TSTP Solution File: ITP097^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP097^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n003.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 22:16:17 EDT 2024

% Result   : Theorem 0.44s 0.60s
% Output   : CNFRefutation 0.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   33 (  12 unt;  18 typ;   0 def)
%            Number of atoms       :   20 (   4 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  216 (   6   ~;   3   |;   1   &; 205   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   7 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   3 con; 0-2 aty)
%            Number of variables   :    6 (   0   ^   6   !;   0   ?;   6   :)

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

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

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

thf(decl_sort4,type,
    num: $tType ).

thf(decl_22,type,
    archim1371465213g_real: real > int ).

thf(decl_30,type,
    nat2: int > nat ).

thf(decl_32,type,
    ring_1_of_int_real: int > real ).

thf(decl_36,type,
    semiri2110766477t_real: nat > real ).

thf(decl_39,type,
    bit0: num > num ).

thf(decl_40,type,
    one: num ).

thf(decl_41,type,
    numeral_numeral_int: num > int ).

thf(decl_43,type,
    numeral_numeral_real: num > real ).

thf(decl_46,type,
    ord_less_eq_int: int > int > $o ).

thf(decl_49,type,
    ord_less_eq_real: real > real > $o ).

thf(decl_50,type,
    power_power_int: int > nat > int ).

thf(decl_54,type,
    log: real > real > real ).

thf(decl_55,type,
    powr_real: real > real > real ).

thf(decl_57,type,
    d: int ).

thf(conj_0,conjecture,
    ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(fact_28_of__int__le__iff,axiom,
    ! [X26: int,X13: int] :
      ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X26 ) @ ( ring_1_of_int_real @ X13 ) )
    <=> ( ord_less_eq_int @ X26 @ X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_of__int__le__iff) ).

thf(fact_103__092_060open_0622_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_A_092_060le_062_A2_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062,axiom,
    ord_less_eq_real @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103__092_060open_0622_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_A_092_060le_062_A2_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062) ).

thf(fact_53__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062,axiom,
    ( ( ring_1_of_int_real @ d )
    = ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062) ).

thf(fact_102__092_060open_0622_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_A_061_Areal__of__int_A_I2_A_094_Anat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062,axiom,
    ( ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) )
    = ( ring_1_of_int_real @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102__092_060open_0622_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_A_061_Areal__of__int_A_I2_A_094_Anat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062) ).

thf(c_0_5,negated_conjecture,
    ~ ( ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

thf(c_0_6,plain,
    ! [X959: int,X960: int] :
      ( ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ X959 ) @ ( ring_1_of_int_real @ X960 ) )
        | ( ord_less_eq_int @ X959 @ X960 ) )
      & ( ~ ( ord_less_eq_int @ X959 @ X960 )
        | ( ord_less_eq_real @ ( ring_1_of_int_real @ X959 ) @ ( ring_1_of_int_real @ X960 ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_28_of__int__le__iff])])]) ).

thf(c_0_7,plain,
    ord_less_eq_real @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[fact_103__092_060open_0622_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_A_092_060le_062_A2_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062]) ).

thf(c_0_8,plain,
    ( ( ring_1_of_int_real @ d )
    = ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ),
    inference(split_conjunct,[status(thm)],[fact_53__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062]) ).

thf(c_0_9,plain,
    ( ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) )
    = ( ring_1_of_int_real @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[fact_102__092_060open_0622_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_A_061_Areal__of__int_A_I2_A_094_Anat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062]) ).

thf(c_0_10,negated_conjecture,
    ~ ( ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_5]) ).

thf(c_0_11,plain,
    ! [X3: int,X4: int] :
      ( ( ord_less_eq_int @ X3 @ X4 )
      | ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ ( ring_1_of_int_real @ X4 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_12,plain,
    ord_less_eq_real @ ( ring_1_of_int_real @ d ) @ ( ring_1_of_int_real @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).

