TSTP Solution File: SYO068^4.010 by E---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.2.0
% Problem  : SYO068^4.010 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n025.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 Jun 24 20:29:09 EDT 2024

% Result   : Theorem 0.19s 0.51s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   37
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   98 (  36 unt;   0 typ;   0 def)
%            Number of atoms       :  529 (  16 equ;   0 cnn)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives : 1424 ( 219   ~; 256   |;  30   &; 873   @)
%                                         (   0 <=>;  46  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   42 (  40 usr;   2 con; 0-3 aty)
%            Number of variables   :  219 (  34   ^ 185   !;   0   ?; 219   :)

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

thf(decl_23,type,
    mnot: ( $i > $o ) > $i > $o ).

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

thf(decl_26,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_27,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

thf(decl_28,type,
    iatom: ( $i > $o ) > $i > $o ).

thf(decl_34,type,
    iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_38,type,
    ivalid: ( $i > $o ) > $o ).

thf(decl_42,type,
    p0: $i > $o ).

thf(decl_43,type,
    p1: $i > $o ).

thf(decl_44,type,
    p10: $i > $o ).

thf(decl_45,type,
    p2: $i > $o ).

thf(decl_46,type,
    p3: $i > $o ).

thf(decl_47,type,
    p4: $i > $o ).

thf(decl_48,type,
    p5: $i > $o ).

thf(decl_49,type,
    p6: $i > $o ).

thf(decl_50,type,
    p7: $i > $o ).

thf(decl_51,type,
    p8: $i > $o ).

thf(decl_52,type,
    p9: $i > $o ).

thf(decl_53,type,
    esk1_1: $i > $i ).

thf(decl_54,type,
    esk2_2: $i > $i > $i ).

thf(decl_55,type,
    esk3_1: $i > $i ).

thf(decl_56,type,
    esk4_2: $i > $i > $i ).

thf(decl_57,type,
    esk5_1: $i > $i ).

thf(decl_58,type,
    esk6_2: $i > $i > $i ).

thf(decl_59,type,
    esk7_1: $i > $i ).

thf(decl_60,type,
    esk8_2: $i > $i > $i ).

thf(decl_61,type,
    esk9_1: $i > $i ).

thf(decl_62,type,
    esk10_2: $i > $i > $i ).

thf(decl_63,type,
    esk11_1: $i > $i ).

thf(decl_64,type,
    esk12_2: $i > $i > $i ).

thf(decl_65,type,
    esk13_1: $i > $i ).

thf(decl_66,type,
    esk14_2: $i > $i > $i ).

thf(decl_67,type,
    esk15_1: $i > $i ).

thf(decl_68,type,
    esk16_2: $i > $i > $i ).

thf(decl_69,type,
    esk17_1: $i > $i ).

thf(decl_70,type,
    esk18_2: $i > $i > $i ).

thf(decl_71,type,
    esk19_1: $i > $i ).

thf(decl_72,type,
    esk20_2: $i > $i > $i ).

thf(decl_73,type,
    esk21_0: $i ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [X10: $i > $o,X11: $i > $o] : ( mor @ ( mnot @ X10 ) @ X11 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',mimplies) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [X4: $i > $o,X5: $i] :
          ~ ( X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',mnot) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
          ( ( X6 @ X5 )
          | ( X7 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',mor) ).

thf(iimplies,axiom,
    ( iimplies
    = ( ^ [X12: $i > $o,X14: $i > $o] : ( mimplies @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',iimplies) ).

thf(mbox_s4,axiom,
    ( mbox_s4
    = ( ^ [X12: $i > $o,X1: $i] :
        ! [X2: $i] :
          ( ( irel @ X1 @ X2 )
         => ( X12 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',mbox_s4) ).

thf(iatom,axiom,
    ( iatom
    = ( ^ [X12: $i > $o] : X12 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',iatom) ).

thf(ivalid,axiom,
    ( ivalid
    = ( ^ [X15: $i > $o] :
        ! [X13: $i] : ( X15 @ X13 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',ivalid) ).

thf(axiom11,axiom,
    ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',axiom11) ).

thf(axiom1,axiom,
    ivalid @ ( iatom @ p10 ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',axiom1) ).

thf(refl_axiom,axiom,
    ! [X1: $i] : ( irel @ X1 @ X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',refl_axiom) ).

thf(axiom10,axiom,
    ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',axiom10) ).

thf(axiom9,axiom,
    ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',axiom9) ).

thf(axiom8,axiom,
    ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',axiom8) ).

thf(axiom7,axiom,
    ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',axiom7) ).

thf(axiom6,axiom,
    ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',axiom6) ).

thf(axiom5,axiom,
    ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',axiom5) ).

thf(axiom4,axiom,
    ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',axiom4) ).

thf(axiom3,axiom,
    ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',axiom3) ).

thf(axiom2,axiom,
    ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',axiom2) ).

thf(con,conjecture,
    ivalid @ ( iatom @ p0 ),
    file('/export/starexec/sandbox2/tmp/tmp.7GBvHveN1H/E---3.1_23862.p',con) ).

thf(c_0_20,plain,
    ( mimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mimplies]) ).

thf(c_0_21,plain,
    ( mnot
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ( Z0 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mnot]) ).

