TSTP Solution File: ITP132^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP132^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n016.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 22:16:27 EDT 2024

% Result   : Theorem 0.43s 0.56s
% Output   : CNFRefutation 0.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   27 (   9 unt;  15 typ;   0 def)
%            Number of atoms       :   36 (  17 equ;   0 cnn)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  158 (  14   ~;  11   |;   8   &; 122   @)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   26 (  26   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :   23 (  10   ^  13   !;   0   ?;  23   :)

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

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

thf(decl_23,type,
    minus_minus_nat: nat > nat > nat ).

thf(decl_24,type,
    one_one_nat: nat ).

thf(decl_25,type,
    times_times_nat: nat > nat > nat ).

thf(decl_26,type,
    zero_zero_nat: nat ).

thf(decl_27,type,
    groups1842438620at_nat: ( nat > nat ) > set_nat > nat ).

thf(decl_29,type,
    number1551313001itions: ( nat > nat ) > nat > $o ).

thf(decl_31,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(decl_36,type,
    set_ord_atMost_nat: nat > set_nat ).

thf(decl_40,type,
    k: nat ).

thf(decl_41,type,
    n: nat ).

thf(decl_42,type,
    p: nat > nat ).

thf(decl_61,type,
    esk19_2: ( nat > nat ) > nat > nat ).

thf(decl_137,type,
    esk92_1: ( nat > nat ) > nat > nat ).

thf(conj_0,conjecture,
    ( ( minus_minus_nat
      @ ( groups1842438620at_nat
        @ ^ [X3: nat] : ( times_times_nat @ ( p @ X3 ) @ X3 )
        @ ( set_ord_atMost_nat @ n ) )
      @ k )
    = ( minus_minus_nat @ n @ k ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(fact_61_partitions__def,axiom,
    ( number1551313001itions
    = ( ^ [X67: nat > nat,X10: nat] :
          ( ! [X3: nat] :
              ( ( ( X67 @ X3 )
               != zero_zero_nat )
             => ( ( ord_less_eq_nat @ one_one_nat @ X3 )
                & ( ord_less_eq_nat @ X3 @ X10 ) ) )
          & ( ( groups1842438620at_nat
              @ ^ [X3: nat] : ( times_times_nat @ ( X67 @ X3 ) @ X3 )
              @ ( set_ord_atMost_nat @ X10 ) )
            = X10 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_partitions__def) ).

thf(fact_0_partitions,axiom,
    number1551313001itions @ p @ n,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_partitions) ).

thf(c_0_3,negated_conjecture,
    ( ( minus_minus_nat
      @ ( groups1842438620at_nat
        @ ^ [Z0: nat] : ( times_times_nat @ ( p @ Z0 ) @ Z0 )
        @ ( set_ord_atMost_nat @ n ) )
      @ k )
   != ( minus_minus_nat @ n @ k ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])])]) ).

thf(c_0_4,plain,
    ! [X799: nat > nat,X800: nat] :
      ( ( number1551313001itions @ X799 @ X800 )
    <=> ( ! [X3: nat] :
            ( ( ( X799 @ X3 )
             != zero_zero_nat )
           => ( ( ord_less_eq_nat @ one_one_nat @ X3 )
              & ( ord_less_eq_nat @ X3 @ X800 ) ) )
        & ( ( groups1842438620at_nat
            @ ^ [Z0: nat] : ( times_times_nat @ ( X799 @ Z0 ) @ Z0 )
            @ ( set_ord_atMost_nat @ X800 ) )
          = X800 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_61_partitions__def])])]) ).

thf(c_0_5,negated_conjecture,
    ( ( minus_minus_nat
      @ ( groups1842438620at_nat
        @ ^ [Z0: nat] : ( times_times_nat @ ( p @ Z0 ) @ Z0 )
        @ ( set_ord_atMost_nat @ n ) )
      @ k )
   != ( minus_minus_nat @ n @ k ) ),
    inference(fof_nnf,[status(thm)],[c_0_3]) ).

thf(c_0_6,plain,
    ! [X1491: nat,X4: nat > nat] :
      ( ( esk92_1 @ X4 @ X1491 )
      = ( times_times_nat @ ( X4 @ X1491 ) @ X1491 ) ),
    introduced(definition) ).

