TSTP Solution File: NUM768^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM768^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n027.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 01:17:11 EDT 2024

% Result   : Theorem 1.15s 0.61s
% Output   : CNFRefutation 1.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   89 (  26 unt;  17 typ;   0 def)
%            Number of atoms       :  150 (  34 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  825 (  45   ~;  38   |;   2   &; 729   @)
%                                         (   2 <=>;   8  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   28 (  28   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   4 con; 0-3 aty)
%            Number of variables   :  125 (   8   ^ 117   !;   0   ?; 125   :)

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

thf(decl_sort2,type,
    nat: $tType ).

thf(decl_22,type,
    x: frac ).

thf(decl_23,type,
    y: frac ).

thf(decl_24,type,
    some: ( nat > $o ) > $o ).

thf(decl_25,type,
    ts: nat > nat > nat ).

thf(decl_26,type,
    num: frac > nat ).

thf(decl_27,type,
    den: frac > nat ).

thf(decl_28,type,
    pl: nat > nat > nat ).

thf(decl_29,type,
    eq: frac > frac > $o ).

thf(decl_30,type,
    pf: frac > frac > frac ).

thf(decl_31,type,
    fr: nat > nat > frac ).

thf(decl_32,type,
    ind: ( nat > $o ) > nat ).

thf(decl_33,type,
    amone: ( nat > $o ) > $o ).

thf(decl_34,type,
    epred1_0: nat > $o ).

thf(decl_35,type,
    epred2_2: nat > nat > nat > $o ).

thf(decl_40,type,
    esk5_2: nat > nat > nat ).

thf(satz8b,axiom,
    ! [X2: nat,X3: nat] :
      ( amone
      @ ^ [X4: nat] :
          ( X2
          = ( pl @ X3 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz8b) ).

thf(satz29,axiom,
    ! [X2: nat,X3: nat] :
      ( ( ts @ X2 @ X3 )
      = ( ts @ X3 @ X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).

thf(oneax,axiom,
    ! [X17: nat > $o] :
      ( ~ ( ( amone @ X17 )
         => ~ ( some @ X17 ) )
     => ( X17 @ ( ind @ X17 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneax) ).

thf(satz57,axiom,
    ! [X15: nat,X16: nat,X13: nat] : ( eq @ ( pf @ ( fr @ X15 @ X13 ) @ ( fr @ X16 @ X13 ) ) @ ( fr @ ( pl @ X15 @ X16 ) @ X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz57) ).

thf(satz56,axiom,
    ! [X8: frac,X9: frac,X10: frac,X11: frac] :
      ( ( eq @ X8 @ X9 )
     => ( ( eq @ X10 @ X11 )
       => ( eq @ ( pf @ X8 @ X10 ) @ ( pf @ X9 @ X11 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56) ).

thf(satz37,axiom,
    ! [X14: frac] : ( eq @ X14 @ X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).

thf(satz40,axiom,
    ! [X12: frac,X13: nat] : ( eq @ X12 @ ( fr @ ( ts @ ( num @ X12 ) @ X13 ) @ ( ts @ ( den @ X12 ) @ X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz40) ).

thf(m,axiom,
    ( some
    @ ^ [X1: nat] :
        ( ( ts @ ( num @ x ) @ ( den @ y ) )
        = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).

thf(satz67c,conjecture,
    ( eq
    @ ( pf @ y
      @ ( fr
        @ ( ind
          @ ^ [X19: nat] :
              ( ( ts @ ( num @ x ) @ ( den @ y ) )
              = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X19 ) ) )
        @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
    @ x ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz67c) ).

thf(satz39,axiom,
    ! [X5: frac,X6: frac,X7: frac] :
      ( ( eq @ X5 @ X6 )
     => ( ( eq @ X6 @ X7 )
       => ( eq @ X5 @ X7 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39) ).

