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FindProof---0.1.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : LCL674+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n001.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 : Fri Sep 25 02:02:36 PM UTC 2026

% Result   : Theorem 5.12s 1.10s
% Output   : Proof 5.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   42 (   8 unt;   0 def)
%            Number of atoms       :  589 (   0 equ)
%            Maximal formula atoms :  121 (  14 avg)
%            Number of connectives :  943 ( 396   ~; 317   |; 229   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   15 (  14 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   1 con; 0-1 aty)
%            Number of variables   :  100 (   0 sgn  76   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y,Z] :
      ( ( r1(Y,Z)
        & r1(X,Y) )
     => r1(X,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).

fof(f1_nnf,plain,
    ! [X,Y,Z] :
      ( r1(X,Z)
      | ~ r1(Y,Z)
      | ~ r1(X,Y) ),
    inference(nnf_transformation,[status(thm)],[f1]) ).

fof(f1_sk,plain,
    ! [X,Y,Z] :
      ( r1(X,Z)
      | ~ r1(Y,Z)
      | ~ r1(X,Y) ),
    inference(skolemisation,[status(esa)],[f1_nnf]) ).

cnf(c1,plain,
    ( r1(X0,X2)
    | ~ r1(X1,X2)
    | ~ r1(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f1_sk]) ).

fof(f0,axiom,
    ! [X] : r1(X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

fof(f0_nnf,plain,
    ! [X] : r1(X,X),
    inference(nnf_transformation,[status(thm)],[f0]) ).

fof(f0_sk,plain,
    ! [X] : r1(X,X),
    inference(skolemisation,[status(esa)],[f0_nnf]) ).

cnf(c0,plain,
    r1(X0,X0),
    inference(cnf_transformation,[status(esa)],[f0_sk]) ).

fof(f2,conjecture,
    ~ ? [X] :
        ~ ( ~ ( p100(X)
              & ~ p101(X)
              & ! [Y] :
                  ( ( ( ~ p101(Y)
                      | p100(Y) )
                    & ( ~ p102(Y)
                      | p101(Y) )
                    & ( ~ p103(Y)
                      | p102(Y) )
                    & ( ~ p104(Y)
                      | p103(Y) )
                    & ( ~ p105(Y)
                      | p104(Y) )
                    & ( ~ p106(Y)
                      | p105(Y) )
                    & ( ~ p100(Y)
                      | ( ( ~ p1(Y)
                          | ! [X] :
                              ( ~ p100(X)
                              | p1(X)
                              | ~ r1(Y,X) ) )
                        & ( p1(Y)
                          | ! [X] :
                              ( ~ p100(X)
                              | ~ p1(X)
                              | ~ r1(Y,X) ) ) ) )
                    & ( ~ p101(Y)
                      | ( ( ~ p2(Y)
                          | ! [X] :
                              ( ~ p101(X)
                              | p2(X)
                              | ~ r1(Y,X) ) )
                        & ( p2(Y)
                          | ! [X] :
                              ( ~ p101(X)
                              | ~ p2(X)
                              | ~ r1(Y,X) ) ) ) )
                    & ( ~ p102(Y)
                      | ( ( ~ p3(Y)
                          | ! [X] :
                              ( ~ p102(X)
                              | p3(X)
                              | ~ r1(Y,X) ) )
                        & ( p3(Y)
                          | ! [X] :
                              ( ~ p102(X)
                              | ~ p3(X)
                              | ~ r1(Y,X) ) ) ) )
                    & ( ~ p103(Y)
                      | ( ( ~ p4(Y)
                          | ! [X] :
                              ( ~ p103(X)
                              | p4(X)
                              | ~ r1(Y,X) ) )
