TSTP Solution File: LCL688+1.001 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : LCL688+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 08:30:02 EDT 2023

% Result   : Theorem 2.23s 0.77s
% Output   : Refutation 2.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   80 (  10 unt;   0 def)
%            Number of atoms       :  691 (   0 equ)
%            Maximal formula atoms :   80 (   8 avg)
%            Number of connectives : 1189 ( 578   ~; 433   |; 158   &)
%                                         (   6 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   7 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-1 aty)
%            Number of variables   :  386 (; 309   !;  77   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f15306,plain,
    $false,
    inference(avatar_sat_refutation,[],[f551,f925,f2151,f8815,f9137,f15165,f15305]) ).

fof(f15305,plain,
    spl13_1336,
    inference(avatar_contradiction_clause,[],[f15304]) ).

fof(f15304,plain,
    ( $false
    | spl13_1336 ),
    inference(resolution,[],[f15188,f45]) ).

fof(f45,plain,
    r1(sK0,sK2),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ( ! [X1] :
        ( ( p1(sK1(X1))
          & r1(X1,sK1(X1)) )
        | ! [X3] :
            ( ! [X4] :
                ( ~ p1(X4)
                | ~ r1(X3,X4) )
            | ~ r1(X1,X3) )
        | ~ r1(sK0,X1) )
    & ! [X6] :
        ( ( ~ p2(sK3(X6))
          & r1(X6,sK3(X6)) )
        | ~ r1(sK2,X6) )
    & r1(sK0,sK2)
    & ~ p1(sK5)
    & r1(sK4,sK5)
    & ! [X11] :
        ( p1(X11)
        | ~ r1(sK6,X11) )
    & r1(sK4,sK6)
    & r1(sK0,sK4)
    & ( ( ! [X13] :
            ( ~ p1(X13)
            | ! [X14] :
                ( p1(X14)
                | ~ r1(X13,X14) )
            | ~ r1(sK7,X13) )
        & ~ p1(sK7)
        & r1(sK0,sK7) )
      | ! [X15] :
          ( ( ~ p1(sK8(X15))
            & r1(X15,sK8(X15)) )
          | ~ r1(sK0,X15) )
      | p1(sK0) )
    & ! [X17] :
        ( ( ! [X18] :
              ( ! [X19] :
                  ( ( ! [X21] :
                        ( ~ p2(X21)
                        | ~ r1(sK9(X19),X21) )
                    & r1(X19,sK9(X19)) )
                  | ~ r1(X18,X19) )
              | ~ p2(X18)
              | ! [X22] :
                  ( ( p2(X22)
                    & r1(X22,sK10(X22)) )
                  | ~ r1(X18,X22) )
              | ~ r1(X17,X18) )
          & ! [X24] :
              ( ( p2(sK11(X24))
                & r1(sK11(X24),sK12(X24))
                & r1(X24,sK11(X24)) )
              | ~ r1(X17,X24) ) )
        | ~ r1(sK0,X17) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12])],[f10,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13]) ).