thf(satz40a,axiom,
    ! [X18: frac,X13: nat] : ( eq @ ( fr @ ( ts @ ( num @ X18 ) @ X13 ) @ ( ts @ ( den @ X18 ) @ X13 ) ) @ X18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz40a) ).

thf(c_0_11,plain,
    ! [X2: nat,X3: nat] :
      ( amone
      @ ^ [Z0: nat] :
          ( X2
          = ( pl @ X3 @ Z0 ) ) ),
    inference(fof_simplification,[status(thm)],[satz8b]) ).

thf(c_0_12,plain,
    ! [X63: nat] :
      ( ( ~ ( epred1_0 @ X63 )
        | ( ( ts @ ( num @ x ) @ ( den @ y ) )
          = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X63 ) ) )
      & ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
         != ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X63 ) )
        | ( epred1_0 @ X63 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).

thf(c_0_13,plain,
    ! [X52: nat,X53: nat] :
      ( ( ts @ X52 @ X53 )
      = ( ts @ X53 @ X52 ) ),
    inference(variable_rename,[status(thm)],[satz29]) ).

thf(c_0_14,plain,
    ! [X17: nat > $o] :
      ( ~ ( ( amone @ X17 )
         => ~ ( some @ X17 ) )
     => ( X17 @ ( ind @ X17 ) ) ),
    inference(fof_simplification,[status(thm)],[oneax]) ).

thf(c_0_15,plain,
    ! [X40: nat,X41: nat] :
      ( amone
      @ ^ [Z0: nat] :
          ( X40
          = ( pl @ X41 @ Z0 ) ) ),
    inference(variable_rename,[status(thm)],[c_0_11]) ).

thf(c_0_16,plain,
    ! [X61: nat,X1: nat,X2: nat] :
      ( ( epred2_2 @ X2 @ X1 @ X61 )
    <=> ( X1
        = ( pl @ X2 @ X61 ) ) ),
    introduced(definition) ).

thf(c_0_17,plain,
    ! [X54: nat,X55: nat,X56: nat] : ( eq @ ( pf @ ( fr @ X54 @ X56 ) @ ( fr @ X55 @ X56 ) ) @ ( fr @ ( pl @ X54 @ X55 ) @ X56 ) ),
    inference(variable_rename,[status(thm)],[satz57]) ).

thf(c_0_18,plain,
    ! [X1: nat] :
      ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
        = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X1 ) )
      | ~ ( epred1_0 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_19,plain,
    ! [X2: nat,X1: nat] :
      ( ( ts @ X1 @ X2 )
      = ( ts @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_20,plain,
    ! [X45: frac,X46: frac,X47: frac,X48: frac] :
      ( ~ ( eq @ X45 @ X46 )
      | ~ ( eq @ X47 @ X48 )
      | ( eq @ ( pf @ X45 @ X47 ) @ ( pf @ X46 @ X48 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz56])])]) ).

thf(c_0_21,plain,
    ! [X51: frac] : ( eq @ X51 @ X51 ),
    inference(variable_rename,[status(thm)],[satz37]) ).

thf(c_0_22,plain,
    ! [X49: frac,X50: nat] : ( eq @ X49 @ ( fr @ ( ts @ ( num @ X49 ) @ X50 ) @ ( ts @ ( den @ X49 ) @ X50 ) ) ),
    inference(variable_rename,[status(thm)],[satz40]) ).

thf(c_0_23,plain,
    ! [X64: nat,X65: nat,X66: nat] :
      ( ( ~ ( epred2_2 @ X66 @ X65 @ X64 )
        | ( X65
          = ( pl @ X66 @ X64 ) ) )
      & ( ( X65
         != ( pl @ X66 @ X64 ) )
        | ( epred2_2 @ X66 @ X65 @ X64 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).

thf(c_0_24,plain,
    ! [X57: nat > $o] :
      ( ~ ( amone @ X57 )
      | ~ ( some @ X57 )
      | ( X57 @ ( ind @ X57 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).

