TSTP Solution File: ITP094^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP094^1 : TPTP v8.2.0. Released v7.5.0.
% 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 : Mon May 20 22:16:16 EDT 2024

% Result   : Theorem 0.20s 0.57s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   46 (  10 unt;  13 typ;   0 def)
%            Number of atoms       :   88 (  40 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  245 (  26   ~;  28   |;   3   &; 182   @)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :   38 (   6   ^  32   !;   0   ?;  38   :)

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

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

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

thf(decl_26,type,
    finite_finite_real: set_real > $o ).

thf(decl_37,type,
    zero_zero_poly_real: poly_real ).

thf(decl_38,type,
    zero_zero_real: real ).

thf(decl_72,type,
    pderiv_real: poly_real > poly_real ).

thf(decl_77,type,
    poly_real2: poly_real > real > real ).

thf(decl_108,type,
    collect_real: ( real > $o ) > set_real ).

thf(decl_114,type,
    p: poly_real ).

thf(decl_119,type,
    esk4_2: ( real > $o ) > ( real > $o ) > real ).

thf(decl_123,type,
    epred1_0: real > $o ).

thf(decl_124,type,
    epred2_1: poly_real > real > $o ).

thf(fact_125_Collect__cong,axiom,
    ! [X170: real > $o,X171: real > $o] :
      ( ! [X42: real] :
          ( ( X170 @ X42 )
        <=> ( X171 @ X42 ) )
     => ( ( collect_real @ X170 )
        = ( collect_real @ X171 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Collect__cong) ).

thf(fact_2_poly__roots__finite,axiom,
    ! [X5: poly_real] :
      ( ( X5 != zero_zero_poly_real )
     => ( finite_finite_real
        @ ( collect_real
          @ ^ [X6: real] :
              ( ( poly_real2 @ X5 @ X6 )
              = zero_zero_real ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_poly__roots__finite) ).

thf(conj_0,conjecture,
    ( finite_finite_real
    @ ( collect_real
      @ ^ [X339: real] :
          ( ( poly_real2 @ ( pderiv_real @ p ) @ X339 )
          = zero_zero_real ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(fact_4__092_060open_062pderiv_Ap_A_092_060noteq_062_A0_092_060close_062,axiom,
    ( ( pderiv_real @ p )
   != zero_zero_poly_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062pderiv_Ap_A_092_060noteq_062_A0_092_060close_062) ).

thf(c_0_4,plain,
    ! [X452: real,X453: poly_real] :
      ( ( ~ ( epred2_1 @ X453 @ X452 )
        | ( ( poly_real2 @ X453 @ X452 )
          = zero_zero_real ) )
      & ( ( ( poly_real2 @ X453 @ X452 )
         != zero_zero_real )
        | ( epred2_1 @ X453 @ X452 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).

thf(c_0_5,plain,
    ! [X398: real > $o,X399: real > $o] :
      ( ( ~ ( X398 @ ( esk4_2 @ X398 @ X399 ) )
        | ~ ( X399 @ ( esk4_2 @ X398 @ X399 ) )
        | ( ( collect_real @ X398 )
          = ( collect_real @ X399 ) ) )
      & ( ( X398 @ ( esk4_2 @ X398 @ X399 ) )
        | ( X399 @ ( esk4_2 @ X398 @ X399 ) )
        | ( ( collect_real @ X398 )
          = ( collect_real @ X399 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_125_Collect__cong])])])])]) ).

thf(c_0_6,plain,
    ! [X454: real] :
      ( ( ~ ( epred1_0 @ X454 )
        | ( ( poly_real2 @ ( pderiv_real @ p ) @ X454 )
          = zero_zero_real ) )
      & ( ( ( poly_real2 @ ( pderiv_real @ p ) @ X454 )
         != zero_zero_real )
        | ( epred1_0 @ X454 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).

thf(c_0_7,plain,
    ! [X4: poly_real,X6: real] :
      ( ( ( poly_real2 @ X4 @ X6 )
        = zero_zero_real )
      | ~ ( epred2_1 @ X4 @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_8,plain,
    ! [X15: real > $o,X16: real > $o] :
      ( ( X15 @ ( esk4_2 @ X15 @ X16 ) )
      | ( X16 @ ( esk4_2 @ X15 @ X16 ) )
      | ( ( collect_real @ X15 )
        = ( collect_real @ X16 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_9,plain,
    ! [X5: poly_real] :
      ( ( X5 != zero_zero_poly_real )
     => ( finite_finite_real
        @ ( collect_real
          @ ^ [Z0: real] :
              ( ( poly_real2 @ X5 @ Z0 )
              = zero_zero_real ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_2_poly__roots__finite])]) ).

