TSTP Solution File: SET648^3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET648^3 : TPTP v8.2.0. Released v3.6.0.
% 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 : Tue May 21 02:55:09 EDT 2024

% Result   : Theorem 0.21s 0.52s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   27 (  13 unt;   9 typ;   0 def)
%            Number of atoms       :   37 (  10 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   82 (   8   ~;   4   |;   5   &;  57   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   57 (  57   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   3 con; 0-4 aty)
%            Number of variables   :   49 (  24   ^  19   !;   6   ?;  49   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_33,type,
    subset: ( $i > $o ) > ( $i > $o ) > $o ).

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

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

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

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

thf(decl_57,type,
    epred1_0: $i > $i > $o ).

thf(decl_58,type,
    epred2_0: $i > $o ).

thf(decl_59,type,
    esk1_0: $i ).

thf(decl_60,type,
    esk2_0: $i ).

thf(subset,axiom,
    ( subset
    = ( ^ [X16: $i > $o,X17: $i > $o] :
        ! [X4: $i] :
          ( ( X16 @ X4 )
         => ( X17 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',subset) ).

thf(cartesian_product,axiom,
    ( cartesian_product
    = ( ^ [X22: $i > $o,X23: $i > $o,X4: $i,X24: $i] :
          ( ( X22 @ X4 )
          & ( X23 @ X24 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',cartesian_product) ).

thf(sub_rel,axiom,
    ( sub_rel
    = ( ^ [X26: $i > $i > $o,X27: $i > $i > $o] :
        ! [X1: $i,X3: $i] :
          ( ( X26 @ X1 @ X3 )
         => ( X27 @ X1 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',sub_rel) ).

thf(rel_codomain,axiom,
    ( rel_codomain
    = ( ^ [X28: $i > $i > $o,X3: $i] :
        ? [X1: $i] : ( X28 @ X1 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',rel_codomain) ).

thf(rel_domain,axiom,
    ( rel_domain
    = ( ^ [X28: $i > $i > $o,X1: $i] :
        ? [X3: $i] : ( X28 @ X1 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',rel_domain) ).

thf(thm,conjecture,
    ! [X28: $i > $i > $o,X36: $i > $o] :
      ( ( subset @ ( rel_codomain @ X28 ) @ X36 )
     => ( sub_rel @ X28 @ ( cartesian_product @ ( rel_domain @ X28 ) @ X36 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(c_0_6,plain,
    ( subset
    = ( ^ [Z0: $i > $o,Z1: $i > $o] :
        ! [X4: $i] :
          ( ( Z0 @ X4 )
         => ( Z1 @ X4 ) ) ) ),
    inference(fof_simplification,[status(thm)],[subset]) ).

thf(c_0_7,plain,
    ( cartesian_product
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i,Z3: $i] :
          ( ( Z0 @ Z2 )
          & ( Z1 @ Z3 ) ) ) ),
    inference(fof_simplification,[status(thm)],[cartesian_product]) ).

thf(c_0_8,plain,
    ( sub_rel
    = ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o] :
        ! [X1: $i,X3: $i] :
          ( ( Z0 @ X1 @ X3 )
         => ( Z1 @ X1 @ X3 ) ) ) ),
    inference(fof_simplification,[status(thm)],[sub_rel]) ).

thf(c_0_9,plain,
    ( rel_codomain
    = ( ^ [Z0: $i > $i > $o,Z1: $i] :
        ? [X1: $i] : ( Z0 @ X1 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[rel_codomain]) ).

thf(c_0_10,plain,
    ( rel_domain
    = ( ^ [Z0: $i > $i > $o,Z1: $i] :
        ? [X3: $i] : ( Z0 @ Z1 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[rel_domain]) ).

thf(c_0_11,negated_conjecture,
    ~ ! [X28: $i > $i > $o,X36: $i > $o] :
        ( ! [X48: $i] :
            ( ? [X47: $i] : ( X28 @ X47 @ X48 )
           => ( X36 @ X48 ) )
       => ! [X50: $i,X51: $i] :
            ( ( X28 @ X50 @ X51 )
           => ( ? [X49: $i] : ( X28 @ X50 @ X49 )
              & ( X36 @ X51 ) ) ) ),
    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(assume_negation,[status(cth)],[thm]),c_0_6]),c_0_7]),c_0_8]),c_0_9]),c_0_10]) ).

