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Vampire---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : LCL688+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:56:16 AM UTC 2026

% Result   : Theorem 6.68s 7.00s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   11
% Syntax   : Number of formulae    :  114 (  25 unt;   8 def)
%            Number of atoms       : 2046 (   0 equ)
%            Maximal formula atoms :  184 (  17 avg)
%            Number of connectives : 3612 (1680   ~;1345   |; 582   &)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   70 (  11 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   14 (  13 usr;   5 prp; 0-2 aty)
%            Number of functors    :   49 (  49 usr;  22 con; 0-1 aty)
%            Number of variables   : 1153 (   0 sgn 935   !; 218   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] : r1(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( ( r1(X0,X1)
        & r1(X1,X2) )
     => r1(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).

fof(f3,conjecture,
    ~ ? [X0] :
        ~ ( ~ ! [X1] :
                ( ~ r1(X0,X1)
                | ~ p4(X1) )
          | ~ ! [X1] :
                ( ~ r1(X0,X1)
                | ~ ( ~ ! [X0] :
                          ( ~ r1(X1,X0)
                          | ~ ( ~ ! [X1] :
                                    ( ~ r1(X0,X1)
                                    | ~ ( ~ ! [X0] :
                                              ( ~ r1(X1,X0)
                                              | ~ ( ~ ! [X1] :
                                                        ( ~ r1(X0,X1)
                                                        | ~ ( ~ ! [X0] :
                                                                  ( ~ r1(X1,X0)
                                                                  | ~ ( ~ ! [X1] :
                                                                            ( ~ r1(X0,X1)
                                                                            | ~ ( ~ ! [X0] :
                                                                                      ( ~ r1(X1,X0)
                                                                                      | ~ ( ~ ! [X1] :
                                                                                                ( ~ r1(X0,X1)
                                                                                                | ~ ( ~ ! [X0] :
                                                                                                          ( ~ r1(X1,X0)
                                                                                                          | ~ ! [X1] :
                                                                                                                ( ~ r1(X0,X1)
                                                                                                                | ! [X0] :
                                                                                                                    ( ~ r1(X1,X0)
                                                                                                                    | p3(X0) )
                                                                                                                | ~ p2(X1) ) )
                                                                                                    | ~ ! [X0] :
                                                                                                          ( ~ r1(X1,X0)
                                                                                                          | ~ ( ~ ! [X1] :
                                                                                                                    ( ~ r1(X0,X1)
                                                                                                                    | ~ ( ! [X0] :
                                                                                                                            ( ~ r1(X1,X0)
                                                                                                                            | p3(X0) )
                                                                                                                        | ~ p2(X1) ) )
                                                                                                              & p2(X0)
                                                                                                              & ~ ! [X1] :
                                                                                                                    ( ~ r1(X0,X1)
                                                                                                                    | ~ ! [X0] :
                                                                                                                          ( ~ r1(X1,X0)
                                                                                                                          | ~ ! [X1] :
                                                                                                                                ( ~ r1(X0,X1)
                                                                                                                                | ~ p2(X1) ) ) ) ) ) ) )
                                                                                          | ( ~ p1(X0)
                                                                                            & ~ ! [X1] :
                                                                                                  ( ~ r1(X0,X1)
                                                                                                  | ~ ! [X0] :
                                                                                                        ( ~ r1(X1,X0)
                                                                                                        | p1(X0) ) )
                                                                                            & ! [X1] :
                                                                                                ( ~ r1(X0,X1)
                                                                                                | p1(X1)
                                                                                                | ~ ! [X0] :
                                                                                                      ( ~ r1(X1,X0)
                                                                                                      | ~ ( ~ ! [X1] :
                                                                                                                ( ~ r1(X0,X1)
                                                                                                                | p1(X1) )
                                                                                                          & p1(X0) ) ) ) ) ) )
                                                                                | ( ~ p1(X1)
                                                                                  & ~ ! [X0] :
                                                                                        ( ~ r1(X1,X0)
                                                                                        | ~ ! [X1] :
                                                                                              ( ~ r1(X0,X1)
                                                                                              | p1(X1) ) )
                                                                                  & ! [X0] :
                                                                                      ( ~ r1(X1,X0)
                                                                                      | p1(X0)
                                                                                      | ~ ! [X1] :
                                                                                            ( ~ r1(X0,X1)
                                                                                            | ~ ( ~ ! [X0] :
                                                                                                      ( ~ r1(X1,X0)
                                                                                                      | p1(X0) )
                                                                                                & p1(X1) ) ) ) ) ) )
                                                                      | ( ~ p1(X0)
                                                                        & ~ ! [X1] :
                                                                              ( ~ r1(X0,X1)
                                                                              | ~ ! [X0] :
                                                                                    ( ~ r1(X1,X0)
                                                                                    | p1(X0) ) )
                                                                        & ! [X1] :
                                                                            ( ~ r1(X0,X1)
                                                                            | p1(X1)
                                                                            | ~ ! [X0] :
                                                                                  ( ~ r1(X1,X0)
                                                                                  | ~ ( ~ ! [X1] :
                                                                                            ( ~ r1(X0,X1)
                                                                                            | p1(X1) )
                                                                                      & p1(X0) ) ) ) ) ) )
                                                            | ( ~ p1(X1)
                                                              & ~ ! [X0] :
                                                                    ( ~ r1(X1,X0)
                                                                    | ~ ! [X1] :
                                                                          ( ~ r1(X0,X1)
                                                                          | p1(X1) ) )
                                                              & ! [X0] :
                                                                  ( ~ r1(X1,X0)
                                                                  | p1(X0)
                                                                  | ~ ! [X1] :
                                                                        ( ~ r1(X0,X1)
                                                                        | ~ ( ~ ! [X0] :
                                                                                  ( ~ r1(X1,X0)
                                                                                  | p1(X0) )
                                                                            & p1(X1) ) ) ) ) ) )
                                                  | ( ~ p1(X0)
                                                    & ~ ! [X1] :
                                                          ( ~ r1(X0,X1)
                                                          | ~ ! [X0] :
                                                                ( ~ r1(X1,X0)
                                                                | p1(X0) ) )
                                                    & ! [X1] :
                                                        ( ~ r1(X0,X1)
                                                        | p1(X1)
                                                        | ~ ! [X0] :
                                                              ( ~ r1(X1,X0)
                                                              | ~ ( ~ ! [X1] :
                                                                        ( ~ r1(X0,X1)
                                                                        | p1(X1) )
                                                                  & p1(X0) ) ) ) ) ) )
                                        | ( ~ p1(X1)
                                          & ~ ! [X0] :
                                                ( ~ r1(X1,X0)
                                                | ~ ! [X1] :
                                                      ( ~ r1(X0,X1)
                                                      | p1(X1) ) )
                                          & ! [X0] :
                                              ( ~ r1(X1,X0)
                                              | p1(X0)
                                              | ~ ! [X1] :
                                                    ( ~ r1(X0,X1)
                                                    | ~ ( ~ ! [X0] :
                                                              ( ~ r1(X1,X0)
                                                              | p1(X0) )
                                                        & p1(X1) ) ) ) ) ) )
                              | ( ~ p1(X0)
                                & ~ ! [X1] :
                                      ( ~ r1(X0,X1)
                                      | ~ ! [X0] :
                                            ( ~ r1(X1,X0)
                                            | p1(X0) ) )
                                & ! [X1] :
                                    ( ~ r1(X0,X1)
                                    | p1(X1)
                                    | ~ ! [X0] :
                                          ( ~ r1(X1,X0)
                                          | ~ ( ~ ! [X1] :
                                                    ( ~ r1(X0,X1)
                                                    | p1(X1) )
                                              & p1(X0) ) ) ) ) ) )
                    | ( ~ p1(X1)
                      & ~ ! [X0] :
                            ( ~ r1(X1,X0)
                            | ~ ! [X1] :
                                  ( ~ r1(X0,X1)
                                  | p1(X1) ) )
                      & ! [X0] :
                          ( ~ r1(X1,X0)
                          | p1(X0)
                          | ~ ! [X1] :
                                ( ~ r1(X0,X1)
                                | ~ ( ~ ! [X0] :
                                          ( ~ r1(X1,X0)
                                          | p1(X0) )
                                    & p1(X1) ) ) ) ) ) )
          | ( ~ p1(X0)
            & ~ ! [X1] :
                  ( ~ r1(X0,X1)
                  | ~ ! [X0] :
                        ( ~ r1(X1,X0)
                        | p1(X0) ) )
            & ! [X1] :
                ( ~ r1(X0,X1)
                | p1(X1)
                | ~ ! [X0] :
                      ( ~ r1(X1,X0)
                      | ~ ( ~ ! [X1] :
                                ( ~ r1(X0,X1)
                                | p1(X1) )
                          & p1(X0) ) ) ) )
          | ! [X1] :
              ( ~ r1(X0,X1)
              | ! [X0] :
                  ( ~ r1(X1,X0)
                  | ~ ! [X1] :
                        ( ~ r1(X0,X1)
                        | p1(X1) ) )
              | ! [X0] :
                  ( ~ r1(X1,X0)
                  | p1(X0) ) )
          | ! [X1] :
              ( ~ r1(X0,X1)
              | ! [X0] :
                  ( ~ r1(X1,X0)
                  | ! [X1] :
                      ( ~ r1(X0,X1)
                      | ~ ! [X0] :
                            ( ~ r1(X1,X0)
                            | p1(X0) ) )
                  | ! [X1] :
                      ( ~ r1(X0,X1)
                      | p1(X1) ) )
              | ! [X0] :
                  ( ~ r1(X1,X0)
                  | ! [X1] :
                      ( ~ r1(X0,X1)
                      | ! [X0] :
                          ( ~ r1(X1,X0)
                          | ~ ! [X1] :
                                ( ~ r1(X0,X1)
                                | p1(X1) ) )
                      | ! [X0] :
                          ( ~ r1(X1,X0)
                          | p1(X0) ) )
                  | ! [X1] :
                      ( ~ r1(X0,X1)
                      | ! [X0] :
                          ( ~ r1(X1,X0)
                          | ! [X1] :
                              ( ~ r1(X0,X1)
                              | ~ ! [X0] :
                                    ( ~ r1(X1,X0)
                                    | p1(X0) ) )
                          | ! [X1] :
                              ( ~ r1(X0,X1)
                              | p1(X1) ) )
                      | ! [X0] :
                          ( ~ r1(X1,X0)
                          | ! [X1] :
                              ( ~ r1(X0,X1)
                              | ! [X0] :
                                  ( ~ r1(X1,X0)
                                  | ~ ! [X1] :
                                        ( ~ r1(X0,X1)
                                        | p1(X1) ) )
                              | ! [X0] :
                                  ( ~ r1(X1,X0)
                                  | p1(X0) ) )
                          | ! [X1] :
                              ( ~ r1(X0,X1)
                              | ~ ! [X0] :
                                    ( ~ r1(X1,X0)
                                    | ~ ! [X1] :
                                          ( ~ r1(X0,X1)
                                          | p2(X1) ) ) )
                          | ~ ! [X1] :
                                ( ~ r1(X0,X1)
                                | ! [X0] :
                                    ( ~ r1(X1,X0)
                                    | ! [X1] :
                                        ( ~ r1(X0,X1)
                                        | ~ p1(X1) ) )
                                | ~ ! [X0] :
                                      ( ~ r1(X1,X0)
                                      | ~ p1(X0) ) ) )
                      | ~ ! [X0] :
                            ( ~ r1(X1,X0)
                            | ! [X1] :
                                ( ~ r1(X0,X1)
                                | ! [X0] :
                                    ( ~ r1(X1,X0)
                                    | ~ p1(X0) ) )
                            | ~ ! [X1] :
                                  ( ~ r1(X0,X1)
                                  | ~ p1(X1) ) ) )
                  | ~ ! [X1] :
                        ( ~ r1(X0,X1)
                        | ! [X0] :
                            ( ~ r1(X1,X0)
                            | ! [X1] :
                                ( ~ r1(X0,X1)
                                | ~ p1(X1) ) )
                        | ~ ! [X0] :
                              ( ~ r1(X1,X0)
                              | ~ p1(X0) ) ) )
              | ~ ! [X0] :
                    ( ~ r1(X1,X0)
                    | ! [X1] :
                        ( ~ r1(X0,X1)
                        | ! [X0] :
                            ( ~ r1(X1,X0)
                            | ~ p1(X0) ) )
                    | ~ ! [X1] :
                          ( ~ r1(X0,X1)
                          | ~ p1(X1) ) ) )
          | ~ ! [X1] :
                ( ~ r1(X0,X1)
                | ! [X0] :
                    ( ~ r1(X1,X0)
                    | ! [X1] :
                        ( ~ r1(X0,X1)
                        | ~ p1(X1) ) )
                | ~ ! [X0] :
                      ( ~ r1(X1,X0)
                      | ~ p1(X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).