fof(f13,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( ? [X2] :
                ( p1(X2)
                & r1(X1,X2) )
            | ! [X3] :
                ( ! [X4] :
                    ( ~ p1(X4)
                    | ~ r1(X3,X4) )
                | ~ r1(X1,X3) )
            | ~ r1(X0,X1) )
        & ? [X5] :
            ( ! [X6] :
                ( ? [X7] :
                    ( ~ p2(X7)
                    & r1(X6,X7) )
                | ~ r1(X5,X6) )
            & r1(X0,X5) )
        & ? [X8] :
            ( ? [X9] :
                ( ~ p1(X9)
                & r1(X8,X9) )
            & ? [X10] :
                ( ! [X11] :
                    ( p1(X11)
                    | ~ r1(X10,X11) )
                & r1(X8,X10) )
            & r1(X0,X8) )
        & ( ? [X12] :
              ( ! [X13] :
                  ( ~ p1(X13)
                  | ! [X14] :
                      ( p1(X14)
                      | ~ r1(X13,X14) )
                  | ~ r1(X12,X13) )
              & ~ p1(X12)
              & r1(X0,X12) )
          | ! [X15] :
              ( ? [X16] :
                  ( ~ p1(X16)
                  & r1(X15,X16) )
              | ~ r1(X0,X15) )
          | p1(X0) )
        & ! [X17] :
            ( ( ! [X18] :
                  ( ! [X19] :
                      ( ? [X20] :
                          ( ! [X21] :
                              ( ~ p2(X21)
                              | ~ r1(X20,X21) )
                          & r1(X19,X20) )
                      | ~ r1(X18,X19) )
                  | ~ p2(X18)
                  | ! [X22] :
                      ( ( p2(X22)
                        & ? [X23] : r1(X22,X23) )
                      | ~ r1(X18,X22) )
                  | ~ r1(X17,X18) )
              & ! [X24] :
                  ( ? [X25] :
                      ( p2(X25)
                      & ? [X26] : r1(X25,X26)
                      & r1(X24,X25) )
                  | ~ r1(X17,X24) ) )
            | ~ r1(X0,X17) ) )
   => ( ! [X1] :
          ( ? [X2] :
              ( p1(X2)
              & r1(X1,X2) )
          | ! [X3] :
              ( ! [X4] :
                  ( ~ p1(X4)
                  | ~ r1(X3,X4) )
              | ~ r1(X1,X3) )
          | ~ r1(sK0,X1) )
      & ? [X5] :
          ( ! [X6] :
              ( ? [X7] :
                  ( ~ p2(X7)
                  & r1(X6,X7) )
              | ~ r1(X5,X6) )
          & r1(sK0,X5) )
      & ? [X8] :
          ( ? [X9] :
              ( ~ p1(X9)
              & r1(X8,X9) )
          & ? [X10] :
              ( ! [X11] :
                  ( p1(X11)
                  | ~ r1(X10,X11) )
              & r1(X8,X10) )
          & r1(sK0,X8) )
      & ( ? [X12] :
            ( ! [X13] :
                ( ~ p1(X13)
                | ! [X14] :
                    ( p1(X14)
                    | ~ r1(X13,X14) )
                | ~ r1(X12,X13) )
            & ~ p1(X12)
            & r1(sK0,X12) )
        | ! [X15] :
            ( ? [X16] :
                ( ~ p1(X16)
                & r1(X15,X16) )
            | ~ r1(sK0,X15) )
        | p1(sK0) )
      & ! [X17] :
          ( ( ! [X18] :
                ( ! [X19] :
                    ( ? [X20] :
                        ( ! [X21] :
                            ( ~ p2(X21)
                            | ~ r1(X20,X21) )
                        & r1(X19,X20) )
                    | ~ r1(X18,X19) )
                | ~ p2(X18)
                | ! [X22] :
                    ( ( p2(X22)
                      & ? [X23] : r1(X22,X23) )
                    | ~ r1(X18,X22) )
                | ~ r1(X17,X18) )
            & ! [X24] :
                ( ? [X25] :
                    ( p2(X25)
                    & ? [X26] : r1(X25,X26)
                    & r1(X24,X25) )
                | ~ r1(X17,X24) ) )
          | ~ r1(sK0,X17) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ! [X1] :
      ( ? [X2] :
          ( p1(X2)
          & r1(X1,X2) )
     => ( p1(sK1(X1))
        & r1(X1,sK1(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ( ? [X5] :
        ( ! [X6] :
            ( ? [X7] :
                ( ~ p2(X7)
                & r1(X6,X7) )
            | ~ r1(X5,X6) )
        & r1(sK0,X5) )
   => ( ! [X6] :
          ( ? [X7] :
              ( ~ p2(X7)
              & r1(X6,X7) )
          | ~ r1(sK2,X6) )
      & r1(sK0,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ! [X6] :
      ( ? [X7] :
          ( ~ p2(X7)
          & r1(X6,X7) )
     => ( ~ p2(sK3(X6))
        & r1(X6,sK3(X6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ( ? [X8] :
        ( ? [X9] :
            ( ~ p1(X9)
            & r1(X8,X9) )
        & ? [X10] :
            ( ! [X11] :
                ( p1(X11)
                | ~ r1(X10,X11) )
            & r1(X8,X10) )
        & r1(sK0,X8) )
   => ( ? [X9] :
          ( ~ p1(X9)
          & r1(sK4,X9) )
      & ? [X10] :
          ( ! [X11] :
              ( p1(X11)
              | ~ r1(X10,X11) )
          & r1(sK4,X10) )
      & r1(sK0,sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ( ? [X9] :
        ( ~ p1(X9)
        & r1(sK4,X9) )
   => ( ~ p1(sK5)
      & r1(sK4,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ( ? [X10] :
        ( ! [X11] :
            ( p1(X11)
            | ~ r1(X10,X11) )
        & r1(sK4,X10) )
   => ( ! [X11] :
          ( p1(X11)
          | ~ r1(sK6,X11) )
      & r1(sK4,sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ( ? [X12] :
        ( ! [X13] :
            ( ~ p1(X13)
            | ! [X14] :
                ( p1(X14)
                | ~ r1(X13,X14) )
            | ~ r1(X12,X13) )
        & ~ p1(X12)
        & r1(sK0,X12) )
   => ( ! [X13] :
          ( ~ p1(X13)
          | ! [X14] :
              ( p1(X14)
              | ~ r1(X13,X14) )
          | ~ r1(sK7,X13) )
      & ~ p1(sK7)
      & r1(sK0,sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X15] :
      ( ? [X16] :
          ( ~ p1(X16)
          & r1(X15,X16) )
     => ( ~ p1(sK8(X15))
        & r1(X15,sK8(X15)) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X19] :
      ( ? [X20] :
          ( ! [X21] :
              ( ~ p2(X21)
              | ~ r1(X20,X21) )
          & r1(X19,X20) )
     => ( ! [X21] :
            ( ~ p2(X21)
            | ~ r1(sK9(X19),X21) )
        & r1(X19,sK9(X19)) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X22] :
      ( ? [X23] : r1(X22,X23)
     => r1(X22,sK10(X22)) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X24] :
      ( ? [X25] :
          ( p2(X25)
          & ? [X26] : r1(X25,X26)
          & r1(X24,X25) )
     => ( p2(sK11(X24))
        & ? [X26] : r1(sK11(X24),X26)
        & r1(X24,sK11(X24)) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X24] :
      ( ? [X26] : r1(sK11(X24),X26)
     => r1(sK11(X24),sK12(X24)) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ? [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( p1(X2)
              & r1(X1,X2) )
          | ! [X3] :
              ( ! [X4] :
                  ( ~ p1(X4)
                  | ~ r1(X3,X4) )
              | ~ r1(X1,X3) )
          | ~ r1(X0,X1) )
      & ? [X5] :
          ( ! [X6] :
              ( ? [X7] :
                  ( ~ p2(X7)
                  & r1(X6,X7) )
              | ~ r1(X5,X6) )
          & r1(X0,X5) )
      & ? [X8] :
          ( ? [X9] :
              ( ~ p1(X9)
              & r1(X8,X9) )
          & ? [X10] :
              ( ! [X11] :
                  ( p1(X11)
                  | ~ r1(X10,X11) )
              & r1(X8,X10) )
          & r1(X0,X8) )
      & ( ? [X12] :
            ( ! [X13] :
                ( ~ p1(X13)
                | ! [X14] :
                    ( p1(X14)
                    | ~ r1(X13,X14) )
                | ~ r1(X12,X13) )
            & ~ p1(X12)
            & r1(X0,X12) )
        | ! [X15] :
            ( ? [X16] :
                ( ~ p1(X16)
                & r1(X15,X16) )
            | ~ r1(X0,X15) )
        | p1(X0) )
      & ! [X17] :
          ( ( ! [X18] :
                ( ! [X19] :
                    ( ? [X20] :
                        ( ! [X21] :
                            ( ~ p2(X21)
                            | ~ r1(X20,X21) )
                        & r1(X19,X20) )
                    | ~ r1(X18,X19) )
                | ~ p2(X18)
                | ! [X22] :
                    ( ( p2(X22)
                      & ? [X23] : r1(X22,X23) )
                    | ~ r1(X18,X22) )
                | ~ r1(X17,X18) )
            & ! [X24] :
                ( ? [X25] :
                    ( p2(X25)
                    & ? [X26] : r1(X25,X26)
                    & r1(X24,X25) )
                | ~ r1(X17,X24) ) )
          | ~ r1(X0,X17) ) ),
    inference(flattening,[],[f9]) ).

