TSTP Solution File: LCL644+1.005 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : LCL644+1.005 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 00:10:31 EDT 2024

% Result   : Theorem 4.76s 2.14s
% Output   : Refutation 5.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   17 (   4 unt;   8 typ;   0 def)
%            Number of atoms       : 1129 (   0 equ;   0 cnn)
%            Maximal formula atoms :  225 ( 125 avg)
%            Number of connectives : 3309 ( 667   ~; 760   |; 360   &;1522   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (  18 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :  400 (   0   ^ 396   !;   4   ?; 400   :)

% Comments : 
%------------------------------------------------------------------------------
thf(r1_type,type,
    r1: $i > $i > $o ).

thf(p6_type,type,
    p6: $i > $o ).

thf(p5_type,type,
    p5: $i > $o ).

thf(p4_type,type,
    p4: $i > $o ).

thf(p3_type,type,
    p3: $i > $o ).

thf(p2_type,type,
    p2: $i > $o ).

thf(p1_type,type,
    p1: $i > $o ).

thf(sk46_type,type,
    sk46: $i ).

thf(1,conjecture,
    ~ ? [A: $i] :
        ~ ( ~ ( ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ~ ( ( p6 @ B )
                      & ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p6 @ C ) ) )
                  | ( p5 @ B ) )
              | ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ( p6 @ B )
                  | ~ ( ( p5 @ B )
                      & ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p5 @ C ) )
                      & ( p5 @ B ) ) )
              | ~ ( ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ~ ( ( p6 @ C )
                              & ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p6 @ D ) ) )
                          | ( p5 @ C ) )
                      | ( p6 @ B )
                      | ~ ( ( p5 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p5 @ C ) )
                          & ( p5 @ B ) ) )
                  & ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ~ ( ( p6 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p6 @ C ) ) )
                      | ( p5 @ B )
                      | ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p6 @ C )
                          | ~ ( ( p5 @ C )
                              & ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p5 @ D ) )
                              & ( p5 @ C ) ) ) )
                  & ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ~ ( ( p6 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p6 @ C ) ) )
                      | ( p5 @ B )
                      | ( p6 @ B )
                      | ~ ( ( p5 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p5 @ C ) )
                          & ( p5 @ B ) ) ) ) )
          | ~ ( ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ~ ( ( p5 @ B )
                      & ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p5 @ C ) ) )
                  | ( p4 @ B ) )
              | ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ( p5 @ B )
                  | ~ ( ( p4 @ B )
                      & ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p4 @ C ) )
                      & ( p4 @ B ) ) )
              | ~ ( ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ~ ( ( p5 @ C )
                              & ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p5 @ D ) ) )
                          | ( p4 @ C ) )
                      | ( p5 @ B )
                      | ~ ( ( p4 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p4 @ C ) )
                          & ( p4 @ B ) ) )
                  & ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ~ ( ( p5 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p5 @ C ) ) )
                      | ( p4 @ B )
                      | ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p5 @ C )
                          | ~ ( ( p4 @ C )
                              & ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p4 @ D ) )
                              & ( p4 @ C ) ) ) )
                  & ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ~ ( ( p5 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p5 @ C ) ) )
                      | ( p4 @ B )
                      | ( p5 @ B )
                      | ~ ( ( p4 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p4 @ C ) )
                          & ( p4 @ B ) ) ) ) )
          | ~ ( ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ~ ( ( p4 @ B )
                      & ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p4 @ C ) ) )
                  | ( p3 @ B ) )
              | ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ( p4 @ B )
                  | ~ ( ( p3 @ B )
                      & ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p3 @ C ) )
                      & ( p3 @ B ) ) )
              | ~ ( ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ~ ( ( p4 @ C )
