TSTP Solution File: GRA032^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : GRA032^2 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n014.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 : Mon May 20 20:41:03 EDT 2024

% Result   : Theorem 0.20s 0.55s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   42 (   5 unt;  20 typ;   0 def)
%            Number of atoms       :  310 (   7 equ;   0 cnn)
%            Maximal formula atoms :  135 (  14 avg)
%            Number of connectives : 1128 ( 181   ~; 143   |; 162   &; 632   @)
%                                         (   1 <=>;   8  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   51 (  14 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :  374 ( 374   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  20 usr;   2 con; 0-2 aty)
%            Number of variables   :   61 (   0   ^  59   !;   2   ?;  61   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    epred1_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > $o ).

thf(decl_23,type,
    epred2_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( $o > $o ) > $o ).

thf(decl_24,type,
    epred3_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( $o > $o ) > $o ).

thf(decl_25,type,
    epred4_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( $o > $o ) > $o ).

thf(decl_26,type,
    epred5_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( $o > $o ) > $o ).

thf(decl_27,type,
    epred6_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( $o > $o ) > $o ).

thf(decl_28,type,
    epred7_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ).

thf(decl_29,type,
    epred8_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ).

thf(decl_30,type,
    epred9_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( $o > $o ) > $o ).

thf(decl_31,type,
    epred10_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( $o > $o ) > $o ).

thf(decl_32,type,
    epred11_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( $o > $o ) > $o ).

thf(decl_33,type,
    epred12_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( $o > $o ) > $o ).

thf(decl_34,type,
    epred13_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( $o > $o ) > $o ).

thf(decl_35,type,
    epred14_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( $o > $o ) > $o ).

thf(decl_36,type,
    epred15_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ).

thf(decl_37,type,
    epred16_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ).

thf(decl_38,type,
    epred17_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ).

thf(decl_39,type,
    epred18_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ).

thf(decl_40,type,
    epred19_1: ( ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o ).

thf(decl_95,type,
    esk54_1: $o > $o ).

thf(ramsey_l_3_6_16a,conjecture,
    ? [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ! [X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
          ( ( X1 @ X2 @ X3 )
         => ( X1 @ X3 @ X2 ) )
      & ! [X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o,X7: ( ( $o > $o ) > $o ) > $o,X8: ( ( $o > $o ) > $o ) > $o] :
          ( ( ( X7 @ X4 )
            & ~ ( X7 @ X5 )
            & ~ ( X7 @ X6 )
            & ~ ( X8 @ X4 )
            & ( X8 @ X5 )
            & ~ ( X8 @ X6 ) )
         => ( ~ ( X1 @ X5 @ X4 )
            | ~ ( X1 @ X6 @ X4 )
            | ~ ( X1 @ X6 @ X5 ) ) )
      & ! [X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o,X9: ( $o > $o ) > $o,X10: ( $o > $o ) > $o,X11: ( $o > $o ) > $o,X7: ( ( $o > $o ) > $o ) > $o,X8: ( ( $o > $o ) > $o ) > $o,X12: ( ( $o > $o ) > $o ) > $o,X13: ( ( $o > $o ) > $o ) > $o,X14: ( ( $o > $o ) > $o ) > $o] :
          ( ( ( X7 @ X4 )
            & ~ ( X7 @ X5 )
            & ~ ( X7 @ X6 )
            & ~ ( X7 @ X9 )
            & ~ ( X7 @ X10 )
            & ~ ( X7 @ X11 )
            & ~ ( X8 @ X4 )
            & ( X8 @ X5 )
            & ~ ( X8 @ X6 )
            & ~ ( X8 @ X9 )
            & ~ ( X8 @ X10 )
            & ~ ( X8 @ X11 )
            & ~ ( X12 @ X4 )
            & ~ ( X12 @ X5 )
            & ( X12 @ X6 )
            & ~ ( X12 @ X9 )
            & ~ ( X12 @ X10 )
            & ~ ( X12 @ X11 )
            & ~ ( X13 @ X4 )
            & ~ ( X13 @ X5 )
            & ~ ( X13 @ X6 )
            & ( X13 @ X9 )
            & ~ ( X13 @ X10 )
            & ~ ( X13 @ X11 )
            & ~ ( X14 @ X4 )
            & ~ ( X14 @ X5 )
            & ~ ( X14 @ X6 )
            & ~ ( X14 @ X9 )
            & ( X14 @ X10 )
            & ~ ( X14 @ X11 ) )
         => ( ( X1 @ X5 @ X4 )
            | ( X1 @ X6 @ X4 )
            | ( X1 @ X6 @ X5 )
            | ( X1 @ X9 @ X4 )
            | ( X1 @ X9 @ X5 )
            | ( X1 @ X9 @ X6 )
            | ( X1 @ X10 @ X4 )
            | ( X1 @ X10 @ X5 )
            | ( X1 @ X10 @ X6 )
            | ( X1 @ X10 @ X9 )
            | ( X1 @ X11 @ X4 )
            | ( X1 @ X11 @ X5 )
            | ( X1 @ X11 @ X6 )
            | ( X1 @ X11 @ X9 )
            | ( X1 @ X11 @ X10 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ramsey_l_3_6_16a) ).