fof(f9,plain,
    ? [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( p1(X2)
              & r1(X1,X2) )
          | ! [X3] :
              ( ! [X4] :
                  ( ~ p1(X4)
                  | ~ r1(X3,X4) )
              | ~ r1(X1,X3) )
          | ~ r1(X0,X1) )
      & ? [X5] :
          ( ! [X6] :
              ( ? [X7] :
                  ( ~ p2(X7)
                  & r1(X6,X7) )
              | ~ r1(X5,X6) )
          & r1(X0,X5) )
      & ? [X8] :
          ( ? [X9] :
              ( ~ p1(X9)
              & r1(X8,X9) )
          & ? [X10] :
              ( ! [X11] :
                  ( p1(X11)
                  | ~ r1(X10,X11) )
              & r1(X8,X10) )
          & r1(X0,X8) )
      & ( ? [X12] :
            ( ! [X13] :
                ( ~ p1(X13)
                | ! [X14] :
                    ( p1(X14)
                    | ~ r1(X13,X14) )
                | ~ r1(X12,X13) )
            & ~ p1(X12)
            & r1(X0,X12) )
        | ! [X15] :
            ( ? [X16] :
                ( ~ p1(X16)
                & r1(X15,X16) )
            | ~ r1(X0,X15) )
        | p1(X0) )
      & ! [X17] :
          ( ( ! [X18] :
                ( ! [X19] :
                    ( ? [X20] :
                        ( ! [X21] :
                            ( ~ p2(X21)
                            | ~ r1(X20,X21) )
                        & r1(X19,X20) )
                    | ~ r1(X18,X19) )
                | ~ p2(X18)
                | ! [X22] :
                    ( ( p2(X22)
                      & ? [X23] : r1(X22,X23) )
                    | ~ r1(X18,X22) )
                | ~ r1(X17,X18) )
            & ! [X24] :
                ( ? [X25] :
                    ( p2(X25)
                    & ? [X26] : r1(X25,X26)
                    & r1(X24,X25) )
                | ~ r1(X17,X24) ) )
          | ~ r1(X0,X17) ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,plain,
    ? [X0] :
      ~ ( ~ ! [X1] :
              ( ~ ! [X2] :
                    ( ~ p1(X2)
                    | ~ r1(X1,X2) )
              | ! [X3] :
                  ( ! [X4] :
                      ( ~ p1(X4)
                      | ~ r1(X3,X4) )
                  | ~ r1(X1,X3) )
              | ~ r1(X0,X1) )
        | ! [X5] :
            ( ~ ! [X6] :
                  ( ~ ! [X7] :
                        ( p2(X7)
                        | ~ r1(X6,X7) )
                  | ~ r1(X5,X6) )
            | ~ r1(X0,X5) )
        | ! [X8] :
            ( ! [X9] :
                ( p1(X9)
                | ~ r1(X8,X9) )
            | ! [X10] :
                ( ~ ! [X11] :
                      ( p1(X11)
                      | ~ r1(X10,X11) )
                | ~ r1(X8,X10) )
            | ~ r1(X0,X8) )
        | ( ! [X12] :
              ( ~ ! [X13] :
                    ( ~ ( p1(X13)
                        & ~ ! [X14] :
                              ( p1(X14)
                              | ~ r1(X13,X14) ) )
                    | ~ r1(X12,X13) )
              | p1(X12)
              | ~ r1(X0,X12) )
          & ~ ! [X15] :
                ( ~ ! [X16] :
                      ( p1(X16)
                      | ~ r1(X15,X16) )
                | ~ r1(X0,X15) )
          & ~ p1(X0) )
        | ~ ! [X17] :
              ( ~ ( ~ ! [X18] :
                        ( ~ ( ~ ! [X19] :
                                  ( ~ ! [X20] :
                                        ( ~ ! [X21] :
                                              ( ~ p2(X21)
                                              | ~ r1(X20,X21) )
                                        | ~ r1(X19,X20) )
                                  | ~ r1(X18,X19) )
                            & p2(X18)
                            & ~ ! [X22] :
                                  ( ~ ( ~ p2(X22)
                                      | ! [X23] : ~ r1(X22,X23) )
                                  | ~ r1(X18,X22) ) )
                        | ~ r1(X17,X18) )
                  | ~ ! [X24] :
                        ( ~ ! [X25] :
                              ( ~ p2(X25)
                              | ! [X26] : ~ r1(X25,X26)
                              | ~ r1(X24,X25) )
                        | ~ r1(X17,X24) ) )
              | ~ r1(X0,X17) ) ),
    inference(pure_predicate_removal,[],[f7]) ).

