TSTP Solution File: NUM690^4 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM690^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n018.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 01:15:36 EDT 2024

% Result   : Theorem 0.16s 0.52s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   80 (  36 unt;  21 typ;   0 def)
%            Number of atoms       :  272 (  48 equ;   0 cnn)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  595 (  56   ~;  41   |;   8   &; 444   @)
%                                         (   0 <=>;  46  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   45 (  45   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  21 usr;   7 con; 0-3 aty)
%            Number of variables   :  120 (  82   ^  38   !;   0   ?; 120   :)

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

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

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

thf(decl_61,type,
    imp: $o > $o > $o ).

thf(decl_62,type,
    d_not: $o > $o ).

thf(decl_67,type,
    l_or: $o > $o > $o ).

thf(decl_72,type,
    l_some: $i > ( $i > $o ) > $o ).

thf(decl_77,type,
    e_is: $i > $i > $i > $o ).

thf(decl_123,type,
    nat: $i ).

thf(decl_124,type,
    n_is: $i > $i > $o ).

thf(decl_127,type,
    n_some: ( $i > $o ) > $o ).

thf(decl_142,type,
    n_pl: $i > $i > $i ).

thf(decl_147,type,
    diffprop: $i > $i > $i > $o ).

thf(decl_148,type,
    d_29_ii: $i > $i > $o ).

thf(decl_149,type,
    iii: $i > $i > $o ).

thf(decl_151,type,
    moreis: $i > $i > $o ).

thf(decl_152,type,
    lessis: $i > $i > $o ).

thf(decl_155,type,
    esk1_0: $i ).

thf(decl_156,type,
    esk2_0: $i ).

thf(decl_157,type,
    esk3_0: $i ).

thf(decl_158,type,
    esk4_0: $i ).

thf(def_d_not,axiom,
    ( d_not
    = ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_d_not) ).

thf(def_imp,axiom,
    ( imp
    = ( ^ [X74: $o,X75: $o] :
          ( X74
         => X75 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_imp) ).

thf(def_d_29_ii,axiom,
    ( d_29_ii
    = ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_d_29_ii) ).

thf(def_l_or,axiom,
    ( l_or
    = ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_l_or) ).

thf(def_e_is,axiom,
    ( e_is
    = ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_e_is) ).

thf(def_iii,axiom,
    ( iii
    = ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_iii) ).

thf(def_all_of,axiom,
    ( all_of
    = ( ^ [X3: $i > $o,X2: $i > $o] :
        ! [X4: $i] :
          ( ( is_of @ X4 @ X3 )
         => ( X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_all_of) ).

thf(def_is_of,axiom,
    ( is_of
    = ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_is_of) ).

thf(def_moreis,axiom,
    ( moreis
    = ( ^ [X1: $i,X229: $i] : ( l_or @ ( d_29_ii @ X1 @ X229 ) @ ( n_is @ X1 @ X229 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_moreis) ).

thf(def_n_some,axiom,
    ( n_some
    = ( l_some @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_some) ).

thf(def_n_is,axiom,
    ( n_is
    = ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_is) ).

thf(def_lessis,axiom,
    ( lessis
    = ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_lessis) ).

thf(satz22b,axiom,
    ( all_of
    @ ^ [X1: $i] : ( in @ X1 @ nat )
    @ ^ [X1: $i] :
        ( all_of
        @ ^ [X313: $i] : ( in @ X313 @ nat )
        @ ^ [X314: $i] :
            ( all_of
            @ ^ [X4: $i] : ( in @ X4 @ nat )
            @ ^ [X4: $i] :
                ( all_of
                @ ^ [X13: $i] : ( in @ X13 @ nat )
                @ ^ [X13: $i] :
                    ( ( d_29_ii @ X1 @ X314 )
                   => ( ( moreis @ X4 @ X13 )
                     => ( d_29_ii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X314 @ X13 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22b) ).

