TSTP Solution File: ALG266^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG266^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n019.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 May 20 18:05:57 EDT 2024

% Result   : Theorem 0.24s 0.55s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   63 (  10 unt;  23 typ;   0 def)
%            Number of atoms       :   95 (  30 equ;   0 cnn)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives : 1233 (  42   ~;  70   |;  11   &;1046   @)
%                                         (   7 <=>;  57  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (  10 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  131 ( 131   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  21 usr;  10 con; 0-3 aty)
%            Number of variables   :  148 (  16   ^ 132   !;   0   ?; 148   :)

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

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

thf(decl_22,type,
    one: term ).

thf(decl_24,type,
    lam: term > term ).

thf(decl_25,type,
    sub: term > subst > term ).

thf(decl_26,type,
    id: subst ).

thf(decl_27,type,
    sh: subst ).

thf(decl_28,type,
    push: term > subst > subst ).

thf(decl_29,type,
    comp: subst > subst > subst ).

thf(decl_41,type,
    axvarshift: $o ).

thf(decl_73,type,
    hoasinduction_lem3a_lthm: $o ).

thf(decl_75,type,
    hoasinduction_lem3aa: $o ).

thf(decl_93,type,
    hoaslam: subst > ( subst > term > term ) > term ).

thf(decl_122,type,
    hoasinduction_lem3a: $o ).

thf(decl_142,type,
    axvarid: $o ).

thf(decl_144,type,
    esk1_1: ( subst > term > subst > $o ) > subst > term > term ).

thf(decl_145,type,
    esk2_2: ( subst > term > subst > $o ) > term > term ).

thf(decl_146,type,
    epred1_0: subst > term > subst > $o ).

thf(decl_147,type,
    esk3_1: ( subst > term > term ) > subst ).

thf(decl_148,type,
    esk4_1: ( subst > term > term ) > term ).

thf(decl_149,type,
    esk5_1: ( subst > term > term ) > subst ).

thf(decl_150,type,
    esk6_1: ( subst > term > term ) > term ).

thf(decl_151,type,
    esk7_0: term ).

thf(hoasinduction_lem3aa,axiom,
    ( hoasinduction_lem3aa
  <=> ! [X22: subst > term > subst > $o] :
        ( ! [X12: subst > term > term] :
            ( ! [X3: subst,X1: term,X4: subst] :
                ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
                = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
           => ( ! [X1: term] :
                  ( ( X22 @ id @ X1 @ id )
                 => ( X22 @ id @ ( X12 @ id @ X1 ) @ id ) )
             => ( X22 @ id
                @ ( hoaslam @ id
                  @ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
                @ id ) ) )
       => ! [X1: term] :
            ( ! [X2: term] :
                ( ( X22 @ id @ X2 @ id )
               => ( X22 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
           => ( X22 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3aa) ).

thf(hoasinduction_lem3a,axiom,
    ( hoasinduction_lem3a
  <=> ! [X25: subst > term > subst > $o] :
        ( ! [X12: subst > term > term] :
            ( ! [X3: subst,X1: term,X4: subst] :
                ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
                = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
           => ( ! [X1: term] :
                  ( ( X25 @ id @ X1 @ id )
                 => ( X25 @ id @ ( X12 @ id @ X1 ) @ id ) )
             => ( X25 @ id
                @ ( hoaslam @ id
                  @ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
                @ id ) ) )
       => ! [X1: term] :
            ( ! [X2: term] :
                ( ( X25 @ id @ X2 @ id )
               => ( X25 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
           => ( X25 @ id @ ( lam @ X1 ) @ id ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3a) ).

thf(hoasinduction_lem3a_lthm,axiom,
    ( hoasinduction_lem3a_lthm
  <=> ( axvarid
     => ( axvarshift
       => ( hoasinduction_lem3aa
         => hoasinduction_lem3a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3a_lthm) ).

thf(axvarid,axiom,
    ( axvarid
  <=> ! [X1: term] :
        ( ( sub @ X1 @ id )
        = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axvarid) ).

