TSTP Solution File: SWV445^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SWV445^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n015.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 05:24:52 EDT 2024

% Result   : Theorem 0.16s 0.46s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  105 (  48 unt;  29 typ;   0 def)
%            Number of atoms       :  349 (  34 equ;   0 cnn)
%            Maximal formula atoms :   48 (   4 avg)
%            Number of connectives : 1136 ( 175   ~; 184   |;  12   &; 724   @)
%                                         (   0 <=>;  41  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   7 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  132 ( 132   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   30 (  28 usr;   8 con; 0-6 aty)
%            Number of variables   :  242 (  72   ^ 170   !;   0   ?; 242   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    individuals: $tType ).

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

thf(decl_29,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

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

thf(decl_37,type,
    mvalid: ( $i > $o ) > $o ).

thf(decl_41,type,
    reli: $i > $i > $o ).

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

thf(decl_43,type,
    cs4_atom: ( $i > $o ) > $i > $o ).

thf(decl_46,type,
    cs4_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_50,type,
    cs4_box: ( $i > $o ) > $i > $o ).

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

thf(decl_53,type,
    bl_atom: ( $i > $o ) > $i > $o ).

thf(decl_54,type,
    bl_princ: ( $i > $o ) > $i > $o ).

thf(decl_57,type,
    bl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_61,type,
    bl_says: individuals > ( $i > $o ) > $i > $o ).

thf(decl_62,type,
    bl_valid: ( $i > $o ) > $o ).

thf(decl_64,type,
    esk1_2: ( $i > $o ) > $i > $i ).

thf(decl_65,type,
    esk2_2: ( $i > $o ) > $i > $i ).

thf(decl_70,type,
    esk7_0: individuals ).

thf(decl_71,type,
    epred1_0: $i > $o ).

thf(decl_72,type,
    esk8_0: $i ).

thf(decl_73,type,
    esk9_0: $i ).

thf(decl_74,type,
    esk10_3: $i > $i > $i > $i ).

thf(decl_75,type,
    esk11_6: $i > $i > $i > $i > $i > $i > $i ).

thf(decl_76,type,
    esk12_0: $i ).

thf(decl_77,type,
    esk13_0: $i ).

thf(decl_78,type,
    esk14_0: $i ).

thf(decl_79,type,
    esk15_0: $i ).

thf(mimpl,axiom,
    ( mimpl
    = ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mimpl) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [X2: $i > $o,X3: $i] :
          ~ ( X2 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
          ( ( X4 @ X3 )
          | ( X5 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).

thf(cs4_atom,axiom,
    ( cs4_atom
    = ( ^ [X11: $i > $o] : ( mbox @ reli @ X11 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_atom) ).

thf(mbox,axiom,
    ( mbox
    = ( ^ [X10: $i > $i > $o,X11: $i > $o,X1: $i] :
        ! [X12: $i] :
          ( ( X10 @ X1 @ X12 )
         => ( X11 @ X12 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).

thf(cs4_impl,axiom,
    ( cs4_impl
    = ( ^ [X19: $i > $o,X20: $i > $o] : ( mbox @ reli @ ( mimpl @ X19 @ X20 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_impl) ).

thf(cs4_box,axiom,
    ( cs4_box
    = ( ^ [X19: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X19 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_box) ).

thf(bl_princ,axiom,
    ( bl_princ
    = ( ^ [X11: $i > $o] : ( cs4_atom @ X11 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_princ) ).

thf(bl_atom,axiom,
    ( bl_atom
    = ( ^ [X11: $i > $o] : ( cs4_atom @ X11 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_atom) ).

thf(bl_impl,axiom,
    ( bl_impl
    = ( ^ [X19: $i > $o,X20: $i > $o] : ( cs4_impl @ X19 @ X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_impl) ).

thf(bl_says,axiom,
    ( bl_says
    = ( ^ [X23: individuals,X19: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ X23 ) ) @ X19 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_says) ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [X11: $i > $o] :
        ! [X15: $i] : ( X11 @ X15 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).

thf(bl_valid_def,axiom,
    ( bl_valid
    = ( ^ [Z0: $i > $o] :
        ! [X47: $i] : ( Z0 @ X47 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_valid_def) ).

thf(bl_c4,conjecture,
    ! [X23: individuals,X19: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ X23 @ ( bl_says @ X23 @ ( bl_atom @ X19 ) ) ) @ ( bl_says @ X23 @ ( bl_atom @ X19 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_c4) ).

