  & ( n0 = A ) ) )
           => ( ( n1 @ ( xinit_noise @ a_select2 ) )
              = ( n2 @ ( xinit_noise @ a_select2 ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(85,plain,
    ~ ( ( ! [A: $i,B: $i] :
            ( ( ( n2 @ ( B @ leq ) )
              & ( n2 @ ( A @ leq ) )
              & ( B @ ( n0 @ leq ) )
              & ( A @ ( n0 @ leq ) ) )
           => ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
              = ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
        & ! [A: $i,B: $i] :
            ( ( ( n5 @ ( B @ leq ) )
              & ( n5 @ ( A @ leq ) )
              & ( B @ ( n0 @ leq ) )
              & ( A @ ( n0 @ leq ) ) )
           => ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
              = ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) ) )
     => ! [A: $i,B: $i] :
          ( ( ( n5 @ ( B @ leq ) )
            & ( n5 @ ( A @ leq ) )
            & ( B @ ( n0 @ leq ) )
            & ( A @ ( n0 @ leq ) ) )
         => ( ( ( n2 = B )
              & ( n2 = A )
              & ( n1 = B )
              & ( n1 = A )
              & ~ ( ( n5 = B )
                  & ( n5 = A ) )
              & ~ ( ( n5 = A )
                  & ( n4 = B ) )
              & ~ ( ( n5 = B )
                  & ( n4 = A ) )
              & ~ ( ( n4 = B )
                  & ( n4 = A ) )
              & ~ ( ( n5 = A )
                  & ( n3 = B ) )
              & ~ ( ( n4 = A )
                  & ( n3 = B ) )
              & ~ ( ( n5 = B )
                  & ( n3 = A ) )
              & ~ ( ( n4 = B )
                  & ( n3 = A ) )
              & ~ ( ( n3 = B )
                  & ( n3 = A ) )
              & ~ ( ( n5 = A )
                  & ( n2 = B ) )
              & ~ ( ( n4 = A )
                  & ( n2 = B ) )
              & ~ ( ( n3 = A )
                  & ( n2 = B ) )
              & ~ ( ( n5 = B )
                  & ( n2 = A ) )
              & ~ ( ( n4 = B )
                  & ( n2 = A ) )
              & ~ ( ( n3 = B )
                  & ( n2 = A ) )
              & ~ ( ( n2 = B )
                  & ( n2 = A ) )
              & ~ ( ( n5 = A )
                  & ( n1 = B ) )
              & ~ ( ( n4 = A )
                  & ( n1 = B ) )
              & ~ ( ( n3 = A )
                  & ( n1 = B ) )
              & ~ ( ( n2 = A )
                  & ( n1 = B ) )
              & ~ ( ( n5 = B )
                  & ( n1 = A ) )
              & ~ ( ( n4 = B )
                  & ( n1 = A ) )
              & ~ ( ( n3 = B )
                  & ( n1 = A ) )
              & ~ ( ( n2 = B )
                  & ( n1 = A ) )
              & ~ ( ( n5 = A )
                  & ( n0 = B ) )
              & ~ ( ( n4 = A )
                  & ( n0 = B ) )
              & ~ ( ( n3 = A )
                  & ( n0 = B ) )
              & ~ ( ( n2 = A )
                  & ( n0 = B ) )
              & ~ ( ( n5 = B )
                  & ( n0 = A ) )
              & ~ ( ( n4 = B )
                  & ( n0 = A ) )
              & ~ ( ( n3 = B )
                  & ( n0 = A ) ) )
           => ( ( n1 @ ( xinit_noise @ a_select2 ) )
              = ( n2 @ ( xinit_noise @ a_select2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(86,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( n1 @ ( xinit_noise @ a_select2 ) )
       != ( n2 @ ( xinit_noise @ a_select2 ) ) )
      & ( n2 = sk2 )
      & ( n2 = sk1 )
      & ( n1 = sk2 )
      & ( n1 = sk1 )
      & ( ( n5 != sk2 )
        | ( n5 != sk1 ) )
      & ( ( n5 != sk1 )
        | ( n4 != sk2 ) )
      & ( ( n5 != sk2 )
        | ( n4 != sk1 ) )
      & ( ( n4 != sk2 )
        | ( n4 != sk1 ) )
      & ( ( n5 != sk1 )
        | ( n3 != sk2 ) )
      & ( ( n4 != sk1 )
        | ( n3 != sk2 ) )
      & ( ( n5 != sk2 )
        | ( n3 != sk1 ) )
      & ( ( n4 != sk2 )
        | ( n3 != sk1 ) )
      & ( ( n3 != sk2 )
        | ( n3 != sk1 ) )
      & ( ( n5 != sk1 )
        | ( n2 != sk2 ) )
      & ( ( n4 != sk1 )
        | ( n2 != sk2 ) )
      & ( ( n3 != sk1 )
        | ( n2 != sk2 ) )
      & ( ( n5 != sk2 )
        | ( n2 != sk1 ) )
      & ( ( n4 != sk2 )
        | ( n2 != sk1 ) )
      & ( ( n3 != sk2 )
        | ( n2 != sk1 ) )
      & ( ( n2 != sk2 )
        | ( n2 != sk1 ) )
      & ( ( n5 != sk1 )
        | ( n1 != sk2 ) )
      & ( ( n4 != sk1 )
        | ( n1 != sk2 ) )
      & ( ( n3 != sk1 )
        | ( n1 != sk2 ) )
      & ( ( n2 != sk1 )
        | ( n1 != sk2 ) )
      & ( ( n5 != sk2 )
        | ( n1 != sk1 ) )
      & ( ( n4 != sk2 )
        | ( n1 != sk1 ) )
      & ( ( n3 != sk2 )
        | ( n1 != sk1 ) )
      & ( ( n2 != sk2 )
        | ( n1 != sk1 ) )
      & ( ( n5 != sk1 )
        | ( n0 != sk2 ) )
      & ( ( n4 != sk1 )
        | ( n0 != sk2 ) )
      & ( ( n3 != sk1 )
        | ( n0 != sk2 ) )
      & ( ( n2 != sk1 )
        | ( n0 != sk2 ) )
      & ( ( n5 != sk2 )
        | ( n0 != sk1 ) )
      & ( ( n4 != sk2 )
        | ( n0 != sk1 ) )
      & ( ( n3 != sk2 )
        | ( n0 != sk1 ) )
      & ( n5 @ ( sk2 @ leq ) )
      & ( n5 @ ( sk1 @ leq ) )
      & ( sk2 @ ( n0 @ leq ) )
      & ( sk1 @ ( n0 @ leq ) )
      & ( ( ( D @ ( C @ ( r_ds1_filter @ a_select3 ) ) )
          = ( C @ ( D @ ( r_ds1_filter @ a_select3 ) ) ) )
        | ~ ( n2 @ ( D @ leq ) )
        | ~ ( n2 @ ( C @ leq ) )
        | ~ ( D @ ( n0 @ leq ) )
        | ~ ( C @ ( n0 @ leq ) ) )
      & ( ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
          = ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) )
        | ~ ( n5 @ ( B @ leq ) )
        | ~ ( n5 @ ( A @ leq ) )
        | ~ ( B @ ( n0 @ leq ) )
        | ~ ( A @ ( n0 @ leq ) ) ) ),
    inference(cnf,[status(esa)],[85]) ).