thf(axvarshift,axiom,
    ( axvarshift
  <=> ( ( push @ one @ sh )
      = id ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axvarshift) ).

thf(thm,conjecture,
    hoasinduction_lem3a_lthm,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(c_0_6,plain,
    ( hoasinduction_lem3aa
  <=> ! [X22: subst > term > subst > $o] :
        ( ! [X12: subst > term > term] :
            ( ! [X3: subst,X1: term,X4: subst] :
                ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
                = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
           => ( ! [X1: term] :
                  ( ( X22 @ id @ X1 @ id )
                 => ( X22 @ id @ ( X12 @ id @ X1 ) @ id ) )
             => ( X22 @ id
                @ ( hoaslam @ id
                  @ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
                @ id ) ) )
       => ! [X1: term] :
            ( ! [X2: term] :
                ( ( X22 @ id @ X2 @ id )
               => ( X22 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
           => ( X22 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
    inference(fof_simplification,[status(thm)],[hoasinduction_lem3aa]) ).

thf(c_0_7,plain,
    ( hoasinduction_lem3a
  <=> ! [X25: subst > term > subst > $o] :
        ( ! [X12: subst > term > term] :
            ( ! [X3: subst,X1: term,X4: subst] :
                ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
                = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
           => ( ! [X1: term] :
                  ( ( X25 @ id @ X1 @ id )
                 => ( X25 @ id @ ( X12 @ id @ X1 ) @ id ) )
             => ( X25 @ id
                @ ( hoaslam @ id
                  @ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
                @ id ) ) )
       => ! [X1: term] :
            ( ! [X2: term] :
                ( ( X25 @ id @ X2 @ id )
               => ( X25 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
           => ( X25 @ id @ ( lam @ X1 ) @ id ) ) ) ),
    inference(fof_simplification,[status(thm)],[hoasinduction_lem3a]) ).

thf(c_0_8,axiom,
    ( hoasinduction_lem3a_lthm
    = ( ! [X45: term] :
          ( ( sub @ X45 @ id )
          = X45 )
     => ( ( ( push @ one @ sh )
          = id )
       => ( ! [X46: subst > term > subst > $o] :
              ( ! [X47: subst > term > term] :
                  ( ! [X48: subst,X49: term,X50: subst] :
                      ( ( sub @ ( X47 @ X48 @ X49 ) @ X50 )
                      = ( X47 @ ( comp @ X48 @ X50 ) @ ( sub @ X49 @ X50 ) ) )
                 => ( ! [X51: term] :
                        ( ( X46 @ id @ X51 @ id )
                       => ( X46 @ id @ ( X47 @ id @ X51 ) @ id ) )
                   => ( X46 @ id
                      @ ( hoaslam @ id
                        @ ^ [Z0: subst,Z1: term] : ( X47 @ Z0 @ Z1 ) )
                      @ id ) ) )
             => ! [X52: term] :
                  ( ! [X53: term] :
                      ( ( X46 @ id @ X53 @ id )
                     => ( X46 @ id @ ( sub @ X52 @ ( push @ X53 @ id ) ) @ id ) )
                 => ( X46 @ id @ ( lam @ ( sub @ X52 @ ( push @ one @ sh ) ) ) @ id ) ) )
         => ! [X54: subst > term > subst > $o] :
              ( ! [X55: subst > term > term] :
                  ( ! [X56: subst,X57: term,X58: subst] :
                      ( ( sub @ ( X55 @ X56 @ X57 ) @ X58 )
                      = ( X55 @ ( comp @ X56 @ X58 ) @ ( sub @ X57 @ X58 ) ) )
                 => ( ! [X59: term] :
                        ( ( X54 @ id @ X59 @ id )
                       => ( X54 @ id @ ( X55 @ id @ X59 ) @ id ) )
                   => ( X54 @ id
                      @ ( hoaslam @ id
                        @ ^ [Z0: subst,Z1: term] : ( X55 @ Z0 @ Z1 ) )
                      @ id ) ) )
             => ! [X60: term] :
                  ( ! [X61: term] :
                      ( ( X54 @ id @ X61 @ id )
                     => ( X54 @ id @ ( sub @ X60 @ ( push @ X61 @ id ) ) @ id ) )
                 => ( X54 @ id @ ( lam @ X60 ) @ id ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoasinduction_lem3a_lthm,axvarid]),axvarshift]),c_0_6]),c_0_7]) ).

