TSTP Solution File: SYO474^6 by E---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.2.0
% Problem  : SYO474^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n024.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 Jun 24 20:31:48 EDT 2024

% Result   : Theorem 0.19s 0.50s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   37 (  24 unt;   0 typ;   0 def)
%            Number of atoms       :  124 (  18 equ;   0 cnn)
%            Maximal formula atoms :   21 (   3 avg)
%            Number of connectives :  274 (  46   ~;  40   |;  10   &; 172   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   4 con; 0-3 aty)
%            Number of variables   :   77 (  33   ^  44   !;   0   ?;  77   :)

% Comments : 
%------------------------------------------------------------------------------
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_40,type,
    msymmetric: ( $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_55,type,
    mdia_s5: ( $i > $o ) > $i > $o ).

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

thf(decl_57,type,
    esk1_0: $i ).

thf(decl_58,type,
    esk2_1: $i > $i ).

thf(decl_59,type,
    esk3_1: $i > $i ).

thf(decl_60,type,
    esk4_0: $i ).

thf(decl_61,type,
    esk5_0: $i ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.wXIj6edSNr/E---3.1_13239.p',mimplies) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [X6: $i > $o,X3: $i] :
          ~ ( X6 @ X3 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.wXIj6edSNr/E---3.1_13239.p',mnot) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
          ( ( X6 @ X3 )
          | ( X7 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.wXIj6edSNr/E---3.1_13239.p',mor) ).

thf(mdia_s5,axiom,
    ( mdia_s5
    = ( ^ [X6: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X6 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.wXIj6edSNr/E---3.1_13239.p',mdia_s5) ).

thf(mbox_s5,axiom,
    ( mbox_s5
    = ( ^ [X6: $i > $o,X3: $i] :
        ! [X14: $i] :
          ( ~ ( rel_s5 @ X3 @ X14 )
          | ( X6 @ X14 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.wXIj6edSNr/E---3.1_13239.p',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/tmp/tmp.wXIj6edSNr/E---3.1_13239.p',mtransitive) ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [X6: $i > $o] :
        ! [X3: $i] : ( X6 @ X3 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.wXIj6edSNr/E---3.1_13239.p',mvalid) ).

thf(msymmetric,axiom,
    ( msymmetric
    = ( ^ [X13: $i > $i > $o] :
        ! [X15: $i,X16: $i] :
          ( ( X13 @ X15 @ X16 )
         => ( X13 @ X16 @ X15 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.wXIj6edSNr/E---3.1_13239.p',msymmetric) ).

thf(a2,axiom,
    mtransitive @ rel_s5,
    file('/export/starexec/sandbox2/tmp/tmp.wXIj6edSNr/E---3.1_13239.p',a2) ).

thf(prove,conjecture,
    mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ) @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mbox_s5 @ p ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.wXIj6edSNr/E---3.1_13239.p',prove) ).

thf(a3,axiom,
    msymmetric @ rel_s5,
    file('/export/starexec/sandbox2/tmp/tmp.wXIj6edSNr/E---3.1_13239.p',a3) ).

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,
    ( mdia_s5
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ! [X21: $i] :
              ( ~ ( rel_s5 @ Z1 @ X21 )
              | ~ ( Z0 @ X21 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mdia_s5]) ).

thf(c_0_15,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_16,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_17,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_18,plain,
    ( mvalid
    = ( ^ [Z0: $i > $o] :
        ! [X3: $i] : ( Z0 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[mvalid]) ).

thf(c_0_19,plain,
    ( mdia_s5
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ! [X21: $i] :
              ( ~ ( rel_s5 @ Z1 @ X21 )
              | ~ ( Z0 @ X21 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_12]),c_0_15]) ).

thf(c_0_20,plain,
    ( msymmetric
    = ( ^ [Z0: $i > $i > $o] :
        ! [X15: $i,X16: $i] :
          ( ( Z0 @ X15 @ X16 )
         => ( Z0 @ X16 @ X15 ) ) ) ),
    inference(fof_simplification,[status(thm)],[msymmetric]) ).

thf(c_0_21,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_16]) ).

thf(c_0_22,negated_conjecture,
    ~ ! [X35: $i] :
        ( ~ ! [X31: $i] :
              ( ~ ( rel_s5 @ X35 @ X31 )
              | ~ ! [X29: $i] :
                    ( ~ ( rel_s5 @ X31 @ X29 )
                    | ~ ( p @ X29 )
                    | ! [X28: $i] :
                        ( ~ ( rel_s5 @ X29 @ X28 )
                        | ( p @ X28 ) ) )
              | ! [X30: $i] :
                  ( ~ ( rel_s5 @ X31 @ X30 )
                  | ( p @ X30 ) ) )
        | ~ ~ ! [X33: $i] :
                ( ~ ( rel_s5 @ X35 @ X33 )
                | ~ ! [X32: $i] :
                      ( ~ ( rel_s5 @ X33 @ X32 )
                      | ( p @ X32 ) ) )
        | ! [X34: $i] :
            ( ~ ( rel_s5 @ X35 @ X34 )
            | ( p @ X34 ) ) ),
    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(assume_negation,[status(cth)],[prove]),c_0_17]),c_0_18]),c_0_15]),c_0_19])]) ).

