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Vampire-SAT---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : LCL650+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n026.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 11:59:24 AM UTC 2026

% Result   : Theorem 0.19s 0.48s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   41 (   9 unt;   2 def)
%            Number of atoms       :  453 (   0 equ)
%            Maximal formula atoms :   43 (  11 avg)
%            Number of connectives :  829 ( 417   ~; 318   |;  92   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (  11 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   11 (  10 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :  245 (   0 sgn 226   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ~ ? [X0] :
        ~ ( ! [X1] :
              ( ~ r1(X0,X1)
              | ! [X0] :
                  ( ~ r1(X1,X0)
                  | ! [X1] :
                      ( ~ r1(X0,X1)
                      | ! [X0] :
                          ( ~ r1(X1,X0)
                          | ( ~ p8(X0)
                            & ~ p6(X0)
                            & ~ p4(X0)
                            & ~ p2(X0) ) ) ) ) )
          | ! [X1] :
              ( ~ r1(X0,X1)
              | p5(X1) )
          | ~ ! [X1] :
                ( ~ r1(X0,X1)
                | ~ ( ~ ! [X0] :
                          ( ~ r1(X1,X0)
                          | ! [X1] :
                              ( ~ r1(X0,X1)
                              | ! [X0] :
                                  ( ~ r1(X1,X0)
                                  | ~ ( ( ~ p3(X0)
                                        & ~ p1(X0) )
                                      | ( p1(X0)
                                        & p3(X0) ) ) ) ) )
                    | ! [X0] :
                        ( ~ r1(X1,X0)
                        | p4(X0) )
                    | ~ ! [X0] :
                          ( ~ r1(X1,X0)
                          | ~ ( ~ ! [X1] :
                                    ( ~ r1(X0,X1)
                                    | ! [X0] :
                                        ( ~ r1(X1,X0)
                                        | ~ ( ( ~ p2(X0)
                                              & ~ p3(X0) )
                                            | ( p3(X0)
                                              & p2(X0) ) ) ) )
                              | ! [X1] :
                                  ( ~ r1(X0,X1)
                                  | p3(X1) )
                              | ~ ! [X1] :
                                    ( ~ r1(X0,X1)
                                    | ~ ~ ! [X0] :
                                            ( ~ r1(X1,X0)
                                            | ~ ( ( ~ p1(X0)
                                                  & ~ p2(X0) )
                                                | ( p2(X0)
                                                  & p1(X0) ) ) ) ) ) ) ) )
          | ! [X1] :
              ( ~ r1(X0,X1)
              | ! [X0] :
                  ( ~ r1(X1,X0)
                  | ! [X1] :
                      ( ~ r1(X0,X1)
                      | ! [X0] :
                          ( ~ r1(X1,X0)
                          | ( p4(X0)
                            & p3(X0)
                            & p2(X0)
                            & p1(X0) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).