thf(c_0_9,negated_conjecture,
    ~ ( ! [X62: term] :
          ( ( sub @ X62 @ id )
          = X62 )
     => ( ( ( push @ one @ sh )
          = id )
       => ( ! [X63: subst > term > subst > $o] :
              ( ! [X64: subst > term > term] :
                  ( ! [X65: subst,X66: term,X67: subst] :
                      ( ( sub @ ( X64 @ X65 @ X66 ) @ X67 )
                      = ( X64 @ ( comp @ X65 @ X67 ) @ ( sub @ X66 @ X67 ) ) )
                 => ( ! [X68: term] :
                        ( ( X63 @ id @ X68 @ id )
                       => ( X63 @ id @ ( X64 @ id @ X68 ) @ id ) )
                   => ( X63 @ id
                      @ ( hoaslam @ id
                        @ ^ [Z0: subst,Z1: term] : ( X64 @ Z0 @ Z1 ) )
                      @ id ) ) )
             => ! [X69: term] :
                  ( ! [X70: term] :
                      ( ( X63 @ id @ X70 @ id )
                     => ( X63 @ id @ ( sub @ X69 @ ( push @ X70 @ id ) ) @ id ) )
                 => ( X63 @ id @ ( lam @ ( sub @ X69 @ ( push @ one @ sh ) ) ) @ id ) ) )
         => ! [X71: subst > term > subst > $o] :
              ( ! [X72: subst > term > term] :
                  ( ! [X73: subst,X74: term,X75: subst] :
                      ( ( sub @ ( X72 @ X73 @ X74 ) @ X75 )
                      = ( X72 @ ( comp @ X73 @ X75 ) @ ( sub @ X74 @ X75 ) ) )
                 => ( ! [X76: term] :
                        ( ( X71 @ id @ X76 @ id )
                       => ( X71 @ id @ ( X72 @ id @ X76 ) @ id ) )
                   => ( X71 @ id
                      @ ( hoaslam @ id
                        @ ^ [Z0: subst,Z1: term] : ( X72 @ Z0 @ Z1 ) )
                      @ id ) ) )
             => ! [X77: term] :
                  ( ! [X78: term] :
                      ( ( X71 @ id @ X78 @ id )
                     => ( X71 @ id @ ( sub @ X77 @ ( push @ X78 @ id ) ) @ id ) )
                 => ( X71 @ id @ ( lam @ X77 ) @ id ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_8]) ).

