TSTP Solution File: SYO386^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO386^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n010.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 : Tue May 21 08:45:49 EDT 2024

% Result   : Theorem 0.20s 0.48s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   54 (  13 unt;  12 typ;   0 def)
%            Number of atoms       :  231 (   0 equ;   0 cnn)
%            Maximal formula atoms :   35 (   5 avg)
%            Number of connectives :  911 ( 149   ~; 132   |;  57   &; 573   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   58 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  12 usr;   5 con; 0-3 aty)
%            Number of variables   :  219 (   0   ^ 219   !;   0   ?; 219   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    cQ_4: $i > $i > $i > $o ).

thf(decl_23,type,
    f: $i > $i ).

thf(decl_24,type,
    cP_3: $i > $i > $o ).

thf(decl_25,type,
    cQ_3: $i > $i > $i > $o ).

thf(decl_26,type,
    d: $i ).

thf(decl_27,type,
    c: $i ).

thf(decl_28,type,
    b: $i ).

thf(decl_29,type,
    a: $i ).

thf(decl_30,type,
    cP_2: $i > $i > $o ).

thf(decl_31,type,
    cQ_2: $i > $i > $i > $o ).

thf(decl_32,type,
    cP_1: $i > $i > $o ).

thf(decl_33,type,
    cQ_1: $i > $i > $i > $o ).

thf(cTHM409_3,conjecture,
    ~ ( ( cQ_1 @ a @ b @ c )
      & ( cP_1 @ a @ a )
      & ( cP_1 @ b @ b )
      & ( cP_1 @ c @ c )
      & ! [X1: $i] : ( cP_1 @ d @ X1 )
      & ! [X1: $i,X2: $i] :
          ( ~ ( cP_1 @ X1 @ X2 )
          | ( cP_1 @ ( f @ X1 ) @ X2 ) )
      & ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
          ( ~ ( cQ_1 @ X1 @ X2 @ X3 )
          | ~ ( cP_1 @ ( f @ X1 ) @ X4 )
          | ~ ( cP_1 @ ( f @ X2 ) @ X5 )
          | ~ ( cP_1 @ ( f @ X3 ) @ X6 )
          | ( cQ_2 @ X4 @ X5 @ X6 ) )
      & ( cP_2 @ a @ a )
      & ( cP_2 @ b @ b )
      & ( cP_2 @ c @ c )
      & ! [X1: $i] : ( cP_2 @ d @ X1 )
      & ! [X1: $i,X2: $i] :
          ( ~ ( cP_2 @ X1 @ X2 )
          | ( cP_2 @ ( f @ X1 ) @ X2 ) )
      & ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
          ( ~ ( cQ_2 @ X1 @ X2 @ X3 )
          | ~ ( cP_2 @ ( f @ X1 ) @ X4 )
          | ~ ( cP_2 @ ( f @ X2 ) @ X5 )
          | ~ ( cP_2 @ ( f @ X3 ) @ X6 )
          | ( cQ_3 @ X4 @ X5 @ X6 ) )
      & ( cP_3 @ a @ a )
      & ( cP_3 @ b @ b )
      & ( cP_3 @ c @ c )
      & ! [X1: $i] : ( cP_3 @ d @ X1 )
      & ! [X1: $i,X2: $i] :
          ( ~ ( cP_3 @ X1 @ X2 )
          | ( cP_3 @ ( f @ X1 ) @ X2 ) )
      & ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
          ( ~ ( cQ_3 @ X1 @ X2 @ X3 )
          | ~ ( cP_3 @ ( f @ X1 ) @ X4 )
          | ~ ( cP_3 @ ( f @ X2 ) @ X5 )
          | ~ ( cP_3 @ ( f @ X3 ) @ X6 )
          | ( cQ_4 @ X4 @ X5 @ X6 ) )
      & ! [X1: $i,X2: $i,X3: $i] :
          ~ ( cQ_4 @ X1 @ X2 @ X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM409_3) ).

