TSTP Solution File: LCL601^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : LCL601^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n009.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 23:46:57 EDT 2024

% Result   : Theorem 0.17s 0.50s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   88 (  22 unt;  16 typ;   0 def)
%            Number of atoms       :  223 (  13 equ;   0 cnn)
%            Maximal formula atoms :   27 (   3 avg)
%            Number of connectives :  942 ( 113   ~; 201   |;  16   &; 602   @)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   33 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  130 ( 130   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   7 con; 0-3 aty)
%            Number of variables   :  194 (  28   ^ 166   !;   0   ?; 194   :)

% Comments : 
%------------------------------------------------------------------------------
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_52,type,
    transitive: ( $i > $i > $o ) > $o ).

thf(decl_62,type,
    epred1_0: $i > $i > $o ).

thf(decl_63,type,
    epred2_0: $i > $o ).

thf(decl_64,type,
    esk1_0: $i ).

thf(decl_65,type,
    esk2_0: $i ).

thf(decl_66,type,
    esk3_0: $i ).

thf(decl_67,type,
    epred3_0: $i > $i > $o ).

thf(decl_68,type,
    esk4_0: $i ).

thf(decl_69,type,
    esk5_0: $i ).

thf(decl_70,type,
    esk6_0: $i ).

thf(decl_71,type,
    esk7_3: ( $i > $i > $o ) > ( $i > $o ) > $i > $i ).

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

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

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

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

thf(transitive,axiom,
    ( transitive
    = ( ^ [X10: $i > $i > $o] :
        ! [X1: $i,X36: $i,X33: $i] :
          ( ( ( X10 @ X1 @ X36 )
            & ( X10 @ X36 @ X33 ) )
         => ( X10 @ X1 @ X33 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',transitive) ).

thf(thm,conjecture,
    ( ! [X10: $i > $i > $o,X28: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X10 @ X28 ) @ ( mbox @ X10 @ ( mbox @ X10 @ X28 ) ) ) )
  <=> ! [X10: $i > $i > $o] : ( transitive @ X10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(c_0_7,plain,
    ( mimpl
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mimpl]) ).

thf(c_0_8,plain,
    ( mnot
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ( Z0 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mnot]) ).

thf(c_0_9,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

thf(c_0_10,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_7,c_0_8]),c_0_9]) ).

thf(c_0_11,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_12,plain,
    ( mvalid
    = ( ^ [Z0: $i > $o] :
        ! [X15: $i] : ( Z0 @ X15 ) ) ),
    inference(fof_simplification,[status(thm)],[mvalid]) ).

thf(c_0_13,plain,
    ( transitive
    = ( ^ [Z0: $i > $i > $o] :
        ! [X1: $i,X36: $i,X33: $i] :
          ( ( ( Z0 @ X1 @ X36 )
            & ( Z0 @ X36 @ X33 ) )
         => ( Z0 @ X1 @ X33 ) ) ) ),
    inference(fof_simplification,[status(thm)],[transitive]) ).

thf(c_0_14,negated_conjecture,
    ~ ( ! [X10: $i > $i > $o,X28: $i > $o,X61: $i] :
          ( ~ ! [X58: $i] :
                ( ( X10 @ X61 @ X58 )
               => ( X28 @ X58 ) )
          | ! [X60: $i] :
              ( ( X10 @ X61 @ X60 )
             => ! [X59: $i] :
                  ( ( X10 @ X60 @ X59 )
                 => ( X28 @ X59 ) ) ) )
    <=> ! [X10: $i > $i > $o,X62: $i,X63: $i,X64: $i] :
          ( ( ( X10 @ X62 @ X63 )
            & ( X10 @ X63 @ X64 ) )
         => ( X10 @ X62 @ X64 ) ) ),
    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)],[thm]),c_0_10]),c_0_11]),c_0_12]),c_0_13]) ).