thf(c_0_10,negated_conjecture,
    ! [X79: term,X80: subst > term > subst > $o,X82: subst,X83: term,X84: subst,X85: term,X86: term,X89: subst > term > term,X95: term] :
      ( ( ( sub @ X79 @ id )
        = X79 )
      & ( ( push @ one @ sh )
        = id )
      & ( ( X80 @ id @ ( esk2_2 @ X80 @ X86 ) @ id )
        | ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
        | ( ( sub @ ( esk1_1 @ X80 @ X82 @ X83 ) @ X84 )
          = ( esk1_1 @ X80 @ ( comp @ X82 @ X84 ) @ ( sub @ X83 @ X84 ) ) ) )
      & ( ~ ( X80 @ id @ ( sub @ X86 @ ( push @ ( esk2_2 @ X80 @ X86 ) @ id ) ) @ id )
        | ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
        | ( ( sub @ ( esk1_1 @ X80 @ X82 @ X83 ) @ X84 )
          = ( esk1_1 @ X80 @ ( comp @ X82 @ X84 ) @ ( sub @ X83 @ X84 ) ) ) )
      & ( ( X80 @ id @ ( esk2_2 @ X80 @ X86 ) @ id )
        | ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
        | ~ ( X80 @ id @ X85 @ id )
        | ( X80 @ id @ ( esk1_1 @ X80 @ id @ X85 ) @ id ) )
      & ( ~ ( X80 @ id @ ( sub @ X86 @ ( push @ ( esk2_2 @ X80 @ X86 ) @ id ) ) @ id )
        | ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
        | ~ ( X80 @ id @ X85 @ id )
        | ( X80 @ id @ ( esk1_1 @ X80 @ id @ X85 ) @ id ) )
      & ( ( X80 @ id @ ( esk2_2 @ X80 @ X86 ) @ id )
        | ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
        | ~ ( X80 @ id @ ( hoaslam @ id @ ( esk1_1 @ X80 ) ) @ id ) )
      & ( ~ ( X80 @ id @ ( sub @ X86 @ ( push @ ( esk2_2 @ X80 @ X86 ) @ id ) ) @ id )
        | ( X80 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
        | ~ ( X80 @ id @ ( hoaslam @ id @ ( esk1_1 @ X80 ) ) @ id ) )
      & ( ( epred1_0 @ id @ ( esk6_1 @ X89 ) @ id )
        | ( epred1_0 @ id @ ( hoaslam @ id @ X89 ) @ id )
        | ( ( sub @ ( X89 @ ( esk3_1 @ X89 ) @ ( esk4_1 @ X89 ) ) @ ( esk5_1 @ X89 ) )
         != ( X89 @ ( comp @ ( esk3_1 @ X89 ) @ ( esk5_1 @ X89 ) ) @ ( sub @ ( esk4_1 @ X89 ) @ ( esk5_1 @ X89 ) ) ) ) )
      & ( ~ ( epred1_0 @ id @ ( X89 @ id @ ( esk6_1 @ X89 ) ) @ id )
        | ( epred1_0 @ id @ ( hoaslam @ id @ X89 ) @ id )
        | ( ( sub @ ( X89 @ ( esk3_1 @ X89 ) @ ( esk4_1 @ X89 ) ) @ ( esk5_1 @ X89 ) )
         != ( X89 @ ( comp @ ( esk3_1 @ X89 ) @ ( esk5_1 @ X89 ) ) @ ( sub @ ( esk4_1 @ X89 ) @ ( esk5_1 @ X89 ) ) ) ) )
      & ( ~ ( epred1_0 @ id @ X95 @ id )
        | ( epred1_0 @ id @ ( sub @ esk7_0 @ ( push @ X95 @ id ) ) @ id ) )
      & ~ ( epred1_0 @ id @ ( lam @ esk7_0 ) @ id ) ),
    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_9])])])])])]) ).

thf(c_0_11,negated_conjecture,
    ! [X3: subst,X2: term,X14: subst > term > subst > $o,X4: subst,X1: term] :
      ( ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
      | ( ( sub @ ( esk1_1 @ X14 @ X3 @ X2 ) @ X4 )
        = ( esk1_1 @ X14 @ ( comp @ X3 @ X4 ) @ ( sub @ X2 @ X4 ) ) )
      | ~ ( X14 @ id @ ( sub @ X1 @ ( push @ ( esk2_2 @ X14 @ X1 ) @ id ) ) @ id ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_12,negated_conjecture,
    ( ( push @ one @ sh )
    = id ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: term] :
      ( ( sub @ X1 @ id )
      = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: term,X14: subst > term > subst > $o] :
      ( ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
      | ~ ( X14 @ id @ ( sub @ X1 @ ( push @ ( esk2_2 @ X14 @ X1 ) @ id ) ) @ id )
      | ~ ( X14 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: term,X2: term,X3: subst,X14: subst > term > subst > $o,X4: subst] :
      ( ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
      | ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
      | ( ( sub @ ( esk1_1 @ X14 @ X3 @ X2 ) @ X4 )
        = ( esk1_1 @ X14 @ ( comp @ X3 @ X4 ) @ ( sub @ X2 @ X4 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_16,negated_conjecture,
    ! [X1: term,X3: subst,X14: subst > term > subst > $o,X4: subst,X2: term] :
      ( ( ( esk1_1 @ X14 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) )
        = ( sub @ ( esk1_1 @ X14 @ X3 @ X1 ) @ X4 ) )
      | ( X14 @ id @ ( lam @ X2 ) @ id )
      | ~ ( X14 @ id @ ( sub @ X2 @ ( push @ ( esk2_2 @ X14 @ X2 ) @ id ) ) @ id ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).