fof(f2,negated_conjecture,
    ~ ~ ? [X0] :
          ~ ( ! [X1] :
                ( ~ r1(X0,X1)
                | ! [X0] :
                    ( ~ r1(X1,X0)
                    | ! [X1] :
                        ( ~ r1(X0,X1)
                        | ! [X0] :
                            ( ~ r1(X1,X0)
                            | ( ~ p8(X0)
                              & ~ p6(X0)
                              & ~ p4(X0)
                              & ~ p2(X0) ) ) ) ) )
            | ! [X1] :
                ( ~ r1(X0,X1)
                | p5(X1) )
            | ~ ! [X1] :
                  ( ~ r1(X0,X1)
                  | ~ ( ~ ! [X0] :
                            ( ~ r1(X1,X0)
                            | ! [X1] :
                                ( ~ r1(X0,X1)
                                | ! [X0] :
                                    ( ~ r1(X1,X0)
                                    | ~ ( ( ~ p3(X0)
                                          & ~ p1(X0) )
                                        | ( p1(X0)
                                          & p3(X0) ) ) ) ) )
                      | ! [X0] :
                          ( ~ r1(X1,X0)
                          | p4(X0) )
                      | ~ ! [X0] :
                            ( ~ r1(X1,X0)
                            | ~ ( ~ ! [X1] :
                                      ( ~ r1(X0,X1)
                                      | ! [X0] :
                                          ( ~ r1(X1,X0)
                                          | ~ ( ( ~ p2(X0)
                                                & ~ p3(X0) )
                                              | ( p3(X0)
                                                & p2(X0) ) ) ) )
                                | ! [X1] :
                                    ( ~ r1(X0,X1)
                                    | p3(X1) )
                                | ~ ! [X1] :
                                      ( ~ r1(X0,X1)
                                      | ~ ~ ! [X0] :
                                              ( ~ r1(X1,X0)
                                              | ~ ( ( ~ p1(X0)
                                                    & ~ p2(X0) )
                                                  | ( p2(X0)
                                                    & p1(X0) ) ) ) ) ) ) ) )
            | ! [X1] :
                ( ~ r1(X0,X1)
                | ! [X0] :
                    ( ~ r1(X1,X0)
                    | ! [X1] :
                        ( ~ r1(X0,X1)
                        | ! [X0] :
                            ( ~ r1(X1,X0)
                            | ( p4(X0)
                              & p3(X0)
                              & p2(X0)
                              & p1(X0) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f3,plain,
    ~ ~ ? [X0] :
          ~ ( ! [X1] :
                ( ~ r1(X0,X1)
                | ! [X2] :
                    ( ~ r1(X1,X2)
                    | ! [X3] :
                        ( ~ r1(X2,X3)
                        | ! [X4] :
                            ( ~ r1(X3,X4)
                            | ( ~ p8(X4)
                              & ~ p6(X4)
                              & ~ p4(X4)
                              & ~ p2(X4) ) ) ) ) )
            | ! [X5] :
                ( ~ r1(X0,X5)
                | p5(X5) )
            | ~ ! [X6] :
                  ( ~ r1(X0,X6)
                  | ~ ( ~ ! [X7] :
                            ( ~ r1(X6,X7)
                            | ! [X8] :
                                ( ~ r1(X7,X8)
                                | ! [X9] :
                                    ( ~ r1(X8,X9)
                                    | ~ ( ( ~ p3(X9)
                                          & ~ p1(X9) )
                                        | ( p1(X9)
                                          & p3(X9) ) ) ) ) )
                      | ! [X10] :
                          ( ~ r1(X6,X10)
                          | p4(X10) )
                      | ~ ! [X11] :
                            ( ~ r1(X6,X11)
                            | ~ ( ~ ! [X12] :
                                      ( ~ r1(X11,X12)
                                      | ! [X13] :
                                          ( ~ r1(X12,X13)
                                          | ~ ( ( ~ p2(X13)
                                                & ~ p3(X13) )
                                              | ( p3(X13)
                                                & p2(X13) ) ) ) )
                                | ! [X14] :
                                    ( ~ r1(X11,X14)
                                    | p3(X14) )
                                | ~ ! [X15] :
                                      ( ~ r1(X11,X15)
                                      | ~ ~ ! [X16] :
                                              ( ~ r1(X15,X16)
                                              | ~ ( ( ~ p1(X16)
                                                    & ~ p2(X16) )
                                                  | ( p2(X16)
                                                    & p1(X16) ) ) ) ) ) ) ) )
            | ! [X17] :
                ( ~ r1(X0,X17)
                | ! [X18] :
                    ( ~ r1(X17,X18)
                    | ! [X19] :
                        ( ~ r1(X18,X19)
                        | ! [X20] :
                            ( ~ r1(X19,X20)
                            | ( p4(X20)
                              & p3(X20)
                              & p2(X20)
                              & p1(X20) ) ) ) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f4,plain,
    ? [X0] :
      ~ ( ! [X1] :
            ( ~ r1(X0,X1)
            | ! [X2] :
                ( ~ r1(X1,X2)
                | ! [X3] :
                    ( ~ r1(X2,X3)
                    | ! [X4] :
                        ( ~ r1(X3,X4)
                        | ( ~ p8(X4)
                          & ~ p6(X4)
                          & ~ p4(X4)
                          & ~ p2(X4) ) ) ) ) )
        | ! [X5] :
            ( ~ r1(X0,X5)
            | p5(X5) )
        | ~ ! [X6] :
              ( ~ r1(X0,X6)
              | ~ ( ~ ! [X7] :
                        ( ~ r1(X6,X7)
                        | ! [X8] :
                            ( ~ r1(X7,X8)
                            | ! [X9] :
                                ( ~ r1(X8,X9)
                                | ~ ( ( ~ p3(X9)
                                      & ~ p1(X9) )
                                    | ( p1(X9)
                                      & p3(X9) ) ) ) ) )
                  | ! [X10] :
                      ( ~ r1(X6,X10)
                      | p4(X10) )
                  | ~ ! [X11] :
                        ( ~ r1(X6,X11)
                        | ~ ( ~ ! [X12] :
                                  ( ~ r1(X11,X12)
                                  | ! [X13] :
                                      ( ~ r1(X12,X13)
                                      | ~ ( ( ~ p2(X13)
                                            & ~ p3(X13) )
                                          | ( p3(X13)
                                            & p2(X13) ) ) ) )
                            | ! [X14] :
                                ( ~ r1(X11,X14)
                                | p3(X14) )
                            | ~ ! [X15] :
                                  ( ~ r1(X11,X15)
                                  | ! [X16] :
                                      ( ~ r1(X15,X16)
                                      | ~ ( ( ~ p1(X16)
                                            & ~ p2(X16) )
                                          | ( p2(X16)
                                            & p1(X16) ) ) ) ) ) ) ) )
        | ! [X17] :
            ( ~ r1(X0,X17)
            | ! [X18] :
                ( ~ r1(X17,X18)
                | ! [X19] :
                    ( ~ r1(X18,X19)
                    | ! [X20] :
                        ( ~ r1(X19,X20)
                        | ( p4(X20)
                          & p3(X20)
                          & p2(X20)
                          & p1(X20) ) ) ) ) ) ),
    inference(flattening,[],[f3]) ).

