TSTP Solution File: LCL636+1.001 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL636+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 : Sun May  5 07:48:55 EDT 2024

% Result   : Theorem 0.16s 0.33s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   35 (   7 unt;   0 def)
%            Number of atoms       :  692 (   0 equ)
%            Maximal formula atoms :   69 (  19 avg)
%            Number of connectives : 1166 ( 509   ~; 404   |; 251   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (  10 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   15 (  14 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :  164 ( 139   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f100,plain,
    $false,
    inference(subsumption_resolution,[],[f99,f83]) ).

fof(f83,plain,
    ~ p2(sK9(sK12)),
    inference(resolution,[],[f48,f78]) ).

fof(f78,plain,
    sP6(sK12),
    inference(subsumption_resolution,[],[f77,f75]) ).

fof(f75,plain,
    ~ p101(sK12),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ( p100(sK12)
    & ~ p101(sK12)
    & ( ~ p101(sK12)
      | p100(sK12) )
    & ( ~ p100(sK12)
      | ( ( ~ p1(sK12)
          | ! [X1] :
              ( ~ p100(X1)
              | p1(X1)
              | ~ r1(sK12,X1) ) )
        & ( p1(sK12)
          | ! [X2] :
              ( ~ p100(X2)
              | ~ p1(X2)
              | ~ r1(sK12,X2) ) ) ) )
    & ( ~ p101(sK12)
      | ( ( ~ p2(sK12)
          | ! [X3] :
              ( ~ p101(X3)
              | p2(X3)
              | ~ r1(sK12,X3) ) )
        & ( p2(sK12)
          | ! [X4] :
              ( ~ p101(X4)
              | ~ p2(X4)
              | ~ r1(sK12,X4) ) ) ) )
    & ( ~ p100(sK12)
      | p101(sK12)
      | ( sP7(sK12)
        & sP6(sK12) ) )
    & ! [X5] :
        ( sP5(X5)
        | ~ r1(sK12,X5) )
    & ! [X6] :
        ( p2(X6)
        | ~ r1(sK12,X6) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f41,f42]) ).