thf(c_0_7,plain,
    ! [X985: nat > nat,X986: nat,X987: nat,X988: nat > nat,X989: nat] :
      ( ( ( ord_less_eq_nat @ one_one_nat @ X987 )
        | ( ( X985 @ X987 )
          = zero_zero_nat )
        | ~ ( number1551313001itions @ X985 @ X986 ) )
      & ( ( ord_less_eq_nat @ X987 @ X986 )
        | ( ( X985 @ X987 )
          = zero_zero_nat )
        | ~ ( number1551313001itions @ X985 @ X986 ) )
      & ( ( ( groups1842438620at_nat
            @ ^ [Z0: nat] : ( times_times_nat @ ( X985 @ Z0 ) @ Z0 )
            @ ( set_ord_atMost_nat @ X986 ) )
          = X986 )
        | ~ ( number1551313001itions @ X985 @ X986 ) )
      & ( ( ( X988 @ ( esk19_2 @ X988 @ X989 ) )
         != zero_zero_nat )
        | ( ( groups1842438620at_nat
            @ ^ [Z0: nat] : ( times_times_nat @ ( X988 @ Z0 ) @ Z0 )
            @ ( set_ord_atMost_nat @ X989 ) )
         != X989 )
        | ( number1551313001itions @ X988 @ X989 ) )
      & ( ~ ( ord_less_eq_nat @ one_one_nat @ ( esk19_2 @ X988 @ X989 ) )
        | ~ ( ord_less_eq_nat @ ( esk19_2 @ X988 @ X989 ) @ X989 )
        | ( ( groups1842438620at_nat
            @ ^ [Z0: nat] : ( times_times_nat @ ( X988 @ Z0 ) @ Z0 )
            @ ( set_ord_atMost_nat @ X989 ) )
         != X989 )
        | ( number1551313001itions @ X988 @ X989 ) ) ),
    inference(distribute,[status(thm)],[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_4])])])])])])]) ).

thf(c_0_8,negated_conjecture,
    ( ( minus_minus_nat @ ( groups1842438620at_nat @ ( esk92_1 @ p ) @ ( set_ord_atMost_nat @ n ) ) @ k )
   != ( minus_minus_nat @ n @ k ) ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_5]),c_0_6]) ).

thf(c_0_9,plain,
    ! [X4: nat > nat,X1: nat] :
      ( ( ( groups1842438620at_nat @ ( esk92_1 @ X4 ) @ ( set_ord_atMost_nat @ X1 ) )
        = X1 )
      | ~ ( number1551313001itions @ X4 @ X1 ) ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7]),c_0_6]) ).

thf(c_0_10,plain,
    number1551313001itions @ p @ n,
    inference(split_conjunct,[status(thm)],[fact_0_partitions]) ).