thf(c_0_15,negated_conjecture,
    ! [X68: $i,X75: $i > $i > $o,X76: $i > $o,X77: $i,X79: $i,X80: $i,X81: $i > $i > $o,X82: $i,X83: $i,X84: $i] :
      ( ( ( epred3_0 @ esk4_0 @ esk5_0 )
        | ~ ( epred1_0 @ esk1_0 @ X68 )
        | ( epred2_0 @ X68 ) )
      & ( ( epred3_0 @ esk5_0 @ esk6_0 )
        | ~ ( epred1_0 @ esk1_0 @ X68 )
        | ( epred2_0 @ X68 ) )
      & ( ~ ( epred3_0 @ esk4_0 @ esk6_0 )
        | ~ ( epred1_0 @ esk1_0 @ X68 )
        | ( epred2_0 @ X68 ) )
      & ( ( epred3_0 @ esk4_0 @ esk5_0 )
        | ( epred1_0 @ esk1_0 @ esk2_0 ) )
      & ( ( epred3_0 @ esk5_0 @ esk6_0 )
        | ( epred1_0 @ esk1_0 @ esk2_0 ) )
      & ( ~ ( epred3_0 @ esk4_0 @ esk6_0 )
        | ( epred1_0 @ esk1_0 @ esk2_0 ) )
      & ( ( epred3_0 @ esk4_0 @ esk5_0 )
        | ( epred1_0 @ esk2_0 @ esk3_0 ) )
      & ( ( epred3_0 @ esk5_0 @ esk6_0 )
        | ( epred1_0 @ esk2_0 @ esk3_0 ) )
      & ( ~ ( epred3_0 @ esk4_0 @ esk6_0 )
        | ( epred1_0 @ esk2_0 @ esk3_0 ) )
      & ( ( epred3_0 @ esk4_0 @ esk5_0 )
        | ~ ( epred2_0 @ esk3_0 ) )
      & ( ( epred3_0 @ esk5_0 @ esk6_0 )
        | ~ ( epred2_0 @ esk3_0 ) )
      & ( ~ ( epred3_0 @ esk4_0 @ esk6_0 )
        | ~ ( epred2_0 @ esk3_0 ) )
      & ( ( X75 @ X77 @ ( esk7_3 @ X75 @ X76 @ X77 ) )
        | ~ ( X75 @ X77 @ X79 )
        | ~ ( X75 @ X79 @ X80 )
        | ( X76 @ X80 )
        | ~ ( X81 @ X82 @ X83 )
        | ~ ( X81 @ X83 @ X84 )
        | ( X81 @ X82 @ X84 ) )
      & ( ~ ( X76 @ ( esk7_3 @ X75 @ X76 @ X77 ) )
        | ~ ( X75 @ X77 @ X79 )
        | ~ ( X75 @ X79 @ X80 )
        | ( X76 @ X80 )
        | ~ ( X81 @ X82 @ X83 )
        | ~ ( X81 @ X83 @ X84 )
        | ( X81 @ X82 @ X84 ) ) ),
    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_14])])])])])]) ).

thf(c_0_16,negated_conjecture,
    ! [X1: $i,X2: $i > $o,X3: $i,X10: $i > $i > $o,X15: $i,X13: $i,X12: $i,X25: $i > $i > $o,X20: $i] :
      ( ( X10 @ X1 @ ( esk7_3 @ X10 @ X2 @ X1 ) )
      | ( X2 @ X12 )
      | ( X25 @ X13 @ X20 )
      | ~ ( X10 @ X1 @ X3 )
      | ~ ( X10 @ X3 @ X12 )
      | ~ ( X25 @ X13 @ X15 )
      | ~ ( X25 @ X15 @ X20 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_17,negated_conjecture,
    ( ( epred3_0 @ esk5_0 @ esk6_0 )
    | ( epred1_0 @ esk2_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_18,negated_conjecture,
    ! [X2: $i > $o,X1: $i,X10: $i > $i > $o,X12: $i,X3: $i,X13: $i] :
      ( ( X10 @ X1 @ ( esk7_3 @ X10 @ X2 @ X1 ) )
      | ( epred3_0 @ esk5_0 @ esk6_0 )
      | ( epred1_0 @ X3 @ esk3_0 )
      | ( X2 @ X12 )
      | ~ ( epred1_0 @ X3 @ esk2_0 )
      | ~ ( X10 @ X13 @ X12 )
      | ~ ( X10 @ X1 @ X13 ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

thf(c_0_19,negated_conjecture,
    ! [X3: $i,X2: $i > $o,X1: $i] :
      ( ( epred1_0 @ X1 @ ( esk7_3 @ epred1_0 @ X2 @ X1 ) )
      | ( epred3_0 @ esk5_0 @ esk6_0 )
      | ( epred1_0 @ X3 @ esk3_0 )
      | ( X2 @ esk3_0 )
      | ~ ( epred1_0 @ X3 @ esk2_0 )
      | ~ ( epred1_0 @ X1 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_18,c_0_17]) ).

