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Prover9---2026-6A.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Prover9---2026-6A
% Problem  : LCL644+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n019.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 : Sun Sep 27 07:59:17 AM UTC 2026

% Result   : Theorem 4.96s 5.22s
% Output   : CNFRefutation 4.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    1
% Syntax   : Number of formulae    :    3 (   1 unt;   0 def)
%            Number of atoms       :  451 (   0 equ)
%            Maximal formula atoms :  225 ( 150 avg)
%            Number of connectives :  715 ( 267   ~; 304   |; 144   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (  20 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :  160 (   0 sgn 158   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(main,conjecture,
    ~ ? [X] :
        ~ ( ~ ( ~ ( ! [Y] :
                      ( ~ ( p1(Y)
                          & ! [X] :
                              ( p1(X)
                              | ~ r1(Y,X) )
                          & p1(Y) )
                      | p2(Y)
                      | p1(Y)
                      | ~ ( ! [X] :
                              ( p2(X)
                              | ~ r1(Y,X) )
                          & p2(Y) )
                      | ~ r1(X,Y) )
                  & ! [Y] :
                      ( ! [X] :
                          ( ~ ( p1(X)
                              & ! [Y] :
                                  ( p1(Y)
                                  | ~ r1(X,Y) )
                              & p1(X) )
                          | p2(X)
                          | ~ r1(Y,X) )
                      | p1(Y)
                      | ~ ( ! [X] :
                              ( p2(X)
                              | ~ r1(Y,X) )
                          & p2(Y) )
                      | ~ r1(X,Y) )
                  & ! [Y] :
                      ( ~ ( p1(Y)
                          & ! [X] :
                              ( p1(X)
                              | ~ r1(Y,X) )
                          & p1(Y) )
                      | p2(Y)
                      | ! [X] :
                          ( p1(X)
                          | ~ ( ! [Y] :
                                  ( p2(Y)
                                  | ~ r1(X,Y) )
                              & p2(X) )
                          | ~ r1(Y,X) )
                      | ~ r1(X,Y) ) )
              | ! [Y] :
                  ( ~ ( p1(Y)
                      & ! [X] :
                          ( p1(X)
                          | ~ r1(Y,X) )
                      & p1(Y) )
                  | p2(Y)
                  | ~ r1(X,Y) )
              | ! [Y] :
                  ( p1(Y)
                  | ~ ( ! [X] :
                          ( p2(X)
                          | ~ r1(Y,X) )
                      & p2(Y) )
                  | ~ r1(X,Y) ) )
          | ! [Y] :
              ( ~ ( p5(Y)
                  & ! [X] :
                      ( p5(X)
                      | ~ r1(Y,X) ) )
              | p5(Y)
              | ~ r1(X,Y) )
          | ! [Y] :
              ( ~ ( p5(Y)
                  & ! [X] :
                      ( p5(X)
                      | ~ r1(Y,X) ) )
              | p5(Y)
              | ~ r1(X,Y) )
          | ~ ( ~ ( ! [Y] :
                      ( ~ ( p2(Y)
                          & ! [X] :
                              ( p2(X)
                              | ~ r1(Y,X) )
                          & p2(Y) )
                      | p3(Y)
                      | p2(Y)
                      | ~ ( ! [X] :
                              ( p3(X)
                              | ~ r1(Y,X) )
                          & p3(Y) )
                      | ~ r1(X,Y) )
                  & ! [Y] :
                      ( ! [X] :
                          ( ~ ( p2(X)
                              & ! [Y] :
                                  ( p2(Y)
                                  | ~ r1(X,Y) )
                              & p2(X) )
                          | p3(X)
                          | ~ r1(Y,X) )
                      | p2(Y)
                      | ~ ( ! [X] :
                              ( p3(X)
                              | ~ r1(Y,X) )
                          & p3(Y) )
                      | ~ r1(X,Y) )
                  & ! [Y] :
                      ( ~ ( p2(Y)
                          & ! [X] :
                              ( p2(X)
                              | ~ r1(Y,X) )
                          & p2(Y) )
                      | p3(Y)
                      | ! [X] :
                          ( p2(X)
                          | ~ ( ! [Y] :
                                  ( p3(Y)
                                  | ~ r1(X,Y) )
                              & p3(X) )