thf(c_0_11,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : ITP132^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n016.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   : Sat May 18 16:34:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.21/0.49  Running higher-order theorem proving
% 0.21/0.49  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
% 0.43/0.56  # Version: 3.1.0-ho
% 0.43/0.56  # Preprocessing class: HSLSSMSSSSLNHSA.
% 0.43/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.56  # Starting pre_casc_6 with 1200s (4) cores
% 0.43/0.56  # Starting sh4 with 600s (2) cores
% 0.43/0.56  # Starting pre_casc_4 with 300s (1) cores
% 0.43/0.56  # Starting full_lambda_7 with 300s (1) cores
% 0.43/0.56  # sh4 with pid 8280 completed with status 0
% 0.43/0.56  # Result found by sh4
% 0.43/0.56  # Preprocessing class: HSLSSMSSSSLNHSA.
% 0.43/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.56  # Starting pre_casc_6 with 1200s (4) cores
% 0.43/0.56  # Starting sh4 with 600s (2) cores
% 0.43/0.56  # No SInE strategy applied
% 0.43/0.56  # Search class: HGHSM-FSLM32-MHSFFSBC
% 0.43/0.56  # Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.43/0.56  # Starting ehoh_best4 with 291s (1) cores
% 0.43/0.56  # Starting sh4 with 61s (1) cores
% 0.43/0.56  # sh4 with pid 8290 completed with status 0
% 0.43/0.56  # Result found by sh4
% 0.43/0.56  # Preprocessing class: HSLSSMSSSSLNHSA.
% 0.43/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.56  # Starting pre_casc_6 with 1200s (4) cores
% 0.43/0.56  # Starting sh4 with 600s (2) cores
% 0.43/0.56  # No SInE strategy applied
% 0.43/0.56  # Search class: HGHSM-FSLM32-MHSFFSBC
% 0.43/0.56  # Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.43/0.56  # Starting ehoh_best4 with 291s (1) cores
% 0.43/0.56  # Starting sh4 with 61s (1) cores
% 0.43/0.56  # Preprocessing time       : 0.008 s
% 0.43/0.56  
% 0.43/0.56  # Proof found!
% 0.43/0.56  # SZS status Theorem
% 0.43/0.56  # SZS output start CNFRefutation
% See solution above
% 0.43/0.56  # Parsed axioms                        : 269
% 0.43/0.56  # Removed by relevancy pruning/SinE    : 0
% 0.43/0.56  # Initial clauses                      : 524
% 0.43/0.56  # Removed in clause preprocessing      : 51
% 0.43/0.56  # Initial clauses in saturation        : 473
% 0.43/0.56  # Processed clauses                    : 122
% 0.43/0.56  # ...of these trivial                  : 17
% 0.43/0.56  # ...subsumed                          : 16
% 0.43/0.56  # ...remaining for further processing  : 89
% 0.43/0.56  # Other redundant clauses eliminated   : 47
% 0.43/0.56  # Clauses deleted for lack of memory   : 0
% 0.43/0.56  # Backward-subsumed                    : 2
% 0.43/0.56  # Backward-rewritten                   : 3
% 0.43/0.56  # Generated clauses                    : 121
% 0.43/0.56  # ...of the previous two non-redundant : 62
% 0.43/0.56  # ...aggressively subsumed             : 0
% 0.43/0.56  # Contextual simplify-reflections      : 0
% 0.43/0.56  # Paramodulations                      : 53
% 0.43/0.56  # Factorizations                       : 0
% 0.43/0.56  # NegExts                              : 0
% 0.43/0.56  # Equation resolutions                 : 48
% 0.43/0.56  # Disequality decompositions           : 0
% 0.43/0.56  # Total rewrite steps                  : 67
% 0.43/0.56  # ...of those cached                   : 50
% 0.43/0.56  # Propositional unsat checks           : 0
% 0.43/0.56  #    Propositional check models        : 0
% 0.43/0.56  #    Propositional check unsatisfiable : 0
% 0.43/0.56  #    Propositional clauses             : 0
% 0.43/0.56  #    Propositional clauses after purity: 0
% 0.43/0.56  #    Propositional unsat core size     : 0
% 0.43/0.56  #    Propositional preprocessing time  : 0.000
% 0.43/0.56  #    Propositional encoding time       : 0.000
% 0.43/0.56  #    Propositional solver time         : 0.000
% 0.43/0.56  #    Success case prop preproc time    : 0.000
% 0.43/0.56  #    Success case prop encoding time   : 0.000
% 0.43/0.56  #    Success case prop solver time     : 0.000
% 0.43/0.56  # Current number of processed clauses  : 48
% 0.43/0.56  #    Positive orientable unit clauses  : 25
% 0.43/0.56  #    Positive unorientable unit clauses: 0
% 0.43/0.56  #    Negative unit clauses             : 5
% 0.43/0.56  #    Non-unit-clauses                  : 18
% 0.43/0.56  # Current number of unprocessed clauses: 413
% 0.43/0.56  # ...number of literals in the above   : 1319
% 0.43/0.56  # Current number of archived formulas  : 0
% 0.43/0.56  # Current number of archived clauses   : 5
% 0.43/0.56  # Clause-clause subsumption calls (NU) : 197
% 0.43/0.56  # Rec. Clause-clause subsumption calls : 160
% 0.43/0.56  # Non-unit clause-clause subsumptions  : 15
% 0.43/0.56  # Unit Clause-clause subsumption calls : 21
% 0.43/0.56  # Rewrite failures with RHS unbound    : 0
% 0.43/0.56  # BW rewrite match attempts            : 11
% 0.43/0.56  # BW rewrite match successes           : 3
% 0.43/0.56  # Condensation attempts                : 122
% 0.43/0.56  # Condensation successes               : 0
% 0.43/0.56  # Termbank termtop insertions          : 34232
% 0.43/0.56  # Search garbage collected termcells   : 9341
% 0.43/0.56  
% 0.43/0.56  # -------------------------------------------------
% 0.43/0.56  # User time                : 0.038 s
% 0.43/0.56  # System time              : 0.007 s
% 0.43/0.56  # Total time               : 0.045 s
% 0.43/0.56  # Maximum resident set size: 4148 pages
% 0.43/0.56  
% 0.43/0.56  # -------------------------------------------------
% 0.43/0.56  # User time                : 0.061 s
% 0.43/0.56  # System time              : 0.012 s
% 0.43/0.56  # Total time               : 0.073 s
% 0.43/0.56  # Maximum resident set size: 2144 pages
% 0.43/0.56  % E---3.1 exiting
% 0.43/0.56  % E exiting
%------------------------------------------------------------------------------