TSTP Solution File: SYO444^1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO444^1 : 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 09:00:17 EDT 2024

% Result   : Theorem 8.37s 2.67s
% Output   : Refutation 8.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  100 (  14 unt;  19 typ;   8 def)
%            Number of atoms       :  310 (  28 equ;   0 cnn)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  678 ( 165   ~; 144   |;   2   &; 363   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   43 (  43   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  21 usr;  10 con; 0-3 aty)
%            Number of variables   :   90 (  12   ^  78   !;   0   ?;  90   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

thf(mnot_type,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(mnot_def,definition,
    ( mnot
    = ( ^ [A: $i > $o,B: $i] :
          ~ ( A @ B ) ) ) ).

thf(mor_type,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mor_def,definition,
    ( mor
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( A @ C )
          | ( B @ C ) ) ) ) ).

thf(mequiv_type,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mequiv_def,definition,
    ( mequiv
    = ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ A ) ) ) ) ).

thf(msymmetric_type,type,
    msymmetric: ( $i > $i > $o ) > $o ).

thf(msymmetric_def,definition,
    ( msymmetric
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i,C: $i] :
          ( ( A @ B @ C )
         => ( A @ C @ B ) ) ) ) ).

thf(mtransitive_type,type,
    mtransitive: ( $i > $i > $o ) > $o ).

thf(mtransitive_def,definition,
    ( mtransitive
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i,C: $i,D: $i] :
          ( ( ( A @ B @ C )
            & ( A @ C @ D ) )
         => ( A @ B @ D ) ) ) ) ).

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(mvalid_def,definition,
    ( mvalid
    = ( '!' @ $i ) ) ).

thf(rel_s5_type,type,
    rel_s5: $i > $i > $o ).

thf(mbox_s5_type,type,
    mbox_s5: ( $i > $o ) > $i > $o ).

thf(mbox_s5_def,definition,
    ( mbox_s5
    = ( ^ [A: $i > $o,B: $i] :
        ! [C: $i] :
          ( ~ ( rel_s5 @ B @ C )
          | ( A @ C ) ) ) ) ).

thf(mdia_s5_type,type,
    mdia_s5: ( $i > $o ) > $i > $o ).

thf(mdia_s5_def,definition,
    ( mdia_s5
    = ( ^ [A: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ A ) ) ) ) ) ).

thf(p_type,type,
    p: $i > $o ).

thf(q_type,type,
    q: $i > $o ).

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

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

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

thf(sk4_type,type,
    sk4: $i ).

thf(sk5_type,type,
    sk5: $i ).

thf(sk6_type,type,
    sk6: $i ).

thf(sk7_type,type,
    sk7: $i ).

thf(1,conjecture,
    mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mnot @ ( mdia_s5 @ p ) ) @ ( mdia_s5 @ q ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mnot @ ( mdia_s5 @ p ) ) @ ( mdia_s5 @ q ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [A: $i] :
        ~ ( ~ ( ~ ! [B: $i] :
                    ( ~ ( rel_s5 @ A @ B )
                    | ~ ( p @ B )
                    | ~ ! [C: $i] :
                          ( ~ ( rel_s5 @ B @ C )
                          | ~ ( q @ C ) ) )
              | ! [B: $i] :
                  ( ~ ( rel_s5 @ A @ B )
                  | ~ ( p @ B ) )
              | ~ ! [B: $i] :
                    ( ~ ( rel_s5 @ A @ B )
                    | ~ ( q @ B ) ) )
          | ~ ( ~ ( ! [B: $i] :
                      ( ~ ( rel_s5 @ A @ B )
                      | ~ ( p @ B ) )
                  | ~ ! [B: $i] :
                        ( ~ ( rel_s5 @ A @ B )
                        | ~ ( q @ B ) ) )
              | ! [B: $i] :
                  ( ~ ( rel_s5 @ A @ B )
                  | ~ ( p @ B )
                  | ~ ! [C: $i] :
                        ( ~ ( rel_s5 @ B @ C )
                        | ~ ( q @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    ~ ~ ( ~ ! [A: $i] :
              ( ~ ! [B: $i] :
                    ( ~ ( rel_s5 @ A @ B )
                    | ~ ( p @ B )
                    | ~ ! [C: $i] :
                          ( ~ ( rel_s5 @ B @ C )
                          | ~ ( q @ C ) ) )
              | ! [B: $i] :
                  ( ~ ( rel_s5 @ A @ B )
                  | ~ ( p @ B ) )
              | ~ ! [B: $i] :
                    ( ~ ( rel_s5 @ A @ B )
                    | ~ ( q @ B ) ) )
        | ~ ! [A: $i] :
              ( ~ ( ! [B: $i] :
                      ( ~ ( rel_s5 @ A @ B )
                      | ~ ( p @ B ) )
                  | ~ ! [B: $i] :
                        ( ~ ( rel_s5 @ A @ B )
                        | ~ ( q @ B ) ) )
              | ! [B: $i] :
                  ( ~ ( rel_s5 @ A @ B )
                  | ~ ( p @ B )
                  | ~ ! [C: $i] :
                        ( ~ ( rel_s5 @ B @ C )
                        | ~ ( q @ C ) ) ) ) ),
    inference(miniscope,[status(thm)],[6]) ).