                        & ( p4(Y)
                          | ! [X] :
                              ( ~ p103(X)
                              | ~ p4(X)
                              | ~ r1(Y,X) ) ) ) )
                    & ( ~ p104(Y)
                      | ( ( ~ p5(Y)
                          | ! [X] :
                              ( ~ p104(X)
                              | p5(X)
                              | ~ r1(Y,X) ) )
                        & ( p5(Y)
                          | ! [X] :
                              ( ~ p104(X)
                              | ~ p5(X)
                              | ~ r1(Y,X) ) ) ) )
                    & ( ~ p105(Y)
                      | ( ( ~ p6(Y)
                          | ! [X] :
                              ( ~ p105(X)
                              | p6(X)
                              | ~ r1(Y,X) ) )
                        & ( p6(Y)
                          | ! [X] :
                              ( ~ p105(X)
                              | ~ p6(X)
                              | ~ r1(Y,X) ) ) ) )
                    & ( ~ ( p100(Y)
                          & ~ p101(Y) )
                      | ( ~ ! [X] :
                              ( ~ ( p101(X)
                                  & ~ p102(X)
                                  & p2(X) )
                              | ~ r1(Y,X) )
                        & ~ ! [X] :
                              ( ~ ( p101(X)
                                  & ~ p102(X)
                                  & ~ p2(X) )
                              | ~ r1(Y,X) ) ) )
                    & ( ~ ( p101(Y)
                          & ~ p102(Y) )
                      | ( ~ ! [X] :
                              ( ~ ( p102(X)
                                  & ~ p103(X)
                                  & p3(X) )
                              | ~ r1(Y,X) )
                        & ~ ! [X] :
                              ( ~ ( p102(X)
                                  & ~ p103(X)
                                  & ~ p3(X) )
                              | ~ r1(Y,X) ) ) )
                    & ( ~ ( p102(Y)
                          & ~ p103(Y) )
                      | ( ~ ! [X] :
                              ( ~ ( p103(X)
                                  & ~ p104(X)
                                  & p4(X) )
                              | ~ r1(Y,X) )
                        & ~ ! [X] :
                              ( ~ ( p103(X)
                                  & ~ p104(X)
                                  & ~ p4(X) )
                              | ~ r1(Y,X) ) ) )
                    & ( ~ ( p103(Y)
                          & ~ p104(Y) )
                      | ( ~ ! [X] :
                              ( ~ ( p104(X)
                                  & ~ p105(X)
                                  & p5(X) )
                              | ~ r1(Y,X) )
                        & ~ ! [X] :
                              ( ~ ( p104(X)
                                  & ~ p105(X)
                                  & ~ p5(X) )
                              | ~ r1(Y,X) ) ) )
                    & ( ~ ( p104(Y)
                          & ~ p105(Y) )
                      | ( ~ ! [X] :
                              ( ~ ( p105(X)
                                  & ~ p106(X)
                                  & p6(X) )
                              | ~ r1(Y,X) )
                        & ~ ! [X] :
                              ( ~ ( p105(X)
                                  & ~ p106(X)
                                  & ~ p6(X) )
                              | ~ r1(Y,X) ) ) ) )
                  | ~ r1(X,Y) ) )
          | ~ ! [Y] :
                ( p3(Y)
                | ~ r1(X,Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).

