TSTP Solution File: GRA039^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : GRA039^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n032.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 20:41:05 EDT 2024

% Result   : Theorem 0.14s 0.47s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   61 (   8 unt;  35 typ;   0 def)
%            Number of atoms       :  470 (   5 equ;   0 cnn)
%            Maximal formula atoms :  252 (  18 avg)
%            Number of connectives : 2210 ( 388   ~; 269   |; 384   &;1156   @)
%                                         (   2 <=>;  10  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   90 (  21 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :  776 ( 776   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   38 (  35 usr;   7 con; 0-4 aty)
%            Number of variables   :   98 (   0   ^  96   !;   2   ?;  98   :)

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

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

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

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

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

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

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

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

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

thf(decl_41,type,
    epred20_1: ( ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o ) > $o > $o > $o > $o ).

thf(decl_42,type,
    epred21_1: ( ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o ) > $o > $o > $o > $o ).

thf(decl_43,type,
    epred22_1: ( ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o ) > $o > $o > $o > $o ).

thf(decl_44,type,
    epred23_1: ( ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o ) > $o > $o > $o > $o ).

thf(decl_45,type,
    epred24_1: ( ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o ) > ( $o > $o > $o > $o ) > $o ).

thf(decl_46,type,
    epred25_1: ( ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o ) > ( $o > $o > $o > $o ) > $o ).

thf(decl_47,type,
    epred26_1: ( ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o ) > ( $o > $o > $o > $o ) > $o ).

thf(decl_48,type,
    epred27_1: ( ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o ) > ( $o > $o > $o > $o ) > $o ).

thf(decl_49,type,
    epred28_1: ( ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o ) > ( $o > $o > $o > $o ) > $o ).

thf(decl_50,type,
    epred29_1: ( ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o ) > ( $o > $o > $o > $o ) > $o ).

thf(decl_51,type,
    epred30_1: ( ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o ) > ( $o > $o > $o > $o ) > $o ).

thf(decl_225,type,
    esk170_0: $o ).

thf(decl_226,type,
    esk171_0: $o ).

thf(decl_227,type,
    esk172_0: $o ).

thf(decl_513,type,
    epred67_0: $o ).

thf(decl_518,type,
    epred72_0: $o ).