thf(c_0_25,plain,
    ! [X2: nat,X1: nat] :
      ( ( amone @ ( epred2_2 @ X2 @ X1 ) )
      = $true ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_15]),c_0_16]) ).

thf(c_0_26,plain,
    ( some
    @ ^ [Z0: nat] :
        ( ( ts @ ( num @ x ) @ ( den @ y ) )
        = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Z0 ) ) ),
    inference(fof_simplification,[status(thm)],[m]) ).

thf(c_0_27,plain,
    ! [X60: nat] :
      ( ( epred1_0 @ X60 )
    <=> ( ( ts @ ( num @ x ) @ ( den @ y ) )
        = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X60 ) ) ),
    introduced(definition) ).

thf(c_0_28,negated_conjecture,
    ~ ( eq
      @ ( pf @ y
        @ ( fr
          @ ( ind
            @ ^ [Z0: nat] :
                ( ( ts @ ( num @ x ) @ ( den @ y ) )
                = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Z0 ) ) )
          @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
      @ x ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz67c])])]) ).

thf(c_0_29,plain,
    ! [X42: frac,X43: frac,X44: frac] :
      ( ~ ( eq @ X42 @ X43 )
      | ~ ( eq @ X43 @ X44 )
      | ( eq @ X42 @ X44 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz39])])]) ).

thf(c_0_30,plain,
    ! [X58: frac,X59: nat] : ( eq @ ( fr @ ( ts @ ( num @ X58 ) @ X59 ) @ ( ts @ ( den @ X58 ) @ X59 ) ) @ X58 ),
    inference(variable_rename,[status(thm)],[satz40a]) ).

thf(c_0_31,plain,
    ! [X1: nat,X3: nat,X2: nat] : ( eq @ ( pf @ ( fr @ X1 @ X2 ) @ ( fr @ X3 @ X2 ) ) @ ( fr @ ( pl @ X1 @ X3 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_32,plain,
    ! [X1: nat] :
      ( ( ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ X1 )
        = ( ts @ ( den @ y ) @ ( num @ x ) ) )
      | ~ ( epred1_0 @ X1 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).

thf(c_0_33,plain,
    ! [X5: frac,X6: frac,X7: frac,X8: frac] :
      ( ( eq @ ( pf @ X5 @ X7 ) @ ( pf @ X6 @ X8 ) )
      | ~ ( eq @ X5 @ X6 )
      | ~ ( eq @ X7 @ X8 ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_34,plain,
    ! [X5: frac] : ( eq @ X5 @ X5 ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_35,plain,
    ! [X5: frac,X1: nat] : ( eq @ X5 @ ( fr @ ( ts @ ( num @ X5 ) @ X1 ) @ ( ts @ ( den @ X5 ) @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_36,plain,
    ! [X1: nat,X2: nat,X3: nat] :
      ( ( X2
        = ( pl @ X1 @ X3 ) )
      | ~ ( epred2_2 @ X1 @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

thf(c_0_37,plain,
    ! [X17: nat > $o] :
      ( ( X17 @ ( ind @ X17 ) )
      | ~ ( amone @ X17 )
      | ~ ( some @ X17 ) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_38,plain,
    ! [X1: nat,X2: nat] : ( amone @ ( epred2_2 @ X1 @ X2 ) ),
    inference(cn,[status(thm)],[c_0_25]) ).

thf(c_0_39,plain,
    ( ( some @ epred1_0 )
    = $true ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_26]),c_0_27]) ).

thf(c_0_40,negated_conjecture,
    ~ ( eq
      @ ( pf @ y
        @ ( fr
          @ ( ind
            @ ^ [Z0: nat] :
                ( ( ts @ ( num @ x ) @ ( den @ y ) )
                = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Z0 ) ) )
          @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
      @ x ),
    inference(fof_nnf,[status(thm)],[c_0_28]) ).