fof(f2_neg,negated_conjecture,
    ~ ~ ? [X] :
          ~ ( ~ ( p100(X)
                & ~ p101(X)
                & ! [Y] :
                    ( ( ( ~ p101(Y)
                        | p100(Y) )
                      & ( ~ p102(Y)
                        | p101(Y) )
                      & ( ~ p103(Y)
                        | p102(Y) )
                      & ( ~ p104(Y)
                        | p103(Y) )
                      & ( ~ p105(Y)
                        | p104(Y) )
                      & ( ~ p106(Y)
                        | p105(Y) )
                      & ( ~ p100(Y)
                        | ( ( ~ p1(Y)
                            | ! [X] :
                                ( ~ p100(X)
                                | p1(X)
                                | ~ r1(Y,X) ) )
                          & ( p1(Y)
                            | ! [X] :
                                ( ~ p100(X)
                                | ~ p1(X)
                                | ~ r1(Y,X) ) ) ) )
                      & ( ~ p101(Y)
                        | ( ( ~ p2(Y)
                            | ! [X] :
                                ( ~ p101(X)
                                | p2(X)
                                | ~ r1(Y,X) ) )
                          & ( p2(Y)
                            | ! [X] :
                                ( ~ p101(X)
                                | ~ p2(X)
                                | ~ r1(Y,X) ) ) ) )
                      & ( ~ p102(Y)
                        | ( ( ~ p3(Y)
                            | ! [X] :
                                ( ~ p102(X)
                                | p3(X)
                                | ~ r1(Y,X) ) )
                          & ( p3(Y)
                            | ! [X] :
                                ( ~ p102(X)
                                | ~ p3(X)
                                | ~ r1(Y,X) ) ) ) )
                      & ( ~ p103(Y)
                        | ( ( ~ p4(Y)
                            | ! [X] :
                                ( ~ p103(X)
                                | p4(X)
                                | ~ r1(Y,X) ) )
                          & ( p4(Y)
                            | ! [X] :
                                ( ~ p103(X)
                                | ~ p4(X)
                                | ~ r1(Y,X) ) ) ) )
                      & ( ~ p104(Y)
                        | ( ( ~ p5(Y)
                            | ! [X] :
                                ( ~ p104(X)
                                | p5(X)
                                | ~ r1(Y,X) ) )
                          & ( p5(Y)
                            | ! [X] :
                                ( ~ p104(X)
                                | ~ p5(X)
                                | ~ r1(Y,X) ) ) ) )
                      & ( ~ p105(Y)
                        | ( ( ~ p6(Y)
                            | ! [X] :
                                ( ~ p105(X)
                                | p6(X)
                                | ~ r1(Y,X) ) )
                          & ( p6(Y)
                            | ! [X] :
                                ( ~ p105(X)
                                | ~ p6(X)
                                | ~ r1(Y,X) ) ) ) )
                      & ( ~ ( p100(Y)
                            & ~ p101(Y) )
                        | ( ~ ! [X] :
                                ( ~ ( p101(X)
                                    & ~ p102(X)
                                    & p2(X) )
                                | ~ r1(Y,X) )
                          & ~ ! [X] :
                                ( ~ ( p101(X)
                                    & ~ p102(X)
                                    & ~ p2(X) )
                                | ~ r1(Y,X) ) ) )
                      & ( ~ ( p101(Y)
                            & ~ p102(Y) )
                        | ( ~ ! [X] :
                                ( ~ ( p102(X)
                                    & ~ p103(X)
                                    & p3(X) )
                                | ~ r1(Y,X) )
                          & ~ ! [X] :
                                ( ~ ( p102(X)
                                    & ~ p103(X)
                                    & ~ p3(X) )
                                | ~ r1(Y,X) ) ) )
                      & ( ~ ( p102(Y)
                            & ~ p103(Y) )
                        | ( ~ ! [X] :
                                ( ~ ( p103(X)
                                    & ~ p104(X)
                                    & p4(X) )
                                | ~ r1(Y,X) )
                          & ~ ! [X] :
                                ( ~ ( p103(X)
                                    & ~ p104(X)
                                    & ~ p4(X) )
                                | ~ r1(Y,X) ) ) )
                      & ( ~ ( p103(Y)
                            & ~ p104(Y) )
                        | ( ~ ! [X] :
                                ( ~ ( p104(X)
                                    & ~ p105(X)
                                    & p5(X) )
                                | ~ r1(Y,X) )
                          & ~ ! [X] :
                                ( ~ ( p104(X)
                                    & ~ p105(X)
                                    & ~ p5(X) )
                                | ~ r1(Y,X) ) ) )
                      & ( ~ ( p104(Y)
                            & ~ p105(Y) )
                        | ( ~ ! [X] :
                                ( ~ ( p105(X)
                                    & ~ p106(X)
                                    & p6(X) )
                                | ~ r1(Y,X) )
                          & ~ ! [X] :
                                ( ~ ( p105(X)
                                    & ~ p106(X)
                                    & ~ p6(X) )
                                | ~ r1(Y,X) ) ) ) )
                    | ~ r1(X,Y) ) )
            | ~ ! [Y] :
                  ( p3(Y)
                  | ~ r1(X,Y) ) ),
    inference(negated_conjecture,[status(cth)],[f2]) ).