thf(ramsey_l_6_8_256,conjecture,
    ? [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ! [X2: $o > $o > $o > $o,X3: $o > $o > $o > $o] :
          ( ( X1 @ X2 @ X3 )
         => ( X1 @ X3 @ X2 ) )
      & ! [X4: $o > $o > $o > $o,X5: $o > $o > $o > $o,X6: $o > $o > $o > $o,X7: $o > $o > $o > $o,X8: $o > $o > $o > $o,X9: $o > $o > $o > $o,X10: ( $o > $o > $o > $o ) > $o,X11: ( $o > $o > $o > $o ) > $o,X12: ( $o > $o > $o > $o ) > $o,X13: ( $o > $o > $o > $o ) > $o,X14: ( $o > $o > $o > $o ) > $o] :
          ( ( ( X10 @ X4 )
            & ~ ( X10 @ X5 )
            & ~ ( X10 @ X6 )
            & ~ ( X10 @ X7 )
            & ~ ( X10 @ X8 )
            & ~ ( X10 @ X9 )
            & ~ ( X11 @ X4 )
            & ( X11 @ X5 )
            & ~ ( X11 @ X6 )
            & ~ ( X11 @ X7 )
            & ~ ( X11 @ X8 )
            & ~ ( X11 @ X9 )
            & ~ ( X12 @ X4 )
            & ~ ( X12 @ X5 )
            & ( X12 @ X6 )
            & ~ ( X12 @ X7 )
            & ~ ( X12 @ X8 )
            & ~ ( X12 @ X9 )
            & ~ ( X13 @ X4 )
            & ~ ( X13 @ X5 )
            & ~ ( X13 @ X6 )
            & ( X13 @ X7 )
            & ~ ( X13 @ X8 )
            & ~ ( X13 @ X9 )
            & ~ ( X14 @ X4 )
            & ~ ( X14 @ X5 )
            & ~ ( X14 @ X6 )
            & ~ ( X14 @ X7 )
            & ( X14 @ X8 )
            & ~ ( X14 @ X9 ) )
         => ( ~ ( X1 @ X5 @ X4 )
            | ~ ( X1 @ X6 @ X4 )
            | ~ ( X1 @ X6 @ X5 )
            | ~ ( X1 @ X7 @ X4 )
            | ~ ( X1 @ X7 @ X5 )
            | ~ ( X1 @ X7 @ X6 )
            | ~ ( X1 @ X8 @ X4 )
            | ~ ( X1 @ X8 @ X5 )
            | ~ ( X1 @ X8 @ X6 )
            | ~ ( X1 @ X8 @ X7 )
            | ~ ( X1 @ X9 @ X4 )
            | ~ ( X1 @ X9 @ X5 )
            | ~ ( X1 @ X9 @ X6 )
            | ~ ( X1 @ X9 @ X7 )
            | ~ ( X1 @ X9 @ X8 ) ) )
      & ! [X4: $o > $o > $o > $o,X5: $o > $o > $o > $o,X6: $o > $o > $o > $o,X7: $o > $o > $o > $o,X8: $o > $o > $o > $o,X9: $o > $o > $o > $o,X15: $o > $o > $o > $o,X16: $o > $o > $o > $o,X10: ( $o > $o > $o > $o ) > $o,X11: ( $o > $o > $o > $o ) > $o,X12: ( $o > $o > $o > $o ) > $o,X13: ( $o > $o > $o > $o ) > $o,X14: ( $o > $o > $o > $o ) > $o,X17: ( $o > $o > $o > $o ) > $o,X18: ( $o > $o > $o > $o ) > $o] :
          ( ( ( X10 @ X4 )
            & ~ ( X10 @ X5 )
            & ~ ( X10 @ X6 )
            & ~ ( X10 @ X7 )
            & ~ ( X10 @ X8 )
            & ~ ( X10 @ X9 )
            & ~ ( X10 @ X15 )
            & ~ ( X10 @ X16 )
            & ~ ( X11 @ X4 )
            & ( X11 @ X5 )
            & ~ ( X11 @ X6 )
            & ~ ( X11 @ X7 )
            & ~ ( X11 @ X8 )
            & ~ ( X11 @ X9 )
            & ~ ( X11 @ X15 )
            & ~ ( X11 @ X16 )
            & ~ ( X12 @ X4 )
            & ~ ( X12 @ X5 )
            & ( X12 @ X6 )
            & ~ ( X12 @ X7 )
            & ~ ( X12 @ X8 )
            & ~ ( X12 @ X9 )
            & ~ ( X12 @ X15 )
            & ~ ( X12 @ X16 )
            & ~ ( X13 @ X4 )
            & ~ ( X13 @ X5 )
            & ~ ( X13 @ X6 )
            & ( X13 @ X7 )
            & ~ ( X13 @ X8 )
            & ~ ( X13 @ X9 )
            & ~ ( X13 @ X15 )
            & ~ ( X13 @ X16 )
            & ~ ( X14 @ X4 )
            & ~ ( X14 @ X5 )
            & ~ ( X14 @ X6 )
            & ~ ( X14 @ X7 )
            & ( X14 @ X8 )
            & ~ ( X14 @ X9 )
            & ~ ( X14 @ X15 )
            & ~ ( X14 @ X16 )
            & ~ ( X17 @ X4 )
            & ~ ( X17 @ X5 )
            & ~ ( X17 @ X6 )
            & ~ ( X17 @ X7 )
            & ~ ( X17 @ X8 )
            & ( X17 @ X9 )
            & ~ ( X17 @ X15 )
            & ~ ( X17 @ X16 )
            & ~ ( X18 @ X4 )
            & ~ ( X18 @ X5 )
            & ~ ( X18 @ X6 )
            & ~ ( X18 @ X7 )
            & ~ ( X18 @ X8 )
            & ~ ( X18 @ X9 )
            & ( X18 @ X15 )
            & ~ ( X18 @ X16 ) )
         => ( ( X1 @ X5 @ X4 )
            | ( X1 @ X6 @ X4 )
            | ( X1 @ X6 @ X5 )
            | ( X1 @ X7 @ X4 )
            | ( X1 @ X7 @ X5 )
            | ( X1 @ X7 @ X6 )
            | ( X1 @ X8 @ X4 )
            | ( X1 @ X8 @ X5 )
            | ( X1 @ X8 @ X6 )
            | ( X1 @ X8 @ X7 )
            | ( X1 @ X9 @ X4 )
            | ( X1 @ X9 @ X5 )
            | ( X1 @ X9 @ X6 )
            | ( X1 @ X9 @ X7 )
            | ( X1 @ X9 @ X8 )
            | ( X1 @ X15 @ X4 )
            | ( X1 @ X15 @ X5 )
            | ( X1 @ X15 @ X6 )
            | ( X1 @ X15 @ X7 )
            | ( X1 @ X15 @ X8 )
            | ( X1 @ X15 @ X9 )
            | ( X1 @ X16 @ X4 )
            | ( X1 @ X16 @ X5 )
            | ( X1 @ X16 @ X6 )
            | ( X1 @ X16 @ X7 )
            | ( X1 @ X16 @ X8 )
            | ( X1 @ X16 @ X9 )
            | ( X1 @ X16 @ X15 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ramsey_l_6_8_256) ).