thf(c_0_41,plain,
    ! [X5: frac,X6: frac,X7: frac] :
      ( ( eq @ X5 @ X7 )
      | ~ ( eq @ X5 @ X6 )
      | ~ ( eq @ X6 @ X7 ) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_42,plain,
    ! [X1: nat,X5: frac] : ( eq @ ( fr @ ( ts @ ( num @ X5 ) @ X1 ) @ ( ts @ ( den @ X5 ) @ X1 ) ) @ X5 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_43,plain,
    ! [X1: nat,X2: nat] :
      ( ( eq @ ( pf @ ( fr @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ X1 ) @ ( fr @ X2 @ X1 ) ) @ ( fr @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ X1 ) )
      | ~ ( epred1_0 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

thf(c_0_44,plain,
    ! [X5: frac,X6: frac,X7: frac] :
      ( ( eq @ ( pf @ X5 @ X6 ) @ ( pf @ X7 @ X6 ) )
      | ~ ( eq @ X5 @ X7 ) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

thf(c_0_45,plain,
    ! [X5: frac,X1: nat] : ( eq @ X5 @ ( fr @ ( ts @ X1 @ ( num @ X5 ) ) @ ( ts @ ( den @ X5 ) @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_35,c_0_19]) ).

thf(c_0_46,plain,
    ! [X1: nat,X2: nat] :
      ( ( ( pl @ X1 @ ( ind @ ( epred2_2 @ X1 @ X2 ) ) )
        = X2 )
      | ~ ( some @ ( epred2_2 @ X1 @ X2 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).

thf(c_0_47,plain,
    some @ epred1_0,
    inference(cn,[status(thm)],[c_0_39]) ).

thf(c_0_48,negated_conjecture,
    ( ( eq @ ( pf @ y @ ( fr @ ( ind @ ( epred2_2 @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) @ x )
   != $true ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_40]),c_0_16]) ).

thf(c_0_49,plain,
    ! [X6: frac,X5: frac,X1: nat] :
      ( ( eq @ X5 @ X6 )
      | ~ ( eq @ X5 @ ( fr @ ( ts @ ( num @ X6 ) @ X1 ) @ ( ts @ ( den @ X6 ) @ X1 ) ) ) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

thf(c_0_50,plain,
    ! [X1: nat,X5: frac,X2: nat] :
      ( ( eq @ X5 @ ( fr @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ X1 ) )
      | ~ ( eq @ X5 @ ( pf @ ( fr @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ X1 ) @ ( fr @ X2 @ X1 ) ) )
      | ~ ( epred1_0 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_41,c_0_43]) ).

thf(c_0_51,plain,
    ! [X1: nat,X5: frac,X6: frac] : ( eq @ ( pf @ X5 @ X6 ) @ ( pf @ ( fr @ ( ts @ X1 @ ( num @ X5 ) ) @ ( ts @ ( den @ X5 ) @ X1 ) ) @ X6 ) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

thf(c_0_52,plain,
    ! [X1: nat,X2: nat] :
      ( ( ( pl @ X1 @ ( ind @ ( epred2_2 @ X1 @ X2 ) ) )
        = X2 )
      | ( ( epred2_2 @ X1 @ X2 )
       != epred1_0 ) ),
    inference(ext_sup,[status(thm)],[c_0_46,c_0_47]) ).

thf(c_0_53,negated_conjecture,
    ~ ( eq @ ( pf @ y @ ( fr @ ( ind @ ( epred2_2 @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) @ x ),
    inference(cn,[status(thm)],[c_0_48]) ).

thf(c_0_54,plain,
    ! [X6: frac,X5: frac,X1: nat] :
      ( ( eq @ X5 @ X6 )
      | ~ ( eq @ X5 @ ( fr @ ( ts @ X1 @ ( num @ X6 ) ) @ ( ts @ ( den @ X6 ) @ X1 ) ) ) ),
    inference(spm,[status(thm)],[c_0_49,c_0_19]) ).