fof(f5,plain,
    ? [X0] :
      ~ ( ! [X1] :
            ( ~ r1(X0,X1)
            | ! [X2] :
                ( ~ r1(X1,X2)
                | ! [X3] :
                    ( ~ r1(X2,X3)
                    | ! [X4] :
                        ( ~ r1(X3,X4)
                        | ( ~ p8(X4)
                          & ~ p6(X4)
                          & ~ p4(X4)
                          & ~ p2(X4) ) ) ) ) )
        | ! [X5] : ~ r1(X0,X5)
        | ~ ! [X6] :
              ( ~ r1(X0,X6)
              | ~ ( ~ ! [X7] :
                        ( ~ r1(X6,X7)
                        | ! [X8] :
                            ( ~ r1(X7,X8)
                            | ! [X9] :
                                ( ~ r1(X8,X9)
                                | ~ ( ( ~ p3(X9)
                                      & ~ p1(X9) )
                                    | ( p1(X9)
                                      & p3(X9) ) ) ) ) )
                  | ! [X10] :
                      ( ~ r1(X6,X10)
                      | p4(X10) )
                  | ~ ! [X11] :
                        ( ~ r1(X6,X11)
                        | ~ ( ~ ! [X12] :
                                  ( ~ r1(X11,X12)
                                  | ! [X13] :
                                      ( ~ r1(X12,X13)
                                      | ~ ( ( ~ p2(X13)
                                            & ~ p3(X13) )
                                          | ( p3(X13)
                                            & p2(X13) ) ) ) )
                            | ! [X14] :
                                ( ~ r1(X11,X14)
                                | p3(X14) )
                            | ~ ! [X15] :
                                  ( ~ r1(X11,X15)
                                  | ! [X16] :
                                      ( ~ r1(X15,X16)
                                      | ~ ( ( ~ p1(X16)
                                            & ~ p2(X16) )
                                          | ( p2(X16)
                                            & p1(X16) ) ) ) ) ) ) ) )
        | ! [X17] :
            ( ~ r1(X0,X17)
            | ! [X18] :
                ( ~ r1(X17,X18)
                | ! [X19] :
                    ( ~ r1(X18,X19)
                    | ! [X20] :
                        ( ~ r1(X19,X20)
                        | ( p4(X20)
                          & p3(X20)
                          & p2(X20)
                          & p1(X20) ) ) ) ) ) ),
    inference(pure_predicate_removal,[],[f4]) ).