thf(c_0_12,negated_conjecture,
    ! [X54: $i,X55: $i,X58: $i] :
      ( ( ~ ( epred1_0 @ X55 @ X54 )
        | ( epred2_0 @ X54 ) )
      & ( epred1_0 @ esk1_0 @ esk2_0 )
      & ( ~ ( epred1_0 @ esk1_0 @ X58 )
        | ~ ( epred2_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_11])])])])]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: $i] :
      ( ~ ( epred1_0 @ esk1_0 @ X1 )
      | ~ ( epred2_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_14,negated_conjecture,
    epred1_0 @ esk1_0 @ esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i,X3: $i] :
      ( ( epred2_0 @ X3 )
      | ~ ( epred1_0 @ X1 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_16,negated_conjecture,
    ~ ( epred2_0 @ esk2_0 ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_17,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_16]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET648^3 : TPTP v8.2.0. Released v3.6.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon May 20 11:10:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.21/0.51  Running higher-order theorem proving
% 0.21/0.51  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
% 0.21/0.52  # Version: 3.1.0-ho
% 0.21/0.52  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.52  # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.52  # Starting post_as_ho11 with 300s (1) cores
% 0.21/0.52  # Starting full_lambda_8 with 300s (1) cores
% 0.21/0.52  # post_as_ho3 with pid 9895 completed with status 0
% 0.21/0.52  # Result found by post_as_ho3
% 0.21/0.52  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.52  # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.52  # No SInE strategy applied
% 0.21/0.52  # Search class: HHHNF-FFSF00-SHSSMFNN
% 0.21/0.52  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.52  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.52  # new_ho_10 with pid 9899 completed with status 0
% 0.21/0.52  # Result found by new_ho_10
% 0.21/0.52  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.52  # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.52  # No SInE strategy applied
% 0.21/0.52  # Search class: HHHNF-FFSF00-SHSSMFNN
% 0.21/0.52  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.52  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.52  # Preprocessing time       : 0.001 s
% 0.21/0.52  # Presaturation interreduction done
% 0.21/0.52  
% 0.21/0.52  # Proof found!
% 0.21/0.52  # SZS status Theorem
% 0.21/0.52  # SZS output start CNFRefutation
% See solution above
% 0.21/0.52  # Parsed axioms                        : 71
% 0.21/0.52  # Removed by relevancy pruning/SinE    : 0
% 0.21/0.52  # Initial clauses                      : 38
% 0.21/0.52  # Removed in clause preprocessing      : 35
% 0.21/0.52  # Initial clauses in saturation        : 3
% 0.21/0.52  # Processed clauses                    : 8
% 0.21/0.52  # ...of these trivial                  : 0
% 0.21/0.52  # ...subsumed                          : 0
% 0.21/0.52  # ...remaining for further processing  : 7
% 0.21/0.52  # Other redundant clauses eliminated   : 0
% 0.21/0.52  # Clauses deleted for lack of memory   : 0
% 0.21/0.52  # Backward-subsumed                    : 1
% 0.21/0.52  # Backward-rewritten                   : 0
% 0.21/0.52  # Generated clauses                    : 2
% 0.21/0.52  # ...of the previous two non-redundant : 2
% 0.21/0.52  # ...aggressively subsumed             : 0
% 0.21/0.52  # Contextual simplify-reflections      : 0
% 0.21/0.52  # Paramodulations                      : 2
% 0.21/0.52  # Factorizations                       : 0
% 0.21/0.52  # NegExts                              : 0
% 0.21/0.52  # Equation resolutions                 : 0
% 0.21/0.52  # Disequality decompositions           : 0
% 0.21/0.52  # Total rewrite steps                  : 0
% 0.21/0.52  # ...of those cached                   : 0
% 0.21/0.52  # Propositional unsat checks           : 0
% 0.21/0.52  #    Propositional check models        : 0
% 0.21/0.52  #    Propositional check unsatisfiable : 0
% 0.21/0.52  #    Propositional clauses             : 0
% 0.21/0.52  #    Propositional clauses after purity: 0
% 0.21/0.52  #    Propositional unsat core size     : 0
% 0.21/0.52  #    Propositional preprocessing time  : 0.000
% 0.21/0.52  #    Propositional encoding time       : 0.000
% 0.21/0.52  #    Propositional solver time         : 0.000
% 0.21/0.52  #    Success case prop preproc time    : 0.000
% 0.21/0.52  #    Success case prop encoding time   : 0.000
% 0.21/0.52  #    Success case prop solver time     : 0.000
% 0.21/0.52  # Current number of processed clauses  : 3
% 0.21/0.52  #    Positive orientable unit clauses  : 1
% 0.21/0.52  #    Positive unorientable unit clauses: 0
% 0.21/0.52  #    Negative unit clauses             : 1
% 0.21/0.52  #    Non-unit-clauses                  : 1
% 0.21/0.52  # Current number of unprocessed clauses: 0
% 0.21/0.52  # ...number of literals in the above   : 0
% 0.21/0.52  # Current number of archived formulas  : 0
% 0.21/0.52  # Current number of archived clauses   : 4
% 0.21/0.52  # Clause-clause subsumption calls (NU) : 0
% 0.21/0.52  # Rec. Clause-clause subsumption calls : 0
% 0.21/0.52  # Non-unit clause-clause subsumptions  : 0
% 0.21/0.52  # Unit Clause-clause subsumption calls : 1
% 0.21/0.52  # Rewrite failures with RHS unbound    : 0
% 0.21/0.52  # BW rewrite match attempts            : 0
% 0.21/0.52  # BW rewrite match successes           : 0
% 0.21/0.52  # Condensation attempts                : 8
% 0.21/0.52  # Condensation successes               : 0
% 0.21/0.52  # Termbank termtop insertions          : 1981
% 0.21/0.52  # Search garbage collected termcells   : 263
% 0.21/0.52  
% 0.21/0.52  # -------------------------------------------------
% 0.21/0.52  # User time                : 0.002 s
% 0.21/0.52  # System time              : 0.003 s
% 0.21/0.52  # Total time               : 0.005 s
% 0.21/0.52  # Maximum resident set size: 1912 pages
% 0.21/0.52  
% 0.21/0.52  # -------------------------------------------------
% 0.21/0.52  # User time                : 0.005 s
% 0.21/0.52  # System time              : 0.005 s
% 0.21/0.52  # Total time               : 0.010 s
% 0.21/0.52  # Maximum resident set size: 1804 pages
% 0.21/0.52  % E---3.1 exiting
% 0.21/0.53  % E exiting
%------------------------------------------------------------------------------