thf(c_0_17,negated_conjecture,
    ! [X1: term] :
      ( ( epred1_0 @ id @ ( sub @ esk7_0 @ ( push @ X1 @ id ) ) @ id )
      | ~ ( epred1_0 @ id @ X1 @ id ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_18,negated_conjecture,
    ~ ( epred1_0 @ id @ ( lam @ esk7_0 ) @ id ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_19,negated_conjecture,
    ! [X1: term,X14: subst > term > subst > $o] :
      ( ( X14 @ id @ ( lam @ X1 ) @ id )
      | ~ ( X14 @ id @ ( sub @ X1 @ ( push @ ( esk2_2 @ X14 @ X1 ) @ id ) ) @ id )
      | ~ ( X14 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_12]),c_0_13]) ).

thf(c_0_20,negated_conjecture,
    ! [X1: term,X14: subst > term > subst > $o,X2: term] :
      ( ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
      | ( X14 @ id @ ( esk1_1 @ X14 @ id @ X2 ) @ id )
      | ~ ( X14 @ id @ ( sub @ X1 @ ( push @ ( esk2_2 @ X14 @ X1 ) @ id ) ) @ id )
      | ~ ( X14 @ id @ X2 @ id ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_21,negated_conjecture,
    ! [X1: term,X14: subst > term > subst > $o,X2: term] :
      ( ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
      | ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
      | ( X14 @ id @ ( esk1_1 @ X14 @ id @ X2 ) @ id )
      | ~ ( X14 @ id @ X2 @ id ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_22,negated_conjecture,
    ! [X12: subst > term > term] :
      ( ( epred1_0 @ id @ ( esk6_1 @ X12 ) @ id )
      | ( epred1_0 @ id @ ( hoaslam @ id @ X12 ) @ id )
      | ( ( sub @ ( X12 @ ( esk3_1 @ X12 ) @ ( esk4_1 @ X12 ) ) @ ( esk5_1 @ X12 ) )
       != ( X12 @ ( comp @ ( esk3_1 @ X12 ) @ ( esk5_1 @ X12 ) ) @ ( sub @ ( esk4_1 @ X12 ) @ ( esk5_1 @ X12 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_23,negated_conjecture,
    ! [X1: term,X3: subst,X14: subst > term > subst > $o,X4: subst,X2: term] :
      ( ( ( esk1_1 @ X14 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) )
        = ( sub @ ( esk1_1 @ X14 @ X3 @ X1 ) @ X4 ) )
      | ( X14 @ id @ ( esk2_2 @ X14 @ X2 ) @ id )
      | ( X14 @ id @ ( lam @ X2 ) @ id ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_12]),c_0_13]) ).