thf(c_0_1,negated_conjecture,
    ~ ~ ( ( cQ_1 @ a @ b @ c )
        & ( cP_1 @ a @ a )
        & ( cP_1 @ b @ b )
        & ( cP_1 @ c @ c )
        & ! [X1: $i] : ( cP_1 @ d @ X1 )
        & ! [X1: $i,X2: $i] :
            ( ~ ( cP_1 @ X1 @ X2 )
            | ( cP_1 @ ( f @ X1 ) @ X2 ) )
        & ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
            ( ~ ( cQ_1 @ X1 @ X2 @ X3 )
            | ~ ( cP_1 @ ( f @ X1 ) @ X4 )
            | ~ ( cP_1 @ ( f @ X2 ) @ X5 )
            | ~ ( cP_1 @ ( f @ X3 ) @ X6 )
            | ( cQ_2 @ X4 @ X5 @ X6 ) )
        & ( cP_2 @ a @ a )
        & ( cP_2 @ b @ b )
        & ( cP_2 @ c @ c )
        & ! [X1: $i] : ( cP_2 @ d @ X1 )
        & ! [X1: $i,X2: $i] :
            ( ~ ( cP_2 @ X1 @ X2 )
            | ( cP_2 @ ( f @ X1 ) @ X2 ) )
        & ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
            ( ~ ( cQ_2 @ X1 @ X2 @ X3 )
            | ~ ( cP_2 @ ( f @ X1 ) @ X4 )
            | ~ ( cP_2 @ ( f @ X2 ) @ X5 )
            | ~ ( cP_2 @ ( f @ X3 ) @ X6 )
            | ( cQ_3 @ X4 @ X5 @ X6 ) )
        & ( cP_3 @ a @ a )
        & ( cP_3 @ b @ b )
        & ( cP_3 @ c @ c )
        & ! [X1: $i] : ( cP_3 @ d @ X1 )
        & ! [X1: $i,X2: $i] :
            ( ~ ( cP_3 @ X1 @ X2 )
            | ( cP_3 @ ( f @ X1 ) @ X2 ) )
        & ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
            ( ~ ( cQ_3 @ X1 @ X2 @ X3 )
            | ~ ( cP_3 @ ( f @ X1 ) @ X4 )
            | ~ ( cP_3 @ ( f @ X2 ) @ X5 )
            | ~ ( cP_3 @ ( f @ X3 ) @ X6 )
            | ( cQ_4 @ X4 @ X5 @ X6 ) )
        & ! [X1: $i,X2: $i,X3: $i] :
            ~ ( cQ_4 @ X1 @ X2 @ X3 ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[cTHM409_3])]) ).

thf(c_0_2,negated_conjecture,
    ! [X37: $i,X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i,X50: $i,X51: $i,X52: $i,X53: $i,X54: $i,X55: $i,X56: $i,X57: $i,X58: $i,X59: $i,X60: $i,X61: $i,X62: $i,X63: $i,X64: $i,X65: $i,X66: $i] :
      ( ( cQ_1 @ a @ b @ c )
      & ( cP_1 @ a @ a )
      & ( cP_1 @ b @ b )
      & ( cP_1 @ c @ c )
      & ( cP_1 @ d @ X37 )
      & ( ~ ( cP_1 @ X38 @ X39 )
        | ( cP_1 @ ( f @ X38 ) @ X39 ) )
      & ( ~ ( cQ_1 @ X40 @ X41 @ X42 )
        | ~ ( cP_1 @ ( f @ X40 ) @ X43 )
        | ~ ( cP_1 @ ( f @ X41 ) @ X44 )
        | ~ ( cP_1 @ ( f @ X42 ) @ X45 )
        | ( cQ_2 @ X43 @ X44 @ X45 ) )
      & ( cP_2 @ a @ a )
      & ( cP_2 @ b @ b )
      & ( cP_2 @ c @ c )
      & ( cP_2 @ d @ X46 )
      & ( ~ ( cP_2 @ X47 @ X48 )
        | ( cP_2 @ ( f @ X47 ) @ X48 ) )
      & ( ~ ( cQ_2 @ X49 @ X50 @ X51 )
        | ~ ( cP_2 @ ( f @ X49 ) @ X52 )
        | ~ ( cP_2 @ ( f @ X50 ) @ X53 )
        | ~ ( cP_2 @ ( f @ X51 ) @ X54 )
        | ( cQ_3 @ X52 @ X53 @ X54 ) )
      & ( cP_3 @ a @ a )
      & ( cP_3 @ b @ b )
      & ( cP_3 @ c @ c )
      & ( cP_3 @ d @ X55 )
      & ( ~ ( cP_3 @ X56 @ X57 )
        | ( cP_3 @ ( f @ X56 ) @ X57 ) )
      & ( ~ ( cQ_3 @ X58 @ X59 @ X60 )
        | ~ ( cP_3 @ ( f @ X58 ) @ X61 )
        | ~ ( cP_3 @ ( f @ X59 ) @ X62 )
        | ~ ( cP_3 @ ( f @ X60 ) @ X63 )
        | ( cQ_4 @ X61 @ X62 @ X63 ) )
      & ~ ( cQ_4 @ X64 @ X65 @ X66 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])]) ).

