TSTP Solution File: SET657^3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET657^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n012.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 : Sat May  4 09:19:48 EDT 2024

% Result   : Theorem 0.15s 0.41s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   25 (  14 unt;   9 typ;   0 def)
%            Number of atoms       :   35 (  11 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   55 (   3   ~;   7   |;   1   &;  41   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   49 (  49   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :   41 (  26   ^   5   !;  10   ?;  41   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_27,type,
    union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_33,type,
    subset: ( $i > $o ) > ( $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_54,type,
    rel_field: ( $i > $i > $o ) > $i > $o ).

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

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

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

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

thf(rel_field,axiom,
    ( rel_field
    = ( ^ [X28: $i > $i > $o,X1: $i] :
          ( ( rel_domain @ X28 @ X1 )
          | ( rel_codomain @ X28 @ X1 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.jryTrpH2Og/E---3.1_9917.p',rel_field) ).

thf(rel_codomain,axiom,
    ( rel_codomain
    = ( ^ [X28: $i > $i > $o,X3: $i] :
        ? [X1: $i] : ( X28 @ X1 @ X3 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.jryTrpH2Og/E---3.1_9917.p',rel_codomain) ).

thf(rel_domain,axiom,
    ( rel_domain
    = ( ^ [X28: $i > $i > $o,X1: $i] :
        ? [X3: $i] : ( X28 @ X1 @ X3 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.jryTrpH2Og/E---3.1_9917.p',rel_domain) ).

thf(union,axiom,
    ( union
    = ( ^ [X5: $i > $o,X6: $i > $o,X4: $i] :
          ( ( X5 @ X4 )
          | ( X6 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.jryTrpH2Og/E---3.1_9917.p',union) ).

thf(subset,axiom,
    ( subset
    = ( ^ [X16: $i > $o,X17: $i > $o] :
        ! [X4: $i] :
          ( ( X16 @ X4 )
         => ( X17 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.jryTrpH2Og/E---3.1_9917.p',subset) ).

thf(thm,conjecture,
    ! [X28: $i > $i > $o] :
      ( subset @ ( rel_field @ X28 )
      @ ( union
        @ ^ [X1: $i] : $true
        @ ^ [X1: $i] : $true ) ),
    file('/export/starexec/sandbox/tmp/tmp.jryTrpH2Og/E---3.1_9917.p',thm) ).

thf(c_0_6,plain,
    ( rel_field
    = ( ^ [Z0: $i > $i > $o,Z1: $i] :
          ( ? [X43: $i] : ( Z0 @ Z1 @ X43 )
          | ? [X44: $i] : ( Z0 @ X44 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[rel_field]) ).

thf(c_0_7,plain,
    ( rel_codomain
    = ( ^ [Z0: $i > $i > $o,Z1: $i] :
        ? [X1: $i] : ( Z0 @ X1 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[rel_codomain]) ).

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

thf(c_0_9,plain,
    ( union
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[union]) ).

thf(c_0_10,plain,
    ( subset
    = ( ^ [Z0: $i > $o,Z1: $i > $o] :
        ! [X4: $i] :
          ( ( Z0 @ X4 )
         => ( Z1 @ X4 ) ) ) ),
    inference(fof_simplification,[status(thm)],[subset]) ).

thf(c_0_11,plain,
    ( rel_field
    = ( ^ [Z0: $i > $i > $o,Z1: $i] :
          ( ? [X43: $i] : ( Z0 @ Z1 @ X43 )
          | ? [X44: $i] : ( Z0 @ X44 @ Z1 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).

thf(c_0_12,negated_conjecture,
    ~ ! [X28: $i > $i > $o,X47: $i] :
        ( ( ? [X45: $i] : ( X28 @ X47 @ X45 )
          | ? [X46: $i] : ( X28 @ X46 @ X47 ) )
       => $true ),
    inference(fof_simplification,[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)],[thm])]),c_0_9]),c_0_10]),c_0_11])]) ).

thf(c_0_13,negated_conjecture,
    ( ( ( epred1_0 @ esk1_0 @ esk2_0 )
      | ( epred1_0 @ esk3_0 @ esk1_0 ) )
    & ~ $true ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).

