TSTP Solution File: ITP095^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP095^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.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 0.80s 0.88s
% Output   : CNFRefutation 0.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   52 (  21 unt;  25 typ;   0 def)
%            Number of atoms       :   44 (  15 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  343 (  18   ~;  11   |;   0   &; 308   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  20 usr;   9 con; 0-2 aty)
%            Number of variables   :   28 (   0   ^  28   !;   0   ?;  28   :)

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

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

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

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

thf(decl_sort5,type,
    nat: $tType ).

thf(decl_24,type,
    abs_abs_real: real > real ).

thf(decl_31,type,
    one_one_real: real ).

thf(decl_32,type,
    zero_zero_int: int ).

thf(decl_38,type,
    zero_zero_real: real ).

thf(decl_41,type,
    ring_1_Ints_real: set_real ).

thf(decl_45,type,
    ring_1_of_int_real: int > real ).

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

thf(decl_53,type,
    ord_less_eq_real: real > real > $o ).

thf(decl_58,type,
    degree_real: poly_real > nat ).

thf(decl_62,type,
    poly_real2: poly_real > real > real ).

thf(decl_66,type,
    coeff_real: poly_real > nat > real ).

thf(decl_67,type,
    power_power_int: int > nat > int ).

thf(decl_72,type,
    power_power_real: real > nat > real ).

thf(decl_77,type,
    divide_divide_real: real > real > real ).

thf(decl_81,type,
    member_real: real > set_real > $o ).

thf(decl_84,type,
    a2: int ).

thf(decl_85,type,
    b: int ).

thf(decl_86,type,
    n: nat ).

thf(decl_87,type,
    p: poly_real ).

thf(decl_105,type,
    esk15_1: poly_real > nat ).

thf(conj_0,conjecture,
    ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ ( degree_real @ p ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(fact_154_int__poly__rat__no__root__ge,axiom,
    ! [X6: poly_real,X2: int,X80: int] :
      ( ! [X30: nat] : ( member_real @ ( coeff_real @ X6 @ X30 ) @ ring_1_Ints_real )
     => ( ( ord_less_int @ zero_zero_int @ X2 )
       => ( ( ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X80 ) @ ( ring_1_of_int_real @ X2 ) ) )
           != zero_zero_real )
         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ X2 ) @ ( degree_real @ X6 ) ) ) @ ( abs_abs_real @ ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X80 ) @ ( ring_1_of_int_real @ X2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_int__poly__rat__no__root__ge) ).

thf(fact_23_of__int__power,axiom,
    ! [X5: int,X7: nat] :
      ( ( ring_1_of_int_real @ ( power_power_int @ X5 @ X7 ) )
      = ( power_power_real @ ( ring_1_of_int_real @ X5 ) @ X7 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_of__int__power) ).

thf(fact_6_n__def,axiom,
    ( n
    = ( degree_real @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_n__def) ).

thf(fact_2_p_I1_J,axiom,
    ! [X1: nat] : ( member_real @ ( coeff_real @ p @ X1 ) @ ring_1_Ints_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_p_I1_J) ).

thf(fact_5_no__root,axiom,
    ( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) )
   != zero_zero_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_no__root) ).

thf(fact_3_b,axiom,
    ord_less_int @ zero_zero_int @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_b) ).

thf(c_0_7,negated_conjecture,
    ~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ ( degree_real @ p ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

thf(c_0_8,plain,
    ! [X6: poly_real,X2: int,X80: int] :
      ( ! [X30: nat] : ( member_real @ ( coeff_real @ X6 @ X30 ) @ ring_1_Ints_real )
     => ( ( ord_less_int @ zero_zero_int @ X2 )
       => ( ( ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X80 ) @ ( ring_1_of_int_real @ X2 ) ) )
           != zero_zero_real )
         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ X2 ) @ ( degree_real @ X6 ) ) ) @ ( abs_abs_real @ ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X80 ) @ ( ring_1_of_int_real @ X2 ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_154_int__poly__rat__no__root__ge]) ).