thf(c_0_1,plain,
    ! [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ( epred2_1 @ X1 )
    <=> ! [X4: $o > $o > $o > $o,X5: $o > $o > $o > $o,X6: $o > $o > $o > $o,X7: $o > $o > $o > $o,X8: $o > $o > $o > $o,X9: $o > $o > $o > $o,X15: $o > $o > $o > $o,X16: $o > $o > $o > $o,X10: ( $o > $o > $o > $o ) > $o,X11: ( $o > $o > $o > $o ) > $o,X12: ( $o > $o > $o > $o ) > $o,X13: ( $o > $o > $o > $o ) > $o,X14: ( $o > $o > $o > $o ) > $o,X17: ( $o > $o > $o > $o ) > $o,X18: ( $o > $o > $o > $o ) > $o] :
          ( ( ( X10 @ X4 )
            & ~ ( X10 @ X5 )
            & ~ ( X10 @ X6 )
            & ~ ( X10 @ X7 )
            & ~ ( X10 @ X8 )
            & ~ ( X10 @ X9 )
            & ~ ( X10 @ X15 )
            & ~ ( X10 @ X16 )
            & ~ ( X11 @ X4 )
            & ( X11 @ X5 )
            & ~ ( X11 @ X6 )
            & ~ ( X11 @ X7 )
            & ~ ( X11 @ X8 )
            & ~ ( X11 @ X9 )
            & ~ ( X11 @ X15 )
            & ~ ( X11 @ X16 )
            & ~ ( X12 @ X4 )
            & ~ ( X12 @ X5 )
            & ( X12 @ X6 )
            & ~ ( X12 @ X7 )
            & ~ ( X12 @ X8 )
            & ~ ( X12 @ X9 )
            & ~ ( X12 @ X15 )
            & ~ ( X12 @ X16 )
            & ~ ( X13 @ X4 )
            & ~ ( X13 @ X5 )
            & ~ ( X13 @ X6 )
            & ( X13 @ X7 )
            & ~ ( X13 @ X8 )
            & ~ ( X13 @ X9 )
            & ~ ( X13 @ X15 )
            & ~ ( X13 @ X16 )
            & ~ ( X14 @ X4 )
            & ~ ( X14 @ X5 )
            & ~ ( X14 @ X6 )
            & ~ ( X14 @ X7 )
            & ( X14 @ X8 )
            & ~ ( X14 @ X9 )
            & ~ ( X14 @ X15 )
            & ~ ( X14 @ X16 )
            & ~ ( X17 @ X4 )
            & ~ ( X17 @ X5 )
            & ~ ( X17 @ X6 )
            & ~ ( X17 @ X7 )
            & ~ ( X17 @ X8 )
            & ( X17 @ X9 )
            & ~ ( X17 @ X15 )
            & ~ ( X17 @ X16 )
            & ~ ( X18 @ X4 )
            & ~ ( X18 @ X5 )
            & ~ ( X18 @ X6 )
            & ~ ( X18 @ X7 )
            & ~ ( X18 @ X8 )
            & ~ ( X18 @ X9 )
            & ( X18 @ X15 )
            & ~ ( X18 @ X16 ) )
         => ( ( X1 @ X5 @ X4 )
            | ( X1 @ X6 @ X4 )
            | ( X1 @ X6 @ X5 )
            | ( X1 @ X7 @ X4 )
            | ( X1 @ X7 @ X5 )
            | ( X1 @ X7 @ X6 )
            | ( X1 @ X8 @ X4 )
            | ( X1 @ X8 @ X5 )
            | ( X1 @ X8 @ X6 )
            | ( X1 @ X8 @ X7 )
            | ( X1 @ X9 @ X4 )
            | ( X1 @ X9 @ X5 )
            | ( X1 @ X9 @ X6 )
            | ( X1 @ X9 @ X7 )
            | ( X1 @ X9 @ X8 )
            | ( X1 @ X15 @ X4 )
            | ( X1 @ X15 @ X5 )
            | ( X1 @ X15 @ X6 )
            | ( X1 @ X15 @ X7 )
            | ( X1 @ X15 @ X8 )
            | ( X1 @ X15 @ X9 )
            | ( X1 @ X16 @ X4 )
            | ( X1 @ X16 @ X5 )
            | ( X1 @ X16 @ X6 )
            | ( X1 @ X16 @ X7 )
            | ( X1 @ X16 @ X8 )
            | ( X1 @ X16 @ X9 )
            | ( X1 @ X16 @ X15 ) ) ) ),
    introduced(definition) ).