fof(f7,plain,
    ? [X0] :
      ~ ( ~ ! [X1] :
              ( ~ ! [X2] :
                    ( ~ p1(X2)
                    | ~ r1(X1,X2) )
              | ! [X3] :
                  ( ! [X4] :
                      ( ~ p1(X4)
                      | ~ r1(X3,X4) )
                  | ~ r1(X1,X3) )
              | ~ r1(X0,X1) )
        | ! [X5] :
            ( ~ ! [X6] :
                  ( ~ ! [X7] :
                        ( p2(X7)
                        | ~ r1(X6,X7) )
                  | ~ r1(X5,X6) )
            | ~ r1(X0,X5) )
        | ! [X8] :
            ( ! [X9] :
                ( p1(X9)
                | ~ r1(X8,X9) )
            | ! [X10] :
                ( ~ ! [X11] :
                      ( p1(X11)
                      | ~ r1(X10,X11) )
                | ~ r1(X8,X10) )
            | ~ r1(X0,X8) )
        | ( ! [X12] :
              ( ~ ! [X13] :
                    ( ~ ( p1(X13)
                        & ~ ! [X14] :
                              ( p1(X14)
                              | ~ r1(X13,X14) ) )
                    | ~ r1(X12,X13) )
              | p1(X12)
              | ~ r1(X0,X12) )
          & ~ ! [X15] :
                ( ~ ! [X16] :
                      ( p1(X16)
                      | ~ r1(X15,X16) )
                | ~ r1(X0,X15) )
          & ~ p1(X0) )
        | ~ ! [X17] :
              ( ~ ( ~ ! [X18] :
                        ( ~ ( ~ ! [X19] :
                                  ( ~ ! [X20] :
                                        ( ~ ! [X21] :
                                              ( ~ p2(X21)
                                              | ~ r1(X20,X21) )
                                        | ~ r1(X19,X20) )
                                  | ~ r1(X18,X19) )
                            & p2(X18)
                            & ~ ! [X22] :
                                  ( ~ ( ~ p2(X22)
                                      | ! [X23] : ~ r1(X22,X23) )
                                  | ~ r1(X18,X22) ) )
                        | ~ r1(X17,X18) )
                  | ~ ! [X24] :
                        ( ~ ! [X25] :
                              ( ~ p2(X25)
                              | ! [X26] : ~ r1(X25,X26)
                              | ~ r1(X24,X25) )
                        | ~ r1(X17,X24) ) )
              | ~ r1(X0,X17) )
        | ~ ! [X27] :
              ( ~ p4(X27)
              | ~ r1(X0,X27) ) ),
    inference(pure_predicate_removal,[],[f6]) ).