thf(c_0_22,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

thf(c_0_23,plain,
    ( iimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ! [X24: $i] :
                ( ( irel @ Z2 @ X24 )
               => ( Z0 @ X24 ) )
          | ! [X25: $i] :
              ( ( irel @ Z2 @ X25 )
             => ( Z1 @ X25 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iimplies]) ).

thf(c_0_24,plain,
    ( mimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

thf(c_0_25,plain,
    ( mbox_s4
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X2: $i] :
          ( ( irel @ Z1 @ X2 )
         => ( Z0 @ X2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mbox_s4]) ).

thf(c_0_26,plain,
    ( iatom
    = ( ^ [Z0: $i > $o] : Z0 ) ),
    inference(fof_simplification,[status(thm)],[iatom]) ).

thf(c_0_27,plain,
    ( iimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ! [X24: $i] :
                ( ( irel @ Z2 @ X24 )
               => ( Z0 @ X24 ) )
          | ! [X25: $i] :
              ( ( irel @ Z2 @ X25 )
             => ( Z1 @ X25 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).

thf(c_0_28,plain,
    ( ivalid
    = ( ^ [Z0: $i > $o] :
        ! [X13: $i] : ( Z0 @ X13 ) ) ),
    inference(fof_simplification,[status(thm)],[ivalid]) ).

thf(c_0_29,plain,
    ! [X87: $i] :
      ( ~ ! [X85: $i] :
            ( ( irel @ X87 @ X85 )
           => ( p10 @ X85 ) )
      | ! [X86: $i] :
          ( ( irel @ X87 @ X86 )
         => ( ~ ! [X83: $i] :
                  ( ( irel @ X86 @ X83 )
                 => ( p10 @ X83 ) )
            | ! [X84: $i] :
                ( ( irel @ X86 @ X84 )
               => ( p9 @ X84 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom11,c_0_26]),c_0_27]),c_0_28]) ).

thf(c_0_30,plain,
    ! [X37: $i] : ( p10 @ X37 ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom1,c_0_26]),c_0_28]) ).

thf(c_0_31,plain,
    ! [X139: $i,X141: $i,X143: $i] :
      ( ( ( irel @ X141 @ ( esk20_2 @ X139 @ X141 ) )
        | ~ ( irel @ X141 @ X143 )
        | ( p9 @ X143 )
        | ~ ( irel @ X139 @ X141 )
        | ( irel @ X139 @ ( esk19_1 @ X139 ) ) )
      & ( ~ ( p10 @ ( esk20_2 @ X139 @ X141 ) )
        | ~ ( irel @ X141 @ X143 )
        | ( p9 @ X143 )
        | ~ ( irel @ X139 @ X141 )
        | ( irel @ X139 @ ( esk19_1 @ X139 ) ) )
      & ( ( irel @ X141 @ ( esk20_2 @ X139 @ X141 ) )
        | ~ ( irel @ X141 @ X143 )
        | ( p9 @ X143 )
        | ~ ( irel @ X139 @ X141 )
        | ~ ( p10 @ ( esk19_1 @ X139 ) ) )
      & ( ~ ( p10 @ ( esk20_2 @ X139 @ X141 ) )
        | ~ ( irel @ X141 @ X143 )
        | ( p9 @ X143 )
        | ~ ( irel @ X139 @ X141 )
        | ~ ( p10 @ ( esk19_1 @ X139 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])])])]) ).

thf(c_0_32,plain,
    ! [X93: $i] : ( p10 @ X93 ),
    inference(variable_rename,[status(thm)],[c_0_30]) ).

thf(c_0_33,plain,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( p9 @ X3 )
      | ~ ( p10 @ ( esk20_2 @ X1 @ X2 ) )
      | ~ ( irel @ X2 @ X3 )
      | ~ ( irel @ X1 @ X2 )
      | ~ ( p10 @ ( esk19_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

thf(c_0_34,plain,
    ! [X1: $i] : ( p10 @ X1 ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_35,plain,
    ! [X89: $i] : ( irel @ X89 @ X89 ),
    inference(variable_rename,[status(thm)],[refl_axiom]) ).

thf(c_0_36,plain,
    ! [X82: $i] :
      ( ~ ! [X80: $i] :
            ( ( irel @ X82 @ X80 )
           => ( p9 @ X80 ) )
      | ! [X81: $i] :
          ( ( irel @ X82 @ X81 )
         => ( ~ ! [X78: $i] :
                  ( ( irel @ X81 @ X78 )
                 => ( p9 @ X78 ) )
            | ! [X79: $i] :
                ( ( irel @ X81 @ X79 )
               => ( p8 @ X79 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom10,c_0_26]),c_0_27]),c_0_28]) ).

thf(c_0_37,plain,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( p9 @ X1 )
      | ~ ( irel @ X2 @ X1 )
      | ~ ( irel @ X3 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_34])]) ).