fof(f2_nnf,plain,
    ? [X] :
      ( p100(X)
      & ~ p101(X)
      & ! [Y] :
          ( ( ( ~ p101(Y)
              | p100(Y) )
            & ( ~ p102(Y)
              | p101(Y) )
            & ( ~ p103(Y)
              | p102(Y) )
            & ( ~ p104(Y)
              | p103(Y) )
            & ( ~ p105(Y)
              | p104(Y) )
            & ( ~ p106(Y)
              | p105(Y) )
            & ( ~ p100(Y)
              | ( ( ~ p1(Y)
                  | ! [X] :
                      ( ~ p100(X)
                      | p1(X)
                      | ~ r1(Y,X) ) )
                & ( p1(Y)
                  | ! [X] :
                      ( ~ p100(X)
                      | ~ p1(X)
                      | ~ r1(Y,X) ) ) ) )
            & ( ~ p101(Y)
              | ( ( ~ p2(Y)
                  | ! [X] :
                      ( ~ p101(X)
                      | p2(X)
                      | ~ r1(Y,X) ) )
                & ( p2(Y)
                  | ! [X] :
                      ( ~ p101(X)
                      | ~ p2(X)
                      | ~ r1(Y,X) ) ) ) )
            & ( ~ p102(Y)
              | ( ( ~ p3(Y)
                  | ! [X] :
                      ( ~ p102(X)
                      | p3(X)
                      | ~ r1(Y,X) ) )
                & ( p3(Y)
                  | ! [X] :
                      ( ~ p102(X)
                      | ~ p3(X)
                      | ~ r1(Y,X) ) ) ) )
            & ( ~ p103(Y)
              | ( ( ~ p4(Y)
                  | ! [X] :
                      ( ~ p103(X)
                      | p4(X)
                      | ~ r1(Y,X) ) )
                & ( p4(Y)
                  | ! [X] :
                      ( ~ p103(X)
                      | ~ p4(X)
                      | ~ r1(Y,X) ) ) ) )
            & ( ~ p104(Y)
              | ( ( ~ p5(Y)
                  | ! [X] :
                      ( ~ p104(X)
                      | p5(X)
                      | ~ r1(Y,X) ) )
                & ( p5(Y)
                  | ! [X] :
                      ( ~ p104(X)
                      | ~ p5(X)
                      | ~ r1(Y,X) ) ) ) )
            & ( ~ p105(Y)
              | ( ( ~ p6(Y)
                  | ! [X] :
                      ( ~ p105(X)
                      | p6(X)
                      | ~ r1(Y,X) ) )
                & ( p6(Y)
                  | ! [X] :
                      ( ~ p105(X)
                      | ~ p6(X)
                      | ~ r1(Y,X) ) ) ) )
            & ( ~ p100(Y)
              | p101(Y)
              | ( ? [X] :
                    ( p101(X)
                    & ~ p102(X)
                    & p2(X)
                    & r1(Y,X) )
                & ? [X] :
                    ( p101(X)
                    & ~ p102(X)
                    & ~ p2(X)
                    & r1(Y,X) ) ) )
            & ( ~ p101(Y)
              | p102(Y)
              | ( ? [X] :
                    ( p102(X)
                    & ~ p103(X)
                    & p3(X)
                    & r1(Y,X) )
                & ? [X] :
                    ( p102(X)
                    & ~ p103(X)
                    & ~ p3(X)
                    & r1(Y,X) ) ) )
            & ( ~ p102(Y)
              | p103(Y)
              | ( ? [X] :
                    ( p103(X)
                    & ~ p104(X)
                    & p4(X)
                    & r1(Y,X) )
                & ? [X] :
                    ( p103(X)
                    & ~ p104(X)
                    & ~ p4(X)
                    & r1(Y,X) ) ) )
            & ( ~ p103(Y)
              | p104(Y)
              | ( ? [X] :
                    ( p104(X)
                    & ~ p105(X)
                    & p5(X)
                    & r1(Y,X) )
                & ? [X] :
                    ( p104(X)
                    & ~ p105(X)
                    & ~ p5(X)
                    & r1(Y,X) ) ) )
            & ( ~ p104(Y)
              | p105(Y)
              | ( ? [X] :
                    ( p105(X)
                    & ~ p106(X)
                    & p6(X)
                    & r1(Y,X) )
                & ? [X] :
                    ( p105(X)
                    & ~ p106(X)
                    & ~ p6(X)
                    & r1(Y,X) ) ) ) )
          | ~ r1(X,Y) )
      & ! [Y] :
          ( p3(Y)
          | ~ r1(X,Y) ) ),
    inference(nnf_transformation,[status(thm)],[f2_neg]) ).