thf(c_0_3,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i,X5: $i,X4: $i,X6: $i] :
      ( ( cQ_2 @ X4 @ X5 @ X6 )
      | ~ ( cQ_1 @ X1 @ X2 @ X3 )
      | ~ ( cP_1 @ ( f @ X1 ) @ X4 )
      | ~ ( cP_1 @ ( f @ X2 ) @ X5 )
      | ~ ( cP_1 @ ( f @ X3 ) @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_4,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( cP_1 @ ( f @ X1 ) @ X2 )
      | ~ ( cP_1 @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_5,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i,X5: $i,X4: $i,X6: $i] :
      ( ( cQ_3 @ X4 @ X5 @ X6 )
      | ~ ( cQ_2 @ X1 @ X2 @ X3 )
      | ~ ( cP_2 @ ( f @ X1 ) @ X4 )
      | ~ ( cP_2 @ ( f @ X2 ) @ X5 )
      | ~ ( cP_2 @ ( f @ X3 ) @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_6,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( cP_2 @ ( f @ X1 ) @ X2 )
      | ~ ( cP_2 @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_7,negated_conjecture,
    ! [X1: $i,X2: $i,X4: $i,X6: $i,X5: $i,X3: $i] :
      ( ( cQ_2 @ X1 @ X2 @ X3 )
      | ~ ( cP_1 @ ( f @ X4 ) @ X2 )
      | ~ ( cP_1 @ ( f @ X5 ) @ X1 )
      | ~ ( cQ_1 @ X5 @ X4 @ X6 )
      | ~ ( cP_1 @ X6 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_3,c_0_4]) ).

thf(c_0_8,negated_conjecture,
    ! [X1: $i,X2: $i,X4: $i,X6: $i,X5: $i,X3: $i] :
      ( ( cQ_3 @ X1 @ X2 @ X3 )
      | ~ ( cP_2 @ ( f @ X4 ) @ X2 )
      | ~ ( cP_2 @ ( f @ X5 ) @ X1 )
      | ~ ( cQ_2 @ X5 @ X4 @ X6 )
      | ~ ( cP_2 @ X6 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

thf(c_0_9,negated_conjecture,
    ! [X1: $i,X4: $i,X6: $i,X5: $i,X3: $i,X2: $i] :
      ( ( cQ_2 @ X1 @ X2 @ X3 )
      | ~ ( cP_1 @ ( f @ X4 ) @ X1 )
      | ~ ( cQ_1 @ X4 @ X5 @ X6 )
      | ~ ( cP_1 @ X6 @ X3 )
      | ~ ( cP_1 @ X5 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_7,c_0_4]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i,X4: $i,X6: $i,X5: $i,X3: $i,X2: $i] :
      ( ( cQ_3 @ X1 @ X2 @ X3 )
      | ~ ( cP_2 @ ( f @ X4 ) @ X1 )
      | ~ ( cQ_2 @ X4 @ X5 @ X6 )
      | ~ ( cP_2 @ X6 @ X3 )
      | ~ ( cP_2 @ X5 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_8,c_0_6]) ).

thf(c_0_11,negated_conjecture,
    ! [X2: $i,X6: $i,X5: $i,X4: $i,X3: $i,X1: $i] :
      ( ( cQ_2 @ X1 @ X2 @ X3 )
      | ~ ( cQ_1 @ X4 @ X5 @ X6 )
      | ~ ( cP_1 @ X6 @ X3 )
      | ~ ( cP_1 @ X5 @ X2 )
      | ~ ( cP_1 @ X4 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_4]) ).