thf(c_0_1,plain,
    ! [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ( epred1_1 @ X1 )
    <=> ! [X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o,X9: ( $o > $o ) > $o,X10: ( $o > $o ) > $o,X11: ( $o > $o ) > $o,X7: ( ( $o > $o ) > $o ) > $o,X8: ( ( $o > $o ) > $o ) > $o,X12: ( ( $o > $o ) > $o ) > $o,X13: ( ( $o > $o ) > $o ) > $o,X14: ( ( $o > $o ) > $o ) > $o] :
          ( ( ( X7 @ X4 )
            & ~ ( X7 @ X5 )
            & ~ ( X7 @ X6 )
            & ~ ( X7 @ X9 )
            & ~ ( X7 @ X10 )
            & ~ ( X7 @ X11 )
            & ~ ( X8 @ X4 )
            & ( X8 @ X5 )
            & ~ ( X8 @ X6 )
            & ~ ( X8 @ X9 )
            & ~ ( X8 @ X10 )
            & ~ ( X8 @ X11 )
            & ~ ( X12 @ X4 )
            & ~ ( X12 @ X5 )
            & ( X12 @ X6 )
            & ~ ( X12 @ X9 )
            & ~ ( X12 @ X10 )
            & ~ ( X12 @ X11 )
            & ~ ( X13 @ X4 )
            & ~ ( X13 @ X5 )
            & ~ ( X13 @ X6 )
            & ( X13 @ X9 )
            & ~ ( X13 @ X10 )
            & ~ ( X13 @ X11 )
            & ~ ( X14 @ X4 )
            & ~ ( X14 @ X5 )
            & ~ ( X14 @ X6 )
            & ~ ( X14 @ X9 )
            & ( X14 @ X10 )
            & ~ ( X14 @ X11 ) )
         => ( ( X1 @ X5 @ X4 )
            | ( X1 @ X6 @ X4 )
            | ( X1 @ X6 @ X5 )
            | ( X1 @ X9 @ X4 )
            | ( X1 @ X9 @ X5 )
            | ( X1 @ X9 @ X6 )
            | ( X1 @ X10 @ X4 )
            | ( X1 @ X10 @ X5 )
            | ( X1 @ X10 @ X6 )
            | ( X1 @ X10 @ X9 )
            | ( X1 @ X11 @ X4 )
            | ( X1 @ X11 @ X5 )
            | ( X1 @ X11 @ X6 )
            | ( X1 @ X11 @ X9 )
            | ( X1 @ X11 @ X10 ) ) ) ),
    introduced(definition) ).