thf(c_0_23,plain,
    ! [X26: $i,X27: $i] :
      ( ( rel_s5 @ X26 @ X27 )
     => ( rel_s5 @ X27 @ X26 ) ),
    inference(apply_def,[status(thm)],[a3,c_0_20]) ).

thf(c_0_24,plain,
    ! [X37: $i,X38: $i,X39: $i] :
      ( ~ ( rel_s5 @ X37 @ X38 )
      | ~ ( rel_s5 @ X38 @ X39 )
      | ( rel_s5 @ X37 @ X39 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).

thf(c_0_25,negated_conjecture,
    ! [X43: $i,X46: $i,X48: $i] :
      ( ( ( rel_s5 @ X43 @ ( esk2_1 @ X43 ) )
        | ~ ( rel_s5 @ X43 @ X46 )
        | ( p @ X46 )
        | ~ ( rel_s5 @ esk1_0 @ X43 ) )
      & ( ( p @ ( esk2_1 @ X43 ) )
        | ~ ( rel_s5 @ X43 @ X46 )
        | ( p @ X46 )
        | ~ ( rel_s5 @ esk1_0 @ X43 ) )
      & ( ( rel_s5 @ ( esk2_1 @ X43 ) @ ( esk3_1 @ X43 ) )
        | ~ ( rel_s5 @ X43 @ X46 )
        | ( p @ X46 )
        | ~ ( rel_s5 @ esk1_0 @ X43 ) )
      & ( ~ ( p @ ( esk3_1 @ X43 ) )
        | ~ ( rel_s5 @ X43 @ X46 )
        | ( p @ X46 )
        | ~ ( rel_s5 @ esk1_0 @ X43 ) )
      & ( rel_s5 @ esk1_0 @ esk4_0 )
      & ( ~ ( rel_s5 @ esk4_0 @ X48 )
        | ( p @ X48 ) )
      & ( rel_s5 @ esk1_0 @ esk5_0 )
      & ~ ( p @ esk5_0 ) ),
    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_22])])])])])]) ).

thf(c_0_26,plain,
    ! [X40: $i,X41: $i] :
      ( ~ ( rel_s5 @ X40 @ X41 )
      | ( rel_s5 @ X41 @ X40 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).

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_24]) ).

thf(c_0_28,negated_conjecture,
    rel_s5 @ esk1_0 @ esk5_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_29,plain,
    ! [X3: $i,X14: $i] :
      ( ( rel_s5 @ X14 @ X3 )
      | ~ ( rel_s5 @ X3 @ X14 ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_30,negated_conjecture,
    rel_s5 @ esk1_0 @ esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_31,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s5 @ X3 @ esk5_0 )
      | ~ ( rel_s5 @ X3 @ esk1_0 ) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

thf(c_0_32,negated_conjecture,
    rel_s5 @ esk4_0 @ esk1_0,
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

thf(c_0_33,negated_conjecture,
    ! [X3: $i] :
      ( ( p @ X3 )
      | ~ ( rel_s5 @ esk4_0 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_34,negated_conjecture,
    rel_s5 @ esk4_0 @ esk5_0,
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