thf(c_0_12,negated_conjecture,
    cQ_1 @ a @ b @ c,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i,X5: $i,X4: $i,X6: $i] :
      ( ( cQ_4 @ X4 @ X5 @ X6 )
      | ~ ( cQ_3 @ X1 @ X2 @ X3 )
      | ~ ( cP_3 @ ( f @ X1 ) @ X4 )
      | ~ ( cP_3 @ ( f @ X2 ) @ X5 )
      | ~ ( cP_3 @ ( f @ X3 ) @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i] :
      ~ ( cQ_4 @ X1 @ X2 @ X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_15,negated_conjecture,
    ! [X2: $i,X6: $i,X5: $i,X4: $i,X3: $i,X1: $i] :
      ( ( cQ_3 @ X1 @ X2 @ X3 )
      | ~ ( cQ_2 @ X4 @ X5 @ X6 )
      | ~ ( cP_2 @ X6 @ X3 )
      | ~ ( cP_2 @ X5 @ X2 )
      | ~ ( cP_2 @ X4 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_6]) ).

thf(c_0_16,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( cQ_2 @ X1 @ X2 @ X3 )
      | ~ ( cP_1 @ c @ X3 )
      | ~ ( cP_1 @ b @ X2 )
      | ~ ( cP_1 @ a @ X1 ) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_17,negated_conjecture,
    ! [X6: $i,X5: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
      ( ~ ( cP_3 @ ( f @ X1 ) @ X2 )
      | ~ ( cP_3 @ ( f @ X3 ) @ X4 )
      | ~ ( cP_3 @ ( f @ X5 ) @ X6 )
      | ~ ( cQ_3 @ X5 @ X3 @ X1 ) ),
    inference(sr,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_18,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( cP_3 @ ( f @ X1 ) @ X2 )
      | ~ ( cP_3 @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_19,negated_conjecture,
    ! [X3: $i,X2: $i,X5: $i,X6: $i,X4: $i,X1: $i] :
      ( ( cQ_3 @ X1 @ X2 @ X3 )
      | ~ ( cP_1 @ c @ X4 )
      | ~ ( cP_1 @ b @ X5 )
      | ~ ( cP_1 @ a @ X6 )
      | ~ ( cP_2 @ X4 @ X3 )
      | ~ ( cP_2 @ X5 @ X2 )
      | ~ ( cP_2 @ X6 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

thf(c_0_20,negated_conjecture,
    cP_1 @ c @ c,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_21,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i,X4: $i,X5: $i,X6: $i] :
      ( ~ ( cP_3 @ ( f @ X1 ) @ X2 )
      | ~ ( cP_3 @ ( f @ X3 ) @ X4 )
      | ~ ( cQ_3 @ X3 @ X1 @ X5 )
      | ~ ( cP_3 @ X5 @ X6 ) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

thf(c_0_22,negated_conjecture,
    ! [X2: $i,X4: $i,X5: $i,X3: $i,X1: $i] :
      ( ( cQ_3 @ X1 @ X2 @ X3 )
      | ~ ( cP_1 @ b @ X4 )
      | ~ ( cP_1 @ a @ X5 )
      | ~ ( cP_2 @ c @ X3 )
      | ~ ( cP_2 @ X4 @ X2 )
      | ~ ( cP_2 @ X5 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

thf(c_0_23,negated_conjecture,
    cP_1 @ b @ b,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_24,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ~ ( cP_3 @ ( f @ X1 ) @ X2 )
      | ~ ( cQ_3 @ X1 @ X3 @ X4 )
      | ~ ( cP_3 @ X4 @ X5 )
      | ~ ( cP_3 @ X3 @ X6 ) ),
    inference(spm,[status(thm)],[c_0_21,c_0_18]) ).

