TSTP Solution File: LCL626^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : LCL626^1 : TPTP v8.2.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n011.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 23:47:01 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   45 (  21 unt;  14 typ;   0 def)
%            Number of atoms       :   79 (  15 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  197 (  24   ~;  16   |;  14   &; 128   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   66 (  66   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   5 con; 0-3 aty)
%            Number of variables   :   75 (  30   ^  42   !;   3   ?;  75   :)

% 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_61,type,
    upwards_well_founded: ( $i > $i > $o ) > $o ).

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

thf(decl_63,type,
    esk1_1: ( $i > $o ) > $i ).

thf(decl_64,type,
    epred1_0: $i > $o ).

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

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

thf(decl_67,type,
    esk4_0: $i ).

thf(decl_68,type,
    esk5_0: $i ).

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

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

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

thf(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/sandbox2/benchmark/Axioms/SET008^2.ax',transitive) ).

thf(upwards_well_founded,axiom,
    ( upwards_well_founded
    = ( ^ [X10: $i > $i > $o] :
        ! [X45: $i > $o,X33: $i] :
          ( ( X45 @ X33 )
         => ? [X46: $i] :
              ( ( X45 @ X46 )
              & ! [X15: $i] :
                  ( ( X10 @ X46 @ X46 )
                 => ~ ( X45 @ X15 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',upwards_well_founded) ).

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

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

thf(upwf_trans,axiom,
    ( ( transitive @ r )
    & ( upwards_well_founded @ r ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upwf_trans) ).

thf(k4,conjecture,
    ! [X47: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X47 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X47 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k4) ).

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

thf(c_0_10,plain,
    ( mnot
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ( Z0 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mnot]) ).

thf(c_0_11,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

thf(c_0_12,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_13,plain,
    ( upwards_well_founded
    = ( ^ [Z0: $i > $i > $o] :
        ! [X45: $i > $o,X33: $i] :
          ( ( X45 @ X33 )
         => ? [X46: $i] :
              ( ( X45 @ X46 )
              & ! [X15: $i] :
                  ( ( Z0 @ X46 @ X46 )
                 => ~ ( X45 @ X15 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[upwards_well_founded]) ).

thf(c_0_14,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_9,c_0_10]),c_0_11]) ).

thf(c_0_15,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_16,plain,
    ( mvalid
    = ( ^ [Z0: $i > $o] :
        ! [X15: $i] : ( Z0 @ X15 ) ) ),
    inference(fof_simplification,[status(thm)],[mvalid]) ).

thf(c_0_17,plain,
    ( ! [X57: $i,X58: $i,X59: $i] :
        ( ( ( r @ X57 @ X58 )
          & ( r @ X58 @ X59 ) )
       => ( r @ X57 @ X59 ) )
    & ! [X60: $i > $o,X61: $i] :
        ( ( X60 @ X61 )
       => ? [X62: $i] :
            ( ( X60 @ X62 )
            & ! [X63: $i] :
                ( ( r @ X62 @ X62 )
               => ~ ( X60 @ X63 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[upwf_trans,c_0_12]),c_0_13]) ).

thf(c_0_18,negated_conjecture,
    ~ ! [X47: $i > $o,X68: $i] :
        ( ~ ! [X64: $i] :
              ( ( r @ X68 @ X64 )
             => ( X47 @ X64 ) )
        | ! [X67: $i] :
            ( ( r @ X68 @ X67 )
           => ! [X66: $i] :
                ( ( r @ X67 @ X66 )
               => ! [X65: $i] :
                    ( ( r @ X66 @ X65 )
                   => ( X47 @ X65 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[k4]),c_0_14]),c_0_15]),c_0_16]) ).

thf(c_0_19,plain,
    ! [X69: $i,X70: $i,X71: $i,X72: $i > $o,X73: $i,X75: $i] :
      ( ( ~ ( r @ X69 @ X70 )
        | ~ ( r @ X70 @ X71 )
        | ( r @ X69 @ X71 ) )
      & ( ( X72 @ ( esk1_1 @ X72 ) )
        | ~ ( X72 @ X73 ) )
      & ( ~ ( r @ ( esk1_1 @ X72 ) @ ( esk1_1 @ X72 ) )
        | ~ ( X72 @ X75 )
        | ~ ( X72 @ X73 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])])])]) ).