                          | ~ r1(Y,X) )
                      | ~ r1(X,Y) ) )
              | ! [Y] :
                  ( ~ ( p2(Y)
                      & ! [X] :
                          ( p2(X)
                          | ~ r1(Y,X) )
                      & p2(Y) )
                  | p3(Y)
                  | ~ r1(X,Y) )
              | ! [Y] :
                  ( p2(Y)
                  | ~ ( ! [X] :
                          ( p3(X)
                          | ~ r1(Y,X) )
                      & p3(Y) )
                  | ~ r1(X,Y) ) )
          | ~ ( ~ ( ! [Y] :
                      ( ~ ( p3(Y)
                          & ! [X] :
                              ( p3(X)
                              | ~ r1(Y,X) )
                          & p3(Y) )
                      | p4(Y)
                      | p3(Y)
                      | ~ ( ! [X] :
                              ( p4(X)
                              | ~ r1(Y,X) )
                          & p4(Y) )
                      | ~ r1(X,Y) )
                  & ! [Y] :
                      ( ! [X] :
                          ( ~ ( p3(X)
                              & ! [Y] :
                                  ( p3(Y)
                                  | ~ r1(X,Y) )
                              & p3(X) )
                          | p4(X)
                          | ~ r1(Y,X) )
                      | p3(Y)
                      | ~ ( ! [X] :
                              ( p4(X)
                              | ~ r1(Y,X) )
                          & p4(Y) )
                      | ~ r1(X,Y) )
                  & ! [Y] :
                      ( ~ ( p3(Y)
                          & ! [X] :
                              ( p3(X)
                              | ~ r1(Y,X) )
                          & p3(Y) )
                      | p4(Y)
                      | ! [X] :
                          ( p3(X)
                          | ~ ( ! [Y] :
                                  ( p4(Y)
                                  | ~ r1(X,Y) )
                              & p4(X) )
                          | ~ r1(Y,X) )
                      | ~ r1(X,Y) ) )
              | ! [Y] :
                  ( ~ ( p3(Y)
                      & ! [X] :
                          ( p3(X)
                          | ~ r1(Y,X) )
                      & p3(Y) )
                  | p4(Y)
                  | ~ r1(X,Y) )
              | ! [Y] :
                  ( p3(Y)
                  | ~ ( ! [X] :
                          ( p4(X)
                          | ~ r1(Y,X) )
                      & p4(Y) )
                  | ~ r1(X,Y) ) )
          | ~ ( ~ ( ! [Y] :
                      ( ~ ( p4(Y)
                          & ! [X] :
                              ( p4(X)
                              | ~ r1(Y,X) )
                          & p4(Y) )
                      | p5(Y)
                      | p4(Y)
                      | ~ ( ! [X] :
                              ( p5(X)
                              | ~ r1(Y,X) )
                          & p5(Y) )
                      | ~ r1(X,Y) )
                  & ! [Y] :
                      ( ! [X] :
                          ( ~ ( p4(X)
                              & ! [Y] :
                                  ( p4(Y)
                                  | ~ r1(X,Y) )
                              & p4(X) )
                          | p5(X)
                          | ~ r1(Y,X) )
                      | p4(Y)
                      | ~ ( ! [X] :
                              ( p5(X)
                              | ~ r1(Y,X) )
                          & p5(Y) )
                      | ~ r1(X,Y) )
                  & ! [Y] :
                      ( ~ ( p4(Y)
                          & ! [X] :
                              ( p4(X)
                              | ~ r1(Y,X) )
                          & p4(Y) )
                      | p5(Y)
                      | ! [X] :
                          ( p4(X)
                          | ~ ( ! [Y] :
                                  ( p5(Y)
                                  | ~ r1(X,Y) )
                              & p5(X) )
                          | ~ r1(Y,X) )
                      | ~ r1(X,Y) ) )
              | ! [Y] :
                  ( ~ ( p4(Y)
                      & ! [X] :
                          ( p4(X)
                          | ~ r1(Y,X) )
                      & p4(Y) )
                  | p5(Y)
                  | ~ r1(X,Y) )
              | ! [Y] :
                  ( p4(Y)
                  | ~ ( ! [X] :
                          ( p5(X)
                          | ~ r1(Y,X) )
                      & p5(Y) )
                  | ~ r1(X,Y) ) )
          | ~ ( ~ ( ! [Y] :
                      ( ~ ( p5(Y)
                          & ! [X] :
                              ( p5(X)
                              | ~ r1(Y,X) )