thf(c_0_9,negated_conjecture,
    ~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ ( degree_real @ p ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_7]) ).

thf(c_0_10,plain,
    ! [X1106: poly_real,X1108: int,X1109: int] :
      ( ~ ( member_real @ ( coeff_real @ X1106 @ ( esk15_1 @ X1106 ) ) @ ring_1_Ints_real )
      | ~ ( ord_less_int @ zero_zero_int @ X1108 )
      | ( ( poly_real2 @ X1106 @ ( divide_divide_real @ ( ring_1_of_int_real @ X1109 ) @ ( ring_1_of_int_real @ X1108 ) ) )
        = zero_zero_real )
      | ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ X1108 ) @ ( degree_real @ X1106 ) ) ) @ ( abs_abs_real @ ( poly_real2 @ X1106 @ ( divide_divide_real @ ( ring_1_of_int_real @ X1109 ) @ ( ring_1_of_int_real @ X1108 ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])]) ).

thf(c_0_11,plain,
    ! [X920: int,X921: nat] :
      ( ( ring_1_of_int_real @ ( power_power_int @ X920 @ X921 ) )
      = ( power_power_real @ ( ring_1_of_int_real @ X920 ) @ X921 ) ),
    inference(variable_rename,[status(thm)],[fact_23_of__int__power]) ).

thf(c_0_12,negated_conjecture,
    ~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ ( degree_real @ p ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_13,plain,
    ( n
    = ( degree_real @ p ) ),
    inference(split_conjunct,[status(thm)],[fact_6_n__def]) ).

thf(c_0_14,plain,
    ! [X6: poly_real,X4: int,X2: int] :
      ( ( ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X4 ) @ ( ring_1_of_int_real @ X2 ) ) )
        = zero_zero_real )
      | ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ X2 ) @ ( degree_real @ X6 ) ) ) @ ( abs_abs_real @ ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X4 ) @ ( ring_1_of_int_real @ X2 ) ) ) ) )
      | ~ ( member_real @ ( coeff_real @ X6 @ ( esk15_1 @ X6 ) ) @ ring_1_Ints_real )
      | ~ ( ord_less_int @ zero_zero_int @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_15,plain,
    ! [X2: int,X1: nat] :
      ( ( ring_1_of_int_real @ ( power_power_int @ X2 @ X1 ) )
      = ( power_power_real @ ( ring_1_of_int_real @ X2 ) @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_16,plain,
    ! [X889: nat] : ( member_real @ ( coeff_real @ p @ X889 ) @ ring_1_Ints_real ),
    inference(variable_rename,[status(thm)],[fact_2_p_I1_J]) ).

thf(c_0_17,plain,
    ( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) )
   != zero_zero_real ),
    inference(fof_simplification,[status(thm)],[fact_5_no__root]) ).

thf(c_0_18,negated_conjecture,
    ~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ n ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_19,plain,
    ! [X2: int,X6: poly_real,X4: int] :
      ( ( ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ X4 ) ) )
        = zero_zero_real )
      | ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( ring_1_of_int_real @ ( power_power_int @ X4 @ ( degree_real @ X6 ) ) ) ) @ ( abs_abs_real @ ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ X4 ) ) ) ) )
      | ~ ( member_real @ ( coeff_real @ X6 @ ( esk15_1 @ X6 ) ) @ ring_1_Ints_real )
      | ~ ( ord_less_int @ zero_zero_int @ X4 ) ),
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_20,plain,
    ! [X1: nat] : ( member_real @ ( coeff_real @ p @ X1 ) @ ring_1_Ints_real ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_21,plain,
    ( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) )
   != zero_zero_real ),
    inference(fof_nnf,[status(thm)],[c_0_17]) ).

thf(c_0_22,negated_conjecture,
    ~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( ring_1_of_int_real @ ( power_power_int @ b @ n ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
    inference(spm,[status(thm)],[c_0_18,c_0_15]) ).

