TSTP Solution File: LCL713^1 by Leo-III---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : LCL713^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n020.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 11:15:29 EDT 2024

% Result   : Theorem 28.86s 7.01s
% Output   : Refutation 28.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   87 (  36 unt;   0 typ;   6 def)
%            Number of atoms       :  196 (  37 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 1174 ( 173   ~; 150   |;   2   &; 844   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   9 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   98 (  98   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   8 con; 0-3 aty)
%            Number of variables   :  199 (  42   ^ 157   !;   0   ?; 199   :)

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

thf(mimplies_type,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).

thf(mforall_prop_type,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

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

thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
        ! [D: $i] :
          ( ~ ( A @ C @ D )
          | ( B @ D ) ) ) ) ).

thf(mdia_type,type,
    mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mdia_def,definition,
    ( mdia
    = ( ^ [A: $i > $i > $o,B: $i > $o] : ( mnot @ ( mbox @ A @ ( mnot @ B ) ) ) ) ) ).

thf(meuclidean_type,type,
    meuclidean: ( $i > $i > $o ) > $o ).

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

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

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

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

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

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

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

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

thf(1,conjecture,
    ! [A: $i > $i > $o] :
      ( ( mvalid
        @ ( mforall_prop
          @ ^ [B: $i > $o] : ( mimplies @ ( mdia @ A @ B ) @ ( mbox @ A @ ( mdia @ A @ B ) ) ) ) )
     => ( meuclidean @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i > $o] :
        ( ( mvalid
          @ ( mforall_prop
            @ ^ [B: $i > $o] : ( mimplies @ ( mdia @ A @ B ) @ ( mbox @ A @ ( mdia @ A @ B ) ) ) ) )
       => ( meuclidean @ A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(6,plain,
    sk1 @ sk3 @ sk5,
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ! [D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( sk1 @ A @ C )
      | ~ ( B @ C )
      | ~ ( sk1 @ A @ D )
      | ( B @ ( sk2 @ D @ B @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(17,plain,
    ! [D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ C )
      | ~ ( sk1 @ A @ D )
      | ( B @ ( sk2 @ D @ B @ A ) )
      | ( ( sk1 @ sk3 @ sk5 )
       != ( sk1 @ A @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[6,5]) ).

thf(18,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ~ ( sk1 @ sk3 @ B )
      | ( A @ ( sk2 @ B @ A @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).

thf(72,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ~ ( sk1 @ sk3 @ B )
      | ( A @ ( sk2 @ B @ A @ sk3 ) ) ),
    inference(simp,[status(thm)],[18]) ).

thf(227,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ B @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ sk5 )
       != ( sk1 @ sk3 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[6,72]) ).

thf(228,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ sk5 @ A @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).

thf(309,plain,
    ! [A: $i > $o] :
      ( ~ ~ ( A @ sk5 )
      | ~ ( A
          @ ( sk2 @ sk5
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) ) ),
    inference(prim_subst,[status(thm)],[228:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).

thf(346,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ sk5
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk5 ) ),
    inference(cnf,[status(esa)],[309]) ).

thf(347,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ sk5
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk5 ) ),
    inference(simp,[status(thm)],[346]) ).

thf(300,plain,
    ! [A: $i > $o] :
      ( ( A @ ( sk2 @ sk5 @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ sk5 )
       != ( A @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[6,228]) ).

thf(324,plain,
    sk1 @ sk3 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ),
    inference(pre_uni,[status(thm)],[300:[bind(A,$thf( sk1 @ sk3 ))]]) ).

thf(515,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ B @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) )
       != ( sk1 @ sk3 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[324,72]) ).

thf(516,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[515:[bind(A,$thf( A )),bind(B,$thf( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ))]]) ).

thf(1317,plain,
    ! [A: $i > $o] :
      ( ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ sk5 )
       != ( A @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[6,516]) ).