                              & ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p4 @ D ) ) )
                          | ( p3 @ C ) )
                      | ( p4 @ B )
                      | ~ ( ( p3 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p3 @ C ) )
                          & ( p3 @ B ) ) )
                  & ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ~ ( ( p4 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p4 @ C ) ) )
                      | ( p3 @ B )
                      | ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p4 @ C )
                          | ~ ( ( p3 @ C )
                              & ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p3 @ D ) )
                              & ( p3 @ C ) ) ) )
                  & ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ~ ( ( p4 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p4 @ C ) ) )
                      | ( p3 @ B )
                      | ( p4 @ B )
                      | ~ ( ( p3 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p3 @ C ) )
                          & ( p3 @ B ) ) ) ) )
          | ~ ( ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ~ ( ( p3 @ B )
                      & ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p3 @ C ) ) )
                  | ( p2 @ B ) )
              | ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ( p3 @ B )
                  | ~ ( ( p2 @ B )
                      & ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p2 @ C ) )
                      & ( p2 @ B ) ) )
              | ~ ( ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ~ ( ( p3 @ C )
                              & ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p3 @ D ) ) )
                          | ( p2 @ C ) )
                      | ( p3 @ B )
                      | ~ ( ( p2 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p2 @ C ) )
                          & ( p2 @ B ) ) )
                  & ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ~ ( ( p3 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p3 @ C ) ) )
                      | ( p2 @ B )
                      | ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p3 @ C )
                          | ~ ( ( p2 @ C )
                              & ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p2 @ D ) )
                              & ( p2 @ C ) ) ) )
                  & ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ~ ( ( p3 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p3 @ C ) ) )
                      | ( p2 @ B )
                      | ( p3 @ B )
                      | ~ ( ( p2 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p2 @ C ) )
                          & ( p2 @ B ) ) ) ) )
          | ! [B: $i] :
              ( ~ ( r1 @ A @ B )
              | ( p5 @ B )
              | ~ ( ! [C: $i] :
                      ( ~ ( r1 @ B @ C )
                      | ( p5 @ C ) )
                  & ( p5 @ B ) ) )
          | ! [B: $i] :
              ( ~ ( r1 @ A @ B )
              | ( p5 @ B )
              | ~ ( ! [C: $i] :
                      ( ~ ( r1 @ B @ C )
                      | ( p5 @ C ) )
                  & ( p5 @ B ) ) )
          | ~ ( ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ~ ( ( p2 @ B )
                      & ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p2 @ C ) ) )
                  | ( p1 @ B ) )
              | ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ( p2 @ B )
                  | ~ ( ( p1 @ B )
                      & ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p1 @ C ) )
                      & ( p1 @ B ) ) )
              | ~ ( ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ~ ( ( p2 @ C )
                              & ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p2 @ D ) ) )
                          | ( p1 @ C ) )
                      | ( p2 @ B )
                      | ~ ( ( p1 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p1 @ C ) )
                          & ( p1 @ B ) ) )
                  & ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ~ ( ( p2 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p2 @ C ) ) )
                      | ( p1 @ B )
                      | ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p2 @ C )
                          | ~ ( ( p1 @ C )
                              & ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p1 @ D ) )
                              & ( p1 @ C ) ) ) )
                  & ! [B: $i] :
                      ( ~ ( r1 @ A @ B )
                      | ~ ( ( p2 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p2 @ C ) ) )
                      | ( p1 @ B )
                      | ( p2 @ B )
                      | ~ ( ( p1 @ B )
                          & ! [C: $i] :
                              ( ~ ( r1 @ B @ C )
                              | ( p1 @ C ) )
                          & ( p1 @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).