thf(refl_axiom_i,axiom,
    ! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X19 ) @ X19 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',refl_axiom_i) ).

thf(refl_axiom_r,axiom,
    ! [X19: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ X19 ) @ X19 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',refl_axiom_r) ).

thf(c_0_16,plain,
    ( mimpl
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mimpl]) ).

thf(c_0_17,plain,
    ( mnot
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ( Z0 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mnot]) ).

thf(c_0_18,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

thf(c_0_19,plain,
    ( cs4_atom
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X31: $i] :
          ( ( reli @ Z1 @ X31 )
         => ( Z0 @ X31 ) ) ) ),
    inference(fof_simplification,[status(thm)],[cs4_atom]) ).

thf(c_0_20,plain,
    ( mbox
    = ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
        ! [X12: $i] :
          ( ( Z0 @ Z2 @ X12 )
         => ( Z1 @ X12 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mbox]) ).

thf(c_0_21,plain,
    ( cs4_impl
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
        ! [X32: $i] :
          ( ( reli @ Z2 @ X32 )
         => ( ~ ( Z0 @ X32 )
            | ( Z1 @ X32 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[cs4_impl]) ).

thf(c_0_22,plain,
    ( mimpl
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

thf(c_0_23,plain,
    ( cs4_box
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X36: $i] :
          ( ( reli @ Z1 @ X36 )
         => ! [X35: $i] :
              ( ( relr @ X36 @ X35 )
             => ( Z0 @ X35 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[cs4_box]) ).

thf(c_0_24,plain,
    ( bl_princ
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X39: $i] :
          ( ( reli @ Z1 @ X39 )
         => ( Z0 @ X39 ) ) ) ),
    inference(fof_simplification,[status(thm)],[bl_princ]) ).

thf(c_0_25,plain,
    ( cs4_atom
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X31: $i] :
          ( ( reli @ Z1 @ X31 )
         => ( Z0 @ X31 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_19,c_0_20]) ).

thf(c_0_26,plain,
    ( bl_atom
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X38: $i] :
          ( ( reli @ Z1 @ X38 )
         => ( Z0 @ X38 ) ) ) ),
    inference(fof_simplification,[status(thm)],[bl_atom]) ).

thf(c_0_27,plain,
    ( bl_impl
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
        ! [X40: $i] :
          ( ( reli @ Z2 @ X40 )
         => ( ~ ( Z0 @ X40 )
            | ( Z1 @ X40 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[bl_impl]) ).

thf(c_0_28,plain,
    ( cs4_impl
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
        ! [X32: $i] :
          ( ( reli @ Z2 @ X32 )
         => ( ~ ( Z0 @ X32 )
            | ( Z1 @ X32 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_22]),c_0_20]) ).

thf(c_0_29,plain,
    ( bl_says
    = ( ^ [Z0: individuals,Z1: $i > $o,Z2: $i] :
        ! [X45: $i] :
          ( ( reli @ Z2 @ X45 )
         => ! [X46: $i] :
              ( ( relr @ X45 @ X46 )
             => ! [X44: $i] :
                  ( ( reli @ X46 @ X44 )
                 => ( ~ ! [X43: $i] :
                          ( ( reli @ X44 @ X43 )
                         => ( princ_inj @ Z0 @ X43 ) )
                    | ( Z1 @ X44 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[bl_says]) ).

thf(c_0_30,plain,
    ( cs4_box
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X36: $i] :
          ( ( reli @ Z1 @ X36 )
         => ! [X35: $i] :
              ( ( relr @ X36 @ X35 )
             => ( Z0 @ X35 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_23,c_0_20]) ).

thf(c_0_31,plain,
    ( bl_princ
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X39: $i] :
          ( ( reli @ Z1 @ X39 )
         => ( Z0 @ X39 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_24,c_0_25]) ).

thf(c_0_32,plain,
    ( mvalid
    = ( ^ [Z0: $i > $o] :
        ! [X15: $i] : ( Z0 @ X15 ) ) ),
    inference(fof_simplification,[status(thm)],[mvalid]) ).

thf(c_0_33,plain,
    ( bl_atom
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X38: $i] :
          ( ( reli @ Z1 @ X38 )
         => ( Z0 @ X38 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_26,c_0_25]) ).

thf(c_0_34,plain,
    ( bl_impl
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
        ! [X40: $i] :
          ( ( reli @ Z2 @ X40 )
         => ( ~ ( Z0 @ X40 )
            | ( Z1 @ X40 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_27,c_0_28]) ).