thf(1388,plain,
    sk1 @ sk3 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ),
    inference(pre_uni,[status(thm)],[1317:[bind(A,$thf( sk1 @ sk3 ))]]) ).

thf(1998,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ B @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) )
       != ( sk1 @ sk3 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1388,72]) ).

thf(1999,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[1998:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ))]]) ).

thf(32,plain,
    ! [D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( sk1 @ A @ C )
      | ~ ( B @ C )
      | ~ ( sk1 @ A @ D )
      | ( ( B @ ( sk2 @ D @ B @ A ) )
       != ( ~ ( B @ C ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[5]) ).

thf(42,plain,
    ! [D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( sk1 @ A @ C )
      | ~ ( B @ C )
      | ~ ( sk1 @ A @ D )
      | ( ( B @ ( sk2 @ D @ B @ A ) )
       != ( ~ ( B @ C ) ) ) ),
    inference(simp,[status(thm)],[32]) ).

thf(308,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ~ ( ( A @ sk5 )
          | ( B @ sk5 ) )
      | ( A
        @ ( sk2 @ sk5
          @ ^ [C: $i] :
              ( ( A @ C )
              | ( B @ C ) )
          @ sk3 ) )
      | ( B
        @ ( sk2 @ sk5
          @ ^ [C: $i] :
              ( ( A @ C )
              | ( B @ C ) )
          @ sk3 ) ) ),
    inference(prim_subst,[status(thm)],[228:[bind(A,$thf( ^ [D: $i] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).

thf(342,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( A
        @ ( sk2 @ sk5
          @ ^ [C: $i] :
              ( ( A @ C )
              | ( B @ C ) )
          @ sk3 ) )
      | ( B
        @ ( sk2 @ sk5
          @ ^ [C: $i] :
              ( ( A @ C )
              | ( B @ C ) )
          @ sk3 ) )
      | ~ ( A @ sk5 ) ),
    inference(cnf,[status(esa)],[308]) ).

thf(344,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( A
        @ ( sk2 @ sk5
          @ ^ [C: $i] :
              ( ( A @ C )
              | ( B @ C ) )
          @ sk3 ) )
      | ( B
        @ ( sk2 @ sk5
          @ ^ [C: $i] :
              ( ( A @ C )
              | ( B @ C ) )
          @ sk3 ) )
      | ~ ( A @ sk5 ) ),
    inference(simp,[status(thm)],[342]) ).

thf(36,plain,
    ! [E: $i > $o,D: $i > $o,C: $i,B: $i,A: $i] :
      ( ~ ( sk1 @ A @ B )
      | ~ ( ( D @ B )
          | ( E @ B ) )
      | ~ ( sk1 @ A @ C )
      | ( D
        @ ( sk2 @ C
          @ ^ [F: $i] :
              ( ( D @ F )
              | ( E @ F ) )
          @ A ) )
      | ( E
        @ ( sk2 @ C
          @ ^ [F: $i] :
              ( ( D @ F )
              | ( E @ F ) )
          @ A ) ) ),
    inference(prim_subst,[status(thm)],[5:[bind(A,$thf( A )),bind(B,$thf( ^ [G: $i] : ( ( E @ G ) | ( F @ G ) ) ))]]) ).

thf(59,plain,
    ! [E: $i > $o,D: $i > $o,C: $i,B: $i,A: $i] :
      ( ( D
        @ ( sk2 @ C
          @ ^ [F: $i] :
              ( ( D @ F )
              | ( E @ F ) )
          @ A ) )
      | ( E
        @ ( sk2 @ C
          @ ^ [F: $i] :
              ( ( D @ F )
              | ( E @ F ) )
          @ A ) )
      | ~ ( sk1 @ A @ C )
      | ~ ( D @ B )
      | ~ ( sk1 @ A @ B ) ),
    inference(cnf,[status(esa)],[36]) ).

