TSTP Solution File: ITP115^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP115^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n014.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 22:16:22 EDT 2024

% Result   : Theorem 0.19s 0.54s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   40 (  14 unt;  13 typ;   0 def)
%            Number of atoms       :   72 (  26 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  174 (  27   ~;  26   |;  16   &; 102   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :   13 (   0   ^   9   !;   4   ?;  13   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    set_b: $tType ).

thf(decl_sort2,type,
    b: $tType ).

thf(decl_sort3,type,
    a: $tType ).

thf(decl_25,type,
    inf_inf_set_b: set_b > set_b > set_b ).

thf(decl_31,type,
    bot_bot_set_b: set_b ).

thf(decl_47,type,
    topolo1276428102open_b: set_b > $o ).

thf(decl_49,type,
    member_b: b > set_b > $o ).

thf(decl_50,type,
    a2: b ).

thf(decl_51,type,
    f: a > b ).

thf(decl_52,type,
    thesis: $o ).

thf(decl_53,type,
    x0: a ).

thf(decl_61,type,
    esk8_0: set_b ).

thf(decl_62,type,
    esk9_0: set_b ).

thf(conj_1,conjecture,
    thesis,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,axiom,
    ( ( ( f @ x0 )
     != a2 )
   => ? [X1: set_b,X2: set_b] :
        ( ( topolo1276428102open_b @ X1 )
        & ( topolo1276428102open_b @ X2 )
        & ( member_b @ ( f @ x0 ) @ X1 )
        & ( member_b @ a2 @ X2 )
        & ( ( inf_inf_set_b @ X1 @ X2 )
          = bot_bot_set_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062) ).

thf(fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062,axiom,
    ( a2
   != ( f @ x0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062) ).

thf(conj_0,hypothesis,
    ! [X47: set_b,X588: set_b] :
      ( ( ( topolo1276428102open_b @ X47 )
        & ( topolo1276428102open_b @ X588 )
        & ( member_b @ ( f @ x0 ) @ X47 )
        & ( member_b @ a2 @ X588 )
        & ( ( inf_inf_set_b @ X47 @ X588 )
          = bot_bot_set_b ) )
     => thesis ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(c_0_4,negated_conjecture,
    ~ thesis,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).

thf(c_0_5,plain,
    ( ( ( f @ x0 )
     != a2 )
   => ? [X1: set_b,X2: set_b] :
        ( ( topolo1276428102open_b @ X1 )
        & ( topolo1276428102open_b @ X2 )
        & ( member_b @ ( f @ x0 ) @ X1 )
        & ( member_b @ a2 @ X2 )
        & ( ( inf_inf_set_b @ X1 @ X2 )
          = bot_bot_set_b ) ) ),
    inference(fof_simplification,[status(thm)],[fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062]) ).

thf(c_0_6,plain,
    ( a2
   != ( f @ x0 ) ),
    inference(fof_simplification,[status(thm)],[fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062]) ).

thf(c_0_7,hypothesis,
    ! [X846: set_b,X847: set_b] :
      ( ~ ( topolo1276428102open_b @ X846 )
      | ~ ( topolo1276428102open_b @ X847 )
      | ~ ( member_b @ ( f @ x0 ) @ X846 )
      | ~ ( member_b @ a2 @ X847 )
      | ( ( inf_inf_set_b @ X846 @ X847 )
       != bot_bot_set_b )
      | thesis ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])]) ).

thf(c_0_8,negated_conjecture,
    ~ thesis,
    inference(fof_nnf,[status(thm)],[c_0_4]) ).

thf(c_0_9,plain,
    ( ( ( topolo1276428102open_b @ esk8_0 )
      | ( ( f @ x0 )
        = a2 ) )
    & ( ( topolo1276428102open_b @ esk9_0 )
      | ( ( f @ x0 )
        = a2 ) )
    & ( ( member_b @ ( f @ x0 ) @ esk8_0 )
      | ( ( f @ x0 )
        = a2 ) )
    & ( ( member_b @ a2 @ esk9_0 )
      | ( ( f @ x0 )
        = a2 ) )
    & ( ( ( inf_inf_set_b @ esk8_0 @ esk9_0 )
        = bot_bot_set_b )
      | ( ( f @ x0 )
        = a2 ) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).

thf(c_0_10,plain,
    ( a2
   != ( f @ x0 ) ),
    inference(fof_nnf,[status(thm)],[c_0_6]) ).