fof(f4,negated_conjecture,
    ~ ~ ? [X0] :
          ~ ( ~ ! [X1] :
                  ( ~ r1(X0,X1)
                  | ~ p4(X1) )
            | ~ ! [X1] :
                  ( ~ r1(X0,X1)
                  | ~ ( ~ ! [X0] :
                            ( ~ r1(X1,X0)
                            | ~ ( ~ ! [X1] :
                                      ( ~ r1(X0,X1)
                                      | ~ ( ~ ! [X0] :
                                                ( ~ r1(X1,X0)
                                                | ~ ( ~ ! [X1] :
                                                          ( ~ r1(X0,X1)
                                                          | ~ ( ~ ! [X0] :
                                                                    ( ~ r1(X1,X0)
                                                                    | ~ ( ~ ! [X1] :
                                                                              ( ~ r1(X0,X1)
                                                                              | ~ ( ~ ! [X0] :
                                                                                        ( ~ r1(X1,X0)
                                                                                        | ~ ( ~ ! [X1] :
                                                                                                  ( ~ r1(X0,X1)
                                                                                                  | ~ ( ~ ! [X0] :
                                                                                                            ( ~ r1(X1,X0)
                                                                                                            | ~ ! [X1] :
                                                                                                                  ( ~ r1(X0,X1)
                                                                                                                  | ! [X0] :
                                                                                                                      ( ~ r1(X1,X0)
                                                                                                                      | p3(X0) )
                                                                                                                  | ~ p2(X1) ) )
                                                                                                      | ~ ! [X0] :
                                                                                                            ( ~ r1(X1,X0)
                                                                                                            | ~ ( ~ ! [X1] :
                                                                                                                      ( ~ r1(X0,X1)
                                                                                                                      | ~ ( ! [X0] :
                                                                                                                              ( ~ r1(X1,X0)
                                                                                                                              | p3(X0) )
                                                                                                                          | ~ p2(X1) ) )
                                                                                                                & p2(X0)
                                                                                                                & ~ ! [X1] :
                                                                                                                      ( ~ r1(X0,X1)
                                                                                                                      | ~ ! [X0] :
                                                                                                                            ( ~ r1(X1,X0)
                                                                                                                            | ~ ! [X1] :
                                                                                                                                  ( ~ r1(X0,X1)
                                                                                                                                  | ~ p2(X1) ) ) ) ) ) ) )
                                                                                            | ( ~ p1(X0)
                                                                                              & ~ ! [X1] :
                                                                                                    ( ~ r1(X0,X1)
                                                                                                    | ~ ! [X0] :
                                                                                                          ( ~ r1(X1,X0)
                                                                                                          | p1(X0) ) )
                                                                                              & ! [X1] :
                                                                                                  ( ~ r1(X0,X1)
                                                                                                  | p1(X1)
                                                                                                  | ~ ! [X0] :
                                                                                                        ( ~ r1(X1,X0)
                                                                                                        | ~ ( ~ ! [X1] :
                                                                                                                  ( ~ r1(X0,X1)
                                                                                                                  | p1(X1) )
                                                                                                            & p1(X0) ) ) ) ) ) )
                                                                                  | ( ~ p1(X1)
                                                                                    & ~ ! [X0] :
                                                                                          ( ~ r1(X1,X0)
                                                                                          | ~ ! [X1] :
                                                                                                ( ~ r1(X0,X1)
                                                                                                | p1(X1) ) )
                                                                                    & ! [X0] :
                                                                                        ( ~ r1(X1,X0)
                                                                                        | p1(X0)
                                                                                        | ~ ! [X1] :
                                                                                              ( ~ r1(X0,X1)
                                                                                              | ~ ( ~ ! [X0] :
                                                                                                        ( ~ r1(X1,X0)
                                                                                                        | p1(X0) )
                                                                                                  & p1(X1) ) ) ) ) ) )
                                                                        | ( ~ p1(X0)
                                                                          & ~ ! [X1] :
                                                                                ( ~ r1(X0,X1)
                                                                                | ~ ! [X0] :
                                                                                      ( ~ r1(X1,X0)
                                                                                      | p1(X0) ) )
                                                                          & ! [X1] :
                                                                              ( ~ r1(X0,X1)
                                                                              | p1(X1)
                                                                              | ~ ! [X0] :
                                                                                    ( ~ r1(X1,X0)
                                                                                    | ~ ( ~ ! [X1] :
                                                                                              ( ~ r1(X0,X1)
                                                                                              | p1(X1) )
                                                                                        & p1(X0) ) ) ) ) ) )
                                                              | ( ~ p1(X1)
                                                                & ~ ! [X0] :
                                                                      ( ~ r1(X1,X0)
                                                                      | ~ ! [X1] :
                                                                            ( ~ r1(X0,X1)
                                                                            | p1(X1) ) )
                                                                & ! [X0] :
                                                                    ( ~ r1(X1,X0)
                                                                    | p1(X0)
                                                                    | ~ ! [X1] :
                                                                          ( ~ r1(X0,X1)
                                                                          | ~ ( ~ ! [X0] :
                                                                                    ( ~ r1(X1,X0)
                                                                                    | p1(X0) )
                                                                              & p1(X1) ) ) ) ) ) )
                                                    | ( ~ p1(X0)
                                                      & ~ ! [X1] :
                                                            ( ~ r1(X0,X1)
                                                            | ~ ! [X0] :
                                                                  ( ~ r1(X1,X0)
                                                                  | p1(X0) ) )
                                                      & ! [X1] :
                                                          ( ~ r1(X0,X1)
                                                          | p1(X1)
                                                          | ~ ! [X0] :
                                                                ( ~ r1(X1,X0)
                                                                | ~ ( ~ ! [X1] :
                                                                          ( ~ r1(X0,X1)
                                                                          | p1(X1) )
                                                                    & p1(X0) ) ) ) ) ) )
                                          | ( ~ p1(X1)
                                            & ~ ! [X0] :
                                                  ( ~ r1(X1,X0)
                                                  | ~ ! [X1] :
                                                        ( ~ r1(X0,X1)
                                                        | p1(X1) ) )
                                            & ! [X0] :
                                                ( ~ r1(X1,X0)
                                                | p1(X0)
                                                | ~ ! [X1] :
                                                      ( ~ r1(X0,X1)
                                                      | ~ ( ~ ! [X0] :
                                                                ( ~ r1(X1,X0)
                                                                | p1(X0) )
                                                          & p1(X1) ) ) ) ) ) )
                                | ( ~ p1(X0)
                                  & ~ ! [X1] :
                                        ( ~ r1(X0,X1)
                                        | ~ ! [X0] :
                                              ( ~ r1(X1,X0)
                                              | p1(X0) ) )
                                  & ! [X1] :
                                      ( ~ r1(X0,X1)
                                      | p1(X1)
                                      | ~ ! [X0] :
                                            ( ~ r1(X1,X0)
                                            | ~ ( ~ ! [X1] :
                                                      ( ~ r1(X0,X1)
                                                      | p1(X1) )
                                                & p1(X0) ) ) ) ) ) )
                      | ( ~ p1(X1)
                        & ~ ! [X0] :
                              ( ~ r1(X1,X0)
                              | ~ ! [X1] :
                                    ( ~ r1(X0,X1)
                                    | p1(X1) ) )
                        & ! [X0] :
                            ( ~ r1(X1,X0)
                            | p1(X0)
                            | ~ ! [X1] :
                                  ( ~ r1(X0,X1)
                                  | ~ ( ~ ! [X0] :
                                            ( ~ r1(X1,X0)
                                            | p1(X0) )
                                      & p1(X1) ) ) ) ) ) )
            | ( ~ p1(X0)
              & ~ ! [X1] :
                    ( ~ r1(X0,X1)
                    | ~ ! [X0] :
                          ( ~ r1(X1,X0)
                          | p1(X0) ) )
              & ! [X1] :
                  ( ~ r1(X0,X1)
                  | p1(X1)
                  | ~ ! [X0] :
                        ( ~ r1(X1,X0)
                        | ~ ( ~ ! [X1] :
                                  ( ~ r1(X0,X1)
                                  | p1(X1) )
                            & p1(X0) ) ) ) )
            | ! [X1] :
                ( ~ r1(X0,X1)
                | ! [X0] :
                    ( ~ r1(X1,X0)
                    | ~ ! [X1] :
                          ( ~ r1(X0,X1)
                          | p1(X1) ) )
                | ! [X0] :
                    ( ~ r1(X1,X0)
                    | p1(X0) ) )
            | ! [X1] :
                ( ~ r1(X0,X1)
                | ! [X0] :
                    ( ~ r1(X1,X0)
                    | ! [X1] :
                        ( ~ r1(X0,X1)
                        | ~ ! [X0] :
                              ( ~ r1(X1,X0)
                              | p1(X0) ) )
                    | ! [X1] :
                        ( ~ r1(X0,X1)
                        | p1(X1) ) )
                | ! [X0] :
                    ( ~ r1(X1,X0)
                    | ! [X1] :
                        ( ~ r1(X0,X1)
                        | ! [X0] :
                            ( ~ r1(X1,X0)
                            | ~ ! [X1] :
                                  ( ~ r1(X0,X1)
                                  | p1(X1) ) )
                        | ! [X0] :
                            ( ~ r1(X1,X0)
                            | p1(X0) ) )
                    | ! [X1] :
                        ( ~ r1(X0,X1)
                        | ! [X0] :
                            ( ~ r1(X1,X0)
                            | ! [X1] :
                                ( ~ r1(X0,X1)
                                | ~ ! [X0] :
                                      ( ~ r1(X1,X0)
                                      | p1(X0) ) )
                            | ! [X1] :
                                ( ~ r1(X0,X1)
                                | p1(X1) ) )
                        | ! [X0] :
                            ( ~ r1(X1,X0)
                            | ! [X1] :
                                ( ~ r1(X0,X1)
                                | ! [X0] :
                                    ( ~ r1(X1,X0)
                                    | ~ ! [X1] :
                                          ( ~ r1(X0,X1)
                                          | p1(X1) ) )
                                | ! [X0] :
                                    ( ~ r1(X1,X0)
                                    | p1(X0) ) )
                            | ! [X1] :
                                ( ~ r1(X0,X1)
                                | ~ ! [X0] :
                                      ( ~ r1(X1,X0)
                                      | ~ ! [X1] :
                                            ( ~ r1(X0,X1)
                                            | p2(X1) ) ) )
                            | ~ ! [X1] :
                                  ( ~ r1(X0,X1)
                                  | ! [X0] :
                                      ( ~ r1(X1,X0)
                                      | ! [X1] :
                                          ( ~ r1(X0,X1)
                                          | ~ p1(X1) ) )
                                  | ~ ! [X0] :
                                        ( ~ r1(X1,X0)
                                        | ~ p1(X0) ) ) )
                        | ~ ! [X0] :
                              ( ~ r1(X1,X0)
                              | ! [X1] :
                                  ( ~ r1(X0,X1)
                                  | ! [X0] :
                                      ( ~ r1(X1,X0)
                                      | ~ p1(X0) ) )
                              | ~ ! [X1] :
                                    ( ~ r1(X0,X1)
                                    | ~ p1(X1) ) ) )
                    | ~ ! [X1] :
                          ( ~ r1(X0,X1)
                          | ! [X0] :
                              ( ~ r1(X1,X0)
                              | ! [X1] :
                                  ( ~ r1(X0,X1)
                                  | ~ p1(X1) ) )
                          | ~ ! [X0] :
                                ( ~ r1(X1,X0)
                                | ~ p1(X0) ) ) )
                | ~ ! [X0] :
                      ( ~ r1(X1,X0)
                      | ! [X1] :
                          ( ~ r1(X0,X1)
                          | ! [X0] :
                              ( ~ r1(X1,X0)
                              | ~ p1(X0) ) )
                      | ~ ! [X1] :
                            ( ~ r1(X0,X1)
                            | ~ p1(X1) ) ) )
            | ~ ! [X1] :
                  ( ~ r1(X0,X1)
                  | ! [X0] :
                      ( ~ r1(X1,X0)
                      | ! [X1] :
                          ( ~ r1(X0,X1)
                          | ~ p1(X1) ) )
                  | ~ ! [X0] :
                        ( ~ r1(X1,X0)
                        | ~ p1(X0) ) ) ),
    inference(negated_conjecture,[status(cth)],[f3]) ).

fof(f5,plain,
    ~ ~ ? [X0] :
          ~ ( ~ ! [X1] :
                  ( ~ r1(X0,X1)
                  | ~ p4(X1) )
            | ~ ! [X2] :
                  ( ~ r1(X0,X2)
                  | ~ ( ~ ! [X3] :
                            ( ~ r1(X2,X3)
                            | ~ ( ~ ! [X4] :
                                      ( ~ r1(X3,X4)
                                      | ~ ( ~ ! [X5] :
                                                ( ~ r1(X4,X5)
                                                | ~ ( ~ ! [X6] :
                                                          ( ~ r1(X5,X6)
                                                          | ~ ( ~ ! [X7] :
                                                                    ( ~ r1(X6,X7)
                                                                    | ~ ( ~ ! [X8] :
                                                                              ( ~ r1(X7,X8)
                                                                              | ~ ( ~ ! [X9] :
                                                                                        ( ~ r1(X8,X9)
                                                                                        | ~ ( ~ ! [X10] :
                                                                                                  ( ~ r1(X9,X10)
                                                                                                  | ~ ( ~ ! [X11] :
                                                                                                            ( ~ r1(X10,X11)
                                                                                                            | ~ ! [X12] :
                                                                                                                  ( ~ r1(X11,X12)
                                                                                                                  | ! [X13] :
                                                                                                                      ( ~ r1(X12,X13)
                                                                                                                      | p3(X13) )
                                                                                                                  | ~ p2(X12) ) )
                                                                                                      | ~ ! [X14] :
                                                                                                            ( ~ r1(X10,X14)
                                                                                                            | ~ ( ~ ! [X15] :
                                                                                                                      ( ~ r1(X14,X15)
                                                                                                                      | ~ ( ! [X16] :
                                                                                                                              ( ~ r1(X15,X16)
                                                                                                                              | p3(X16) )
                                                                                                                          | ~ p2(X15) ) )
                                                                                                                & p2(X14)
                                                                                                                & ~ ! [X17] :
                                                                                                                      ( ~ r1(X14,X17)
                                                                                                                      | ~ ! [X18] :
                                                                                                                            ( ~ r1(X17,X18)
                                                                                                                            | ~ ! [X19] :
                                                                                                                                  ( ~ r1(X18,X19)
                                                                                                                                  | ~ p2(X19) ) ) ) ) ) ) )
                                                                                            | ( ~ p1(X9)
                                                                                              & ~ ! [X20] :
                                                                                                    ( ~ r1(X9,X20)
                                                                                                    | ~ ! [X21] :
                                                                                                          ( ~ r1(X20,X21)
                                                                                                          | p1(X21) ) )
                                                                                              & ! [X22] :
                                                                                                  ( ~ r1(X9,X22)
                                                                                                  | p1(X22)
                                                                                                  | ~ ! [X23] :
                                                                                                        ( ~ r1(X22,X23)
                                                                                                        | ~ ( ~ ! [X24] :
                                                                                                                  ( ~ r1(X23,X24)
                                                                                                                  | p1(X24) )
                                                                                                            & p1(X23) ) ) ) ) ) )
                                                                                  | ( ~ p1(X8)
                                                                                    & ~ ! [X25] :
                                                                                          ( ~ r1(X8,X25)
                                                                                          | ~ ! [X26] :
                                                                                                ( ~ r1(X25,X26)
                                                                                                | p1(X26) ) )
                                                                                    & ! [X27] :
                                                                                        ( ~ r1(X8,X27)
                                                                                        | p1(X27)
                                                                                        | ~ ! [X28] :
                                                                                              ( ~ r1(X27,X28)
                                                                                              | ~ ( ~ ! [X29] :
                                                                                                        ( ~ r1(X28,X29)
                                                                                                        | p1(X29) )
                                                                                                  & p1(X28) ) ) ) ) ) )
                                                                        | ( ~ p1(X7)
                                                                          & ~ ! [X30] :
                                                                                ( ~ r1(X7,X30)
                                                                                | ~ ! [X31] :
                                                                                      ( ~ r1(X30,X31)
                                                                                      | p1(X31) ) )
                                                                          & ! [X32] :
                                                                              ( ~ r1(X7,X32)
                                                                              | p1(X32)
                                                                              | ~ ! [X33] :
                                                                                    ( ~ r1(X32,X33)
                                                                                    | ~ ( ~ ! [X34] :
                                                                                              ( ~ r1(X33,X34)
                                                                                              | p1(X34) )
                                                                                        & p1(X33) ) ) ) ) ) )
                                                              | ( ~ p1(X6)
                                                                & ~ ! [X35] :
                                                                      ( ~ r1(X6,X35)
                                                                      | ~ ! [X36] :
                                                                            ( ~ r1(X35,X36)
                                                                            | p1(X36) ) )
                                                                & ! [X37] :
                                                                    ( ~ r1(X6,X37)
                                                                    | p1(X37)
                                                                    | ~ ! [X38] :
                                                                          ( ~ r1(X37,X38)
                                                                          | ~ ( ~ ! [X39] :
                                                                                    ( ~ r1(X38,X39)
                                                                                    | p1(X39) )
                                                                              & p1(X38) ) ) ) ) ) )
                                                    | ( ~ p1(X5)
                                                      & ~ ! [X40] :
                                                            ( ~ r1(X5,X40)
                                                            | ~ ! [X41] :
                                                                  ( ~ r1(X40,X41)
                                                                  | p1(X41) ) )
                                                      & ! [X42] :
                                                          ( ~ r1(X5,X42)
                                                          | p1(X42)
                                                          | ~ ! [X43] :
                                                                ( ~ r1(X42,X43)
                                                                | ~ ( ~ ! [X44] :
                                                                          ( ~ r1(X43,X44)
                                                                          | p1(X44) )
                                                                    & p1(X43) ) ) ) ) ) )
                                          | ( ~ p1(X4)
                                            & ~ ! [X45] :
                                                  ( ~ r1(X4,X45)
                                                  | ~ ! [X46] :
                                                        ( ~ r1(X45,X46)
                                                        | p1(X46) ) )
                                            & ! [X47] :
                                                ( ~ r1(X4,X47)
                                                | p1(X47)
                                                | ~ ! [X48] :
                                                      ( ~ r1(X47,X48)
                                                      | ~ ( ~ ! [X49] :
                                                                ( ~ r1(X48,X49)
                                                                | p1(X49) )
                                                          & p1(X48) ) ) ) ) ) )
                                | ( ~ p1(X3)
                                  & ~ ! [X50] :
                                        ( ~ r1(X3,X50)
                                        | ~ ! [X51] :
                                              ( ~ r1(X50,X51)
                                              | p1(X51) ) )
                                  & ! [X52] :
                                      ( ~ r1(X3,X52)
                                      | p1(X52)
                                      | ~ ! [X53] :
                                            ( ~ r1(X52,X53)
                                            | ~ ( ~ ! [X54] :
                                                      ( ~ r1(X53,X54)
                                                      | p1(X54) )
                                                & p1(X53) ) ) ) ) ) )
                      | ( ~ p1(X2)
                        & ~ ! [X55] :
                              ( ~ r1(X2,X55)
                              | ~ ! [X56] :
                                    ( ~ r1(X55,X56)
                                    | p1(X56) ) )
                        & ! [X57] :
                            ( ~ r1(X2,X57)
                            | p1(X57)
                            | ~ ! [X58] :
                                  ( ~ r1(X57,X58)
                                  | ~ ( ~ ! [X59] :
                                            ( ~ r1(X58,X59)
                                            | p1(X59) )
                                      & p1(X58) ) ) ) ) ) )
            | ( ~ p1(X0)
              & ~ ! [X60] :
                    ( ~ r1(X0,X60)
                    | ~ ! [X61] :
                          ( ~ r1(X60,X61)
                          | p1(X61) ) )
              & ! [X62] :
                  ( ~ r1(X0,X62)
                  | p1(X62)
                  | ~ ! [X63] :
                        ( ~ r1(X62,X63)
                        | ~ ( ~ ! [X64] :
                                  ( ~ r1(X63,X64)
                                  | p1(X64) )
                            & p1(X63) ) ) ) )
            | ! [X65] :
                ( ~ r1(X0,X65)
                | ! [X66] :
                    ( ~ r1(X65,X66)
                    | ~ ! [X67] :
                          ( ~ r1(X66,X67)
                          | p1(X67) ) )
                | ! [X68] :
                    ( ~ r1(X65,X68)
                    | p1(X68) ) )
            | ! [X69] :
                ( ~ r1(X0,X69)
                | ! [X70] :
                    ( ~ r1(X69,X70)
                    | ! [X71] :
                        ( ~ r1(X70,X71)
                        | ~ ! [X72] :
                              ( ~ r1(X71,X72)
                              | p1(X72) ) )
                    | ! [X73] :
                        ( ~ r1(X70,X73)
                        | p1(X73) ) )
                | ! [X74] :
                    ( ~ r1(X69,X74)
                    | ! [X75] :
                        ( ~ r1(X74,X75)
                        | ! [X76] :
                            ( ~ r1(X75,X76)
                            | ~ ! [X77] :
                                  ( ~ r1(X76,X77)
                                  | p1(X77) ) )
                        | ! [X78] :
                            ( ~ r1(X75,X78)
                            | p1(X78) ) )
                    | ! [X79] :
                        ( ~ r1(X74,X79)
                        | ! [X80] :
                            ( ~ r1(X79,X80)
                            | ! [X81] :
                                ( ~ r1(X80,X81)
                                | ~ ! [X82] :
                                      ( ~ r1(X81,X82)
                                      | p1(X82) ) )
                            | ! [X83] :
                                ( ~ r1(X80,X83)
                                | p1(X83) ) )
                        | ! [X84] :
                            ( ~ r1(X79,X84)
                            | ! [X85] :
                                ( ~ r1(X84,X85)
                                | ! [X86] :
                                    ( ~ r1(X85,X86)
                                    | ~ ! [X87] :
                                          ( ~ r1(X86,X87)
                                          | p1(X87) ) )
                                | ! [X88] :
                                    ( ~ r1(X85,X88)
                                    | p1(X88) ) )
                            | ! [X89] :
                                ( ~ r1(X84,X89)
                                | ~ ! [X90] :
                                      ( ~ r1(X89,X90)
                                      | ~ ! [X91] :
                                            ( ~ r1(X90,X91)
                                            | p2(X91) ) ) )
                            | ~ ! [X92] :
                                  ( ~ r1(X84,X92)
                                  | ! [X93] :
                                      ( ~ r1(X92,X93)
                                      | ! [X94] :
                                          ( ~ r1(X93,X94)
                                          | ~ p1(X94) ) )
                                  | ~ ! [X95] :
                                        ( ~ r1(X92,X95)
                                        | ~ p1(X95) ) ) )
                        | ~ ! [X96] :
                              ( ~ r1(X79,X96)
                              | ! [X97] :
                                  ( ~ r1(X96,X97)
                                  | ! [X98] :
                                      ( ~ r1(X97,X98)
                                      | ~ p1(X98) ) )
                              | ~ ! [X99] :
                                    ( ~ r1(X96,X99)
                                    | ~ p1(X99) ) ) )
                    | ~ ! [X100] :
                          ( ~ r1(X74,X100)
                          | ! [X101] :
                              ( ~ r1(X100,X101)
                              | ! [X102] :
                                  ( ~ r1(X101,X102)
                                  | ~ p1(X102) ) )
                          | ~ ! [X103] :
                                ( ~ r1(X100,X103)
                                | ~ p1(X103) ) ) )
                | ~ ! [X104] :
                      ( ~ r1(X69,X104)
                      | ! [X105] :
                          ( ~ r1(X104,X105)
                          | ! [X106] :
                              ( ~ r1(X105,X106)
                              | ~ p1(X106) ) )
                      | ~ ! [X107] :
                            ( ~ r1(X104,X107)
                            | ~ p1(X107) ) ) )
            | ~ ! [X108] :
                  ( ~ r1(X0,X108)
                  | ! [X109] :
                      ( ~ r1(X108,X109)
                      | ! [X110] :
                          ( ~ r1(X109,X110)
                          | ~ p1(X110) ) )
                  | ~ ! [X111] :
                        ( ~ r1(X108,X111)
                        | ~ p1(X111) ) ) ),
    inference(rectify,[],[f4]) ).

