TSTP Solution File: SYO495^6 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO495^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 08:46:24 EDT 2024

% Result   : Theorem 0.21s 0.51s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   51 (  24 unt;  15 typ;   0 def)
%            Number of atoms       :   96 (  17 equ;   0 cnn)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  199 (  25   ~;  26   |;   6   &; 139   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   62 (  62   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   4 con; 0-3 aty)
%            Number of variables   :   76 (  34   ^  42   !;   0   ?;  76   :)

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

thf(decl_24,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(decl_25,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_27,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_31,type,
    mforall_ind: ( mu > $i > $o ) > $i > $o ).

thf(decl_39,type,
    mreflexive: ( $i > $i > $o ) > $o ).

thf(decl_42,type,
    mtransitive: ( $i > $i > $o ) > $o ).

thf(decl_49,type,
    mvalid: ( $i > $o ) > $o ).

thf(decl_53,type,
    rel_s5: $i > $i > $o ).

thf(decl_54,type,
    mbox_s5: ( $i > $o ) > $i > $o ).

thf(decl_56,type,
    f: mu > $i > $o ).

thf(decl_57,type,
    g: mu > $i > $o ).

thf(decl_58,type,
    esk1_0: $i ).

thf(decl_59,type,
    esk2_0: $i ).

thf(decl_60,type,
    esk3_0: mu ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [X6: $i > $o,X3: $i] :
          ~ ( X6 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
          ( ( X6 @ X3 )
          | ( X7 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).

thf(mforall_ind,axiom,
    ( mforall_ind
    = ( ^ [X8: mu > $i > $o,X3: $i] :
        ! [X1: mu] : ( X8 @ X1 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_ind) ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [X6: $i > $o] :
        ! [X3: $i] : ( X6 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).

thf(mbox_s5,axiom,
    ( mbox_s5
    = ( ^ [X6: $i > $o,X3: $i] :
        ! [X14: $i] :
          ( ~ ( rel_s5 @ X3 @ X14 )
          | ( X6 @ X14 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).

thf(mtransitive,axiom,
    ( mtransitive
    = ( ^ [X13: $i > $i > $o] :
        ! [X15: $i,X16: $i,X17: $i] :
          ( ( ( X13 @ X15 @ X16 )
            & ( X13 @ X16 @ X17 ) )
         => ( X13 @ X15 @ X17 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).

thf(prove,conjecture,
    ( mvalid
    @ ( mimplies
      @ ( mforall_ind
        @ ^ [X1: mu] : ( mor @ ( mbox_s5 @ ( f @ X1 ) ) @ ( mbox_s5 @ ( g @ X1 ) ) ) )
      @ ( mbox_s5
        @ ( mforall_ind
          @ ^ [X1: mu] : ( mor @ ( f @ X1 ) @ ( g @ X1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).

thf(a2,axiom,
    mtransitive @ rel_s5,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a2) ).

thf(mreflexive,axiom,
    ( mreflexive
    = ( ^ [X13: $i > $i > $o] :
        ! [X15: $i] : ( X13 @ X15 @ X15 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).

thf(a1,axiom,
    mreflexive @ rel_s5,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a1) ).

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

thf(c_0_12,plain,
    ( mnot
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ( Z0 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mnot]) ).

thf(c_0_13,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

thf(c_0_14,plain,
    ( mimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).

thf(c_0_15,plain,
    ( mforall_ind
    = ( ^ [Z0: mu > $i > $o,Z1: $i] :
        ! [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mforall_ind]) ).

thf(c_0_16,plain,
    ( mvalid
    = ( ^ [Z0: $i > $o] :
        ! [X3: $i] : ( Z0 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[mvalid]) ).

thf(c_0_17,plain,
    ( mbox_s5
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X14: $i] :
          ( ~ ( rel_s5 @ Z1 @ X14 )
          | ( Z0 @ X14 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mbox_s5]) ).

thf(c_0_18,plain,
    ( mtransitive
    = ( ^ [Z0: $i > $i > $o] :
        ! [X15: $i,X16: $i,X17: $i] :
          ( ( ( Z0 @ X15 @ X16 )
            & ( Z0 @ X16 @ X17 ) )
         => ( Z0 @ X15 @ X17 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mtransitive]) ).

thf(c_0_19,negated_conjecture,
    ~ ! [X33: $i] :
        ( ~ ! [X30: mu] :
              ( ! [X28: $i] :
                  ( ~ ( rel_s5 @ X33 @ X28 )
                  | ( f @ X30 @ X28 ) )
              | ! [X29: $i] :
                  ( ~ ( rel_s5 @ X33 @ X29 )
                  | ( g @ X30 @ X29 ) ) )
        | ! [X32: $i] :
            ( ~ ( rel_s5 @ X33 @ X32 )
            | ! [X31: mu] :
                ( ( f @ X31 @ X32 )
                | ( g @ X31 @ X32 ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove])]),c_0_13]),c_0_14]),c_0_15]),c_0_16]),c_0_17])]) ).