thf(c_0_38,plain,
    ! [X1: $i] : ( irel @ X1 @ X1 ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

thf(c_0_39,plain,
    ! [X134: $i,X136: $i,X138: $i] :
      ( ( ( irel @ X136 @ ( esk18_2 @ X134 @ X136 ) )
        | ~ ( irel @ X136 @ X138 )
        | ( p8 @ X138 )
        | ~ ( irel @ X134 @ X136 )
        | ( irel @ X134 @ ( esk17_1 @ X134 ) ) )
      & ( ~ ( p9 @ ( esk18_2 @ X134 @ X136 ) )
        | ~ ( irel @ X136 @ X138 )
        | ( p8 @ X138 )
        | ~ ( irel @ X134 @ X136 )
        | ( irel @ X134 @ ( esk17_1 @ X134 ) ) )
      & ( ( irel @ X136 @ ( esk18_2 @ X134 @ X136 ) )
        | ~ ( irel @ X136 @ X138 )
        | ( p8 @ X138 )
        | ~ ( irel @ X134 @ X136 )
        | ~ ( p9 @ ( esk17_1 @ X134 ) ) )
      & ( ~ ( p9 @ ( esk18_2 @ X134 @ X136 ) )
        | ~ ( irel @ X136 @ X138 )
        | ( p8 @ X138 )
        | ~ ( irel @ X134 @ X136 )
        | ~ ( p9 @ ( esk17_1 @ X134 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])])])]) ).

thf(c_0_40,plain,
    ! [X2: $i,X1: $i] :
      ( ( p9 @ X1 )
      | ~ ( irel @ X2 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

thf(c_0_41,plain,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( p8 @ X3 )
      | ~ ( p9 @ ( esk18_2 @ X1 @ X2 ) )
      | ~ ( irel @ X2 @ X3 )
      | ~ ( irel @ X1 @ X2 )
      | ~ ( p9 @ ( esk17_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

thf(c_0_42,plain,
    ! [X1: $i] : ( p9 @ X1 ),
    inference(spm,[status(thm)],[c_0_40,c_0_38]) ).

thf(c_0_43,plain,
    ! [X77: $i] :
      ( ~ ! [X75: $i] :
            ( ( irel @ X77 @ X75 )
           => ( p8 @ X75 ) )
      | ! [X76: $i] :
          ( ( irel @ X77 @ X76 )
         => ( ~ ! [X73: $i] :
                  ( ( irel @ X76 @ X73 )
                 => ( p8 @ X73 ) )
            | ! [X74: $i] :
                ( ( irel @ X76 @ X74 )
               => ( p7 @ X74 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom9,c_0_26]),c_0_27]),c_0_28]) ).

thf(c_0_44,plain,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( p8 @ X1 )
      | ~ ( irel @ X2 @ X1 )
      | ~ ( irel @ X3 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42])]) ).

thf(c_0_45,plain,
    ! [X129: $i,X131: $i,X133: $i] :
      ( ( ( irel @ X131 @ ( esk16_2 @ X129 @ X131 ) )
        | ~ ( irel @ X131 @ X133 )
        | ( p7 @ X133 )
        | ~ ( irel @ X129 @ X131 )
        | ( irel @ X129 @ ( esk15_1 @ X129 ) ) )
      & ( ~ ( p8 @ ( esk16_2 @ X129 @ X131 ) )
        | ~ ( irel @ X131 @ X133 )
        | ( p7 @ X133 )
        | ~ ( irel @ X129 @ X131 )
        | ( irel @ X129 @ ( esk15_1 @ X129 ) ) )
      & ( ( irel @ X131 @ ( esk16_2 @ X129 @ X131 ) )
        | ~ ( irel @ X131 @ X133 )
        | ( p7 @ X133 )
        | ~ ( irel @ X129 @ X131 )
        | ~ ( p8 @ ( esk15_1 @ X129 ) ) )
      & ( ~ ( p8 @ ( esk16_2 @ X129 @ X131 ) )
        | ~ ( irel @ X131 @ X133 )
        | ( p7 @ X133 )
        | ~ ( irel @ X129 @ X131 )
        | ~ ( p8 @ ( esk15_1 @ X129 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])])])]) ).

thf(c_0_46,plain,
    ! [X2: $i,X1: $i] :
      ( ( p8 @ X1 )
      | ~ ( irel @ X2 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_44,c_0_38]) ).

thf(c_0_47,plain,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( p7 @ X3 )
      | ~ ( p8 @ ( esk16_2 @ X1 @ X2 ) )
      | ~ ( irel @ X2 @ X3 )
      | ~ ( irel @ X1 @ X2 )
      | ~ ( p8 @ ( esk15_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

thf(c_0_48,plain,
    ! [X1: $i] : ( p8 @ X1 ),
    inference(spm,[status(thm)],[c_0_46,c_0_38]) ).

thf(c_0_49,plain,
    ! [X72: $i] :
      ( ~ ! [X70: $i] :
            ( ( irel @ X72 @ X70 )
           => ( p7 @ X70 ) )
      | ! [X71: $i] :
          ( ( irel @ X72 @ X71 )
         => ( ~ ! [X68: $i] :
                  ( ( irel @ X71 @ X68 )
                 => ( p7 @ X68 ) )
            | ! [X69: $i] :
                ( ( irel @ X71 @ X69 )
               => ( p6 @ X69 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom8,c_0_26]),c_0_27]),c_0_28]) ).

thf(c_0_50,plain,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( p7 @ X1 )
      | ~ ( irel @ X2 @ X1 )
      | ~ ( irel @ X3 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_48])]) ).