thf(satz22d,conjecture,
    ( all_of
    @ ^ [X1: $i] : ( in @ X1 @ nat )
    @ ^ [X1: $i] :
        ( all_of
        @ ^ [X317: $i] : ( in @ X317 @ nat )
        @ ^ [X318: $i] :
            ( all_of
            @ ^ [X4: $i] : ( in @ X4 @ nat )
            @ ^ [X4: $i] :
                ( all_of
                @ ^ [X13: $i] : ( in @ X13 @ nat )
                @ ^ [X13: $i] :
                    ( ( iii @ X1 @ X318 )
                   => ( ( lessis @ X4 @ X13 )
                     => ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X318 @ X13 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22d) ).

thf(satz6,axiom,
    ( all_of
    @ ^ [X1: $i] : ( in @ X1 @ nat )
    @ ^ [X1: $i] :
        ( all_of
        @ ^ [X197: $i] : ( in @ X197 @ nat )
        @ ^ [X198: $i] : ( n_is @ ( n_pl @ X1 @ X198 ) @ ( n_pl @ X198 @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).

thf(satz19f,axiom,
    ( all_of
    @ ^ [X1: $i] : ( in @ X1 @ nat )
    @ ^ [X1: $i] :
        ( all_of
        @ ^ [X277: $i] : ( in @ X277 @ nat )
        @ ^ [X278: $i] :
            ( all_of
            @ ^ [X4: $i] : ( in @ X4 @ nat )
            @ ^ [X4: $i] :
                ( ( iii @ X1 @ X278 )
               => ( iii @ ( n_pl @ X4 @ X1 ) @ ( n_pl @ X4 @ X278 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19f) ).

thf(c_0_16,plain,
    ( d_not
    = ( ^ [Z0: $o] :
          ( Z0
         => ~ $true ) ) ),
    inference(fof_simplification,[status(thm)],[def_d_not]) ).

thf(c_0_17,plain,
    ( imp
    = ( ^ [Z0: $o,Z1: $o] :
          ( Z0
         => Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[def_imp]) ).

thf(c_0_18,plain,
    ( d_29_ii
    = ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).

thf(c_0_19,plain,
    ( l_or
    = ( ^ [Z0: $o,Z1: $o] :
          ( ( Z0
           => ~ $true )
         => Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[def_l_or]) ).

thf(c_0_20,plain,
    ( d_not
    = ( ^ [Z0: $o] :
          ( Z0
         => ~ $true ) ) ),
    inference(apply_def,[status(thm)],[c_0_16,c_0_17]) ).

thf(c_0_21,plain,
    ( e_is
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
    inference(fof_simplification,[status(thm)],[def_e_is]) ).

thf(c_0_22,plain,
    ( iii
    = ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[def_iii]) ).

thf(c_0_23,plain,
    ( all_of
    = ( ^ [Z0: $i > $o,Z1: $i > $o] :
        ! [X4: $i] :
          ( ( Z0 @ X4 )
         => ( Z1 @ X4 ) ) ) ),
    inference(fof_simplification,[status(thm)],[def_all_of]) ).

thf(c_0_24,plain,
    ( is_of
    = ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
    inference(fof_simplification,[status(thm)],[def_is_of]) ).

thf(c_0_25,plain,
    ( moreis
    = ( ^ [Z0: $i,Z1: $i] :
          ( ( ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) )
           => ~ $true )
         => ( Z0 = Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[def_moreis]) ).

thf(c_0_26,plain,
    ( d_29_ii
    = ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_18,def_n_some]) ).

thf(c_0_27,plain,
    ( l_or
    = ( ^ [Z0: $o,Z1: $o] :
          ( ( Z0
           => ~ $true )
         => Z1 ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19,c_0_17]),c_0_20]) ).

thf(c_0_28,axiom,
    ( n_is
    = ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
    inference(apply_def,[status(thm)],[def_n_is,c_0_21]) ).