thf(c_0_10,plain,
    ! [X15: real > $o,X16: real > $o] :
      ( ( ( collect_real @ X15 )
        = ( collect_real @ X16 ) )
      | ~ ( X15 @ ( esk4_2 @ X15 @ X16 ) )
      | ~ ( X16 @ ( esk4_2 @ X15 @ X16 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_11,plain,
    ! [X4: poly_real,X6: real] :
      ( ( epred2_1 @ X4 @ X6 )
      | ( ( poly_real2 @ X4 @ X6 )
       != zero_zero_real ) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_12,plain,
    ! [X6: real] :
      ( ( epred1_0 @ X6 )
      | ( ( poly_real2 @ ( pderiv_real @ p ) @ X6 )
       != zero_zero_real ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_13,plain,
    ! [X15: real > $o,X4: poly_real] :
      ( ( ( poly_real2 @ X4 @ ( esk4_2 @ X15 @ ( epred2_1 @ X4 ) ) )
        = zero_zero_real )
      | ( ( collect_real @ X15 )
        = ( collect_real @ ( epred2_1 @ X4 ) ) )
      | ( X15 @ ( esk4_2 @ X15 @ ( epred2_1 @ X4 ) ) ) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

thf(c_0_14,negated_conjecture,
    ~ ( finite_finite_real
      @ ( collect_real
        @ ^ [Z0: real] :
            ( ( poly_real2 @ ( pderiv_real @ p ) @ Z0 )
            = zero_zero_real ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])])]) ).

thf(c_0_15,plain,
    ! [X382: poly_real] :
      ( ( X382 = zero_zero_poly_real )
      | ( finite_finite_real
        @ ( collect_real
          @ ^ [Z0: real] :
              ( ( poly_real2 @ X382 @ Z0 )
              = zero_zero_real ) ) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).

thf(c_0_16,plain,
    ! [X431: real,X4: poly_real] :
      ( ( epred2_1 @ X4 @ X431 )
    <=> ( ( poly_real2 @ X4 @ X431 )
        = zero_zero_real ) ),
    introduced(definition) ).

thf(c_0_17,plain,
    ! [X15: real > $o,X4: poly_real] :
      ( ( ( collect_real @ X15 )
        = ( collect_real @ ( epred2_1 @ X4 ) ) )
      | ( ( poly_real2 @ X4 @ ( esk4_2 @ X15 @ ( epred2_1 @ X4 ) ) )
       != zero_zero_real )
      | ~ ( X15 @ ( esk4_2 @ X15 @ ( epred2_1 @ X4 ) ) ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_18,plain,
    ! [X6: real] :
      ( ( ( poly_real2 @ ( pderiv_real @ p ) @ X6 )
        = zero_zero_real )
      | ~ ( epred1_0 @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_19,plain,
    ! [X15: real > $o] :
      ( ( ( collect_real @ X15 )
        = ( collect_real @ ( epred2_1 @ ( pderiv_real @ p ) ) ) )
      | ( epred1_0 @ ( esk4_2 @ X15 @ ( epred2_1 @ ( pderiv_real @ p ) ) ) )
      | ( X15 @ ( esk4_2 @ X15 @ ( epred2_1 @ ( pderiv_real @ p ) ) ) ) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_20,plain,
    ( ( pderiv_real @ p )
   != zero_zero_poly_real ),
    inference(fof_simplification,[status(thm)],[fact_4__092_060open_062pderiv_Ap_A_092_060noteq_062_A0_092_060close_062]) ).

thf(c_0_21,negated_conjecture,
    ~ ( finite_finite_real
      @ ( collect_real
        @ ^ [Z0: real] :
            ( ( poly_real2 @ ( pderiv_real @ p ) @ Z0 )
            = zero_zero_real ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_14]) ).

thf(c_0_22,plain,
    ! [X430: real] :
      ( ( epred1_0 @ X430 )
    <=> ( ( poly_real2 @ ( pderiv_real @ p ) @ X430 )
        = zero_zero_real ) ),
    introduced(definition) ).

thf(c_0_23,plain,
    ! [X4: poly_real] :
      ( ( X4 = zero_zero_poly_real )
      | ( ( finite_finite_real @ ( collect_real @ ( epred2_1 @ X4 ) ) )
        = $true ) ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_15]),c_0_16]) ).