thf(61,plain,
    ! [E: $i > $o,D: $i > $o,C: $i,B: $i,A: $i] :
      ( ( D
        @ ( sk2 @ C
          @ ^ [F: $i] :
              ( ( D @ F )
              | ( E @ F ) )
          @ A ) )
      | ( E
        @ ( sk2 @ C
          @ ^ [F: $i] :
              ( ( D @ F )
              | ( E @ F ) )
          @ A ) )
      | ~ ( sk1 @ A @ C )
      | ~ ( D @ B )
      | ~ ( sk1 @ A @ B ) ),
    inference(simp,[status(thm)],[59]) ).

thf(8,plain,
    sk1 @ sk3 @ sk4,
    inference(cnf,[status(esa)],[3]) ).

thf(230,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ B @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ sk4 )
       != ( sk1 @ sk3 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8,72]) ).

thf(231,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ sk4 @ A @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).

thf(766,plain,
    ! [A: $i > $o] :
      ( ( A @ ( sk2 @ sk4 @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ sk5 )
       != ( A @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[6,231]) ).

thf(815,plain,
    sk1 @ sk3 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ),
    inference(pre_uni,[status(thm)],[766:[bind(A,$thf( sk1 @ sk3 ))]]) ).

thf(1181,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ B @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) )
       != ( sk1 @ sk3 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[815,72]) ).

thf(1182,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[1181:[bind(A,$thf( A )),bind(B,$thf( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ))]]) ).

thf(2119,plain,
    ! [A: $i > $o] :
      ( ( A @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ sk5 )
       != ( A @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[6,1182]) ).

thf(2208,plain,
    sk1 @ sk3 @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ),
    inference(pre_uni,[status(thm)],[2119:[bind(A,$thf( sk1 @ sk3 ))]]) ).

thf(2566,plain,
    ! [A: $i > $o] :
      ( ~ ~ ( A @ sk5 )
      | ~ ( A
          @ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 )
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) ) ),
    inference(prim_subst,[status(thm)],[1999:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).

thf(2663,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 )
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk5 ) ),
    inference(cnf,[status(esa)],[2566]) ).

thf(2664,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 )
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk5 ) ),
    inference(simp,[status(thm)],[2663]) ).

thf(2406,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ B @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) )
       != ( sk1 @ sk3 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2208,72]) ).

thf(2407,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( A @ ( sk2 @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[2406:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ))]]) ).

thf(4,plain,
    ~ ( sk1 @ sk4 @ sk5 ),
    inference(cnf,[status(esa)],[3]) ).

thf(60,plain,
    ! [E: $i > $o,D: $i > $o,C: $i,B: $i,A: $i] :
      ( ( D
        @ ( sk2 @ C
          @ ^ [F: $i] :
              ( ( D @ F )
              | ( E @ F ) )
          @ A ) )
      | ( E
        @ ( sk2 @ C
          @ ^ [F: $i] :
              ( ( D @ F )
              | ( E @ F ) )
          @ A ) )
      | ~ ( sk1 @ A @ C )
      | ~ ( E @ B )
      | ~ ( sk1 @ A @ B ) ),
    inference(cnf,[status(esa)],[36]) ).

thf(62,plain,
    ! [E: $i > $o,D: $i > $o,C: $i,B: $i,A: $i] :
      ( ( D
        @ ( sk2 @ C
          @ ^ [F: $i] :
              ( ( D @ F )
              | ( E @ F ) )
          @ A ) )
      | ( E
        @ ( sk2 @ C
          @ ^ [F: $i] :
              ( ( D @ F )
              | ( E @ F ) )
          @ A ) )
      | ~ ( sk1 @ A @ C )
      | ~ ( E @ B )
      | ~ ( sk1 @ A @ B ) ),
    inference(simp,[status(thm)],[60]) ).

thf(1337,plain,
    ! [A: $i > $o] :
      ( ~ ~ ( A @ sk5 )
      | ~ ( A
          @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 )
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) ) ),
    inference(prim_subst,[status(thm)],[516:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).

thf(1416,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 )
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk5 ) ),
    inference(cnf,[status(esa)],[1337]) ).