thf(c_0_23,plain,
    ! [X2: int,X4: int] :
      ( ( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ X4 ) ) )
        = zero_zero_real )
      | ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( ring_1_of_int_real @ ( power_power_int @ X4 @ n ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ X4 ) ) ) ) )
      | ~ ( ord_less_int @ zero_zero_int @ X4 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_13]),c_0_20])]) ).

thf(c_0_24,plain,
    ord_less_int @ zero_zero_int @ b,
    inference(split_conjunct,[status(thm)],[fact_3_b]) ).

thf(c_0_25,plain,
    ( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) )
   != zero_zero_real ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_26,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[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
% 0.05/0.14  % Problem    : ITP095^1 : TPTP v8.2.0. Released v7.5.0.
% 0.14/0.15  % Command    : run_E %s %d THM
% 0.15/0.36  % Computer : n021.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat May 18 16:11:23 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.22/0.50  Running higher-order theorem proving
% 0.22/0.50  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/benchmark/theBenchmark.p
% 0.80/0.88  # Version: 3.1.0-ho
% 0.80/0.88  # Preprocessing class: HSLSSMSMSSSNSFA.
% 0.80/0.88  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.88  # Starting new_ho_10 with 900s (3) cores
% 0.80/0.88  # Starting sh2lt with 300s (1) cores
% 0.80/0.88  # Starting new_ho_5 with 300s (1) cores
% 0.80/0.88  # Starting full_lambda_5 with 300s (1) cores
% 0.80/0.88  # Starting sh9 with 300s (1) cores
% 0.80/0.88  # Starting ehoh_best8_lambda with 300s (1) cores
% 0.80/0.88  # new_ho_10 with pid 8925 completed with status 0
% 0.80/0.88  # Result found by new_ho_10
% 0.80/0.88  # Preprocessing class: HSLSSMSMSSSNSFA.
% 0.80/0.88  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.88  # Starting new_ho_10 with 900s (3) cores
% 0.80/0.88  # No SInE strategy applied
% 0.80/0.88  # Search class: HGHSM-FSLM31-MSFFFFBN
% 0.80/0.88  # Scheduled 5 strats onto 3 cores with 900 seconds (900 total)
% 0.80/0.88  # Starting new_ho_10 with 541s (1) cores
% 0.80/0.88  # Starting almost_fo_4 with 91s (1) cores
% 0.80/0.88  # Starting pre_casc_8 with 91s (1) cores
% 0.80/0.88  # new_ho_10 with pid 8934 completed with status 0
% 0.80/0.88  # Result found by new_ho_10
% 0.80/0.88  # Preprocessing class: HSLSSMSMSSSNSFA.
% 0.80/0.88  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.88  # Starting new_ho_10 with 900s (3) cores
% 0.80/0.88  # No SInE strategy applied
% 0.80/0.88  # Search class: HGHSM-FSLM31-MSFFFFBN
% 0.80/0.88  # Scheduled 5 strats onto 3 cores with 900 seconds (900 total)
% 0.80/0.88  # Starting new_ho_10 with 541s (1) cores
% 0.80/0.88  # Preprocessing time       : 0.007 s
% 0.80/0.88  # Presaturation interreduction done
% 0.80/0.88  
% 0.80/0.88  # Proof found!
% 0.80/0.88  # SZS status Theorem
% 0.80/0.88  # SZS output start CNFRefutation
% See solution above
% 0.80/0.88  # Parsed axioms                        : 433
% 0.80/0.88  # Removed by relevancy pruning/SinE    : 0
% 0.80/0.88  # Initial clauses                      : 631
% 0.80/0.88  # Removed in clause preprocessing      : 93
% 0.80/0.88  # Initial clauses in saturation        : 538
% 0.80/0.88  # Processed clauses                    : 3259
% 0.80/0.88  # ...of these trivial                  : 60
% 0.80/0.88  # ...subsumed                          : 1387