                          & p5(Y) )
                      | p6(Y)
                      | p5(Y)
                      | ~ ( ! [X] :
                              ( p6(X)
                              | ~ r1(Y,X) )
                          & p6(Y) )
                      | ~ r1(X,Y) )
                  & ! [Y] :
                      ( ! [X] :
                          ( ~ ( p5(X)
                              & ! [Y] :
                                  ( p5(Y)
                                  | ~ r1(X,Y) )
                              & p5(X) )
                          | p6(X)
                          | ~ r1(Y,X) )
                      | p5(Y)
                      | ~ ( ! [X] :
                              ( p6(X)
                              | ~ r1(Y,X) )
                          & p6(Y) )
                      | ~ r1(X,Y) )
                  & ! [Y] :
                      ( ~ ( p5(Y)
                          & ! [X] :
                              ( p5(X)
                              | ~ r1(Y,X) )
                          & p5(Y) )
                      | p6(Y)
                      | ! [X] :
                          ( p5(X)
                          | ~ ( ! [Y] :
                                  ( p6(Y)
                                  | ~ r1(X,Y) )
                              & p6(X) )
                          | ~ r1(Y,X) )
                      | ~ r1(X,Y) ) )
              | ! [Y] :
                  ( ~ ( p5(Y)
                      & ! [X] :
                          ( p5(X)
                          | ~ r1(Y,X) )
                      & p5(Y) )
                  | p6(Y)
                  | ~ r1(X,Y) )
              | ! [Y] :
                  ( p5(Y)
                  | ~ ( ! [X] :
                          ( p6(X)
                          | ~ r1(Y,X) )
                      & p6(Y) )
                  | ~ r1(X,Y) ) ) ),
    file('theBenchmark.p',main) ).

fof(main_neg,negated_conjecture,
    ~ ~ ? [X] :
          ~ ( ~ ( ~ ( ! [Y] :
                        ( ~ ( p1(Y)
                            & ! [X] :
                                ( p1(X)
                                | ~ r1(Y,X) )
                            & p1(Y) )
                        | p2(Y)
                        | p1(Y)
                        | ~ ( ! [X] :
                                ( p2(X)
                                | ~ r1(Y,X) )
                            & p2(Y) )
                        | ~ r1(X,Y) )
                    & ! [Y] :
                        ( ! [X] :
                            ( ~ ( p1(X)
                                & ! [Y] :
                                    ( p1(Y)
                                    | ~ r1(X,Y) )
                                & p1(X) )
                            | p2(X)
                            | ~ r1(Y,X) )
                        | p1(Y)
                        | ~ ( ! [X] :
                                ( p2(X)
                                | ~ r1(Y,X) )
                            & p2(Y) )
                        | ~ r1(X,Y) )
                    & ! [Y] :
                        ( ~ ( p1(Y)
                            & ! [X] :
                                ( p1(X)
                                | ~ r1(Y,X) )
                            & p1(Y) )
                        | p2(Y)
                        | ! [X] :
                            ( p1(X)
                            | ~ ( ! [Y] :
                                    ( p2(Y)
                                    | ~ r1(X,Y) )
                                & p2(X) )
                            | ~ r1(Y,X) )
                        | ~ r1(X,Y) ) )
                | ! [Y] :
                    ( ~ ( p1(Y)
                        & ! [X] :
                            ( p1(X)
                            | ~ r1(Y,X) )
                        & p1(Y) )
                    | p2(Y)
                    | ~ r1(X,Y) )
                | ! [Y] :
                    ( p1(Y)
                    | ~ ( ! [X] :
                            ( p2(X)
                            | ~ r1(Y,X) )
                        & p2(Y) )
                    | ~ r1(X,Y) ) )
            | ! [Y] :
                ( ~ ( p5(Y)
                    & ! [X] :
                        ( p5(X)
                        | ~ r1(Y,X) ) )
                | p5(Y)
                | ~ r1(X,Y) )
            | ! [Y] :
                ( ~ ( p5(Y)
                    & ! [X] :
                        ( p5(X)
                        | ~ r1(Y,X) ) )
                | p5(Y)
                | ~ r1(X,Y) )
            | ~ ( ~ ( ! [Y] :
                        ( ~ ( p2(Y)
                            & ! [X] :
                                ( p2(X)
                                | ~ r1(Y,X) )
                            & p2(Y) )
                        | p3(Y)