thf(c_0_20,negated_conjecture,
    ! [X78: $i] :
      ( ( ~ ( r @ esk2_0 @ X78 )
        | ( epred1_0 @ X78 ) )
      & ( r @ esk2_0 @ esk3_0 )
      & ( r @ esk3_0 @ esk4_0 )
      & ( r @ esk4_0 @ esk5_0 )
      & ~ ( epred1_0 @ esk5_0 ) ),
    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_18])])])])]) ).

thf(c_0_21,plain,
    ! [X1: $i,X3: $i,X12: $i] :
      ( ( r @ X1 @ X12 )
      | ~ ( r @ X1 @ X3 )
      | ~ ( r @ X3 @ X12 ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_22,negated_conjecture,
    r @ esk4_0 @ esk5_0,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_23,negated_conjecture,
    ! [X1: $i] :
      ( ( epred1_0 @ X1 )
      | ~ ( r @ esk2_0 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_24,negated_conjecture,
    ! [X1: $i] :
      ( ( r @ X1 @ esk5_0 )
      | ~ ( r @ X1 @ esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_25,negated_conjecture,
    ~ ( epred1_0 @ esk5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_26,negated_conjecture,
    r @ esk3_0 @ esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_27,negated_conjecture,
    ~ ( r @ esk2_0 @ esk4_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).

thf(c_0_28,negated_conjecture,
    ! [X1: $i] :
      ( ( r @ X1 @ esk4_0 )
      | ~ ( r @ X1 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_21,c_0_26]) ).