thf(c_0_55,plain,
    ! [X1: nat] :
      ( ( eq @ ( pf @ y @ ( fr @ X1 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) @ ( fr @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
      | ~ ( epred1_0 @ X1 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_19]),c_0_19]) ).

thf(c_0_56,plain,
    ! [X1: nat,X2: nat,X3: nat] :
      ( ( epred2_2 @ X2 @ X1 @ X3 )
      | ( X1
       != ( pl @ X2 @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

thf(c_0_57,plain,
    ! [X1: nat] :
      ( ( epred1_0 @ X1 )
      | ( ( ts @ ( num @ x ) @ ( den @ y ) )
       != ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_58,plain,
    ! [X1: nat,X2: nat] :
      ( ( ( pl @ X1 @ ( ind @ ( epred2_2 @ X1 @ X2 ) ) )
        = X2 )
      | ( ( epred2_2 @ X1 @ X2 @ ( esk5_2 @ X1 @ X2 ) )
      <~> ( epred1_0 @ ( esk5_2 @ X1 @ X2 ) ) ) ),
    inference(neg_ext,[status(thm)],[c_0_52]) ).

thf(c_0_59,negated_conjecture,
    ~ ( eq @ ( pf @ y @ ( fr @ ( ind @ ( epred2_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) @ x ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_19]),c_0_19]) ).

thf(c_0_60,plain,
    ! [X1: nat] :
      ( ( eq @ ( pf @ y @ ( fr @ X1 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) @ x )
      | ~ ( epred1_0 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

thf(c_0_61,plain,
    ! [X1: nat,X2: nat] : ( epred2_2 @ X1 @ ( pl @ X1 @ X2 ) @ X2 ),
    inference(er,[status(thm)],[c_0_56]) ).

thf(c_0_62,plain,
    ! [X1: nat] :
      ( ( epred1_0 @ X1 )
      | ( ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ X1 )
       != ( ts @ ( den @ y ) @ ( num @ x ) ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_19]),c_0_19]) ).

thf(c_0_63,plain,
    ! [X1: nat,X2: nat] :
      ( ( ( pl @ X1 @ ( ind @ ( epred2_2 @ X1 @ X2 ) ) )
        = X2 )
      | ( epred2_2 @ X1 @ X2 @ ( esk5_2 @ X1 @ X2 ) )
      | ( epred1_0 @ ( esk5_2 @ X1 @ X2 ) ) ),
    inference(dynamic_cnf,[status(thm)],[c_0_58]) ).

thf(c_0_64,negated_conjecture,
    ~ ( epred1_0 @ ( ind @ ( epred2_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ) ) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

thf(c_0_65,plain,
    ! [X1: nat] :
      ( ( epred2_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ X1 )
      | ~ ( epred1_0 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_61,c_0_32]) ).

thf(c_0_66,plain,
    epred2_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ ( esk5_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63])]),c_0_64]),c_0_65]) ).

thf(c_0_67,plain,
    ( ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( esk5_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ) )
    = ( ts @ ( den @ y ) @ ( num @ x ) ) ),
    inference(spm,[status(thm)],[c_0_36,c_0_66]) ).

thf(c_0_68,plain,
    ! [X1: nat,X2: nat] :
      ( ( ( pl @ X1 @ ( ind @ ( epred2_2 @ X1 @ X2 ) ) )
        = X2 )
      | ~ ( epred2_2 @ X1 @ X2 @ ( esk5_2 @ X1 @ X2 ) )
      | ~ ( epred1_0 @ ( esk5_2 @ X1 @ X2 ) ) ),
    inference(dynamic_cnf,[status(thm)],[c_0_58]) ).

thf(c_0_69,plain,
    epred1_0 @ ( esk5_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ),
    inference(spm,[status(thm)],[c_0_62,c_0_67]) ).