thf(15,plain,
    ( ( rel_s5 @ sk2 @ sk4 )
    | sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(17,plain,
    ( ( p @ sk4 )
    | sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(11,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk2 @ A )
      | ~ ( p @ A )
      | ( rel_s5 @ A @ ( sk3 @ A ) )
      | sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(42,plain,
    ! [A: $i] :
      ( sk1
      | ~ ( rel_s5 @ sk2 @ A )
      | ( rel_s5 @ A @ ( sk3 @ A ) )
      | ( ( p @ sk4 )
       != ( p @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[17,11]) ).

thf(43,plain,
    ( sk1
    | ~ ( rel_s5 @ sk2 @ sk4 )
    | ( rel_s5 @ sk4 @ ( sk3 @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( sk4 ))]]) ).

thf(372,plain,
    ( sk1
    | ( rel_s5 @ sk4 @ ( sk3 @ sk4 ) )
    | ( ( rel_s5 @ sk2 @ sk4 )
     != ( rel_s5 @ sk2 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[15,43]) ).

thf(373,plain,
    ( sk1
    | ( rel_s5 @ sk4 @ ( sk3 @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[372:[]]) ).

thf(5,axiom,
    msymmetric @ rel_s5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).

thf(26,plain,
    ! [A: $i,B: $i] :
      ( ( rel_s5 @ A @ B )
     => ( rel_s5 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ~ ( rel_s5 @ A @ B )
      | ( rel_s5 @ B @ A ) ),
    inference(cnf,[status(esa)],[26]) ).

thf(423,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( rel_s5 @ B @ A )
      | ( ( rel_s5 @ sk4 @ ( sk3 @ sk4 ) )
       != ( rel_s5 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[373,27]) ).

thf(424,plain,
    ( sk1
    | ( rel_s5 @ ( sk3 @ sk4 ) @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[423:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 @ sk4 ))]]) ).

thf(8,plain,
    ( ~ sk1
    | ( p @ sk7 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(10,plain,
    ( ~ sk1
    | ( rel_s5 @ sk5 @ sk7 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(16,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk5 @ A )
      | ~ ( p @ A )
      | ( rel_s5 @ sk5 @ sk6 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(21,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk5 @ A )
      | ~ ( p @ A )
      | ( rel_s5 @ sk5 @ sk6 ) ),
    inference(simp,[status(thm)],[16]) ).

thf(202,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( p @ A )
      | ( rel_s5 @ sk5 @ sk6 )
      | ( ( rel_s5 @ sk5 @ sk7 )
       != ( rel_s5 @ sk5 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10,21]) ).

thf(203,plain,
    ( ~ sk1
    | ~ ( p @ sk7 )
    | ( rel_s5 @ sk5 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( sk7 ))]]) ).

thf(4,axiom,
    mtransitive @ rel_s5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).

thf(24,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rel_s5 @ A @ B )
        & ( rel_s5 @ B @ C ) )
     => ( rel_s5 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( rel_s5 @ A @ B )
      | ~ ( rel_s5 @ B @ C )
      | ( rel_s5 @ A @ C ) ),
    inference(cnf,[status(esa)],[24]) ).

thf(9,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk5 @ A )
      | ~ ( p @ A )
      | ( q @ sk6 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(19,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk5 @ A )
      | ~ ( p @ A )
      | ( q @ sk6 ) ),
    inference(simp,[status(thm)],[9]) ).