thf(c_0_2,plain,
    ! [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ! [X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o,X9: ( $o > $o ) > $o,X10: ( $o > $o ) > $o,X11: ( $o > $o ) > $o,X7: ( ( $o > $o ) > $o ) > $o,X8: ( ( $o > $o ) > $o ) > $o,X12: ( ( $o > $o ) > $o ) > $o,X13: ( ( $o > $o ) > $o ) > $o,X14: ( ( $o > $o ) > $o ) > $o] :
          ( ( ( X7 @ X4 )
            & ~ ( X7 @ X5 )
            & ~ ( X7 @ X6 )
            & ~ ( X7 @ X9 )
            & ~ ( X7 @ X10 )
            & ~ ( X7 @ X11 )
            & ~ ( X8 @ X4 )
            & ( X8 @ X5 )
            & ~ ( X8 @ X6 )
            & ~ ( X8 @ X9 )
            & ~ ( X8 @ X10 )
            & ~ ( X8 @ X11 )
            & ~ ( X12 @ X4 )
            & ~ ( X12 @ X5 )
            & ( X12 @ X6 )
            & ~ ( X12 @ X9 )
            & ~ ( X12 @ X10 )
            & ~ ( X12 @ X11 )
            & ~ ( X13 @ X4 )
            & ~ ( X13 @ X5 )
            & ~ ( X13 @ X6 )
            & ( X13 @ X9 )
            & ~ ( X13 @ X10 )
            & ~ ( X13 @ X11 )
            & ~ ( X14 @ X4 )
            & ~ ( X14 @ X5 )
            & ~ ( X14 @ X6 )
            & ~ ( X14 @ X9 )
            & ( X14 @ X10 )
            & ~ ( X14 @ X11 ) )
         => ( ( X1 @ X5 @ X4 )
            | ( X1 @ X6 @ X4 )
            | ( X1 @ X6 @ X5 )
            | ( X1 @ X9 @ X4 )
            | ( X1 @ X9 @ X5 )
            | ( X1 @ X9 @ X6 )
            | ( X1 @ X10 @ X4 )
            | ( X1 @ X10 @ X5 )
            | ( X1 @ X10 @ X6 )
            | ( X1 @ X10 @ X9 )
            | ( X1 @ X11 @ X4 )
            | ( X1 @ X11 @ X5 )
            | ( X1 @ X11 @ X6 )
            | ( X1 @ X11 @ X9 )
            | ( X1 @ X11 @ X10 ) ) )
     => ( epred1_1 @ X1 ) ),
    inference(split_equiv,[status(thm)],[c_0_1]) ).

thf(c_0_3,plain,
    ! [X42: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ( ( epred15_1 @ X42 @ ( epred9_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred15_1 @ X42 @ ( epred10_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred15_1 @ X42 @ ( epred11_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred15_1 @ X42 @ ( epred12_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred15_1 @ X42 @ ( epred13_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred15_1 @ X42 @ ( epred14_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred16_1 @ X42 @ ( epred9_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ( epred16_1 @ X42 @ ( epred10_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred16_1 @ X42 @ ( epred11_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred16_1 @ X42 @ ( epred12_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred16_1 @ X42 @ ( epred13_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred16_1 @ X42 @ ( epred14_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred17_1 @ X42 @ ( epred9_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred17_1 @ X42 @ ( epred10_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ( epred17_1 @ X42 @ ( epred11_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred17_1 @ X42 @ ( epred12_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred17_1 @ X42 @ ( epred13_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred17_1 @ X42 @ ( epred14_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred18_1 @ X42 @ ( epred9_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred18_1 @ X42 @ ( epred10_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred18_1 @ X42 @ ( epred11_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ( epred18_1 @ X42 @ ( epred12_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred18_1 @ X42 @ ( epred13_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred18_1 @ X42 @ ( epred14_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred19_1 @ X42 @ ( epred9_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred19_1 @ X42 @ ( epred10_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred19_1 @ X42 @ ( epred11_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred19_1 @ X42 @ ( epred12_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ( epred19_1 @ X42 @ ( epred13_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( epred19_1 @ X42 @ ( epred14_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred10_1 @ X42 ) @ ( epred9_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred11_1 @ X42 ) @ ( epred9_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred11_1 @ X42 ) @ ( epred10_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred12_1 @ X42 ) @ ( epred9_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred12_1 @ X42 ) @ ( epred10_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred12_1 @ X42 ) @ ( epred11_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred13_1 @ X42 ) @ ( epred9_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred13_1 @ X42 ) @ ( epred10_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred13_1 @ X42 ) @ ( epred11_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred13_1 @ X42 ) @ ( epred12_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred14_1 @ X42 ) @ ( epred9_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred14_1 @ X42 ) @ ( epred10_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred14_1 @ X42 ) @ ( epred11_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred14_1 @ X42 ) @ ( epred12_1 @ X42 ) )
        | ( epred1_1 @ X42 ) )
      & ( ~ ( X42 @ ( epred14_1 @ X42 ) @ ( epred13_1 @ X42 ) )
        | ( epred1_1 @ X42 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])]) ).