thf(c_0_13,negated_conjecture,
    ~ ( ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_14,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : ITP097^1 : TPTP v8.2.0. Released v7.5.0.
% 0.03/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n003.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   : Sat May 18 15:56:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  Running higher-order theorem proving
% 0.21/0.50  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
% 0.44/0.60  # Version: 3.1.0-ho
% 0.44/0.60  # Preprocessing class: HSLSSMSMSSSNHFA.
% 0.44/0.60  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.60  # Starting new_ho_10 with 1500s (5) cores
% 0.44/0.60  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.44/0.60  # Starting full_lambda_6 with 300s (1) cores
% 0.44/0.60  # Starting full_lambda_9 with 300s (1) cores
% 0.44/0.60  # new_ho_10 with pid 24175 completed with status 0
% 0.44/0.60  # Result found by new_ho_10
% 0.44/0.60  # Preprocessing class: HSLSSMSMSSSNHFA.
% 0.44/0.60  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.60  # Starting new_ho_10 with 1500s (5) cores
% 0.44/0.60  # No SInE strategy applied
% 0.44/0.60  # Search class: HGHSM-FSLM31-DHFFFFBN
% 0.44/0.60  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.44/0.60  # Starting new_ho_10 with 301s (1) cores
% 0.44/0.60  # Starting sh3 with 301s (1) cores
% 0.44/0.60  # Starting ho_unfolding_3 with 301s (1) cores
% 0.44/0.60  # Starting new_ho_10_cnf2 with 301s (1) cores
% 0.44/0.60  # Starting pre_casc_2 with 296s (1) cores
% 0.44/0.60  # new_ho_10 with pid 24179 completed with status 0
% 0.44/0.60  # Result found by new_ho_10
% 0.44/0.60  # Preprocessing class: HSLSSMSMSSSNHFA.
% 0.44/0.60  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.60  # Starting new_ho_10 with 1500s (5) cores
% 0.44/0.60  # No SInE strategy applied
% 0.44/0.60  # Search class: HGHSM-FSLM31-DHFFFFBN
% 0.44/0.60  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.44/0.60  # Starting new_ho_10 with 301s (1) cores
% 0.44/0.60  # Preprocessing time       : 0.007 s
% 0.44/0.60  # Presaturation interreduction done
% 0.44/0.60  
% 0.44/0.60  # Proof found!
% 0.44/0.60  # SZS status Theorem
% 0.44/0.60  # SZS output start CNFRefutation
% See solution above
% 0.44/0.60  # Parsed axioms                        : 396
% 0.44/0.60  # Removed by relevancy pruning/SinE    : 0
% 0.44/0.60  # Initial clauses                      : 592
% 0.44/0.60  # Removed in clause preprocessing      : 72
% 0.44/0.60  # Initial clauses in saturation        : 520
% 0.44/0.60  # Processed clauses                    : 702
% 0.44/0.60  # ...of these trivial                  : 28
% 0.44/0.60  # ...subsumed                          : 103
% 0.44/0.60  # ...remaining for further processing  : 571
% 0.44/0.60  # Other redundant clauses eliminated   : 91
% 0.44/0.60  # Clauses deleted for lack of memory   : 0
% 0.44/0.60  # Backward-subsumed                    : 0
% 0.44/0.60  # Backward-rewritten                   : 12
% 0.44/0.60  # Generated clauses                    : 272
% 0.44/0.60  # ...of the previous two non-redundant : 130
% 0.44/0.60  # ...aggressively subsumed             : 0
% 0.44/0.60  # Contextual simplify-reflections      : 0
% 0.44/0.60  # Paramodulations                      : 179
% 0.44/0.60  # Factorizations                       : 0
% 0.44/0.60  # NegExts                              : 0
% 0.44/0.60  # Equation resolutions                 : 95
% 0.44/0.60  # Disequality decompositions           : 0
% 0.44/0.60  # Total rewrite steps                  : 281
% 0.44/0.60  # ...of those cached                   : 193
% 0.44/0.60  # Propositional unsat checks           : 0
% 0.44/0.60  #    Propositional check models        : 0
% 0.44/0.60  #    Propositional check unsatisfiable : 0
% 0.44/0.60  #    Propositional clauses             : 0
% 0.44/0.60  #    Propositional clauses after purity: 0
% 0.44/0.60  #    Propositional unsat core size     : 0
% 0.44/0.60  #    Propositional preprocessing time  : 0.000
% 0.44/0.60  #    Propositional encoding time       : 0.000
% 0.44/0.60  #    Propositional solver time         : 0.000
% 0.44/0.60  #    Success case prop preproc time    : 0.000
% 0.44/0.60  #    Success case prop encoding time   : 0.000
% 0.44/0.60  #    Success case prop solver time     : 0.000
% 0.44/0.60  # Current number of processed clauses  : 131
% 0.44/0.60  #    Positive orientable unit clauses  : 60
% 0.44/0.60  #    Positive unorientable unit clauses: 0
% 0.44/0.60  #    Negative unit clauses             : 22
% 0.44/0.60  #    Non-unit-clauses                  : 49
% 0.44/0.60  # Current number of unprocessed clauses: 283
% 0.44/0.60  # ...number of literals in the above   : 604
% 0.44/0.60  # Current number of archived formulas  : 0
% 0.44/0.60  # Current number of archived clauses   : 357
% 0.44/0.60  # Clause-clause subsumption calls (NU) : 14294
% 0.44/0.60  # Rec. Clause-clause subsumption calls : 11314
% 0.44/0.60  # Non-unit clause-clause subsumptions  : 77
% 0.44/0.60  # Unit Clause-clause subsumption calls : 502
% 0.44/0.60  # Rewrite failures with RHS unbound    : 0
% 0.44/0.60  # BW rewrite match attempts            : 21
% 0.44/0.60  # BW rewrite match successes           : 8
% 0.44/0.60  # Condensation attempts                : 702
% 0.44/0.60  # Condensation successes               : 2
% 0.44/0.60  # Termbank termtop insertions          : 38705
% 0.44/0.60  # Search garbage collected termcells   : 8124
% 0.44/0.60  
% 0.44/0.60  # -------------------------------------------------
% 0.44/0.60  # User time                : 0.067 s
% 0.44/0.60  # System time              : 0.012 s
% 0.44/0.60  # Total time               : 0.079 s
% 0.44/0.60  # Maximum resident set size: 4012 pages
% 0.44/0.60  
% 0.44/0.60  # -------------------------------------------------
% 0.44/0.60  # User time                : 0.245 s
% 0.44/0.60  # System time              : 0.028 s
% 0.44/0.60  # Total time               : 0.272 s
% 0.44/0.60  # Maximum resident set size: 2284 pages
% 0.44/0.60  % E---3.1 exiting
% 0.44/0.60  % E exiting
%------------------------------------------------------------------------------