fof(f6,plain,
    ? [X0] :
      ~ ( ~ ! [X1] :
              ( ~ ! [X2] :
                    ( ~ p1(X2)
                    | ~ r1(X1,X2) )
              | ! [X3] :
                  ( ! [X4] :
                      ( ~ p1(X4)
                      | ~ r1(X3,X4) )
                  | ~ r1(X1,X3) )
              | ~ r1(X0,X1) )
        | ! [X5] :
            ( ~ ! [X6] :
                  ( ~ ! [X7] :
                        ( p2(X7)
                        | ~ r1(X6,X7) )
                  | ~ r1(X5,X6) )
            | ~ r1(X0,X5) )
        | ! [X8] :
            ( ! [X9] :
                ( p1(X9)
                | ~ r1(X8,X9) )
            | ! [X10] :
                ( ~ ! [X11] :
                      ( p1(X11)
                      | ~ r1(X10,X11) )
                | ~ r1(X8,X10) )
            | ~ r1(X0,X8) )
        | ( ! [X12] :
              ( ~ ! [X13] :
                    ( ~ ( p1(X13)
                        & ~ ! [X14] :
                              ( p1(X14)
                              | ~ r1(X13,X14) ) )
                    | ~ r1(X12,X13) )
              | p1(X12)
              | ~ r1(X0,X12) )
          & ~ ! [X15] :
                ( ~ ! [X16] :
                      ( p1(X16)
                      | ~ r1(X15,X16) )
                | ~ r1(X0,X15) )
          & ~ p1(X0) )
        | ~ ! [X17] :
              ( ~ ( ~ ! [X18] :
                        ( ~ ( ~ ! [X19] :
                                  ( ~ ! [X20] :
                                        ( ~ ! [X21] :
                                              ( ~ p2(X21)
                                              | ~ r1(X20,X21) )
                                        | ~ r1(X19,X20) )
                                  | ~ r1(X18,X19) )
                            & p2(X18)
                            & ~ ! [X22] :
                                  ( ~ ( ~ p2(X22)
                                      | ! [X23] :
                                          ( p3(X23)
                                          | ~ r1(X22,X23) ) )
                                  | ~ r1(X18,X22) ) )
                        | ~ r1(X17,X18) )
                  | ~ ! [X24] :
                        ( ~ ! [X25] :
                              ( ~ p2(X25)
                              | ! [X26] :
                                  ( p3(X26)
                                  | ~ r1(X25,X26) )
                              | ~ r1(X24,X25) )
                        | ~ r1(X17,X24) ) )
              | ~ r1(X0,X17) )
        | ~ ! [X27] :
              ( ~ p4(X27)
              | ~ r1(X0,X27) ) ),
    inference(flattening,[],[f5]) ).

fof(f5,plain,
    ~ ~ ? [X0] :
          ~ ( ~ ! [X1] :
                  ( ~ ! [X2] :
                        ( ~ p1(X2)
                        | ~ r1(X1,X2) )
                  | ! [X3] :
                      ( ! [X4] :
                          ( ~ p1(X4)
                          | ~ r1(X3,X4) )
                      | ~ r1(X1,X3) )
                  | ~ r1(X0,X1) )
            | ! [X5] :
                ( ~ ! [X6] :
                      ( ~ ! [X7] :
                            ( p2(X7)
                            | ~ r1(X6,X7) )
                      | ~ r1(X5,X6) )
                | ~ r1(X0,X5) )
            | ! [X8] :
                ( ! [X9] :
                    ( p1(X9)
                    | ~ r1(X8,X9) )
                | ! [X10] :
                    ( ~ ! [X11] :
                          ( p1(X11)
                          | ~ r1(X10,X11) )
                    | ~ r1(X8,X10) )
                | ~ r1(X0,X8) )
            | ( ! [X12] :
                  ( ~ ! [X13] :
                        ( ~ ( p1(X13)
                            & ~ ! [X14] :
                                  ( p1(X14)
                                  | ~ r1(X13,X14) ) )
                        | ~ r1(X12,X13) )
                  | p1(X12)
                  | ~ r1(X0,X12) )
              & ~ ! [X15] :
                    ( ~ ! [X16] :
                          ( p1(X16)
                          | ~ r1(X15,X16) )
                    | ~ r1(X0,X15) )
              & ~ p1(X0) )
            | ~ ! [X17] :
                  ( ~ ( ~ ! [X18] :
                            ( ~ ( ~ ! [X19] :
                                      ( ~ ! [X20] :
                                            ( ~ ! [X21] :
                                                  ( ~ p2(X21)
                                                  | ~ r1(X20,X21) )
                                            | ~ r1(X19,X20) )
                                      | ~ r1(X18,X19) )
                                & p2(X18)
                                & ~ ! [X22] :
                                      ( ~ ( ~ p2(X22)
                                          | ! [X23] :
                                              ( p3(X23)
                                              | ~ r1(X22,X23) ) )
                                      | ~ r1(X18,X22) ) )
                            | ~ r1(X17,X18) )
                      | ~ ! [X24] :
                            ( ~ ! [X25] :
                                  ( ~ p2(X25)
                                  | ! [X26] :
                                      ( p3(X26)
                                      | ~ r1(X25,X26) )
                                  | ~ r1(X24,X25) )
                            | ~ r1(X17,X24) ) )
                  | ~ r1(X0,X17) )
            | ~ ! [X27] :
                  ( ~ p4(X27)
                  | ~ r1(X0,X27) ) ),
    inference(rectify,[],[f4]) ).