thf(c_0_4,negated_conjecture,
    ~ ? [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
        ( ! [X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
            ( ( X1 @ X2 @ X3 )
           => ( X1 @ X3 @ X2 ) )
        & ! [X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o,X7: ( ( $o > $o ) > $o ) > $o,X8: ( ( $o > $o ) > $o ) > $o] :
            ( ( ( X7 @ X4 )
              & ~ ( X7 @ X5 )
              & ~ ( X7 @ X6 )
              & ~ ( X8 @ X4 )
              & ( X8 @ X5 )
              & ~ ( X8 @ X6 ) )
           => ( ~ ( X1 @ X5 @ X4 )
              | ~ ( X1 @ X6 @ X4 )
              | ~ ( X1 @ X6 @ X5 ) ) )
        & ( epred1_1 @ X1 ) ),
    inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[ramsey_l_3_6_16a]),c_0_1]) ).

thf(c_0_5,plain,
    ! [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ( epred1_1 @ X1 )
      | ~ ( epred15_1 @ X1 @ ( epred10_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_6,plain,
    ! [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ( epred15_1 @ X1 @ ( epred9_1 @ X1 ) )
      | ( epred1_1 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_7,plain,
    ! [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ( epred1_1 @ X1 )
      | ~ ( X1 @ ( epred10_1 @ X1 ) @ ( epred9_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_8,negated_conjecture,
    ! [X34: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ( ( epred7_1 @ X34 @ ( epred4_1 @ X34 ) )
        | ( X34 @ ( epred2_1 @ X34 ) @ ( epred3_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ~ ( epred7_1 @ X34 @ ( epred5_1 @ X34 ) )
        | ( X34 @ ( epred2_1 @ X34 ) @ ( epred3_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ~ ( epred7_1 @ X34 @ ( epred6_1 @ X34 ) )
        | ( X34 @ ( epred2_1 @ X34 ) @ ( epred3_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ~ ( epred8_1 @ X34 @ ( epred4_1 @ X34 ) )
        | ( X34 @ ( epred2_1 @ X34 ) @ ( epred3_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ( epred8_1 @ X34 @ ( epred5_1 @ X34 ) )
        | ( X34 @ ( epred2_1 @ X34 ) @ ( epred3_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ~ ( epred8_1 @ X34 @ ( epred6_1 @ X34 ) )
        | ( X34 @ ( epred2_1 @ X34 ) @ ( epred3_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ( X34 @ ( epred5_1 @ X34 ) @ ( epred4_1 @ X34 ) )
        | ( X34 @ ( epred2_1 @ X34 ) @ ( epred3_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ( X34 @ ( epred6_1 @ X34 ) @ ( epred4_1 @ X34 ) )
        | ( X34 @ ( epred2_1 @ X34 ) @ ( epred3_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ( X34 @ ( epred6_1 @ X34 ) @ ( epred5_1 @ X34 ) )
        | ( X34 @ ( epred2_1 @ X34 ) @ ( epred3_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ( epred7_1 @ X34 @ ( epred4_1 @ X34 ) )
        | ~ ( X34 @ ( epred3_1 @ X34 ) @ ( epred2_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ~ ( epred7_1 @ X34 @ ( epred5_1 @ X34 ) )
        | ~ ( X34 @ ( epred3_1 @ X34 ) @ ( epred2_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ~ ( epred7_1 @ X34 @ ( epred6_1 @ X34 ) )
        | ~ ( X34 @ ( epred3_1 @ X34 ) @ ( epred2_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ~ ( epred8_1 @ X34 @ ( epred4_1 @ X34 ) )
        | ~ ( X34 @ ( epred3_1 @ X34 ) @ ( epred2_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ( epred8_1 @ X34 @ ( epred5_1 @ X34 ) )
        | ~ ( X34 @ ( epred3_1 @ X34 ) @ ( epred2_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ~ ( epred8_1 @ X34 @ ( epred6_1 @ X34 ) )
        | ~ ( X34 @ ( epred3_1 @ X34 ) @ ( epred2_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ( X34 @ ( epred5_1 @ X34 ) @ ( epred4_1 @ X34 ) )
        | ~ ( X34 @ ( epred3_1 @ X34 ) @ ( epred2_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ( X34 @ ( epred6_1 @ X34 ) @ ( epred4_1 @ X34 ) )
        | ~ ( X34 @ ( epred3_1 @ X34 ) @ ( epred2_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) )
      & ( ( X34 @ ( epred6_1 @ X34 ) @ ( epred5_1 @ X34 ) )
        | ~ ( X34 @ ( epred3_1 @ X34 ) @ ( epred2_1 @ X34 ) )
        | ~ ( epred1_1 @ X34 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).