                        | p2(Y)
                        | ~ ( ! [X] :
                                ( p3(X)
                                | ~ r1(Y,X) )
                            & p3(Y) )
                        | ~ r1(X,Y) )
                    & ! [Y] :
                        ( ! [X] :
                            ( ~ ( p2(X)
                                & ! [Y] :
                                    ( p2(Y)
                                    | ~ r1(X,Y) )
                                & p2(X) )
                            | p3(X)
                            | ~ r1(Y,X) )
                        | p2(Y)
                        | ~ ( ! [X] :
                                ( p3(X)
                                | ~ r1(Y,X) )
                            & p3(Y) )
                        | ~ r1(X,Y) )
                    & ! [Y] :
                        ( ~ ( p2(Y)
                            & ! [X] :
                                ( p2(X)
                                | ~ r1(Y,X) )
                            & p2(Y) )
                        | p3(Y)
                        | ! [X] :
                            ( p2(X)
                            | ~ ( ! [Y] :
                                    ( p3(Y)
                                    | ~ r1(X,Y) )
                                & p3(X) )
                            | ~ r1(Y,X) )
                        | ~ r1(X,Y) ) )
                | ! [Y] :
                    ( ~ ( p2(Y)
                        & ! [X] :
                            ( p2(X)
                            | ~ r1(Y,X) )
                        & p2(Y) )
                    | p3(Y)
                    | ~ r1(X,Y) )
                | ! [Y] :
                    ( p2(Y)
                    | ~ ( ! [X] :
                            ( p3(X)
                            | ~ r1(Y,X) )
                        & p3(Y) )
                    | ~ r1(X,Y) ) )
            | ~ ( ~ ( ! [Y] :
                        ( ~ ( p3(Y)
                            & ! [X] :
                                ( p3(X)
                                | ~ r1(Y,X) )
                            & p3(Y) )
                        | p4(Y)
                        | p3(Y)
                        | ~ ( ! [X] :
                                ( p4(X)
                                | ~ r1(Y,X) )
                            & p4(Y) )
                        | ~ r1(X,Y) )
                    & ! [Y] :
                        ( ! [X] :
                            ( ~ ( p3(X)
                                & ! [Y] :
                                    ( p3(Y)
                                    | ~ r1(X,Y) )
                                & p3(X) )
                            | p4(X)
                            | ~ r1(Y,X) )
                        | p3(Y)
                        | ~ ( ! [X] :
                                ( p4(X)
                                | ~ r1(Y,X) )
                            & p4(Y) )
                        | ~ r1(X,Y) )
                    & ! [Y] :
                        ( ~ ( p3(Y)
                            & ! [X] :
                                ( p3(X)
                                | ~ r1(Y,X) )
                            & p3(Y) )
                        | p4(Y)
                        | ! [X] :
                            ( p3(X)
                            | ~ ( ! [Y] :
                                    ( p4(Y)
                                    | ~ r1(X,Y) )
                                & p4(X) )
                            | ~ r1(Y,X) )
                        | ~ r1(X,Y) ) )
                | ! [Y] :
                    ( ~ ( p3(Y)
                        & ! [X] :
                            ( p3(X)
                            | ~ r1(Y,X) )
                        & p3(Y) )
                    | p4(Y)
                    | ~ r1(X,Y) )
                | ! [Y] :
                    ( p3(Y)
                    | ~ ( ! [X] :
                            ( p4(X)
                            | ~ r1(Y,X) )
                        & p4(Y) )
                    | ~ r1(X,Y) ) )
            | ~ ( ~ ( ! [Y] :
                        ( ~ ( p4(Y)
                            & ! [X] :
                                ( p4(X)
                                | ~ r1(Y,X) )
                            & p4(Y) )
                        | p5(Y)
                        | p4(Y)
                        | ~ ( ! [X] :
                                ( p5(X)
                                | ~ r1(Y,X) )
                            & p5(Y) )
                        | ~ r1(X,Y) )
                    & ! [Y] :
                        ( ! [X] :
                            ( ~ ( p4(X)
                                & ! [Y] :
                                    ( p4(Y)
                                    | ~ r1(X,Y) )