thf(2,negated_conjecture,
    ~ ~ ? [A: $i] :
          ~ ( ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p6 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p6 @ C ) ) )
                    | ( p5 @ B ) )
                | ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ( p6 @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) )
                        & ( p5 @ B ) ) )
                | ~ ( ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ( p6 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p6 @ D ) ) )
                            | ( p5 @ C ) )
                        | ( p6 @ B )
                        | ~ ( ( p5 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p5 @ C ) )
                            & ( p5 @ B ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p6 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p6 @ C ) ) )
                        | ( p5 @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p6 @ C )
                            | ~ ( ( p5 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p5 @ D ) )
                                & ( p5 @ C ) ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p6 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p6 @ C ) ) )
                        | ( p5 @ B )
                        | ( p6 @ B )
                        | ~ ( ( p5 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p5 @ C ) )
                            & ( p5 @ B ) ) ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) ) )
                    | ( p4 @ B ) )
                | ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ( p5 @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) )
                        & ( p4 @ B ) ) )
                | ~ ( ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ( p5 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p5 @ D ) ) )
                            | ( p4 @ C ) )
                        | ( p5 @ B )
                        | ~ ( ( p4 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p4 @ C ) )
                            & ( p4 @ B ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p5 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p5 @ C ) ) )
                        | ( p4 @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C )
                            | ~ ( ( p4 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p4 @ D ) )
                                & ( p4 @ C ) ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p5 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p5 @ C ) ) )
                        | ( p4 @ B )
                        | ( p5 @ B )
                        | ~ ( ( p4 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p4 @ C ) )
                            & ( p4 @ B ) ) ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) ) )
                    | ( p3 @ B ) )
                | ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ( p4 @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) )
                        & ( p3 @ B ) ) )
                | ~ ( ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ( p4 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p4 @ D ) ) )
                            | ( p3 @ C ) )
                        | ( p4 @ B )
                        | ~ ( ( p3 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p3 @ C ) )
                            & ( p3 @ B ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p4 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p4 @ C ) ) )
                        | ( p3 @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C )
                            | ~ ( ( p3 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p3 @ D ) )
                                & ( p3 @ C ) ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p4 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p4 @ C ) ) )
                        | ( p3 @ B )
                        | ( p4 @ B )
                        | ~ ( ( p3 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p3 @ C ) )
                            & ( p3 @ B ) ) ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) ) )
                    | ( p2 @ B ) )
                | ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ( p3 @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) )
                        & ( p2 @ B ) ) )
                | ~ ( ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ( p3 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p3 @ D ) ) )
                            | ( p2 @ C ) )
                        | ( p3 @ B )
                        | ~ ( ( p2 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p2 @ C ) )
                            & ( p2 @ B ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p3 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p3 @ C ) ) )
                        | ( p2 @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C )
                            | ~ ( ( p2 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p2 @ D ) )
                                & ( p2 @ C ) ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p3 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p3 @ C ) ) )
                        | ( p2 @ B )
                        | ( p3 @ B )
                        | ~ ( ( p2 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p2 @ C ) )
                            & ( p2 @ B ) ) ) ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p5 @ B )
                | ~ ( ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p5 @ C ) )
                    & ( p5 @ B ) ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p5 @ B )
                | ~ ( ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p5 @ C ) )
                    & ( p5 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) ) )
                    | ( p1 @ B ) )
                | ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ( p2 @ B )
                    | ~ ( ( p1 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p1 @ C ) )
                        & ( p1 @ B ) ) )
                | ~ ( ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ( p2 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p2 @ D ) ) )
                            | ( p1 @ C ) )
                        | ( p2 @ B )
                        | ~ ( ( p1 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p1 @ C ) )
                            & ( p1 @ B ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p2 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p2 @ C ) ) )
                        | ( p1 @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C )
                            | ~ ( ( p1 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p1 @ D ) )
                                & ( p1 @ C ) ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p2 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p2 @ C ) ) )
                        | ( p1 @ B )