thf(c_0_9,plain,
    ! [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ( epred1_1 @ X1 )
      | ( ( epred10_1 @ X1 )
       != ( epred9_1 @ X1 ) ) ),
    inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_5,c_0_6])]) ).

thf(c_0_10,plain,
    ( ( ( epred10_1 @ $neq )
      = ( epred9_1 @ $neq ) )
    | ( epred1_1 @ $neq ) ),
    inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_7]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ~ ( epred8_1 @ X1 @ ( epred4_1 @ X1 ) )
      | ~ ( X1 @ ( epred3_1 @ X1 ) @ ( epred2_1 @ X1 ) )
      | ~ ( epred1_1 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_12,plain,
    epred1_1 @ $neq,
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ( X1 @ ( epred2_1 @ X1 ) @ ( epred3_1 @ X1 ) )
      | ~ ( epred7_1 @ X1 @ ( epred5_1 @ X1 ) )
      | ~ ( epred1_1 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_14,negated_conjecture,
    ( ( ( epred3_1 @ $neq )
      = ( epred2_1 @ $neq ) )
    | ~ ( epred8_1 @ $neq @ ( epred4_1 @ $neq ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_11]),c_0_12])]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ( epred8_1 @ X1 @ ( epred5_1 @ X1 ) )
      | ~ ( X1 @ ( epred3_1 @ X1 ) @ ( epred2_1 @ X1 ) )
      | ~ ( epred1_1 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_16,negated_conjecture,
    ( ( ( epred3_1 @ $neq )
     != ( epred2_1 @ $neq ) )
    | ~ ( epred7_1 @ $neq @ ( epred5_1 @ $neq ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_13]),c_0_12])]) ).

thf(c_0_17,negated_conjecture,
    ! [X1: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
      ( ( epred7_1 @ X1 @ ( epred4_1 @ X1 ) )
      | ( X1 @ ( epred2_1 @ X1 ) @ ( epred3_1 @ X1 ) )
      | ~ ( epred1_1 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_18,plain,
    ( ( ( epred3_1 @ $neq )
      = ( epred2_1 @ $neq ) )
    | ( ( epred5_1 @ $neq )
     != ( epred4_1 @ $neq ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_14,c_0_15])])])]),c_0_12])]) ).

thf(c_0_19,plain,
    ( ( epred5_1 @ $neq )
   != ( epred4_1 @ $neq ) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_16,c_0_17])])])]),c_0_12])]),c_0_18]) ).

thf(c_0_20,plain,
    ( ( epred5_1 @ $neq @ esk54_1 )
  <~> ( epred4_1 @ $neq @ esk54_1 ) ),
    inference(neg_ext,[status(thm)],[c_0_19]) ).