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

fof(f3,conjecture,
    ~ ? [X0] :
        ~ ( ~ ! [X1] :
                ( ~ ! [X0] :
                      ( ~ p1(X0)
                      | ~ r1(X1,X0) )
                | ! [X0] :
                    ( ! [X1] :
                        ( ~ p1(X1)
                        | ~ r1(X0,X1) )
                    | ~ r1(X1,X0) )
                | ~ r1(X0,X1) )
          | ! [X1] :
              ( ~ ! [X0] :
                    ( ~ ! [X1] :
                          ( p2(X1)
                          | ~ r1(X0,X1) )
                    | ~ r1(X1,X0) )
              | ~ r1(X0,X1) )
          | ! [X1] :
              ( ! [X0] :
                  ( p1(X0)
                  | ~ r1(X1,X0) )
              | ! [X0] :
                  ( ~ ! [X1] :
                        ( p1(X1)
                        | ~ r1(X0,X1) )
                  | ~ r1(X1,X0) )
              | ~ r1(X0,X1) )
          | ( ! [X1] :
                ( ~ ! [X0] :
                      ( ~ ( p1(X0)
                          & ~ ! [X1] :
                                ( p1(X1)
                                | ~ r1(X0,X1) ) )
                      | ~ r1(X1,X0) )
                | p1(X1)
                | ~ r1(X0,X1) )
            & ~ ! [X1] :
                  ( ~ ! [X0] :
                        ( p1(X0)
                        | ~ r1(X1,X0) )
                  | ~ r1(X0,X1) )
            & ~ p1(X0) )
          | ~ ! [X1] :
                ( ~ ( ~ ! [X0] :
                          ( ~ ( ~ ! [X1] :
                                    ( ~ ! [X0] :
                                          ( ~ ! [X1] :
                                                ( ~ p2(X1)
                                                | ~ r1(X0,X1) )
                                          | ~ r1(X1,X0) )
                                    | ~ r1(X0,X1) )
                              & p2(X0)
                              & ~ ! [X1] :
                                    ( ~ ( ~ p2(X1)
                                        | ! [X0] :
                                            ( p3(X0)
                                            | ~ r1(X1,X0) ) )
                                    | ~ r1(X0,X1) ) )
                          | ~ r1(X1,X0) )
                    | ~ ! [X0] :
                          ( ~ ! [X1] :
                                ( ~ p2(X1)
                                | ! [X0] :
                                    ( p3(X0)
                                    | ~ r1(X1,X0) )
                                | ~ r1(X0,X1) )
                          | ~ r1(X1,X0) ) )
                | ~ r1(X0,X1) )
          | ~ ! [X1] :
                ( ~ p4(X1)
                | ~ r1(X0,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.PMrLrUiRRB/Vampire---4.8_3497',main) ).

fof(f15188,plain,
    ( ~ r1(sK0,sK2)
    | spl13_1336 ),
    inference(resolution,[],[f15164,f97]) ).

fof(f97,plain,
    ! [X3] :
      ( p2(sK11(X3))
      | ~ r1(sK0,X3) ),
    inference(resolution,[],[f29,f50]) ).

fof(f50,plain,
    ! [X0] : r1(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] : r1(X0,X0),
    file('/export/starexec/sandbox2/tmp/tmp.PMrLrUiRRB/Vampire---4.8_3497',reflexivity) ).

fof(f29,plain,
    ! [X17,X24] :
      ( ~ r1(sK0,X17)
      | ~ r1(X17,X24)
      | p2(sK11(X24)) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f15164,plain,
    ( ~ p2(sK11(sK2))
    | spl13_1336 ),
    inference(avatar_component_clause,[],[f15163]) ).

fof(f15163,plain,
    ( spl13_1336
  <=> p2(sK11(sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_1336])]) ).

fof(f15165,plain,
    ( ~ spl13_1336
    | spl13_72
    | spl13_71
    | ~ spl13_507 ),
    inference(avatar_split_clause,[],[f15159,f4855,f543,f546,f15163]) ).

fof(f546,plain,
    ( spl13_72
  <=> ! [X7] :
        ( p2(X7)
        | ~ r1(sK11(sK2),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_72])]) ).

fof(f543,plain,
    ( spl13_71
  <=> ! [X8] :
        ( ~ r1(X8,sK11(sK2))
        | ~ r1(sK0,X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_71])]) ).

fof(f4855,plain,
    ( spl13_507
  <=> ! [X4,X5,X3] :
        ( ~ r1(X3,sK11(sK2))
        | ~ r1(sK0,X5)
        | ~ r1(X5,X3)
        | ~ r1(X3,X4)
        | p2(X4)
        | ~ p2(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_507])]) ).

fof(f15159,plain,
    ( ! [X0,X1] :
        ( ~ r1(sK0,X0)
        | ~ r1(X0,sK11(sK2))
        | ~ r1(sK11(sK2),X1)
        | p2(X1)
        | ~ p2(sK11(sK2)) )
    | ~ spl13_507 ),
    inference(resolution,[],[f4856,f50]) ).

fof(f4856,plain,
    ( ! [X3,X4,X5] :
        ( ~ r1(X3,sK11(sK2))
        | ~ r1(sK0,X5)
        | ~ r1(X5,X3)
        | ~ r1(X3,X4)
        | p2(X4)
        | ~ p2(X3) )
    | ~ spl13_507 ),
    inference(avatar_component_clause,[],[f4855]) ).

fof(f9137,plain,
    ( ~ spl13_73
    | spl13_803 ),
    inference(avatar_contradiction_clause,[],[f9131]) ).

fof(f9131,plain,
    ( $false
    | ~ spl13_73
    | spl13_803 ),
    inference(resolution,[],[f8813,f2456]) ).

fof(f2456,plain,
    ( p2(sK11(sK9(sK11(sK2))))
    | ~ spl13_73 ),
    inference(resolution,[],[f280,f1137]) ).