                                & p4(X) )
                            | p5(X)
                            | ~ r1(Y,X) )
                        | p4(Y)
                        | ~ ( ! [X] :
                                ( p5(X)
                                | ~ r1(Y,X) )
                            & p5(Y) )
                        | ~ r1(X,Y) )
                    & ! [Y] :
                        ( ~ ( p4(Y)
                            & ! [X] :
                                ( p4(X)
                                | ~ r1(Y,X) )
                            & p4(Y) )
                        | p5(Y)
                        | ! [X] :
                            ( p4(X)
                            | ~ ( ! [Y] :
                                    ( p5(Y)
                                    | ~ r1(X,Y) )
                                & p5(X) )
                            | ~ r1(Y,X) )
                        | ~ r1(X,Y) ) )
                | ! [Y] :
                    ( ~ ( p4(Y)
                        & ! [X] :
                            ( p4(X)
                            | ~ r1(Y,X) )
                        & p4(Y) )
                    | p5(Y)
                    | ~ r1(X,Y) )
                | ! [Y] :
                    ( p4(Y)
                    | ~ ( ! [X] :
                            ( p5(X)
                            | ~ r1(Y,X) )
                        & p5(Y) )
                    | ~ r1(X,Y) ) )
            | ~ ( ~ ( ! [Y] :
                        ( ~ ( p5(Y)
                            & ! [X] :
                                ( p5(X)
                                | ~ r1(Y,X) )
                            & p5(Y) )
                        | p6(Y)
                        | p5(Y)
                        | ~ ( ! [X] :
                                ( p6(X)
                                | ~ r1(Y,X) )
                            & p6(Y) )
                        | ~ r1(X,Y) )
                    & ! [Y] :
                        ( ! [X] :
                            ( ~ ( p5(X)
                                & ! [Y] :
                                    ( p5(Y)
                                    | ~ r1(X,Y) )
                                & p5(X) )
                            | p6(X)
                            | ~ r1(Y,X) )
                        | p5(Y)
                        | ~ ( ! [X] :
                                ( p6(X)
                                | ~ r1(Y,X) )
                            & p6(Y) )
                        | ~ r1(X,Y) )
                    & ! [Y] :
                        ( ~ ( p5(Y)
                            & ! [X] :
                                ( p5(X)
                                | ~ r1(Y,X) )
                            & p5(Y) )
                        | p6(Y)
                        | ! [X] :
                            ( p5(X)
                            | ~ ( ! [Y] :
                                    ( p6(Y)
                                    | ~ r1(X,Y) )
                                & p6(X) )
                            | ~ r1(Y,X) )
                        | ~ r1(X,Y) ) )
                | ! [Y] :
                    ( ~ ( p5(Y)
                        & ! [X] :
                            ( p5(X)
                            | ~ r1(Y,X) )
                        & p5(Y) )
                    | p6(Y)
                    | ~ r1(X,Y) )
                | ! [Y] :
                    ( p5(Y)
                    | ~ ( ! [X] :
                            ( p6(X)
                            | ~ r1(Y,X) )
                        & p6(Y) )
                    | ~ r1(X,Y) ) ) ),
    inference(assume_negation,[status(cth)],[main]) ).

cnf(c_2,negated_conjecture,
    $false,
    inference(clausify,[status(thm)],[main_neg]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL644+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36  % Computer : n019.cluster.edu
% 0.10/0.36  % Model    : x86_64 x86_64
% 0.10/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36  % Memory   : 8046.5625MB
% 0.10/0.36  % OS       : Linux 6.8.0-71-generic
% 0.10/0.36  % CPULimit : 300
% 0.10/0.36  % WCLimit  : 300
% 0.10/0.36  % DateTime : Fri Sep 25 22:54:34 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37  % Process 3958316 was started by sandbox2 on n019,
% 0.10/0.37  % Fri Sep 25 22:54:34 2026
% 0.10/0.37  % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 4.89/5.19  
% 4.89/5.19  % From the command line: assign(max_seconds, 300).
% 4.96/5.22  
% 4.96/5.22  % SZS status Theorem for theBenchmark
% 4.96/5.22  
% 4.96/5.22  % Proof 1 at 0.00 (+ 0.00) seconds.
% 4.96/5.22  % Length of proof is 2.
% 4.96/5.22  % Level of proof is 1.
% 4.96/5.22  % Maximum clause weight is 0.000.
% 4.96/5.22  % Given clauses 0.
% 4.96/5.22  
% 4.96/5.22  % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------