thf(c_0_20,negated_conjecture,
    ( ( epred3_0 @ esk5_0 @ esk6_0 )
    | ( epred1_0 @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_21,negated_conjecture,
    ( ( epred3_0 @ esk4_0 @ esk5_0 )
    | ( epred1_0 @ esk2_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_22,negated_conjecture,
    ! [X1: $i] :
      ( ( epred3_0 @ esk5_0 @ esk6_0 )
      | ( epred2_0 @ X1 )
      | ~ ( epred1_0 @ esk1_0 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_23,negated_conjecture,
    ! [X2: $i > $o,X1: $i] :
      ( ( epred1_0 @ X1 @ ( esk7_3 @ epred1_0 @ X2 @ X1 ) )
      | ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred3_0 @ esk5_0 @ esk6_0 )
      | ( X2 @ esk3_0 )
      | ~ ( epred1_0 @ X1 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

thf(c_0_24,negated_conjecture,
    ! [X2: $i > $o,X1: $i,X10: $i > $i > $o,X12: $i,X3: $i,X13: $i] :
      ( ( X10 @ X1 @ ( esk7_3 @ X10 @ X2 @ X1 ) )
      | ( epred3_0 @ esk4_0 @ esk5_0 )
      | ( epred1_0 @ X3 @ esk3_0 )
      | ( X2 @ X12 )
      | ~ ( epred1_0 @ X3 @ esk2_0 )
      | ~ ( X10 @ X13 @ X12 )
      | ~ ( X10 @ X1 @ X13 ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_21]) ).

thf(c_0_25,negated_conjecture,
    ! [X1: $i,X2: $i > $o,X3: $i,X10: $i > $i > $o,X15: $i,X13: $i,X12: $i,X25: $i > $i > $o,X20: $i] :
      ( ( X2 @ X12 )
      | ( X25 @ X13 @ X20 )
      | ~ ( X2 @ ( esk7_3 @ X10 @ X2 @ X1 ) )
      | ~ ( X10 @ X1 @ X3 )
      | ~ ( X10 @ X3 @ X12 )
      | ~ ( X25 @ X13 @ X15 )
      | ~ ( X25 @ X15 @ X20 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_26,negated_conjecture,
    ! [X2: $i > $o] :
      ( ( epred2_0 @ ( esk7_3 @ epred1_0 @ X2 @ esk1_0 ) )
      | ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred3_0 @ esk5_0 @ esk6_0 )
      | ( X2 @ esk3_0 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20]) ).

thf(c_0_27,negated_conjecture,
    ( ( epred3_0 @ esk5_0 @ esk6_0 )
    | ~ ( epred2_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_28,negated_conjecture,
    ! [X3: $i,X2: $i > $o,X1: $i] :
      ( ( epred1_0 @ X1 @ ( esk7_3 @ epred1_0 @ X2 @ X1 ) )
      | ( epred3_0 @ esk4_0 @ esk5_0 )
      | ( epred1_0 @ X3 @ esk3_0 )
      | ( X2 @ esk3_0 )
      | ~ ( epred1_0 @ X3 @ esk2_0 )
      | ~ ( epred1_0 @ X1 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_24,c_0_21]) ).