thf(c_0_20,plain,
    ! [X23: $i,X24: $i,X25: $i] :
      ( ( ( rel_s5 @ X23 @ X24 )
        & ( rel_s5 @ X24 @ X25 ) )
     => ( rel_s5 @ X23 @ X25 ) ),
    inference(apply_def,[status(thm)],[a2,c_0_18]) ).

thf(c_0_21,plain,
    ( mreflexive
    = ( ^ [Z0: $i > $i > $o] :
        ! [X15: $i] : ( Z0 @ X15 @ X15 ) ) ),
    inference(fof_simplification,[status(thm)],[mreflexive]) ).

thf(c_0_22,negated_conjecture,
    ! [X41: mu,X42: $i,X43: $i] :
      ( ( ~ ( rel_s5 @ esk1_0 @ X42 )
        | ( f @ X41 @ X42 )
        | ~ ( rel_s5 @ esk1_0 @ X43 )
        | ( g @ X41 @ X43 ) )
      & ( rel_s5 @ esk1_0 @ esk2_0 )
      & ~ ( f @ esk3_0 @ esk2_0 )
      & ~ ( g @ esk3_0 @ esk2_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_19])])])])]) ).

thf(c_0_23,plain,
    ! [X35: $i,X36: $i,X37: $i] :
      ( ~ ( rel_s5 @ X35 @ X36 )
      | ~ ( rel_s5 @ X36 @ X37 )
      | ( rel_s5 @ X35 @ X37 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).

thf(c_0_24,plain,
    ! [X22: $i] : ( rel_s5 @ X22 @ X22 ),
    inference(apply_def,[status(thm)],[a1,c_0_21]) ).

thf(c_0_25,negated_conjecture,
    ! [X3: $i,X1: mu,X14: $i] :
      ( ( f @ X1 @ X3 )
      | ( g @ X1 @ X14 )
      | ~ ( rel_s5 @ esk1_0 @ X3 )
      | ~ ( rel_s5 @ esk1_0 @ X14 ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_26,negated_conjecture,
    rel_s5 @ esk1_0 @ esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_27,plain,
    ! [X14: $i,X3: $i,X15: $i] :
      ( ( rel_s5 @ X3 @ X15 )
      | ~ ( rel_s5 @ X3 @ X14 )
      | ~ ( rel_s5 @ X14 @ X15 ) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

thf(c_0_28,plain,
    ! [X34: $i] : ( rel_s5 @ X34 @ X34 ),
    inference(variable_rename,[status(thm)],[c_0_24]) ).

thf(c_0_29,negated_conjecture,
    ! [X1: mu,X3: $i] :
      ( ( g @ X1 @ esk2_0 )
      | ( f @ X1 @ X3 )
      | ~ ( rel_s5 @ esk1_0 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

thf(c_0_30,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ X3 @ esk2_0 )
      | ~ ( rel_s5 @ X3 @ esk1_0 ) ),
    inference(spm,[status(thm)],[c_0_27,c_0_26]) ).

thf(c_0_31,plain,
    ! [X3: $i] : ( rel_s5 @ X3 @ X3 ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

thf(c_0_32,negated_conjecture,
    ~ ( g @ esk3_0 @ esk2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_33,negated_conjecture,
    ! [X1: mu] :
      ( ( f @ X1 @ esk2_0 )
      | ( g @ X1 @ esk2_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).