thf(c_0_14,negated_conjecture,
    ~ $true,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_15,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[c_0_14]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : SET657^3 : TPTP v8.1.2. Released v3.6.0.
% 0.02/0.11  % Command    : run_E %s %d THM
% 0.10/0.30  % Computer : n012.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Fri May  3 10:11:25 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.15/0.40  Running higher-order theorem proving
% 0.15/0.40  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/tmp/tmp.jryTrpH2Og/E---3.1_9917.p
% 0.15/0.41  # Version: 3.1.0-ho
% 0.15/0.41  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.15/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.15/0.41  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.15/0.41  # Starting almost_fo_3_lam with 300s (1) cores
% 0.15/0.41  # Starting post_as_ho1 with 300s (1) cores
% 0.15/0.41  # ehoh_best2_full_lfho with pid 9996 completed with status 0
% 0.15/0.41  # Result found by ehoh_best2_full_lfho
% 0.15/0.41  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.15/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.15/0.41  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.15/0.41  # No SInE strategy applied
% 0.15/0.41  # Search class: HGHNF-FFSF00-SHSSMFNN
% 0.15/0.41  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.41  # Starting new_ho_10 with 163s (1) cores
% 0.15/0.41  # new_ho_10 with pid 10002 completed with status 0
% 0.15/0.41  # Result found by new_ho_10
% 0.15/0.41  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.15/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.15/0.41  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.15/0.41  # No SInE strategy applied
% 0.15/0.41  # Search class: HGHNF-FFSF00-SHSSMFNN
% 0.15/0.41  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.41  # Starting new_ho_10 with 163s (1) cores
% 0.15/0.41  # Preprocessing time       : 0.001 s
% 0.15/0.41  # Presaturation interreduction done
% 0.15/0.41  
% 0.15/0.41  # Proof found!
% 0.15/0.41  # SZS status Theorem
% 0.15/0.41  # SZS output start CNFRefutation
% See solution above
% 0.15/0.41  # Parsed axioms                        : 71
% 0.15/0.41  # Removed by relevancy pruning/SinE    : 0
% 0.15/0.41  # Initial clauses                      : 37
% 0.15/0.41  # Removed in clause preprocessing      : 35
% 0.15/0.41  # Initial clauses in saturation        : 2
% 0.15/0.41  # Processed clauses                    : 1
% 0.15/0.41  # ...of these trivial                  : 0
% 0.15/0.41  # ...subsumed                          : 0
% 0.15/0.41  # ...remaining for further processing  : 0
% 0.15/0.41  # Other redundant clauses eliminated   : 0
% 0.15/0.41  # Clauses deleted for lack of memory   : 0
% 0.15/0.41  # Backward-subsumed                    : 0
% 0.15/0.41  # Backward-rewritten                   : 0
% 0.15/0.41  # Generated clauses                    : 0
% 0.15/0.41  # ...of the previous two non-redundant : 0
% 0.15/0.41  # ...aggressively subsumed             : 0
% 0.15/0.41  # Contextual simplify-reflections      : 0
% 0.15/0.41  # Paramodulations                      : 0
% 0.15/0.41  # Factorizations                       : 0
% 0.15/0.41  # NegExts                              : 0
% 0.15/0.41  # Equation resolutions                 : 0
% 0.15/0.41  # Disequality decompositions           : 0
% 0.15/0.41  # Total rewrite steps                  : 0
% 0.15/0.41  # ...of those cached                   : 0
% 0.15/0.41  # Propositional unsat checks           : 0
% 0.15/0.41  #    Propositional check models        : 0
% 0.15/0.41  #    Propositional check unsatisfiable : 0
% 0.15/0.41  #    Propositional clauses             : 0
% 0.15/0.41  #    Propositional clauses after purity: 0
% 0.15/0.41  #    Propositional unsat core size     : 0
% 0.15/0.41  #    Propositional preprocessing time  : 0.000
% 0.15/0.41  #    Propositional encoding time       : 0.000
% 0.15/0.41  #    Propositional solver time         : 0.000
% 0.15/0.41  #    Success case prop preproc time    : 0.000
% 0.15/0.41  #    Success case prop encoding time   : 0.000
% 0.15/0.41  #    Success case prop solver time     : 0.000
% 0.15/0.41  # Current number of processed clauses  : 0
% 0.15/0.41  #    Positive orientable unit clauses  : 0
% 0.15/0.41  #    Positive unorientable unit clauses: 0
% 0.15/0.41  #    Negative unit clauses             : 0
% 0.15/0.41  #    Non-unit-clauses                  : 0
% 0.15/0.41  # Current number of unprocessed clauses: 1
% 0.15/0.41  # ...number of literals in the above   : 2
% 0.15/0.41  # Current number of archived formulas  : 0
% 0.15/0.41  # Current number of archived clauses   : 0
% 0.15/0.41  # Clause-clause subsumption calls (NU) : 0
% 0.15/0.41  # Rec. Clause-clause subsumption calls : 0
% 0.15/0.41  # Non-unit clause-clause subsumptions  : 0
% 0.15/0.41  # Unit Clause-clause subsumption calls : 0
% 0.15/0.41  # Rewrite failures with RHS unbound    : 0
% 0.15/0.41  # BW rewrite match attempts            : 0
% 0.15/0.41  # BW rewrite match successes           : 0
% 0.15/0.41  # Condensation attempts                : 1
% 0.15/0.41  # Condensation successes               : 0
% 0.15/0.41  # Termbank termtop insertions          : 1801
% 0.15/0.41  # Search garbage collected termcells   : 171
% 0.15/0.41  
% 0.15/0.41  # -------------------------------------------------
% 0.15/0.41  # User time                : 0.002 s
% 0.15/0.41  # System time              : 0.002 s
% 0.15/0.41  # Total time               : 0.004 s
% 0.15/0.41  # Maximum resident set size: 1904 pages
% 0.15/0.41  
% 0.15/0.41  # -------------------------------------------------
% 0.15/0.41  # User time                : 0.005 s
% 0.15/0.41  # System time              : 0.003 s
% 0.15/0.41  # Total time               : 0.008 s
% 0.15/0.41  # Maximum resident set size: 1804 pages
% 0.15/0.41  % E---3.1 exiting
% 0.15/0.41  % E exiting
%------------------------------------------------------------------------------