thf(c_0_29,negated_conjecture,
    ( ( epred3_0 @ esk4_0 @ esk5_0 )
    | ( epred1_0 @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_30,negated_conjecture,
    ! [X1: $i,X3: $i,X13: $i,X12: $i,X10: $i > $i > $o,X15: $i] :
      ( ( epred3_0 @ esk5_0 @ esk6_0 )
      | ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred2_0 @ X1 )
      | ( X10 @ X3 @ X12 )
      | ~ ( epred1_0 @ esk1_0 @ X13 )
      | ~ ( epred1_0 @ X13 @ X1 )
      | ~ ( X10 @ X15 @ X12 )
      | ~ ( X10 @ X3 @ X15 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

thf(c_0_31,negated_conjecture,
    ! [X1: $i] :
      ( ( epred3_0 @ esk4_0 @ esk5_0 )
      | ( epred2_0 @ X1 )
      | ~ ( epred1_0 @ esk1_0 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_32,negated_conjecture,
    ! [X2: $i > $o,X1: $i] :
      ( ( epred1_0 @ X1 @ ( esk7_3 @ epred1_0 @ X2 @ X1 ) )
      | ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred3_0 @ esk4_0 @ esk5_0 )
      | ( X2 @ esk3_0 )
      | ~ ( epred1_0 @ X1 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

thf(c_0_33,negated_conjecture,
    ! [X1: $i,X10: $i > $i > $o,X12: $i,X3: $i,X13: $i] :
      ( ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred3_0 @ esk5_0 @ esk6_0 )
      | ( X10 @ X1 @ X3 )
      | ( epred2_0 @ X12 )
      | ~ ( epred1_0 @ esk2_0 @ X12 )
      | ~ ( X10 @ X13 @ X3 )
      | ~ ( X10 @ X1 @ X13 ) ),
    inference(spm,[status(thm)],[c_0_30,c_0_20]) ).

thf(c_0_34,negated_conjecture,
    ! [X2: $i > $o] :
      ( ( epred2_0 @ ( esk7_3 @ epred1_0 @ X2 @ esk1_0 ) )
      | ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred3_0 @ esk4_0 @ esk5_0 )
      | ( X2 @ esk3_0 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29]) ).

thf(c_0_35,negated_conjecture,
    ( ( epred3_0 @ esk4_0 @ esk5_0 )
    | ~ ( epred2_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_36,negated_conjecture,
    ! [X1: $i,X10: $i > $i > $o,X3: $i,X12: $i] :
      ( ( epred3_0 @ esk5_0 @ esk6_0 )
      | ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( X10 @ X1 @ X3 )
      | ~ ( X10 @ X12 @ X3 )
      | ~ ( X10 @ X1 @ X12 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_17]),c_0_27]) ).

thf(c_0_37,negated_conjecture,
    ! [X1: $i,X3: $i,X13: $i,X12: $i,X10: $i > $i > $o,X15: $i] :
      ( ( epred3_0 @ esk4_0 @ esk5_0 )
      | ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred2_0 @ X1 )
      | ( X10 @ X3 @ X12 )
      | ~ ( epred1_0 @ esk1_0 @ X13 )
      | ~ ( epred1_0 @ X13 @ X1 )
      | ~ ( X10 @ X15 @ X12 )
      | ~ ( X10 @ X3 @ X15 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_34]),c_0_35]) ).

thf(c_0_38,negated_conjecture,
    ! [X1: $i] :
      ( ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred3_0 @ esk5_0 @ esk6_0 )
      | ( epred1_0 @ X1 @ esk3_0 )
      | ~ ( epred1_0 @ X1 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_36,c_0_17]) ).

thf(c_0_39,negated_conjecture,
    ! [X1: $i,X10: $i > $i > $o,X12: $i,X3: $i,X13: $i] :
      ( ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred3_0 @ esk4_0 @ esk5_0 )
      | ( X10 @ X1 @ X3 )
      | ( epred2_0 @ X12 )
      | ~ ( epred1_0 @ esk2_0 @ X12 )
      | ~ ( X10 @ X13 @ X3 )
      | ~ ( X10 @ X1 @ X13 ) ),
    inference(spm,[status(thm)],[c_0_37,c_0_29]) ).

thf(c_0_40,negated_conjecture,
    ( ( epred3_0 @ esk5_0 @ esk6_0 )
    | ( epred1_0 @ esk1_0 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_38,c_0_20]) ).