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

thf(c_0_3,plain,
    ! [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ! [X4: $o > $o > $o > $o,X5: $o > $o > $o > $o,X6: $o > $o > $o > $o,X7: $o > $o > $o > $o,X8: $o > $o > $o > $o,X9: $o > $o > $o > $o,X15: $o > $o > $o > $o,X16: $o > $o > $o > $o,X10: ( $o > $o > $o > $o ) > $o,X11: ( $o > $o > $o > $o ) > $o,X12: ( $o > $o > $o > $o ) > $o,X13: ( $o > $o > $o > $o ) > $o,X14: ( $o > $o > $o > $o ) > $o,X17: ( $o > $o > $o > $o ) > $o,X18: ( $o > $o > $o > $o ) > $o] :
          ( ( ( X10 @ X4 )
            & ~ ( X10 @ X5 )
            & ~ ( X10 @ X6 )
            & ~ ( X10 @ X7 )
            & ~ ( X10 @ X8 )
            & ~ ( X10 @ X9 )
            & ~ ( X10 @ X15 )
            & ~ ( X10 @ X16 )
            & ~ ( X11 @ X4 )
            & ( X11 @ X5 )
            & ~ ( X11 @ X6 )
            & ~ ( X11 @ X7 )
            & ~ ( X11 @ X8 )
            & ~ ( X11 @ X9 )
            & ~ ( X11 @ X15 )
            & ~ ( X11 @ X16 )
            & ~ ( X12 @ X4 )
            & ~ ( X12 @ X5 )
            & ( X12 @ X6 )
            & ~ ( X12 @ X7 )
            & ~ ( X12 @ X8 )
            & ~ ( X12 @ X9 )
            & ~ ( X12 @ X15 )
            & ~ ( X12 @ X16 )
            & ~ ( X13 @ X4 )
            & ~ ( X13 @ X5 )
            & ~ ( X13 @ X6 )
            & ( X13 @ X7 )
            & ~ ( X13 @ X8 )
            & ~ ( X13 @ X9 )
            & ~ ( X13 @ X15 )
            & ~ ( X13 @ X16 )
            & ~ ( X14 @ X4 )
            & ~ ( X14 @ X5 )
            & ~ ( X14 @ X6 )
            & ~ ( X14 @ X7 )
            & ( X14 @ X8 )
            & ~ ( X14 @ X9 )
            & ~ ( X14 @ X15 )
            & ~ ( X14 @ X16 )
            & ~ ( X17 @ X4 )
            & ~ ( X17 @ X5 )
            & ~ ( X17 @ X6 )
            & ~ ( X17 @ X7 )
            & ~ ( X17 @ X8 )
            & ( X17 @ X9 )
            & ~ ( X17 @ X15 )
            & ~ ( X17 @ X16 )
            & ~ ( X18 @ X4 )
            & ~ ( X18 @ X5 )
            & ~ ( X18 @ X6 )
            & ~ ( X18 @ X7 )
            & ~ ( X18 @ X8 )
            & ~ ( X18 @ X9 )
            & ( X18 @ X15 )
            & ~ ( X18 @ X16 ) )
         => ( ( X1 @ X5 @ X4 )
            | ( X1 @ X6 @ X4 )
            | ( X1 @ X6 @ X5 )
            | ( X1 @ X7 @ X4 )
            | ( X1 @ X7 @ X5 )
            | ( X1 @ X7 @ X6 )
            | ( X1 @ X8 @ X4 )
            | ( X1 @ X8 @ X5 )
            | ( X1 @ X8 @ X6 )
            | ( X1 @ X8 @ X7 )
            | ( X1 @ X9 @ X4 )
            | ( X1 @ X9 @ X5 )
            | ( X1 @ X9 @ X6 )
            | ( X1 @ X9 @ X7 )
            | ( X1 @ X9 @ X8 )
            | ( X1 @ X15 @ X4 )
            | ( X1 @ X15 @ X5 )
            | ( X1 @ X15 @ X6 )
            | ( X1 @ X15 @ X7 )
            | ( X1 @ X15 @ X8 )
            | ( X1 @ X15 @ X9 )
            | ( X1 @ X16 @ X4 )
            | ( X1 @ X16 @ X5 )
            | ( X1 @ X16 @ X6 )
            | ( X1 @ X16 @ X7 )
            | ( X1 @ X16 @ X8 )
            | ( X1 @ X16 @ X9 )
            | ( X1 @ X16 @ X15 ) ) )
     => ( epred2_1 @ X1 ) ),
    inference(split_equiv,[status(thm)],[c_0_1]) ).

thf(c_0_4,negated_conjecture,
    ~ ? [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
        ( ! [X2: $o > $o > $o > $o,X3: $o > $o > $o > $o] :
            ( ( X1 @ X2 @ X3 )
           => ( X1 @ X3 @ X2 ) )
        & ( epred1_1 @ X1 )
        & ( epred2_1 @ X1 ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[ramsey_l_6_8_256]),c_0_2]),c_0_1]) ).