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

fof(f7,plain,
    ? [X0] :
      ~ ( ! [X1] :
            ( ~ r1(X0,X1)
            | ! [X2] :
                ( ~ r1(X1,X2)
                | ! [X3] :
                    ( ~ r1(X2,X3)
                    | ! [X4] : ~ r1(X3,X4) ) ) )
        | ! [X5] : ~ r1(X0,X5)
        | ~ ! [X6] :
              ( ~ r1(X0,X6)
              | ~ ( ~ ! [X7] :
                        ( ~ r1(X6,X7)
                        | ! [X8] :
                            ( ~ r1(X7,X8)
                            | ! [X9] :
                                ( ~ r1(X8,X9)
                                | ~ ( ( ~ p3(X9)
                                      & ~ p1(X9) )
                                    | ( p1(X9)
                                      & p3(X9) ) ) ) ) )
                  | ! [X10] : ~ r1(X6,X10)
                  | ~ ! [X11] :
                        ( ~ r1(X6,X11)
                        | ~ ( ~ ! [X12] :
                                  ( ~ r1(X11,X12)
                                  | ! [X13] :
                                      ( ~ r1(X12,X13)
                                      | ~ ( ( ~ p2(X13)
                                            & ~ p3(X13) )
                                          | ( p3(X13)
                                            & p2(X13) ) ) ) )
                            | ! [X14] :
                                ( ~ r1(X11,X14)
                                | p3(X14) )
                            | ~ ! [X15] :
                                  ( ~ r1(X11,X15)
                                  | ! [X16] :
                                      ( ~ r1(X15,X16)
                                      | ~ ( ( ~ p1(X16)
                                            & ~ p2(X16) )
                                          | ( p2(X16)
                                            & p1(X16) ) ) ) ) ) ) ) )
        | ! [X17] :
            ( ~ r1(X0,X17)
            | ! [X18] :
                ( ~ r1(X17,X18)
                | ! [X19] :
                    ( ~ r1(X18,X19)
                    | ! [X20] : ~ r1(X19,X20) ) ) ) ),
    inference(pure_predicate_removal,[],[f6]) ).

fof(f8,plain,
    ? [X0] :
      ( ? [X1] :
          ( r1(X0,X1)
          & ? [X2] :
              ( r1(X1,X2)
              & ? [X3] :
                  ( r1(X2,X3)
                  & ? [X4] : r1(X3,X4) ) ) )
      & ? [X5] : r1(X0,X5)
      & ! [X6] :
          ( ~ r1(X0,X6)
          | ( ! [X7] :
                ( ~ r1(X6,X7)
                | ! [X8] :
                    ( ~ r1(X7,X8)
                    | ! [X9] :
                        ( ~ r1(X8,X9)
                        | ( ( p3(X9)
                            | p1(X9) )
                          & ( ~ p1(X9)
                            | ~ p3(X9) ) ) ) ) )
            & ? [X10] : r1(X6,X10)
            & ! [X11] :
                ( ~ r1(X6,X11)
                | ( ! [X12] :
                      ( ~ r1(X11,X12)
                      | ! [X13] :
                          ( ~ r1(X12,X13)
                          | ( ( p2(X13)
                              | p3(X13) )
                            & ( ~ p3(X13)
                              | ~ p2(X13) ) ) ) )
                  & ? [X14] :
                      ( r1(X11,X14)
                      & ~ p3(X14) )
                  & ! [X15] :
                      ( ~ r1(X11,X15)
                      | ! [X16] :
                          ( ~ r1(X15,X16)
                          | ( ( p1(X16)
                              | p2(X16) )
                            & ( ~ p2(X16)
                              | ~ p1(X16) ) ) ) ) ) ) ) )
      & ? [X17] :
          ( r1(X0,X17)
          & ? [X18] :
              ( r1(X17,X18)
              & ? [X19] :
                  ( r1(X18,X19)
                  & ? [X20] : r1(X19,X20) ) ) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f9,plain,
    ! [X11,X6,X12,X13] :
      ( p2(X13)
      | p3(X13)
      | ~ r1(X12,X13)
      | ~ r1(X11,X12)
      | ~ r1(X6,X11)
      | ~ r1(sK0,X6) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f10,plain,
    ! [X11,X6,X12,X13] :
      ( ~ p2(X13)
      | ~ p3(X13)
      | ~ r1(X12,X13)
      | ~ r1(X11,X12)
      | ~ r1(X6,X11)
      | ~ r1(sK0,X6) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f11,plain,
    ! [X11,X6,X16,X15] :
      ( p1(X16)
      | p2(X16)
      | ~ r1(X15,X16)
      | ~ r1(X11,X15)
      | ~ r1(X6,X11)
      | ~ r1(sK0,X6) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f12,plain,
    ! [X11,X6,X16,X15] :
      ( ~ p1(X16)
      | ~ p2(X16)
      | ~ r1(X15,X16)
      | ~ r1(X11,X15)
      | ~ r1(X6,X11)
      | ~ r1(sK0,X6) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f13,plain,
    ! [X8,X6,X9,X7] :
      ( p1(X9)
      | p3(X9)
      | ~ r1(X8,X9)
      | ~ r1(X7,X8)
      | ~ r1(X6,X7)
      | ~ r1(sK0,X6) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f14,plain,
    ! [X8,X6,X9,X7] :
      ( ~ p1(X9)
      | ~ p3(X9)
      | ~ r1(X8,X9)
      | ~ r1(X7,X8)
      | ~ r1(X6,X7)
      | ~ r1(sK0,X6) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f17,plain,
    r1(sK8,sK11),
    inference(cnf_transformation,[],[f8]) ).