thf(c_0_35,plain,
    ( bl_says
    = ( ^ [Z0: individuals,Z1: $i > $o,Z2: $i] :
        ! [X45: $i] :
          ( ( reli @ Z2 @ X45 )
         => ! [X46: $i] :
              ( ( relr @ X45 @ X46 )
             => ! [X44: $i] :
                  ( ( reli @ X46 @ X44 )
                 => ( ~ ! [X43: $i] :
                          ( ( reli @ X44 @ X43 )
                         => ( princ_inj @ Z0 @ X43 ) )
                    | ( Z1 @ X44 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,c_0_28]),c_0_30]),c_0_31]) ).

thf(c_0_36,axiom,
    ( bl_valid
    = ( ^ [Z0: $i > $o] :
        ! [X47: $i] : ( Z0 @ X47 ) ) ),
    inference(apply_def,[status(thm)],[bl_valid_def,c_0_32]) ).

thf(c_0_37,negated_conjecture,
    ~ ! [X23: individuals,X19: $i > $o,X84: $i,X83: $i] :
        ( ( reli @ X84 @ X83 )
       => ( ~ ! [X74: $i] :
                ( ( reli @ X83 @ X74 )
               => ! [X75: $i] :
                    ( ( relr @ X74 @ X75 )
                   => ! [X76: $i] :
                        ( ( reli @ X75 @ X76 )
                       => ( ~ ! [X77: $i] :
                                ( ( reli @ X76 @ X77 )
                               => ( princ_inj @ X23 @ X77 ) )
                          | ! [X70: $i] :
                              ( ( reli @ X76 @ X70 )
                             => ! [X71: $i] :
                                  ( ( relr @ X70 @ X71 )
                                 => ! [X72: $i] :
                                      ( ( reli @ X71 @ X72 )
                                     => ( ~ ! [X73: $i] :
                                              ( ( reli @ X72 @ X73 )
                                             => ( princ_inj @ X23 @ X73 ) )
                                        | ! [X69: $i] :
                                            ( ( reli @ X72 @ X69 )
                                           => ( X19 @ X69 ) ) ) ) ) ) ) ) ) )
          | ! [X79: $i] :
              ( ( reli @ X83 @ X79 )
             => ! [X80: $i] :
                  ( ( relr @ X79 @ X80 )
                 => ! [X81: $i] :
                      ( ( reli @ X80 @ X81 )
                     => ( ~ ! [X82: $i] :
                              ( ( reli @ X81 @ X82 )
                             => ( princ_inj @ X23 @ X82 ) )
                        | ! [X78: $i] :
                            ( ( reli @ X81 @ X78 )
                           => ( X19 @ X78 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[bl_c4]),c_0_33]),c_0_34]),c_0_35]),c_0_36]) ).

thf(c_0_38,negated_conjecture,
    ! [X115: $i,X116: $i,X117: $i,X119: $i,X120: $i,X121: $i,X123: $i,X127: $i] :
      ( ( reli @ esk8_0 @ esk9_0 )
      & ( ( reli @ X121 @ ( esk11_6 @ X115 @ X116 @ X117 @ X119 @ X120 @ X121 ) )
        | ~ ( reli @ X121 @ X123 )
        | ( epred1_0 @ X123 )
        | ~ ( reli @ X120 @ X121 )
        | ~ ( relr @ X119 @ X120 )
        | ~ ( reli @ X117 @ X119 )
        | ( reli @ X117 @ ( esk10_3 @ X115 @ X116 @ X117 ) )
        | ~ ( reli @ X116 @ X117 )
        | ~ ( relr @ X115 @ X116 )
        | ~ ( reli @ esk9_0 @ X115 ) )
      & ( ~ ( princ_inj @ esk7_0 @ ( esk11_6 @ X115 @ X116 @ X117 @ X119 @ X120 @ X121 ) )
        | ~ ( reli @ X121 @ X123 )
        | ( epred1_0 @ X123 )
        | ~ ( reli @ X120 @ X121 )
        | ~ ( relr @ X119 @ X120 )
        | ~ ( reli @ X117 @ X119 )
        | ( reli @ X117 @ ( esk10_3 @ X115 @ X116 @ X117 ) )
        | ~ ( reli @ X116 @ X117 )
        | ~ ( relr @ X115 @ X116 )
        | ~ ( reli @ esk9_0 @ X115 ) )
      & ( ( reli @ X121 @ ( esk11_6 @ X115 @ X116 @ X117 @ X119 @ X120 @ X121 ) )
        | ~ ( reli @ X121 @ X123 )
        | ( epred1_0 @ X123 )
        | ~ ( reli @ X120 @ X121 )
        | ~ ( relr @ X119 @ X120 )
        | ~ ( reli @ X117 @ X119 )
        | ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X115 @ X116 @ X117 ) )
        | ~ ( reli @ X116 @ X117 )
        | ~ ( relr @ X115 @ X116 )
        | ~ ( reli @ esk9_0 @ X115 ) )
      & ( ~ ( princ_inj @ esk7_0 @ ( esk11_6 @ X115 @ X116 @ X117 @ X119 @ X120 @ X121 ) )
        | ~ ( reli @ X121 @ X123 )
        | ( epred1_0 @ X123 )
        | ~ ( reli @ X120 @ X121 )
        | ~ ( relr @ X119 @ X120 )
        | ~ ( reli @ X117 @ X119 )
        | ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X115 @ X116 @ X117 ) )
        | ~ ( reli @ X116 @ X117 )
        | ~ ( relr @ X115 @ X116 )
        | ~ ( reli @ esk9_0 @ X115 ) )
      & ( reli @ esk9_0 @ esk12_0 )
      & ( relr @ esk12_0 @ esk13_0 )
      & ( reli @ esk13_0 @ esk14_0 )
      & ( ~ ( reli @ esk14_0 @ X127 )
        | ( princ_inj @ esk7_0 @ X127 ) )
      & ( reli @ esk14_0 @ esk15_0 )
      & ~ ( epred1_0 @ esk15_0 ) ),
    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_37])])])])])]) ).