fof(f6,plain,
    ? [X0] :
      ~ ( ~ ! [X1] :
              ( ~ r1(X0,X1)
              | ~ p4(X1) )
        | ~ ! [X2] :
              ( ~ r1(X0,X2)
              | ~ ( ~ ! [X3] :
                        ( ~ r1(X2,X3)
                        | ~ ( ~ ! [X4] :
                                  ( ~ r1(X3,X4)
                                  | ~ ( ~ ! [X5] :
                                            ( ~ r1(X4,X5)
                                            | ~ ( ~ ! [X6] :
                                                      ( ~ r1(X5,X6)
                                                      | ~ ( ~ ! [X7] :
                                                                ( ~ r1(X6,X7)
                                                                | ~ ( ~ ! [X8] :
                                                                          ( ~ r1(X7,X8)
                                                                          | ~ ( ~ ! [X9] :
                                                                                    ( ~ r1(X8,X9)
                                                                                    | ~ ( ~ ! [X10] :
                                                                                              ( ~ r1(X9,X10)
                                                                                              | ~ ( ~ ! [X11] :
                                                                                                        ( ~ r1(X10,X11)
                                                                                                        | ~ ! [X12] :
                                                                                                              ( ~ r1(X11,X12)
                                                                                                              | ! [X13] :
                                                                                                                  ( ~ r1(X12,X13)
                                                                                                                  | p3(X13) )
                                                                                                              | ~ p2(X12) ) )
                                                                                                  | ~ ! [X14] :
                                                                                                        ( ~ r1(X10,X14)
                                                                                                        | ~ ( ~ ! [X15] :
                                                                                                                  ( ~ r1(X14,X15)
                                                                                                                  | ~ ( ! [X16] :
                                                                                                                          ( ~ r1(X15,X16)
                                                                                                                          | p3(X16) )
                                                                                                                      | ~ p2(X15) ) )
                                                                                                            & p2(X14)
                                                                                                            & ~ ! [X17] :
                                                                                                                  ( ~ r1(X14,X17)
                                                                                                                  | ~ ! [X18] :
                                                                                                                        ( ~ r1(X17,X18)
                                                                                                                        | ~ ! [X19] :
                                                                                                                              ( ~ r1(X18,X19)
                                                                                                                              | ~ p2(X19) ) ) ) ) ) ) )
                                                                                        | ( ~ p1(X9)
                                                                                          & ~ ! [X20] :
                                                                                                ( ~ r1(X9,X20)
                                                                                                | ~ ! [X21] :
                                                                                                      ( ~ r1(X20,X21)
                                                                                                      | p1(X21) ) )
                                                                                          & ! [X22] :
                                                                                              ( ~ r1(X9,X22)
                                                                                              | p1(X22)
                                                                                              | ~ ! [X23] :
                                                                                                    ( ~ r1(X22,X23)
                                                                                                    | ~ ( ~ ! [X24] :
                                                                                                              ( ~ r1(X23,X24)
                                                                                                              | p1(X24) )
                                                                                                        & p1(X23) ) ) ) ) ) )
                                                                              | ( ~ p1(X8)
                                                                                & ~ ! [X25] :
                                                                                      ( ~ r1(X8,X25)
                                                                                      | ~ ! [X26] :
                                                                                            ( ~ r1(X25,X26)
                                                                                            | p1(X26) ) )
                                                                                & ! [X27] :
                                                                                    ( ~ r1(X8,X27)
                                                                                    | p1(X27)
                                                                                    | ~ ! [X28] :
                                                                                          ( ~ r1(X27,X28)
                                                                                          | ~ ( ~ ! [X29] :
                                                                                                    ( ~ r1(X28,X29)
                                                                                                    | p1(X29) )
                                                                                              & p1(X28) ) ) ) ) ) )
                                                                    | ( ~ p1(X7)
                                                                      & ~ ! [X30] :
                                                                            ( ~ r1(X7,X30)
                                                                            | ~ ! [X31] :
                                                                                  ( ~ r1(X30,X31)
                                                                                  | p1(X31) ) )
                                                                      & ! [X32] :
                                                                          ( ~ r1(X7,X32)
                                                                          | p1(X32)
                                                                          | ~ ! [X33] :
                                                                                ( ~ r1(X32,X33)
                                                                                | ~ ( ~ ! [X34] :
                                                                                          ( ~ r1(X33,X34)
                                                                                          | p1(X34) )
                                                                                    & p1(X33) ) ) ) ) ) )
                                                          | ( ~ p1(X6)
                                                            & ~ ! [X35] :
                                                                  ( ~ r1(X6,X35)
                                                                  | ~ ! [X36] :
                                                                        ( ~ r1(X35,X36)
                                                                        | p1(X36) ) )
                                                            & ! [X37] :
                                                                ( ~ r1(X6,X37)
                                                                | p1(X37)
                                                                | ~ ! [X38] :
                                                                      ( ~ r1(X37,X38)
                                                                      | ~ ( ~ ! [X39] :
                                                                                ( ~ r1(X38,X39)
                                                                                | p1(X39) )
                                                                          & p1(X38) ) ) ) ) ) )
                                                | ( ~ p1(X5)
                                                  & ~ ! [X40] :
                                                        ( ~ r1(X5,X40)
                                                        | ~ ! [X41] :
                                                              ( ~ r1(X40,X41)
                                                              | p1(X41) ) )
                                                  & ! [X42] :
                                                      ( ~ r1(X5,X42)
                                                      | p1(X42)
                                                      | ~ ! [X43] :
                                                            ( ~ r1(X42,X43)
                                                            | ~ ( ~ ! [X44] :
                                                                      ( ~ r1(X43,X44)
                                                                      | p1(X44) )
                                                                & p1(X43) ) ) ) ) ) )
                                      | ( ~ p1(X4)
                                        & ~ ! [X45] :
                                              ( ~ r1(X4,X45)
                                              | ~ ! [X46] :
                                                    ( ~ r1(X45,X46)
                                                    | p1(X46) ) )
                                        & ! [X47] :
                                            ( ~ r1(X4,X47)
                                            | p1(X47)
                                            | ~ ! [X48] :
                                                  ( ~ r1(X47,X48)
                                                  | ~ ( ~ ! [X49] :
                                                            ( ~ r1(X48,X49)
                                                            | p1(X49) )
                                                      & p1(X48) ) ) ) ) ) )
                            | ( ~ p1(X3)
                              & ~ ! [X50] :
                                    ( ~ r1(X3,X50)
                                    | ~ ! [X51] :
                                          ( ~ r1(X50,X51)
                                          | p1(X51) ) )
                              & ! [X52] :
                                  ( ~ r1(X3,X52)
                                  | p1(X52)
                                  | ~ ! [X53] :
                                        ( ~ r1(X52,X53)
                                        | ~ ( ~ ! [X54] :
                                                  ( ~ r1(X53,X54)
                                                  | p1(X54) )
                                            & p1(X53) ) ) ) ) ) )
                  | ( ~ p1(X2)
                    & ~ ! [X55] :
                          ( ~ r1(X2,X55)
                          | ~ ! [X56] :
                                ( ~ r1(X55,X56)
                                | p1(X56) ) )
                    & ! [X57] :
                        ( ~ r1(X2,X57)
                        | p1(X57)
                        | ~ ! [X58] :
                              ( ~ r1(X57,X58)
                              | ~ ( ~ ! [X59] :
                                        ( ~ r1(X58,X59)
                                        | p1(X59) )
                                  & p1(X58) ) ) ) ) ) )
        | ( ~ p1(X0)
          & ~ ! [X60] :
                ( ~ r1(X0,X60)
                | ~ ! [X61] :
                      ( ~ r1(X60,X61)
                      | p1(X61) ) )
          & ! [X62] :
              ( ~ r1(X0,X62)
              | p1(X62)
              | ~ ! [X63] :
                    ( ~ r1(X62,X63)
                    | ~ ( ~ ! [X64] :
                              ( ~ r1(X63,X64)
                              | p1(X64) )
                        & p1(X63) ) ) ) )
        | ! [X65] :
            ( ~ r1(X0,X65)
            | ! [X66] :
                ( ~ r1(X65,X66)
                | ~ ! [X67] :
                      ( ~ r1(X66,X67)
                      | p1(X67) ) )
            | ! [X68] :
                ( ~ r1(X65,X68)
                | p1(X68) ) )
        | ! [X69] :
            ( ~ r1(X0,X69)
            | ! [X70] :
                ( ~ r1(X69,X70)
                | ! [X71] :
                    ( ~ r1(X70,X71)
                    | ~ ! [X72] :
                          ( ~ r1(X71,X72)
                          | p1(X72) ) )
                | ! [X73] :
                    ( ~ r1(X70,X73)
                    | p1(X73) ) )
            | ! [X74] :
                ( ~ r1(X69,X74)
                | ! [X75] :
                    ( ~ r1(X74,X75)
                    | ! [X76] :
                        ( ~ r1(X75,X76)
                        | ~ ! [X77] :
                              ( ~ r1(X76,X77)
                              | p1(X77) ) )
                    | ! [X78] :
                        ( ~ r1(X75,X78)
                        | p1(X78) ) )
                | ! [X79] :
                    ( ~ r1(X74,X79)
                    | ! [X80] :
                        ( ~ r1(X79,X80)
                        | ! [X81] :
                            ( ~ r1(X80,X81)
                            | ~ ! [X82] :
                                  ( ~ r1(X81,X82)
                                  | p1(X82) ) )
                        | ! [X83] :
                            ( ~ r1(X80,X83)
                            | p1(X83) ) )
                    | ! [X84] :
                        ( ~ r1(X79,X84)
                        | ! [X85] :
                            ( ~ r1(X84,X85)
                            | ! [X86] :
                                ( ~ r1(X85,X86)
                                | ~ ! [X87] :
                                      ( ~ r1(X86,X87)
                                      | p1(X87) ) )
                            | ! [X88] :
                                ( ~ r1(X85,X88)
                                | p1(X88) ) )
                        | ! [X89] :
                            ( ~ r1(X84,X89)
                            | ~ ! [X90] :
                                  ( ~ r1(X89,X90)
                                  | ~ ! [X91] :
                                        ( ~ r1(X90,X91)
                                        | p2(X91) ) ) )
                        | ~ ! [X92] :
                              ( ~ r1(X84,X92)
                              | ! [X93] :
                                  ( ~ r1(X92,X93)
                                  | ! [X94] :
                                      ( ~ r1(X93,X94)
                                      | ~ p1(X94) ) )
                              | ~ ! [X95] :
                                    ( ~ r1(X92,X95)
                                    | ~ p1(X95) ) ) )
                    | ~ ! [X96] :
                          ( ~ r1(X79,X96)
                          | ! [X97] :
                              ( ~ r1(X96,X97)
                              | ! [X98] :
                                  ( ~ r1(X97,X98)
                                  | ~ p1(X98) ) )
                          | ~ ! [X99] :
                                ( ~ r1(X96,X99)
                                | ~ p1(X99) ) ) )
                | ~ ! [X100] :
                      ( ~ r1(X74,X100)
                      | ! [X101] :
                          ( ~ r1(X100,X101)
                          | ! [X102] :
                              ( ~ r1(X101,X102)
                              | ~ p1(X102) ) )
                      | ~ ! [X103] :
                            ( ~ r1(X100,X103)
                            | ~ p1(X103) ) ) )
            | ~ ! [X104] :
                  ( ~ r1(X69,X104)
                  | ! [X105] :
                      ( ~ r1(X104,X105)
                      | ! [X106] :
                          ( ~ r1(X105,X106)
                          | ~ p1(X106) ) )
                  | ~ ! [X107] :
                        ( ~ r1(X104,X107)
                        | ~ p1(X107) ) ) )
        | ~ ! [X108] :
              ( ~ r1(X0,X108)
              | ! [X109] :
                  ( ~ r1(X108,X109)
                  | ! [X110] :
                      ( ~ r1(X109,X110)
                      | ~ p1(X110) ) )
              | ~ ! [X111] :
                    ( ~ r1(X108,X111)
                    | ~ p1(X111) ) ) ),
    inference(flattening,[],[f5]) ).

fof(f7,plain,
    ! [X0,X1,X2] :
      ( r1(X0,X2)
      | ~ r1(X0,X1)
      | ~ r1(X1,X2) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f8,plain,
    ! [X0,X1,X2] :
      ( r1(X0,X2)
      | ~ r1(X0,X1)
      | ~ r1(X1,X2) ),
    inference(flattening,[],[f7]) ).