thf(c_0_41,negated_conjecture,
    ! [X1: $i,X10: $i > $i > $o,X3: $i,X12: $i] :
      ( ( epred3_0 @ esk4_0 @ esk5_0 )
      | ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( X10 @ X1 @ X3 )
      | ~ ( X10 @ X12 @ X3 )
      | ~ ( X10 @ X1 @ X12 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_21]),c_0_35]) ).

thf(c_0_42,negated_conjecture,
    epred3_0 @ esk5_0 @ esk6_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_40]),c_0_27]) ).

thf(c_0_43,negated_conjecture,
    ! [X1: $i] :
      ( ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred3_0 @ esk4_0 @ esk5_0 )
      | ( epred1_0 @ X1 @ esk3_0 )
      | ~ ( epred1_0 @ X1 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_41,c_0_21]) ).

thf(c_0_44,negated_conjecture,
    ! [X2: $i > $o,X1: $i,X10: $i > $i > $o,X12: $i,X3: $i,X13: $i] :
      ( ( X10 @ X1 @ ( esk7_3 @ X10 @ X2 @ X1 ) )
      | ( epred3_0 @ X3 @ esk6_0 )
      | ( X2 @ X12 )
      | ~ ( epred3_0 @ X3 @ esk5_0 )
      | ~ ( X10 @ X13 @ X12 )
      | ~ ( X10 @ X1 @ X13 ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_42]) ).

thf(c_0_45,negated_conjecture,
    ( ( epred3_0 @ esk4_0 @ esk5_0 )
    | ( epred1_0 @ esk1_0 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_43,c_0_29]) ).

thf(c_0_46,negated_conjecture,
    ! [X3: $i,X2: $i > $o,X1: $i] :
      ( ( epred3_0 @ X1 @ ( esk7_3 @ epred3_0 @ X2 @ X1 ) )
      | ( epred3_0 @ X3 @ esk6_0 )
      | ( X2 @ esk6_0 )
      | ~ ( epred3_0 @ X3 @ esk5_0 )
      | ~ ( epred3_0 @ X1 @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_44,c_0_42]) ).

thf(c_0_47,negated_conjecture,
    epred3_0 @ esk4_0 @ esk5_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_45]),c_0_35]) ).

thf(c_0_48,negated_conjecture,
    ! [X2: $i > $o,X1: $i] :
      ( ( epred3_0 @ X1 @ ( esk7_3 @ epred3_0 @ X2 @ X1 ) )
      | ( epred3_0 @ esk4_0 @ esk6_0 )
      | ( X2 @ esk6_0 )
      | ~ ( epred3_0 @ X1 @ esk5_0 ) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

thf(c_0_49,negated_conjecture,
    ! [X1: $i,X3: $i,X15: $i,X10: $i > $i > $o,X12: $i,X13: $i,X20: $i] :
      ( ( epred3_0 @ esk4_0 @ esk6_0 )
      | ( epred3_0 @ X1 @ esk6_0 )
      | ( epred3_0 @ X1 @ X3 )
      | ( X10 @ X12 @ X13 )
      | ~ ( epred3_0 @ X1 @ esk5_0 )
      | ~ ( epred3_0 @ X15 @ X3 )
      | ~ ( epred3_0 @ X1 @ X15 )
      | ~ ( X10 @ X20 @ X13 )
      | ~ ( X10 @ X12 @ X20 ) ),
    inference(spm,[status(thm)],[c_0_25,c_0_48]) ).

thf(c_0_50,negated_conjecture,
    ( ( epred1_0 @ esk2_0 @ esk3_0 )
    | ~ ( epred3_0 @ esk4_0 @ esk6_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_51,negated_conjecture,
    ! [X1: $i,X3: $i,X12: $i,X10: $i > $i > $o,X13: $i] :
      ( ( epred3_0 @ esk4_0 @ esk6_0 )
      | ( epred3_0 @ X1 @ esk6_0 )
      | ( X10 @ X3 @ X12 )
      | ~ ( epred3_0 @ X1 @ esk5_0 )
      | ~ ( X10 @ X13 @ X12 )
      | ~ ( X10 @ X3 @ X13 ) ),
    inference(spm,[status(thm)],[c_0_49,c_0_42]) ).