thf(c_0_39,negated_conjecture,
    ! [X1: $i,X15: $i,X32: $i,X31: $i,X13: $i,X12: $i,X3: $i] :
      ( ( reli @ X1 @ ( esk11_6 @ X3 @ X12 @ X13 @ X15 @ X31 @ X1 ) )
      | ( epred1_0 @ X32 )
      | ( reli @ X13 @ ( esk10_3 @ X3 @ X12 @ X13 ) )
      | ~ ( reli @ X1 @ X32 )
      | ~ ( reli @ X31 @ X1 )
      | ~ ( relr @ X15 @ X31 )
      | ~ ( reli @ X13 @ X15 )
      | ~ ( reli @ X12 @ X13 )
      | ~ ( relr @ X3 @ X12 )
      | ~ ( reli @ esk9_0 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_40,negated_conjecture,
    reli @ esk14_0 @ esk15_0,
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_41,negated_conjecture,
    ~ ( epred1_0 @ esk15_0 ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_42,negated_conjecture,
    ! [X1: $i] :
      ( ( princ_inj @ esk7_0 @ X1 )
      | ~ ( reli @ esk14_0 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_43,negated_conjecture,
    ! [X1: $i,X13: $i,X12: $i,X15: $i,X3: $i] :
      ( ( reli @ esk14_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ esk14_0 ) )
      | ( reli @ X12 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
      | ~ ( reli @ esk9_0 @ X1 )
      | ~ ( reli @ X15 @ esk14_0 )
      | ~ ( reli @ X12 @ X13 )
      | ~ ( reli @ X3 @ X12 )
      | ~ ( relr @ X13 @ X15 )
      | ~ ( relr @ X1 @ X3 ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).

thf(c_0_44,plain,
    ! [X19: $i > $o,X49: $i] :
      ( ~ ! [X48: $i] :
            ( ( reli @ X49 @ X48 )
           => ( X19 @ X48 ) )
      | ( X19 @ X49 ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[refl_axiom_i,c_0_22]),c_0_20]),c_0_32]) ).

thf(c_0_45,negated_conjecture,
    ! [X15: $i,X32: $i,X31: $i,X13: $i,X12: $i,X3: $i,X1: $i] :
      ( ( epred1_0 @ X32 )
      | ( reli @ X12 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
      | ~ ( princ_inj @ esk7_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ X31 ) )
      | ~ ( reli @ X31 @ X32 )
      | ~ ( reli @ X15 @ X31 )
      | ~ ( relr @ X13 @ X15 )
      | ~ ( reli @ X12 @ X13 )
      | ~ ( reli @ X3 @ X12 )
      | ~ ( relr @ X1 @ X3 )
      | ~ ( reli @ esk9_0 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_46,negated_conjecture,
    ! [X1: $i,X13: $i,X12: $i,X15: $i,X3: $i] :
      ( ( princ_inj @ esk7_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ esk14_0 ) )
      | ( reli @ X12 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
      | ~ ( reli @ esk9_0 @ X1 )
      | ~ ( reli @ X15 @ esk14_0 )
      | ~ ( reli @ X12 @ X13 )
      | ~ ( reli @ X3 @ X12 )
      | ~ ( relr @ X13 @ X15 )
      | ~ ( relr @ X1 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