thf(c_0_34,negated_conjecture,
    ~ ( f @ esk3_0 @ esk2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_35,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem    : SYO495^6 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.15  % Command    : run_E %s %d THM
% 0.15/0.36  % Computer : n005.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon May 20 09:29:53 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.21/0.50  Running higher-order theorem proving
% 0.21/0.50  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
% 0.21/0.51  # Version: 3.1.0-ho
% 0.21/0.51  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.51  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.21/0.51  # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.51  # Starting post_as_ho1 with 300s (1) cores
% 0.21/0.51  # post_as_ho1 with pid 7401 completed with status 0
% 0.21/0.51  # Result found by post_as_ho1
% 0.21/0.51  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.51  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.21/0.51  # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.51  # Starting post_as_ho1 with 300s (1) cores
% 0.21/0.51  # No SInE strategy applied
% 0.21/0.51  # Search class: HGUNF-FFSF00-SHSSMFNN
% 0.21/0.51  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.51  # new_ho_10 with pid 7402 completed with status 0
% 0.21/0.51  # Result found by new_ho_10
% 0.21/0.51  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.51  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.21/0.51  # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.51  # Starting post_as_ho1 with 300s (1) cores
% 0.21/0.51  # No SInE strategy applied
% 0.21/0.51  # Search class: HGUNF-FFSF00-SHSSMFNN
% 0.21/0.51  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.51  # Preprocessing time       : 0.001 s
% 0.21/0.51  # Presaturation interreduction done
% 0.21/0.51  
% 0.21/0.51  # Proof found!
% 0.21/0.51  # SZS status Theorem
% 0.21/0.51  # SZS output start CNFRefutation
% See solution above
% 0.21/0.51  # Parsed axioms                        : 74
% 0.21/0.51  # Removed by relevancy pruning/SinE    : 0
% 0.21/0.51  # Initial clauses                      : 44
% 0.21/0.51  # Removed in clause preprocessing      : 37
% 0.21/0.51  # Initial clauses in saturation        : 7
% 0.21/0.51  # Processed clauses                    : 27
% 0.21/0.51  # ...of these trivial                  : 0
% 0.21/0.51  # ...subsumed                          : 3
% 0.21/0.51  # ...remaining for further processing  : 24
% 0.21/0.51  # Other redundant clauses eliminated   : 0
% 0.21/0.51  # Clauses deleted for lack of memory   : 0
% 0.21/0.51  # Backward-subsumed                    : 0
% 0.21/0.51  # Backward-rewritten                   : 0
% 0.21/0.51  # Generated clauses                    : 25
% 0.21/0.51  # ...of the previous two non-redundant : 15
% 0.21/0.51  # ...aggressively subsumed             : 0
% 0.21/0.51  # Contextual simplify-reflections      : 0
% 0.21/0.51  # Paramodulations                      : 25
% 0.21/0.51  # Factorizations                       : 0
% 0.21/0.51  # NegExts                              : 0
% 0.21/0.51  # Equation resolutions                 : 0
% 0.21/0.51  # Disequality decompositions           : 0
% 0.21/0.51  # Total rewrite steps                  : 9
% 0.21/0.51  # ...of those cached                   : 4
% 0.21/0.51  # Propositional unsat checks           : 0
% 0.21/0.51  #    Propositional check models        : 0
% 0.21/0.51  #    Propositional check unsatisfiable : 0
% 0.21/0.51  #    Propositional clauses             : 0
% 0.21/0.51  #    Propositional clauses after purity: 0
% 0.21/0.51  #    Propositional unsat core size     : 0
% 0.21/0.51  #    Propositional preprocessing time  : 0.000
% 0.21/0.51  #    Propositional encoding time       : 0.000
% 0.21/0.51  #    Propositional solver time         : 0.000
% 0.21/0.51  #    Success case prop preproc time    : 0.000
% 0.21/0.51  #    Success case prop encoding time   : 0.000
% 0.21/0.51  #    Success case prop solver time     : 0.000
% 0.21/0.51  # Current number of processed clauses  : 17
% 0.21/0.51  #    Positive orientable unit clauses  : 3
% 0.21/0.51  #    Positive unorientable unit clauses: 0
% 0.21/0.51  #    Negative unit clauses             : 2
% 0.21/0.51  #    Non-unit-clauses                  : 12
% 0.21/0.51  # Current number of unprocessed clauses: 2
% 0.21/0.51  # ...number of literals in the above   : 4
% 0.21/0.51  # Current number of archived formulas  : 0
% 0.21/0.51  # Current number of archived clauses   : 7
% 0.21/0.51  # Clause-clause subsumption calls (NU) : 33
% 0.21/0.51  # Rec. Clause-clause subsumption calls : 33
% 0.21/0.51  # Non-unit clause-clause subsumptions  : 3
% 0.21/0.51  # Unit Clause-clause subsumption calls : 0
% 0.21/0.51  # Rewrite failures with RHS unbound    : 0
% 0.21/0.51  # BW rewrite match attempts            : 2
% 0.21/0.51  # BW rewrite match successes           : 0
% 0.21/0.51  # Condensation attempts                : 27
% 0.21/0.51  # Condensation successes               : 0
% 0.21/0.51  # Termbank termtop insertions          : 2919
% 0.21/0.51  # Search garbage collected termcells   : 571
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.003 s
% 0.21/0.51  # System time              : 0.003 s
% 0.21/0.51  # Total time               : 0.006 s
% 0.21/0.51  # Maximum resident set size: 1916 pages
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.006 s
% 0.21/0.51  # System time              : 0.005 s
% 0.21/0.51  # Total time               : 0.011 s
% 0.21/0.51  # Maximum resident set size: 1804 pages
% 0.21/0.51  % E---3.1 exiting
% 0.21/0.51  % E exiting
%------------------------------------------------------------------------------