thf(c_0_52,negated_conjecture,
    ! [X2: $i > $o,X1: $i,X10: $i > $i > $o,X12: $i,X3: $i,X13: $i] :
      ( ( X10 @ X1 @ ( esk7_3 @ X10 @ X2 @ X1 ) )
      | ( epred1_0 @ X3 @ esk3_0 )
      | ( X2 @ X12 )
      | ~ ( epred3_0 @ esk4_0 @ esk6_0 )
      | ~ ( epred1_0 @ X3 @ esk2_0 )
      | ~ ( X10 @ X13 @ X12 )
      | ~ ( X10 @ X1 @ X13 ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_50]) ).

thf(c_0_53,negated_conjecture,
    ! [X1: $i] :
      ( ( epred3_0 @ esk4_0 @ esk6_0 )
      | ( epred3_0 @ X1 @ esk6_0 )
      | ~ ( epred3_0 @ X1 @ esk5_0 ) ),
    inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_42])]) ).

thf(c_0_54,negated_conjecture,
    ! [X3: $i,X2: $i > $o,X1: $i] :
      ( ( epred1_0 @ X1 @ ( esk7_3 @ epred1_0 @ X2 @ X1 ) )
      | ( epred1_0 @ X3 @ esk3_0 )
      | ( X2 @ esk3_0 )
      | ~ ( epred3_0 @ esk4_0 @ esk6_0 )
      | ~ ( epred1_0 @ X3 @ esk2_0 )
      | ~ ( epred1_0 @ X1 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_52,c_0_50]) ).

thf(c_0_55,negated_conjecture,
    epred3_0 @ esk4_0 @ esk6_0,
    inference(spm,[status(thm)],[c_0_53,c_0_47]) ).

thf(c_0_56,negated_conjecture,
    ( ( epred1_0 @ esk1_0 @ esk2_0 )
    | ~ ( epred3_0 @ esk4_0 @ esk6_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_57,negated_conjecture,
    ! [X1: $i] :
      ( ( epred2_0 @ X1 )
      | ~ ( epred3_0 @ esk4_0 @ esk6_0 )
      | ~ ( epred1_0 @ esk1_0 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_58,negated_conjecture,
    ! [X3: $i,X2: $i > $o,X1: $i] :
      ( ( epred1_0 @ X1 @ ( esk7_3 @ epred1_0 @ X2 @ X1 ) )
      | ( epred1_0 @ X3 @ esk3_0 )
      | ( X2 @ esk3_0 )
      | ~ ( epred1_0 @ X3 @ esk2_0 )
      | ~ ( epred1_0 @ X1 @ esk2_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).

thf(c_0_59,negated_conjecture,
    epred1_0 @ esk1_0 @ esk2_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_55])]) ).

thf(c_0_60,negated_conjecture,
    ! [X1: $i] :
      ( ( epred2_0 @ X1 )
      | ~ ( epred1_0 @ esk1_0 @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_55])]) ).

thf(c_0_61,negated_conjecture,
    ! [X2: $i > $o,X1: $i] :
      ( ( epred1_0 @ X1 @ ( esk7_3 @ epred1_0 @ X2 @ X1 ) )
      | ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( X2 @ esk3_0 )
      | ~ ( epred1_0 @ X1 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

thf(c_0_62,negated_conjecture,
    ( ~ ( epred3_0 @ esk4_0 @ esk6_0 )
    | ~ ( epred2_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_63,negated_conjecture,
    ! [X2: $i > $o] :
      ( ( epred2_0 @ ( esk7_3 @ epred1_0 @ X2 @ esk1_0 ) )
      | ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( X2 @ esk3_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_59])]) ).

thf(c_0_64,negated_conjecture,
    ~ ( epred2_0 @ esk3_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_55])]) ).

thf(c_0_65,negated_conjecture,
    ! [X1: $i,X3: $i,X13: $i,X12: $i,X10: $i > $i > $o,X15: $i] :
      ( ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred2_0 @ X1 )
      | ( X10 @ X3 @ X12 )
      | ~ ( epred1_0 @ esk1_0 @ X13 )
      | ~ ( epred1_0 @ X13 @ X1 )
      | ~ ( X10 @ X15 @ X12 )
      | ~ ( X10 @ X3 @ X15 ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_63]),c_0_64]) ).