thf(1417,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 )
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk5 ) ),
    inference(simp,[status(thm)],[1416]) ).

thf(28,plain,
    ! [D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ C )
      | ~ ( sk1 @ A @ D )
      | ( B @ ( sk2 @ D @ B @ A ) )
      | ( ( sk1 @ A @ C )
       != ( sk1 @ A @ D ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[5]) ).

thf(51,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ C )
      | ~ ( sk1 @ A @ C )
      | ( B @ ( sk2 @ C @ B @ A ) ) ),
    inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).

thf(2716,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ C )
      | ( B @ ( sk2 @ C @ B @ A ) )
      | ( ( sk1 @ sk3 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) )
       != ( sk1 @ A @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[815,51]) ).

thf(2717,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) )
      | ( A @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[2716:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ))]]) ).

thf(2904,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) )
      | ( A @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
    inference(simp,[status(thm)],[2717]) ).

thf(15,plain,
    ! [H: $i,G: $i,F: $i > $o,E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( sk1 @ A @ C )
      | ~ ( B @ C )
      | ~ ( sk1 @ A @ D )
      | ~ ( sk1 @ E @ G )
      | ~ ( sk1 @ E @ H )
      | ( F @ ( sk2 @ H @ F @ E ) )
      | ( ( B @ ( sk2 @ D @ B @ A ) )
       != ( F @ G ) ) ),
    inference(paramod_ordered,[status(thm)],[5,5]) ).

thf(44,plain,
    ! [H: $i,G: $i,F: $i > $o,E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( sk1 @ A @ C )
      | ~ ( B @ C )
      | ~ ( sk1 @ A @ D )
      | ~ ( sk1 @ E @ G )
      | ~ ( sk1 @ E @ H )
      | ( F @ ( sk2 @ H @ F @ E ) )
      | ( ( B @ ( sk2 @ D @ B @ A ) )
       != ( F @ G ) ) ),
    inference(pre_uni,[status(thm)],[15:[]]) ).

thf(45,plain,
    ! [H: $i,G: $i,F: $i > $o,E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
      ( ( F @ ( sk2 @ H @ F @ E ) )
      | ~ ( sk1 @ E @ H )
      | ~ ( sk1 @ E @ G )
      | ~ ( sk1 @ A @ D )
      | ~ ( B @ C )
      | ~ ( sk1 @ A @ C )
      | ( ( B @ ( sk2 @ D @ B @ A ) )
       != ( F @ G ) ) ),
    inference(pre_uni,[status(thm)],[44:[]]) ).

thf(1336,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
       != ( ~ ( A @ sk5 ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[516]) ).

thf(1389,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
       != ( ~ ( A @ sk5 ) ) ) ),
    inference(simp,[status(thm)],[1336]) ).

thf(2153,plain,
    ! [A: $i > $o] :
      ( ~ ~ ( A @ sk5 )
      | ~ ( A
          @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 )
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) ) ),
    inference(prim_subst,[status(thm)],[1182:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).

thf(2256,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 )
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk5 ) ),
    inference(cnf,[status(esa)],[2153]) ).

thf(2257,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 )
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk5 ) ),
    inference(simp,[status(thm)],[2256]) ).

thf(7,plain,
    ! [D: $i,C: $i,B: $i > $o,A: $i] :
      ( ~ ( sk1 @ A @ C )
      | ~ ( B @ C )
      | ~ ( sk1 @ A @ D )
      | ( sk1 @ D @ ( sk2 @ D @ B @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(780,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( ( A @ ( sk2 @ sk4 @ A @ sk3 ) )
       != ( ~ ( A @ sk5 ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[231]) ).

thf(823,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( ( A @ ( sk2 @ sk4 @ A @ sk3 ) )
       != ( ~ ( A @ sk5 ) ) ) ),
    inference(simp,[status(thm)],[780]) ).