fof(f42,plain,
    ( ? [X0] :
        ( p100(X0)
        & ~ p101(X0)
        & ( ~ p101(X0)
          | p100(X0) )
        & ( ~ p100(X0)
          | ( ( ~ p1(X0)
              | ! [X1] :
                  ( ~ p100(X1)
                  | p1(X1)
                  | ~ r1(X0,X1) ) )
            & ( p1(X0)
              | ! [X2] :
                  ( ~ p100(X2)
                  | ~ p1(X2)
                  | ~ r1(X0,X2) ) ) ) )
        & ( ~ p101(X0)
          | ( ( ~ p2(X0)
              | ! [X3] :
                  ( ~ p101(X3)
                  | p2(X3)
                  | ~ r1(X0,X3) ) )
            & ( p2(X0)
              | ! [X4] :
                  ( ~ p101(X4)
                  | ~ p2(X4)
                  | ~ r1(X0,X4) ) ) ) )
        & ( ~ p100(X0)
          | p101(X0)
          | ( sP7(X0)
            & sP6(X0) ) )
        & ! [X5] :
            ( sP5(X5)
            | ~ r1(X0,X5) )
        & ! [X6] :
            ( p2(X6)
            | ~ r1(X0,X6) ) )
   => ( p100(sK12)
      & ~ p101(sK12)
      & ( ~ p101(sK12)
        | p100(sK12) )
      & ( ~ p100(sK12)
        | ( ( ~ p1(sK12)
            | ! [X1] :
                ( ~ p100(X1)
                | p1(X1)
                | ~ r1(sK12,X1) ) )
          & ( p1(sK12)
            | ! [X2] :
                ( ~ p100(X2)
                | ~ p1(X2)
                | ~ r1(sK12,X2) ) ) ) )
      & ( ~ p101(sK12)
        | ( ( ~ p2(sK12)
            | ! [X3] :
                ( ~ p101(X3)
                | p2(X3)
                | ~ r1(sK12,X3) ) )
          & ( p2(sK12)
            | ! [X4] :
                ( ~ p101(X4)
                | ~ p2(X4)
                | ~ r1(sK12,X4) ) ) ) )
      & ( ~ p100(sK12)
        | p101(sK12)
        | ( sP7(sK12)
          & sP6(sK12) ) )
      & ! [X5] :
          ( sP5(X5)
          | ~ r1(sK12,X5) )
      & ! [X6] :
          ( p2(X6)
          | ~ r1(sK12,X6) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ? [X0] :
      ( p100(X0)
      & ~ p101(X0)
      & ( ~ p101(X0)
        | p100(X0) )
      & ( ~ p100(X0)
        | ( ( ~ p1(X0)
            | ! [X1] :
                ( ~ p100(X1)
                | p1(X1)
                | ~ r1(X0,X1) ) )
          & ( p1(X0)
            | ! [X2] :
                ( ~ p100(X2)
                | ~ p1(X2)
                | ~ r1(X0,X2) ) ) ) )
      & ( ~ p101(X0)
        | ( ( ~ p2(X0)
            | ! [X3] :
                ( ~ p101(X3)
                | p2(X3)
                | ~ r1(X0,X3) ) )
          & ( p2(X0)
            | ! [X4] :
                ( ~ p101(X4)
                | ~ p2(X4)
                | ~ r1(X0,X4) ) ) ) )
      & ( ~ p100(X0)
        | p101(X0)
        | ( sP7(X0)
          & sP6(X0) ) )
      & ! [X5] :
          ( sP5(X5)
          | ~ r1(X0,X5) )
      & ! [X6] :
          ( p2(X6)
          | ~ r1(X0,X6) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ? [X0] :
      ( p100(X0)
      & ~ p101(X0)
      & ( ~ p101(X0)
        | p100(X0) )
      & ( ~ p100(X0)
        | ( ( ~ p1(X0)
            | ! [X1] :
                ( ~ p100(X1)
                | p1(X1)
                | ~ r1(X0,X1) ) )
          & ( p1(X0)
            | ! [X2] :
                ( ~ p100(X2)
                | ~ p1(X2)
                | ~ r1(X0,X2) ) ) ) )
      & ( ~ p101(X0)
        | ( ( ~ p2(X0)
            | ! [X3] :
                ( ~ p101(X3)
                | p2(X3)
                | ~ r1(X0,X3) ) )
          & ( p2(X0)
            | ! [X4] :
                ( ~ p101(X4)
                | ~ p2(X4)
                | ~ r1(X0,X4) ) ) ) )
      & ( ~ p100(X0)
        | p101(X0)
        | ( sP7(X0)
          & sP6(X0) ) )
      & ! [X7] :
          ( sP5(X7)
          | ~ r1(X0,X7) )
      & ! [X14] :
          ( p2(X14)
          | ~ r1(X0,X14) ) ),
    inference(definition_folding,[],[f7,f15,f14,f13,f12,f11,f10,f9,f8]) ).

fof(f8,plain,
    ! [X7] :
      ( ? [X13] :
          ( p101(X13)
          & ~ p2(X13)
          & r1(X7,X13) )
      | ~ sP0(X7) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f9,plain,
    ! [X7] :
      ( ? [X12] :
          ( p101(X12)
          & p2(X12)
          & r1(X7,X12) )
      | ~ sP1(X7) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f10,plain,
    ! [X7] :
      ( ~ p100(X7)
      | p101(X7)
      | ( sP1(X7)
        & sP0(X7) )
      | ~ sP2(X7) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f11,plain,
    ! [X7] :
      ( ~ p101(X7)
      | ( ( ~ p2(X7)
          | ! [X10] :
              ( ~ p101(X10)
              | p2(X10)
              | ~ r1(X7,X10) ) )
        & ( p2(X7)
          | ! [X11] :
              ( ~ p101(X11)
              | ~ p2(X11)
              | ~ r1(X7,X11) ) ) )
      | ~ sP3(X7) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f12,plain,
    ! [X7] :
      ( ~ p100(X7)
      | ( ( ~ p1(X7)
          | ! [X8] :
              ( ~ p100(X8)
              | p1(X8)
              | ~ r1(X7,X8) ) )
        & ( p1(X7)
          | ! [X9] :
              ( ~ p100(X9)
              | ~ p1(X9)
              | ~ r1(X7,X9) ) ) )
      | ~ sP4(X7) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f13,plain,
    ! [X7] :
      ( ( ( ~ p101(X7)
          | p100(X7) )
        & sP4(X7)
        & sP3(X7)
        & sP2(X7) )
      | ~ sP5(X7) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