fof(f9,plain,
    ? [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ~ p4(X1) )
      & ! [X2] :
          ( ~ r1(X0,X2)
          | ( ! [X3] :
                ( ~ r1(X2,X3)
                | ( ! [X4] :
                      ( ~ r1(X3,X4)
                      | ( ! [X5] :
                            ( ~ r1(X4,X5)
                            | ( ! [X6] :
                                  ( ~ r1(X5,X6)
                                  | ( ! [X7] :
                                        ( ~ r1(X6,X7)
                                        | ( ! [X8] :
                                              ( ~ r1(X7,X8)
                                              | ( ! [X9] :
                                                    ( ~ r1(X8,X9)
                                                    | ( ! [X10] :
                                                          ( ~ r1(X9,X10)
                                                          | ( ! [X11] :
                                                                ( ~ r1(X10,X11)
                                                                | ? [X12] :
                                                                    ( r1(X11,X12)
                                                                    & ? [X13] :
                                                                        ( r1(X12,X13)
                                                                        & ~ p3(X13) )
                                                                    & p2(X12) ) )
                                                            & ! [X14] :
                                                                ( ~ r1(X10,X14)
                                                                | ! [X15] :
                                                                    ( ~ r1(X14,X15)
                                                                    | ( ? [X16] :
                                                                          ( r1(X15,X16)
                                                                          & ~ p3(X16) )
                                                                      & p2(X15) ) )
                                                                | ~ p2(X14)
                                                                | ! [X17] :
                                                                    ( ~ r1(X14,X17)
                                                                    | ? [X18] :
                                                                        ( r1(X17,X18)
                                                                        & ! [X19] :
                                                                            ( ~ r1(X18,X19)
                                                                            | ~ p2(X19) ) ) ) ) ) )
                                                      & ( p1(X9)
                                                        | ! [X20] :
                                                            ( ~ r1(X9,X20)
                                                            | ? [X21] :
                                                                ( r1(X20,X21)
                                                                & ~ p1(X21) ) )
                                                        | ? [X22] :
                                                            ( r1(X9,X22)
                                                            & ~ p1(X22)
                                                            & ! [X23] :
                                                                ( ~ r1(X22,X23)
                                                                | ! [X24] :
                                                                    ( ~ r1(X23,X24)
                                                                    | p1(X24) )
                                                                | ~ p1(X23) ) ) ) ) )
                                                & ( p1(X8)
                                                  | ! [X25] :
                                                      ( ~ r1(X8,X25)
                                                      | ? [X26] :
                                                          ( r1(X25,X26)
                                                          & ~ p1(X26) ) )
                                                  | ? [X27] :
                                                      ( r1(X8,X27)
                                                      & ~ p1(X27)
                                                      & ! [X28] :
                                                          ( ~ r1(X27,X28)
                                                          | ! [X29] :
                                                              ( ~ r1(X28,X29)
                                                              | p1(X29) )
                                                          | ~ p1(X28) ) ) ) ) )
                                          & ( p1(X7)
                                            | ! [X30] :
                                                ( ~ r1(X7,X30)
                                                | ? [X31] :
                                                    ( r1(X30,X31)
                                                    & ~ p1(X31) ) )
                                            | ? [X32] :
                                                ( r1(X7,X32)
                                                & ~ p1(X32)
                                                & ! [X33] :
                                                    ( ~ r1(X32,X33)
                                                    | ! [X34] :
                                                        ( ~ r1(X33,X34)
                                                        | p1(X34) )
                                                    | ~ p1(X33) ) ) ) ) )
                                    & ( p1(X6)
                                      | ! [X35] :
                                          ( ~ r1(X6,X35)
                                          | ? [X36] :
                                              ( r1(X35,X36)
                                              & ~ p1(X36) ) )
                                      | ? [X37] :
                                          ( r1(X6,X37)
                                          & ~ p1(X37)
                                          & ! [X38] :
                                              ( ~ r1(X37,X38)
                                              | ! [X39] :
                                                  ( ~ r1(X38,X39)
                                                  | p1(X39) )
                                              | ~ p1(X38) ) ) ) ) )
                              & ( p1(X5)
                                | ! [X40] :
                                    ( ~ r1(X5,X40)
                                    | ? [X41] :
                                        ( r1(X40,X41)
                                        & ~ p1(X41) ) )
                                | ? [X42] :
                                    ( r1(X5,X42)
                                    & ~ p1(X42)
                                    & ! [X43] :
                                        ( ~ r1(X42,X43)
                                        | ! [X44] :
                                            ( ~ r1(X43,X44)
                                            | p1(X44) )
                                        | ~ p1(X43) ) ) ) ) )
                        & ( p1(X4)
                          | ! [X45] :
                              ( ~ r1(X4,X45)
                              | ? [X46] :
                                  ( r1(X45,X46)
                                  & ~ p1(X46) ) )
                          | ? [X47] :
                              ( r1(X4,X47)
                              & ~ p1(X47)
                              & ! [X48] :
                                  ( ~ r1(X47,X48)
                                  | ! [X49] :
                                      ( ~ r1(X48,X49)
                                      | p1(X49) )
                                  | ~ p1(X48) ) ) ) ) )
                  & ( p1(X3)
                    | ! [X50] :
                        ( ~ r1(X3,X50)
                        | ? [X51] :
                            ( r1(X50,X51)
                            & ~ p1(X51) ) )
                    | ? [X52] :
                        ( r1(X3,X52)
                        & ~ p1(X52)
                        & ! [X53] :
                            ( ~ r1(X52,X53)
                            | ! [X54] :
                                ( ~ r1(X53,X54)
                                | p1(X54) )
                            | ~ p1(X53) ) ) ) ) )
            & ( p1(X2)
              | ! [X55] :
                  ( ~ r1(X2,X55)
                  | ? [X56] :
                      ( r1(X55,X56)
                      & ~ p1(X56) ) )
              | ? [X57] :
                  ( r1(X2,X57)
                  & ~ p1(X57)
                  & ! [X58] :
                      ( ~ r1(X57,X58)
                      | ! [X59] :
                          ( ~ r1(X58,X59)
                          | p1(X59) )
                      | ~ p1(X58) ) ) ) ) )
      & ( p1(X0)
        | ! [X60] :
            ( ~ r1(X0,X60)
            | ? [X61] :
                ( r1(X60,X61)
                & ~ p1(X61) ) )
        | ? [X62] :
            ( r1(X0,X62)
            & ~ p1(X62)
            & ! [X63] :
                ( ~ r1(X62,X63)
                | ! [X64] :
                    ( ~ r1(X63,X64)
                    | p1(X64) )
                | ~ p1(X63) ) ) )
      & ? [X65] :
          ( r1(X0,X65)
          & ? [X66] :
              ( r1(X65,X66)
              & ! [X67] :
                  ( ~ r1(X66,X67)
                  | p1(X67) ) )
          & ? [X68] :
              ( r1(X65,X68)
              & ~ p1(X68) ) )
      & ? [X69] :
          ( r1(X0,X69)
          & ? [X70] :
              ( r1(X69,X70)
              & ? [X71] :
                  ( r1(X70,X71)
                  & ! [X72] :
                      ( ~ r1(X71,X72)
                      | p1(X72) ) )
              & ? [X73] :
                  ( r1(X70,X73)
                  & ~ p1(X73) ) )
          & ? [X74] :
              ( r1(X69,X74)
              & ? [X75] :
                  ( r1(X74,X75)
                  & ? [X76] :
                      ( r1(X75,X76)
                      & ! [X77] :
                          ( ~ r1(X76,X77)
                          | p1(X77) ) )
                  & ? [X78] :
                      ( r1(X75,X78)
                      & ~ p1(X78) ) )
              & ? [X79] :
                  ( r1(X74,X79)
                  & ? [X80] :
                      ( r1(X79,X80)
                      & ? [X81] :
                          ( r1(X80,X81)
                          & ! [X82] :
                              ( ~ r1(X81,X82)
                              | p1(X82) ) )
                      & ? [X83] :
                          ( r1(X80,X83)
                          & ~ p1(X83) ) )
                  & ? [X84] :
                      ( r1(X79,X84)
                      & ? [X85] :
                          ( r1(X84,X85)
                          & ? [X86] :
                              ( r1(X85,X86)
                              & ! [X87] :
                                  ( ~ r1(X86,X87)
                                  | p1(X87) ) )
                          & ? [X88] :
                              ( r1(X85,X88)
                              & ~ p1(X88) ) )
                      & ? [X89] :
                          ( r1(X84,X89)
                          & ! [X90] :
                              ( ~ r1(X89,X90)
                              | ? [X91] :
                                  ( r1(X90,X91)
                                  & ~ p2(X91) ) ) )
                      & ! [X92] :
                          ( ~ r1(X84,X92)
                          | ! [X93] :
                              ( ~ r1(X92,X93)
                              | ! [X94] :
                                  ( ~ r1(X93,X94)
                                  | ~ p1(X94) ) )
                          | ? [X95] :
                              ( r1(X92,X95)
                              & p1(X95) ) ) )
                  & ! [X96] :
                      ( ~ r1(X79,X96)
                      | ! [X97] :
                          ( ~ r1(X96,X97)
                          | ! [X98] :
                              ( ~ r1(X97,X98)
                              | ~ p1(X98) ) )
                      | ? [X99] :
                          ( r1(X96,X99)
                          & p1(X99) ) ) )
              & ! [X100] :
                  ( ~ r1(X74,X100)
                  | ! [X101] :
                      ( ~ r1(X100,X101)
                      | ! [X102] :
                          ( ~ r1(X101,X102)
                          | ~ p1(X102) ) )
                  | ? [X103] :
                      ( r1(X100,X103)
                      & p1(X103) ) ) )
          & ! [X104] :
              ( ~ r1(X69,X104)
              | ! [X105] :
                  ( ~ r1(X104,X105)
                  | ! [X106] :
                      ( ~ r1(X105,X106)
                      | ~ p1(X106) ) )
              | ? [X107] :
                  ( r1(X104,X107)
                  & p1(X107) ) ) )
      & ! [X108] :
          ( ~ r1(X0,X108)
          | ! [X109] :
              ( ~ r1(X108,X109)
              | ! [X110] :
                  ( ~ r1(X109,X110)
                  | ~ p1(X110) ) )
          | ? [X111] :
              ( r1(X108,X111)
              & p1(X111) ) ) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f10,plain,
    ? [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ~ p4(X1) )
      & ! [X2] :
          ( ~ r1(X0,X2)
          | ( ! [X3] :
                ( ~ r1(X2,X3)
                | ( ! [X4] :
                      ( ~ r1(X3,X4)
                      | ( ! [X5] :
                            ( ~ r1(X4,X5)
                            | ( ! [X6] :
                                  ( ~ r1(X5,X6)
                                  | ( ! [X7] :
                                        ( ~ r1(X6,X7)
                                        | ( ! [X8] :
                                              ( ~ r1(X7,X8)
                                              | ( ! [X9] :
                                                    ( ~ r1(X8,X9)
                                                    | ( ! [X10] :
                                                          ( ~ r1(X9,X10)
                                                          | ( ! [X11] :
                                                                ( ~ r1(X10,X11)
                                                                | ? [X12] :
                                                                    ( r1(X11,X12)
                                                                    & ? [X13] :
                                                                        ( r1(X12,X13)
                                                                        & ~ p3(X13) )
                                                                    & p2(X12) ) )
                                                            & ! [X14] :
                                                                ( ~ r1(X10,X14)
                                                                | ! [X15] :
                                                                    ( ~ r1(X14,X15)
                                                                    | ( ? [X16] :
                                                                          ( r1(X15,X16)
                                                                          & ~ p3(X16) )
                                                                      & p2(X15) ) )
                                                                | ~ p2(X14)
                                                                | ! [X17] :
                                                                    ( ~ r1(X14,X17)
                                                                    | ? [X18] :
                                                                        ( r1(X17,X18)
                                                                        & ! [X19] :
                                                                            ( ~ r1(X18,X19)
                                                                            | ~ p2(X19) ) ) ) ) ) )
                                                      & ( p1(X9)
                                                        | ! [X20] :
                                                            ( ~ r1(X9,X20)
                                                            | ? [X21] :
                                                                ( r1(X20,X21)
                                                                & ~ p1(X21) ) )
                                                        | ? [X22] :
                                                            ( r1(X9,X22)
                                                            & ~ p1(X22)
                                                            & ! [X23] :
                                                                ( ~ r1(X22,X23)
                                                                | ! [X24] :
                                                                    ( ~ r1(X23,X24)
                                                                    | p1(X24) )
                                                                | ~ p1(X23) ) ) ) ) )
                                                & ( p1(X8)
                                                  | ! [X25] :
                                                      ( ~ r1(X8,X25)
                                                      | ? [X26] :
                                                          ( r1(X25,X26)
                                                          & ~ p1(X26) ) )
                                                  | ? [X27] :
                                                      ( r1(X8,X27)
                                                      & ~ p1(X27)
                                                      & ! [X28] :
                                                          ( ~ r1(X27,X28)
                                                          | ! [X29] :
                                                              ( ~ r1(X28,X29)
                                                              | p1(X29) )
                                                          | ~ p1(X28) ) ) ) ) )
                                          & ( p1(X7)
                                            | ! [X30] :
                                                ( ~ r1(X7,X30)
                                                | ? [X31] :
                                                    ( r1(X30,X31)
                                                    & ~ p1(X31) ) )
                                            | ? [X32] :
                                                ( r1(X7,X32)
                                                & ~ p1(X32)
                                                & ! [X33] :
                                                    ( ~ r1(X32,X33)
                                                    | ! [X34] :
                                                        ( ~ r1(X33,X34)
                                                        | p1(X34) )
                                                    | ~ p1(X33) ) ) ) ) )
                                    & ( p1(X6)
                                      | ! [X35] :
                                          ( ~ r1(X6,X35)
                                          | ? [X36] :
                                              ( r1(X35,X36)
                                              & ~ p1(X36) ) )
                                      | ? [X37] :
                                          ( r1(X6,X37)
                                          & ~ p1(X37)
                                          & ! [X38] :
                                              ( ~ r1(X37,X38)
                                              | ! [X39] :
                                                  ( ~ r1(X38,X39)
                                                  | p1(X39) )
                                              | ~ p1(X38) ) ) ) ) )
                              & ( p1(X5)
                                | ! [X40] :
                                    ( ~ r1(X5,X40)
                                    | ? [X41] :
                                        ( r1(X40,X41)
                                        & ~ p1(X41) ) )
                                | ? [X42] :
                                    ( r1(X5,X42)
                                    & ~ p1(X42)
                                    & ! [X43] :
                                        ( ~ r1(X42,X43)
                                        | ! [X44] :
                                            ( ~ r1(X43,X44)
                                            | p1(X44) )
                                        | ~ p1(X43) ) ) ) ) )
                        & ( p1(X4)
                          | ! [X45] :
                              ( ~ r1(X4,X45)
                              | ? [X46] :
                                  ( r1(X45,X46)
                                  & ~ p1(X46) ) )
                          | ? [X47] :
                              ( r1(X4,X47)
                              & ~ p1(X47)
                              & ! [X48] :
                                  ( ~ r1(X47,X48)
                                  | ! [X49] :
                                      ( ~ r1(X48,X49)
                                      | p1(X49) )
                                  | ~ p1(X48) ) ) ) ) )
                  & ( p1(X3)
                    | ! [X50] :
                        ( ~ r1(X3,X50)
                        | ? [X51] :
                            ( r1(X50,X51)
                            & ~ p1(X51) ) )
                    | ? [X52] :
                        ( r1(X3,X52)
                        & ~ p1(X52)
                        & ! [X53] :
                            ( ~ r1(X52,X53)
                            | ! [X54] :
                                ( ~ r1(X53,X54)
                                | p1(X54) )
                            | ~ p1(X53) ) ) ) ) )
            & ( p1(X2)
              | ! [X55] :
                  ( ~ r1(X2,X55)
                  | ? [X56] :
                      ( r1(X55,X56)
                      & ~ p1(X56) ) )
              | ? [X57] :
                  ( r1(X2,X57)
                  & ~ p1(X57)
                  & ! [X58] :
                      ( ~ r1(X57,X58)
                      | ! [X59] :
                          ( ~ r1(X58,X59)
                          | p1(X59) )
                      | ~ p1(X58) ) ) ) ) )
      & ( p1(X0)
        | ! [X60] :
            ( ~ r1(X0,X60)
            | ? [X61] :
                ( r1(X60,X61)
                & ~ p1(X61) ) )
        | ? [X62] :
            ( r1(X0,X62)
            & ~ p1(X62)
            & ! [X63] :
                ( ~ r1(X62,X63)
                | ! [X64] :
                    ( ~ r1(X63,X64)
                    | p1(X64) )
                | ~ p1(X63) ) ) )
      & ? [X65] :
          ( r1(X0,X65)
          & ? [X66] :
              ( r1(X65,X66)
              & ! [X67] :
                  ( ~ r1(X66,X67)
                  | p1(X67) ) )
          & ? [X68] :
              ( r1(X65,X68)
              & ~ p1(X68) ) )
      & ? [X69] :
          ( r1(X0,X69)
          & ? [X70] :
              ( r1(X69,X70)
              & ? [X71] :
                  ( r1(X70,X71)
                  & ! [X72] :
                      ( ~ r1(X71,X72)
                      | p1(X72) ) )
              & ? [X73] :
                  ( r1(X70,X73)
                  & ~ p1(X73) ) )
          & ? [X74] :
              ( r1(X69,X74)
              & ? [X75] :
                  ( r1(X74,X75)
                  & ? [X76] :
                      ( r1(X75,X76)
                      & ! [X77] :
                          ( ~ r1(X76,X77)
                          | p1(X77) ) )
                  & ? [X78] :
                      ( r1(X75,X78)
                      & ~ p1(X78) ) )
              & ? [X79] :
                  ( r1(X74,X79)
                  & ? [X80] :
                      ( r1(X79,X80)
                      & ? [X81] :
                          ( r1(X80,X81)
                          & ! [X82] :
                              ( ~ r1(X81,X82)
                              | p1(X82) ) )
                      & ? [X83] :
                          ( r1(X80,X83)
                          & ~ p1(X83) ) )
                  & ? [X84] :
                      ( r1(X79,X84)
                      & ? [X85] :
                          ( r1(X84,X85)
                          & ? [X86] :
                              ( r1(X85,X86)
                              & ! [X87] :
                                  ( ~ r1(X86,X87)
                                  | p1(X87) ) )
                          & ? [X88] :
                              ( r1(X85,X88)
                              & ~ p1(X88) ) )
                      & ? [X89] :
                          ( r1(X84,X89)
                          & ! [X90] :
                              ( ~ r1(X89,X90)
                              | ? [X91] :
                                  ( r1(X90,X91)
                                  & ~ p2(X91) ) ) )
                      & ! [X92] :
                          ( ~ r1(X84,X92)
                          | ! [X93] :
                              ( ~ r1(X92,X93)
                              | ! [X94] :
                                  ( ~ r1(X93,X94)
                                  | ~ p1(X94) ) )
                          | ? [X95] :
                              ( r1(X92,X95)
                              & p1(X95) ) ) )
                  & ! [X96] :
                      ( ~ r1(X79,X96)
                      | ! [X97] :
                          ( ~ r1(X96,X97)
                          | ! [X98] :
                              ( ~ r1(X97,X98)
                              | ~ p1(X98) ) )
                      | ? [X99] :
                          ( r1(X96,X99)
                          & p1(X99) ) ) )
              & ! [X100] :
                  ( ~ r1(X74,X100)
                  | ! [X101] :
                      ( ~ r1(X100,X101)
                      | ! [X102] :
                          ( ~ r1(X101,X102)
                          | ~ p1(X102) ) )
                  | ? [X103] :
                      ( r1(X100,X103)
                      & p1(X103) ) ) )
          & ! [X104] :
              ( ~ r1(X69,X104)
              | ! [X105] :
                  ( ~ r1(X104,X105)
                  | ! [X106] :
                      ( ~ r1(X105,X106)
                      | ~ p1(X106) ) )
              | ? [X107] :
                  ( r1(X104,X107)
                  & p1(X107) ) ) )
      & ! [X108] :
          ( ~ r1(X0,X108)
          | ! [X109] :
              ( ~ r1(X108,X109)
              | ! [X110] :
                  ( ~ r1(X109,X110)
                  | ~ p1(X110) ) )
          | ? [X111] :
              ( r1(X108,X111)
              & p1(X111) ) ) ),
    inference(flattening,[],[f9]) ).