fof(f2_sk,plain,
    ! [Y,X] :
      ( p100(sk0)
      & ~ p101(sk0)
      & ( ( ( ~ p101(Y)
            | p100(Y) )
          & ( ~ p102(Y)
            | p101(Y) )
          & ( ~ p103(Y)
            | p102(Y) )
          & ( ~ p104(Y)
            | p103(Y) )
          & ( ~ p105(Y)
            | p104(Y) )
          & ( ~ p106(Y)
            | p105(Y) )
          & ( ~ p100(Y)
            | ( ( ~ p1(Y)
                | ~ p100(X)
                | p1(X)
                | ~ r1(Y,X) )
              & ( p1(Y)
                | ~ p100(X)
                | ~ p1(X)
                | ~ r1(Y,X) ) ) )
          & ( ~ p101(Y)
            | ( ( ~ p2(Y)
                | ~ p101(X)
                | p2(X)
                | ~ r1(Y,X) )
              & ( p2(Y)
                | ~ p101(X)
                | ~ p2(X)
                | ~ r1(Y,X) ) ) )
          & ( ~ p102(Y)
            | ( ( ~ p3(Y)
                | ~ p102(X)
                | p3(X)
                | ~ r1(Y,X) )
              & ( p3(Y)
                | ~ p102(X)
                | ~ p3(X)
                | ~ r1(Y,X) ) ) )
          & ( ~ p103(Y)
            | ( ( ~ p4(Y)
                | ~ p103(X)
                | p4(X)
                | ~ r1(Y,X) )
              & ( p4(Y)
                | ~ p103(X)
                | ~ p4(X)
                | ~ r1(Y,X) ) ) )
          & ( ~ p104(Y)
            | ( ( ~ p5(Y)
                | ~ p104(X)
                | p5(X)
                | ~ r1(Y,X) )
              & ( p5(Y)
                | ~ p104(X)
                | ~ p5(X)
                | ~ r1(Y,X) ) ) )
          & ( ~ p105(Y)
            | ( ( ~ p6(Y)
                | ~ p105(X)
                | p6(X)
                | ~ r1(Y,X) )
              & ( p6(Y)
                | ~ p105(X)
                | ~ p6(X)
                | ~ r1(Y,X) ) ) )
          & ( ~ p100(Y)
            | p101(Y)
            | ( p101(sk10(Y))
              & ~ p102(sk10(Y))
              & p2(sk10(Y))
              & r1(Y,sk10(Y))
              & p101(sk9(Y))
              & ~ p102(sk9(Y))
              & ~ p2(sk9(Y))
              & r1(Y,sk9(Y)) ) )
          & ( ~ p101(Y)
            | p102(Y)
            | ( p102(sk8(Y))
              & ~ p103(sk8(Y))
              & p3(sk8(Y))
              & r1(Y,sk8(Y))
              & p102(sk7(Y))
              & ~ p103(sk7(Y))
              & ~ p3(sk7(Y))
              & r1(Y,sk7(Y)) ) )
          & ( ~ p102(Y)
            | p103(Y)
            | ( p103(sk6(Y))
              & ~ p104(sk6(Y))
              & p4(sk6(Y))
              & r1(Y,sk6(Y))
              & p103(sk5(Y))
              & ~ p104(sk5(Y))
              & ~ p4(sk5(Y))
              & r1(Y,sk5(Y)) ) )
          & ( ~ p103(Y)
            | p104(Y)
            | ( p104(sk4(Y))
              & ~ p105(sk4(Y))
              & p5(sk4(Y))
              & r1(Y,sk4(Y))
              & p104(sk3(Y))
              & ~ p105(sk3(Y))
              & ~ p5(sk3(Y))
              & r1(Y,sk3(Y)) ) )
          & ( ~ p104(Y)
            | p105(Y)
            | ( p105(sk2(Y))
              & ~ p106(sk2(Y))
              & p6(sk2(Y))
              & r1(Y,sk2(Y))
              & p105(sk1(Y))
              & ~ p106(sk1(Y))
              & ~ p6(sk1(Y))
              & r1(Y,sk1(Y)) ) ) )
        | ~ r1(sk0,Y) )
      & ( p3(Y)
        | ~ r1(sk0,Y) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4,sk5,sk6,sk7,sk8,sk9,sk10])],[f2_nnf]) ).