thf(88,plain,
    n1 = sk1,
    inference(cnfConj,[status(thm)],[86]) ).

thf(134,plain,
    sk1 = n1,
    inference(lifteq,[status(thm)],[88]) ).

thf(107,plain,
    n2 = sk1,
    inference(cnfConj,[status(thm)],[86]) ).

thf(161,plain,
    sk1 = n2,
    inference(lifteq,[status(thm)],[107]) ).

thf(623,plain,
    n1 = n2,
    inference(rewrite,[status(thm)],[161,134]) ).

thf(624,plain,
    sk1 = n2,
    inference(rewrite,[status(thm)],[134,623]) ).

thf(95,plain,
    ( ( n2 != sk2 )
    | ( n1 != sk1 ) ),
    inference(cnfConj,[status(thm)],[86]) ).

thf(130,plain,
    ( ( sk2 != n2 )
    | ( sk1 != n1 ) ),
    inference(lifteq,[status(thm)],[95]) ).

thf(103,plain,
    n2 = sk2,
    inference(cnfConj,[status(thm)],[86]) ).

thf(154,plain,
    sk2 = n2,
    inference(lifteq,[status(thm)],[103]) ).

thf(628,plain,
    ( ( n2 != n2 )
    | ( sk1 != n2 ) ),
    inference(rewrite,[status(thm)],[130,154,623]) ).

thf(629,plain,
    sk1 != n2,
    inference(simp,[status(thm)],[628]) ).

thf(630,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[624,629]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : SWV226+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.12  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.48  % Computer : n004.cluster.edu
% 0.23/0.48  % Model    : x86_64 x86_64
% 0.23/0.48  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48  % Memory   : 8046.5625MB
% 0.23/0.48  % OS       : Linux 6.8.0-71-generic
% 0.23/0.48  % CPULimit : 300
% 0.23/0.48  % WCLimit  : 300
% 0.23/0.48  % DateTime : Sat Sep 26 13:20:36 UTC 2026
% 0.23/0.49  % CPUTime  : 
% 0.23/0.49  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.44/1.33  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.39/1.75  % [INFO] 	 Parsing done (415ms). 
% 2.39/1.77  % [INFO] 	 Running in sequential loop mode. 
% 3.70/2.36  % [INFO] 	 eprover registered as external prover. 
% 3.70/2.37  % [INFO] 	 Scanning for conjecture ... 
% 4.36/2.63  % [INFO] 	 Found a conjecture (or negated_conjecture) and 84 axioms. Running axiom selection ... 
% 4.84/2.81  % [INFO] 	 Axiom selection finished. Selected 82 axioms (removed 2 axioms). 
% 5.14/2.97  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 5.14/2.99  % [INFO] 	 Type checking passed. 
% 5.14/3.00  % [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 ... 
% 13.55/5.70  % [INFO] 	 Killing All external provers ... 
% 13.55/5.71  % Time passed: 5007ms (effective reasoning time: 3924ms)
% 13.55/5.71  % 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)>
% 13.55/5.71  % Axioms used in derivation (0): 
% 13.55/5.71  % No. of inferences in proof: 17
% 13.55/5.71  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5007 ms resp. 3924 ms w/o parsing
% 14.17/5.81  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.17/5.82  % [INFO] 	 Killing All external provers ... 
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