fof(f11,definition,
    ! [X8] :
      ( ! [X9] :
          ( ~ r1(X8,X9)
          | ( ! [X10] :
                ( ~ r1(X9,X10)
                | ( ! [X11] :
                      ( ~ r1(X10,X11)
                      | ? [X12] :
                          ( r1(X11,X12)
                          & ? [X13] :
                              ( r1(X12,X13)
                              & ~ p3(X13) )
                          & p2(X12) ) )
                  & ! [X14] :
                      ( ~ r1(X10,X14)
                      | ! [X15] :
                          ( ~ r1(X14,X15)
                          | ( ? [X16] :
                                ( r1(X15,X16)
                                & ~ p3(X16) )
                            & p2(X15) ) )
                      | ~ p2(X14)
                      | ! [X17] :
                          ( ~ r1(X14,X17)
                          | ? [X18] :
                              ( r1(X17,X18)
                              & ! [X19] :
                                  ( ~ r1(X18,X19)
                                  | ~ p2(X19) ) ) ) ) ) )
            & ( p1(X9)
              | ! [X20] :
                  ( ~ r1(X9,X20)
                  | ? [X21] :
                      ( r1(X20,X21)
                      & ~ p1(X21) ) )
              | ? [X22] :
                  ( r1(X9,X22)
                  & ~ p1(X22)
                  & ! [X23] :
                      ( ~ r1(X22,X23)
                      | ! [X24] :
                          ( ~ r1(X23,X24)
                          | p1(X24) )
                      | ~ p1(X23) ) ) ) ) )
      | ~ sP0(X8) ),
    introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).

fof(f12,definition,
    ! [X6] :
      ( ! [X7] :
          ( ~ r1(X6,X7)
          | ( ! [X8] :
                ( ~ r1(X7,X8)
                | ( sP0(X8)
                  & ( p1(X8)
                    | ! [X25] :
                        ( ~ r1(X8,X25)
                        | ? [X26] :
                            ( r1(X25,X26)
                            & ~ p1(X26) ) )
                    | ? [X27] :
                        ( r1(X8,X27)
                        & ~ p1(X27)
                        & ! [X28] :
                            ( ~ r1(X27,X28)
                            | ! [X29] :
                                ( ~ r1(X28,X29)
                                | p1(X29) )
                            | ~ p1(X28) ) ) ) ) )
            & ( p1(X7)
              | ! [X30] :
                  ( ~ r1(X7,X30)
                  | ? [X31] :
                      ( r1(X30,X31)
                      & ~ p1(X31) ) )
              | ? [X32] :
                  ( r1(X7,X32)
                  & ~ p1(X32)
                  & ! [X33] :
                      ( ~ r1(X32,X33)
                      | ! [X34] :
                          ( ~ r1(X33,X34)
                          | p1(X34) )
                      | ~ p1(X33) ) ) ) ) )
      | ~ sP1(X6) ),
    introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).

fof(f13,definition,
    ! [X4] :
      ( ! [X5] :
          ( ~ r1(X4,X5)
          | ( ! [X6] :
                ( ~ r1(X5,X6)
                | ( sP1(X6)
                  & ( p1(X6)
                    | ! [X35] :
                        ( ~ r1(X6,X35)
                        | ? [X36] :
                            ( r1(X35,X36)
                            & ~ p1(X36) ) )
                    | ? [X37] :
                        ( r1(X6,X37)
                        & ~ p1(X37)
                        & ! [X38] :
                            ( ~ r1(X37,X38)
                            | ! [X39] :
                                ( ~ r1(X38,X39)
                                | p1(X39) )
                            | ~ p1(X38) ) ) ) ) )
            & ( p1(X5)
              | ! [X40] :
                  ( ~ r1(X5,X40)
                  | ? [X41] :
                      ( r1(X40,X41)
                      & ~ p1(X41) ) )
              | ? [X42] :
                  ( r1(X5,X42)
                  & ~ p1(X42)
                  & ! [X43] :
                      ( ~ r1(X42,X43)
                      | ! [X44] :
                          ( ~ r1(X43,X44)
                          | p1(X44) )
                      | ~ p1(X43) ) ) ) ) )
      | ~ sP2(X4) ),
    introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).

fof(f14,definition,
    ! [X2] :
      ( ! [X3] :
          ( ~ r1(X2,X3)
          | ( ! [X4] :
                ( ~ r1(X3,X4)
                | ( sP2(X4)
                  & ( p1(X4)
                    | ! [X45] :
                        ( ~ r1(X4,X45)
                        | ? [X46] :
                            ( r1(X45,X46)
                            & ~ p1(X46) ) )
                    | ? [X47] :
                        ( r1(X4,X47)
                        & ~ p1(X47)
                        & ! [X48] :
                            ( ~ r1(X47,X48)
                            | ! [X49] :
                                ( ~ r1(X48,X49)
                                | p1(X49) )
                            | ~ p1(X48) ) ) ) ) )
            & ( p1(X3)
              | ! [X50] :
                  ( ~ r1(X3,X50)
                  | ? [X51] :
                      ( r1(X50,X51)
                      & ~ p1(X51) ) )
              | ? [X52] :
                  ( r1(X3,X52)
                  & ~ p1(X52)
                  & ! [X53] :
                      ( ~ r1(X52,X53)
                      | ! [X54] :
                          ( ~ r1(X53,X54)
                          | p1(X54) )
                      | ~ p1(X53) ) ) ) ) )
      | ~ sP3(X2) ),
    introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).

fof(f15,plain,
    ? [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ~ p4(X1) )
      & ! [X2] :
          ( ~ r1(X0,X2)
          | ( sP3(X2)
            & ( p1(X2)
              | ! [X55] :
                  ( ~ r1(X2,X55)
                  | ? [X56] :
                      ( r1(X55,X56)
                      & ~ p1(X56) ) )
              | ? [X57] :
                  ( r1(X2,X57)
                  & ~ p1(X57)
                  & ! [X58] :
                      ( ~ r1(X57,X58)
                      | ! [X59] :
                          ( ~ r1(X58,X59)
                          | p1(X59) )
                      | ~ p1(X58) ) ) ) ) )
      & ( p1(X0)
        | ! [X60] :
            ( ~ r1(X0,X60)
            | ? [X61] :
                ( r1(X60,X61)
                & ~ p1(X61) ) )
        | ? [X62] :
            ( r1(X0,X62)
            & ~ p1(X62)
            & ! [X63] :
                ( ~ r1(X62,X63)
                | ! [X64] :
                    ( ~ r1(X63,X64)
                    | p1(X64) )
                | ~ p1(X63) ) ) )
      & ? [X65] :
          ( r1(X0,X65)
          & ? [X66] :
              ( r1(X65,X66)
              & ! [X67] :
                  ( ~ r1(X66,X67)
                  | p1(X67) ) )
          & ? [X68] :
              ( r1(X65,X68)
              & ~ p1(X68) ) )
      & ? [X69] :
          ( r1(X0,X69)
          & ? [X70] :
              ( r1(X69,X70)
              & ? [X71] :
                  ( r1(X70,X71)
                  & ! [X72] :
                      ( ~ r1(X71,X72)
                      | p1(X72) ) )
              & ? [X73] :
                  ( r1(X70,X73)
                  & ~ p1(X73) ) )
          & ? [X74] :
              ( r1(X69,X74)
              & ? [X75] :
                  ( r1(X74,X75)
                  & ? [X76] :
                      ( r1(X75,X76)
                      & ! [X77] :
                          ( ~ r1(X76,X77)
                          | p1(X77) ) )
                  & ? [X78] :
                      ( r1(X75,X78)
                      & ~ p1(X78) ) )
              & ? [X79] :
                  ( r1(X74,X79)
                  & ? [X80] :
                      ( r1(X79,X80)
                      & ? [X81] :
                          ( r1(X80,X81)
                          & ! [X82] :
                              ( ~ r1(X81,X82)
                              | p1(X82) ) )
                      & ? [X83] :
                          ( r1(X80,X83)
                          & ~ p1(X83) ) )
                  & ? [X84] :
                      ( r1(X79,X84)
                      & ? [X85] :
                          ( r1(X84,X85)
                          & ? [X86] :
                              ( r1(X85,X86)
                              & ! [X87] :
                                  ( ~ r1(X86,X87)
                                  | p1(X87) ) )
                          & ? [X88] :
                              ( r1(X85,X88)
                              & ~ p1(X88) ) )
                      & ? [X89] :
                          ( r1(X84,X89)
                          & ! [X90] :
                              ( ~ r1(X89,X90)
                              | ? [X91] :
                                  ( r1(X90,X91)
                                  & ~ p2(X91) ) ) )
                      & ! [X92] :
                          ( ~ r1(X84,X92)
                          | ! [X93] :
                              ( ~ r1(X92,X93)
                              | ! [X94] :
                                  ( ~ r1(X93,X94)
                                  | ~ p1(X94) ) )
                          | ? [X95] :
                              ( r1(X92,X95)
                              & p1(X95) ) ) )
                  & ! [X96] :
                      ( ~ r1(X79,X96)
                      | ! [X97] :
                          ( ~ r1(X96,X97)
                          | ! [X98] :
                              ( ~ r1(X97,X98)
                              | ~ p1(X98) ) )
                      | ? [X99] :
                          ( r1(X96,X99)
                          & p1(X99) ) ) )
              & ! [X100] :
                  ( ~ r1(X74,X100)
                  | ! [X101] :
                      ( ~ r1(X100,X101)
                      | ! [X102] :
                          ( ~ r1(X101,X102)
                          | ~ p1(X102) ) )
                  | ? [X103] :
                      ( r1(X100,X103)
                      & p1(X103) ) ) )
          & ! [X104] :
              ( ~ r1(X69,X104)
              | ! [X105] :
                  ( ~ r1(X104,X105)
                  | ! [X106] :
                      ( ~ r1(X105,X106)
                      | ~ p1(X106) ) )
              | ? [X107] :
                  ( r1(X104,X107)
                  & p1(X107) ) ) )
      & ! [X108] :
          ( ~ r1(X0,X108)
          | ! [X109] :
              ( ~ r1(X108,X109)
              | ! [X110] :
                  ( ~ r1(X109,X110)
                  | ~ p1(X110) ) )
          | ? [X111] :
              ( r1(X108,X111)
              & p1(X111) ) ) ),
    inference(definition_folding,[],[f10,f14,f13,f12,f11]) ).

fof(f16,plain,
    ! [X2] :
      ( ! [X3] :
          ( ~ r1(X2,X3)
          | ( ! [X4] :
                ( ~ r1(X3,X4)
                | ( sP2(X4)
                  & ( p1(X4)
                    | ! [X45] :
                        ( ~ r1(X4,X45)
                        | ? [X46] :
                            ( r1(X45,X46)
                            & ~ p1(X46) ) )
                    | ? [X47] :
                        ( r1(X4,X47)
                        & ~ p1(X47)
                        & ! [X48] :
                            ( ~ r1(X47,X48)
                            | ! [X49] :
                                ( ~ r1(X48,X49)
                                | p1(X49) )
                            | ~ p1(X48) ) ) ) ) )
            & ( p1(X3)
              | ! [X50] :
                  ( ~ r1(X3,X50)
                  | ? [X51] :
                      ( r1(X50,X51)
                      & ~ p1(X51) ) )
              | ? [X52] :
                  ( r1(X3,X52)
                  & ~ p1(X52)
                  & ! [X53] :
                      ( ~ r1(X52,X53)
                      | ! [X54] :
                          ( ~ r1(X53,X54)
                          | p1(X54) )
                      | ~ p1(X53) ) ) ) ) )
      | ~ sP3(X2) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f17,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ( ! [X2] :
                ( ~ r1(X1,X2)
                | ( sP2(X2)
                  & ( p1(X2)
                    | ! [X3] :
                        ( ~ r1(X2,X3)
                        | ? [X4] :
                            ( r1(X3,X4)
                            & ~ p1(X4) ) )
                    | ? [X5] :
                        ( r1(X2,X5)
                        & ~ p1(X5)
                        & ! [X6] :
                            ( ~ r1(X5,X6)
                            | ! [X7] :
                                ( ~ r1(X6,X7)
                                | p1(X7) )
                            | ~ p1(X6) ) ) ) ) )
            & ( p1(X1)
              | ! [X8] :
                  ( ~ r1(X1,X8)
                  | ? [X9] :
                      ( r1(X8,X9)
                      & ~ p1(X9) ) )
              | ? [X10] :
                  ( r1(X1,X10)
                  & ~ p1(X10)
                  & ! [X11] :
                      ( ~ r1(X10,X11)
                      | ! [X12] :
                          ( ~ r1(X11,X12)
                          | p1(X12) )
                      | ~ p1(X11) ) ) ) ) )
      | ~ sP3(X0) ),
    inference(rectify,[],[f16]) ).