thf(c_0_24,plain,
    ! [X15: real > $o] :
      ( ( ( collect_real @ X15 )
        = ( collect_real @ ( epred2_1 @ ( pderiv_real @ p ) ) ) )
      | ~ ( epred1_0 @ ( esk4_2 @ X15 @ ( epred2_1 @ ( pderiv_real @ p ) ) ) )
      | ~ ( X15 @ ( esk4_2 @ X15 @ ( epred2_1 @ ( pderiv_real @ p ) ) ) ) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

thf(c_0_25,plain,
    ( ( ( collect_real @ ( epred2_1 @ ( pderiv_real @ p ) ) )
      = ( collect_real @ epred1_0 ) )
    | ( epred1_0 @ ( esk4_2 @ epred1_0 @ ( epred2_1 @ ( pderiv_real @ p ) ) ) ) ),
    inference(ef,[status(thm)],[c_0_19]) ).

thf(c_0_26,plain,
    ( ( pderiv_real @ p )
   != zero_zero_poly_real ),
    inference(fof_nnf,[status(thm)],[c_0_20]) ).

thf(c_0_27,negated_conjecture,
    ( ( finite_finite_real @ ( collect_real @ epred1_0 ) )
   != $true ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_21]),c_0_22]) ).

thf(c_0_28,plain,
    ! [X4: poly_real] :
      ( ( X4 = zero_zero_poly_real )
      | ( finite_finite_real @ ( collect_real @ ( epred2_1 @ X4 ) ) ) ),
    inference(cn,[status(thm)],[c_0_23]) ).

thf(c_0_29,plain,
    ( ( collect_real @ ( epred2_1 @ ( pderiv_real @ p ) ) )
    = ( collect_real @ epred1_0 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).

thf(c_0_30,plain,
    ( ( pderiv_real @ p )
   != zero_zero_poly_real ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_31,negated_conjecture,
    ~ ( finite_finite_real @ ( collect_real @ epred1_0 ) ),
    inference(cn,[status(thm)],[c_0_27]) ).

