TSTP Solution File: LCL962^16 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : LCL962^16 : TPTP v8.2.0. Released v8.1.0.
% 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 : Mon May 20 23:55:01 EDT 2024

% Result   : Theorem 0.20s 0.48s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   48 (  19 unt;  13 typ;   0 def)
%            Number of atoms       :   94 (   8 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  223 (  28   ~;  21   |;   2   &; 160   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   29 (  29   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :   42 (  18   ^  24   !;   0   ?;  42   :)

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

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

thf(decl_22,type,
    mrel: mindex > mworld > mworld > $o ).

thf(decl_23,type,
    '#b': mindex ).

thf(decl_24,type,
    '#a': mindex ).

thf(decl_25,type,
    mactual: mworld ).

thf(decl_26,type,
    mlocal: ( mworld > $o ) > $o ).

thf(decl_27,type,
    mnot: ( mworld > $o ) > mworld > $o ).

thf(decl_30,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(decl_32,type,
    mbox: mindex > ( mworld > $o ) > mworld > $o ).

thf(decl_34,type,
    p: mworld > $o ).

thf(decl_35,type,
    esk1_1: mworld > mworld ).

thf(decl_36,type,
    esk2_0: mworld ).

thf(mlocal_def,axiom,
    ( mlocal
    = ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).

thf(mnot_def,axiom,
    ( mnot
    = ( ^ [X2: mworld > $o,X3: mworld] :
          ~ ( X2 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).

thf(mimplies_def,axiom,
    ( mimplies
    = ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
          ( ( X2 @ X3 )
         => ( X4 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).

thf(mbox_def,axiom,
    ( mbox
    = ( ^ [X5: mindex,X1: mworld > $o,X3: mworld] :
        ! [X6: mworld] :
          ( ( mrel @ X5 @ X3 @ X6 )
         => ( X1 @ X6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).

thf(ab_axiom_2,axiom,
    mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_2) ).

thf(not_a_axiom_1,axiom,
    mlocal @ ( mnot @ p ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_a_axiom_1) ).

thf(ab_axiom_1,axiom,
    mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_1) ).

thf(conj,conjecture,
    mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

thf('mrel_#b_reflexive',axiom,
    ! [X3: mworld] : ( mrel @ '#b' @ X3 @ X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#b_reflexive') ).

thf(c_0_9,plain,
    ( mlocal
    = ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
    inference(fof_simplification,[status(thm)],[mlocal_def]) ).

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

thf(c_0_11,plain,
    ( mimplies
    = ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
          ( ( Z0 @ Z2 )
         => ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mimplies_def]) ).

thf(c_0_12,plain,
    ( mbox
    = ( ^ [Z0: mindex,Z1: mworld > $o,Z2: mworld] :
        ! [X6: mworld] :
          ( ( mrel @ Z0 @ Z2 @ X6 )
         => ( Z1 @ X6 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mbox_def]) ).

thf(c_0_13,plain,
    ( ~ ! [X18: mworld] :
          ( ( mrel @ '#b' @ mactual @ X18 )
         => ( p @ X18 ) )
   => ! [X20: mworld] :
        ( ( mrel @ '#a' @ mactual @ X20 )
       => ~ ! [X19: mworld] :
              ( ( mrel @ '#b' @ X20 @ X19 )
             => ( p @ X19 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ab_axiom_2,c_0_9]),c_0_10]),c_0_11]),c_0_12]) ).

thf(c_0_14,plain,
    ~ ( p @ mactual ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[not_a_axiom_1,c_0_9]),c_0_10])]) ).

thf(c_0_15,plain,
    ! [X17: mworld] :
      ( ( mrel @ '#a' @ mactual @ X17 )
     => ( ( p @ X17 )
       => ! [X16: mworld] :
            ( ( mrel @ '#b' @ X17 @ X16 )
           => ( p @ X16 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ab_axiom_1,c_0_9]),c_0_11]),c_0_12]) ).

thf(c_0_16,negated_conjecture,
    ~ ! [X21: mworld] :
        ( ( mrel @ '#a' @ mactual @ X21 )
       => ~ ( p @ X21 ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[conj]),c_0_9]),c_0_10]),c_0_12])]) ).

thf(c_0_17,plain,
    ! [X32: mworld,X33: mworld] :
      ( ( ( mrel @ '#b' @ X33 @ ( esk1_1 @ X33 ) )
        | ~ ( mrel @ '#a' @ mactual @ X33 )
        | ~ ( mrel @ '#b' @ mactual @ X32 )
        | ( p @ X32 ) )
      & ( ~ ( p @ ( esk1_1 @ X33 ) )
        | ~ ( mrel @ '#a' @ mactual @ X33 )
        | ~ ( mrel @ '#b' @ mactual @ X32 )
        | ( p @ X32 ) ) ),
    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_13])])])])])]) ).