thf(c_0_29,plain,
    ( lessis
    = ( ^ [Z0: $i,Z1: $i] :
          ( ( ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) )
           => ~ $true )
         => ( Z0 = Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[def_lessis]) ).

thf(c_0_30,plain,
    ( iii
    = ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_22,def_n_some]) ).

thf(c_0_31,plain,
    ( all_of
    = ( ^ [Z0: $i > $o,Z1: $i > $o] :
        ! [X4: $i] :
          ( ( Z0 @ X4 )
         => ( Z1 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_23,c_0_24]) ).

thf(c_0_32,plain,
    ( moreis
    = ( ^ [Z0: $i,Z1: $i] :
          ( ( ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) )
           => ~ $true )
         => ( Z0 = Z1 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]) ).

thf(c_0_33,plain,
    ( lessis
    = ( ^ [Z0: $i,Z1: $i] :
          ( ( ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) )
           => ~ $true )
         => ( Z0 = Z1 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,c_0_30]),c_0_27]),c_0_28]) ).

thf(c_0_34,plain,
    ! [X522: $i] :
      ( ( in @ X522 @ nat )
     => ! [X521: $i] :
          ( ( in @ X521 @ nat )
         => ! [X520: $i] :
              ( ( in @ X520 @ nat )
             => ! [X519: $i] :
                  ( ( in @ X519 @ nat )
                 => ( ( l_some @ nat @ ( diffprop @ X522 @ X521 ) )
                   => ( ( ( ( l_some @ nat @ ( diffprop @ X520 @ X519 ) )
                         => ~ $true )
                       => ( X520 = X519 ) )
                     => ( l_some @ nat @ ( diffprop @ ( n_pl @ X522 @ X520 ) @ ( n_pl @ X521 @ X519 ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz22b]),c_0_26]),c_0_31]),c_0_32]) ).

thf(c_0_35,negated_conjecture,
    ~ ! [X389: $i] :
        ( ( in @ X389 @ nat )
       => ! [X388: $i] :
            ( ( in @ X388 @ nat )
           => ! [X387: $i] :
                ( ( in @ X387 @ nat )
               => ! [X386: $i] :
                    ( ( in @ X386 @ nat )
                   => ( ( l_some @ nat @ ( diffprop @ X388 @ X389 ) )
                     => ( ( ( ( l_some @ nat @ ( diffprop @ X386 @ X387 ) )
                           => ~ $true )
                         => ( X387 = X386 ) )
                       => ( l_some @ nat @ ( diffprop @ ( n_pl @ X388 @ X386 ) @ ( n_pl @ X389 @ X387 ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz22d])]),c_0_33]),c_0_30]),c_0_31]) ).

thf(c_0_36,plain,
    ! [X404: $i] :
      ( ( in @ X404 @ nat )
     => ! [X403: $i] :
          ( ( in @ X403 @ nat )
         => ( ( n_pl @ X404 @ X403 )
            = ( n_pl @ X403 @ X404 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz6]),c_0_31]),c_0_28]) ).

thf(c_0_37,plain,
    ! [X714: $i,X715: $i,X716: $i,X717: $i] :
      ( ( ~ ( l_some @ nat @ ( diffprop @ X716 @ X717 ) )
        | ~ $true
        | ( l_some @ nat @ ( diffprop @ ( n_pl @ X714 @ X716 ) @ ( n_pl @ X715 @ X717 ) ) )
        | ~ ( l_some @ nat @ ( diffprop @ X714 @ X715 ) )
        | ~ ( in @ X717 @ nat )
        | ~ ( in @ X716 @ nat )
        | ~ ( in @ X715 @ nat )
        | ~ ( in @ X714 @ nat ) )
      & ( ( X716 != X717 )
        | ( l_some @ nat @ ( diffprop @ ( n_pl @ X714 @ X716 ) @ ( n_pl @ X715 @ X717 ) ) )
        | ~ ( l_some @ nat @ ( diffprop @ X714 @ X715 ) )
        | ~ ( in @ X717 @ nat )
        | ~ ( in @ X716 @ nat )
        | ~ ( in @ X715 @ nat )
        | ~ ( in @ X714 @ nat ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])])]) ).