thf(c_0_35,negated_conjecture,
    ~ ( p @ esk5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_36,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYO474^6 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun Jun 23 09:09:54 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.19/0.48  Running higher-order theorem proving
% 0.19/0.48  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/tmp/tmp.wXIj6edSNr/E---3.1_13239.p
% 0.19/0.50  # Version: 3.2.0-ho
% 0.19/0.50  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.19/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.19/0.50  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.19/0.50  # Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.50  # Starting post_as_ho1 with 300s (1) cores
% 0.19/0.50  # ehoh_best2_full_lfho with pid 13318 completed with status 0
% 0.19/0.50  # Result found by ehoh_best2_full_lfho
% 0.19/0.50  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.19/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.19/0.50  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.19/0.50  # No SInE strategy applied
% 0.19/0.50  # Search class: HGUNF-FFSF11-SHSSMFNN
% 0.19/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.50  # Starting sh7 with 163s (1) cores
% 0.19/0.50  # sh7 with pid 13322 completed with status 0
% 0.19/0.50  # Result found by sh7
% 0.19/0.50  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.19/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.19/0.50  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.19/0.50  # No SInE strategy applied
% 0.19/0.50  # Search class: HGUNF-FFSF11-SHSSMFNN
% 0.19/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.50  # Starting sh7 with 163s (1) cores
% 0.19/0.50  # Preprocessing time       : 0.001 s
% 0.19/0.50  # Presaturation interreduction done
% 0.19/0.50  
% 0.19/0.50  # Proof found!
% 0.19/0.50  # SZS status Theorem
% 0.19/0.50  # SZS output start CNFRefutation
% See solution above
% 0.19/0.50  # Parsed axioms                        : 73
% 0.19/0.50  # Removed by relevancy pruning/SinE    : 0
% 0.19/0.50  # Initial clauses                      : 47
% 0.19/0.50  # Removed in clause preprocessing      : 36
% 0.19/0.50  # Initial clauses in saturation        : 11
% 0.19/0.50  # Processed clauses                    : 29
% 0.19/0.50  # ...of these trivial                  : 0
% 0.19/0.50  # ...subsumed                          : 0
% 0.19/0.50  # ...remaining for further processing  : 29
% 0.19/0.50  # Other redundant clauses eliminated   : 0
% 0.19/0.50  # Clauses deleted for lack of memory   : 0
% 0.19/0.50  # Backward-subsumed                    : 0
% 0.19/0.50  # Backward-rewritten                   : 0
% 0.19/0.50  # Generated clauses                    : 30
% 0.19/0.50  # ...of the previous two non-redundant : 23
% 0.19/0.50  # ...aggressively subsumed             : 0
% 0.19/0.50  # Contextual simplify-reflections      : 0
% 0.19/0.50  # Paramodulations                      : 30
% 0.19/0.50  # Factorizations                       : 0
% 0.19/0.50  # NegExts                              : 0
% 0.19/0.50  # Equation resolutions                 : 0
% 0.19/0.50  # Disequality decompositions           : 0
% 0.19/0.50  # Total rewrite steps                  : 5
% 0.19/0.50  # ...of those cached                   : 1
% 0.19/0.50  # Propositional unsat checks           : 0
% 0.19/0.50  #    Propositional check models        : 0
% 0.19/0.50  #    Propositional check unsatisfiable : 0
% 0.19/0.50  #    Propositional clauses             : 0
% 0.19/0.50  #    Propositional clauses after purity: 0
% 0.19/0.50  #    Propositional unsat core size     : 0
% 0.19/0.50  #    Propositional preprocessing time  : 0.000
% 0.19/0.50  #    Propositional encoding time       : 0.000
% 0.19/0.50  #    Propositional solver time         : 0.000
% 0.19/0.50  #    Success case prop preproc time    : 0.000
% 0.19/0.50  #    Success case prop encoding time   : 0.000
% 0.19/0.50  #    Success case prop solver time     : 0.000
% 0.19/0.50  # Current number of processed clauses  : 18
% 0.19/0.50  #    Positive orientable unit clauses  : 8
% 0.19/0.50  #    Positive unorientable unit clauses: 0
% 0.19/0.50  #    Negative unit clauses             : 1
% 0.19/0.50  #    Non-unit-clauses                  : 9
% 0.19/0.50  # Current number of unprocessed clauses: 14
% 0.19/0.50  # ...number of literals in the above   : 39
% 0.19/0.50  # Current number of archived formulas  : 0
% 0.19/0.50  # Current number of archived clauses   : 11
% 0.19/0.50  # Clause-clause subsumption calls (NU) : 41
% 0.19/0.50  # Rec. Clause-clause subsumption calls : 41
% 0.19/0.50  # Non-unit clause-clause subsumptions  : 0
% 0.19/0.50  # Unit Clause-clause subsumption calls : 0
% 0.19/0.50  # Rewrite failures with RHS unbound    : 0
% 0.19/0.50  # BW rewrite match attempts            : 6
% 0.19/0.50  # BW rewrite match successes           : 0
% 0.19/0.50  # Condensation attempts                : 0
% 0.19/0.50  # Condensation successes               : 0
% 0.19/0.50  # Termbank termtop insertions          : 3262
% 0.19/0.50  # Search garbage collected termcells   : 708
% 0.19/0.50  
% 0.19/0.50  # -------------------------------------------------
% 0.19/0.50  # User time                : 0.007 s
% 0.19/0.50  # System time              : 0.002 s
% 0.19/0.50  # Total time               : 0.009 s
% 0.19/0.50  # Maximum resident set size: 1896 pages
% 0.19/0.50  
% 0.19/0.50  # -------------------------------------------------
% 0.19/0.50  # User time                : 0.010 s
% 0.19/0.50  # System time              : 0.003 s
% 0.19/0.50  # Total time               : 0.013 s
% 0.19/0.50  # Maximum resident set size: 1796 pages
% 0.19/0.50  % E---3.1 exiting
% 0.19/0.50  % E exiting
%------------------------------------------------------------------------------