TSTP Solution File: SYN357^7 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYN357^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n025.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 07:44:25 EDT 2024

% Result   : Theorem 0.21s 0.51s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   41 (  18 unt;  16 typ;   0 def)
%            Number of atoms       :   83 (  16 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  182 (  30   ~;  21   |;   5   &; 120   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   60 (  60   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   4 con; 0-3 aty)
%            Number of variables   :   58 (  36   ^  22   !;   0   ?;  58   :)

% 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_31,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_36,type,
    exists_in_world: mu > $i > $o ).

thf(decl_37,type,
    mforall_ind: ( mu > $i > $o ) > $i > $o ).

thf(decl_38,type,
    mexists_ind: ( mu > $i > $o ) > $i > $o ).

thf(decl_50,type,
    mvalid: ( $i > $o ) > $o ).

thf(decl_54,type,
    rel_s4: $i > $i > $o ).

thf(decl_55,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

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

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

thf(decl_60,type,
    esk3_0: $i ).

thf(decl_61,type,
    esk4_0: mu ).

thf(decl_62,type,
    esk5_1: mu > $i ).

thf(decl_63,type,
    esk6_1: mu > $i ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [X4: $i > $o,X3: $i] :
          ~ ( X4 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
          ( ( X4 @ X3 )
          | ( X5 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).

thf(mexists_ind,axiom,
    ( mexists_ind
    = ( ^ [X13: mu > $i > $o] :
          ( mnot
          @ ( mforall_ind
            @ ^ [X14: mu] : ( mnot @ ( X13 @ X14 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mexists_ind) ).

thf(mforall_ind,axiom,
    ( mforall_ind
    = ( ^ [X11: mu > $i > $o,X3: $i] :
        ! [X12: mu] :
          ( ( exists_in_world @ X12 @ X3 )
         => ( X11 @ X12 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [X4: $i > $o] :
        ! [X3: $i] : ( X4 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).

thf(mbox_s4,axiom,
    ( mbox_s4
    = ( ^ [X4: $i > $o,X3: $i] :
        ! [X7: $i] :
          ( ~ ( rel_s4 @ X3 @ X7 )
          | ( X4 @ X7 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).

thf(x2108,conjecture,
    ( mvalid
    @ ( mbox_s4
      @ ( mforall_ind
        @ ^ [X20: mu] :
            ( mexists_ind
            @ ^ [X21: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ X20 ) ) @ ( mbox_s4 @ ( big_p @ X21 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2108) ).

thf(c_0_8,plain,
    ( mimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mimplies]) ).

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

thf(c_0_10,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

thf(c_0_11,plain,
    ( mexists_ind
    = ( ^ [Z0: mu > $i > $o,Z1: $i] :
          ~ ! [X28: mu] :
              ( ( exists_in_world @ X28 @ Z1 )
             => ~ ( Z0 @ X28 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mexists_ind]) ).

thf(c_0_12,plain,
    ( mforall_ind
    = ( ^ [Z0: mu > $i > $o,Z1: $i] :
        ! [X12: mu] :
          ( ( exists_in_world @ X12 @ Z1 )
         => ( Z0 @ X12 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mforall_ind]) ).

thf(c_0_13,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_8,c_0_9]),c_0_10]) ).

thf(c_0_14,plain,
    ( mexists_ind
    = ( ^ [Z0: mu > $i > $o,Z1: $i] :
          ~ ! [X28: mu] :
              ( ( exists_in_world @ X28 @ Z1 )
             => ~ ( Z0 @ X28 @ Z1 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_9]),c_0_12]) ).

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

thf(c_0_16,plain,
    ( mbox_s4
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X7: $i] :
          ( ~ ( rel_s4 @ Z1 @ X7 )
          | ( Z0 @ X7 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mbox_s4]) ).

thf(c_0_17,negated_conjecture,
    ~ ! [X41: $i,X40: $i] :
        ( ~ ( rel_s4 @ X41 @ X40 )
        | ! [X39: mu] :
            ( ( exists_in_world @ X39 @ X40 )
           => ~ ! [X38: mu] :
                  ( ( exists_in_world @ X38 @ X40 )
                 => ~ ! [X37: $i] :
                        ( ~ ( rel_s4 @ X40 @ X37 )
                        | ~ ! [X35: $i] :
                              ( ~ ( rel_s4 @ X37 @ X35 )
                              | ( big_p @ X39 @ X35 ) )
                        | ! [X36: $i] :
                            ( ~ ( rel_s4 @ X37 @ X36 )
                            | ( big_p @ X38 @ X36 ) ) ) ) ) ),
    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)],[x2108])]),c_0_13]),c_0_12]),c_0_14]),c_0_15]),c_0_16])]) ).

