TSTP Solution File: SWV401+1 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SWV401+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% 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 : Mon Jun 24 17:28:53 EDT 2024

% Result   : Theorem 135.05s 25.34s
% Output   : Refutation 135.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   89 (  22 unt;   0 typ;   0 def)
%            Number of atoms       :  241 (  78 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 1082 (  91   ~;  81   |;  20   &; 867   @)
%                                         (   2 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   8 con; 0-3 aty)
%            Number of variables   :  214 (   0   ^ 214   !;   0   ?; 214   :)

% Comments : 
%------------------------------------------------------------------------------
thf(pair_in_list_type,type,
    pair_in_list: $i > $i > $i > $o ).

thf(less_than_type,type,
    less_than: $i > $i > $o ).

thf(update_slb_type,type,
    update_slb: $i > $i > $i ).

thf(insert_slb_type,type,
    insert_slb: $i > $i > $i ).

thf(pair_type,type,
    pair: $i > $i > $i ).

thf(strictly_less_than_type,type,
    strictly_less_than: $i > $i > $o ).

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

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

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

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

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

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

thf(1,conjecture,
    ! [A: $i] :
      ( ! [B: $i,C: $i,D: $i] :
          ( ( ( pair_in_list @ A @ B @ C )
            & ( less_than @ D @ C ) )
         => ( pair_in_list @ ( update_slb @ A @ D ) @ B @ C ) )
     => ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
          ( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ B @ C )
            & ( less_than @ D @ C ) )
         => ( pair_in_list @ ( update_slb @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ D ) @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l37_co) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ! [B: $i,C: $i,D: $i] :
            ( ( ( pair_in_list @ A @ B @ C )
              & ( less_than @ D @ C ) )
           => ( pair_in_list @ ( update_slb @ A @ D ) @ B @ C ) )
       => ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
            ( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ B @ C )
              & ( less_than @ D @ C ) )
           => ( pair_in_list @ ( update_slb @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ D ) @ B @ C ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(21,plain,
    ~ ! [A: $i] :
        ( ! [B: $i,C: $i,D: $i] :
            ( ( ( pair_in_list @ A @ B @ C )
              & ( less_than @ D @ C ) )
           => ( pair_in_list @ ( update_slb @ A @ D ) @ B @ C ) )
       => ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
            ( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ B @ C )
              & ( less_than @ D @ C ) )
           => ( pair_in_list @ ( update_slb @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ D ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(22,plain,
    ~ ( pair_in_list @ ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) @ sk2 @ sk3 ),
    inference(cnf,[status(esa)],[21]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ( less_than @ A @ B )
      | ( less_than @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).

thf(70,plain,
    ! [A: $i,B: $i] :
      ( ( less_than @ A @ B )
      | ( less_than @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(71,plain,
    ! [B: $i,A: $i] :
      ( ( less_than @ A @ B )
      | ( less_than @ B @ A ) ),
    inference(cnf,[status(esa)],[70]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( strictly_less_than @ A @ B )
    <=> ( ( less_than @ A @ B )
        & ~ ( less_than @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).

thf(56,plain,
    ! [A: $i,B: $i] :
      ( ( ( strictly_less_than @ A @ B )
       => ( ( less_than @ A @ B )
          & ~ ( less_than @ B @ A ) ) )
      & ( ( ( less_than @ A @ B )
          & ~ ( less_than @ B @ A ) )
       => ( strictly_less_than @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(57,plain,
    ( ! [A: $i,B: $i] :
        ( ( strictly_less_than @ A @ B )
       => ( ( less_than @ A @ B )
          & ~ ( less_than @ B @ A ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( less_than @ A @ B )
          & ~ ( less_than @ B @ A ) )
       => ( strictly_less_than @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[56]) ).

thf(58,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ( less_than @ B @ A )
      | ( strictly_less_than @ A @ B ) ),
    inference(cnf,[status(esa)],[57]) ).

thf(61,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ( less_than @ B @ A )
      | ( strictly_less_than @ A @ B ) ),
    inference(simp,[status(thm)],[58]) ).