thf(c_0_51,plain,
    ! [X124: $i,X126: $i,X128: $i] :
      ( ( ( irel @ X126 @ ( esk14_2 @ X124 @ X126 ) )
        | ~ ( irel @ X126 @ X128 )
        | ( p6 @ X128 )
        | ~ ( irel @ X124 @ X126 )
        | ( irel @ X124 @ ( esk13_1 @ X124 ) ) )
      & ( ~ ( p7 @ ( esk14_2 @ X124 @ X126 ) )
        | ~ ( irel @ X126 @ X128 )
        | ( p6 @ X128 )
        | ~ ( irel @ X124 @ X126 )
        | ( irel @ X124 @ ( esk13_1 @ X124 ) ) )
      & ( ( irel @ X126 @ ( esk14_2 @ X124 @ X126 ) )
        | ~ ( irel @ X126 @ X128 )
        | ( p6 @ X128 )
        | ~ ( irel @ X124 @ X126 )
        | ~ ( p7 @ ( esk13_1 @ X124 ) ) )
      & ( ~ ( p7 @ ( esk14_2 @ X124 @ X126 ) )
        | ~ ( irel @ X126 @ X128 )
        | ( p6 @ X128 )
        | ~ ( irel @ X124 @ X126 )
        | ~ ( p7 @ ( esk13_1 @ X124 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])])])]) ).

thf(c_0_52,plain,
    ! [X2: $i,X1: $i] :
      ( ( p7 @ X1 )
      | ~ ( irel @ X2 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_50,c_0_38]) ).

thf(c_0_53,plain,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( p6 @ X3 )
      | ~ ( p7 @ ( esk14_2 @ X1 @ X2 ) )
      | ~ ( irel @ X2 @ X3 )
      | ~ ( irel @ X1 @ X2 )
      | ~ ( p7 @ ( esk13_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

thf(c_0_54,plain,
    ! [X1: $i] : ( p7 @ X1 ),
    inference(spm,[status(thm)],[c_0_52,c_0_38]) ).

thf(c_0_55,plain,
    ! [X67: $i] :
      ( ~ ! [X65: $i] :
            ( ( irel @ X67 @ X65 )
           => ( p6 @ X65 ) )
      | ! [X66: $i] :
          ( ( irel @ X67 @ X66 )
         => ( ~ ! [X63: $i] :
                  ( ( irel @ X66 @ X63 )
                 => ( p6 @ X63 ) )
            | ! [X64: $i] :
                ( ( irel @ X66 @ X64 )
               => ( p5 @ X64 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom7,c_0_26]),c_0_27]),c_0_28]) ).

thf(c_0_56,plain,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( p6 @ X1 )
      | ~ ( irel @ X2 @ X1 )
      | ~ ( irel @ X3 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_54])]) ).

thf(c_0_57,plain,
    ! [X119: $i,X121: $i,X123: $i] :
      ( ( ( irel @ X121 @ ( esk12_2 @ X119 @ X121 ) )
        | ~ ( irel @ X121 @ X123 )
        | ( p5 @ X123 )
        | ~ ( irel @ X119 @ X121 )
        | ( irel @ X119 @ ( esk11_1 @ X119 ) ) )
      & ( ~ ( p6 @ ( esk12_2 @ X119 @ X121 ) )
        | ~ ( irel @ X121 @ X123 )
        | ( p5 @ X123 )
        | ~ ( irel @ X119 @ X121 )
        | ( irel @ X119 @ ( esk11_1 @ X119 ) ) )
      & ( ( irel @ X121 @ ( esk12_2 @ X119 @ X121 ) )
        | ~ ( irel @ X121 @ X123 )
        | ( p5 @ X123 )
        | ~ ( irel @ X119 @ X121 )
        | ~ ( p6 @ ( esk11_1 @ X119 ) ) )
      & ( ~ ( p6 @ ( esk12_2 @ X119 @ X121 ) )
        | ~ ( irel @ X121 @ X123 )
        | ( p5 @ X123 )
        | ~ ( irel @ X119 @ X121 )
        | ~ ( p6 @ ( esk11_1 @ X119 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])])])]) ).

thf(c_0_58,plain,
    ! [X2: $i,X1: $i] :
      ( ( p6 @ X1 )
      | ~ ( irel @ X2 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_56,c_0_38]) ).

thf(c_0_59,plain,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( p5 @ X3 )
      | ~ ( p6 @ ( esk12_2 @ X1 @ X2 ) )
      | ~ ( irel @ X2 @ X3 )
      | ~ ( irel @ X1 @ X2 )
      | ~ ( p6 @ ( esk11_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

thf(c_0_60,plain,
    ! [X1: $i] : ( p6 @ X1 ),
    inference(spm,[status(thm)],[c_0_58,c_0_38]) ).

thf(c_0_61,plain,
    ! [X62: $i] :
      ( ~ ! [X60: $i] :
            ( ( irel @ X62 @ X60 )
           => ( p5 @ X60 ) )
      | ! [X61: $i] :
          ( ( irel @ X62 @ X61 )
         => ( ~ ! [X58: $i] :
                  ( ( irel @ X61 @ X58 )
                 => ( p5 @ X58 ) )
            | ! [X59: $i] :
                ( ( irel @ X61 @ X59 )
               => ( p4 @ X59 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom6,c_0_26]),c_0_27]),c_0_28]) ).