thf(c_0_32,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : ITP094^1 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n012.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 17:36:08 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  Running higher-order theorem proving
% 0.20/0.48  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
% 0.20/0.57  # Version: 3.1.0-ho
% 0.20/0.57  # Preprocessing class: HSLSSMSMSSLNHSA.
% 0.20/0.57  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.57  # Starting ho_unfolding_8 with 900s (3) cores
% 0.20/0.57  # Starting new_bool_8 with 300s (1) cores
% 0.20/0.57  # Starting post_as_ho6 with 300s (1) cores
% 0.20/0.57  # Starting ho_unfolding_1 with 300s (1) cores
% 0.20/0.57  # Starting full_lambda_4 with 300s (1) cores
% 0.20/0.57  # Starting pre_casc_5 with 300s (1) cores
% 0.20/0.57  # post_as_ho6 with pid 12709 completed with status 0
% 0.20/0.57  # Result found by post_as_ho6
% 0.20/0.57  # Preprocessing class: HSLSSMSMSSLNHSA.
% 0.20/0.57  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.57  # Starting ho_unfolding_8 with 900s (3) cores
% 0.20/0.57  # Starting new_bool_8 with 300s (1) cores
% 0.20/0.57  # Starting post_as_ho6 with 300s (1) cores
% 0.20/0.57  # SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 0.20/0.57  # Search class: HGUSM-FFMM31-MHSFFSBN
% 0.20/0.57  # partial match(2): HGUSM-FSLM31-MHSFFSBN
% 0.20/0.57  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.57  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.57  # new_ho_10 with pid 12718 completed with status 0
% 0.20/0.57  # Result found by new_ho_10
% 0.20/0.57  # Preprocessing class: HSLSSMSMSSLNHSA.
% 0.20/0.57  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.57  # Starting ho_unfolding_8 with 900s (3) cores
% 0.20/0.57  # Starting new_bool_8 with 300s (1) cores
% 0.20/0.57  # Starting post_as_ho6 with 300s (1) cores
% 0.20/0.57  # SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 0.20/0.57  # Search class: HGUSM-FFMM31-MHSFFSBN
% 0.20/0.57  # partial match(2): HGUSM-FSLM31-MHSFFSBN
% 0.20/0.57  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.57  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.57  # Preprocessing time       : 0.004 s
% 0.20/0.57  # Presaturation interreduction done
% 0.20/0.57  
% 0.20/0.57  # Proof found!
% 0.20/0.57  # SZS status Theorem
% 0.20/0.57  # SZS output start CNFRefutation
% See solution above
% 0.20/0.57  # Parsed axioms                        : 450
% 0.20/0.57  # Removed by relevancy pruning/SinE    : 413
% 0.20/0.57  # Initial clauses                      : 69
% 0.20/0.57  # Removed in clause preprocessing      : 9
% 0.20/0.57  # Initial clauses in saturation        : 60
% 0.20/0.57  # Processed clauses                    : 300
% 0.20/0.57  # ...of these trivial                  : 1
% 0.20/0.57  # ...subsumed                          : 55
% 0.20/0.57  # ...remaining for further processing  : 244
% 0.20/0.57  # Other redundant clauses eliminated   : 2
% 0.20/0.57  # Clauses deleted for lack of memory   : 0
% 0.20/0.57  # Backward-subsumed                    : 2
% 0.20/0.57  # Backward-rewritten                   : 7
% 0.20/0.57  # Generated clauses                    : 1086
% 0.20/0.57  # ...of the previous two non-redundant : 994
% 0.20/0.57  # ...aggressively subsumed             : 0
% 0.20/0.57  # Contextual simplify-reflections      : 1
% 0.20/0.57  # Paramodulations                      : 1032
% 0.20/0.57  # Factorizations                       : 44
% 0.20/0.57  # NegExts                              : 2
% 0.20/0.57  # Equation resolutions                 : 8
% 0.20/0.57  # Disequality decompositions           : 0
% 0.20/0.57  # Total rewrite steps                  : 261
% 0.20/0.57  # ...of those cached                   : 237
% 0.20/0.57  # Propositional unsat checks           : 0
% 0.20/0.57  #    Propositional check models        : 0
% 0.20/0.57  #    Propositional check unsatisfiable : 0
% 0.20/0.57  #    Propositional clauses             : 0
% 0.20/0.57  #    Propositional clauses after purity: 0
% 0.20/0.57  #    Propositional unsat core size     : 0
% 0.20/0.57  #    Propositional preprocessing time  : 0.000
% 0.20/0.57  #    Propositional encoding time       : 0.000
% 0.20/0.57  #    Propositional solver time         : 0.000
% 0.20/0.57  #    Success case prop preproc time    : 0.000
% 0.20/0.57  #    Success case prop encoding time   : 0.000
% 0.20/0.57  #    Success case prop solver time     : 0.000
% 0.20/0.57  # Current number of processed clauses  : 177
% 0.20/0.57  #    Positive orientable unit clauses  : 17
% 0.20/0.57  #    Positive unorientable unit clauses: 0
% 0.20/0.57  #    Negative unit clauses             : 9
% 0.20/0.57  #    Non-unit-clauses                  : 151
% 0.20/0.57  # Current number of unprocessed clauses: 787
% 0.20/0.57  # ...number of literals in the above   : 2516
% 0.20/0.57  # Current number of archived formulas  : 0
% 0.20/0.57  # Current number of archived clauses   : 65
% 0.20/0.57  # Clause-clause subsumption calls (NU) : 3711
% 0.20/0.57  # Rec. Clause-clause subsumption calls : 2063
% 0.20/0.57  # Non-unit clause-clause subsumptions  : 35
% 0.20/0.57  # Unit Clause-clause subsumption calls : 10
% 0.20/0.57  # Rewrite failures with RHS unbound    : 0
% 0.20/0.57  # BW rewrite match attempts            : 2
% 0.20/0.57  # BW rewrite match successes           : 1
% 0.20/0.57  # Condensation attempts                : 300
% 0.20/0.57  # Condensation successes               : 2
% 0.20/0.57  # Termbank termtop insertions          : 32187
% 0.20/0.57  # Search garbage collected termcells   : 3395
% 0.20/0.57  
% 0.20/0.57  # -------------------------------------------------
% 0.20/0.57  # User time                : 0.059 s
% 0.20/0.57  # System time              : 0.005 s
% 0.20/0.57  # Total time               : 0.064 s
% 0.20/0.57  # Maximum resident set size: 2824 pages
% 0.20/0.57  
% 0.20/0.57  # -------------------------------------------------
% 0.20/0.57  # User time                : 0.070 s
% 0.20/0.57  # System time              : 0.008 s
% 0.20/0.57  # Total time               : 0.078 s
% 0.20/0.57  # Maximum resident set size: 2384 pages
% 0.20/0.57  % E---3.1 exiting
% 0.20/0.57  % E exiting
%------------------------------------------------------------------------------