thf(c_0_18,plain,
    ! [X22: mworld] : ( mrel @ '#b' @ X22 @ X22 ),
    inference(variable_rename,[status(thm)],['mrel_#b_reflexive']) ).

thf(c_0_19,plain,
    ~ ( p @ mactual ),
    inference(fof_nnf,[status(thm)],[c_0_14]) ).

thf(c_0_20,plain,
    ! [X30: mworld,X31: mworld] :
      ( ~ ( mrel @ '#a' @ mactual @ X30 )
      | ~ ( p @ X30 )
      | ~ ( mrel @ '#b' @ X30 @ X31 )
      | ( p @ X31 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).

thf(c_0_21,negated_conjecture,
    ( ( mrel @ '#a' @ mactual @ esk2_0 )
    & ( p @ esk2_0 ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).

thf(c_0_22,plain,
    ! [X3: mworld,X6: mworld] :
      ( ( mrel @ '#b' @ X3 @ ( esk1_1 @ X3 ) )
      | ( p @ X6 )
      | ~ ( mrel @ '#a' @ mactual @ X3 )
      | ~ ( mrel @ '#b' @ mactual @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_23,plain,
    ! [X3: mworld] : ( mrel @ '#b' @ X3 @ X3 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_24,plain,
    ~ ( p @ mactual ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_25,plain,
    ! [X3: mworld,X6: mworld] :
      ( ( p @ X6 )
      | ~ ( mrel @ '#a' @ mactual @ X3 )
      | ~ ( p @ X3 )
      | ~ ( mrel @ '#b' @ X3 @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_26,negated_conjecture,
    mrel @ '#a' @ mactual @ esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_27,negated_conjecture,
    p @ esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_28,plain,
    ! [X3: mworld] :
      ( ( mrel @ '#b' @ X3 @ ( esk1_1 @ X3 ) )
      | ~ ( mrel @ '#a' @ mactual @ X3 ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

thf(c_0_29,negated_conjecture,
    ! [X3: mworld] :
      ( ( p @ X3 )
      | ~ ( mrel @ '#b' @ esk2_0 @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).

thf(c_0_30,negated_conjecture,
    mrel @ '#b' @ esk2_0 @ ( esk1_1 @ esk2_0 ),
    inference(spm,[status(thm)],[c_0_28,c_0_26]) ).

thf(c_0_31,plain,
    ! [X3: mworld,X6: mworld] :
      ( ( p @ X6 )
      | ~ ( p @ ( esk1_1 @ X3 ) )
      | ~ ( mrel @ '#a' @ mactual @ X3 )
      | ~ ( mrel @ '#b' @ mactual @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_32,negated_conjecture,
    p @ ( esk1_1 @ esk2_0 ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

thf(c_0_33,negated_conjecture,
    ! [X3: mworld] :
      ( ( p @ X3 )
      | ~ ( mrel @ '#b' @ mactual @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_26])]) ).