fof(f18,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ( ! [X2] :
                ( ~ r1(X1,X2)
                | ( sP2(X2)
                  & ( p1(X2)
                    | ! [X3] :
                        ( ~ r1(X2,X3)
                        | ( r1(X3,sK4(X3))
                          & ~ p1(sK4(X3)) ) )
                    | ( r1(X2,sK5(X2))
                      & ~ p1(sK5(X2))
                      & ! [X6] :
                          ( ~ r1(sK5(X2),X6)
                          | ! [X7] :
                              ( ~ r1(X6,X7)
                              | p1(X7) )
                          | ~ p1(X6) ) ) ) ) )
            & ( p1(X1)
              | ! [X8] :
                  ( ~ r1(X1,X8)
                  | ( r1(X8,sK6(X8))
                    & ~ p1(sK6(X8)) ) )
              | ( r1(X1,sK7(X1))
                & ~ p1(sK7(X1))
                & ! [X11] :
                    ( ~ r1(sK7(X1),X11)
                    | ! [X12] :
                        ( ~ r1(X11,X12)
                        | p1(X12) )
                    | ~ p1(X11) ) ) ) ) )
      | ~ sP3(X0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X4,sK4(X3)),skolemize(X5,sK5(X2)),skolemize(X9,sK6(X8)),skolemize(X10,sK7(X1))],[f17]) ).

fof(f19,plain,
    ! [X4] :
      ( ! [X5] :
          ( ~ r1(X4,X5)
          | ( ! [X6] :
                ( ~ r1(X5,X6)
                | ( sP1(X6)
                  & ( p1(X6)
                    | ! [X35] :
                        ( ~ r1(X6,X35)
                        | ? [X36] :
                            ( r1(X35,X36)
                            & ~ p1(X36) ) )
                    | ? [X37] :
                        ( r1(X6,X37)
                        & ~ p1(X37)
                        & ! [X38] :
                            ( ~ r1(X37,X38)
                            | ! [X39] :
                                ( ~ r1(X38,X39)
                                | p1(X39) )
                            | ~ p1(X38) ) ) ) ) )
            & ( p1(X5)
              | ! [X40] :
                  ( ~ r1(X5,X40)
                  | ? [X41] :
                      ( r1(X40,X41)
                      & ~ p1(X41) ) )
              | ? [X42] :
                  ( r1(X5,X42)
                  & ~ p1(X42)
                  & ! [X43] :
                      ( ~ r1(X42,X43)
                      | ! [X44] :
                          ( ~ r1(X43,X44)
                          | p1(X44) )
                      | ~ p1(X43) ) ) ) ) )
      | ~ sP2(X4) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f20,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ( ! [X2] :
                ( ~ r1(X1,X2)
                | ( sP1(X2)
                  & ( p1(X2)
                    | ! [X3] :
                        ( ~ r1(X2,X3)
                        | ? [X4] :
                            ( r1(X3,X4)
                            & ~ p1(X4) ) )
                    | ? [X5] :
                        ( r1(X2,X5)
                        & ~ p1(X5)
                        & ! [X6] :
                            ( ~ r1(X5,X6)
                            | ! [X7] :
                                ( ~ r1(X6,X7)
                                | p1(X7) )
                            | ~ p1(X6) ) ) ) ) )
            & ( p1(X1)
              | ! [X8] :
                  ( ~ r1(X1,X8)
                  | ? [X9] :
                      ( r1(X8,X9)
                      & ~ p1(X9) ) )
              | ? [X10] :
                  ( r1(X1,X10)
                  & ~ p1(X10)
                  & ! [X11] :
                      ( ~ r1(X10,X11)
                      | ! [X12] :
                          ( ~ r1(X11,X12)
                          | p1(X12) )
                      | ~ p1(X11) ) ) ) ) )
      | ~ sP2(X0) ),
    inference(rectify,[],[f19]) ).

fof(f21,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ( ! [X2] :
                ( ~ r1(X1,X2)
                | ( sP1(X2)
                  & ( p1(X2)
                    | ! [X3] :
                        ( ~ r1(X2,X3)
                        | ( r1(X3,sK8(X3))
                          & ~ p1(sK8(X3)) ) )
                    | ( r1(X2,sK9(X2))
                      & ~ p1(sK9(X2))
                      & ! [X6] :
                          ( ~ r1(sK9(X2),X6)
                          | ! [X7] :
                              ( ~ r1(X6,X7)
                              | p1(X7) )
                          | ~ p1(X6) ) ) ) ) )
            & ( p1(X1)
              | ! [X8] :
                  ( ~ r1(X1,X8)
                  | ( r1(X8,sK10(X8))
                    & ~ p1(sK10(X8)) ) )
              | ( r1(X1,sK11(X1))
                & ~ p1(sK11(X1))
                & ! [X11] :
                    ( ~ r1(sK11(X1),X11)
                    | ! [X12] :
                        ( ~ r1(X11,X12)
                        | p1(X12) )
                    | ~ p1(X11) ) ) ) ) )
      | ~ sP2(X0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X4,sK8(X3)),skolemize(X5,sK9(X2)),skolemize(X9,sK10(X8)),skolemize(X10,sK11(X1))],[f20]) ).

fof(f22,plain,
    ! [X6] :
      ( ! [X7] :
          ( ~ r1(X6,X7)
          | ( ! [X8] :
                ( ~ r1(X7,X8)
                | ( sP0(X8)
                  & ( p1(X8)
                    | ! [X25] :
                        ( ~ r1(X8,X25)
                        | ? [X26] :
                            ( r1(X25,X26)
                            & ~ p1(X26) ) )
                    | ? [X27] :
                        ( r1(X8,X27)
                        & ~ p1(X27)
                        & ! [X28] :
                            ( ~ r1(X27,X28)
                            | ! [X29] :
                                ( ~ r1(X28,X29)
                                | p1(X29) )
                            | ~ p1(X28) ) ) ) ) )
            & ( p1(X7)
              | ! [X30] :
                  ( ~ r1(X7,X30)
                  | ? [X31] :
                      ( r1(X30,X31)
                      & ~ p1(X31) ) )
              | ? [X32] :
                  ( r1(X7,X32)
                  & ~ p1(X32)
                  & ! [X33] :
                      ( ~ r1(X32,X33)
                      | ! [X34] :
                          ( ~ r1(X33,X34)
                          | p1(X34) )
                      | ~ p1(X33) ) ) ) ) )
      | ~ sP1(X6) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f23,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ( ! [X2] :
                ( ~ r1(X1,X2)
                | ( sP0(X2)
                  & ( p1(X2)
                    | ! [X3] :
                        ( ~ r1(X2,X3)
                        | ? [X4] :
                            ( r1(X3,X4)
                            & ~ p1(X4) ) )
                    | ? [X5] :
                        ( r1(X2,X5)
                        & ~ p1(X5)
                        & ! [X6] :
                            ( ~ r1(X5,X6)
                            | ! [X7] :
                                ( ~ r1(X6,X7)
                                | p1(X7) )
                            | ~ p1(X6) ) ) ) ) )
            & ( p1(X1)
              | ! [X8] :
                  ( ~ r1(X1,X8)
                  | ? [X9] :
                      ( r1(X8,X9)
                      & ~ p1(X9) ) )
              | ? [X10] :
                  ( r1(X1,X10)
                  & ~ p1(X10)
                  & ! [X11] :
                      ( ~ r1(X10,X11)
                      | ! [X12] :
                          ( ~ r1(X11,X12)
                          | p1(X12) )
                      | ~ p1(X11) ) ) ) ) )
      | ~ sP1(X0) ),
    inference(rectify,[],[f22]) ).

fof(f24,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ( ! [X2] :
                ( ~ r1(X1,X2)
                | ( sP0(X2)
                  & ( p1(X2)
                    | ! [X3] :
                        ( ~ r1(X2,X3)
                        | ( r1(X3,sK12(X3))
                          & ~ p1(sK12(X3)) ) )
                    | ( r1(X2,sK13(X2))
                      & ~ p1(sK13(X2))
                      & ! [X6] :
                          ( ~ r1(sK13(X2),X6)
                          | ! [X7] :
                              ( ~ r1(X6,X7)
                              | p1(X7) )
                          | ~ p1(X6) ) ) ) ) )
            & ( p1(X1)
              | ! [X8] :
                  ( ~ r1(X1,X8)
                  | ( r1(X8,sK14(X8))
                    & ~ p1(sK14(X8)) ) )
              | ( r1(X1,sK15(X1))
                & ~ p1(sK15(X1))
                & ! [X11] :
                    ( ~ r1(sK15(X1),X11)
                    | ! [X12] :
                        ( ~ r1(X11,X12)
                        | p1(X12) )
                    | ~ p1(X11) ) ) ) ) )
      | ~ sP1(X0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X4,sK12(X3)),skolemize(X5,sK13(X2)),skolemize(X9,sK14(X8)),skolemize(X10,sK15(X1))],[f23]) ).

fof(f25,plain,
    ! [X8] :
      ( ! [X9] :
          ( ~ r1(X8,X9)
          | ( ! [X10] :
                ( ~ r1(X9,X10)
                | ( ! [X11] :
                      ( ~ r1(X10,X11)
                      | ? [X12] :
                          ( r1(X11,X12)
                          & ? [X13] :
                              ( r1(X12,X13)
                              & ~ p3(X13) )
                          & p2(X12) ) )
                  & ! [X14] :
                      ( ~ r1(X10,X14)
                      | ! [X15] :
                          ( ~ r1(X14,X15)
                          | ( ? [X16] :
                                ( r1(X15,X16)
                                & ~ p3(X16) )
                            & p2(X15) ) )
                      | ~ p2(X14)
                      | ! [X17] :
                          ( ~ r1(X14,X17)
                          | ? [X18] :
                              ( r1(X17,X18)
                              & ! [X19] :
                                  ( ~ r1(X18,X19)
                                  | ~ p2(X19) ) ) ) ) ) )
            & ( p1(X9)
              | ! [X20] :
                  ( ~ r1(X9,X20)
                  | ? [X21] :
                      ( r1(X20,X21)
                      & ~ p1(X21) ) )
              | ? [X22] :
                  ( r1(X9,X22)
                  & ~ p1(X22)
                  & ! [X23] :
                      ( ~ r1(X22,X23)
                      | ! [X24] :
                          ( ~ r1(X23,X24)
                          | p1(X24) )
                      | ~ p1(X23) ) ) ) ) )
      | ~ sP0(X8) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f26,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ( ! [X2] :
                ( ~ r1(X1,X2)
                | ( ! [X3] :
                      ( ~ r1(X2,X3)
                      | ? [X4] :
                          ( r1(X3,X4)
                          & ? [X5] :
                              ( r1(X4,X5)
                              & ~ p3(X5) )
                          & p2(X4) ) )
                  & ! [X6] :
                      ( ~ r1(X2,X6)
                      | ! [X7] :
                          ( ~ r1(X6,X7)
                          | ( ? [X8] :
                                ( r1(X7,X8)
                                & ~ p3(X8) )
                            & p2(X7) ) )
                      | ~ p2(X6)
                      | ! [X9] :
                          ( ~ r1(X6,X9)
                          | ? [X10] :
                              ( r1(X9,X10)
                              & ! [X11] :
                                  ( ~ r1(X10,X11)
                                  | ~ p2(X11) ) ) ) ) ) )
            & ( p1(X1)
              | ! [X12] :
                  ( ~ r1(X1,X12)
                  | ? [X13] :
                      ( r1(X12,X13)
                      & ~ p1(X13) ) )
              | ? [X14] :
                  ( r1(X1,X14)
                  & ~ p1(X14)
                  & ! [X15] :
                      ( ~ r1(X14,X15)
                      | ! [X16] :
                          ( ~ r1(X15,X16)
                          | p1(X16) )
                      | ~ p1(X15) ) ) ) ) )
      | ~ sP0(X0) ),
    inference(rectify,[],[f25]) ).

fof(f27,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ( ! [X2] :
                ( ~ r1(X1,X2)
                | ( ! [X3] :
                      ( ~ r1(X2,X3)
                      | ( r1(X3,sK16(X3))
                        & r1(sK16(X3),sK17(X3))
                        & ~ p3(sK17(X3))
                        & p2(sK16(X3)) ) )
                  & ! [X6] :
                      ( ~ r1(X2,X6)
                      | ! [X7] :
                          ( ~ r1(X6,X7)
                          | ( r1(X7,sK18(X7))
                            & ~ p3(sK18(X7))
                            & p2(X7) ) )
                      | ~ p2(X6)
                      | ! [X9] :
                          ( ~ r1(X6,X9)
                          | ( r1(X9,sK19(X9))
                            & ! [X11] :
                                ( ~ r1(sK19(X9),X11)
                                | ~ p2(X11) ) ) ) ) ) )
            & ( p1(X1)
              | ! [X12] :
                  ( ~ r1(X1,X12)
                  | ( r1(X12,sK20(X12))
                    & ~ p1(sK20(X12)) ) )
              | ( r1(X1,sK21(X1))
                & ~ p1(sK21(X1))
                & ! [X15] :
                    ( ~ r1(sK21(X1),X15)
                    | ! [X16] :
                        ( ~ r1(X15,X16)
                        | p1(X16) )
                    | ~ p1(X15) ) ) ) ) )
      | ~ sP0(X0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19,sK20,sK21]),skolemize(X4,sK16(X3)),skolemize(X5,sK17(X3)),skolemize(X8,sK18(X7)),skolemize(X10,sK19(X9)),skolemize(X13,sK20(X12)),skolemize(X14,sK21(X1))],[f26]) ).

fof(f28,plain,
    ? [X0] :
      ( ! [X1] :
          ( ~ r1(X0,X1)
          | ~ p4(X1) )
      & ! [X2] :
          ( ~ r1(X0,X2)
          | ( sP3(X2)
            & ( p1(X2)
              | ! [X3] :
                  ( ~ r1(X2,X3)
                  | ? [X4] :
                      ( r1(X3,X4)
                      & ~ p1(X4) ) )
              | ? [X5] :
                  ( r1(X2,X5)
                  & ~ p1(X5)
                  & ! [X6] :
                      ( ~ r1(X5,X6)
                      | ! [X7] :
                          ( ~ r1(X6,X7)
                          | p1(X7) )
                      | ~ p1(X6) ) ) ) ) )
      & ( p1(X0)
        | ! [X8] :
            ( ~ r1(X0,X8)
            | ? [X9] :
                ( r1(X8,X9)
                & ~ p1(X9) ) )
        | ? [X10] :
            ( r1(X0,X10)
            & ~ p1(X10)
            & ! [X11] :
                ( ~ r1(X10,X11)
                | ! [X12] :
                    ( ~ r1(X11,X12)
                    | p1(X12) )
                | ~ p1(X11) ) ) )
      & ? [X13] :
          ( r1(X0,X13)
          & ? [X14] :
              ( r1(X13,X14)
              & ! [X15] :
                  ( ~ r1(X14,X15)
                  | p1(X15) ) )
          & ? [X16] :
              ( r1(X13,X16)
              & ~ p1(X16) ) )
      & ? [X17] :
          ( r1(X0,X17)
          & ? [X18] :
              ( r1(X17,X18)
              & ? [X19] :
                  ( r1(X18,X19)
                  & ! [X20] :
                      ( ~ r1(X19,X20)
                      | p1(X20) ) )
              & ? [X21] :
                  ( r1(X18,X21)
                  & ~ p1(X21) ) )
          & ? [X22] :
              ( r1(X17,X22)
              & ? [X23] :
                  ( r1(X22,X23)
                  & ? [X24] :
                      ( r1(X23,X24)
                      & ! [X25] :
                          ( ~ r1(X24,X25)
                          | p1(X25) ) )
                  & ? [X26] :
                      ( r1(X23,X26)
                      & ~ p1(X26) ) )
              & ? [X27] :
                  ( r1(X22,X27)
                  & ? [X28] :
                      ( r1(X27,X28)
                      & ? [X29] :
                          ( r1(X28,X29)
                          & ! [X30] :
                              ( ~ r1(X29,X30)
                              | p1(X30) ) )
                      & ? [X31] :
                          ( r1(X28,X31)
                          & ~ p1(X31) ) )
                  & ? [X32] :
                      ( r1(X27,X32)
                      & ? [X33] :
                          ( r1(X32,X33)
                          & ? [X34] :
                              ( r1(X33,X34)
                              & ! [X35] :
                                  ( ~ r1(X34,X35)
                                  | p1(X35) ) )
                          & ? [X36] :
                              ( r1(X33,X36)
                              & ~ p1(X36) ) )
                      & ? [X37] :
                          ( r1(X32,X37)
                          & ! [X38] :
                              ( ~ r1(X37,X38)
                              | ? [X39] :
                                  ( r1(X38,X39)
                                  & ~ p2(X39) ) ) )
                      & ! [X40] :
                          ( ~ r1(X32,X40)
                          | ! [X41] :
                              ( ~ r1(X40,X41)
                              | ! [X42] :
                                  ( ~ r1(X41,X42)
                                  | ~ p1(X42) ) )
                          | ? [X43] :
                              ( r1(X40,X43)
                              & p1(X43) ) ) )
                  & ! [X44] :
                      ( ~ r1(X27,X44)
                      | ! [X45] :
                          ( ~ r1(X44,X45)
                          | ! [X46] :
                              ( ~ r1(X45,X46)
                              | ~ p1(X46) ) )
                      | ? [X47] :
                          ( r1(X44,X47)
                          & p1(X47) ) ) )
              & ! [X48] :
                  ( ~ r1(X22,X48)
                  | ! [X49] :
                      ( ~ r1(X48,X49)
                      | ! [X50] :
                          ( ~ r1(X49,X50)
                          | ~ p1(X50) ) )
                  | ? [X51] :
                      ( r1(X48,X51)
                      & p1(X51) ) ) )
          & ! [X52] :
              ( ~ r1(X17,X52)
              | ! [X53] :
                  ( ~ r1(X52,X53)
                  | ! [X54] :
                      ( ~ r1(X53,X54)
                      | ~ p1(X54) ) )
              | ? [X55] :
                  ( r1(X52,X55)
                  & p1(X55) ) ) )
      & ! [X56] :
          ( ~ r1(X0,X56)
          | ! [X57] :
              ( ~ r1(X56,X57)
              | ! [X58] :
                  ( ~ r1(X57,X58)
                  | ~ p1(X58) ) )
          | ? [X59] :
              ( r1(X56,X59)
              & p1(X59) ) ) ),
    inference(rectify,[],[f15]) ).