thf(c_0_5,plain,
    ! [X63: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ( ( epred24_1 @ X63 @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred24_1 @ X63 @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred24_1 @ X63 @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred24_1 @ X63 @ ( epred19_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred24_1 @ X63 @ ( epred20_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred24_1 @ X63 @ ( epred21_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred24_1 @ X63 @ ( epred22_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred24_1 @ X63 @ ( epred23_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred25_1 @ X63 @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ( epred25_1 @ X63 @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred25_1 @ X63 @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred25_1 @ X63 @ ( epred19_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred25_1 @ X63 @ ( epred20_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred25_1 @ X63 @ ( epred21_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred25_1 @ X63 @ ( epred22_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred25_1 @ X63 @ ( epred23_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred26_1 @ X63 @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred26_1 @ X63 @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ( epred26_1 @ X63 @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred26_1 @ X63 @ ( epred19_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred26_1 @ X63 @ ( epred20_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred26_1 @ X63 @ ( epred21_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred26_1 @ X63 @ ( epred22_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred26_1 @ X63 @ ( epred23_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred27_1 @ X63 @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred27_1 @ X63 @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred27_1 @ X63 @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ( epred27_1 @ X63 @ ( epred19_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred27_1 @ X63 @ ( epred20_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred27_1 @ X63 @ ( epred21_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred27_1 @ X63 @ ( epred22_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred27_1 @ X63 @ ( epred23_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred28_1 @ X63 @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred28_1 @ X63 @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred28_1 @ X63 @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred28_1 @ X63 @ ( epred19_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ( epred28_1 @ X63 @ ( epred20_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred28_1 @ X63 @ ( epred21_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred28_1 @ X63 @ ( epred22_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred28_1 @ X63 @ ( epred23_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred29_1 @ X63 @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred29_1 @ X63 @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred29_1 @ X63 @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred29_1 @ X63 @ ( epred19_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred29_1 @ X63 @ ( epred20_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ( epred29_1 @ X63 @ ( epred21_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred29_1 @ X63 @ ( epred22_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred29_1 @ X63 @ ( epred23_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred30_1 @ X63 @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred30_1 @ X63 @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred30_1 @ X63 @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred30_1 @ X63 @ ( epred19_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred30_1 @ X63 @ ( epred20_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred30_1 @ X63 @ ( epred21_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ( epred30_1 @ X63 @ ( epred22_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( epred30_1 @ X63 @ ( epred23_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred17_1 @ X63 ) @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred18_1 @ X63 ) @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred18_1 @ X63 ) @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred19_1 @ X63 ) @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred19_1 @ X63 ) @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred19_1 @ X63 ) @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred20_1 @ X63 ) @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred20_1 @ X63 ) @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred20_1 @ X63 ) @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred20_1 @ X63 ) @ ( epred19_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred21_1 @ X63 ) @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred21_1 @ X63 ) @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred21_1 @ X63 ) @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred21_1 @ X63 ) @ ( epred19_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred21_1 @ X63 ) @ ( epred20_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred22_1 @ X63 ) @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred22_1 @ X63 ) @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred22_1 @ X63 ) @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred22_1 @ X63 ) @ ( epred19_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred22_1 @ X63 ) @ ( epred20_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred22_1 @ X63 ) @ ( epred21_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred23_1 @ X63 ) @ ( epred16_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred23_1 @ X63 ) @ ( epred17_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred23_1 @ X63 ) @ ( epred18_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred23_1 @ X63 ) @ ( epred19_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred23_1 @ X63 ) @ ( epred20_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred23_1 @ X63 ) @ ( epred21_1 @ X63 ) )
        | ( epred2_1 @ X63 ) )
      & ( ~ ( X63 @ ( epred23_1 @ X63 ) @ ( epred22_1 @ X63 ) )
        | ( epred2_1 @ X63 ) ) ),
    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_3])])])])]) ).

thf(c_0_6,negated_conjecture,
    ! [X48: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ( ( X48 @ ( epred3_1 @ X48 ) @ ( epred4_1 @ X48 ) )
        | ~ ( epred1_1 @ X48 )
        | ~ ( epred2_1 @ X48 ) )
      & ( ~ ( X48 @ ( epred4_1 @ X48 ) @ ( epred3_1 @ X48 ) )
        | ~ ( epred1_1 @ X48 )
        | ~ ( epred2_1 @ X48 ) ) ),
    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_4])])])])]) ).

thf(c_0_7,plain,
    ! [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ( epred2_1 @ X1 )
      | ~ ( epred24_1 @ X1 @ ( epred17_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_8,plain,
    ! [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ( epred24_1 @ X1 @ ( epred16_1 @ X1 ) )
      | ( epred2_1 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_9,plain,
    ! [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ( epred2_1 @ X1 )
      | ~ ( X1 @ ( epred17_1 @ X1 ) @ ( epred16_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ~ ( X1 @ ( epred4_1 @ X1 ) @ ( epred3_1 @ X1 ) )
      | ~ ( epred1_1 @ X1 )
      | ~ ( epred2_1 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_11,plain,
    ! [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ( epred2_1 @ X1 )
      | ( ( epred17_1 @ X1 )
       != ( epred16_1 @ X1 ) ) ),
    inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_7,c_0_8])]) ).