thf(c_0_11,hypothesis,
    ! [X1: set_b,X2: set_b] :
      ( thesis
      | ~ ( topolo1276428102open_b @ X1 )
      | ~ ( topolo1276428102open_b @ X2 )
      | ~ ( member_b @ ( f @ x0 ) @ X1 )
      | ~ ( member_b @ a2 @ X2 )
      | ( ( inf_inf_set_b @ X1 @ X2 )
       != bot_bot_set_b ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_12,negated_conjecture,
    ~ thesis,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_13,plain,
    ( ( member_b @ ( f @ x0 ) @ esk8_0 )
    | ( ( f @ x0 )
      = a2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_14,plain,
    ( a2
   != ( f @ x0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_15,plain,
    ( ( topolo1276428102open_b @ esk8_0 )
    | ( ( f @ x0 )
      = a2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_16,hypothesis,
    ! [X2: set_b,X1: set_b] :
      ( ( ( inf_inf_set_b @ X1 @ X2 )
       != bot_bot_set_b )
      | ~ ( member_b @ ( f @ x0 ) @ X1 )
      | ~ ( member_b @ a2 @ X2 )
      | ~ ( topolo1276428102open_b @ X2 )
      | ~ ( topolo1276428102open_b @ X1 ) ),
    inference(sr,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_17,plain,
    member_b @ ( f @ x0 ) @ esk8_0,
    inference(sr,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_18,plain,
    topolo1276428102open_b @ esk8_0,
    inference(sr,[status(thm)],[c_0_15,c_0_14]) ).

thf(c_0_19,plain,
    ( ( member_b @ a2 @ esk9_0 )
    | ( ( f @ x0 )
      = a2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_20,plain,
    ( ( ( inf_inf_set_b @ esk8_0 @ esk9_0 )
      = bot_bot_set_b )
    | ( ( f @ x0 )
      = a2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_21,plain,
    ( ( topolo1276428102open_b @ esk9_0 )
    | ( ( f @ x0 )
      = a2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_22,hypothesis,
    ! [X1: set_b] :
      ( ( ( inf_inf_set_b @ esk8_0 @ X1 )
       != bot_bot_set_b )
      | ~ ( member_b @ a2 @ X1 )
      | ~ ( topolo1276428102open_b @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).

thf(c_0_23,plain,
    member_b @ a2 @ esk9_0,
    inference(sr,[status(thm)],[c_0_19,c_0_14]) ).

thf(c_0_24,plain,
    ( ( inf_inf_set_b @ esk8_0 @ esk9_0 )
    = bot_bot_set_b ),
    inference(sr,[status(thm)],[c_0_20,c_0_14]) ).

thf(c_0_25,plain,
    topolo1276428102open_b @ esk9_0,
    inference(sr,[status(thm)],[c_0_21,c_0_14]) ).