fof(f18,plain,
    r1(sK5,sK8),
    inference(cnf_transformation,[],[f8]) ).

fof(f21,plain,
    r1(sK3,sK5),
    inference(cnf_transformation,[],[f8]) ).

fof(f24,plain,
    r1(sK0,sK3),
    inference(cnf_transformation,[],[f8]) ).

fof(f29,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( p3(X0)
      | ~ r1(X1,X0)
      | ~ r1(X2,X1)
      | ~ r1(X3,X2)
      | ~ r1(sK0,X3)
      | ~ p2(X0)
      | ~ r1(X4,X0)
      | ~ r1(X5,X4)
      | ~ r1(X6,X5)
      | ~ r1(sK0,X6) ),
    inference(resolution,[],[f13,f12]) ).

fof(f30,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( p3(X0)
      | ~ r1(X1,X0)
      | ~ r1(X2,X1)
      | ~ r1(X3,X2)
      | ~ r1(sK0,X3)
      | ~ r1(X4,X0)
      | ~ r1(X5,X4)
      | ~ r1(X6,X5)
      | ~ r1(sK0,X6) ),
    inference(forward_subsumption_resolution,[],[f29,f9]) ).

fof(f32,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ p3(X0)
      | ~ r1(X1,X0)
      | ~ r1(X2,X1)
      | ~ r1(X3,X2)
      | ~ r1(sK0,X3)
      | p2(X0)
      | ~ r1(X4,X0)
      | ~ r1(X5,X4)
      | ~ r1(X6,X5)
      | ~ r1(sK0,X6) ),
    inference(resolution,[],[f14,f11]) ).

fof(f33,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ p3(X0)
      | ~ r1(X1,X0)
      | ~ r1(X2,X1)
      | ~ r1(X3,X2)
      | ~ r1(sK0,X3)
      | ~ r1(X4,X0)
      | ~ r1(X5,X4)
      | ~ r1(X6,X5)
      | ~ r1(sK0,X6) ),
    inference(forward_subsumption_resolution,[],[f32,f10]) ).

fof(f34,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ r1(X1,X0)
      | ~ r1(X2,X1)
      | ~ r1(X3,X2)
      | ~ r1(sK0,X3)
      | ~ r1(X4,X0)
      | ~ r1(X5,X4)
      | ~ r1(X6,X5)
      | ~ r1(sK0,X6) ),
    inference(forward_subsumption_resolution,[],[f33,f30]) ).

fof(f45,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ r1(X0,sK8)
      | ~ r1(X1,X0)
      | ~ r1(sK0,X1)
      | ~ r1(X2,sK11)
      | ~ r1(X3,X2)
      | ~ r1(X4,X3)
      | ~ r1(sK0,X4) ),
    inference(resolution,[],[f34,f17]) ).

fof(f68,definition,
    ( spl12_1
  <=> ! [X4,X3] :
        ( ~ r1(X3,sK8)
        | ~ r1(sK0,X4)
        | ~ r1(X4,X3) ) ),
    introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).

fof(f69,plain,
    ( ! [X3,X4] :
        ( ~ r1(X3,sK8)
        | ~ r1(sK0,X4)
        | ~ r1(X4,X3) )
    | ~ spl12_1 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f71,definition,
    ( spl12_2
  <=> ! [X2,X0,X1] :
        ( ~ r1(X0,sK11)
        | ~ r1(sK0,X2)
        | ~ r1(X2,X1)
        | ~ r1(X1,X0) ) ),
    introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).

fof(f72,plain,
    ( ! [X2,X0,X1] :
        ( ~ r1(X0,sK11)
        | ~ r1(sK0,X2)
        | ~ r1(X2,X1)
        | ~ r1(X1,X0) )
    | ~ spl12_2 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f124,plain,
    ( spl12_2
    | spl12_1 ),
    inference(avatar_split_clause,[],[f45,f68,f71]) ).