thf(c_0_70,plain,
    ( ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ind @ ( epred2_2 @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ) ) )
    = ( ts @ ( den @ y ) @ ( num @ x ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_66])]) ).

thf(c_0_71,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_70]),c_0_64]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM768^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.13/0.33  % Computer : n027.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon May 20 04:01:22 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.20/0.46  Running higher-order theorem proving
% 0.20/0.46  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
% 1.15/0.61  # Version: 3.1.0-ho
% 1.15/0.61  # partial match(1): HSSSSMSSSSMCSSA
% 1.15/0.61  # Preprocessing class: HSMSSMSSSSMCSSA.
% 1.15/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.15/0.61  # Starting ho_unfolding_3 with 1500s (5) cores
% 1.15/0.61  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 1.15/0.61  # Starting new_bool_3 with 300s (1) cores
% 1.15/0.61  # Starting new_bool_1 with 300s (1) cores
% 1.15/0.61  # ho_unfolding_3 with pid 25509 completed with status 0
% 1.15/0.61  # Result found by ho_unfolding_3
% 1.15/0.61  # partial match(1): HSSSSMSSSSMCSSA
% 1.15/0.61  # Preprocessing class: HSMSSMSSSSMCSSA.
% 1.15/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.15/0.61  # Starting ho_unfolding_3 with 1500s (5) cores
% 1.15/0.61  # No SInE strategy applied
% 1.15/0.61  # Search class: HHUSM-FFSF21-DSSFFFBN
% 1.15/0.61  # partial match(4): FHUSM-FFSF21-DFFFFFNN
% 1.15/0.61  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.15/0.61  # Starting G-E--_041_C18_F1_PI_AE_Q4_CS_SP_S0Y with 541s (1) cores
% 1.15/0.61  # Starting ho_unfolding_3 with 151s (1) cores
% 1.15/0.61  # Starting new_bool_3 with 271s (1) cores
% 1.15/0.61  # Starting U----_206d_02_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.15/0.61  # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 1.15/0.61  # new_bool_3 with pid 25517 completed with status 0
% 1.15/0.61  # Result found by new_bool_3
% 1.15/0.61  # partial match(1): HSSSSMSSSSMCSSA
% 1.15/0.61  # Preprocessing class: HSMSSMSSSSMCSSA.
% 1.15/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.15/0.61  # Starting ho_unfolding_3 with 1500s (5) cores
% 1.15/0.61  # No SInE strategy applied
% 1.15/0.61  # Search class: HHUSM-FFSF21-DSSFFFBN
% 1.15/0.61  # partial match(4): FHUSM-FFSF21-DFFFFFNN
% 1.15/0.61  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.15/0.61  # Starting G-E--_041_C18_F1_PI_AE_Q4_CS_SP_S0Y with 541s (1) cores
% 1.15/0.61  # Starting ho_unfolding_3 with 151s (1) cores
% 1.15/0.61  # Starting new_bool_3 with 271s (1) cores
% 1.15/0.61  # Preprocessing time       : 0.001 s
% 1.15/0.61  # Presaturation interreduction done
% 1.15/0.61  
% 1.15/0.61  # Proof found!
% 1.15/0.61  # SZS status Theorem
% 1.15/0.61  # SZS output start CNFRefutation
% See solution above
% 1.15/0.61  # Parsed axioms                        : 25
% 1.15/0.61  # Removed by relevancy pruning/SinE    : 0
% 1.15/0.61  # Initial clauses                      : 29
% 1.15/0.61  # Removed in clause preprocessing      : 14
% 1.15/0.61  # Initial clauses in saturation        : 15
% 1.15/0.61  # Processed clauses                    : 574
% 1.15/0.61  # ...of these trivial                  : 51
% 1.15/0.61  # ...subsumed                          : 238