thf(c_0_62,plain,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( p5 @ X1 )
      | ~ ( irel @ X2 @ X1 )
      | ~ ( irel @ X3 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_60])]) ).

thf(c_0_63,plain,
    ! [X114: $i,X116: $i,X118: $i] :
      ( ( ( irel @ X116 @ ( esk10_2 @ X114 @ X116 ) )
        | ~ ( irel @ X116 @ X118 )
        | ( p4 @ X118 )
        | ~ ( irel @ X114 @ X116 )
        | ( irel @ X114 @ ( esk9_1 @ X114 ) ) )
      & ( ~ ( p5 @ ( esk10_2 @ X114 @ X116 ) )
        | ~ ( irel @ X116 @ X118 )
        | ( p4 @ X118 )
        | ~ ( irel @ X114 @ X116 )
        | ( irel @ X114 @ ( esk9_1 @ X114 ) ) )
      & ( ( irel @ X116 @ ( esk10_2 @ X114 @ X116 ) )
        | ~ ( irel @ X116 @ X118 )
        | ( p4 @ X118 )
        | ~ ( irel @ X114 @ X116 )
        | ~ ( p5 @ ( esk9_1 @ X114 ) ) )
      & ( ~ ( p5 @ ( esk10_2 @ X114 @ X116 ) )
        | ~ ( irel @ X116 @ X118 )
        | ( p4 @ X118 )
        | ~ ( irel @ X114 @ X116 )
        | ~ ( p5 @ ( esk9_1 @ X114 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])])])]) ).

thf(c_0_64,plain,
    ! [X2: $i,X1: $i] :
      ( ( p5 @ X1 )
      | ~ ( irel @ X2 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_62,c_0_38]) ).

thf(c_0_65,plain,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( p4 @ X3 )
      | ~ ( p5 @ ( esk10_2 @ X1 @ X2 ) )
      | ~ ( irel @ X2 @ X3 )
      | ~ ( irel @ X1 @ X2 )
      | ~ ( p5 @ ( esk9_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

thf(c_0_66,plain,
    ! [X1: $i] : ( p5 @ X1 ),
    inference(spm,[status(thm)],[c_0_64,c_0_38]) ).

thf(c_0_67,plain,
    ! [X57: $i] :
      ( ~ ! [X55: $i] :
            ( ( irel @ X57 @ X55 )
           => ( p4 @ X55 ) )
      | ! [X56: $i] :
          ( ( irel @ X57 @ X56 )
         => ( ~ ! [X53: $i] :
                  ( ( irel @ X56 @ X53 )
                 => ( p4 @ X53 ) )
            | ! [X54: $i] :
                ( ( irel @ X56 @ X54 )
               => ( p3 @ X54 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom5,c_0_26]),c_0_27]),c_0_28]) ).

thf(c_0_68,plain,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( p4 @ X1 )
      | ~ ( irel @ X2 @ X1 )
      | ~ ( irel @ X3 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_66])]) ).

thf(c_0_69,plain,
    ! [X109: $i,X111: $i,X113: $i] :
      ( ( ( irel @ X111 @ ( esk8_2 @ X109 @ X111 ) )
        | ~ ( irel @ X111 @ X113 )
        | ( p3 @ X113 )
        | ~ ( irel @ X109 @ X111 )
        | ( irel @ X109 @ ( esk7_1 @ X109 ) ) )
      & ( ~ ( p4 @ ( esk8_2 @ X109 @ X111 ) )
        | ~ ( irel @ X111 @ X113 )
        | ( p3 @ X113 )
        | ~ ( irel @ X109 @ X111 )
        | ( irel @ X109 @ ( esk7_1 @ X109 ) ) )
      & ( ( irel @ X111 @ ( esk8_2 @ X109 @ X111 ) )
        | ~ ( irel @ X111 @ X113 )
        | ( p3 @ X113 )
        | ~ ( irel @ X109 @ X111 )
        | ~ ( p4 @ ( esk7_1 @ X109 ) ) )
      & ( ~ ( p4 @ ( esk8_2 @ X109 @ X111 ) )
        | ~ ( irel @ X111 @ X113 )
        | ( p3 @ X113 )
        | ~ ( irel @ X109 @ X111 )
        | ~ ( p4 @ ( esk7_1 @ X109 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])])])]) ).

thf(c_0_70,plain,
    ! [X2: $i,X1: $i] :
      ( ( p4 @ X1 )
      | ~ ( irel @ X2 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_68,c_0_38]) ).

thf(c_0_71,plain,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( p3 @ X3 )
      | ~ ( p4 @ ( esk8_2 @ X1 @ X2 ) )
      | ~ ( irel @ X2 @ X3 )
      | ~ ( irel @ X1 @ X2 )
      | ~ ( p4 @ ( esk7_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

thf(c_0_72,plain,
    ! [X1: $i] : ( p4 @ X1 ),
    inference(spm,[status(thm)],[c_0_70,c_0_38]) ).