thf(c_0_47,plain,
    ! [X85: $i > $o,X86: $i] :
      ( ( ( reli @ X86 @ ( esk1_2 @ X85 @ X86 ) )
        | ( X85 @ X86 ) )
      & ( ~ ( X85 @ ( esk1_2 @ X85 @ X86 ) )
        | ( X85 @ X86 ) ) ),
    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_44])])])])]) ).

thf(c_0_48,plain,
    ! [X19: $i > $o,X51: $i] :
      ( ~ ! [X50: $i] :
            ( ( relr @ X51 @ X50 )
           => ( X19 @ X50 ) )
      | ( X19 @ X51 ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[refl_axiom_r,c_0_22]),c_0_20]),c_0_32]) ).

thf(c_0_49,negated_conjecture,
    ! [X1: $i,X3: $i,X15: $i,X13: $i,X31: $i,X12: $i] :
      ( ( reli @ X1 @ ( esk10_3 @ X3 @ X12 @ X1 ) )
      | ( epred1_0 @ X13 )
      | ~ ( reli @ esk9_0 @ X3 )
      | ~ ( reli @ esk14_0 @ X13 )
      | ~ ( reli @ X15 @ esk14_0 )
      | ~ ( reli @ X1 @ X31 )
      | ~ ( reli @ X12 @ X1 )
      | ~ ( relr @ X31 @ X15 )
      | ~ ( relr @ X3 @ X12 ) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

thf(c_0_50,plain,
    ! [X2: $i > $o,X1: $i] :
      ( ( X2 @ X1 )
      | ~ ( X2 @ ( esk1_2 @ X2 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

thf(c_0_51,plain,
    ! [X2: $i > $o,X1: $i] :
      ( ( reli @ X1 @ ( esk1_2 @ X2 @ X1 ) )
      | ( X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

thf(c_0_52,plain,
    ! [X88: $i > $o,X89: $i] :
      ( ( ( relr @ X89 @ ( esk2_2 @ X88 @ X89 ) )
        | ( X88 @ X89 ) )
      & ( ~ ( X88 @ ( esk2_2 @ X88 @ X89 ) )
        | ( X88 @ X89 ) ) ),
    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_48])])])])]) ).

thf(c_0_53,negated_conjecture,
    ! [X1: $i,X15: $i,X3: $i,X13: $i,X12: $i] :
      ( ( reli @ X1 @ ( esk10_3 @ X3 @ X12 @ X1 ) )
      | ~ ( reli @ esk9_0 @ X3 )
      | ~ ( reli @ X13 @ esk14_0 )
      | ~ ( reli @ X1 @ X15 )
      | ~ ( reli @ X12 @ X1 )
      | ~ ( relr @ X15 @ X13 )
      | ~ ( relr @ X3 @ X12 ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_40]),c_0_41]) ).

thf(c_0_54,plain,
    ! [X1: $i] : ( reli @ X1 @ X1 ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

thf(c_0_55,plain,
    ! [X2: $i > $o,X1: $i] :
      ( ( X2 @ X1 )
      | ~ ( X2 @ ( esk2_2 @ X2 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

thf(c_0_56,plain,
    ! [X2: $i > $o,X1: $i] :
      ( ( relr @ X1 @ ( esk2_2 @ X2 @ X1 ) )
      | ( X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

thf(c_0_57,negated_conjecture,
    ! [X1: $i,X15: $i,X32: $i,X31: $i,X13: $i,X12: $i,X3: $i] :
      ( ( reli @ X1 @ ( esk11_6 @ X3 @ X12 @ X13 @ X15 @ X31 @ X1 ) )
      | ( epred1_0 @ X32 )
      | ~ ( reli @ X1 @ X32 )
      | ~ ( reli @ X31 @ X1 )
      | ~ ( relr @ X15 @ X31 )
      | ~ ( reli @ X13 @ X15 )
      | ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X3 @ X12 @ X13 ) )
      | ~ ( reli @ X12 @ X13 )
      | ~ ( relr @ X3 @ X12 )
      | ~ ( reli @ esk9_0 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_58,negated_conjecture,
    ! [X1: $i,X3: $i,X13: $i,X12: $i] :
      ( ( reli @ X1 @ ( esk10_3 @ X3 @ X12 @ X1 ) )
      | ~ ( reli @ esk9_0 @ X3 )
      | ~ ( relr @ X13 @ esk14_0 )
      | ~ ( reli @ X1 @ X13 )
      | ~ ( reli @ X12 @ X1 )
      | ~ ( relr @ X3 @ X12 ) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