thf(c_0_66,negated_conjecture,
    ! [X1: $i,X10: $i > $i > $o,X12: $i,X3: $i,X13: $i] :
      ( ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( X10 @ X1 @ X3 )
      | ( epred2_0 @ X12 )
      | ~ ( epred1_0 @ esk2_0 @ X12 )
      | ~ ( X10 @ X13 @ X3 )
      | ~ ( X10 @ X1 @ X13 ) ),
    inference(spm,[status(thm)],[c_0_65,c_0_59]) ).

thf(c_0_67,negated_conjecture,
    epred1_0 @ esk2_0 @ esk3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_55])]) ).

thf(c_0_68,negated_conjecture,
    ! [X1: $i,X10: $i > $i > $o,X3: $i,X12: $i] :
      ( ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( X10 @ X1 @ X3 )
      | ~ ( X10 @ X12 @ X3 )
      | ~ ( X10 @ X1 @ X12 ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_64]) ).

thf(c_0_69,negated_conjecture,
    ! [X1: $i] :
      ( ( epred1_0 @ esk1_0 @ esk3_0 )
      | ( epred1_0 @ X1 @ esk3_0 )
      | ~ ( epred1_0 @ X1 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_68,c_0_67]) ).

thf(c_0_70,negated_conjecture,
    epred1_0 @ esk1_0 @ esk3_0,
    inference(spm,[status(thm)],[c_0_69,c_0_59]) ).