thf(24,plain,
    pair_in_list @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk2 @ sk3,
    inference(cnf,[status(esa)],[21]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
    <=> ( ( pair_in_list @ A @ C @ E )
        | ( ( B = C )
          & ( D = E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).

thf(72,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
       => ( ( pair_in_list @ A @ C @ E )
          | ( ( B = C )
            & ( D = E ) ) ) )
      & ( ( ( pair_in_list @ A @ C @ E )
          | ( ( B = C )
            & ( D = E ) ) )
       => ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(73,plain,
    ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
       => ( ( pair_in_list @ A @ C @ E )
          | ( ( B = C )
            & ( D = E ) ) ) )
    & ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( ( pair_in_list @ A @ C @ E )
          | ( ( B = C )
            & ( D = E ) ) )
       => ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
    inference(miniscope,[status(thm)],[72]) ).

thf(76,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
      | ( pair_in_list @ A @ C @ E )
      | ( D = E ) ),
    inference(cnf,[status(esa)],[73]) ).

thf(81,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
      | ( pair_in_list @ A @ C @ E ) ),
    inference(lifteq,[status(thm)],[76]) ).

thf(4403,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ( pair_in_list @ A @ C @ E )
      | ( ( pair_in_list @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk2 @ sk3 )
       != ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[24,81]) ).

thf(4404,plain,
    ( ( sk6 = sk3 )
    | ( pair_in_list @ sk1 @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[4403:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 )),bind(C,$thf( sk2 )),bind(D,$thf( sk6 )),bind(E,$thf( sk3 ))]]) ).

thf(23,plain,
    less_than @ sk4 @ sk3,
    inference(cnf,[status(esa)],[21]) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( pair_in_list @ sk1 @ A @ B )
      | ~ ( less_than @ C @ B )
      | ( pair_in_list @ ( update_slb @ sk1 @ C ) @ A @ B ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(103,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( pair_in_list @ sk1 @ A @ B )
      | ( pair_in_list @ ( update_slb @ sk1 @ C ) @ A @ B )
      | ( ( less_than @ sk4 @ sk3 )
       != ( less_than @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[23,25]) ).

thf(104,plain,
    ! [A: $i] :
      ( ~ ( pair_in_list @ sk1 @ A @ sk3 )
      | ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ A @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).

thf(74,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( pair_in_list @ A @ C @ E )
      | ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
    inference(cnf,[status(esa)],[73]) ).

thf(78,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( pair_in_list @ A @ C @ E )
      | ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
    inference(simp,[status(thm)],[74]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( strictly_less_than @ D @ C )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).

thf(49,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( strictly_less_than @ D @ C )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(50,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( strictly_less_than @ D @ C )
      | ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
    inference(cnf,[status(esa)],[49]) ).

thf(51,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) )
      | ~ ( strictly_less_than @ D @ C ) ),
    inference(lifteq,[status(thm)],[50]) ).

thf(1692,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( strictly_less_than @ D @ C )
      | ~ ( pair_in_list @ ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) @ sk2 @ sk3 )
      | ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
       != ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[51,22]) ).

thf(1693,plain,
    ( ~ ( strictly_less_than @ sk6 @ sk4 )
    | ~ ( pair_in_list @ ( insert_slb @ ( update_slb @ sk1 @ sk4 ) @ ( pair @ sk5 @ sk4 ) ) @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[1692:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 )),bind(C,$thf( sk4 )),bind(D,$thf( sk6 ))]]) ).

thf(3495,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( pair_in_list @ A @ C @ E )
      | ~ ( strictly_less_than @ sk6 @ sk4 )
      | ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
       != ( pair_in_list @ ( insert_slb @ ( update_slb @ sk1 @ sk4 ) @ ( pair @ sk5 @ sk4 ) ) @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[78,1693]) ).

thf(3496,plain,
    ( ~ ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ sk2 @ sk3 )
    | ~ ( strictly_less_than @ sk6 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[3495:[bind(A,$thf( update_slb @ sk1 @ sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( sk2 )),bind(D,$thf( sk4 )),bind(E,$thf( sk3 ))]]) ).

thf(3959,plain,
    ! [A: $i] :
      ( ~ ( pair_in_list @ sk1 @ A @ sk3 )
      | ~ ( strictly_less_than @ sk6 @ sk4 )
      | ( ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ A @ sk3 )
       != ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[104,3496]) ).