fof(f1137,plain,
    ( r1(sK11(sK2),sK9(sK11(sK2)))
    | ~ spl13_73 ),
    inference(resolution,[],[f550,f50]) ).

fof(f550,plain,
    ( ! [X6] :
        ( ~ r1(sK11(sK2),X6)
        | r1(X6,sK9(X6)) )
    | ~ spl13_73 ),
    inference(avatar_component_clause,[],[f549]) ).

fof(f549,plain,
    ( spl13_73
  <=> ! [X6] :
        ( ~ r1(sK11(sK2),X6)
        | r1(X6,sK9(X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_73])]) ).

fof(f280,plain,
    ! [X2] :
      ( ~ r1(sK11(sK2),X2)
      | p2(sK11(X2)) ),
    inference(resolution,[],[f246,f29]) ).

fof(f246,plain,
    r1(sK0,sK11(sK2)),
    inference(resolution,[],[f215,f133]) ).

fof(f133,plain,
    ! [X3] :
      ( ~ r1(sK2,X3)
      | r1(sK0,X3) ),
    inference(resolution,[],[f51,f45]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( ~ r1(X0,X1)
      | ~ r1(X1,X2)
      | r1(X0,X2) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1,X2] :
      ( r1(X0,X2)
      | ~ r1(X1,X2)
      | ~ r1(X0,X1) ),
    inference(flattening,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( r1(X0,X2)
      | ~ r1(X1,X2)
      | ~ r1(X0,X1) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( ( r1(X1,X2)
        & r1(X0,X1) )
     => r1(X0,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.PMrLrUiRRB/Vampire---4.8_3497',transitivity) ).

fof(f215,plain,
    r1(sK2,sK11(sK2)),
    inference(resolution,[],[f106,f50]) ).

fof(f106,plain,
    ! [X1] :
      ( ~ r1(sK2,X1)
      | r1(X1,sK11(X1)) ),
    inference(resolution,[],[f27,f45]) ).

fof(f27,plain,
    ! [X17,X24] :
      ( ~ r1(sK0,X17)
      | ~ r1(X17,X24)
      | r1(X24,sK11(X24)) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f8813,plain,
    ( ~ p2(sK11(sK9(sK11(sK2))))
    | spl13_803 ),
    inference(avatar_component_clause,[],[f8812]) ).

fof(f8812,plain,
    ( spl13_803
  <=> p2(sK11(sK9(sK11(sK2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_803])]) ).

fof(f8815,plain,
    ( spl13_507
    | ~ spl13_803
    | ~ spl13_73 ),
    inference(avatar_split_clause,[],[f8809,f549,f8812,f4855]) ).

fof(f8809,plain,
    ( ! [X3,X4,X5] :
        ( ~ p2(sK11(sK9(sK11(sK2))))
        | ~ r1(X3,sK11(sK2))
        | ~ p2(X3)
        | p2(X4)
        | ~ r1(X3,X4)
        | ~ r1(X5,X3)
        | ~ r1(sK0,X5) )
    | ~ spl13_73 ),
    inference(resolution,[],[f2338,f33]) ).

fof(f33,plain,
    ! [X21,X18,X19,X17,X22] :
      ( ~ r1(sK9(X19),X21)
      | ~ p2(X21)
      | ~ r1(X18,X19)
      | ~ p2(X18)
      | p2(X22)
      | ~ r1(X18,X22)
      | ~ r1(X17,X18)
      | ~ r1(sK0,X17) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f2338,plain,
    ( r1(sK9(sK11(sK2)),sK11(sK9(sK11(sK2))))
    | ~ spl13_73 ),
    inference(resolution,[],[f2056,f106]) ).

fof(f2056,plain,
    ( r1(sK2,sK9(sK11(sK2)))
    | ~ spl13_73 ),
    inference(resolution,[],[f1137,f248]) ).

fof(f248,plain,
    ! [X0] :
      ( ~ r1(sK11(sK2),X0)
      | r1(sK2,X0) ),
    inference(resolution,[],[f215,f51]) ).

fof(f2151,plain,
    ~ spl13_72,
    inference(avatar_contradiction_clause,[],[f2150]) ).

fof(f2150,plain,
    ( $false
    | ~ spl13_72 ),
    inference(resolution,[],[f2140,f215]) ).

fof(f2140,plain,
    ( ~ r1(sK2,sK11(sK2))
    | ~ spl13_72 ),
    inference(resolution,[],[f2087,f47]) ).

fof(f47,plain,
    ! [X6] :
      ( ~ p2(sK3(X6))
      | ~ r1(sK2,X6) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f2087,plain,
    ( p2(sK3(sK11(sK2)))
    | ~ spl13_72 ),
    inference(resolution,[],[f547,f247]) ).

fof(f247,plain,
    r1(sK11(sK2),sK3(sK11(sK2))),
    inference(resolution,[],[f215,f46]) ).

fof(f46,plain,
    ! [X6] :
      ( ~ r1(sK2,X6)
      | r1(X6,sK3(X6)) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f547,plain,
    ( ! [X7] :
        ( ~ r1(sK11(sK2),X7)
        | p2(X7) )
    | ~ spl13_72 ),
    inference(avatar_component_clause,[],[f546]) ).