thf(c_0_59,plain,
    ! [X1: $i] : ( relr @ X1 @ X1 ),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

thf(c_0_60,negated_conjecture,
    ! [X1: $i,X13: $i,X12: $i,X15: $i,X3: $i] :
      ( ( reli @ esk14_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ esk14_0 ) )
      | ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
      | ~ ( reli @ esk9_0 @ X1 )
      | ~ ( reli @ X15 @ esk14_0 )
      | ~ ( reli @ X12 @ X13 )
      | ~ ( reli @ X3 @ X12 )
      | ~ ( relr @ X13 @ X15 )
      | ~ ( relr @ X1 @ X3 ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_40]),c_0_41]) ).

thf(c_0_61,negated_conjecture,
    ! [X1: $i,X3: $i,X12: $i] :
      ( ( reli @ X1 @ ( esk10_3 @ X3 @ X12 @ X1 ) )
      | ~ ( reli @ esk9_0 @ X3 )
      | ~ ( reli @ X1 @ esk14_0 )
      | ~ ( reli @ X12 @ X1 )
      | ~ ( relr @ X3 @ X12 ) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

thf(c_0_62,negated_conjecture,
    ! [X15: $i,X32: $i,X31: $i,X13: $i,X12: $i,X3: $i,X1: $i] :
      ( ( epred1_0 @ X32 )
      | ~ ( princ_inj @ esk7_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ X31 ) )
      | ~ ( reli @ X31 @ X32 )
      | ~ ( reli @ X15 @ X31 )
      | ~ ( relr @ X13 @ X15 )
      | ~ ( reli @ X12 @ X13 )
      | ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
      | ~ ( reli @ X3 @ X12 )
      | ~ ( relr @ X1 @ X3 )
      | ~ ( reli @ esk9_0 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_63,negated_conjecture,
    ! [X1: $i,X13: $i,X12: $i,X15: $i,X3: $i] :
      ( ( princ_inj @ esk7_0 @ ( esk11_6 @ X1 @ X3 @ X12 @ X13 @ X15 @ esk14_0 ) )
      | ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X1 @ X3 @ X12 ) )
      | ~ ( reli @ esk9_0 @ X1 )
      | ~ ( reli @ X15 @ esk14_0 )
      | ~ ( reli @ X12 @ X13 )
      | ~ ( reli @ X3 @ X12 )
      | ~ ( relr @ X13 @ X15 )
      | ~ ( relr @ X1 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_42,c_0_60]) ).

thf(c_0_64,negated_conjecture,
    ! [X1: $i,X3: $i] :
      ( ( reli @ esk14_0 @ ( esk10_3 @ X1 @ X3 @ esk14_0 ) )
      | ~ ( reli @ esk9_0 @ X1 )
      | ~ ( reli @ X3 @ esk14_0 )
      | ~ ( relr @ X1 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_61,c_0_54]) ).

thf(c_0_65,negated_conjecture,
    ! [X1: $i,X3: $i,X15: $i,X31: $i,X13: $i,X12: $i] :
      ( ( epred1_0 @ X1 )
      | ~ ( princ_inj @ esk7_0 @ ( esk10_3 @ X3 @ X12 @ X13 ) )
      | ~ ( reli @ esk9_0 @ X3 )
      | ~ ( reli @ esk14_0 @ X1 )
      | ~ ( reli @ X15 @ esk14_0 )
      | ~ ( reli @ X13 @ X31 )
      | ~ ( reli @ X12 @ X13 )
      | ~ ( relr @ X31 @ X15 )
      | ~ ( relr @ X3 @ X12 ) ),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

thf(c_0_66,negated_conjecture,
    ! [X1: $i,X3: $i] :
      ( ( princ_inj @ esk7_0 @ ( esk10_3 @ X1 @ X3 @ esk14_0 ) )
      | ~ ( reli @ esk9_0 @ X1 )
      | ~ ( reli @ X3 @ esk14_0 )
      | ~ ( relr @ X1 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_42,c_0_64]) ).