thf(c_0_73,plain,
    ! [X52: $i] :
      ( ~ ! [X50: $i] :
            ( ( irel @ X52 @ X50 )
           => ( p3 @ X50 ) )
      | ! [X51: $i] :
          ( ( irel @ X52 @ X51 )
         => ( ~ ! [X48: $i] :
                  ( ( irel @ X51 @ X48 )
                 => ( p3 @ X48 ) )
            | ! [X49: $i] :
                ( ( irel @ X51 @ X49 )
               => ( p2 @ X49 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom4,c_0_26]),c_0_27]),c_0_28]) ).

thf(c_0_74,plain,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( p3 @ X1 )
      | ~ ( irel @ X2 @ X1 )
      | ~ ( irel @ X3 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_72])]) ).

thf(c_0_75,plain,
    ! [X104: $i,X106: $i,X108: $i] :
      ( ( ( irel @ X106 @ ( esk6_2 @ X104 @ X106 ) )
        | ~ ( irel @ X106 @ X108 )
        | ( p2 @ X108 )
        | ~ ( irel @ X104 @ X106 )
        | ( irel @ X104 @ ( esk5_1 @ X104 ) ) )
      & ( ~ ( p3 @ ( esk6_2 @ X104 @ X106 ) )
        | ~ ( irel @ X106 @ X108 )
        | ( p2 @ X108 )
        | ~ ( irel @ X104 @ X106 )
        | ( irel @ X104 @ ( esk5_1 @ X104 ) ) )
      & ( ( irel @ X106 @ ( esk6_2 @ X104 @ X106 ) )
        | ~ ( irel @ X106 @ X108 )
        | ( p2 @ X108 )
        | ~ ( irel @ X104 @ X106 )
        | ~ ( p3 @ ( esk5_1 @ X104 ) ) )
      & ( ~ ( p3 @ ( esk6_2 @ X104 @ X106 ) )
        | ~ ( irel @ X106 @ X108 )
        | ( p2 @ X108 )
        | ~ ( irel @ X104 @ X106 )
        | ~ ( p3 @ ( esk5_1 @ X104 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])])])])])]) ).

thf(c_0_76,plain,
    ! [X2: $i,X1: $i] :
      ( ( p3 @ X1 )
      | ~ ( irel @ X2 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_74,c_0_38]) ).

thf(c_0_77,plain,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( p2 @ X3 )
      | ~ ( p3 @ ( esk6_2 @ X1 @ X2 ) )
      | ~ ( irel @ X2 @ X3 )
      | ~ ( irel @ X1 @ X2 )
      | ~ ( p3 @ ( esk5_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_75]) ).

thf(c_0_78,plain,
    ! [X1: $i] : ( p3 @ X1 ),
    inference(spm,[status(thm)],[c_0_76,c_0_38]) ).

thf(c_0_79,plain,
    ! [X47: $i] :
      ( ~ ! [X45: $i] :
            ( ( irel @ X47 @ X45 )
           => ( p2 @ X45 ) )
      | ! [X46: $i] :
          ( ( irel @ X47 @ X46 )
         => ( ~ ! [X43: $i] :
                  ( ( irel @ X46 @ X43 )
                 => ( p2 @ X43 ) )
            | ! [X44: $i] :
                ( ( irel @ X46 @ X44 )
               => ( p1 @ X44 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom3,c_0_26]),c_0_27]),c_0_28]) ).

thf(c_0_80,plain,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( p2 @ X1 )
      | ~ ( irel @ X2 @ X1 )
      | ~ ( irel @ X3 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78]),c_0_78])]) ).

thf(c_0_81,plain,
    ! [X99: $i,X101: $i,X103: $i] :
      ( ( ( irel @ X101 @ ( esk4_2 @ X99 @ X101 ) )
        | ~ ( irel @ X101 @ X103 )
        | ( p1 @ X103 )
        | ~ ( irel @ X99 @ X101 )
        | ( irel @ X99 @ ( esk3_1 @ X99 ) ) )
      & ( ~ ( p2 @ ( esk4_2 @ X99 @ X101 ) )
        | ~ ( irel @ X101 @ X103 )
        | ( p1 @ X103 )
        | ~ ( irel @ X99 @ X101 )
        | ( irel @ X99 @ ( esk3_1 @ X99 ) ) )
      & ( ( irel @ X101 @ ( esk4_2 @ X99 @ X101 ) )
        | ~ ( irel @ X101 @ X103 )
        | ( p1 @ X103 )
        | ~ ( irel @ X99 @ X101 )
        | ~ ( p2 @ ( esk3_1 @ X99 ) ) )
      & ( ~ ( p2 @ ( esk4_2 @ X99 @ X101 ) )
        | ~ ( irel @ X101 @ X103 )
        | ( p1 @ X103 )
        | ~ ( irel @ X99 @ X101 )
        | ~ ( p2 @ ( esk3_1 @ X99 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])])])])]) ).

thf(c_0_82,plain,
    ! [X2: $i,X1: $i] :
      ( ( p2 @ X1 )
      | ~ ( irel @ X2 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_80,c_0_38]) ).

thf(c_0_83,plain,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( p1 @ X3 )
      | ~ ( p2 @ ( esk4_2 @ X1 @ X2 ) )
      | ~ ( irel @ X2 @ X3 )
      | ~ ( irel @ X1 @ X2 )
      | ~ ( p2 @ ( esk3_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_81]) ).