thf(158,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( p @ A )
      | ( q @ sk6 )
      | ( ( rel_s5 @ sk5 @ sk7 )
       != ( rel_s5 @ sk5 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10,19]) ).

thf(159,plain,
    ( ~ sk1
    | ~ ( p @ sk7 )
    | ( q @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( sk7 ))]]) ).

thf(242,plain,
    ( ~ sk1
    | ( q @ sk6 )
    | ( ( p @ sk7 )
     != ( p @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[8,159]) ).

thf(243,plain,
    ( ~ sk1
    | ( q @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[242:[]]) ).

thf(14,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk7 @ A )
      | ~ ( q @ A ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(18,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk7 @ A )
      | ~ ( q @ A ) ),
    inference(simp,[status(thm)],[14]) ).

thf(60,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( rel_s5 @ A @ B )
      | ~ sk1
      | ~ ( q @ C )
      | ( ( rel_s5 @ B @ A )
       != ( rel_s5 @ sk7 @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[27,18]) ).

thf(61,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ A @ sk7 )
      | ~ sk1
      | ~ ( q @ A ) ),
    inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( A )),bind(B,$thf( sk7 )),bind(C,$thf( A ))]]) ).

thf(253,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ A @ sk7 )
      | ( ( q @ sk6 )
       != ( q @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[243,61]) ).

thf(254,plain,
    ( ~ sk1
    | ~ ( rel_s5 @ sk6 @ sk7 ) ),
    inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( sk6 ))]]) ).

thf(345,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( rel_s5 @ A @ B )
      | ~ ( rel_s5 @ B @ C )
      | ~ sk1
      | ( ( rel_s5 @ A @ C )
       != ( rel_s5 @ sk6 @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[25,254]) ).

thf(346,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk6 @ A )
      | ~ ( rel_s5 @ A @ sk7 )
      | ~ sk1 ),
    inference(pattern_uni,[status(thm)],[345:[bind(A,$thf( sk6 )),bind(B,$thf( B )),bind(C,$thf( sk7 ))]]) ).

thf(354,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk6 @ A )
      | ~ ( rel_s5 @ A @ sk7 )
      | ~ sk1 ),
    inference(simp,[status(thm)],[346]) ).

thf(466,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk6 @ A )
      | ( ( rel_s5 @ sk5 @ sk7 )
       != ( rel_s5 @ A @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[10,354]) ).

thf(467,plain,
    ( ~ sk1
    | ~ ( rel_s5 @ sk6 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[466:[bind(A,$thf( sk5 ))]]) ).

thf(512,plain,
    ! [B: $i,A: $i] :
      ( ~ ( rel_s5 @ A @ B )
      | ~ sk1
      | ( ( rel_s5 @ B @ A )
       != ( rel_s5 @ sk6 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[27,467]) ).

thf(513,plain,
    ( ~ ( rel_s5 @ sk5 @ sk6 )
    | ~ sk1 ),
    inference(pattern_uni,[status(thm)],[512:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(562,plain,
    ( ~ sk1
    | ~ ( p @ sk7 )
    | ( ( rel_s5 @ sk5 @ sk6 )
     != ( rel_s5 @ sk5 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[203,513]) ).

thf(563,plain,
    ( ~ sk1
    | ~ ( p @ sk7 ) ),
    inference(pattern_uni,[status(thm)],[562:[]]) ).

thf(587,plain,
    ( ~ sk1
    | ( ( p @ sk7 )
     != ( p @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[8,563]) ).

thf(588,plain,
    ~ sk1,
    inference(pattern_uni,[status(thm)],[587:[]]) ).

thf(643,plain,
    ( $false
    | ( rel_s5 @ ( sk3 @ sk4 ) @ sk4 ) ),
    inference(rewrite,[status(thm)],[424,588]) ).

thf(644,plain,
    rel_s5 @ ( sk3 @ sk4 ) @ sk4,
    inference(simp,[status(thm)],[643]) ).

thf(68,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( rel_s5 @ B @ A )
      | ( ( rel_s5 @ sk2 @ sk4 )
       != ( rel_s5 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[15,27]) ).

thf(69,plain,
    ( sk1
    | ( rel_s5 @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).

thf(293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( sk1
      | ~ ( rel_s5 @ A @ B )
      | ( rel_s5 @ A @ C )
      | ( ( rel_s5 @ sk4 @ sk2 )
       != ( rel_s5 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[69,25]) ).