thf(c_0_38,negated_conjecture,
    ( ( in @ esk1_0 @ nat )
    & ( in @ esk2_0 @ nat )
    & ( in @ esk3_0 @ nat )
    & ( in @ esk4_0 @ nat )
    & ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
    & ( ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) )
      | ( esk3_0 = esk4_0 ) )
    & ( $true
      | ( esk3_0 = esk4_0 ) )
    & ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ) ),
    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_35])])])])]) ).

thf(c_0_39,plain,
    ! [X602: $i,X603: $i] :
      ( ~ ( in @ X602 @ nat )
      | ~ ( in @ X603 @ nat )
      | ( ( n_pl @ X602 @ X603 )
        = ( n_pl @ X603 @ X602 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])]) ).

thf(c_0_40,plain,
    ! [X1: $i,X4: $i,X6: $i,X5: $i] :
      ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X6 @ X4 ) ) )
      | ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) )
      | ~ $true
      | ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) )
      | ~ ( in @ X4 @ nat )
      | ~ ( in @ X1 @ nat )
      | ~ ( in @ X6 @ nat )
      | ~ ( in @ X5 @ nat ) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

thf(c_0_41,negated_conjecture,
    ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk2_0 @ esk4_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_42,plain,
    ! [X1: $i,X4: $i] :
      ( ( ( n_pl @ X1 @ X4 )
        = ( n_pl @ X4 @ X1 ) )
      | ~ ( in @ X1 @ nat )
      | ~ ( in @ X4 @ nat ) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

thf(c_0_43,negated_conjecture,
    in @ esk2_0 @ nat,
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_44,negated_conjecture,
    in @ esk4_0 @ nat,
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_45,plain,
    ! [X1: $i,X6: $i,X5: $i,X4: $i] :
      ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X6 @ X4 ) ) )
      | ~ ( in @ X6 @ nat )
      | ~ ( in @ X5 @ nat )
      | ~ ( in @ X4 @ nat )
      | ~ ( in @ X1 @ nat )
      | ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) )
      | ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) ) ),
    inference(cn,[status(thm)],[c_0_40]) ).

thf(c_0_46,negated_conjecture,
    l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_47,negated_conjecture,
    in @ esk1_0 @ nat,
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_48,negated_conjecture,
    in @ esk3_0 @ nat,
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_49,negated_conjecture,
    ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk4_0 @ esk2_0 ) @ ( n_pl @ esk1_0 @ esk3_0 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44])]) ).

thf(c_0_50,negated_conjecture,
    ( ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) )
    | ( esk3_0 = esk4_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_51,negated_conjecture,
    ~ ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_45]),c_0_46]),c_0_47]),c_0_43]),c_0_48]),c_0_44])]) ).

thf(c_0_52,plain,
    ! [X438: $i] :
      ( ( in @ X438 @ nat )
     => ! [X437: $i] :
          ( ( in @ X437 @ nat )
         => ! [X436: $i] :
              ( ( in @ X436 @ nat )
             => ( ( l_some @ nat @ ( diffprop @ X437 @ X438 ) )
               => ( l_some @ nat @ ( diffprop @ ( n_pl @ X436 @ X437 ) @ ( n_pl @ X436 @ X438 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz19f]),c_0_30]),c_0_31]) ).

thf(c_0_53,negated_conjecture,
    ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk4_0 @ esk2_0 ) @ ( n_pl @ esk3_0 @ esk1_0 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_42]),c_0_48]),c_0_47])]) ).

thf(c_0_54,negated_conjecture,
    esk4_0 = esk3_0,
    inference(sr,[status(thm)],[c_0_50,c_0_51]) ).