thf(c_0_24,negated_conjecture,
    ! [X12: subst > term > term] :
      ( ( epred1_0 @ id @ ( hoaslam @ id @ X12 ) @ id )
      | ~ ( epred1_0 @ id @ ( X12 @ id @ ( esk6_1 @ X12 ) ) @ id )
      | ( ( sub @ ( X12 @ ( esk3_1 @ X12 ) @ ( esk4_1 @ X12 ) ) @ ( esk5_1 @ X12 ) )
       != ( X12 @ ( comp @ ( esk3_1 @ X12 ) @ ( esk5_1 @ X12 ) ) @ ( sub @ ( esk4_1 @ X12 ) @ ( esk5_1 @ X12 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_25,negated_conjecture,
    ! [X1: term,X3: subst,X4: subst] :
      ( ( ( esk1_1 @ epred1_0 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) )
        = ( sub @ ( esk1_1 @ epred1_0 @ X3 @ X1 ) @ X4 ) )
      | ~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

thf(c_0_26,negated_conjecture,
    ( ~ ( epred1_0 @ id @ ( hoaslam @ id @ ( esk1_1 @ epred1_0 ) ) @ id )
    | ~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_18]) ).

thf(c_0_27,negated_conjecture,
    ! [X14: subst > term > subst > $o,X2: term,X1: term] :
      ( ( X14 @ id @ ( esk1_1 @ X14 @ id @ X1 ) @ id )
      | ( X14 @ id @ ( lam @ X2 ) @ id )
      | ~ ( X14 @ id @ ( sub @ X2 @ ( push @ ( esk2_2 @ X14 @ X2 ) @ id ) ) @ id )
      | ~ ( X14 @ id @ X1 @ id ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_12]),c_0_13]) ).

thf(c_0_28,negated_conjecture,
    ! [X14: subst > term > subst > $o,X2: term,X1: term] :
      ( ( X14 @ id @ ( esk1_1 @ X14 @ id @ X1 ) @ id )
      | ( X14 @ id @ ( esk2_2 @ X14 @ X2 ) @ id )
      | ( X14 @ id @ ( lam @ X2 ) @ id )
      | ~ ( X14 @ id @ X1 @ id ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_12]),c_0_13]) ).

thf(c_0_29,negated_conjecture,
    ! [X14: subst > term > subst > $o,X1: term] :
      ( ( epred1_0 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id )
      | ( epred1_0 @ id @ ( esk6_1 @ ( esk1_1 @ X14 ) ) @ id )
      | ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
      | ( X14 @ id @ ( lam @ X1 ) @ id ) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

thf(c_0_30,negated_conjecture,
    ! [X1: term,X14: subst > term > subst > $o] :
      ( ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
      | ( X14 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
      | ~ ( X14 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_31,negated_conjecture,
    ( ~ ( epred1_0 @ id @ ( esk1_1 @ epred1_0 @ id @ ( esk6_1 @ ( esk1_1 @ epred1_0 ) ) ) @ id )
    | ~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

thf(c_0_32,negated_conjecture,
    ! [X1: term] :
      ( ( epred1_0 @ id @ ( esk1_1 @ epred1_0 @ id @ X1 ) @ id )
      | ~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id )
      | ~ ( epred1_0 @ id @ X1 @ id ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_17]),c_0_18]) ).

thf(c_0_33,negated_conjecture,
    ( ( epred1_0 @ id @ ( esk6_1 @ ( esk1_1 @ epred1_0 ) ) @ id )
    | ~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_25]),c_0_26]) ).

thf(c_0_34,negated_conjecture,
    ! [X1: term,X14: subst > term > subst > $o] :
      ( ( epred1_0 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id )
      | ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
      | ( X14 @ id @ ( lam @ X1 ) @ id )
      | ~ ( epred1_0 @ id @ ( esk1_1 @ X14 @ id @ ( esk6_1 @ ( esk1_1 @ X14 ) ) ) @ id ) ),
    inference(spm,[status(thm)],[c_0_24,c_0_23]) ).