                        | ( p2 @ B )
                        | ~ ( ( p1 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p1 @ C ) )
                            & ( p1 @ B ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ~ ? [A: $i] :
          ~ ( ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p6 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p6 @ C ) ) )
                    | ( p5 @ B ) )
                | ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ( p6 @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) )
                        & ( p5 @ B ) ) )
                | ~ ( ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ( p6 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p6 @ D ) ) )
                            | ( p5 @ C ) )
                        | ( p6 @ B )
                        | ~ ( ( p5 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p5 @ C ) )
                            & ( p5 @ B ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p6 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p6 @ C ) ) )
                        | ( p5 @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p6 @ C )
                            | ~ ( ( p5 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p5 @ D ) )
                                & ( p5 @ C ) ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p6 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p6 @ C ) ) )
                        | ( p5 @ B )
                        | ( p6 @ B )
                        | ~ ( ( p5 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p5 @ C ) )
                            & ( p5 @ B ) ) ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) ) )
                    | ( p4 @ B ) )
                | ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ( p5 @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) )
                        & ( p4 @ B ) ) )
                | ~ ( ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ( p5 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p5 @ D ) ) )
                            | ( p4 @ C ) )
                        | ( p5 @ B )
                        | ~ ( ( p4 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p4 @ C ) )
                            & ( p4 @ B ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p5 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p5 @ C ) ) )
                        | ( p4 @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C )
                            | ~ ( ( p4 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p4 @ D ) )
                                & ( p4 @ C ) ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p5 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p5 @ C ) ) )
                        | ( p4 @ B )
                        | ( p5 @ B )
                        | ~ ( ( p4 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p4 @ C ) )
                            & ( p4 @ B ) ) ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) ) )
                    | ( p3 @ B ) )
                | ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ( p4 @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) )
                        & ( p3 @ B ) ) )
                | ~ ( ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ( p4 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p4 @ D ) ) )
                            | ( p3 @ C ) )
                        | ( p4 @ B )
                        | ~ ( ( p3 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p3 @ C ) )
                            & ( p3 @ B ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p4 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p4 @ C ) ) )
                        | ( p3 @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C )
                            | ~ ( ( p3 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p3 @ D ) )
                                & ( p3 @ C ) ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p4 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p4 @ C ) ) )
                        | ( p3 @ B )
                        | ( p4 @ B )
                        | ~ ( ( p3 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p3 @ C ) )
                            & ( p3 @ B ) ) ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) ) )
                    | ( p2 @ B ) )
                | ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ( p3 @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) )
                        & ( p2 @ B ) ) )
                | ~ ( ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ( p3 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p3 @ D ) ) )
                            | ( p2 @ C ) )
                        | ( p3 @ B )
                        | ~ ( ( p2 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p2 @ C ) )
                            & ( p2 @ B ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p3 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p3 @ C ) ) )
                        | ( p2 @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C )
                            | ~ ( ( p2 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p2 @ D ) )
                                & ( p2 @ C ) ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p3 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p3 @ C ) ) )
                        | ( p2 @ B )
                        | ( p3 @ B )
                        | ~ ( ( p2 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p2 @ C ) )
                            & ( p2 @ B ) ) ) ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p5 @ B )
                | ~ ( ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p5 @ C ) )
                    & ( p5 @ B ) ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p5 @ B )
                | ~ ( ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p5 @ C ) )
                    & ( p5 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) ) )
                    | ( p1 @ B ) )
                | ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ( p2 @ B )
                    | ~ ( ( p1 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p1 @ C ) )
                        & ( p1 @ B ) ) )
                | ~ ( ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ( p2 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p2 @ D ) ) )
                            | ( p1 @ C ) )
                        | ( p2 @ B )
                        | ~ ( ( p1 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p1 @ C ) )
                            & ( p1 @ B ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p2 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p2 @ C ) ) )
                        | ( p1 @ B )
                        | ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C )
                            | ~ ( ( p1 @ C )
                                & ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ( p1 @ D ) )