fof(f162,plain,
    ( ! [X0,X1] :
        ( ~ r1(sK0,X0)
        | ~ r1(X0,X1)
        | ~ r1(X1,sK8) )
    | ~ spl12_2 ),
    inference(resolution,[],[f72,f17]) ).

fof(f168,plain,
    ( spl12_1
    | ~ spl12_2 ),
    inference(avatar_split_clause,[],[f162,f71,f68]) ).

fof(f169,plain,
    ( ! [X0] :
        ( ~ r1(sK0,X0)
        | ~ r1(X0,sK5) )
    | ~ spl12_1 ),
    inference(resolution,[],[f69,f18]) ).

fof(f173,plain,
    ( ~ r1(sK0,sK3)
    | ~ spl12_1 ),
    inference(resolution,[],[f169,f21]) ).

fof(f174,plain,
    ( $false
    | ~ spl12_1 ),
    inference(forward_subsumption_resolution,[],[f173,f24]) ).

fof(f175,plain,
    ~ spl12_1,
    inference(avatar_contradiction_clause,[],[f174]) ).

cnf(s10,plain,
    ( spl12_1
    | spl12_2 ),
    inference(sat_conversion,[],[f124]) ).

cnf(s20,plain,
    ( spl12_1
    | ~ spl12_2 ),
    inference(sat_conversion,[],[f168]) ).

cnf(s21,plain,
    ~ spl12_1,
    inference(sat_conversion,[],[f175]) ).

cnf(s22,plain,
    ~ spl12_2,
    inference(rat,[],[s20,s21]) ).

cnf(s24,plain,
    $false,
    inference(rat,[],[s10,s22,s21]) ).

fof(f176,plain,
    $false,
    inference(avatar_sat_refutation,[],[s24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL650+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39  % Computer : n026.cluster.edu
% 0.13/0.39  % Model    : x86_64 x86_64
% 0.13/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39  % Memory   : 8046.5625MB
% 0.13/0.39  % OS       : Linux 6.8.0-71-generic
% 0.13/0.39  % CPULimit : 300
% 0.13/0.39  % WCLimit  : 300
% 0.13/0.39  % DateTime : Sun Sep 27 16:18:57 UTC 2026
% 0.13/0.40  % CPUTime  : 
% 0.13/0.40  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43  Running first-order model finding
% 0.13/0.43  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48  % (3040612)Will run a generic schedule for satisfiability detection.
% 0.19/0.48  % (3040617)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4094722938_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.48  % TRYING [1]
% 0.19/0.48  % TRYING [2]
% 0.19/0.48  % TRYING [3]
% 0.19/0.48  % TRYING [4]
% 0.19/0.48  % TRYING [5]
% 0.19/0.48  % (3040618)% WARNING: option uhcvi not known.
% 0.19/0.48  % TRYING [6]
% 0.19/0.48  % TRYING [7]
% 0.19/0.48  % (3040618)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3442989743:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.48  % (3040619)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2346117601:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.48  % (3040620)dis+10_1_sil=32000:sp=arity:random_seed=1339927435:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.48  % (3040622)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=390103892:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.48  % (3040621)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2983148174:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.48  % TRYING [8]
% 0.19/0.48  % (3040623)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=396039902:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.48  % TRYING [9]
% 0.19/0.48  % TRYING [10]
% 0.19/0.48  % (3040618) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3040612-3040618"...
% 0.19/0.48  % (3040621) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3040612-3040621"...
% 0.19/0.48  % (3040622) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3040612-3040622"...
% 0.19/0.48  % (3040620) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3040612-3040620"...
% 0.19/0.48  % (3040621)...printing done.
% 0.19/0.48  % (3040618)...printing done.
% 0.19/0.48  % TRYING [11]
% 0.19/0.48  % (3040621)Refutation found. Thanks to Tanya!
% 0.19/0.48  % SZS status Theorem for theBenchmark
% 0.19/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48  % (3040621)------------------------------
% 0.19/0.48  % (3040621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.48  % (3040621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.48  % (3040621)CaDiCaL version: 2.1.3
% 0.19/0.48  % (3040621)Termination reason: Refutation
% 0.19/0.48  % (3040621)Time elapsed: 0.007 s
% 0.19/0.48  % (3040621)Peak memory usage: 12 MB
% 0.19/0.48  % (3040621)Instructions burned: 12 (million)
% 0.19/0.48  % (3040612)Success in time 0.04 s
% 0.19/0.48  % Vampire exiting
%------------------------------------------------------------------------------