thf(c_0_67,negated_conjecture,
    ! [X1: $i,X3: $i,X13: $i,X12: $i,X15: $i] :
      ( ( epred1_0 @ X1 )
      | ~ ( reli @ esk9_0 @ X3 )
      | ~ ( reli @ esk14_0 @ X1 )
      | ~ ( reli @ X12 @ esk14_0 )
      | ~ ( reli @ esk14_0 @ X13 )
      | ~ ( reli @ X15 @ esk14_0 )
      | ~ ( relr @ X13 @ X12 )
      | ~ ( relr @ X3 @ X15 ) ),
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

thf(c_0_68,negated_conjecture,
    reli @ esk9_0 @ esk12_0,
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_69,negated_conjecture,
    ! [X1: $i,X13: $i,X12: $i,X3: $i] :
      ( ( epred1_0 @ X1 )
      | ~ ( reli @ esk14_0 @ X1 )
      | ~ ( reli @ X3 @ esk14_0 )
      | ~ ( reli @ esk14_0 @ X12 )
      | ~ ( reli @ X13 @ esk14_0 )
      | ~ ( relr @ esk12_0 @ X13 )
      | ~ ( relr @ X12 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_67,c_0_68]) ).

thf(c_0_70,negated_conjecture,
    ! [X12: $i,X3: $i,X1: $i] :
      ( ~ ( reli @ X1 @ esk14_0 )
      | ~ ( reli @ esk14_0 @ X3 )
      | ~ ( reli @ X12 @ esk14_0 )
      | ~ ( relr @ esk12_0 @ X12 )
      | ~ ( relr @ X3 @ X1 ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_40]),c_0_41]) ).

thf(c_0_71,negated_conjecture,
    ! [X3: $i,X1: $i] :
      ( ~ ( reli @ esk14_0 @ X1 )
      | ~ ( reli @ X3 @ esk14_0 )
      | ~ ( relr @ esk12_0 @ X3 )
      | ~ ( relr @ X1 @ esk14_0 ) ),
    inference(spm,[status(thm)],[c_0_70,c_0_54]) ).

thf(c_0_72,negated_conjecture,
    relr @ esk12_0 @ esk13_0,
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_73,negated_conjecture,
    reli @ esk13_0 @ esk14_0,
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_74,negated_conjecture,
    ! [X1: $i] :
      ( ~ ( reli @ esk14_0 @ X1 )
      | ~ ( relr @ X1 @ esk14_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).