thf(c_0_34,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23]),c_0_24]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : LCL962^16 : TPTP v8.2.0. Released v8.1.0.
% 0.12/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 02:25:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  Running higher-order theorem proving
% 0.20/0.47  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
% 0.20/0.48  # Version: 3.1.0-ho
% 0.20/0.48  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.48  # Starting post_as_ho3 with 300s (1) cores
% 0.20/0.48  # Starting post_as_ho11 with 300s (1) cores
% 0.20/0.48  # Starting full_lambda_8 with 300s (1) cores
% 0.20/0.48  # new_ho_10_cnf2 with pid 29545 completed with status 0
% 0.20/0.48  # Result found by new_ho_10_cnf2
% 0.20/0.48  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.48  # No SInE strategy applied
% 0.20/0.48  # Search class: HGUNS-FFSF11-SHSSMFNN
% 0.20/0.48  # partial match(1): HGUNF-FFSF11-SHSSMFNN
% 0.20/0.48  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.48  # Starting sh7 with 811s (1) cores
% 0.20/0.48  # Starting new_ho_10_cnf2 with 151s (1) cores
% 0.20/0.48  # Starting post_as_ho1 with 136s (1) cores
% 0.20/0.48  # Starting lpo5_fix with 136s (1) cores
% 0.20/0.48  # Starting lpo1_def_fix with 136s (1) cores
% 0.20/0.48  # sh7 with pid 29549 completed with status 0
% 0.20/0.48  # Result found by sh7
% 0.20/0.48  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.48  # No SInE strategy applied
% 0.20/0.48  # Search class: HGUNS-FFSF11-SHSSMFNN
% 0.20/0.48  # partial match(1): HGUNF-FFSF11-SHSSMFNN
% 0.20/0.48  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.48  # Starting sh7 with 811s (1) cores
% 0.20/0.48  # Preprocessing time       : 0.001 s
% 0.20/0.48  # Presaturation interreduction done
% 0.20/0.48  
% 0.20/0.48  # Proof found!
% 0.20/0.48  # SZS status Theorem
% 0.20/0.48  # SZS output start CNFRefutation
% See solution above
% 0.20/0.48  # Parsed axioms                        : 31
% 0.20/0.48  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.48  # Initial clauses                      : 25
% 0.20/0.48  # Removed in clause preprocessing      : 15
% 0.20/0.48  # Initial clauses in saturation        : 10
% 0.20/0.48  # Processed clauses                    : 29
% 0.20/0.48  # ...of these trivial                  : 0
% 0.20/0.48  # ...subsumed                          : 1
% 0.20/0.48  # ...remaining for further processing  : 28
% 0.20/0.48  # Other redundant clauses eliminated   : 0
% 0.20/0.48  # Clauses deleted for lack of memory   : 0
% 0.20/0.48  # Backward-subsumed                    : 2
% 0.20/0.48  # Backward-rewritten                   : 0
% 0.20/0.48  # Generated clauses                    : 17
% 0.20/0.48  # ...of the previous two non-redundant : 10
% 0.20/0.48  # ...aggressively subsumed             : 0
% 0.20/0.48  # Contextual simplify-reflections      : 0
% 0.20/0.48  # Paramodulations                      : 17
% 0.20/0.48  # Factorizations                       : 0
% 0.20/0.48  # NegExts                              : 0
% 0.20/0.48  # Equation resolutions                 : 0
% 0.20/0.48  # Disequality decompositions           : 0
% 0.20/0.48  # Total rewrite steps                  : 5
% 0.20/0.48  # ...of those cached                   : 2
% 0.20/0.48  # Propositional unsat checks           : 0
% 0.20/0.48  #    Propositional check models        : 0
% 0.20/0.48  #    Propositional check unsatisfiable : 0
% 0.20/0.48  #    Propositional clauses             : 0
% 0.20/0.48  #    Propositional clauses after purity: 0
% 0.20/0.48  #    Propositional unsat core size     : 0
% 0.20/0.48  #    Propositional preprocessing time  : 0.000
% 0.20/0.48  #    Propositional encoding time       : 0.000
% 0.20/0.48  #    Propositional solver time         : 0.000
% 0.20/0.48  #    Success case prop preproc time    : 0.000
% 0.20/0.48  #    Success case prop encoding time   : 0.000
% 0.20/0.48  #    Success case prop solver time     : 0.000
% 0.20/0.48  # Current number of processed clauses  : 16
% 0.20/0.48  #    Positive orientable unit clauses  : 7
% 0.20/0.48  #    Positive unorientable unit clauses: 0
% 0.20/0.49  #    Negative unit clauses             : 1
% 0.20/0.49  #    Non-unit-clauses                  : 8
% 0.20/0.49  # Current number of unprocessed clauses: 1
% 0.20/0.49  # ...number of literals in the above   : 2
% 0.20/0.49  # Current number of archived formulas  : 0
% 0.20/0.49  # Current number of archived clauses   : 12
% 0.20/0.49  # Clause-clause subsumption calls (NU) : 8
% 0.20/0.49  # Rec. Clause-clause subsumption calls : 5
% 0.20/0.49  # Non-unit clause-clause subsumptions  : 2
% 0.20/0.49  # Unit Clause-clause subsumption calls : 0
% 0.20/0.49  # Rewrite failures with RHS unbound    : 0
% 0.20/0.49  # BW rewrite match attempts            : 3
% 0.20/0.49  # BW rewrite match successes           : 0
% 0.20/0.49  # Condensation attempts                : 0
% 0.20/0.49  # Condensation successes               : 0
% 0.20/0.49  # Termbank termtop insertions          : 1813
% 0.20/0.49  # Search garbage collected termcells   : 377
% 0.20/0.49  
% 0.20/0.49  # -------------------------------------------------
% 0.20/0.49  # User time                : 0.006 s
% 0.20/0.49  # System time              : 0.002 s
% 0.20/0.49  # Total time               : 0.007 s
% 0.20/0.49  # Maximum resident set size: 1860 pages
% 0.20/0.49  
% 0.20/0.49  # -------------------------------------------------
% 0.20/0.49  # User time                : 0.014 s
% 0.20/0.49  # System time              : 0.007 s
% 0.20/0.49  # Total time               : 0.021 s
% 0.20/0.49  # Maximum resident set size: 1744 pages
% 0.20/0.49  % E---3.1 exiting
% 0.20/0.49  % E exiting
%------------------------------------------------------------------------------