thf(c_0_26,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : ITP115^1 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat May 18 16:01:23 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running higher-order theorem proving
% 0.19/0.47  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
% 0.19/0.54  # Version: 3.1.0-ho
% 0.19/0.54  # Preprocessing class: HSLSSMSSSSMNSFA.
% 0.19/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54  # Starting post_as_ho6 with 1500s (5) cores
% 0.19/0.54  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.54  # Starting sh8 with 300s (1) cores
% 0.19/0.54  # Starting post_as_ho1 with 300s (1) cores
% 0.19/0.54  # post_as_ho6 with pid 30346 completed with status 0
% 0.19/0.54  # Result found by post_as_ho6
% 0.19/0.54  # Preprocessing class: HSLSSMSSSSMNSFA.
% 0.19/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54  # Starting post_as_ho6 with 1500s (5) cores
% 0.19/0.54  # SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 0.19/0.54  # Search class: HGHSM-FFLM31-MSFFFFNN
% 0.19/0.54  # partial match(1): HGHSM-FSLM31-MSFFFFNN
% 0.19/0.54  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.54  # Starting new_ho_10 with 811s (1) cores
% 0.19/0.54  # Starting post_as_ho6 with 151s (1) cores
% 0.19/0.54  # Starting new_bool_1 with 136s (1) cores
% 0.19/0.54  # Starting new_bool_2 with 136s (1) cores
% 0.19/0.54  # Starting new_bool_9 with 136s (1) cores
% 0.19/0.54  # new_ho_10 with pid 30350 completed with status 0
% 0.19/0.54  # Result found by new_ho_10
% 0.19/0.54  # Preprocessing class: HSLSSMSSSSMNSFA.
% 0.19/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54  # Starting post_as_ho6 with 1500s (5) cores
% 0.19/0.54  # SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 0.19/0.54  # Search class: HGHSM-FFLM31-MSFFFFNN
% 0.19/0.54  # partial match(1): HGHSM-FSLM31-MSFFFFNN
% 0.19/0.54  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.54  # Starting new_ho_10 with 811s (1) cores
% 0.19/0.54  # Preprocessing time       : 0.003 s
% 0.19/0.54  # Presaturation interreduction done
% 0.19/0.54  
% 0.19/0.54  # Proof found!
% 0.19/0.54  # SZS status Theorem
% 0.19/0.54  # SZS output start CNFRefutation
% See solution above
% 0.19/0.54  # Parsed axioms                        : 393
% 0.19/0.54  # Removed by relevancy pruning/SinE    : 288
% 0.19/0.54  # Initial clauses                      : 174
% 0.19/0.54  # Removed in clause preprocessing      : 7
% 0.19/0.54  # Initial clauses in saturation        : 167
% 0.19/0.54  # Processed clauses                    : 344
% 0.19/0.54  # ...of these trivial                  : 15
% 0.19/0.54  # ...subsumed                          : 84
% 0.19/0.54  # ...remaining for further processing  : 245
% 0.19/0.54  # Other redundant clauses eliminated   : 31
% 0.19/0.54  # Clauses deleted for lack of memory   : 0
% 0.19/0.54  # Backward-subsumed                    : 0
% 0.19/0.54  # Backward-rewritten                   : 3
% 0.19/0.54  # Generated clauses                    : 1136
% 0.19/0.54  # ...of the previous two non-redundant : 870
% 0.19/0.54  # ...aggressively subsumed             : 0
% 0.19/0.54  # Contextual simplify-reflections      : 4
% 0.19/0.54  # Paramodulations                      : 1100
% 0.19/0.54  # Factorizations                       : 4
% 0.19/0.54  # NegExts                              : 0
% 0.19/0.54  # Equation resolutions                 : 35
% 0.19/0.54  # Disequality decompositions           : 0
% 0.19/0.54  # Total rewrite steps                  : 592
% 0.19/0.54  # ...of those cached                   : 409
% 0.19/0.54  # Propositional unsat checks           : 0
% 0.19/0.54  #    Propositional check models        : 0
% 0.19/0.54  #    Propositional check unsatisfiable : 0
% 0.19/0.54  #    Propositional clauses             : 0
% 0.19/0.54  #    Propositional clauses after purity: 0
% 0.19/0.54  #    Propositional unsat core size     : 0
% 0.19/0.54  #    Propositional preprocessing time  : 0.000
% 0.19/0.54  #    Propositional encoding time       : 0.000
% 0.19/0.54  #    Propositional solver time         : 0.000
% 0.19/0.54  #    Success case prop preproc time    : 0.000
% 0.19/0.54  #    Success case prop encoding time   : 0.000
% 0.19/0.54  #    Success case prop solver time     : 0.000
% 0.19/0.54  # Current number of processed clauses  : 120
% 0.19/0.54  #    Positive orientable unit clauses  : 33
% 0.19/0.54  #    Positive unorientable unit clauses: 3
% 0.19/0.54  #    Negative unit clauses             : 6
% 0.19/0.54  #    Non-unit-clauses                  : 78
% 0.19/0.54  # Current number of unprocessed clauses: 787
% 0.19/0.54  # ...number of literals in the above   : 1919
% 0.19/0.54  # Current number of archived formulas  : 0
% 0.19/0.54  # Current number of archived clauses   : 111
% 0.19/0.54  # Clause-clause subsumption calls (NU) : 1931
% 0.19/0.54  # Rec. Clause-clause subsumption calls : 988
% 0.19/0.54  # Non-unit clause-clause subsumptions  : 41
% 0.19/0.54  # Unit Clause-clause subsumption calls : 41
% 0.19/0.54  # Rewrite failures with RHS unbound    : 0
% 0.19/0.54  # BW rewrite match attempts            : 94
% 0.19/0.54  # BW rewrite match successes           : 73
% 0.19/0.54  # Condensation attempts                : 344
% 0.19/0.54  # Condensation successes               : 5
% 0.19/0.54  # Termbank termtop insertions          : 24151
% 0.19/0.54  # Search garbage collected termcells   : 4988
% 0.19/0.54  
% 0.19/0.54  # -------------------------------------------------
% 0.19/0.54  # User time                : 0.039 s
% 0.19/0.54  # System time              : 0.007 s
% 0.19/0.54  # Total time               : 0.047 s
% 0.19/0.54  # Maximum resident set size: 3164 pages
% 0.19/0.54  
% 0.19/0.54  # -------------------------------------------------
% 0.19/0.54  # User time                : 0.181 s
% 0.19/0.54  # System time              : 0.022 s
% 0.19/0.54  # Total time               : 0.203 s
% 0.19/0.54  # Maximum resident set size: 2476 pages
% 0.19/0.54  % E---3.1 exiting
% 0.19/0.54  % E exiting
%------------------------------------------------------------------------------