TSTP Solution File: LCL724^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : LCL724^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n017.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 23:53:15 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   53 (  22 unt;  13 typ;   0 def)
%            Number of atoms       :  122 (  15 equ;   0 cnn)
%            Maximal formula atoms :   22 (   3 avg)
%            Number of connectives :  266 (  44   ~;  46   |;  12   &; 161   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   51 (  51   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   5 con; 0-3 aty)
%            Number of variables   :   68 (  28   ^  40   !;   0   ?;  68   :)

% 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_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_s4: $i > $i > $o ).

thf(decl_54,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

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

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

thf(decl_58,type,
    esk2_0: $i ).

thf(decl_59,type,
    esk3_0: $i ).

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

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

thf(mbox_s4,axiom,
    ( mbox_s4
    = ( ^ [X6: $i > $o,X3: $i] :
        ! [X14: $i] :
          ( ~ ( rel_s4 @ X3 @ X14 )
          | ( X6 @ X14 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).

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

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(conj,conjecture,
    ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) )
    & ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

thf(a1,axiom,
    mreflexive @ rel_s4,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).

thf(a2,axiom,
    mtransitive @ rel_s4,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a2) ).

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

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

thf(c_0_12,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

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_10,c_0_11]),c_0_12]) ).

thf(c_0_14,plain,
    ( mvalid
    = ( ^ [Z0: $i > $o] :
        ! [X3: $i] : ( Z0 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[mvalid]) ).

thf(c_0_15,plain,
    ( mbox_s4
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X14: $i] :
          ( ~ ( rel_s4 @ Z1 @ X14 )
          | ( Z0 @ X14 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mbox_s4]) ).

thf(c_0_16,plain,
    ( mreflexive
    = ( ^ [Z0: $i > $i > $o] :
        ! [X15: $i] : ( Z0 @ X15 @ X15 ) ) ),
    inference(fof_simplification,[status(thm)],[mreflexive]) ).

thf(c_0_17,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_18,negated_conjecture,
    ~ ( ! [X27: $i] :
          ( ~ ! [X26: $i] :
                ( ~ ( rel_s4 @ X27 @ X26 )
                | ( phi @ X26 ) )
          | ( phi @ X27 ) )
      & ! [X31: $i] :
          ( ~ ! [X28: $i] :
                ( ~ ( rel_s4 @ X31 @ X28 )
                | ( phi @ X28 ) )
          | ! [X30: $i] :
              ( ~ ( rel_s4 @ X31 @ X30 )
              | ! [X29: $i] :
                  ( ~ ( rel_s4 @ X30 @ X29 )
                  | ( phi @ X29 ) ) ) ) ),
    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_13]),c_0_14]),c_0_15])]) ).

thf(c_0_19,plain,
    ! [X22: $i] : ( rel_s4 @ X22 @ X22 ),
    inference(apply_def,[status(thm)],[a1,c_0_16]) ).

thf(c_0_20,plain,
    ! [X23: $i,X24: $i,X25: $i] :
      ( ( ( rel_s4 @ X23 @ X24 )
        & ( rel_s4 @ X24 @ X25 ) )
     => ( rel_s4 @ X23 @ X25 ) ),
    inference(apply_def,[status(thm)],[a2,c_0_17]) ).

thf(c_0_21,negated_conjecture,
    ! [X37: $i,X39: $i] :
      ( ( ~ ( rel_s4 @ esk2_0 @ X39 )
        | ( phi @ X39 )
        | ~ ( rel_s4 @ esk1_0 @ X37 )
        | ( phi @ X37 ) )
      & ( ( rel_s4 @ esk2_0 @ esk3_0 )
        | ~ ( rel_s4 @ esk1_0 @ X37 )
        | ( phi @ X37 ) )
      & ( ( rel_s4 @ esk3_0 @ esk4_0 )
        | ~ ( rel_s4 @ esk1_0 @ X37 )
        | ( phi @ X37 ) )
      & ( ~ ( phi @ esk4_0 )
        | ~ ( rel_s4 @ esk1_0 @ X37 )
        | ( phi @ X37 ) )
      & ( ~ ( rel_s4 @ esk2_0 @ X39 )
        | ( phi @ X39 )
        | ~ ( phi @ esk1_0 ) )
      & ( ( rel_s4 @ esk2_0 @ esk3_0 )
        | ~ ( phi @ esk1_0 ) )
      & ( ( rel_s4 @ esk3_0 @ esk4_0 )
        | ~ ( phi @ esk1_0 ) )
      & ( ~ ( phi @ esk4_0 )
        | ~ ( phi @ esk1_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_18])])])])])]) ).