thf(3960,plain,
    ( ~ ( pair_in_list @ sk1 @ sk2 @ sk3 )
    | ~ ( strictly_less_than @ sk6 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[3959:[bind(A,$thf( sk2 ))]]) ).

thf(6165,plain,
    ( ( sk6 = sk3 )
    | ~ ( strictly_less_than @ sk6 @ sk4 )
    | ( ( pair_in_list @ sk1 @ sk2 @ sk3 )
     != ( pair_in_list @ sk1 @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[4404,3960]) ).

thf(6166,plain,
    ( ( sk6 = sk3 )
    | ~ ( strictly_less_than @ sk6 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[6165:[]]) ).

thf(77,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
      | ( pair_in_list @ A @ C @ E )
      | ( B = C ) ),
    inference(cnf,[status(esa)],[73]) ).

thf(82,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
      | ( pair_in_list @ A @ C @ E ) ),
    inference(lifteq,[status(thm)],[77]) ).

thf(6452,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( pair_in_list @ A @ C @ E )
      | ( ( pair_in_list @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk2 @ sk3 )
       != ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[24,82]) ).

thf(6453,plain,
    ( ( sk5 = sk2 )
    | ( pair_in_list @ sk1 @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[6452:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 )),bind(C,$thf( sk2 )),bind(D,$thf( sk6 )),bind(E,$thf( sk3 ))]]) ).

thf(8796,plain,
    ( ( sk5 = sk2 )
    | ~ ( strictly_less_than @ sk6 @ sk4 )
    | ( ( pair_in_list @ sk1 @ sk2 @ sk3 )
     != ( pair_in_list @ sk1 @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[6453,3960]) ).

thf(8797,plain,
    ( ( sk5 = sk2 )
    | ~ ( strictly_less_than @ sk6 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[8796:[]]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( less_than @ C @ D )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).

thf(83,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( less_than @ C @ D )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(84,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ C @ D )
      | ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    inference(cnf,[status(esa)],[83]) ).

thf(85,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) )
        = ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) )
      | ~ ( less_than @ C @ D ) ),
    inference(lifteq,[status(thm)],[84]) ).

thf(9054,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) )
        = ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) )
      | ( ( less_than @ sk4 @ sk3 )
       != ( less_than @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[23,85]) ).

thf(9055,plain,
    ! [B: $i,A: $i] :
      ( ( insert_slb @ ( update_slb @ A @ sk4 ) @ ( pair @ B @ sk3 ) )
      = ( update_slb @ ( insert_slb @ A @ ( pair @ B @ sk3 ) ) @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[9054:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( sk3 ))]]) ).

thf(75,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B != C )
      | ( D != E )
      | ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
    inference(cnf,[status(esa)],[73]) ).

thf(79,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B != C )
      | ( D != E )
      | ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
    inference(lifteq,[status(thm)],[75]) ).

thf(80,plain,
    ! [C: $i,B: $i,A: $i] : ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B @ C ),
    inference(simp,[status(thm)],[79]) ).

thf(744,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B @ C )
     != ( pair_in_list @ ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) @ sk2 @ sk3 ) ),
    inference(paramod_ordered,[status(thm)],[80,22]) ).

thf(752,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( insert_slb @ A @ ( pair @ B @ C ) )
       != ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) )
      | ( B != sk2 )
      | ( C != sk3 ) ),
    inference(simp,[status(thm)],[744]) ).

thf(755,plain,
    ! [A: $i] :
      ( ( insert_slb @ A @ ( pair @ sk2 @ sk3 ) )
     != ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) ),
    inference(simp,[status(thm)],[752]) ).

thf(9716,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ sk3 ) ) @ sk4 )
       != ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) )
      | ( ( insert_slb @ ( update_slb @ A @ sk4 ) @ ( pair @ B @ sk3 ) )
       != ( insert_slb @ C @ ( pair @ sk2 @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9055,755]) ).