thf(294,plain,
    ! [A: $i] :
      ( sk1
      | ~ ( rel_s5 @ A @ sk4 )
      | ( rel_s5 @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( sk2 ))]]) ).

thf(908,plain,
    ! [A: $i] :
      ( $false
      | ~ ( rel_s5 @ A @ sk4 )
      | ( rel_s5 @ A @ sk2 ) ),
    inference(rewrite,[status(thm)],[294,588]) ).

thf(909,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ A @ sk4 )
      | ( rel_s5 @ A @ sk2 ) ),
    inference(simp,[status(thm)],[908]) ).

thf(923,plain,
    ! [A: $i] :
      ( ( rel_s5 @ A @ sk2 )
      | ( ( rel_s5 @ ( sk3 @ sk4 ) @ sk4 )
       != ( rel_s5 @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[644,909]) ).

thf(924,plain,
    rel_s5 @ ( sk3 @ sk4 ) @ sk2,
    inference(pattern_uni,[status(thm)],[923:[bind(A,$thf( sk3 @ sk4 ))]]) ).

thf(13,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk2 @ A )
      | ~ ( p @ A )
      | ( q @ ( sk3 @ A ) )
      | sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(107,plain,
    ! [A: $i] :
      ( sk1
      | ~ ( p @ A )
      | ( q @ ( sk3 @ A ) )
      | ( ( rel_s5 @ sk2 @ sk4 )
       != ( rel_s5 @ sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[15,13]) ).

thf(108,plain,
    ( sk1
    | ~ ( p @ sk4 )
    | ( q @ ( sk3 @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( sk4 ))]]) ).

thf(121,plain,
    ( sk1
    | ( q @ ( sk3 @ sk4 ) )
    | ( ( p @ sk4 )
     != ( p @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[17,108]) ).

thf(122,plain,
    ( sk1
    | ( q @ ( sk3 @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[121:[]]) ).

thf(12,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk2 @ A )
      | ~ ( q @ A )
      | sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(20,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk2 @ A )
      | ~ ( q @ A )
      | sk1 ),
    inference(simp,[status(thm)],[12]) ).

thf(56,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( rel_s5 @ A @ B )
      | ~ ( q @ C )
      | sk1
      | ( ( rel_s5 @ B @ A )
       != ( rel_s5 @ sk2 @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[27,20]) ).

thf(57,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ A @ sk2 )
      | ~ ( q @ A )
      | sk1 ),
    inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).

thf(606,plain,
    ! [A: $i] :
      ( sk1
      | ~ ( rel_s5 @ A @ sk2 )
      | ( ( q @ ( sk3 @ sk4 ) )
       != ( q @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[122,57]) ).

thf(607,plain,
    ( sk1
    | ~ ( rel_s5 @ ( sk3 @ sk4 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[606:[bind(A,$thf( sk3 @ sk4 ))]]) ).

thf(784,plain,
    ( $false
    | ~ ( rel_s5 @ ( sk3 @ sk4 ) @ sk2 ) ),
    inference(rewrite,[status(thm)],[607,588]) ).

thf(785,plain,
    ~ ( rel_s5 @ ( sk3 @ sk4 ) @ sk2 ),
    inference(simp,[status(thm)],[784]) ).

thf(933,plain,
    $false,
    inference(rewrite,[status(thm)],[924,785]) ).

thf(934,plain,
    $false,
    inference(simp,[status(thm)],[933]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem  : SYO444^1 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n026.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Mon May 20 08:58:54 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.96/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.46/1.06  % [INFO] 	 Parsing done (162ms). 
% 1.46/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.94/1.27  % [INFO] 	 nitpick registered as external prover. 
% 1.94/1.28  % [INFO] 	 Scanning for conjecture ... 
% 2.30/1.38  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 2.30/1.40  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 2.30/1.40  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.30/1.41  % [INFO] 	 Type checking passed. 
% 2.30/1.41  % [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 ... 
% 8.37/2.66  % [INFO] 	 Killing All external provers ... 
% 8.37/2.67  % Time passed: 2148ms (effective reasoning time: 1590ms)
% 8.37/2.67  % 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)>
% 8.37/2.67  % Axioms used in derivation (2): a3, a2
% 8.37/2.67  % No. of inferences in proof: 73
% 8.37/2.67  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2148 ms resp. 1590 ms w/o parsing
% 8.37/2.72  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.37/2.72  % [INFO] 	 Killing All external provers ... 
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