fof(f29,plain,
    ( ! [X1] :
        ( ~ r1(sK22,X1)
        | ~ p4(X1) )
    & ! [X2] :
        ( ~ r1(sK22,X2)
        | ( sP3(X2)
          & ( p1(X2)
            | ! [X3] :
                ( ~ r1(X2,X3)
                | ( r1(X3,sK23(X3))
                  & ~ p1(sK23(X3)) ) )
            | ( r1(X2,sK24(X2))
              & ~ p1(sK24(X2))
              & ! [X6] :
                  ( ~ r1(sK24(X2),X6)
                  | ! [X7] :
                      ( ~ r1(X6,X7)
                      | p1(X7) )
                  | ~ p1(X6) ) ) ) ) )
    & ( p1(sK22)
      | ! [X8] :
          ( ~ r1(sK22,X8)
          | ( r1(X8,sK25(X8))
            & ~ p1(sK25(X8)) ) )
      | ( r1(sK22,sK26)
        & ~ p1(sK26)
        & ! [X11] :
            ( ~ r1(sK26,X11)
            | ! [X12] :
                ( ~ r1(X11,X12)
                | p1(X12) )
            | ~ p1(X11) ) ) )
    & r1(sK22,sK27)
    & r1(sK27,sK28)
    & ! [X15] :
        ( ~ r1(sK28,X15)
        | p1(X15) )
    & r1(sK27,sK29)
    & ~ p1(sK29)
    & r1(sK22,sK30)
    & r1(sK30,sK31)
    & r1(sK31,sK32)
    & ! [X20] :
        ( ~ r1(sK32,X20)
        | p1(X20) )
    & r1(sK31,sK33)
    & ~ p1(sK33)
    & r1(sK30,sK34)
    & r1(sK34,sK35)
    & r1(sK35,sK36)
    & ! [X25] :
        ( ~ r1(sK36,X25)
        | p1(X25) )
    & r1(sK35,sK37)
    & ~ p1(sK37)
    & r1(sK34,sK38)
    & r1(sK38,sK39)
    & r1(sK39,sK40)
    & ! [X30] :
        ( ~ r1(sK40,X30)
        | p1(X30) )
    & r1(sK39,sK41)
    & ~ p1(sK41)
    & r1(sK38,sK42)
    & r1(sK42,sK43)
    & r1(sK43,sK44)
    & ! [X35] :
        ( ~ r1(sK44,X35)
        | p1(X35) )
    & r1(sK43,sK45)
    & ~ p1(sK45)
    & r1(sK42,sK46)
    & ! [X38] :
        ( ~ r1(sK46,X38)
        | ( r1(X38,sK47(X38))
          & ~ p2(sK47(X38)) ) )
    & ! [X40] :
        ( ~ r1(sK42,X40)
        | ! [X41] :
            ( ~ r1(X40,X41)
            | ! [X42] :
                ( ~ r1(X41,X42)
                | ~ p1(X42) ) )
        | ( r1(X40,sK48(X40))
          & p1(sK48(X40)) ) )
    & ! [X44] :
        ( ~ r1(sK38,X44)
        | ! [X45] :
            ( ~ r1(X44,X45)
            | ! [X46] :
                ( ~ r1(X45,X46)
                | ~ p1(X46) ) )
        | ( r1(X44,sK49(X44))
          & p1(sK49(X44)) ) )
    & ! [X48] :
        ( ~ r1(sK34,X48)
        | ! [X49] :
            ( ~ r1(X48,X49)
            | ! [X50] :
                ( ~ r1(X49,X50)
                | ~ p1(X50) ) )
        | ( r1(X48,sK50(X48))
          & p1(sK50(X48)) ) )
    & ! [X52] :
        ( ~ r1(sK30,X52)
        | ! [X53] :
            ( ~ r1(X52,X53)
            | ! [X54] :
                ( ~ r1(X53,X54)
                | ~ p1(X54) ) )
        | ( r1(X52,sK51(X52))
          & p1(sK51(X52)) ) )
    & ! [X56] :
        ( ~ r1(sK22,X56)
        | ! [X57] :
            ( ~ r1(X56,X57)
            | ! [X58] :
                ( ~ r1(X57,X58)
                | ~ p1(X58) ) )
        | ( r1(X56,sK52(X56))
          & p1(sK52(X56)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30,sK31,sK32,sK33,sK34,sK35,sK36,sK37,sK38,sK39,sK40,sK41,sK42,sK43,sK44,sK45,sK46,sK47,sK48,sK49,sK50,sK51,sK52]),skolemize(X0,sK22),skolemize(X4,sK23(X3)),skolemize(X5,sK24(X2)),skolemize(X9,sK25(X8)),skolemize(X10,sK26),skolemize(X13,sK27),skolemize(X14,sK28),skolemize(X16,sK29),skolemize(X17,sK30),skolemize(X18,sK31),skolemize(X19,sK32),skolemize(X21,sK33),skolemize(X22,sK34),skolemize(X23,sK35),skolemize(X24,sK36),skolemize(X26,sK37),skolemize(X27,sK38),skolemize(X28,sK39),skolemize(X29,sK40),skolemize(X31,sK41),skolemize(X32,sK42),skolemize(X33,sK43),skolemize(X34,sK44),skolemize(X36,sK45),skolemize(X37,sK46),skolemize(X39,sK47(X38)),skolemize(X43,sK48(X40)),skolemize(X47,sK49(X44)),skolemize(X51,sK50(X48)),skolemize(X55,sK51(X52)),skolemize(X59,sK52(X56))],[f28]) ).

fof(f30,plain,
    ! [X0] : r1(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f31,plain,
    ! [X2,X0,X1] :
      ( ~ r1(X1,X2)
      | ~ r1(X0,X1)
      | r1(X0,X2) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( ~ sP3(X0)
      | ~ r1(X1,X2)
      | sP2(X2)
      | ~ r1(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f57,plain,
    ! [X2,X0,X1] :
      ( ~ sP2(X0)
      | ~ r1(X1,X2)
      | sP1(X2)
      | ~ r1(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f70,plain,
    ! [X2,X0,X1] :
      ( ~ sP1(X0)
      | ~ r1(X1,X2)
      | sP0(X2)
      | ~ r1(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f77,plain,
    ! [X2,X0,X11,X1,X6,X9,X7] :
      ( ~ sP0(X0)
      | ~ r1(X1,X2)
      | ~ r1(X2,X6)
      | ~ r1(X6,X7)
      | p2(X7)
      | ~ p2(X6)
      | ~ r1(X6,X9)
      | ~ r1(sK19(X9),X11)
      | ~ p2(X11)
      | ~ r1(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f78,plain,
    ! [X2,X0,X1,X6,X9,X7] :
      ( ~ sP0(X0)
      | ~ r1(X1,X2)
      | ~ r1(X2,X6)
      | ~ r1(X6,X7)
      | p2(X7)
      | ~ p2(X6)
      | ~ r1(X6,X9)
      | r1(X9,sK19(X9))
      | ~ r1(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f83,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0)
      | ~ r1(X1,X2)
      | ~ r1(X2,X3)
      | p2(sK16(X3))
      | ~ r1(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f86,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0)
      | ~ r1(X1,X2)
      | ~ r1(X2,X3)
      | r1(X3,sK16(X3))
      | ~ r1(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f97,plain,
    ! [X38] :
      ( ~ p2(sK47(X38))
      | ~ r1(sK46,X38) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f98,plain,
    ! [X38] :
      ( ~ r1(sK46,X38)
      | r1(X38,sK47(X38)) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f99,plain,
    r1(sK42,sK46),
    inference(cnf_transformation,[],[f29]) ).

fof(f105,plain,
    r1(sK38,sK42),
    inference(cnf_transformation,[],[f29]) ).

fof(f111,plain,
    r1(sK34,sK38),
    inference(cnf_transformation,[],[f29]) ).

fof(f117,plain,
    r1(sK30,sK34),
    inference(cnf_transformation,[],[f29]) ).

fof(f123,plain,
    r1(sK22,sK30),
    inference(cnf_transformation,[],[f29]) ).

fof(f141,plain,
    ! [X2] :
      ( ~ r1(sK22,X2)
      | sP3(X2) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f167,plain,
    sP3(sK30),
    inference(resolution,[],[f123,f141]) ).

fof(f169,plain,
    ! [X0,X1] :
      ( ~ r1(sK30,X0)
      | sP2(X1)
      | ~ r1(X0,X1) ),
    inference(resolution,[],[f167,f44]) ).

fof(f236,plain,
    ! [X0] :
      ( ~ r1(sK34,X0)
      | sP2(X0) ),
    inference(resolution,[],[f169,f117]) ).

fof(f239,plain,
    sP2(sK38),
    inference(resolution,[],[f236,f111]) ).

fof(f242,plain,
    ! [X0,X1] :
      ( ~ r1(sK38,X0)
      | sP1(X1)
      | ~ r1(X0,X1) ),
    inference(resolution,[],[f239,f57]) ).

fof(f251,plain,
    ! [X0] :
      ( ~ r1(sK42,X0)
      | sP1(X0) ),
    inference(resolution,[],[f242,f105]) ).

fof(f253,plain,
    ! [X0] :
      ( ~ r1(sK38,X0)
      | sP1(X0) ),
    inference(resolution,[],[f242,f30]) ).

fof(f254,plain,
    sP1(sK46),
    inference(resolution,[],[f251,f99]) ).

fof(f257,plain,
    ! [X0,X1] :
      ( ~ r1(sK46,X0)
      | sP0(X1)
      | ~ r1(X0,X1) ),
    inference(resolution,[],[f254,f70]) ).

fof(f259,plain,
    ! [X0] :
      ( ~ r1(sK46,X0)
      | sP0(X0) ),
    inference(resolution,[],[f257,f30]) ).

fof(f288,plain,
    sP0(sK46),
    inference(resolution,[],[f259,f30]) ).

fof(f291,plain,
    ! [X2,X0,X1] :
      ( ~ r1(sK46,X0)
      | ~ r1(X1,X2)
      | r1(X2,sK16(X2))
      | ~ r1(X0,X1) ),
    inference(resolution,[],[f288,f86]) ).

fof(f293,plain,
    ! [X2,X0,X1] :
      ( ~ r1(sK46,X0)
      | ~ r1(X1,X2)
      | p2(sK16(X2))
      | ~ r1(X0,X1) ),
    inference(resolution,[],[f288,f83]) ).

fof(f563,plain,
    sP1(sK38),
    inference(resolution,[],[f253,f30]) ).

fof(f564,plain,
    ! [X0,X1] :
      ( ~ r1(sK38,X0)
      | sP0(X1)
      | ~ r1(X0,X1) ),
    inference(resolution,[],[f563,f70]) ).

fof(f573,plain,
    ! [X0] :
      ( ~ r1(sK38,X0)
      | sP0(X0) ),
    inference(resolution,[],[f564,f30]) ).

fof(f641,plain,
    ! [X0,X1] :
      ( ~ r1(sK46,X0)
      | p2(sK16(X1))
      | ~ r1(X0,X1) ),
    inference(resolution,[],[f293,f30]) ).

fof(f654,plain,
    ! [X0,X1] :
      ( ~ r1(sK46,X0)
      | r1(X1,sK16(X1))
      | ~ r1(X0,X1) ),
    inference(resolution,[],[f291,f30]) ).

fof(f2434,plain,
    sP0(sK42),
    inference(resolution,[],[f573,f105]) ).

fof(f2442,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ r1(sK42,X0)
      | ~ r1(X1,X2)
      | ~ r1(X2,X3)
      | p2(X3)
      | ~ p2(X2)
      | ~ r1(X2,X4)
      | r1(X4,sK19(X4))
      | ~ r1(X0,X1) ),
    inference(resolution,[],[f2434,f78]) ).

fof(f2444,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ r1(sK19(X4),X5)
      | ~ r1(X1,X2)
      | ~ r1(X2,X3)
      | p2(X3)
      | ~ p2(X2)
      | ~ r1(X2,X4)
      | ~ r1(X0,X1)
      | ~ p2(X5)
      | ~ r1(sK42,X0) ),
    inference(resolution,[],[f2434,f77]) ).

fof(f2601,plain,
    ! [X2,X3,X0,X1] :
      ( ~ r1(sK42,X0)
      | ~ r1(X1,X2)
      | p2(X2)
      | ~ p2(X1)
      | ~ r1(X1,X3)
      | r1(X3,sK19(X3))
      | ~ r1(X0,X1) ),
    inference(resolution,[],[f2442,f30]) ).

fof(f2751,plain,
    ! [X2,X0,X1] :
      ( ~ r1(sK42,X0)
      | p2(X1)
      | ~ p2(X0)
      | ~ r1(X0,X2)
      | r1(X2,sK19(X2))
      | ~ r1(X0,X1) ),
    inference(resolution,[],[f2601,f30]) ).

fof(f2808,plain,
    ! [X0] :
      ( ~ r1(sK46,X0)
      | p2(sK16(X0)) ),
    inference(resolution,[],[f641,f30]) ).

fof(f2810,plain,
    p2(sK16(sK46)),
    inference(resolution,[],[f2808,f30]) ).

fof(f2828,definition,
    ( spl53_222
  <=> ! [X3] :
        ( ~ r1(sK16(sK46),X3)
        | r1(X3,sK19(X3)) ) ),
    introduced(definition,[new_symbols(definition,[spl53_222])],[avatar_definition]) ).

fof(f2829,plain,
    ( ! [X3] :
        ( ~ r1(sK16(sK46),X3)
        | r1(X3,sK19(X3)) )
    | ~ spl53_222 ),
    inference(avatar_component_clause,[],[f2828]) ).

fof(f2831,definition,
    ( spl53_223
  <=> ! [X1] :
        ( ~ r1(sK16(sK46),X1)
        | p2(X1) ) ),
    introduced(definition,[new_symbols(definition,[spl53_223])],[avatar_definition]) ).

fof(f2832,plain,
    ( ! [X1] :
        ( ~ r1(sK16(sK46),X1)
        | p2(X1) )
    | ~ spl53_223 ),
    inference(avatar_component_clause,[],[f2831]) ).

fof(f2864,plain,
    ( r1(sK16(sK46),sK19(sK16(sK46)))
    | ~ spl53_222 ),
    inference(resolution,[],[f2829,f30]) ).