thf(c_0_35,negated_conjecture,
    ! [X1: term,X14: subst > term > subst > $o,X2: term] :
      ( ( epred1_0 @ id @ ( esk1_1 @ epred1_0 @ id @ ( esk6_1 @ ( esk1_1 @ X14 ) ) ) @ id )
      | ( epred1_0 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id )
      | ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ X1 ) @ id )
      | ( X14 @ id @ ( esk2_2 @ X14 @ X2 ) @ id )
      | ( epred1_0 @ id @ ( lam @ X1 ) @ id )
      | ( X14 @ id @ ( lam @ X2 ) @ id ) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

thf(c_0_36,negated_conjecture,
    ! [X1: term,X14: subst > term > subst > $o] :
      ( ( X14 @ id @ ( esk2_2 @ X14 @ X1 ) @ id )
      | ( X14 @ id @ ( lam @ X1 ) @ id )
      | ~ ( X14 @ id @ ( hoaslam @ id @ ( esk1_1 @ X14 ) ) @ id ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_12]),c_0_13]) ).

thf(c_0_37,negated_conjecture,
    ~ ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ esk7_0 ) @ id ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).

thf(c_0_38,negated_conjecture,
    ! [X1: term] :
      ( ( epred1_0 @ id @ ( esk2_2 @ epred1_0 @ X1 ) @ id )
      | ( epred1_0 @ id @ ( lam @ X1 ) @ id ) ),
    inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35])]),c_0_36]) ).