thf(c_0_29,negated_conjecture,
    r @ esk2_0 @ esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_30,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem    : LCL626^1 : TPTP v8.2.0. Bugfixed v7.3.0.
% 0.08/0.09  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n011.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Mon May 20 03:25:37 EDT 2024
% 0.09/0.29  % CPUTime    : 
% 0.14/0.38  Running higher-order theorem proving
% 0.14/0.38  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
% 0.14/0.39  # Version: 3.1.0-ho
% 0.14/0.39  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.14/0.39  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.39  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.14/0.39  # Starting post_as_ho3 with 300s (1) cores
% 0.14/0.39  # Starting post_as_ho11 with 300s (1) cores
% 0.14/0.39  # Starting full_lambda_8 with 300s (1) cores
% 0.14/0.39  # post_as_ho11 with pid 8496 completed with status 0
% 0.14/0.39  # Result found by post_as_ho11
% 0.14/0.39  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.14/0.39  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.39  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.14/0.39  # Starting post_as_ho3 with 300s (1) cores
% 0.14/0.39  # Starting post_as_ho11 with 300s (1) cores
% 0.14/0.39  # No SInE strategy applied
% 0.14/0.39  # Search class: HHHNF-FFSS11-SHSSMSBC
% 0.14/0.39  # partial match(2): HHHNF-FFSF11-SHSSMMBC
% 0.14/0.39  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.39  # Starting new_ho_10 with 135s (1) cores
% 0.14/0.39  # new_ho_10 with pid 8504 completed with status 0
% 0.14/0.39  # Result found by new_ho_10
% 0.14/0.39  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.14/0.39  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.39  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.14/0.39  # Starting post_as_ho3 with 300s (1) cores
% 0.14/0.39  # Starting post_as_ho11 with 300s (1) cores
% 0.14/0.39  # No SInE strategy applied
% 0.14/0.39  # Search class: HHHNF-FFSS11-SHSSMSBC
% 0.14/0.39  # partial match(2): HHHNF-FFSF11-SHSSMMBC
% 0.14/0.39  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.39  # Starting new_ho_10 with 135s (1) cores
% 0.14/0.39  # Preprocessing time       : 0.001 s
% 0.14/0.39  # Presaturation interreduction done
% 0.14/0.39  
% 0.14/0.39  # Proof found!
% 0.14/0.39  # SZS status Theorem
% 0.14/0.39  # SZS output start CNFRefutation
% See solution above
% 0.14/0.39  # Parsed axioms                        : 80
% 0.14/0.39  # Removed by relevancy pruning/SinE    : 0
% 0.14/0.39  # Initial clauses                      : 50
% 0.14/0.39  # Removed in clause preprocessing      : 42
% 0.14/0.39  # Initial clauses in saturation        : 8
% 0.14/0.39  # Processed clauses                    : 26
% 0.14/0.39  # ...of these trivial                  : 0
% 0.14/0.39  # ...subsumed                          : 0
% 0.14/0.39  # ...remaining for further processing  : 26
% 0.14/0.39  # Other redundant clauses eliminated   : 0
% 0.14/0.39  # Clauses deleted for lack of memory   : 0
% 0.14/0.39  # Backward-subsumed                    : 0
% 0.14/0.39  # Backward-rewritten                   : 0
% 0.14/0.39  # Generated clauses                    : 24
% 0.14/0.39  # ...of the previous two non-redundant : 17
% 0.14/0.39  # ...aggressively subsumed             : 0
% 0.14/0.39  # Contextual simplify-reflections      : 0
% 0.14/0.39  # Paramodulations                      : 24
% 0.14/0.39  # Factorizations                       : 0
% 0.14/0.39  # NegExts                              : 0
% 0.14/0.39  # Equation resolutions                 : 0
% 0.14/0.39  # Disequality decompositions           : 0
% 0.14/0.39  # Total rewrite steps                  : 7
% 0.14/0.39  # ...of those cached                   : 2
% 0.14/0.39  # Propositional unsat checks           : 0
% 0.14/0.39  #    Propositional check models        : 0
% 0.14/0.39  #    Propositional check unsatisfiable : 0
% 0.14/0.39  #    Propositional clauses             : 0
% 0.14/0.39  #    Propositional clauses after purity: 0
% 0.14/0.39  #    Propositional unsat core size     : 0
% 0.14/0.39  #    Propositional preprocessing time  : 0.000
% 0.14/0.39  #    Propositional encoding time       : 0.000
% 0.14/0.39  #    Propositional solver time         : 0.000
% 0.14/0.39  #    Success case prop preproc time    : 0.000
% 0.14/0.39  #    Success case prop encoding time   : 0.000
% 0.14/0.39  #    Success case prop solver time     : 0.000
% 0.14/0.39  # Current number of processed clauses  : 18
% 0.14/0.39  #    Positive orientable unit clauses  : 9
% 0.14/0.39  #    Positive unorientable unit clauses: 0
% 0.14/0.39  #    Negative unit clauses             : 2
% 0.14/0.39  #    Non-unit-clauses                  : 7
% 0.14/0.39  # Current number of unprocessed clauses: 5
% 0.14/0.39  # ...number of literals in the above   : 11
% 0.14/0.39  # Current number of archived formulas  : 0
% 0.14/0.39  # Current number of archived clauses   : 8
% 0.14/0.39  # Clause-clause subsumption calls (NU) : 3
% 0.14/0.39  # Rec. Clause-clause subsumption calls : 3
% 0.14/0.39  # Non-unit clause-clause subsumptions  : 0
% 0.14/0.39  # Unit Clause-clause subsumption calls : 1
% 0.14/0.39  # Rewrite failures with RHS unbound    : 0
% 0.14/0.39  # BW rewrite match attempts            : 0
% 0.14/0.39  # BW rewrite match successes           : 0
% 0.14/0.39  # Condensation attempts                : 26
% 0.14/0.39  # Condensation successes               : 0
% 0.14/0.39  # Termbank termtop insertions          : 2734
% 0.14/0.39  # Search garbage collected termcells   : 426
% 0.14/0.39  
% 0.14/0.39  # -------------------------------------------------
% 0.14/0.39  # User time                : 0.004 s
% 0.14/0.39  # System time              : 0.002 s
% 0.14/0.39  # Total time               : 0.006 s
% 0.14/0.39  # Maximum resident set size: 1908 pages
% 0.14/0.39  
% 0.14/0.39  # -------------------------------------------------
% 0.14/0.39  # User time                : 0.006 s
% 0.14/0.39  # System time              : 0.002 s
% 0.14/0.39  # Total time               : 0.009 s
% 0.14/0.39  # Maximum resident set size: 1820 pages
% 0.14/0.39  % E---3.1 exiting
% 0.14/0.40  % E exiting
%------------------------------------------------------------------------------