% 1.15/0.61  # ...remaining for further processing  : 285
% 1.15/0.61  # Other redundant clauses eliminated   : 2
% 1.15/0.61  # Clauses deleted for lack of memory   : 0
% 1.15/0.61  # Backward-subsumed                    : 6
% 1.15/0.61  # Backward-rewritten                   : 1
% 1.15/0.61  # Generated clauses                    : 5391
% 1.15/0.61  # ...of the previous two non-redundant : 4909
% 1.15/0.61  # ...aggressively subsumed             : 0
% 1.15/0.61  # Contextual simplify-reflections      : 1
% 1.15/0.61  # Paramodulations                      : 5327
% 1.15/0.61  # Factorizations                       : 0
% 1.15/0.61  # NegExts                              : 13
% 1.15/0.61  # Equation resolutions                 : 3
% 1.15/0.61  # Disequality decompositions           : 0
% 1.15/0.61  # Total rewrite steps                  : 597
% 1.15/0.61  # ...of those cached                   : 524
% 1.15/0.61  # Propositional unsat checks           : 0
% 1.15/0.61  #    Propositional check models        : 0
% 1.15/0.61  #    Propositional check unsatisfiable : 0
% 1.15/0.61  #    Propositional clauses             : 0
% 1.15/0.61  #    Propositional clauses after purity: 0
% 1.15/0.61  #    Propositional unsat core size     : 0
% 1.15/0.61  #    Propositional preprocessing time  : 0.000
% 1.15/0.61  #    Propositional encoding time       : 0.000
% 1.15/0.61  #    Propositional solver time         : 0.000
% 1.15/0.61  #    Success case prop preproc time    : 0.000
% 1.15/0.61  #    Success case prop encoding time   : 0.000
% 1.15/0.61  #    Success case prop solver time     : 0.000
% 1.15/0.61  # Current number of processed clauses  : 250
% 1.15/0.61  #    Positive orientable unit clauses  : 71
% 1.15/0.61  #    Positive unorientable unit clauses: 1
% 1.15/0.61  #    Negative unit clauses             : 2
% 1.15/0.61  #    Non-unit-clauses                  : 176
% 1.15/0.61  # Current number of unprocessed clauses: 4357
% 1.15/0.61  # ...number of literals in the above   : 5781
% 1.15/0.61  # Current number of archived formulas  : 0
% 1.15/0.61  # Current number of archived clauses   : 34
% 1.15/0.61  # Clause-clause subsumption calls (NU) : 6907
% 1.15/0.61  # Rec. Clause-clause subsumption calls : 5769
% 1.15/0.61  # Non-unit clause-clause subsumptions  : 245
% 1.15/0.61  # Unit Clause-clause subsumption calls : 234
% 1.15/0.61  # Rewrite failures with RHS unbound    : 0
% 1.15/0.61  # BW rewrite match attempts            : 591
% 1.15/0.61  # BW rewrite match successes           : 4
% 1.15/0.61  # Condensation attempts                : 0
% 1.15/0.61  # Condensation successes               : 0
% 1.15/0.61  # Termbank termtop insertions          : 210201
% 1.15/0.61  # Search garbage collected termcells   : 204
% 1.15/0.61  
% 1.15/0.61  # -------------------------------------------------
% 1.15/0.61  # User time                : 0.130 s
% 1.15/0.61  # System time              : 0.006 s
% 1.15/0.61  # Total time               : 0.136 s
% 1.15/0.61  # Maximum resident set size: 1908 pages
% 1.15/0.61  
% 1.15/0.61  # -------------------------------------------------
% 1.15/0.61  # User time                : 0.621 s
% 1.15/0.61  # System time              : 0.024 s
% 1.15/0.61  # Total time               : 0.645 s
% 1.15/0.61  # Maximum resident set size: 1748 pages
% 1.15/0.61  % E---3.1 exiting
% 1.15/0.61  % E exiting
%------------------------------------------------------------------------------