thf(c_0_84,plain,
    ! [X1: $i] : ( p2 @ X1 ),
    inference(spm,[status(thm)],[c_0_82,c_0_38]) ).

thf(c_0_85,plain,
    ! [X42: $i] :
      ( ~ ! [X40: $i] :
            ( ( irel @ X42 @ X40 )
           => ( p1 @ X40 ) )
      | ! [X41: $i] :
          ( ( irel @ X42 @ X41 )
         => ( ~ ! [X38: $i] :
                  ( ( irel @ X41 @ X38 )
                 => ( p1 @ X38 ) )
            | ! [X39: $i] :
                ( ( irel @ X41 @ X39 )
               => ( p0 @ X39 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom2,c_0_26]),c_0_27]),c_0_28]) ).

thf(c_0_86,plain,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( p1 @ X1 )
      | ~ ( irel @ X2 @ X1 )
      | ~ ( irel @ X3 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84]),c_0_84])]) ).

thf(c_0_87,plain,
    ! [X94: $i,X96: $i,X98: $i] :
      ( ( ( irel @ X96 @ ( esk2_2 @ X94 @ X96 ) )
        | ~ ( irel @ X96 @ X98 )
        | ( p0 @ X98 )
        | ~ ( irel @ X94 @ X96 )
        | ( irel @ X94 @ ( esk1_1 @ X94 ) ) )
      & ( ~ ( p1 @ ( esk2_2 @ X94 @ X96 ) )
        | ~ ( irel @ X96 @ X98 )
        | ( p0 @ X98 )
        | ~ ( irel @ X94 @ X96 )
        | ( irel @ X94 @ ( esk1_1 @ X94 ) ) )
      & ( ( irel @ X96 @ ( esk2_2 @ X94 @ X96 ) )
        | ~ ( irel @ X96 @ X98 )
        | ( p0 @ X98 )
        | ~ ( irel @ X94 @ X96 )
        | ~ ( p1 @ ( esk1_1 @ X94 ) ) )
      & ( ~ ( p1 @ ( esk2_2 @ X94 @ X96 ) )
        | ~ ( irel @ X96 @ X98 )
        | ( p0 @ X98 )
        | ~ ( irel @ X94 @ X96 )
        | ~ ( p1 @ ( esk1_1 @ X94 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])])])])]) ).

thf(c_0_88,plain,
    ! [X2: $i,X1: $i] :
      ( ( p1 @ X1 )
      | ~ ( irel @ X2 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_86,c_0_38]) ).

thf(c_0_89,plain,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( p0 @ X3 )
      | ~ ( p1 @ ( esk2_2 @ X1 @ X2 ) )
      | ~ ( irel @ X2 @ X3 )
      | ~ ( irel @ X1 @ X2 )
      | ~ ( p1 @ ( esk1_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_87]) ).

thf(c_0_90,plain,
    ! [X1: $i] : ( p1 @ X1 ),
    inference(spm,[status(thm)],[c_0_88,c_0_38]) ).

thf(c_0_91,negated_conjecture,
    ~ ! [X88: $i] : ( p0 @ X88 ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[con]),c_0_26]),c_0_28]) ).

thf(c_0_92,plain,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( p0 @ X1 )
      | ~ ( irel @ X2 @ X1 )
      | ~ ( irel @ X3 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90]),c_0_90])]) ).

thf(c_0_93,negated_conjecture,
    ~ ( p0 @ esk21_0 ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])])])]) ).

thf(c_0_94,plain,
    ! [X2: $i,X1: $i] :
      ( ( p0 @ X1 )
      | ~ ( irel @ X2 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_92,c_0_38]) ).

thf(c_0_95,negated_conjecture,
    ~ ( p0 @ esk21_0 ),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

thf(c_0_96,plain,
    ! [X1: $i] : ( p0 @ X1 ),
    inference(spm,[status(thm)],[c_0_94,c_0_38]) ).