thf(9717,plain,
    ! [A: $i] :
      ( ( update_slb @ ( insert_slb @ A @ ( pair @ sk2 @ sk3 ) ) @ sk4 )
     != ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[9716:[bind(A,$thf( D )),bind(B,$thf( sk2 )),bind(C,$thf( update_slb @ D @ sk4 ))]]) ).

thf(9839,plain,
    ! [A: $i] :
      ( ( update_slb @ ( insert_slb @ A @ ( pair @ sk2 @ sk3 ) ) @ sk4 )
     != ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) ),
    inference(simp,[status(thm)],[9717]) ).

thf(13207,plain,
    ! [A: $i] :
      ( ( ( insert_slb @ A @ ( pair @ sk2 @ sk3 ) )
       != ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) )
      | ( sk4 != sk4 ) ),
    inference(simp,[status(thm)],[9839]) ).

thf(13532,plain,
    ! [A: $i] :
      ( ( insert_slb @ A @ ( pair @ sk2 @ sk3 ) )
     != ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) ),
    inference(simp,[status(thm)],[13207]) ).

thf(14694,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( ( pair @ sk5 @ sk6 )
       != ( pair @ sk2 @ sk3 ) ) ),
    inference(simp,[status(thm)],[13532]) ).

thf(14926,plain,
    ( ( pair @ sk5 @ sk6 )
   != ( pair @ sk2 @ sk3 ) ),
    inference(simp,[status(thm)],[14694]) ).

thf(14947,plain,
    ( ( sk5 != sk2 )
    | ( sk6 != sk3 ) ),
    inference(simp,[status(thm)],[14926]) ).

thf(15357,plain,
    ( ~ ( strictly_less_than @ sk6 @ sk4 )
    | ( sk6 != sk3 )
    | ( sk5 != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[8797,14947]) ).

thf(15358,plain,
    ( ~ ( strictly_less_than @ sk6 @ sk4 )
    | ( sk6 != sk3 ) ),
    inference(pattern_uni,[status(thm)],[15357:[]]) ).

thf(16324,plain,
    ( ~ ( strictly_less_than @ sk6 @ sk4 )
    | ( sk6 != sk6 ) ),
    inference(paramod_ordered,[status(thm)],[6166,15358]) ).

thf(16325,plain,
    ~ ( strictly_less_than @ sk6 @ sk4 ),
    inference(pattern_uni,[status(thm)],[16324:[]]) ).

thf(16364,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ( less_than @ B @ A )
      | ( ( strictly_less_than @ A @ B )
       != ( strictly_less_than @ sk6 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[61,16325]) ).

thf(16365,plain,
    ( ~ ( less_than @ sk6 @ sk4 )
    | ( less_than @ sk4 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[16364:[bind(A,$thf( sk6 )),bind(B,$thf( sk4 ))]]) ).

thf(19552,plain,
    ! [B: $i,A: $i] :
      ( ( less_than @ B @ A )
      | ( less_than @ sk4 @ sk6 )
      | ( ( less_than @ A @ B )
       != ( less_than @ sk6 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[71,16365]) ).

thf(19553,plain,
    ( ( less_than @ sk4 @ sk6 )
    | ( less_than @ sk4 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[19552:[bind(A,$thf( sk6 )),bind(B,$thf( sk4 ))]]) ).

thf(19616,plain,
    less_than @ sk4 @ sk6,
    inference(simp,[status(thm)],[19553]) ).

thf(19634,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) )
        = ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) )
      | ( ( less_than @ sk4 @ sk6 )
       != ( less_than @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[19616,85]) ).

thf(19635,plain,
    ! [B: $i,A: $i] :
      ( ( insert_slb @ ( update_slb @ A @ sk4 ) @ ( pair @ B @ sk6 ) )
      = ( update_slb @ ( insert_slb @ A @ ( pair @ B @ sk6 ) ) @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[19634:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( sk6 ))]]) ).

thf(15391,plain,
    ( ( pair_in_list @ sk1 @ sk2 @ sk3 )
    | ( sk6 != sk3 )
    | ( sk5 != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[6453,14947]) ).

thf(15392,plain,
    ( ( pair_in_list @ sk1 @ sk2 @ sk3 )
    | ( sk6 != sk3 ) ),
    inference(pattern_uni,[status(thm)],[15391:[]]) ).