thf(c_0_21,plain,
    $false,
    inference(dynamic_cnf,[status(thm)],[c_0_20]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : GRA032^2 : TPTP v8.2.0. Released v3.6.0.
% 0.10/0.13  % Command    : run_E %s %d THM
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat May 18 12:46:53 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.20/0.47  Running higher-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.55  # Version: 3.1.0-ho
% 0.20/0.55  # Preprocessing class: HSMSSMSSSSSNHHA.
% 0.20/0.55  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55  # Starting full_lambda_6 with 900s (3) cores
% 0.20/0.55  # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.55  # Starting lpo6_lambda_fix with 300s (1) cores
% 0.20/0.55  # Starting ho_unfolding_1 with 300s (1) cores
% 0.20/0.55  # Starting new_ho_10_unif with 300s (1) cores
% 0.20/0.55  # Starting ho_unfolding_2 with 300s (1) cores
% 0.20/0.55  # full_lambda_6 with pid 1876 completed with status 0
% 0.20/0.55  # Result found by full_lambda_6
% 0.20/0.55  # Preprocessing class: HSMSSMSSSSSNHHA.
% 0.20/0.55  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55  # Starting full_lambda_6 with 900s (3) cores
% 0.20/0.55  # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.20/0.55  # Search class: HGHNF-FFMF00-SHHFFMBN
% 0.20/0.55  # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 0.20/0.55  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.55  # Starting full_lambda_6 with 91s (1) cores
% 0.20/0.55  # Starting ho_unfolding_3 with 163s (1) cores
% 0.20/0.55  # new_ho_10 with pid 1883 completed with status 9
% 0.20/0.55  # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.20/0.55  # full_lambda_6 with pid 1885 completed with status 9
% 0.20/0.55  # Starting pre_casc_2 with 163s (1) cores
% 0.20/0.55  # ho_unfolding_3 with pid 1887 completed with status 9
% 0.20/0.55  # Starting sh3 with 157s (1) cores
% 0.20/0.55  # new_ho_10_cnf2 with pid 1895 completed with status 9
% 0.20/0.55  # pre_casc_2 with pid 1897 completed with status 9
% 0.20/0.55  # sh3 with pid 1898 completed with status 9
% 0.20/0.55  # Schedule exhausted
% 0.20/0.55  
% 0.20/0.55  # -------------------------------------------------
% 0.20/0.55  # User time                : 0.069 s
% 0.20/0.55  # System time              : 0.013 s
% 0.20/0.55  # Total time               : 0.081 s
% 0.20/0.55  # Maximum resident set size: 2044 pages
% 0.20/0.55  # executing default schedule for 899.919 seconds.
% 0.20/0.55  # Scheduled 7 strats onto 3 cores with 899 seconds (887 total)
% 0.20/0.55  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 129s (1) cores
% 0.20/0.55  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 129s (1) cores
% 0.20/0.55  # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 129s (1) cores
% 0.20/0.55  # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 1905 completed with status 9
% 0.20/0.55  # Starting lpo1_def_fix with 129s (1) cores
% 0.20/0.55  # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1903 completed with status 9
% 0.20/0.55  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 129s (1) cores
% 0.20/0.55  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1904 completed with status 9
% 0.20/0.55  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 129s (1) cores
% 0.20/0.55  # H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with pid 1909 completed with status 9
% 0.20/0.55  # Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S4S with 113s (1) cores
% 0.20/0.55  # G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 1908 completed with status 9
% 0.20/0.55  # G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S4S with pid 1913 completed with status 9
% 0.20/0.55  # lpo1_def_fix with pid 1906 completed with status 0
% 0.20/0.55  # Result found by lpo1_def_fix
% 0.20/0.55  # Preprocessing class: HSMSSMSSSSSNHHA.
% 0.20/0.55  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55  # Starting full_lambda_6 with 900s (3) cores
% 0.20/0.55  # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.20/0.55  # Search class: HGHNF-FFMF00-SHHFFMBN
% 0.20/0.55  # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 0.20/0.55  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.55  # Starting full_lambda_6 with 91s (1) cores
% 0.20/0.55  # Starting ho_unfolding_3 with 163s (1) cores
% 0.20/0.55  # new_ho_10 with pid 1883 completed with status 9
% 0.20/0.55  # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.20/0.55  # full_lambda_6 with pid 1885 completed with status 9
% 0.20/0.55  # Starting pre_casc_2 with 163s (1) cores
% 0.20/0.55  # ho_unfolding_3 with pid 1887 completed with status 9
% 0.20/0.55  # Starting sh3 with 157s (1) cores
% 0.20/0.55  # new_ho_10_cnf2 with pid 1895 completed with status 9
% 0.20/0.55  # pre_casc_2 with pid 1897 completed with status 9
% 0.20/0.55  # sh3 with pid 1898 completed with status 9
% 0.20/0.55  # Schedule exhausted
% 0.20/0.55  