fof(f14,plain,
    ! [X0] :
      ( ? [X6] :
          ( p101(X6)
          & ~ p2(X6)
          & r1(X0,X6) )
      | ~ sP6(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f15,plain,
    ! [X0] :
      ( ? [X5] :
          ( p101(X5)
          & p2(X5)
          & r1(X0,X5) )
      | ~ sP7(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f7,plain,
    ? [X0] :
      ( p100(X0)
      & ~ p101(X0)
      & ( ~ p101(X0)
        | p100(X0) )
      & ( ~ p100(X0)
        | ( ( ~ p1(X0)
            | ! [X1] :
                ( ~ p100(X1)
                | p1(X1)
                | ~ r1(X0,X1) ) )
          & ( p1(X0)
            | ! [X2] :
                ( ~ p100(X2)
                | ~ p1(X2)
                | ~ r1(X0,X2) ) ) ) )
      & ( ~ p101(X0)
        | ( ( ~ p2(X0)
            | ! [X3] :
                ( ~ p101(X3)
                | p2(X3)
                | ~ r1(X0,X3) ) )
          & ( p2(X0)
            | ! [X4] :
                ( ~ p101(X4)
                | ~ p2(X4)
                | ~ r1(X0,X4) ) ) ) )
      & ( ~ p100(X0)
        | p101(X0)
        | ( ? [X5] :
              ( p101(X5)
              & p2(X5)
              & r1(X0,X5) )
          & ? [X6] :
              ( p101(X6)
              & ~ p2(X6)
              & r1(X0,X6) ) ) )
      & ! [X7] :
          ( ( ( ~ p101(X7)
              | p100(X7) )
            & ( ~ p100(X7)
              | ( ( ~ p1(X7)
                  | ! [X8] :
                      ( ~ p100(X8)
                      | p1(X8)
                      | ~ r1(X7,X8) ) )
                & ( p1(X7)
                  | ! [X9] :
                      ( ~ p100(X9)
                      | ~ p1(X9)
                      | ~ r1(X7,X9) ) ) ) )
            & ( ~ p101(X7)
              | ( ( ~ p2(X7)
                  | ! [X10] :
                      ( ~ p101(X10)
                      | p2(X10)
                      | ~ r1(X7,X10) ) )
                & ( p2(X7)
                  | ! [X11] :
                      ( ~ p101(X11)
                      | ~ p2(X11)
                      | ~ r1(X7,X11) ) ) ) )
            & ( ~ p100(X7)
              | p101(X7)
              | ( ? [X12] :
                    ( p101(X12)
                    & p2(X12)
                    & r1(X7,X12) )
                & ? [X13] :
                    ( p101(X13)
                    & ~ p2(X13)
                    & r1(X7,X13) ) ) ) )
          | ~ r1(X0,X7) )
      & ! [X14] :
          ( p2(X14)
          | ~ r1(X0,X14) ) ),
    inference(flattening,[],[f6]) ).