thf(c_0_55,plain,
    ! [X631: $i,X632: $i,X633: $i] :
      ( ~ ( in @ X631 @ nat )
      | ~ ( in @ X632 @ nat )
      | ~ ( in @ X633 @ nat )
      | ~ ( l_some @ nat @ ( diffprop @ X632 @ X631 ) )
      | ( l_some @ nat @ ( diffprop @ ( n_pl @ X633 @ X632 ) @ ( n_pl @ X633 @ X631 ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).

thf(c_0_56,negated_conjecture,
    ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk3_0 @ esk2_0 ) @ ( n_pl @ esk3_0 @ esk1_0 ) ) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

thf(c_0_57,plain,
    ! [X5: $i,X4: $i,X1: $i] :
      ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X4 ) @ ( n_pl @ X5 @ X1 ) ) )
      | ~ ( in @ X1 @ nat )
      | ~ ( in @ X4 @ nat )
      | ~ ( in @ X5 @ nat )
      | ~ ( l_some @ nat @ ( diffprop @ X4 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

thf(c_0_58,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_46]),c_0_48]),c_0_43]),c_0_47])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : NUM690^4 : TPTP v8.2.0. Released v7.1.0.
% 0.05/0.11  % Command    : run_E %s %d THM
% 0.11/0.31  % Computer : n018.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Mon May 20 06:59:07 EDT 2024
% 0.11/0.31  % 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
% 0.16/0.52  # Version: 3.1.0-ho
% 0.16/0.52  # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.16/0.52  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.52  # Starting lpo1_fix with 900s (3) cores
% 0.16/0.52  # Starting full_lambda_9 with 300s (1) cores
% 0.16/0.52  # Starting almost_fo_4 with 300s (1) cores
% 0.16/0.52  # Starting new_ho_9 with 300s (1) cores
% 0.16/0.52  # Starting pre_casc_4 with 300s (1) cores
% 0.16/0.52  # Starting ho_unfolding_6 with 300s (1) cores
% 0.16/0.52  # full_lambda_9 with pid 8771 completed with status 0
% 0.16/0.52  # Result found by full_lambda_9
% 0.16/0.52  # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.16/0.52  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.52  # Starting lpo1_fix with 900s (3) cores
% 0.16/0.52  # Starting full_lambda_9 with 300s (1) cores
% 0.16/0.52  # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.16/0.52  # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.16/0.52  # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.16/0.52  # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.52  # Starting full_lambda_5 with 25s (1) cores
% 0.16/0.52  # full_lambda_5 with pid 8776 completed with status 0
% 0.16/0.52  # Result found by full_lambda_5
% 0.16/0.52  # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.16/0.52  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.52  # Starting lpo1_fix with 900s (3) cores
% 0.16/0.52  # Starting full_lambda_9 with 300s (1) cores
% 0.16/0.52  # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.16/0.52  # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.16/0.52  # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.16/0.52  # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.52  # Starting full_lambda_5 with 25s (1) cores
% 0.16/0.52  # Preprocessing time       : 0.004 s
% 0.16/0.52  # Presaturation interreduction done
% 0.16/0.52  
% 0.16/0.52  # Proof found!
% 0.16/0.52  # SZS status Theorem
% 0.16/0.52  # SZS output start CNFRefutation
% See solution above
% 0.16/0.52  # Parsed axioms                        : 394
% 0.16/0.52  # Removed by relevancy pruning/SinE    : 263
% 0.16/0.52  # Initial clauses                      : 346
% 0.16/0.52  # Removed in clause preprocessing      : 175
% 0.16/0.52  # Initial clauses in saturation        : 171