cnf(c35,plain,
    ( ~ p100(X1)
    | p101(X1)
    | r1(X1,sk9(X1))
    | ~ r1(sk0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(p99,plain,
    ( ~ p100(sk0)
    | p101(sk0)
    | r1(sk0,sk9(sk0)) ),
    inference(resolution,[status(thm)],[c0,c35]) ).

cnf(c62,plain,
    p100(sk0),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(p112,plain,
    ( p101(sk0)
    | r1(sk0,sk9(sk0)) ),
    inference(resolution,[status(thm)],[p99,c62]) ).

cnf(p315,plain,
    ( p101(sk0)
    | r1(sk0,X0)
    | ~ r1(sk9(sk0),X0) ),
    inference(resolution,[status(thm)],[c1,p112]) ).

cnf(c27,plain,
    ( ~ p101(X1)
    | p102(X1)
    | r1(X1,sk7(X1))
    | ~ r1(sk0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(p149,plain,
    ( ~ p101(sk9(sk0))
    | p102(sk9(sk0))
    | r1(sk9(sk0),sk7(sk9(sk0)))
    | p101(sk0) ),
    inference(resolution,[status(thm)],[p112,c27]) ).

cnf(c38,plain,
    ( ~ p100(X1)
    | p101(X1)
    | p101(sk9(X1))
    | ~ r1(sk0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(p89,plain,
    ( ~ p100(sk0)
    | p101(sk0)
    | p101(sk9(sk0)) ),
    inference(resolution,[status(thm)],[c0,c38]) ).

cnf(p109,plain,
    ( p101(sk0)
    | p101(sk9(sk0)) ),
    inference(resolution,[status(thm)],[p89,c62]) ).

cnf(p247,plain,
    ( p101(sk0)
    | p102(sk9(sk0))
    | r1(sk9(sk0),sk7(sk9(sk0)))
    | p101(sk0) ),
    inference(resolution,[status(thm)],[p149,p109]) ).

cnf(p248,plain,
    ( p102(sk9(sk0))
    | r1(sk9(sk0),sk7(sk9(sk0)))
    | p101(sk0) ),
    inference(factoring,[status(thm)],[p247]) ).

cnf(p321,plain,
    ( p102(sk9(sk0))
    | p101(sk0)
    | p101(sk0)
    | r1(sk0,sk7(sk9(sk0))) ),
    inference(resolution,[status(thm)],[p315,p248]) ).

cnf(p325,plain,
    ( p102(sk9(sk0))
    | p101(sk0)
    | r1(sk0,sk7(sk9(sk0))) ),
    inference(factoring,[status(thm)],[p321]) ).

cnf(c2,plain,
    ( p3(X1)
    | ~ r1(sk0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(p326,plain,
    ( p3(sk7(sk9(sk0)))
    | p102(sk9(sk0))
    | p101(sk0) ),
    inference(resolution,[status(thm)],[p325,c2]) ).

cnf(c28,plain,
    ( ~ p101(X1)
    | p102(X1)
    | ~ p3(sk7(X1))
    | ~ r1(sk0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(p137,plain,
    ( ~ p101(sk9(sk0))
    | p102(sk9(sk0))
    | ~ p3(sk7(sk9(sk0)))
    | p101(sk0) ),
    inference(resolution,[status(thm)],[p112,c28]) ).

cnf(p384,plain,
    ( ~ p101(sk9(sk0))
    | p102(sk9(sk0))
    | p101(sk0)
    | p102(sk9(sk0))
    | p101(sk0) ),
    inference(resolution,[status(thm)],[p326,p137]) ).

cnf(p566,plain,
    ( ~ p101(sk9(sk0))
    | p101(sk0)
    | p102(sk9(sk0))
    | p101(sk0) ),
    inference(factoring,[status(thm)],[p384]) ).

cnf(p567,plain,
    ( ~ p101(sk9(sk0))
    | p102(sk9(sk0))
    | p101(sk0) ),
    inference(factoring,[status(thm)],[p566]) ).

cnf(p568,plain,
    ( p101(sk0)
    | p102(sk9(sk0))
    | p101(sk0) ),
    inference(resolution,[status(thm)],[p567,p109]) ).

cnf(p569,plain,
    ( p102(sk9(sk0))
    | p101(sk0) ),
    inference(factoring,[status(thm)],[p568]) ).

cnf(c37,plain,
    ( ~ p100(X1)
    | p101(X1)
    | ~ p102(sk9(X1))
    | ~ r1(sk0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(p88,plain,
    ( ~ p100(sk0)
    | p101(sk0)
    | ~ p102(sk9(sk0)) ),
    inference(resolution,[status(thm)],[c0,c37]) ).

cnf(p570,plain,
    ( ~ p100(sk0)
    | p101(sk0)
    | p101(sk0) ),
    inference(resolution,[status(thm)],[p569,p88]) ).

cnf(p576,plain,
    ( ~ p100(sk0)
    | p101(sk0) ),
    inference(factoring,[status(thm)],[p570]) ).

cnf(p577,plain,
    p101(sk0),
    inference(resolution,[status(thm)],[p576,c62]) ).

cnf(c61,plain,
    ~ p101(sk0),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(p578,plain,
    $false,
    inference(resolution,[status(thm)],[p577,c61]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL674+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03  % Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36  % Computer : n001.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Thu Sep 24 00:18:05 UTC 2026
% 0.10/0.36  % CPUTime  : 
% 0.10/0.36  Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.12/1.10  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.12/1.10  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------