thf(c_0_22,plain,
    ! [X32: $i] : ( rel_s4 @ X32 @ X32 ),
    inference(variable_rename,[status(thm)],[c_0_19]) ).

thf(c_0_23,plain,
    ! [X33: $i,X34: $i,X35: $i] :
      ( ~ ( rel_s4 @ X33 @ X34 )
      | ~ ( rel_s4 @ X34 @ X35 )
      | ( rel_s4 @ X33 @ X35 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).

thf(c_0_24,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ esk3_0 @ esk4_0 )
      | ( phi @ X3 )
      | ~ ( rel_s4 @ esk1_0 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_25,plain,
    ! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_26,negated_conjecture,
    ( ( rel_s4 @ esk3_0 @ esk4_0 )
    | ~ ( phi @ esk1_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_27,negated_conjecture,
    ! [X3: $i,X14: $i] :
      ( ( phi @ X3 )
      | ( phi @ X14 )
      | ~ ( rel_s4 @ esk2_0 @ X3 )
      | ~ ( rel_s4 @ esk1_0 @ X14 ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_28,negated_conjecture,
    ! [X3: $i] :
      ( ( phi @ X3 )
      | ~ ( rel_s4 @ esk2_0 @ X3 )
      | ~ ( phi @ esk1_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_29,plain,
    ! [X14: $i,X3: $i,X15: $i] :
      ( ( rel_s4 @ X3 @ X15 )
      | ~ ( rel_s4 @ X3 @ X14 )
      | ~ ( rel_s4 @ X14 @ X15 ) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

thf(c_0_30,negated_conjecture,
    rel_s4 @ esk3_0 @ esk4_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

thf(c_0_31,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ esk2_0 @ esk3_0 )
      | ( phi @ X3 )
      | ~ ( rel_s4 @ esk1_0 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_32,negated_conjecture,
    ( ( rel_s4 @ esk2_0 @ esk3_0 )
    | ~ ( phi @ esk1_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_33,negated_conjecture,
    ! [X3: $i] :
      ( ( phi @ X3 )
      | ~ ( phi @ esk4_0 )
      | ~ ( rel_s4 @ esk1_0 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_34,negated_conjecture,
    ( ~ ( phi @ esk4_0 )
    | ~ ( phi @ esk1_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_35,negated_conjecture,
    ! [X3: $i] :
      ( ( phi @ X3 )
      | ~ ( rel_s4 @ esk2_0 @ X3 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_28]) ).

thf(c_0_36,negated_conjecture,
    ! [X3: $i] :
      ( ( rel_s4 @ X3 @ esk4_0 )
      | ~ ( rel_s4 @ X3 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

thf(c_0_37,negated_conjecture,
    rel_s4 @ esk2_0 @ esk3_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_32]) ).

thf(c_0_38,negated_conjecture,
    ~ ( phi @ esk4_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_34]) ).