thf(c_0_25,negated_conjecture,
    ! [X2: $i,X4: $i,X3: $i,X1: $i] :
      ( ( cQ_3 @ X1 @ X2 @ X3 )
      | ~ ( cP_1 @ a @ X4 )
      | ~ ( cP_2 @ c @ X3 )
      | ~ ( cP_2 @ b @ X2 )
      | ~ ( cP_2 @ X4 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

thf(c_0_26,negated_conjecture,
    cP_1 @ a @ a,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_27,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i,X4: $i,X5: $i,X6: $i] :
      ( ~ ( cQ_3 @ X1 @ X2 @ X3 )
      | ~ ( cP_3 @ X3 @ X4 )
      | ~ ( cP_3 @ X2 @ X5 )
      | ~ ( cP_3 @ X1 @ X6 ) ),
    inference(spm,[status(thm)],[c_0_24,c_0_18]) ).

thf(c_0_28,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( cQ_3 @ X1 @ X2 @ X3 )
      | ~ ( cP_2 @ c @ X3 )
      | ~ ( cP_2 @ b @ X2 )
      | ~ ( cP_2 @ a @ X1 ) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

thf(c_0_29,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ~ ( cP_2 @ c @ X1 )
      | ~ ( cP_2 @ b @ X2 )
      | ~ ( cP_2 @ a @ X3 )
      | ~ ( cP_3 @ X1 @ X4 )
      | ~ ( cP_3 @ X2 @ X5 )
      | ~ ( cP_3 @ X3 @ X6 ) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

thf(c_0_30,negated_conjecture,
    cP_2 @ c @ c,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_31,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( cP_2 @ b @ X1 )
      | ~ ( cP_2 @ a @ X2 )
      | ~ ( cP_3 @ c @ X3 )
      | ~ ( cP_3 @ X1 @ X4 )
      | ~ ( cP_3 @ X2 @ X5 ) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

thf(c_0_32,negated_conjecture,
    cP_2 @ b @ b,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_33,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( cP_2 @ a @ X1 )
      | ~ ( cP_3 @ c @ X2 )
      | ~ ( cP_3 @ b @ X3 )
      | ~ ( cP_3 @ X1 @ X4 ) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

thf(c_0_34,negated_conjecture,
    cP_2 @ a @ a,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_35,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ~ ( cP_3 @ c @ X1 )
      | ~ ( cP_3 @ b @ X2 )
      | ~ ( cP_3 @ a @ X3 ) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

thf(c_0_36,negated_conjecture,
    cP_3 @ c @ c,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_37,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ~ ( cP_3 @ b @ X1 )
      | ~ ( cP_3 @ a @ X2 ) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

thf(c_0_38,negated_conjecture,
    cP_3 @ b @ b,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_39,negated_conjecture,
    cP_3 @ a @ a,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_40,negated_conjecture,
    ! [X1: $i] :
      ~ ( cP_3 @ a @ X1 ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