thf(c_0_97,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : SYO068^4.010 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun Jun 23 10:38:09 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.19/0.48  Running higher-order theorem proving
% 0.19/0.48  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/tmp/tmp.7GBvHveN1H/E---3.1_23862.p
% 0.19/0.51  # Version: 3.2.0-ho
% 0.19/0.51  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.19/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.19/0.51  # Starting post_as_ho3 with 300s (1) cores
% 0.19/0.51  # Starting post_as_ho11 with 300s (1) cores
% 0.19/0.51  # Starting full_lambda_8 with 300s (1) cores
% 0.19/0.51  # new_ho_10_cnf2 with pid 23940 completed with status 0
% 0.19/0.51  # Result found by new_ho_10_cnf2
% 0.19/0.51  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.19/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.19/0.51  # No SInE strategy applied
% 0.19/0.51  # Search class: HGUNS-FFMF21-SHSSMFNN
% 0.19/0.51  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.51  # Starting new_ho_10 with 811s (1) cores
% 0.19/0.51  # Starting new_ho_10_cnf2 with 151s (1) cores
% 0.19/0.51  # Starting ho_unfolding_6 with 136s (1) cores
% 0.19/0.51  # Starting sh4l with 136s (1) cores
% 0.19/0.51  # Starting ehoh_best_nonlift_rwall with 136s (1) cores
% 0.19/0.51  # ho_unfolding_6 with pid 23949 completed with status 0
% 0.19/0.51  # Result found by ho_unfolding_6
% 0.19/0.51  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.19/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.19/0.51  # No SInE strategy applied
% 0.19/0.51  # Search class: HGUNS-FFMF21-SHSSMFNN
% 0.19/0.51  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.51  # Starting new_ho_10 with 811s (1) cores
% 0.19/0.51  # Starting new_ho_10_cnf2 with 151s (1) cores
% 0.19/0.51  # Starting ho_unfolding_6 with 136s (1) cores
% 0.19/0.51  # Preprocessing time       : 0.004 s
% 0.19/0.51  
% 0.19/0.51  # Proof found!
% 0.19/0.51  # SZS status Theorem
% 0.19/0.51  # SZS output start CNFRefutation
% See solution above
% 0.19/0.51  # Parsed axioms                        : 64
% 0.19/0.51  # Removed by relevancy pruning/SinE    : 0
% 0.19/0.51  # Initial clauses                      : 75
% 0.19/0.51  # Removed in clause preprocessing      : 31
% 0.19/0.51  # Initial clauses in saturation        : 44
% 0.19/0.51  # Processed clauses                    : 77
% 0.19/0.51  # ...of these trivial                  : 4
% 0.19/0.51  # ...subsumed                          : 3
% 0.19/0.51  # ...remaining for further processing  : 70
% 0.19/0.51  # Other redundant clauses eliminated   : 0
% 0.19/0.51  # Clauses deleted for lack of memory   : 0
% 0.19/0.51  # Backward-subsumed                    : 29
% 0.19/0.51  # Backward-rewritten                   : 28
% 0.19/0.51  # Generated clauses                    : 30
% 0.19/0.51  # ...of the previous two non-redundant : 56
% 0.19/0.51  # ...aggressively subsumed             : 0
% 0.19/0.51  # Contextual simplify-reflections      : 0
% 0.19/0.51  # Paramodulations                      : 30
% 0.19/0.51  # Factorizations                       : 0
% 0.19/0.51  # NegExts                              : 0
% 0.19/0.51  # Equation resolutions                 : 0
% 0.19/0.51  # Disequality decompositions           : 0
% 0.19/0.51  # Total rewrite steps                  : 45
% 0.19/0.51  # ...of those cached                   : 0
% 0.19/0.51  # Propositional unsat checks           : 0
% 0.19/0.51  #    Propositional check models        : 0
% 0.19/0.51  #    Propositional check unsatisfiable : 0
% 0.19/0.51  #    Propositional clauses             : 0
% 0.19/0.51  #    Propositional clauses after purity: 0
% 0.19/0.51  #    Propositional unsat core size     : 0
% 0.19/0.51  #    Propositional preprocessing time  : 0.000
% 0.19/0.51  #    Propositional encoding time       : 0.000
% 0.19/0.51  #    Propositional solver time         : 0.000
% 0.19/0.51  #    Success case prop preproc time    : 0.000
% 0.19/0.51  #    Success case prop encoding time   : 0.000
% 0.19/0.51  #    Success case prop solver time     : 0.000
% 0.19/0.51  # Current number of processed clauses  : 13
% 0.19/0.51  #    Positive orientable unit clauses  : 12
% 0.19/0.51  #    Positive unorientable unit clauses: 0
% 0.19/0.51  #    Negative unit clauses             : 0
% 0.19/0.51  #    Non-unit-clauses                  : 1
% 0.19/0.51  # Current number of unprocessed clauses: 23
% 0.19/0.51  # ...number of literals in the above   : 92
% 0.19/0.51  # Current number of archived formulas  : 0
% 0.19/0.51  # Current number of archived clauses   : 57
% 0.19/0.51  # Clause-clause subsumption calls (NU) : 531
% 0.19/0.51  # Rec. Clause-clause subsumption calls : 149
% 0.19/0.51  # Non-unit clause-clause subsumptions  : 22
% 0.19/0.51  # Unit Clause-clause subsumption calls : 116
% 0.19/0.51  # Rewrite failures with RHS unbound    : 0
% 0.19/0.51  # BW rewrite match attempts            : 38
% 0.19/0.51  # BW rewrite match successes           : 38
% 0.19/0.51  # Condensation attempts                : 77
% 0.19/0.51  # Condensation successes               : 0
% 0.19/0.51  # Termbank termtop insertions          : 9783
% 0.19/0.51  # Search garbage collected termcells   : 2253
% 0.19/0.51  
% 0.19/0.51  # -------------------------------------------------
% 0.19/0.51  # User time                : 0.015 s
% 0.19/0.51  # System time              : 0.004 s
% 0.19/0.51  # Total time               : 0.020 s
% 0.19/0.51  # Maximum resident set size: 2300 pages
% 0.19/0.51  
% 0.19/0.51  # -------------------------------------------------
% 0.19/0.51  # User time                : 0.041 s
% 0.19/0.51  # System time              : 0.021 s
% 0.19/0.51  # Total time               : 0.062 s
% 0.19/0.51  # Maximum resident set size: 1768 pages
% 0.19/0.51  % E---3.1 exiting
% 0.19/0.51  % E exiting
%------------------------------------------------------------------------------