thf(c_0_12,plain,
    ( ( ( epred17_1 @ $neq )
      = ( epred16_1 @ $neq ) )
    | ( epred2_1 @ $neq ) ),
    inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_9]) ).

thf(c_0_13,plain,
    ! [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ! [X4: $o > $o > $o > $o,X5: $o > $o > $o > $o,X6: $o > $o > $o > $o,X7: $o > $o > $o > $o,X8: $o > $o > $o > $o,X9: $o > $o > $o > $o,X10: ( $o > $o > $o > $o ) > $o,X11: ( $o > $o > $o > $o ) > $o,X12: ( $o > $o > $o > $o ) > $o,X13: ( $o > $o > $o > $o ) > $o,X14: ( $o > $o > $o > $o ) > $o] :
          ( ( ( X10 @ X4 )
            & ~ ( X10 @ X5 )
            & ~ ( X10 @ X6 )
            & ~ ( X10 @ X7 )
            & ~ ( X10 @ X8 )
            & ~ ( X10 @ X9 )
            & ~ ( X11 @ X4 )
            & ( X11 @ X5 )
            & ~ ( X11 @ X6 )
            & ~ ( X11 @ X7 )
            & ~ ( X11 @ X8 )
            & ~ ( X11 @ X9 )
            & ~ ( X12 @ X4 )
            & ~ ( X12 @ X5 )
            & ( X12 @ X6 )
            & ~ ( X12 @ X7 )
            & ~ ( X12 @ X8 )
            & ~ ( X12 @ X9 )
            & ~ ( X13 @ X4 )
            & ~ ( X13 @ X5 )
            & ~ ( X13 @ X6 )
            & ( X13 @ X7 )
            & ~ ( X13 @ X8 )
            & ~ ( X13 @ X9 )
            & ~ ( X14 @ X4 )
            & ~ ( X14 @ X5 )
            & ~ ( X14 @ X6 )
            & ~ ( X14 @ X7 )
            & ( X14 @ X8 )
            & ~ ( X14 @ X9 ) )
         => ( ~ ( X1 @ X5 @ X4 )
            | ~ ( X1 @ X6 @ X4 )
            | ~ ( X1 @ X6 @ X5 )
            | ~ ( X1 @ X7 @ X4 )
            | ~ ( X1 @ X7 @ X5 )
            | ~ ( X1 @ X7 @ X6 )
            | ~ ( X1 @ X8 @ X4 )
            | ~ ( X1 @ X8 @ X5 )
            | ~ ( X1 @ X8 @ X6 )
            | ~ ( X1 @ X8 @ X7 )
            | ~ ( X1 @ X9 @ X4 )
            | ~ ( X1 @ X9 @ X5 )
            | ~ ( X1 @ X9 @ X6 )
            | ~ ( X1 @ X9 @ X7 )
            | ~ ( X1 @ X9 @ X8 ) ) )
     => ( epred1_1 @ X1 ) ),
    inference(split_equiv,[status(thm)],[c_0_2]) ).

thf(c_0_14,negated_conjecture,
    ( ( ( epred4_1 @ $neq )
      = ( epred3_1 @ $neq ) )
    | ~ ( epred1_1 @ $neq )
    | ~ ( epred2_1 @ $neq ) ),
    inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_10]) ).

thf(c_0_15,plain,
    epred2_1 @ $neq,
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_16,plain,
    ! [X51: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ( ( epred11_1 @ X51 @ ( epred5_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred11_1 @ X51 @ ( epred6_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred11_1 @ X51 @ ( epred7_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred11_1 @ X51 @ ( epred8_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred11_1 @ X51 @ ( epred9_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred11_1 @ X51 @ ( epred10_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred12_1 @ X51 @ ( epred5_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( epred12_1 @ X51 @ ( epred6_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred12_1 @ X51 @ ( epred7_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred12_1 @ X51 @ ( epred8_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred12_1 @ X51 @ ( epred9_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred12_1 @ X51 @ ( epred10_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred13_1 @ X51 @ ( epred5_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred13_1 @ X51 @ ( epred6_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( epred13_1 @ X51 @ ( epred7_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred13_1 @ X51 @ ( epred8_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred13_1 @ X51 @ ( epred9_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred13_1 @ X51 @ ( epred10_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred14_1 @ X51 @ ( epred5_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred14_1 @ X51 @ ( epred6_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred14_1 @ X51 @ ( epred7_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( epred14_1 @ X51 @ ( epred8_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred14_1 @ X51 @ ( epred9_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred14_1 @ X51 @ ( epred10_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred15_1 @ X51 @ ( epred5_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred15_1 @ X51 @ ( epred6_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred15_1 @ X51 @ ( epred7_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred15_1 @ X51 @ ( epred8_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( epred15_1 @ X51 @ ( epred9_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ~ ( epred15_1 @ X51 @ ( epred10_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred6_1 @ X51 ) @ ( epred5_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred7_1 @ X51 ) @ ( epred5_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred7_1 @ X51 ) @ ( epred6_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred8_1 @ X51 ) @ ( epred5_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred8_1 @ X51 ) @ ( epred6_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred8_1 @ X51 ) @ ( epred7_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred9_1 @ X51 ) @ ( epred5_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred9_1 @ X51 ) @ ( epred6_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred9_1 @ X51 ) @ ( epred7_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred9_1 @ X51 ) @ ( epred8_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred10_1 @ X51 ) @ ( epred5_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred10_1 @ X51 ) @ ( epred6_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred10_1 @ X51 ) @ ( epred7_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred10_1 @ X51 ) @ ( epred8_1 @ X51 ) )
        | ( epred1_1 @ X51 ) )
      & ( ( X51 @ ( epred10_1 @ X51 ) @ ( epred9_1 @ X51 ) )
        | ( epred1_1 @ X51 ) ) ),
    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_13])])])])]) ).