thf(17955,plain,
    ( ( pair_in_list @ sk1 @ sk2 @ sk3 )
    | ( sk6 != sk6 ) ),
    inference(paramod_ordered,[status(thm)],[4404,15392]) ).

thf(17956,plain,
    pair_in_list @ sk1 @ sk2 @ sk3,
    inference(pattern_uni,[status(thm)],[17955:[]]) ).

thf(18066,plain,
    ! [A: $i] :
      ( ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ A @ sk3 )
      | ( ( pair_in_list @ sk1 @ sk2 @ sk3 )
       != ( pair_in_list @ sk1 @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[17956,104]) ).

thf(18067,plain,
    pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ sk2 @ sk3,
    inference(pattern_uni,[status(thm)],[18066:[bind(A,$thf( sk2 ))]]) ).

thf(18667,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
      | ( ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ sk2 @ sk3 )
       != ( pair_in_list @ A @ C @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[18067,78]) ).

thf(18668,plain,
    ! [B: $i,A: $i] : ( pair_in_list @ ( insert_slb @ ( update_slb @ sk1 @ sk4 ) @ ( pair @ A @ B ) ) @ sk2 @ sk3 ),
    inference(pattern_uni,[status(thm)],[18667:[bind(A,$thf( update_slb @ sk1 @ sk4 )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( D )),bind(E,$thf( sk3 ))]]) ).

thf(18808,plain,
    ! [B: $i,A: $i] : ( pair_in_list @ ( insert_slb @ ( update_slb @ sk1 @ sk4 ) @ ( pair @ A @ B ) ) @ sk2 @ sk3 ),
    inference(simp,[status(thm)],[18668]) ).

thf(56447,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( pair_in_list @ ( update_slb @ ( insert_slb @ A @ ( pair @ B @ sk6 ) ) @ sk4 ) @ sk2 @ sk3 )
      | ( ( insert_slb @ ( update_slb @ A @ sk4 ) @ ( pair @ B @ sk6 ) )
       != ( insert_slb @ ( update_slb @ sk1 @ sk4 ) @ ( pair @ C @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[19635,18808]) ).

thf(56448,plain,
    ! [A: $i] : ( pair_in_list @ ( update_slb @ ( insert_slb @ sk1 @ ( pair @ A @ sk6 ) ) @ sk4 ) @ sk2 @ sk3 ),
    inference(pattern_uni,[status(thm)],[56447:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( sk6 ))]]) ).

thf(56772,plain,
    ! [A: $i] : ( pair_in_list @ ( update_slb @ ( insert_slb @ sk1 @ ( pair @ A @ sk6 ) ) @ sk4 ) @ sk2 @ sk3 ),
    inference(simp,[status(thm)],[56448]) ).

thf(57243,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[22,56772]) ).

thf(57244,plain,
    $false,
    inference(simp,[status(thm)],[57243]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV401+1 : TPTP v8.2.0. Released v3.3.0.
% 0.11/0.12  % Command  : run_Leo-III %s %d SAT
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu Jun 20 14:17:25 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 1.04/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.24/1.06  % [INFO] 	 Parsing done (138ms). 
% 1.24/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.29  % [INFO] 	 nitpick registered as external prover. 
% 1.75/1.29  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.36  % [INFO] 	 Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ... 
% 2.16/1.41  % [INFO] 	 Axiom selection finished. Selected 18 axioms (removed 0 axioms). 
% 2.16/1.43  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.16/1.44  % [INFO] 	 Type checking passed. 
% 2.16/1.44  % [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 ... 
% 135.05/25.33  % [INFO] 	 Killing All external provers ... 
% 135.05/25.34  % Time passed: 24808ms (effective reasoning time: 24259ms)
% 135.05/25.34  % 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)>
% 135.05/25.34  % Axioms used in derivation (5): stricly_smaller_definition, totality, ax23, ax30, ax29
% 135.05/25.34  % No. of inferences in proof: 89
% 135.05/25.34  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 24808 ms resp. 24259 ms w/o parsing
% 135.13/25.42  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 135.13/25.42  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------