                                & ( p1 @ C ) ) ) )
                    & ! [B: $i] :
                        ( ~ ( r1 @ A @ B )
                        | ~ ( ( p2 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p2 @ C ) ) )
                        | ( p1 @ B )
                        | ( p2 @ B )
                        | ~ ( ( p1 @ B )
                            & ! [C: $i] :
                                ( ~ ( r1 @ B @ C )
                                | ( p1 @ C ) )
                            & ( p1 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ? [A: $i] :
      ~ ( ~ ( ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( ( p6 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p6 @ C ) ) )
                | ( p5 @ B ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p6 @ B )
                | ~ ( ( p5 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p5 @ C ) )
                    & ( p5 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ( p6 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p6 @ D ) ) )
                        | ( p5 @ C ) )
                    | ( p6 @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) )
                        & ( p5 @ B ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p6 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p6 @ C ) ) )
                    | ( p5 @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p6 @ C )
                        | ~ ( ( p5 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p5 @ D ) )
                            & ( p5 @ C ) ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p6 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p6 @ C ) ) )
                    | ( p5 @ B )
                    | ( p6 @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) )
                        & ( p5 @ B ) ) ) ) )
        | ~ ( ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( ( p5 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p5 @ C ) ) )
                | ( p4 @ B ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p5 @ B )
                | ~ ( ( p4 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p4 @ C ) )
                    & ( p4 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ( p5 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p5 @ D ) ) )
                        | ( p4 @ C ) )
                    | ( p5 @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) )
                        & ( p4 @ B ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) ) )
                    | ( p4 @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p5 @ C )
                        | ~ ( ( p4 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p4 @ D ) )
                            & ( p4 @ C ) ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) ) )
                    | ( p4 @ B )
                    | ( p5 @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) )
                        & ( p4 @ B ) ) ) ) )
        | ~ ( ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( ( p4 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p4 @ C ) ) )
                | ( p3 @ B ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p4 @ B )
                | ~ ( ( p3 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p3 @ C ) )
                    & ( p3 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ( p4 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p4 @ D ) ) )
                        | ( p3 @ C ) )
                    | ( p4 @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) )
                        & ( p3 @ B ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) ) )
                    | ( p3 @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p4 @ C )
                        | ~ ( ( p3 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p3 @ D ) )
                            & ( p3 @ C ) ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) ) )
                    | ( p3 @ B )
                    | ( p4 @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) )
                        & ( p3 @ B ) ) ) ) )
        | ~ ( ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( ( p3 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p3 @ C ) ) )
                | ( p2 @ B ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p3 @ B )
                | ~ ( ( p2 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p2 @ C ) )
                    & ( p2 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ( p3 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p3 @ D ) ) )
                        | ( p2 @ C ) )
                    | ( p3 @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) )
                        & ( p2 @ B ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) ) )
                    | ( p2 @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p3 @ C )
                        | ~ ( ( p2 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p2 @ D ) )
                            & ( p2 @ C ) ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) ) )
                    | ( p2 @ B )
                    | ( p3 @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) )
                        & ( p2 @ B ) ) ) ) )
        | ! [B: $i] :
            ( ~ ( r1 @ A @ B )
            | ( p5 @ B )
            | ~ ( ! [C: $i] :
                    ( ~ ( r1 @ B @ C )
                    | ( p5 @ C ) )
                & ( p5 @ B ) ) )
        | ! [B: $i] :
            ( ~ ( r1 @ A @ B )
            | ( p5 @ B )
            | ~ ( ! [C: $i] :
                    ( ~ ( r1 @ B @ C )
                    | ( p5 @ C ) )
                & ( p5 @ B ) ) )
        | ~ ( ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( ( p2 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p2 @ C ) ) )
                | ( p1 @ B ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p2 @ B )
                | ~ ( ( p1 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p1 @ C ) )
                    & ( p1 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ( p2 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p2 @ D ) ) )
                        | ( p1 @ C ) )
                    | ( p2 @ B )
                    | ~ ( ( p1 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p1 @ C ) )
                        & ( p1 @ B ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) ) )
                    | ( p1 @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p2 @ C )
                        | ~ ( ( p1 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p1 @ D ) )
                            & ( p1 @ C ) ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) ) )
                    | ( p1 @ B )
                    | ( p2 @ B )
                    | ~ ( ( p1 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p1 @ C ) )
                        & ( p1 @ B ) ) ) ) ) ),
    inference(polarity_switch,[status(thm)],[3]) ).