thf(c_0_39,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),c_0_38]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : LCL724^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.00/0.10  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n017.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 01:59:07 EDT 2024
% 0.09/0.29  % CPUTime    : 
% 0.14/0.39  Running higher-order theorem proving
% 0.14/0.39  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
% 0.14/0.40  # Version: 3.1.0-ho
% 0.14/0.40  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.14/0.40  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.14/0.40  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.14/0.40  # Starting almost_fo_3_lam with 300s (1) cores
% 0.14/0.40  # Starting post_as_ho1 with 300s (1) cores
% 0.14/0.40  # ehoh_best2_full_lfho with pid 15530 completed with status 0
% 0.14/0.40  # Result found by ehoh_best2_full_lfho
% 0.14/0.40  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.14/0.40  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.14/0.40  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.14/0.40  # No SInE strategy applied
% 0.14/0.40  # Search class: HGHNF-FFSF00-SHSSMFNN
% 0.14/0.40  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.40  # Starting new_ho_10 with 163s (1) cores
% 0.14/0.40  # new_ho_10 with pid 15533 completed with status 0
% 0.14/0.40  # Result found by new_ho_10
% 0.14/0.40  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.14/0.40  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.14/0.40  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.14/0.40  # No SInE strategy applied
% 0.14/0.40  # Search class: HGHNF-FFSF00-SHSSMFNN
% 0.14/0.40  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.40  # Starting new_ho_10 with 163s (1) cores
% 0.14/0.40  # Preprocessing time       : 0.001 s
% 0.14/0.40  # Presaturation interreduction done
% 0.14/0.40  
% 0.14/0.40  # Proof found!
% 0.14/0.40  # SZS status Theorem
% 0.14/0.40  # SZS output start CNFRefutation
% See solution above
% 0.14/0.40  # Parsed axioms                        : 72
% 0.14/0.40  # Removed by relevancy pruning/SinE    : 0
% 0.14/0.40  # Initial clauses                      : 46
% 0.14/0.40  # Removed in clause preprocessing      : 36
% 0.14/0.40  # Initial clauses in saturation        : 10
% 0.14/0.40  # Processed clauses                    : 31
% 0.14/0.40  # ...of these trivial                  : 0
% 0.14/0.40  # ...subsumed                          : 1
% 0.14/0.40  # ...remaining for further processing  : 30
% 0.14/0.40  # Other redundant clauses eliminated   : 0
% 0.14/0.40  # Clauses deleted for lack of memory   : 0
% 0.14/0.40  # Backward-subsumed                    : 8
% 0.14/0.40  # Backward-rewritten                   : 2
% 0.14/0.40  # Generated clauses                    : 18
% 0.14/0.40  # ...of the previous two non-redundant : 14
% 0.14/0.40  # ...aggressively subsumed             : 0
% 0.14/0.40  # Contextual simplify-reflections      : 4
% 0.14/0.40  # Paramodulations                      : 18
% 0.14/0.40  # Factorizations                       : 0
% 0.14/0.40  # NegExts                              : 0
% 0.14/0.40  # Equation resolutions                 : 0
% 0.14/0.40  # Disequality decompositions           : 0
% 0.14/0.40  # Total rewrite steps                  : 5
% 0.14/0.40  # ...of those cached                   : 0
% 0.14/0.40  # Propositional unsat checks           : 0
% 0.14/0.40  #    Propositional check models        : 0
% 0.14/0.40  #    Propositional check unsatisfiable : 0
% 0.14/0.40  #    Propositional clauses             : 0
% 0.14/0.40  #    Propositional clauses after purity: 0
% 0.14/0.40  #    Propositional unsat core size     : 0
% 0.14/0.40  #    Propositional preprocessing time  : 0.000
% 0.14/0.40  #    Propositional encoding time       : 0.000
% 0.14/0.40  #    Propositional solver time         : 0.000
% 0.14/0.40  #    Success case prop preproc time    : 0.000
% 0.14/0.40  #    Success case prop encoding time   : 0.000
% 0.14/0.40  #    Success case prop solver time     : 0.000
% 0.14/0.40  # Current number of processed clauses  : 10
% 0.14/0.40  #    Positive orientable unit clauses  : 5
% 0.14/0.40  #    Positive unorientable unit clauses: 0
% 0.14/0.40  #    Negative unit clauses             : 1
% 0.14/0.40  #    Non-unit-clauses                  : 4
% 0.14/0.40  # Current number of unprocessed clauses: 1
% 0.14/0.40  # ...number of literals in the above   : 3
% 0.14/0.40  # Current number of archived formulas  : 0
% 0.14/0.40  # Current number of archived clauses   : 20
% 0.14/0.40  # Clause-clause subsumption calls (NU) : 22
% 0.14/0.40  # Rec. Clause-clause subsumption calls : 16
% 0.14/0.40  # Non-unit clause-clause subsumptions  : 7
% 0.14/0.40  # Unit Clause-clause subsumption calls : 11
% 0.14/0.40  # Rewrite failures with RHS unbound    : 0
% 0.14/0.40  # BW rewrite match attempts            : 8
% 0.14/0.40  # BW rewrite match successes           : 4
% 0.14/0.40  # Condensation attempts                : 31
% 0.14/0.40  # Condensation successes               : 0
% 0.14/0.40  # Termbank termtop insertions          : 2910
% 0.14/0.40  # Search garbage collected termcells   : 533
% 0.14/0.40  
% 0.14/0.40  # -------------------------------------------------
% 0.14/0.40  # User time                : 0.006 s
% 0.14/0.40  # System time              : 0.001 s
% 0.14/0.40  # Total time               : 0.007 s
% 0.14/0.40  # Maximum resident set size: 1904 pages
% 0.14/0.40  
% 0.14/0.40  # -------------------------------------------------
% 0.14/0.40  # User time                : 0.007 s
% 0.14/0.40  # System time              : 0.003 s
% 0.14/0.40  # Total time               : 0.010 s
% 0.14/0.40  # Maximum resident set size: 1800 pages
% 0.14/0.40  % E---3.1 exiting
% 0.14/0.40  % E exiting
%------------------------------------------------------------------------------