thf(c_0_17,negated_conjecture,
    ! [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ( X1 @ ( epred3_1 @ X1 ) @ ( epred4_1 @ X1 ) )
      | ~ ( epred1_1 @ X1 )
      | ~ ( epred2_1 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_18,negated_conjecture,
    ( ( ( epred4_1 @ $neq )
      = ( epred3_1 @ $neq ) )
    | ~ ( epred1_1 @ $neq ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).

thf(c_0_19,plain,
    ! [X1: ( $o > $o > $o > $o ) > ( $o > $o > $o > $o ) > $o] :
      ( ( X1 @ ( epred10_1 @ X1 ) @ ( epred5_1 @ X1 ) )
      | ( epred1_1 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_20,negated_conjecture,
    ~ ( epred1_1 @ $neq ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_17]),c_0_15])]),c_0_18]) ).

thf(c_0_21,plain,
    ( ( epred10_1 @ $neq )
   != ( epred5_1 @ $neq ) ),
    inference(sr,[status(thm)],[inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_19]),c_0_20]) ).

thf(c_0_22,plain,
    ( ( epred10_1 @ $neq @ esk170_0 @ esk171_0 @ esk172_0 )
  <~> ( epred5_1 @ $neq @ esk170_0 @ esk171_0 @ esk172_0 ) ),
    inference(neg_ext,[status(thm)],[c_0_21]) ).

thf(c_0_23,plain,
    epred67_0,
    inference(dynamic_cnf,[status(thm)],[c_0_22]) ).

thf(c_0_24,plain,
    epred72_0,
    inference(dynamic_cnf,[status(thm)],[c_0_22]) ).