fof(f6,plain,
    ? [X0] :
      ( p100(X0)
      & ~ p101(X0)
      & ( ~ p101(X0)
        | p100(X0) )
      & ( ~ p100(X0)
        | ( ( ~ p1(X0)
            | ! [X1] :
                ( ~ p100(X1)
                | p1(X1)
                | ~ r1(X0,X1) ) )
          & ( p1(X0)
            | ! [X2] :
                ( ~ p100(X2)
                | ~ p1(X2)
                | ~ r1(X0,X2) ) ) ) )
      & ( ~ p101(X0)
        | ( ( ~ p2(X0)
            | ! [X3] :
                ( ~ p101(X3)
                | p2(X3)
                | ~ r1(X0,X3) ) )
          & ( p2(X0)
            | ! [X4] :
                ( ~ p101(X4)
                | ~ p2(X4)
                | ~ r1(X0,X4) ) ) ) )
      & ( ~ p100(X0)
        | p101(X0)
        | ( ? [X5] :
              ( p101(X5)
              & p2(X5)
              & r1(X0,X5) )
          & ? [X6] :
              ( p101(X6)
              & ~ p2(X6)
              & r1(X0,X6) ) ) )
      & ! [X7] :
          ( ( ( ~ p101(X7)
              | p100(X7) )
            & ( ~ p100(X7)
              | ( ( ~ p1(X7)
                  | ! [X8] :
                      ( ~ p100(X8)
                      | p1(X8)
                      | ~ r1(X7,X8) ) )
                & ( p1(X7)
                  | ! [X9] :
                      ( ~ p100(X9)
                      | ~ p1(X9)
                      | ~ r1(X7,X9) ) ) ) )
            & ( ~ p101(X7)
              | ( ( ~ p2(X7)
                  | ! [X10] :
                      ( ~ p101(X10)
                      | p2(X10)
                      | ~ r1(X7,X10) ) )
                & ( p2(X7)
                  | ! [X11] :
                      ( ~ p101(X11)
                      | ~ p2(X11)
                      | ~ r1(X7,X11) ) ) ) )
            & ( ~ p100(X7)
              | p101(X7)
              | ( ? [X12] :
                    ( p101(X12)
                    & p2(X12)
                    & r1(X7,X12) )
                & ? [X13] :
                    ( p101(X13)
                    & ~ p2(X13)
                    & r1(X7,X13) ) ) ) )
          | ~ r1(X0,X7) )
      & ! [X14] :
          ( p2(X14)
          | ~ r1(X0,X14) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,plain,
    ? [X0] :
      ~ ( ~ ( p100(X0)
            & ~ p101(X0)
            & ( ~ p101(X0)
              | p100(X0) )
            & ( ~ p100(X0)
              | ( ( ~ p1(X0)
                  | ! [X1] :
                      ( ~ p100(X1)
                      | p1(X1)
                      | ~ r1(X0,X1) ) )
                & ( p1(X0)
                  | ! [X2] :
                      ( ~ p100(X2)
                      | ~ p1(X2)
                      | ~ r1(X0,X2) ) ) ) )
            & ( ~ p101(X0)
              | ( ( ~ p2(X0)
                  | ! [X3] :
                      ( ~ p101(X3)
                      | p2(X3)
                      | ~ r1(X0,X3) ) )
                & ( p2(X0)
                  | ! [X4] :
                      ( ~ p101(X4)
                      | ~ p2(X4)
                      | ~ r1(X0,X4) ) ) ) )
            & ( ~ ( p100(X0)
                  & ~ p101(X0) )
              | ( ~ ! [X5] :
                      ( ~ ( p101(X5)
                          & p2(X5) )
                      | ~ r1(X0,X5) )
                & ~ ! [X6] :
                      ( ~ ( p101(X6)
                          & ~ p2(X6) )
                      | ~ r1(X0,X6) ) ) )
            & ! [X7] :
                ( ( ( ~ p101(X7)
                    | p100(X7) )
                  & ( ~ p100(X7)
                    | ( ( ~ p1(X7)
                        | ! [X8] :
                            ( ~ p100(X8)
                            | p1(X8)
                            | ~ r1(X7,X8) ) )
                      & ( p1(X7)
                        | ! [X9] :
                            ( ~ p100(X9)
                            | ~ p1(X9)
                            | ~ r1(X7,X9) ) ) ) )
                  & ( ~ p101(X7)
                    | ( ( ~ p2(X7)
                        | ! [X10] :
                            ( ~ p101(X10)
                            | p2(X10)
                            | ~ r1(X7,X10) ) )
                      & ( p2(X7)
                        | ! [X11] :
                            ( ~ p101(X11)
                            | ~ p2(X11)
                            | ~ r1(X7,X11) ) ) ) )
                  & ( ~ ( p100(X7)
                        & ~ p101(X7) )
                    | ( ~ ! [X12] :
                            ( ~ ( p101(X12)
                                & p2(X12) )
                            | ~ r1(X7,X12) )
                      & ~ ! [X13] :
                            ( ~ ( p101(X13)
                                & ~ p2(X13) )
                            | ~ r1(X7,X13) ) ) ) )
                | ~ r1(X0,X7) ) )
        | ~ ! [X14] :
              ( p2(X14)
              | ~ r1(X0,X14) ) ),
    inference(pure_predicate_removal,[],[f4]) ).