fof(f925,plain,
    ~ spl13_71,
    inference(avatar_contradiction_clause,[],[f924]) ).

fof(f924,plain,
    ( $false
    | ~ spl13_71 ),
    inference(resolution,[],[f850,f50]) ).

fof(f850,plain,
    ( ~ r1(sK0,sK0)
    | ~ spl13_71 ),
    inference(resolution,[],[f544,f246]) ).

fof(f544,plain,
    ( ! [X8] :
        ( ~ r1(X8,sK11(sK2))
        | ~ r1(sK0,X8) )
    | ~ spl13_71 ),
    inference(avatar_component_clause,[],[f543]) ).

fof(f551,plain,
    ( spl13_71
    | spl13_72
    | spl13_73 ),
    inference(avatar_split_clause,[],[f521,f549,f546,f543]) ).

fof(f521,plain,
    ! [X8,X6,X7] :
      ( ~ r1(sK11(sK2),X6)
      | r1(X6,sK9(X6))
      | p2(X7)
      | ~ r1(sK11(sK2),X7)
      | ~ r1(X8,sK11(sK2))
      | ~ r1(sK0,X8) ),
    inference(resolution,[],[f125,f50]) ).

fof(f125,plain,
    ! [X2,X3,X0,X1] :
      ( ~ r1(sK2,X0)
      | ~ r1(sK11(X0),X1)
      | r1(X1,sK9(X1))
      | p2(X2)
      | ~ r1(sK11(X0),X2)
      | ~ r1(X3,sK11(X0))
      | ~ r1(sK0,X3) ),
    inference(resolution,[],[f95,f31]) ).

fof(f31,plain,
    ! [X18,X19,X17,X22] :
      ( ~ p2(X18)
      | ~ r1(X18,X19)
      | r1(X19,sK9(X19))
      | p2(X22)
      | ~ r1(X18,X22)
      | ~ r1(X17,X18)
      | ~ r1(sK0,X17) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f95,plain,
    ! [X1] :
      ( p2(sK11(X1))
      | ~ r1(sK2,X1) ),
    inference(resolution,[],[f29,f45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LCL688+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36  % Computer : n027.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Thu Aug 24 21:44:33 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_NEQ problem
% 0.14/0.36  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.PMrLrUiRRB/Vampire---4.8_3497
% 0.14/0.36  % (3639)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (3647)ott+10_8_br=off:cond=on:fsr=off:gsp=on:nm=16:nwc=3.0:sims=off:sp=reverse_frequency:urr=on_415 on Vampire---4 for (415ds/0Mi)
% 0.21/0.42  % (3640)lrs-1_7_acc=on:amm=off:anc=all:bs=on:bsr=on:cond=fast:flr=on:fsr=off:gsp=on:lcm=reverse:lma=on:msp=off:nm=0:nwc=1.2:sp=frequency:stl=188_1354 on Vampire---4 for (1354ds/0Mi)
% 0.21/0.42  % (3645)ott-1010_5_add=off:amm=off:anc=none:bce=on:cond=fast:flr=on:lma=on:nm=2:nwc=1.1:sp=occurrence:tgt=ground_470 on Vampire---4 for (470ds/0Mi)
% 0.21/0.42  % (3642)lrs+11_4:3_aac=none:add=off:amm=off:anc=none:bd=preordered:bs=on:bce=on:flr=on:fsd=off:fsr=off:fde=none:nwc=2.5:sims=off:sp=reverse_arity:tgt=full:stl=188_1106 on Vampire---4 for (1106ds/0Mi)
% 0.21/0.42  % (3649)dis+3_1024_av=off:fsr=off:gsp=on:lcm=predicate:nm=4:sos=all:sp=weighted_frequency_338 on Vampire---4 for (338ds/0Mi)
% 0.21/0.42  % (3641)dis-1002_1_av=off:bsr=on:cond=on:flr=on:fsr=off:gsp=on:nwc=2.0:sims=off_1218 on Vampire---4 for (1218ds/0Mi)
% 0.21/0.43  % (3644)dis-1_128_add=large:amm=sco:anc=all_dependent:bs=on:bsr=on:bce=on:cond=fast:fsr=off:gsp=on:gs=on:gsem=off:lcm=predicate:lma=on:nm=32:nwc=4.0:nicw=on:sac=on:sp=weighted_frequency_692 on Vampire---4 for (692ds/0Mi)
% 2.23/0.77  % (3642)First to succeed.
% 2.23/0.77  % (3642)Refutation found. Thanks to Tanya!
% 2.23/0.77  % SZS status Theorem for Vampire---4
% 2.23/0.77  % SZS output start Proof for Vampire---4
% See solution above
% 2.23/0.77  % (3642)------------------------------
% 2.23/0.77  % (3642)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 2.23/0.77  % (3642)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 2.23/0.77  % (3642)Termination reason: Refutation
% 2.23/0.77  
% 2.23/0.77  % (3642)Memory used [KB]: 13816
% 2.23/0.77  % (3642)Time elapsed: 0.330 s
% 2.23/0.77  % (3642)------------------------------
% 2.23/0.77  % (3642)------------------------------
% 2.23/0.77  % (3639)Success in time 0.409 s
% 2.23/0.77  % Vampire---4.8 exiting
%------------------------------------------------------------------------------