thf(c_0_18,negated_conjecture,
    ! [X54: mu,X56: $i] :
      ( ( rel_s4 @ esk2_0 @ esk3_0 )
      & ( exists_in_world @ esk4_0 @ esk3_0 )
      & ( ( rel_s4 @ esk3_0 @ ( esk5_1 @ X54 ) )
        | ~ ( exists_in_world @ X54 @ esk3_0 ) )
      & ( ~ ( rel_s4 @ ( esk5_1 @ X54 ) @ X56 )
        | ( big_p @ esk4_0 @ X56 )
        | ~ ( exists_in_world @ X54 @ esk3_0 ) )
      & ( ( rel_s4 @ ( esk5_1 @ X54 ) @ ( esk6_1 @ X54 ) )
        | ~ ( exists_in_world @ X54 @ esk3_0 ) )
      & ( ~ ( big_p @ X54 @ ( esk6_1 @ X54 ) )
        | ~ ( exists_in_world @ X54 @ esk3_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_17])])])])])]) ).

thf(c_0_19,negated_conjecture,
    ! [X3: $i,X10: mu] :
      ( ( big_p @ esk4_0 @ X3 )
      | ~ ( rel_s4 @ ( esk5_1 @ X10 ) @ X3 )
      | ~ ( exists_in_world @ X10 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_20,negated_conjecture,
    ! [X10: mu] :
      ( ( rel_s4 @ ( esk5_1 @ X10 ) @ ( esk6_1 @ X10 ) )
      | ~ ( exists_in_world @ X10 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_21,negated_conjecture,
    ! [X10: mu] :
      ( ~ ( big_p @ X10 @ ( esk6_1 @ X10 ) )
      | ~ ( exists_in_world @ X10 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_22,negated_conjecture,
    ! [X10: mu] :
      ( ( big_p @ esk4_0 @ ( esk6_1 @ X10 ) )
      | ~ ( exists_in_world @ X10 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

thf(c_0_23,negated_conjecture,
    exists_in_world @ esk4_0 @ esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_24,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SYN357^7 : TPTP v8.2.0. Released v5.5.0.
% 0.08/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n025.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 13:43:38 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.21/0.49  Running higher-order theorem proving
% 0.21/0.49  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
% 0.21/0.51  # 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  # ehoh_best2_full_lfho with pid 1241 completed with status 0
% 0.21/0.51  # Result found by ehoh_best2_full_lfho
% 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  # No SInE strategy applied
% 0.21/0.51  # Search class: HHHNS-FFSF11-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 1248 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  # No SInE strategy applied
% 0.21/0.51  # Search class: HHHNS-FFSF11-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       : 0.003 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                      : 47
% 0.21/0.51  # Removed in clause preprocessing      : 37
% 0.21/0.51  # Initial clauses in saturation        : 10
% 0.21/0.51  # Processed clauses                    : 25
% 0.21/0.51  # ...of these trivial                  : 0
% 0.21/0.51  # ...subsumed                          : 0
% 0.21/0.51  # ...remaining for further processing  : 25
% 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                    : 13
% 0.21/0.51  # ...of the previous two non-redundant : 9
% 0.21/0.51  # ...aggressively subsumed             : 0
% 0.21/0.51  # Contextual simplify-reflections      : 0
% 0.21/0.51  # Paramodulations                      : 13
% 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                  : 2
% 0.21/0.51  # ...of those cached                   : 0
% 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  : 15
% 0.21/0.51  #    Positive orientable unit clauses  : 5
% 0.21/0.51  #    Positive unorientable unit clauses: 0
% 0.21/0.51  #    Negative unit clauses             : 0
% 0.21/0.51  #    Non-unit-clauses                  : 10
% 0.21/0.51  # Current number of unprocessed clauses: 4
% 0.21/0.51  # ...number of literals in the above   : 12
% 0.21/0.51  # Current number of archived formulas  : 0
% 0.21/0.51  # Current number of archived clauses   : 10
% 0.21/0.51  # Clause-clause subsumption calls (NU) : 6
% 0.21/0.51  # Rec. Clause-clause subsumption calls : 4
% 0.21/0.51  # Non-unit clause-clause subsumptions  : 0
% 0.21/0.51  # Unit Clause-clause subsumption calls : 1
% 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                : 25
% 0.21/0.51  # Condensation successes               : 0
% 0.21/0.51  # Termbank termtop insertions          : 3129
% 0.21/0.51  # Search garbage collected termcells   : 754
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.008 s
% 0.21/0.51  # System time              : 0.003 s
% 0.21/0.51  # Total time               : 0.010 s
% 0.21/0.51  # Maximum resident set size: 1896 pages
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.010 s
% 0.21/0.51  # System time              : 0.005 s
% 0.21/0.51  # Total time               : 0.015 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
%------------------------------------------------------------------------------