fof(f4,plain,
    ? [X0] :
      ~ ( ~ ( p100(X0)
            & ~ p101(X0)
            & ( ~ p101(X0)
              | p100(X0) )
            & ( ~ p102(X0)
              | p101(X0) )
            & ( ~ p100(X0)
              | ( ( ~ p1(X0)
                  | ! [X1] :
                      ( ~ p100(X1)
                      | p1(X1)
                      | ~ r1(X0,X1) ) )
                & ( p1(X0)
                  | ! [X2] :
                      ( ~ p100(X2)
                      | ~ p1(X2)
                      | ~ r1(X0,X2) ) ) ) )
            & ( ~ p101(X0)
              | ( ( ~ p2(X0)
                  | ! [X3] :
                      ( ~ p101(X3)
                      | p2(X3)
                      | ~ r1(X0,X3) ) )
                & ( p2(X0)
                  | ! [X4] :
                      ( ~ p101(X4)
                      | ~ p2(X4)
                      | ~ r1(X0,X4) ) ) ) )
            & ( ~ ( p100(X0)
                  & ~ p101(X0) )
              | ( ~ ! [X5] :
                      ( ~ ( p101(X5)
                          & ~ p102(X5)
                          & p2(X5) )
                      | ~ r1(X0,X5) )
                & ~ ! [X6] :
                      ( ~ ( p101(X6)
                          & ~ p102(X6)
                          & ~ p2(X6) )
                      | ~ r1(X0,X6) ) ) )
            & ! [X7] :
                ( ( ( ~ p101(X7)
                    | p100(X7) )
                  & ( ~ p102(X7)
                    | p101(X7) )
                  & ( ~ p100(X7)
                    | ( ( ~ p1(X7)
                        | ! [X8] :
                            ( ~ p100(X8)
                            | p1(X8)
                            | ~ r1(X7,X8) ) )
                      & ( p1(X7)
                        | ! [X9] :
                            ( ~ p100(X9)
                            | ~ p1(X9)
                            | ~ r1(X7,X9) ) ) ) )
                  & ( ~ p101(X7)
                    | ( ( ~ p2(X7)
                        | ! [X10] :
                            ( ~ p101(X10)
                            | p2(X10)
                            | ~ r1(X7,X10) ) )
                      & ( p2(X7)
                        | ! [X11] :
                            ( ~ p101(X11)
                            | ~ p2(X11)
                            | ~ r1(X7,X11) ) ) ) )
                  & ( ~ ( p100(X7)
                        & ~ p101(X7) )
                    | ( ~ ! [X12] :
                            ( ~ ( p101(X12)
                                & ~ p102(X12)
                                & p2(X12) )
                            | ~ r1(X7,X12) )
                      & ~ ! [X13] :
                            ( ~ ( p101(X13)
                                & ~ p102(X13)
                                & ~ p2(X13) )
                            | ~ r1(X7,X13) ) ) ) )
                | ~ r1(X0,X7) ) )
        | ~ ! [X14] :
              ( p2(X14)
              | ~ r1(X0,X14) ) ),
    inference(flattening,[],[f3]) ).