thf(c_0_75,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_59]),c_0_54])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10  % Problem    : SWV445^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.11  % Command    : run_E %s %d THM
% 0.10/0.31  % Computer : n015.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Sun May 19 06:54:08 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.16/0.42  Running higher-order theorem proving
% 0.16/0.42  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
% 0.16/0.46  # Version: 3.1.0-ho
% 0.16/0.46  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.16/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.16/0.46  # Starting post_as_ho3 with 300s (1) cores
% 0.16/0.46  # Starting post_as_ho11 with 300s (1) cores
% 0.16/0.46  # Starting full_lambda_8 with 300s (1) cores
% 0.16/0.46  # new_ho_10_cnf2 with pid 19917 completed with status 0
% 0.16/0.46  # Result found by new_ho_10_cnf2
% 0.16/0.46  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.16/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.16/0.46  # No SInE strategy applied
% 0.16/0.46  # Search class: HGUNF-FFMS32-SHSSMSBN
% 0.16/0.46  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.46  # Starting new_ho_10_cnf2 with 901s (1) cores
% 0.16/0.46  # Starting sh5l with 151s (1) cores
% 0.16/0.46  # Starting lpo1_def_fix with 151s (1) cores
% 0.16/0.46  # Starting lpo1_lambda_fix with 151s (1) cores
% 0.16/0.46  # Starting full_lambda_2 with 146s (1) cores
% 0.16/0.46  # lpo1_def_fix with pid 19926 completed with status 0
% 0.16/0.46  # Result found by lpo1_def_fix
% 0.16/0.46  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.16/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.16/0.46  # No SInE strategy applied
% 0.16/0.46  # Search class: HGUNF-FFMS32-SHSSMSBN
% 0.16/0.46  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.46  # Starting new_ho_10_cnf2 with 901s (1) cores
% 0.16/0.46  # Starting sh5l with 151s (1) cores
% 0.16/0.46  # Starting lpo1_def_fix with 151s (1) cores
% 0.16/0.46  # Preprocessing time       : 0.005 s
% 0.16/0.46  # Presaturation interreduction done
% 0.16/0.46  
% 0.16/0.46  # Proof found!
% 0.16/0.46  # SZS status Theorem
% 0.16/0.46  # SZS output start CNFRefutation
% See solution above
% 0.16/0.46  # Parsed axioms                        : 84
% 0.16/0.46  # Removed by relevancy pruning/SinE    : 0
% 0.16/0.46  # Initial clauses                      : 66
% 0.16/0.46  # Removed in clause preprocessing      : 43
% 0.16/0.46  # Initial clauses in saturation        : 23
% 0.16/0.46  # Processed clauses                    : 129
% 0.16/0.46  # ...of these trivial                  : 0
% 0.16/0.46  # ...subsumed                          : 5
% 0.16/0.46  # ...remaining for further processing  : 124
% 0.16/0.46  # Other redundant clauses eliminated   : 2
% 0.16/0.46  # Clauses deleted for lack of memory   : 0
% 0.16/0.46  # Backward-subsumed                    : 23
% 0.16/0.46  # Backward-rewritten                   : 4
% 0.16/0.46  # Generated clauses                    : 338
% 0.16/0.46  # ...of the previous two non-redundant : 292
% 0.16/0.46  # ...aggressively subsumed             : 0
% 0.16/0.46  # Contextual simplify-reflections      : 0
% 0.16/0.46  # Paramodulations                      : 305
% 0.16/0.46  # Factorizations                       : 0
% 0.16/0.46  # NegExts                              : 0
% 0.16/0.46  # Equation resolutions                 : 2
% 0.16/0.46  # Disequality decompositions           : 0
% 0.16/0.46  # Total rewrite steps                  : 33
% 0.16/0.46  # ...of those cached                   : 22
% 0.16/0.46  # Propositional unsat checks           : 0
% 0.16/0.46  #    Propositional check models        : 0
% 0.16/0.46  #    Propositional check unsatisfiable : 0
% 0.16/0.46  #    Propositional clauses             : 0
% 0.16/0.46  #    Propositional clauses after purity: 0
% 0.16/0.46  #    Propositional unsat core size     : 0
% 0.16/0.46  #    Propositional preprocessing time  : 0.000
% 0.16/0.46  #    Propositional encoding time       : 0.000
% 0.16/0.46  #    Propositional solver time         : 0.000
% 0.16/0.46  #    Success case prop preproc time    : 0.000
% 0.16/0.46  #    Success case prop encoding time   : 0.000
% 0.16/0.46  #    Success case prop solver time     : 0.000
% 0.16/0.46  # Current number of processed clauses  : 74
% 0.16/0.46  #    Positive orientable unit clauses  : 16
% 0.16/0.46  #    Positive unorientable unit clauses: 0
% 0.16/0.46  #    Negative unit clauses             : 3
% 0.16/0.46  #    Non-unit-clauses                  : 55
% 0.16/0.46  # Current number of unprocessed clauses: 202
% 0.16/0.46  # ...number of literals in the above   : 1191
% 0.16/0.46  # Current number of archived formulas  : 0
% 0.16/0.46  # Current number of archived clauses   : 50
% 0.16/0.46  # Clause-clause subsumption calls (NU) : 3017
% 0.16/0.46  # Rec. Clause-clause subsumption calls : 561
% 0.16/0.46  # Non-unit clause-clause subsumptions  : 26
% 0.16/0.46  # Unit Clause-clause subsumption calls : 148
% 0.16/0.46  # Rewrite failures with RHS unbound    : 0
% 0.16/0.46  # BW rewrite match attempts            : 16
% 0.16/0.46  # BW rewrite match successes           : 3
% 0.16/0.46  # Condensation attempts                : 0
% 0.16/0.46  # Condensation successes               : 0
% 0.16/0.46  # Termbank termtop insertions          : 19350
% 0.16/0.46  # Search garbage collected termcells   : 1859
% 0.16/0.46  
% 0.16/0.46  # -------------------------------------------------
% 0.16/0.46  # User time                : 0.026 s
% 0.16/0.46  # System time              : 0.006 s
% 0.16/0.46  # Total time               : 0.032 s
% 0.16/0.46  # Maximum resident set size: 2156 pages
% 0.16/0.46  
% 0.16/0.46  # -------------------------------------------------
% 0.16/0.46  # User time                : 0.114 s
% 0.16/0.46  # System time              : 0.031 s
% 0.16/0.46  # Total time               : 0.145 s
% 0.16/0.46  # Maximum resident set size: 1788 pages
% 0.16/0.46  % E---3.1 exiting
% 0.16/0.46  % E exiting
%------------------------------------------------------------------------------