% 0.20/0.55  # -------------------------------------------------
% 0.20/0.55  # User time                : 0.069 s
% 0.20/0.55  # System time              : 0.013 s
% 0.20/0.55  # Total time               : 0.081 s
% 0.20/0.55  # Maximum resident set size: 2044 pages
% 0.20/0.55  # executing default schedule for 899.919 seconds.
% 0.20/0.55  # Scheduled 7 strats onto 3 cores with 899 seconds (887 total)
% 0.20/0.55  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 129s (1) cores
% 0.20/0.55  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 129s (1) cores
% 0.20/0.55  # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 129s (1) cores
% 0.20/0.55  # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 1905 completed with status 9
% 0.20/0.55  # Starting lpo1_def_fix with 129s (1) cores
% 0.20/0.55  # Preprocessing time       : 0.002 s
% 0.20/0.55  # Presaturation interreduction done
% 0.20/0.55  
% 0.20/0.55  # Proof found!
% 0.20/0.55  # SZS status Theorem
% 0.20/0.55  # SZS output start CNFRefutation
% See solution above
% 0.20/0.55  # Parsed axioms                        : 1
% 0.20/0.55  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.55  # Initial clauses                      : 63
% 0.20/0.55  # Removed in clause preprocessing      : 0
% 0.20/0.55  # Initial clauses in saturation        : 63
% 0.20/0.55  # Processed clauses                    : 225
% 0.20/0.55  # ...of these trivial                  : 8
% 0.20/0.55  # ...subsumed                          : 39
% 0.20/0.55  # ...remaining for further processing  : 178
% 0.20/0.55  # Other redundant clauses eliminated   : 59
% 0.20/0.55  # Clauses deleted for lack of memory   : 0
% 0.20/0.55  # Backward-subsumed                    : 1
% 0.20/0.55  # Backward-rewritten                   : 1
% 0.20/0.55  # Generated clauses                    : 470
% 0.20/0.55  # ...of the previous two non-redundant : 361
% 0.20/0.55  # ...aggressively subsumed             : 0
% 0.20/0.55  # Contextual simplify-reflections      : 1
% 0.20/0.55  # Paramodulations                      : 12
% 0.20/0.55  # Factorizations                       : 0
% 0.20/0.55  # NegExts                              : 54
% 0.20/0.55  # Equation resolutions                 : 59
% 0.20/0.55  # Disequality decompositions           : 0
% 0.20/0.55  # Total rewrite steps                  : 48
% 0.20/0.55  # ...of those cached                   : 44
% 0.20/0.55  # Propositional unsat checks           : 0
% 0.20/0.55  #    Propositional check models        : 0
% 0.20/0.55  #    Propositional check unsatisfiable : 0
% 0.20/0.55  #    Propositional clauses             : 0
% 0.20/0.55  #    Propositional clauses after purity: 0
% 0.20/0.55  #    Propositional unsat core size     : 0
% 0.20/0.55  #    Propositional preprocessing time  : 0.000
% 0.20/0.55  #    Propositional encoding time       : 0.000
% 0.20/0.55  #    Propositional solver time         : 0.000
% 0.20/0.55  #    Success case prop preproc time    : 0.000
% 0.20/0.55  #    Success case prop encoding time   : 0.000
% 0.20/0.55  #    Success case prop solver time     : 0.000
% 0.20/0.55  # Current number of processed clauses  : 108
% 0.20/0.55  #    Positive orientable unit clauses  : 5
% 0.20/0.55  #    Positive unorientable unit clauses: 0
% 0.20/0.55  #    Negative unit clauses             : 2
% 0.20/0.55  #    Non-unit-clauses                  : 101
% 0.20/0.55  # Current number of unprocessed clauses: 243
% 0.20/0.55  # ...number of literals in the above   : 597
% 0.20/0.55  # Current number of archived formulas  : 0
% 0.20/0.55  # Current number of archived clauses   : 70
% 0.20/0.55  # Clause-clause subsumption calls (NU) : 1172
% 0.20/0.55  # Rec. Clause-clause subsumption calls : 939
% 0.20/0.55  # Non-unit clause-clause subsumptions  : 23
% 0.20/0.55  # Unit Clause-clause subsumption calls : 173
% 0.20/0.55  # Rewrite failures with RHS unbound    : 0
% 0.20/0.55  # BW rewrite match attempts            : 1
% 0.20/0.55  # BW rewrite match successes           : 1
% 0.20/0.55  # Condensation attempts                : 0
% 0.20/0.55  # Condensation successes               : 0
% 0.20/0.55  # Termbank termtop insertions          : 30877
% 0.20/0.55  # Search garbage collected termcells   : 1376
% 0.20/0.55  
% 0.20/0.55  # -------------------------------------------------
% 0.20/0.55  # User time                : 0.125 s
% 0.20/0.55  # System time              : 0.022 s
% 0.20/0.55  # Total time               : 0.147 s
% 0.20/0.55  # Maximum resident set size: 2100 pages
% 0.20/0.55  
% 0.20/0.55  # -------------------------------------------------
% 0.20/0.55  # User time                : 0.127 s
% 0.20/0.55  # System time              : 0.023 s
% 0.20/0.55  # Total time               : 0.150 s
% 0.20/0.55  # Maximum resident set size: 1764 pages
% 0.20/0.55  % E---3.1 exiting
% 0.20/0.55  % E exiting
%------------------------------------------------------------------------------