fof(f3,plain,
    ~ ~ ? [X0] :
          ~ ( ~ ( p100(X0)
                & ~ p101(X0)
                & ( ~ p101(X0)
                  | p100(X0) )
                & ( ~ p102(X0)
                  | p101(X0) )
                & ( ~ p100(X0)
                  | ( ( ~ p1(X0)
                      | ! [X1] :
                          ( ~ p100(X1)
                          | p1(X1)
                          | ~ r1(X0,X1) ) )
                    & ( p1(X0)
                      | ! [X2] :
                          ( ~ p100(X2)
                          | ~ p1(X2)
                          | ~ r1(X0,X2) ) ) ) )
                & ( ~ p101(X0)
                  | ( ( ~ p2(X0)
                      | ! [X3] :
                          ( ~ p101(X3)
                          | p2(X3)
                          | ~ r1(X0,X3) ) )
                    & ( p2(X0)
                      | ! [X4] :
                          ( ~ p101(X4)
                          | ~ p2(X4)
                          | ~ r1(X0,X4) ) ) ) )
                & ( ~ ( p100(X0)
                      & ~ p101(X0) )
                  | ( ~ ! [X5] :
                          ( ~ ( p101(X5)
                              & ~ p102(X5)
                              & p2(X5) )
                          | ~ r1(X0,X5) )
                    & ~ ! [X6] :
                          ( ~ ( p101(X6)
                              & ~ p102(X6)
                              & ~ p2(X6) )
                          | ~ r1(X0,X6) ) ) )
                & ! [X7] :
                    ( ( ( ~ p101(X7)
                        | p100(X7) )
                      & ( ~ p102(X7)
                        | p101(X7) )
                      & ( ~ p100(X7)
                        | ( ( ~ p1(X7)
                            | ! [X8] :
                                ( ~ p100(X8)
                                | p1(X8)
                                | ~ r1(X7,X8) ) )
                          & ( p1(X7)
                            | ! [X9] :
                                ( ~ p100(X9)
                                | ~ p1(X9)
                                | ~ r1(X7,X9) ) ) ) )
                      & ( ~ p101(X7)
                        | ( ( ~ p2(X7)
                            | ! [X10] :
                                ( ~ p101(X10)
                                | p2(X10)
                                | ~ r1(X7,X10) ) )
                          & ( p2(X7)
                            | ! [X11] :
                                ( ~ p101(X11)
                                | ~ p2(X11)
                                | ~ r1(X7,X11) ) ) ) )
                      & ( ~ ( p100(X7)
                            & ~ p101(X7) )
                        | ( ~ ! [X12] :
                                ( ~ ( p101(X12)
                                    & ~ p102(X12)
                                    & p2(X12) )
                                | ~ r1(X7,X12) )
                          & ~ ! [X13] :
                                ( ~ ( p101(X13)
                                    & ~ p102(X13)
                                    & ~ p2(X13) )
                                | ~ r1(X7,X13) ) ) ) )
                    | ~ r1(X0,X7) ) )
            | ~ ! [X14] :
                  ( p2(X14)
                  | ~ r1(X0,X14) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ~ ? [X0] :
          ~ ( ~ ( p100(X0)
                & ~ p101(X0)
                & ( ~ p101(X0)
                  | p100(X0) )
                & ( ~ p102(X0)
                  | p101(X0) )
                & ( ~ p100(X0)
                  | ( ( ~ p1(X0)
                      | ! [X1] :
                          ( ~ p100(X1)
                          | p1(X1)
                          | ~ r1(X0,X1) ) )
                    & ( p1(X0)
                      | ! [X1] :
                          ( ~ p100(X1)
                          | ~ p1(X1)
                          | ~ r1(X0,X1) ) ) ) )
                & ( ~ p101(X0)
                  | ( ( ~ p2(X0)
                      | ! [X1] :
                          ( ~ p101(X1)
                          | p2(X1)
                          | ~ r1(X0,X1) ) )
                    & ( p2(X0)
                      | ! [X1] :
                          ( ~ p101(X1)
                          | ~ p2(X1)
                          | ~ r1(X0,X1) ) ) ) )
                & ( ~ ( p100(X0)
                      & ~ p101(X0) )
                  | ( ~ ! [X1] :
                          ( ~ ( p101(X1)
                              & ~ p102(X1)
                              & p2(X1) )
                          | ~ r1(X0,X1) )
                    & ~ ! [X1] :
                          ( ~ ( p101(X1)
                              & ~ p102(X1)
                              & ~ p2(X1) )
                          | ~ r1(X0,X1) ) ) )
                & ! [X1] :
                    ( ( ( ~ p101(X1)