% 0.16/0.52  # Processed clauses                    : 366
% 0.16/0.52  # ...of these trivial                  : 5
% 0.16/0.52  # ...subsumed                          : 90
% 0.16/0.52  # ...remaining for further processing  : 271
% 0.16/0.52  # Other redundant clauses eliminated   : 23
% 0.16/0.52  # Clauses deleted for lack of memory   : 0
% 0.16/0.52  # Backward-subsumed                    : 0
% 0.16/0.52  # Backward-rewritten                   : 2
% 0.16/0.52  # Generated clauses                    : 749
% 0.16/0.52  # ...of the previous two non-redundant : 721
% 0.16/0.52  # ...aggressively subsumed             : 0
% 0.16/0.52  # Contextual simplify-reflections      : 1
% 0.16/0.52  # Paramodulations                      : 557
% 0.16/0.52  # Factorizations                       : 2
% 0.16/0.52  # NegExts                              : 2
% 0.16/0.52  # Equation resolutions                 : 29
% 0.16/0.52  # Disequality decompositions           : 0
% 0.16/0.52  # Total rewrite steps                  : 143
% 0.16/0.52  # ...of those cached                   : 126
% 0.16/0.52  # Propositional unsat checks           : 0
% 0.16/0.52  #    Propositional check models        : 0
% 0.16/0.52  #    Propositional check unsatisfiable : 0
% 0.16/0.52  #    Propositional clauses             : 0
% 0.16/0.52  #    Propositional clauses after purity: 0
% 0.16/0.52  #    Propositional unsat core size     : 0
% 0.16/0.52  #    Propositional preprocessing time  : 0.000
% 0.16/0.52  #    Propositional encoding time       : 0.000
% 0.16/0.52  #    Propositional solver time         : 0.000
% 0.16/0.52  #    Success case prop preproc time    : 0.000
% 0.16/0.52  #    Success case prop encoding time   : 0.000
% 0.16/0.52  #    Success case prop solver time     : 0.000
% 0.16/0.52  # Current number of processed clauses  : 142
% 0.16/0.52  #    Positive orientable unit clauses  : 20
% 0.16/0.52  #    Positive unorientable unit clauses: 0
% 0.16/0.52  #    Negative unit clauses             : 17
% 0.16/0.52  #    Non-unit-clauses                  : 105
% 0.16/0.52  # Current number of unprocessed clauses: 636
% 0.16/0.52  # ...number of literals in the above   : 3248
% 0.16/0.52  # Current number of archived formulas  : 0
% 0.16/0.52  # Current number of archived clauses   : 114
% 0.16/0.52  # Clause-clause subsumption calls (NU) : 6020
% 0.16/0.52  # Rec. Clause-clause subsumption calls : 1343
% 0.16/0.52  # Non-unit clause-clause subsumptions  : 80
% 0.16/0.52  # Unit Clause-clause subsumption calls : 134
% 0.16/0.52  # Rewrite failures with RHS unbound    : 0
% 0.16/0.52  # BW rewrite match attempts            : 5
% 0.16/0.52  # BW rewrite match successes           : 1
% 0.16/0.52  # Condensation attempts                : 0
% 0.16/0.52  # Condensation successes               : 0
% 0.16/0.52  # Termbank termtop insertions          : 65767
% 0.16/0.52  # Search garbage collected termcells   : 17389
% 0.16/0.52  
% 0.16/0.52  # -------------------------------------------------
% 0.16/0.52  # User time                : 0.070 s
% 0.16/0.52  # System time              : 0.007 s
% 0.16/0.52  # Total time               : 0.077 s
% 0.16/0.52  # Maximum resident set size: 4932 pages
% 0.16/0.52  
% 0.16/0.52  # -------------------------------------------------
% 0.16/0.52  # User time                : 0.078 s
% 0.16/0.52  # System time              : 0.010 s
% 0.16/0.52  # Total time               : 0.088 s
% 0.16/0.52  # Maximum resident set size: 2372 pages
% 0.16/0.52  % E---3.1 exiting
% 0.16/0.52  % E exiting
%------------------------------------------------------------------------------