thf(c_0_39,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_18]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : ALG266^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.13/0.39  % Computer : n019.cluster.edu
% 0.13/0.39  % Model    : x86_64 x86_64
% 0.13/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39  % Memory   : 8042.1875MB
% 0.13/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.39  % CPULimit   : 300
% 0.13/0.39  % WCLimit    : 300
% 0.13/0.39  % DateTime   : Sat May 18 22:49:53 EDT 2024
% 0.13/0.39  % CPUTime    : 
% 0.24/0.51  Running higher-order theorem proving
% 0.24/0.51  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
% 0.24/0.55  # Version: 3.1.0-ho
% 0.24/0.55  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.24/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.55  # Starting post_as_ho1 with 300s (1) cores
% 0.24/0.55  # Starting post_as_ho5 with 300s (1) cores
% 0.24/0.55  # Starting post_as_ho10 with 300s (1) cores
% 0.24/0.55  # post_as_ho5 with pid 4611 completed with status 0
% 0.24/0.55  # Result found by post_as_ho5
% 0.24/0.55  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.24/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.55  # Starting post_as_ho1 with 300s (1) cores
% 0.24/0.55  # Starting post_as_ho5 with 300s (1) cores
% 0.24/0.55  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.24/0.55  # Search class: HGUSF-FFMF21-MHFMMMBN
% 0.24/0.55  # partial match(2): HGUSS-FFMF31-MHFMMMBN
% 0.24/0.55  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.55  # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.24/0.55  # new_ho_10_cnf2 with pid 4613 completed with status 0
% 0.24/0.55  # Result found by new_ho_10_cnf2
% 0.24/0.55  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.24/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.55  # Starting post_as_ho1 with 300s (1) cores
% 0.24/0.55  # Starting post_as_ho5 with 300s (1) cores
% 0.24/0.55  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.24/0.55  # Search class: HGUSF-FFMF21-MHFMMMBN
% 0.24/0.55  # partial match(2): HGUSS-FFMF31-MHFMMMBN
% 0.24/0.55  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.55  # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.24/0.55  # Preprocessing time       : 0.004 s
% 0.24/0.55  # Presaturation interreduction done
% 0.24/0.55  
% 0.24/0.55  # Proof found!
% 0.24/0.55  # SZS status Theorem
% 0.24/0.55  # SZS output start CNFRefutation
% See solution above
% 0.24/0.55  # Parsed axioms                        : 238
% 0.24/0.55  # Removed by relevancy pruning/SinE    : 232
% 0.24/0.55  # Initial clauses                      : 12
% 0.24/0.55  # Removed in clause preprocessing      : 0
% 0.24/0.55  # Initial clauses in saturation        : 12
% 0.24/0.55  # Processed clauses                    : 65
% 0.24/0.55  # ...of these trivial                  : 4
% 0.24/0.55  # ...subsumed                          : 13
% 0.24/0.55  # ...remaining for further processing  : 48
% 0.24/0.55  # Other redundant clauses eliminated   : 0
% 0.24/0.55  # Clauses deleted for lack of memory   : 0
% 0.24/0.55  # Backward-subsumed                    : 15
% 0.24/0.55  # Backward-rewritten                   : 1
% 0.24/0.55  # Generated clauses                    : 123
% 0.24/0.55  # ...of the previous two non-redundant : 113
% 0.24/0.55  # ...aggressively subsumed             : 0
% 0.24/0.55  # Contextual simplify-reflections      : 8
% 0.24/0.55  # Paramodulations                      : 113
% 0.24/0.55  # Factorizations                       : 4
% 0.24/0.55  # NegExts                              : 0
% 0.24/0.55  # Equation resolutions                 : 0
% 0.24/0.55  # Disequality decompositions           : 0
% 0.24/0.55  # Total rewrite steps                  : 31
% 0.24/0.55  # ...of those cached                   : 24
% 0.24/0.55  # Propositional unsat checks           : 0
% 0.24/0.55  #    Propositional check models        : 0
% 0.24/0.55  #    Propositional check unsatisfiable : 0
% 0.24/0.55  #    Propositional clauses             : 0
% 0.24/0.55  #    Propositional clauses after purity: 0
% 0.24/0.55  #    Propositional unsat core size     : 0
% 0.24/0.55  #    Propositional preprocessing time  : 0.000
% 0.24/0.55  #    Propositional encoding time       : 0.000
% 0.24/0.55  #    Propositional solver time         : 0.000
% 0.24/0.55  #    Success case prop preproc time    : 0.000
% 0.24/0.55  #    Success case prop encoding time   : 0.000
% 0.24/0.55  #    Success case prop solver time     : 0.000
% 0.24/0.55  # Current number of processed clauses  : 20
% 0.24/0.55  #    Positive orientable unit clauses  : 4
% 0.24/0.55  #    Positive unorientable unit clauses: 0
% 0.24/0.55  #    Negative unit clauses             : 2
% 0.24/0.55  #    Non-unit-clauses                  : 14
% 0.24/0.55  # Current number of unprocessed clauses: 61
% 0.24/0.55  # ...number of literals in the above   : 399
% 0.24/0.55  # Current number of archived formulas  : 0
% 0.24/0.55  # Current number of archived clauses   : 28
% 0.24/0.55  # Clause-clause subsumption calls (NU) : 190
% 0.24/0.55  # Rec. Clause-clause subsumption calls : 106
% 0.24/0.55  # Non-unit clause-clause subsumptions  : 31
% 0.24/0.55  # Unit Clause-clause subsumption calls : 9
% 0.24/0.55  # Rewrite failures with RHS unbound    : 0
% 0.24/0.55  # BW rewrite match attempts            : 3
% 0.24/0.55  # BW rewrite match successes           : 1
% 0.24/0.55  # Condensation attempts                : 65
% 0.24/0.55  # Condensation successes               : 2
% 0.24/0.55  # Termbank termtop insertions          : 12977
% 0.24/0.55  # Search garbage collected termcells   : 2330
% 0.24/0.55  
% 0.24/0.55  # -------------------------------------------------
% 0.24/0.55  # User time                : 0.016 s
% 0.24/0.55  # System time              : 0.004 s
% 0.24/0.55  # Total time               : 0.020 s
% 0.24/0.55  # Maximum resident set size: 2556 pages
% 0.24/0.55  
% 0.24/0.55  # -------------------------------------------------
% 0.24/0.55  # User time                : 0.027 s
% 0.24/0.55  # System time              : 0.005 s
% 0.24/0.55  # Total time               : 0.032 s
% 0.24/0.55  # Maximum resident set size: 2076 pages
% 0.24/0.55  % E---3.1 exiting
% 0.24/0.55  % E exiting
%------------------------------------------------------------------------------