                        | p100(X1) )
                      & ( ~ p102(X1)
                        | p101(X1) )
                      & ( ~ p100(X1)
                        | ( ( ~ p1(X1)
                            | ! [X0] :
                                ( ~ p100(X0)
                                | p1(X0)
                                | ~ r1(X1,X0) ) )
                          & ( p1(X1)
                            | ! [X0] :
                                ( ~ p100(X0)
                                | ~ p1(X0)
                                | ~ r1(X1,X0) ) ) ) )
                      & ( ~ p101(X1)
                        | ( ( ~ p2(X1)
                            | ! [X0] :
                                ( ~ p101(X0)
                                | p2(X0)
                                | ~ r1(X1,X0) ) )
                          & ( p2(X1)
                            | ! [X0] :
                                ( ~ p101(X0)
                                | ~ p2(X0)
                                | ~ r1(X1,X0) ) ) ) )
                      & ( ~ ( p100(X1)
                            & ~ p101(X1) )
                        | ( ~ ! [X0] :
                                ( ~ ( p101(X0)
                                    & ~ p102(X0)
                                    & p2(X0) )
                                | ~ r1(X1,X0) )
                          & ~ ! [X0] :
                                ( ~ ( p101(X0)
                                    & ~ p102(X0)
                                    & ~ p2(X0) )
                                | ~ r1(X1,X0) ) ) ) )
                    | ~ r1(X0,X1) ) )
            | ~ ! [X1] :
                  ( p2(X1)
                  | ~ r1(X0,X1) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ~ ? [X0] :
        ~ ( ~ ( p100(X0)
              & ~ p101(X0)
              & ( ~ p101(X0)
                | p100(X0) )
              & ( ~ p102(X0)
                | p101(X0) )
              & ( ~ p100(X0)
                | ( ( ~ p1(X0)
                    | ! [X1] :
                        ( ~ p100(X1)
                        | p1(X1)
                        | ~ r1(X0,X1) ) )
                  & ( p1(X0)
                    | ! [X1] :
                        ( ~ p100(X1)
                        | ~ p1(X1)
                        | ~ r1(X0,X1) ) ) ) )
              & ( ~ p101(X0)
                | ( ( ~ p2(X0)
                    | ! [X1] :
                        ( ~ p101(X1)
                        | p2(X1)
                        | ~ r1(X0,X1) ) )
                  & ( p2(X0)
                    | ! [X1] :
                        ( ~ p101(X1)
                        | ~ p2(X1)
                        | ~ r1(X0,X1) ) ) ) )
              & ( ~ ( p100(X0)
                    & ~ p101(X0) )
                | ( ~ ! [X1] :
                        ( ~ ( p101(X1)
                            & ~ p102(X1)
                            & p2(X1) )
                        | ~ r1(X0,X1) )
                  & ~ ! [X1] :
                        ( ~ ( p101(X1)
                            & ~ p102(X1)
                            & ~ p2(X1) )
                        | ~ r1(X0,X1) ) ) )
              & ! [X1] :
                  ( ( ( ~ p101(X1)
                      | p100(X1) )
                    & ( ~ p102(X1)
                      | p101(X1) )
                    & ( ~ p100(X1)
                      | ( ( ~ p1(X1)
                          | ! [X0] :
                              ( ~ p100(X0)
                              | p1(X0)
                              | ~ r1(X1,X0) ) )
                        & ( p1(X1)
                          | ! [X0] :
                              ( ~ p100(X0)
                              | ~ p1(X0)
                              | ~ r1(X1,X0) ) ) ) )
                    & ( ~ p101(X1)
                      | ( ( ~ p2(X1)
                          | ! [X0] :
                              ( ~ p101(X0)
                              | p2(X0)
                              | ~ r1(X1,X0) ) )
                        & ( p2(X1)
                          | ! [X0] :
                              ( ~ p101(X0)
                              | ~ p2(X0)
                              | ~ r1(X1,X0) ) ) ) )
                    & ( ~ ( p100(X1)
                          & ~ p101(X1) )
                      | ( ~ ! [X0] :
                              ( ~ ( p101(X0)
                                  & ~ p102(X0)
                                  & p2(X0) )
                              | ~ r1(X1,X0) )
                        & ~ ! [X0] :
                              ( ~ ( p101(X0)
                                  & ~ p102(X0)
                                  & ~ p2(X0) )
                              | ~ r1(X1,X0) ) ) ) )
                  | ~ r1(X0,X1) ) )
          | ~ ! [X1] :
                ( p2(X1)
                | ~ r1(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).