thf(5,plain,
    ~ ! [A: $i] :
        ( ~ ( ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( ( p6 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p6 @ C ) ) )
                | ( p5 @ B ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p6 @ B )
                | ~ ( ( p5 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p5 @ C ) )
                    & ( p5 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ( p6 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p6 @ D ) ) )
                        | ( p5 @ C ) )
                    | ( p6 @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) )
                        & ( p5 @ B ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p6 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p6 @ C ) ) )
                    | ( p5 @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p6 @ C )
                        | ~ ( ( p5 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p5 @ D ) )
                            & ( p5 @ C ) ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p6 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p6 @ C ) ) )
                    | ( p5 @ B )
                    | ( p6 @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) )
                        & ( p5 @ B ) ) ) ) )
        | ~ ( ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( ( p5 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p5 @ C ) ) )
                | ( p4 @ B ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p5 @ B )
                | ~ ( ( p4 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p4 @ C ) )
                    & ( p4 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ( p5 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p5 @ D ) ) )
                        | ( p4 @ C ) )
                    | ( p5 @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) )
                        & ( p4 @ B ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) ) )
                    | ( p4 @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p5 @ C )
                        | ~ ( ( p4 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p4 @ D ) )
                            & ( p4 @ C ) ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p5 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p5 @ C ) ) )
                    | ( p4 @ B )
                    | ( p5 @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) )
                        & ( p4 @ B ) ) ) ) )
        | ~ ( ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( ( p4 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p4 @ C ) ) )
                | ( p3 @ B ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p4 @ B )
                | ~ ( ( p3 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p3 @ C ) )
                    & ( p3 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ( p4 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p4 @ D ) ) )
                        | ( p3 @ C ) )
                    | ( p4 @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) )
                        & ( p3 @ B ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) ) )
                    | ( p3 @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p4 @ C )
                        | ~ ( ( p3 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p3 @ D ) )
                            & ( p3 @ C ) ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p4 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p4 @ C ) ) )
                    | ( p3 @ B )
                    | ( p4 @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) )
                        & ( p3 @ B ) ) ) ) )
        | ~ ( ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( ( p3 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p3 @ C ) ) )
                | ( p2 @ B ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p3 @ B )
                | ~ ( ( p2 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p2 @ C ) )
                    & ( p2 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ( p3 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p3 @ D ) ) )
                        | ( p2 @ C ) )
                    | ( p3 @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) )
                        & ( p2 @ B ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) ) )
                    | ( p2 @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p3 @ C )
                        | ~ ( ( p2 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p2 @ D ) )
                            & ( p2 @ C ) ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p3 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p3 @ C ) ) )
                    | ( p2 @ B )
                    | ( p3 @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) )
                        & ( p2 @ B ) ) ) ) )
        | ! [B: $i] :
            ( ~ ( r1 @ A @ B )
            | ( p5 @ B )
            | ~ ( ! [C: $i] :
                    ( ~ ( r1 @ B @ C )
                    | ( p5 @ C ) )
                & ( p5 @ B ) ) )
        | ! [B: $i] :
            ( ~ ( r1 @ A @ B )
            | ( p5 @ B )
            | ~ ( ! [C: $i] :
                    ( ~ ( r1 @ B @ C )
                    | ( p5 @ C ) )
                & ( p5 @ B ) ) )
        | ~ ( ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( ( p2 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p2 @ C ) ) )
                | ( p1 @ B ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p2 @ B )
                | ~ ( ( p1 @ B )
                    & ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p1 @ C ) )
                    & ( p1 @ B ) ) )
            | ~ ( ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ( p2 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p2 @ D ) ) )
                        | ( p1 @ C ) )
                    | ( p2 @ B )
                    | ~ ( ( p1 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p1 @ C ) )
                        & ( p1 @ B ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) ) )
                    | ( p1 @ B )
                    | ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p2 @ C )
                        | ~ ( ( p1 @ C )
                            & ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p1 @ D ) )
                            & ( p1 @ C ) ) ) )
                & ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ( ( p2 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p2 @ C ) ) )
                    | ( p1 @ B )
                    | ( p2 @ B )
                    | ~ ( ( p1 @ B )
                        & ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ( p1 @ C ) )
                        & ( p1 @ B ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[4]) ).

thf(52,plain,
    ~ ( p5 @ sk46 ),
    inference(cnf,[status(esa)],[5]) ).

thf(15,plain,
    p5 @ sk46,
    inference(cnf,[status(esa)],[5]) ).

thf(199,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[52,15]) ).

thf(200,plain,
    $false,
    inference(simp,[status(thm)],[199]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : LCL644+1.005 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n025.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon May 20 01:57:24 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.99/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.35/1.02  % [INFO] 	 Parsing done (135ms). 
% 1.35/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.86/1.26  % [INFO] 	 nitpick registered as external prover. 
% 1.86/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.14/1.39  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.28/1.43  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.28/1.43  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.28/1.44  % [INFO] 	 Type checking passed. 
% 2.28/1.44  % [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 ... 
% 4.70/2.13  % [INFO] 	 Killing All external provers ... 
% 4.70/2.13  % Time passed: 1586ms (effective reasoning time: 1096ms)
% 4.70/2.14  % 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)>
% 4.76/2.14  % Axioms used in derivation (0): 
% 4.76/2.14  % No. of inferences in proof: 9
% 4.76/2.14  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1586 ms resp. 1096 ms w/o parsing
% 5.03/2.24  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.03/2.24  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------