fof(f2866,plain,
    ( ! [X0] :
        ( ~ r1(X0,sK16(sK46))
        | r1(X0,sK19(sK16(sK46))) )
    | ~ spl53_222 ),
    inference(resolution,[],[f2864,f31]) ).

fof(f2875,definition,
    ( spl53_233
  <=> ! [X0,X3,X2,X1] :
        ( ~ r1(X0,X1)
        | ~ r1(sK42,X3)
        | ~ r1(X3,X0)
        | ~ r1(X1,sK16(sK46))
        | ~ p2(X1)
        | p2(X2)
        | ~ r1(X1,X2) ) ),
    introduced(definition,[new_symbols(definition,[spl53_233])],[avatar_definition]) ).

fof(f2876,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ r1(X1,sK16(sK46))
        | ~ r1(sK42,X3)
        | ~ r1(X3,X0)
        | ~ r1(X0,X1)
        | ~ p2(X1)
        | p2(X2)
        | ~ r1(X1,X2) )
    | ~ spl53_233 ),
    inference(avatar_component_clause,[],[f2875]) ).

fof(f3243,plain,
    ! [X0] :
      ( ~ r1(sK46,X0)
      | r1(X0,sK16(X0)) ),
    inference(resolution,[],[f654,f30]) ).

fof(f3246,plain,
    r1(sK46,sK16(sK46)),
    inference(resolution,[],[f3243,f30]) ).

fof(f3247,plain,
    ( r1(sK46,sK19(sK16(sK46)))
    | ~ spl53_222 ),
    inference(resolution,[],[f3246,f2866]) ).

fof(f3248,plain,
    r1(sK16(sK46),sK47(sK16(sK46))),
    inference(resolution,[],[f3246,f98]) ).

fof(f3264,plain,
    ! [X0] :
      ( ~ r1(X0,sK46)
      | r1(X0,sK16(sK46)) ),
    inference(resolution,[],[f3246,f31]) ).

fof(f3270,plain,
    r1(sK42,sK16(sK46)),
    inference(resolution,[],[f3264,f99]) ).

fof(f3346,plain,
    ! [X0,X1] :
      ( p2(X0)
      | ~ p2(sK16(sK46))
      | ~ r1(sK16(sK46),X1)
      | r1(X1,sK19(X1))
      | ~ r1(sK16(sK46),X0) ),
    inference(resolution,[],[f3270,f2751]) ).

fof(f3379,plain,
    ( p2(sK16(sK19(sK16(sK46))))
    | ~ spl53_222 ),
    inference(resolution,[],[f3247,f2808]) ).

fof(f3380,plain,
    ( r1(sK19(sK16(sK46)),sK16(sK19(sK16(sK46))))
    | ~ spl53_222 ),
    inference(resolution,[],[f3247,f3243]) ).

fof(f3454,plain,
    ( p2(sK47(sK16(sK46)))
    | ~ spl53_223 ),
    inference(resolution,[],[f2832,f3248]) ).

fof(f3459,plain,
    ( ~ r1(sK46,sK16(sK46))
    | ~ spl53_223 ),
    inference(resolution,[],[f3454,f97]) ).

fof(f3519,plain,
    ( $false
    | ~ spl53_223 ),
    inference(forward_subsumption_resolution,[],[f3459,f3246]) ).

fof(f3520,plain,
    ~ spl53_223,
    inference(avatar_contradiction_clause,[],[f3519]) ).

fof(f3525,plain,
    ! [X0,X1] :
      ( p2(X0)
      | ~ r1(sK16(sK46),X1)
      | r1(X1,sK19(X1))
      | ~ r1(sK16(sK46),X0) ),
    inference(forward_subsumption_resolution,[],[f3346,f2810]) ).

fof(f3526,plain,
    ( spl53_222
    | spl53_223 ),
    inference(avatar_split_clause,[],[f3525,f2831,f2828]) ).

fof(f3669,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ r1(X0,X1)
        | ~ r1(X1,X2)
        | p2(X2)
        | ~ p2(X1)
        | ~ r1(X1,sK16(sK46))
        | ~ r1(X3,X0)
        | ~ p2(sK16(sK19(sK16(sK46))))
        | ~ r1(sK42,X3) )
    | ~ spl53_222 ),
    inference(resolution,[],[f3380,f2444]) ).

fof(f3703,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ r1(X0,X1)
        | ~ r1(X1,X2)
        | p2(X2)
        | ~ p2(X1)
        | ~ r1(X1,sK16(sK46))
        | ~ r1(X3,X0)
        | ~ r1(sK42,X3) )
    | ~ spl53_222 ),
    inference(forward_subsumption_resolution,[],[f3669,f3379]) ).

fof(f3705,plain,
    ( spl53_233
    | ~ spl53_222 ),
    inference(avatar_split_clause,[],[f3703,f2828,f2875]) ).

fof(f3842,plain,
    ( ! [X2,X0,X1] :
        ( ~ r1(sK42,X0)
        | ~ r1(X0,X1)
        | ~ r1(X1,sK16(sK46))
        | ~ p2(sK16(sK46))
        | p2(X2)
        | ~ r1(sK16(sK46),X2) )
    | ~ spl53_233 ),
    inference(resolution,[],[f2876,f30]) ).

fof(f3845,plain,
    ( ! [X2,X0,X1] :
        ( ~ r1(sK42,X0)
        | ~ r1(X0,X1)
        | ~ r1(X1,sK16(sK46))
        | p2(X2)
        | ~ r1(sK16(sK46),X2) )
    | ~ spl53_233 ),
    inference(forward_subsumption_resolution,[],[f3842,f2810]) ).

fof(f3847,definition,
    ( spl53_325
  <=> ! [X0,X1] :
        ( ~ r1(sK42,X0)
        | ~ r1(X1,sK16(sK46))
        | ~ r1(X0,X1) ) ),
    introduced(definition,[new_symbols(definition,[spl53_325])],[avatar_definition]) ).

fof(f3848,plain,
    ( ! [X0,X1] :
        ( ~ r1(X1,sK16(sK46))
        | ~ r1(sK42,X0)
        | ~ r1(X0,X1) )
    | ~ spl53_325 ),
    inference(avatar_component_clause,[],[f3847]) ).

fof(f3849,plain,
    ( spl53_223
    | spl53_325
    | ~ spl53_233 ),
    inference(avatar_split_clause,[],[f3845,f2875,f3847,f2831]) ).

fof(f4046,plain,
    ( $false
    | ~ spl53_325 ),
    inference(unit_resulting_resolution,[],[f3848,f99,f30,f3246]) ).

fof(f4056,plain,
    ~ spl53_325,
    inference(avatar_contradiction_clause,[],[f4046]) ).

cnf(s223,plain,
    ~ spl53_223,
    inference(sat_conversion,[],[f3520]) ).

cnf(s225,plain,
    ( spl53_222
    | spl53_223 ),
    inference(sat_conversion,[],[f3526]) ).

cnf(s261,plain,
    ( ~ spl53_222
    | spl53_233 ),
    inference(sat_conversion,[],[f3705]) ).

cnf(s298,plain,
    ( spl53_223
    | ~ spl53_233
    | spl53_325 ),
    inference(sat_conversion,[],[f3849]) ).

cnf(s319,plain,
    ~ spl53_325,
    inference(sat_conversion,[],[f4056]) ).

cnf(s320,plain,
    ( spl53_223
    | ~ spl53_233 ),
    inference(rat,[],[s298,s319]) ).

cnf(s321,plain,
    ~ spl53_233,
    inference(rat,[],[s320,s223]) ).

cnf(s322,plain,
    spl53_222,
    inference(rat,[],[s225,s223]) ).

cnf(s323,plain,
    $false,
    inference(rat,[],[s261,s321,s322]) ).

fof(f4057,plain,
    $false,
    inference(avatar_sat_refutation,[],[s323]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL688+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.39  % Computer : n010.cluster.edu
% 0.12/5.39  % Model    : x86_64 x86_64
% 0.12/5.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39  % Memory   : 8046.5625MB
% 0.12/5.39  % OS       : Linux 6.8.0-71-generic
% 0.12/5.39  % CPULimit : 300
% 0.12/5.39  % WCLimit  : 300
% 0.12/5.39  % DateTime : Sun Sep 27 16:39:31 UTC 2026
% 0.12/5.39  % CPUTime  : 
% 0.12/5.39  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.43  Running first-order theorem proving
% 0.15/5.43  Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.68/7.00  % (1154684)Detected formulas, will run a generic FOF schedule.
% 6.68/7.00  % (1154690)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3233003483:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.68/7.00  % (1154694)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3182495373:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.68/7.00  % (1154693)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1599396184:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.68/7.00  % (1154691)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3749652437:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.68/7.00  % (1154689)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1309293900:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.68/7.00  % (1154692)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1396594170:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.68/7.00  % (1154695)dis-21_1_sil=8000:lcm=predicate:random_seed=3692339163:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 6.68/7.00  % (1154692)Instruction limit reached! 
% 6.68/7.00  % (1154692)------------------------------
% 6.68/7.00  % (1154692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154692)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154692)Termination reason: Instruction limit
% 6.68/7.00  % (1154692)Termination phase: Saturation
% 6.68/7.00  % (1154692)Time elapsed: 0.059 s
% 6.68/7.00  % (1154692)Peak memory usage: 92 MB
% 6.68/7.00  % (1154692)Instructions burned: 110 (million)
% 6.68/7.00  % (1154693)Instruction limit reached! 
% 6.68/7.00  % (1154693)------------------------------
% 6.68/7.00  % (1154693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154693)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154693)Termination reason: Instruction limit
% 6.68/7.00  % (1154693)Termination phase: Saturation
% 6.68/7.00  % (1154693)Time elapsed: 0.063 s
% 6.68/7.00  % (1154693)Peak memory usage: 88 MB
% 6.68/7.00  % (1154693)Instructions burned: 119 (million)
% 6.68/7.00  % (1154695)Instruction limit reached! 
% 6.68/7.00  % (1154695)------------------------------
% 6.68/7.00  % (1154695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154695)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154695)Termination reason: Instruction limit
% 6.68/7.00  % (1154695)Termination phase: Saturation
% 6.68/7.00  % (1154695)Time elapsed: 0.068 s
% 6.68/7.00  % (1154695)Peak memory usage: 89 MB
% 6.68/7.00  % (1154695)Instructions burned: 129 (million)
% 6.68/7.00  % (1154694)Instruction limit reached! 
% 6.68/7.00  % (1154694)------------------------------
% 6.68/7.00  % (1154694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154694)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154694)Termination reason: Instruction limit
% 6.68/7.00  % (1154694)Termination phase: Saturation
% 6.68/7.00  % (1154694)Time elapsed: 0.092 s
% 6.68/7.00  % (1154694)Peak memory usage: 89 MB
% 6.68/7.00  % (1154694)Instructions burned: 140 (million)
% 6.68/7.00  % (1154705)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1146751571:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.68/7.00  % (1154703)lrs+10_1_sil=8000:sp=occurrence:random_seed=3131994764:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.68/7.00  % (1154704)lrs+10_1_sil=32000:urr=on:br=off:random_seed=546222235:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.68/7.00  % (1154706)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1537172881:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.68/7.00  % (1154704)Instruction limit reached! 
% 6.68/7.00  % (1154704)------------------------------
% 6.68/7.00  % (1154704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154704)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154704)Termination reason: Instruction limit
% 6.68/7.00  % (1154704)Termination phase: Saturation
% 6.68/7.00  % (1154704)Time elapsed: 0.075 s
% 6.68/7.00  % (1154704)Peak memory usage: 88 MB
% 6.68/7.00  % (1154704)Instructions burned: 158 (million)
% 6.68/7.00  % (1154706)Instruction limit reached! 
% 6.68/7.00  % (1154706)------------------------------
% 6.68/7.00  % (1154706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154706)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154706)Termination reason: Instruction limit
% 6.68/7.00  % (1154706)Termination phase: Saturation
% 6.68/7.00  % (1154706)Time elapsed: 0.114 s
% 6.68/7.00  % (1154706)Peak memory usage: 89 MB
% 6.68/7.00  % (1154706)Instructions burned: 249 (million)
% 6.68/7.00  % (1154703)Instruction limit reached! 
% 6.68/7.00  % (1154703)------------------------------
% 6.68/7.00  % (1154703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154703)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154703)Termination reason: Instruction limit
% 6.68/7.00  % (1154703)Termination phase: Saturation
% 6.68/7.00  % (1154703)Time elapsed: 0.158 s
% 6.68/7.00  % (1154703)Peak memory usage: 93 MB
% 6.68/7.00  % (1154703)Instructions burned: 287 (million)
% 6.68/7.00  % (1154705)Instruction limit reached! 
% 6.68/7.00  % (1154705)------------------------------
% 6.68/7.00  % (1154705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154705)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154705)Termination reason: Instruction limit
% 6.68/7.00  % (1154705)Termination phase: Saturation
% 6.68/7.00  % (1154705)Time elapsed: 0.199 s
% 6.68/7.00  % (1154705)Peak memory usage: 92 MB
% 6.68/7.00  % (1154705)Instructions burned: 325 (million)
% 6.68/7.00  % (1154711)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3336142453:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.68/7.00  % (1154712)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3123811246:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.68/7.00  % (1154713)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3948407992:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.68/7.00  % (1154714)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4164027603:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.68/7.00  % (1154713)Instruction limit reached! 
% 6.68/7.00  % (1154713)------------------------------
% 6.68/7.00  % (1154713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154713)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154713)Termination reason: Instruction limit
% 6.68/7.00  % (1154713)Termination phase: Saturation
% 6.68/7.00  % (1154713)Time elapsed: 0.064 s
% 6.68/7.00  % (1154713)Peak memory usage: 91 MB
% 6.68/7.00  % (1154713)Instructions burned: 114 (million)
% 6.68/7.00  % (1154711)Instruction limit reached! 
% 6.68/7.00  % (1154711)------------------------------
% 6.68/7.00  % (1154711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154711)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154711)Termination reason: Instruction limit
% 6.68/7.00  % (1154711)Termination phase: Saturation
% 6.68/7.00  % (1154711)Time elapsed: 0.152 s
% 6.68/7.00  % (1154711)Peak memory usage: 90 MB
% 6.68/7.00  % (1154711)Instructions burned: 294 (million)
% 6.68/7.00  % (1154714)Instruction limit reached! 
% 6.68/7.00  % (1154714)------------------------------
% 6.68/7.00  % (1154714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154714)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154714)Termination reason: Instruction limit
% 6.68/7.00  % (1154714)Termination phase: Saturation
% 6.68/7.00  % (1154714)Time elapsed: 0.066 s
% 6.68/7.00  % (1154714)Peak memory usage: 89 MB
% 6.68/7.00  % (1154714)Instructions burned: 127 (million)
% 6.68/7.00  % (1154719)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1038450063:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.68/7.00  % (1154720)lrs+10_1_sil=8000:sp=occurrence:random_seed=2791944282:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.68/7.00  % (1154690)First to succeed.
% 6.68/7.00  % (1154690)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1154684"
% 6.68/7.00  % (1154721)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3697999542:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.68/7.00  % (1154719)Instruction limit reached! 
% 6.68/7.00  % (1154719)------------------------------
% 6.68/7.00  % (1154719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.68/7.00  % (1154719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/7.00  % (1154719)CaDiCaL version: 2.1.3
% 6.68/7.00  % (1154719)Termination reason: Instruction limit
% 6.68/7.00  % (1154719)Termination phase: Saturation
% 6.68/7.00  % (1154719)Time elapsed: 0.056 s
% 6.68/7.00  % (1154719)Peak memory usage: 89 MB
% 6.68/7.00  % (1154719)Instructions burned: 114 (million)
% 6.68/7.00  % (1154690)Refutation found. Thanks to Tanya!
% 6.68/7.00  % SZS status Theorem for theBenchmark
% 6.68/7.00  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/7.20  % (1154690)------------------------------
% 0.17/7.20  % (1154690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/7.20  % (1154690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/7.20  % (1154690)CaDiCaL version: 2.1.3
% 0.17/7.20  % (1154690)Termination reason: Refutation
% 0.17/7.20  % (1154690)Time elapsed: 0.826 s
% 0.17/7.20  % (1154690)Peak memory usage: 135 MB
% 0.17/7.20  % (1154690)Instructions burned: 2455 (million)
% 0.17/7.20  % (1154690)------------------------------
% 0.17/7.20  % (1154690)------------------------------
% 0.17/7.20  % (1154684)Success in time 1.13 s
% 0.17/7.20  % Vampire exiting
%------------------------------------------------------------------------------