fof(f77,plain,
    ( p101(sK12)
    | sP6(sK12) ),
    inference(subsumption_resolution,[],[f68,f76]) ).

fof(f76,plain,
    p100(sK12),
    inference(cnf_transformation,[],[f43]) ).

fof(f68,plain,
    ( ~ p100(sK12)
    | p101(sK12)
    | sP6(sK12) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f48,plain,
    ! [X0] :
      ( ~ sP6(X0)
      | ~ p2(sK9(X0)) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0] :
      ( ( p101(sK9(X0))
        & ~ p2(sK9(X0))
        & r1(X0,sK9(X0)) )
      | ~ sP6(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f22,f23]) ).

fof(f23,plain,
    ! [X0] :
      ( ? [X1] :
          ( p101(X1)
          & ~ p2(X1)
          & r1(X0,X1) )
     => ( p101(sK9(X0))
        & ~ p2(sK9(X0))
        & r1(X0,sK9(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0] :
      ( ? [X1] :
          ( p101(X1)
          & ~ p2(X1)
          & r1(X0,X1) )
      | ~ sP6(X0) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X0] :
      ( ? [X6] :
          ( p101(X6)
          & ~ p2(X6)
          & r1(X0,X6) )
      | ~ sP6(X0) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f99,plain,
    p2(sK9(sK12)),
    inference(resolution,[],[f95,f66]) ).

fof(f66,plain,
    ! [X6] :
      ( ~ r1(sK12,X6)
      | p2(X6) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f95,plain,
    r1(sK12,sK9(sK12)),
    inference(resolution,[],[f47,f78]) ).

fof(f47,plain,
    ! [X0] :
      ( ~ sP6(X0)
      | r1(X0,sK9(X0)) ),
    inference(cnf_transformation,[],[f24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : LCL636+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31  % Computer : n017.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Fri May  3 13:32:21 EDT 2024
% 0.16/0.31  % CPUTime    : 
% 0.16/0.32  % (18194)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33  % (18199)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.16/0.33  % (18200)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.16/0.33  % (18196)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.33  % (18201)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.16/0.33  % (18198)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.16/0.33  % (18197)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.16/0.33  % (18195)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.16/0.33  % (18199)First to succeed.
% 0.16/0.33  TRYING [1]
% 0.16/0.33  % (18200)Also succeeded, but the first one will report.
% 0.16/0.33  TRYING [2]
% 0.16/0.33  % (18197)Also succeeded, but the first one will report.
% 0.16/0.33  TRYING [1]
% 0.16/0.33  TRYING [1]
% 0.16/0.33  TRYING [2]
% 0.16/0.33  TRYING [3]
% 0.16/0.33  TRYING [2]
% 0.16/0.33  TRYING [3]
% 0.16/0.33  TRYING [3]
% 0.16/0.33  % (18199)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18194"
% 0.16/0.33  TRYING [1]
% 0.16/0.33  TRYING [4]
% 0.16/0.33  TRYING [2]
% 0.16/0.33  % (18196)Also succeeded, but the first one will report.
% 0.16/0.33  % (18198)Also succeeded, but the first one will report.
% 0.16/0.33  TRYING [3]
% 0.16/0.33  % (18199)Refutation found. Thanks to Tanya!
% 0.16/0.33  % SZS status Theorem for theBenchmark
% 0.16/0.33  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.33  % (18199)------------------------------
% 0.16/0.33  % (18199)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.33  % (18199)Termination reason: Refutation
% 0.16/0.33  
% 0.16/0.33  % (18199)Memory used [KB]: 823
% 0.16/0.33  % (18199)Time elapsed: 0.004 s
% 0.16/0.33  % (18199)Instructions burned: 7 (million)
% 0.16/0.33  % (18194)Success in time 0.018 s
%------------------------------------------------------------------------------