thf(c_0_41,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_39,c_0_40]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : SYO386^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n010.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 08:56:23 EDT 2024
% 0.13/0.34  % 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
% 0.20/0.48  # Version: 3.1.0-ho
% 0.20/0.48  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.48  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.48  # Starting full_lambda_5 with 300s (1) cores
% 0.20/0.48  # Starting new_ho_10_unif with 300s (1) cores
% 0.20/0.48  # full_lambda_5 with pid 13201 completed with status 0
% 0.20/0.48  # Result found by full_lambda_5
% 0.20/0.48  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.48  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.48  # Starting full_lambda_5 with 300s (1) cores
% 0.20/0.48  # No SInE strategy applied
% 0.20/0.48  # Search class: HHUNS-FFSM11-SFFFFFNN
% 0.20/0.48  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.48  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.48  # new_ho_10 with pid 13205 completed with status 0
% 0.20/0.48  # Result found by new_ho_10
% 0.20/0.48  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.48  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.48  # Starting full_lambda_5 with 300s (1) cores
% 0.20/0.48  # No SInE strategy applied
% 0.20/0.48  # Search class: HHUNS-FFSM11-SFFFFFNN
% 0.20/0.48  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.48  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.48  # Preprocessing time       : 0.001 s
% 0.20/0.48  # Presaturation interreduction done
% 0.20/0.48  
% 0.20/0.48  # Proof found!
% 0.20/0.48  # SZS status Theorem
% 0.20/0.48  # SZS output start CNFRefutation
% See solution above
% 0.20/0.48  # Parsed axioms                        : 13
% 0.20/0.48  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.48  # Initial clauses                      : 32
% 0.20/0.48  # Removed in clause preprocessing      : 12
% 0.20/0.48  # Initial clauses in saturation        : 20
% 0.20/0.48  # Processed clauses                    : 60
% 0.20/0.48  # ...of these trivial                  : 0
% 0.20/0.48  # ...subsumed                          : 0
% 0.20/0.48  # ...remaining for further processing  : 60
% 0.20/0.48  # Other redundant clauses eliminated   : 0
% 0.20/0.48  # Clauses deleted for lack of memory   : 0
% 0.20/0.48  # Backward-subsumed                    : 2
% 0.20/0.48  # Backward-rewritten                   : 0
% 0.20/0.48  # Generated clauses                    : 21
% 0.20/0.48  # ...of the previous two non-redundant : 20
% 0.20/0.48  # ...aggressively subsumed             : 0
% 0.20/0.48  # Contextual simplify-reflections      : 0
% 0.20/0.48  # Paramodulations                      : 20
% 0.20/0.48  # Factorizations                       : 0
% 0.20/0.48  # NegExts                              : 0
% 0.20/0.48  # Equation resolutions                 : 0
% 0.20/0.48  # Disequality decompositions           : 0
% 0.20/0.48  # Total rewrite steps                  : 0
% 0.20/0.48  # ...of those cached                   : 0
% 0.20/0.48  # Propositional unsat checks           : 0
% 0.20/0.48  #    Propositional check models        : 0
% 0.20/0.48  #    Propositional check unsatisfiable : 0
% 0.20/0.48  #    Propositional clauses             : 0
% 0.20/0.48  #    Propositional clauses after purity: 0
% 0.20/0.48  #    Propositional unsat core size     : 0
% 0.20/0.48  #    Propositional preprocessing time  : 0.000
% 0.20/0.48  #    Propositional encoding time       : 0.000
% 0.20/0.48  #    Propositional solver time         : 0.000
% 0.20/0.48  #    Success case prop preproc time    : 0.000
% 0.20/0.48  #    Success case prop encoding time   : 0.000
% 0.20/0.48  #    Success case prop solver time     : 0.000
% 0.20/0.48  # Current number of processed clauses  : 37
% 0.20/0.48  #    Positive orientable unit clauses  : 12
% 0.20/0.48  #    Positive unorientable unit clauses: 0
% 0.20/0.48  #    Negative unit clauses             : 2
% 0.20/0.48  #    Non-unit-clauses                  : 23
% 0.20/0.48  # Current number of unprocessed clauses: 0
% 0.20/0.48  # ...number of literals in the above   : 0
% 0.20/0.48  # Current number of archived formulas  : 0
% 0.20/0.48  # Current number of archived clauses   : 23
% 0.20/0.48  # Clause-clause subsumption calls (NU) : 165
% 0.20/0.48  # Rec. Clause-clause subsumption calls : 47
% 0.20/0.48  # Non-unit clause-clause subsumptions  : 1
% 0.20/0.48  # Unit Clause-clause subsumption calls : 9
% 0.20/0.48  # Rewrite failures with RHS unbound    : 0
% 0.20/0.48  # BW rewrite match attempts            : 0
% 0.20/0.48  # BW rewrite match successes           : 0
% 0.20/0.48  # Condensation attempts                : 60
% 0.20/0.48  # Condensation successes               : 0
% 0.20/0.48  # Termbank termtop insertions          : 3284
% 0.20/0.48  # Search garbage collected termcells   : 288
% 0.20/0.48  
% 0.20/0.48  # -------------------------------------------------
% 0.20/0.48  # User time                : 0.004 s
% 0.20/0.48  # System time              : 0.003 s
% 0.20/0.48  # Total time               : 0.007 s
% 0.20/0.48  # Maximum resident set size: 1696 pages
% 0.20/0.48  
% 0.20/0.48  # -------------------------------------------------
% 0.20/0.48  # User time                : 0.006 s
% 0.20/0.48  # System time              : 0.004 s
% 0.20/0.48  # Total time               : 0.009 s
% 0.20/0.48  # Maximum resident set size: 1716 pages
% 0.20/0.48  % E---3.1 exiting
% 0.20/0.48  % E exiting
%------------------------------------------------------------------------------