thf(3128,plain,
    ! [A: $i > $o] :
      ( ( A @ ( sk2 @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ sk5 )
       != ( A @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[6,2407]) ).

thf(3273,plain,
    sk1 @ sk3 @ ( sk2 @ ( sk2 @ ( sk2 @ sk4 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ),
    inference(pre_uni,[status(thm)],[3128:[bind(A,$thf( sk1 @ sk3 ))]]) ).

thf(306,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( ( A @ ( sk2 @ sk5 @ A @ sk3 ) )
       != ( ~ ( A @ sk5 ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[228]) ).

thf(331,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk5 )
      | ( ( A @ ( sk2 @ sk5 @ A @ sk3 ) )
       != ( ~ ( A @ sk5 ) ) ) ),
    inference(simp,[status(thm)],[306]) ).

thf(9,plain,
    ( ( sk1 @ sk4 @ sk5 )
   != ( sk1 @ sk3 @ sk5 ) ),
    inference(paramod_ordered,[status(thm)],[6,4]) ).

thf(10,plain,
    ( ( sk4 != sk3 )
    | ( sk5 != sk5 ) ),
    inference(simp,[status(thm)],[9]) ).

thf(11,plain,
    sk4 != sk3,
    inference(simp,[status(thm)],[10]) ).

thf(2529,plain,
    ! [A: $i > $o] :
      ( ( A @ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) )
      | ( ( sk1 @ sk3 @ sk5 )
       != ( A @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[6,1999]) ).

thf(2584,plain,
    sk1 @ sk3 @ ( sk2 @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ) @ ( sk1 @ sk3 ) @ sk3 ),
    inference(pre_uni,[status(thm)],[2529:[bind(A,$thf( sk1 @ sk3 ))]]) ).

thf(2719,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ C )
      | ( B @ ( sk2 @ C @ B @ A ) )
      | ( ( sk1 @ sk3 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) )
       != ( sk1 @ A @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[324,51]) ).

thf(2720,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) )
      | ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[2719:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ))]]) ).

thf(2907,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) )
      | ( A @ ( sk2 @ ( sk2 @ sk5 @ ( sk1 @ sk3 ) @ sk3 ) @ A @ sk3 ) ) ),
    inference(simp,[status(thm)],[2720]) ).

thf(783,plain,
    ! [A: $i > $o] :
      ( ~ ~ ( A @ sk5 )
      | ~ ( A
          @ ( sk2 @ sk4
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) ) ),
    inference(prim_subst,[status(thm)],[231:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).

thf(832,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ sk4
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk5 ) ),
    inference(cnf,[status(esa)],[783]) ).

thf(833,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ sk4
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk5 ) ),
    inference(simp,[status(thm)],[832]) ).

thf(4696,plain,
    $false,
    inference(e,[status(thm)],[347,5,1999,42,344,228,61,6,815,324,1182,2208,2664,3,2407,8,4,62,1417,2904,45,1389,1388,2257,7,516,823,3273,331,11,72,2584,231,2907,833,51]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL713^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.07/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n020.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 : Sat Jun 22 15:14:40 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.97/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.41/1.01  % [INFO] 	 Parsing done (147ms). 
% 1.41/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.91/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.91/1.24  % [INFO] 	 Scanning for conjecture ... 
% 2.29/1.35  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.29/1.37  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.29/1.37  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.29/1.37  % [INFO] 	 Type checking passed. 
% 2.29/1.37  % [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 ... 
% 28.86/7.00  % External prover 'e' found a proof!
% 28.86/7.00  % [INFO] 	 Killing All external provers ... 
% 28.86/7.00  % Time passed: 6472ms (effective reasoning time: 5980ms)
% 28.86/7.00  % 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)>
% 28.86/7.01  % Axioms used in derivation (0): 
% 28.86/7.01  % No. of inferences in proof: 81
% 28.86/7.01  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6472 ms resp. 5980 ms w/o parsing
% 28.86/7.06  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.86/7.06  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------