thf(c_0_71,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_70]),c_0_64]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : LCL601^1 : TPTP v8.2.0. Released v3.6.0.
% 0.12/0.12  % Command    : run_E %s %d THM
% 0.12/0.32  % Computer : n009.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Mon May 20 02:56:22 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.17/0.45  Running higher-order theorem proving
% 0.17/0.45  Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.17/0.50  # Version: 3.1.0-ho
% 0.17/0.50  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.17/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.50  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.17/0.50  # Starting post_as_ho3 with 300s (1) cores
% 0.17/0.50  # Starting post_as_ho11 with 300s (1) cores
% 0.17/0.50  # Starting full_lambda_8 with 300s (1) cores
% 0.17/0.50  # full_lambda_8 with pid 3437 completed with status 0
% 0.17/0.50  # Result found by full_lambda_8
% 0.17/0.50  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.17/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.50  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.17/0.50  # Starting post_as_ho3 with 300s (1) cores
% 0.17/0.50  # Starting post_as_ho11 with 300s (1) cores
% 0.17/0.50  # Starting full_lambda_8 with 300s (1) cores
% 0.17/0.50  # No SInE strategy applied
% 0.17/0.50  # Search class: HGHNF-FFSS33-SHSSMSBN
% 0.17/0.50  # partial match(1): HGHNF-FFSS33-SHHSMSBN
% 0.17/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.17/0.50  # new_ho_10 with pid 3441 completed with status 0
% 0.17/0.50  # Result found by new_ho_10
% 0.17/0.50  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.17/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.50  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.17/0.50  # Starting post_as_ho3 with 300s (1) cores
% 0.17/0.50  # Starting post_as_ho11 with 300s (1) cores
% 0.17/0.50  # Starting full_lambda_8 with 300s (1) cores
% 0.17/0.50  # No SInE strategy applied
% 0.17/0.50  # Search class: HGHNF-FFSS33-SHSSMSBN
% 0.17/0.50  # partial match(1): HGHNF-FFSS33-SHHSMSBN
% 0.17/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.17/0.50  # Preprocessing time       : 0.001 s
% 0.17/0.50  # Presaturation interreduction done
% 0.17/0.50  
% 0.17/0.50  # Proof found!
% 0.17/0.50  # SZS status Theorem
% 0.17/0.50  # SZS output start CNFRefutation
% See solution above
% 0.17/0.50  # Parsed axioms                        : 78
% 0.17/0.50  # Removed by relevancy pruning/SinE    : 0
% 0.17/0.50  # Initial clauses                      : 55
% 0.17/0.50  # Removed in clause preprocessing      : 41
% 0.17/0.50  # Initial clauses in saturation        : 14
% 0.17/0.50  # Processed clauses                    : 227
% 0.17/0.50  # ...of these trivial                  : 0
% 0.17/0.50  # ...subsumed                          : 77
% 0.17/0.50  # ...remaining for further processing  : 150
% 0.17/0.50  # Other redundant clauses eliminated   : 0
% 0.17/0.50  # Clauses deleted for lack of memory   : 0
% 0.17/0.50  # Backward-subsumed                    : 53
% 0.17/0.50  # Backward-rewritten                   : 55
% 0.17/0.50  # Generated clauses                    : 469
% 0.17/0.50  # ...of the previous two non-redundant : 462
% 0.17/0.50  # ...aggressively subsumed             : 0
% 0.17/0.50  # Contextual simplify-reflections      : 10
% 0.17/0.50  # Paramodulations                      : 469
% 0.17/0.50  # Factorizations                       : 0
% 0.17/0.50  # NegExts                              : 0
% 0.17/0.50  # Equation resolutions                 : 0
% 0.17/0.50  # Disequality decompositions           : 0
% 0.17/0.50  # Total rewrite steps                  : 64
% 0.17/0.50  # ...of those cached                   : 58
% 0.17/0.50  # Propositional unsat checks           : 0
% 0.17/0.50  #    Propositional check models        : 0
% 0.17/0.50  #    Propositional check unsatisfiable : 0
% 0.17/0.50  #    Propositional clauses             : 0
% 0.17/0.50  #    Propositional clauses after purity: 0
% 0.17/0.50  #    Propositional unsat core size     : 0
% 0.17/0.50  #    Propositional preprocessing time  : 0.000
% 0.17/0.50  #    Propositional encoding time       : 0.000
% 0.17/0.50  #    Propositional solver time         : 0.000
% 0.17/0.50  #    Success case prop preproc time    : 0.000
% 0.17/0.50  #    Success case prop encoding time   : 0.000
% 0.17/0.50  #    Success case prop solver time     : 0.000
% 0.17/0.50  # Current number of processed clauses  : 28
% 0.17/0.50  #    Positive orientable unit clauses  : 7
% 0.17/0.50  #    Positive unorientable unit clauses: 0
% 0.17/0.50  #    Negative unit clauses             : 1
% 0.17/0.50  #    Non-unit-clauses                  : 20
% 0.17/0.50  # Current number of unprocessed clauses: 77
% 0.17/0.50  # ...number of literals in the above   : 587
% 0.17/0.50  # Current number of archived formulas  : 0
% 0.17/0.50  # Current number of archived clauses   : 122
% 0.17/0.50  # Clause-clause subsumption calls (NU) : 2252
% 0.17/0.50  # Rec. Clause-clause subsumption calls : 761
% 0.17/0.50  # Non-unit clause-clause subsumptions  : 140
% 0.17/0.50  # Unit Clause-clause subsumption calls : 6
% 0.17/0.50  # Rewrite failures with RHS unbound    : 0
% 0.17/0.50  # BW rewrite match attempts            : 5
% 0.17/0.50  # BW rewrite match successes           : 5
% 0.17/0.50  # Condensation attempts                : 227
% 0.17/0.50  # Condensation successes               : 2
% 0.17/0.50  # Termbank termtop insertions          : 31940
% 0.17/0.50  # Search garbage collected termcells   : 551
% 0.17/0.50  
% 0.17/0.50  # -------------------------------------------------
% 0.17/0.50  # User time                : 0.041 s
% 0.17/0.50  # System time              : 0.002 s
% 0.17/0.50  # Total time               : 0.043 s
% 0.17/0.50  # Maximum resident set size: 2044 pages
% 0.17/0.50  
% 0.17/0.50  # -------------------------------------------------
% 0.17/0.50  # User time                : 0.045 s
% 0.17/0.50  # System time              : 0.003 s
% 0.17/0.50  # Total time               : 0.048 s
% 0.17/0.50  # Maximum resident set size: 1816 pages
% 0.17/0.50  % E---3.1 exiting
% 0.17/0.50  % E exiting
%------------------------------------------------------------------------------