thf(c_0_25,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_22]),c_0_23]),c_0_24])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : GRA039^1 : TPTP v8.2.0. Released v3.6.0.
% 0.00/0.10  % Command    : run_E %s %d THM
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit   : 300
% 0.10/0.29  % WCLimit    : 300
% 0.10/0.29  % DateTime   : Sat May 18 12:32:52 EDT 2024
% 0.10/0.29  % CPUTime    : 
% 0.14/0.39  Running higher-order theorem proving
% 0.14/0.39  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
% 0.14/0.47  # Version: 3.1.0-ho
% 0.14/0.47  # Preprocessing class: HSMSSMSSSSSNHHA.
% 0.14/0.47  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47  # Starting full_lambda_6 with 900s (3) cores
% 0.14/0.47  # Starting post_as_ho1 with 300s (1) cores
% 0.14/0.47  # Starting lpo6_lambda_fix with 300s (1) cores
% 0.14/0.47  # Starting ho_unfolding_1 with 300s (1) cores
% 0.14/0.47  # Starting new_ho_10_unif with 300s (1) cores
% 0.14/0.47  # Starting ho_unfolding_2 with 300s (1) cores
% 0.14/0.47  # full_lambda_6 with pid 24342 completed with status 0
% 0.14/0.47  # Result found by full_lambda_6
% 0.14/0.47  # Preprocessing class: HSMSSMSSSSSNHHA.
% 0.14/0.47  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47  # Starting full_lambda_6 with 900s (3) cores
% 0.14/0.47  # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.14/0.47  # Search class: HGHNF-FFMF00-SHHFFSBN
% 0.14/0.47  # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 0.14/0.47  # Starting sh2lt with 185s (1) cores
% 0.14/0.47  # Starting full_lambda_6 with 91s (1) cores
% 0.14/0.47  # Starting new_bool_1 with 184s (1) cores
% 0.14/0.47  # sh2lt with pid 24348 completed with status 0
% 0.14/0.47  # Result found by sh2lt
% 0.14/0.47  # Preprocessing class: HSMSSMSSSSSNHHA.
% 0.14/0.47  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47  # Starting full_lambda_6 with 900s (3) cores
% 0.14/0.47  # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.14/0.47  # Search class: HGHNF-FFMF00-SHHFFSBN
% 0.14/0.47  # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 0.14/0.47  # Starting sh2lt with 185s (1) cores
% 0.14/0.47  # Preprocessing time       : 0.001 s
% 0.14/0.47  # Presaturation interreduction done
% 0.14/0.47  
% 0.14/0.47  # Proof found!
% 0.14/0.47  # SZS status Theorem
% 0.14/0.47  # SZS output start CNFRefutation
% See solution above
% 0.14/0.47  # Parsed axioms                        : 1
% 0.14/0.47  # Removed by relevancy pruning/SinE    : 0
% 0.14/0.47  # Initial clauses                      : 131
% 0.14/0.47  # Removed in clause preprocessing      : 0
% 0.14/0.47  # Initial clauses in saturation        : 131
% 0.14/0.47  # Processed clauses                    : 674
% 0.14/0.47  # ...of these trivial                  : 44
% 0.14/0.47  # ...subsumed                          : 91
% 0.14/0.47  # ...remaining for further processing  : 538
% 0.14/0.47  # Other redundant clauses eliminated   : 74
% 0.14/0.47  # Clauses deleted for lack of memory   : 0
% 0.14/0.47  # Backward-subsumed                    : 11
% 0.14/0.47  # Backward-rewritten                   : 5
% 0.14/0.47  # Generated clauses                    : 2327
% 0.14/0.47  # ...of the previous two non-redundant : 1603
% 0.14/0.47  # ...aggressively subsumed             : 0
% 0.14/0.47  # Contextual simplify-reflections      : 2
% 0.14/0.47  # Paramodulations                      : 54
% 0.14/0.47  # Factorizations                       : 0
% 0.14/0.47  # NegExts                              : 425
% 0.14/0.47  # Equation resolutions                 : 74
% 0.14/0.47  # Disequality decompositions           : 0
% 0.14/0.47  # Total rewrite steps                  : 90
% 0.14/0.47  # ...of those cached                   : 86
% 0.14/0.47  # Propositional unsat checks           : 0
% 0.14/0.47  #    Propositional check models        : 0
% 0.14/0.47  #    Propositional check unsatisfiable : 0
% 0.14/0.47  #    Propositional clauses             : 0
% 0.14/0.47  #    Propositional clauses after purity: 0
% 0.14/0.47  #    Propositional unsat core size     : 0
% 0.14/0.47  #    Propositional preprocessing time  : 0.000
% 0.14/0.47  #    Propositional encoding time       : 0.000
% 0.14/0.47  #    Propositional solver time         : 0.000
% 0.14/0.47  #    Success case prop preproc time    : 0.000
% 0.14/0.47  #    Success case prop encoding time   : 0.000
% 0.14/0.47  #    Success case prop solver time     : 0.000
% 0.14/0.47  # Current number of processed clauses  : 382
% 0.14/0.47  #    Positive orientable unit clauses  : 4
% 0.14/0.47  #    Positive unorientable unit clauses: 0
% 0.14/0.47  #    Negative unit clauses             : 136
% 0.14/0.47  #    Non-unit-clauses                  : 242
% 0.14/0.47  # Current number of unprocessed clauses: 1177
% 0.14/0.47  # ...number of literals in the above   : 3818
% 0.14/0.47  # Current number of archived formulas  : 0
% 0.14/0.47  # Current number of archived clauses   : 156
% 0.14/0.47  # Clause-clause subsumption calls (NU) : 7751
% 0.14/0.47  # Rec. Clause-clause subsumption calls : 5839
% 0.14/0.47  # Non-unit clause-clause subsumptions  : 67
% 0.14/0.47  # Unit Clause-clause subsumption calls : 1000
% 0.14/0.47  # Rewrite failures with RHS unbound    : 0
% 0.14/0.47  # BW rewrite match attempts            : 2
% 0.14/0.47  # BW rewrite match successes           : 2
% 0.14/0.47  # Condensation attempts                : 0
% 0.14/0.47  # Condensation successes               : 0
% 0.14/0.47  # Termbank termtop insertions          : 199070
% 0.14/0.47  # Search garbage collected termcells   : 2993
% 0.14/0.47  
% 0.14/0.47  # -------------------------------------------------
% 0.14/0.47  # User time                : 0.067 s
% 0.14/0.47  # System time              : 0.005 s
% 0.14/0.47  # Total time               : 0.072 s
% 0.14/0.47  # Maximum resident set size: 2372 pages
% 0.14/0.47  
% 0.14/0.47  # -------------------------------------------------
% 0.14/0.47  # User time                : 0.172 s
% 0.14/0.47  # System time              : 0.013 s
% 0.14/0.47  # Total time               : 0.185 s
% 0.14/0.47  # Maximum resident set size: 1764 pages
% 0.14/0.47  % E---3.1 exiting
% 0.14/0.47  % E exiting
%------------------------------------------------------------------------------