% 0.80/0.88  # ...remaining for further processing  : 1812
% 0.80/0.88  # Other redundant clauses eliminated   : 81
% 0.80/0.88  # Clauses deleted for lack of memory   : 0
% 0.80/0.88  # Backward-subsumed                    : 34
% 0.80/0.88  # Backward-rewritten                   : 35
% 0.80/0.88  # Generated clauses                    : 14761
% 0.80/0.88  # ...of the previous two non-redundant : 11734
% 0.80/0.88  # ...aggressively subsumed             : 0
% 0.80/0.88  # Contextual simplify-reflections      : 12
% 0.80/0.88  # Paramodulations                      : 14656
% 0.80/0.88  # Factorizations                       : 4
% 0.80/0.88  # NegExts                              : 2
% 0.80/0.88  # Equation resolutions                 : 99
% 0.80/0.88  # Disequality decompositions           : 0
% 0.80/0.88  # Total rewrite steps                  : 11147
% 0.80/0.88  # ...of those cached                   : 10710
% 0.80/0.88  # Propositional unsat checks           : 0
% 0.80/0.88  #    Propositional check models        : 0
% 0.80/0.88  #    Propositional check unsatisfiable : 0
% 0.80/0.88  #    Propositional clauses             : 0
% 0.80/0.88  #    Propositional clauses after purity: 0
% 0.80/0.88  #    Propositional unsat core size     : 0
% 0.80/0.88  #    Propositional preprocessing time  : 0.000
% 0.80/0.88  #    Propositional encoding time       : 0.000
% 0.80/0.88  #    Propositional solver time         : 0.000
% 0.80/0.88  #    Success case prop preproc time    : 0.000
% 0.80/0.88  #    Success case prop encoding time   : 0.000
% 0.80/0.88  #    Success case prop solver time     : 0.000
% 0.80/0.88  # Current number of processed clauses  : 1257
% 0.80/0.88  #    Positive orientable unit clauses  : 160
% 0.80/0.88  #    Positive unorientable unit clauses: 0
% 0.80/0.88  #    Negative unit clauses             : 53
% 0.80/0.88  #    Non-unit-clauses                  : 1044
% 0.80/0.88  # Current number of unprocessed clauses: 9337
% 0.80/0.88  # ...number of literals in the above   : 32218
% 0.80/0.88  # Current number of archived formulas  : 0
% 0.80/0.88  # Current number of archived clauses   : 501
% 0.80/0.88  # Clause-clause subsumption calls (NU) : 144678
% 0.80/0.88  # Rec. Clause-clause subsumption calls : 100539
% 0.80/0.88  # Non-unit clause-clause subsumptions  : 602
% 0.80/0.88  # Unit Clause-clause subsumption calls : 8089
% 0.80/0.88  # Rewrite failures with RHS unbound    : 0
% 0.80/0.88  # BW rewrite match attempts            : 23
% 0.80/0.88  # BW rewrite match successes           : 18
% 0.80/0.88  # Condensation attempts                : 3263
% 0.80/0.88  # Condensation successes               : 23
% 0.80/0.88  # Termbank termtop insertions          : 270170
% 0.80/0.88  # Search garbage collected termcells   : 9681
% 0.80/0.88  
% 0.80/0.88  # -------------------------------------------------
% 0.80/0.88  # User time                : 0.339 s
% 0.80/0.88  # System time              : 0.017 s
% 0.80/0.88  # Total time               : 0.356 s
% 0.80/0.88  # Maximum resident set size: 4184 pages
% 0.80/0.88  
% 0.80/0.88  # -------------------------------------------------
% 0.80/0.88  # User time                : 0.972 s
% 0.80/0.88  # System time              : 0.050 s
% 0.80/0.88  # Total time               : 1.022 s
% 0.80/0.88  # Maximum resident set size: 2324 pages
% 0.80/0.88  % E---3.1 exiting
% 0.80/0.89  % E exiting
%------------------------------------------------------------------------------