TSTP Solution File: ITP048^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP048^1 : 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 22:16:03 EDT 2024

% Result   : Theorem 1.10s 0.68s
% Output   : CNFRefutation 1.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   47 (  20 unt;  15 typ;   0 def)
%            Number of atoms       :   54 (  13 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  284 (  19   ~;  14   |;   1   &; 243   @)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :   40 (   2   ^  38   !;   0   ?;  40   :)

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

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

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

thf(decl_sort4,type,
    list_P559422087at_nat: $tType ).

thf(decl_33,type,
    min_dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat ).

thf(decl_36,type,
    plus_plus_nat: nat > nat > nat ).

thf(decl_37,type,
    size_s1990949619at_nat: list_P559422087at_nat > nat ).

thf(decl_39,type,
    ord_less_nat: nat > nat > $o ).

thf(decl_40,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(decl_43,type,
    c: product_prod_nat_nat > capacity ).

thf(decl_47,type,
    p1a: list_P559422087at_nat ).

thf(decl_49,type,
    p2_a: list_P559422087at_nat ).

thf(decl_51,type,
    s: nat ).

thf(decl_52,type,
    t: nat ).

thf(decl_54,type,
    ua: nat ).

thf(fact_75_add_Ocommute,axiom,
    ( plus_plus_nat
    = ( ^ [X32: nat,X33: nat] : ( plus_plus_nat @ X33 @ X32 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add_Ocommute) ).

thf(conj_0,conjecture,
    ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(fact_99_add__strict__mono,axiom,
    ! [X5: nat,X6: nat,X4: nat,X13: nat] :
      ( ( ord_less_nat @ X5 @ X6 )
     => ( ( ord_less_nat @ X4 @ X13 )
       => ( ord_less_nat @ ( plus_plus_nat @ X5 @ X4 ) @ ( plus_plus_nat @ X6 @ X13 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_add__strict__mono) ).

thf(fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062,axiom,
    ( ( min_dist_capacity @ c @ s @ t )
    = ( plus_plus_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( min_dist_capacity @ c @ ua @ t ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062) ).

thf(fact_56_le__neq__implies__less,axiom,
    ! [X2: nat,X3: nat] :
      ( ( ord_less_eq_nat @ X2 @ X3 )
     => ( ( X2 != X3 )
       => ( ord_less_nat @ X2 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_le__neq__implies__less) ).

thf(fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062,axiom,
    ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( size_s1990949619at_nat @ p1a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062) ).

thf(fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062,axiom,
    ord_less_eq_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062) ).

thf(fact_3_nat__add__left__cancel__less,axiom,
    ! [X1: nat,X2: nat,X3: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ X1 @ X2 ) @ ( plus_plus_nat @ X1 @ X3 ) )
    <=> ( ord_less_nat @ X2 @ X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nat__add__left__cancel__less) ).

thf(c_0_8,plain,
    ! [X715: nat,X716: nat] :
      ( ( plus_plus_nat @ X715 @ X716 )
      = ( plus_plus_nat @ X716 @ X715 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_75_add_Ocommute])]) ).

thf(c_0_9,negated_conjecture,
    ~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

thf(c_0_10,plain,
    ! [X991: nat,X992: nat] :
      ( ( plus_plus_nat @ X991 @ X992 )
      = ( plus_plus_nat @ X992 @ X991 ) ),
    inference(variable_rename,[status(thm)],[c_0_8]) ).

thf(c_0_11,negated_conjecture,
    ~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_9]) ).

thf(c_0_12,plain,
    ! [X1044: nat,X1045: nat,X1046: nat,X1047: nat] :
      ( ~ ( ord_less_nat @ X1044 @ X1045 )
      | ~ ( ord_less_nat @ X1046 @ X1047 )
      | ( ord_less_nat @ ( plus_plus_nat @ X1044 @ X1046 ) @ ( plus_plus_nat @ X1045 @ X1047 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_99_add__strict__mono])])]) ).

thf(c_0_13,plain,
    ( ( min_dist_capacity @ c @ s @ t )
    = ( plus_plus_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( min_dist_capacity @ c @ ua @ t ) ) ),
    inference(split_conjunct,[status(thm)],[fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062]) ).

thf(c_0_14,plain,
    ! [X2: nat,X1: nat] :
      ( ( plus_plus_nat @ X1 @ X2 )
      = ( plus_plus_nat @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_15,negated_conjecture,
    ~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_16,plain,
    ! [X1: nat,X2: nat,X3: nat,X4: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ X1 @ X3 ) @ ( plus_plus_nat @ X2 @ X4 ) )
      | ~ ( ord_less_nat @ X1 @ X2 )
      | ~ ( ord_less_nat @ X3 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_17,plain,
    ( ( plus_plus_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( min_dist_capacity @ c @ s @ ua ) )
    = ( min_dist_capacity @ c @ s @ t ) ),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_18,plain,
    ! [X2: nat,X3: nat] :
      ( ( ord_less_eq_nat @ X2 @ X3 )
     => ( ( X2 != X3 )
       => ( ord_less_nat @ X2 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_56_le__neq__implies__less]) ).

thf(c_0_19,negated_conjecture,
    ~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p2_a ) @ ( size_s1990949619at_nat @ p1a ) ) ),
    inference(rw,[status(thm)],[c_0_15,c_0_14]) ).

thf(c_0_20,plain,
    ! [X2: nat,X1: nat] :
      ( ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ X1 @ X2 ) )
      | ~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ X2 )
      | ~ ( ord_less_nat @ ( min_dist_capacity @ c @ ua @ t ) @ X1 ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

thf(c_0_21,plain,
    ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( size_s1990949619at_nat @ p1a ),
    inference(split_conjunct,[status(thm)],[fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062]) ).

thf(c_0_22,plain,
    ! [X748: nat,X749: nat] :
      ( ~ ( ord_less_eq_nat @ X748 @ X749 )
      | ( X748 = X749 )
      | ( ord_less_nat @ X748 @ X749 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).

thf(c_0_23,negated_conjecture,
    ~ ( ord_less_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

thf(c_0_24,plain,
    ! [X1: nat,X2: nat] :
      ( ( X1 = X2 )
      | ( ord_less_nat @ X1 @ X2 )
      | ~ ( ord_less_eq_nat @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_25,plain,
    ord_less_eq_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ),
    inference(split_conjunct,[status(thm)],[fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062]) ).

thf(c_0_26,plain,
    ! [X886: nat,X887: nat,X888: nat] :
      ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ X886 @ X887 ) @ ( plus_plus_nat @ X886 @ X888 ) )
        | ( ord_less_nat @ X887 @ X888 ) )
      & ( ~ ( ord_less_nat @ X887 @ X888 )
        | ( ord_less_nat @ ( plus_plus_nat @ X886 @ X887 ) @ ( plus_plus_nat @ X886 @ X888 ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_nat__add__left__cancel__less])])]) ).

thf(c_0_27,negated_conjecture,
    ( ( min_dist_capacity @ c @ ua @ t )
    = ( size_s1990949619at_nat @ p2_a ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

thf(c_0_28,plain,
    ! [X1: nat,X3: nat,X2: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ X3 @ X1 ) @ ( plus_plus_nat @ X3 @ X2 ) )
      | ~ ( ord_less_nat @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_29,plain,
    ( ( plus_plus_nat @ ( size_s1990949619at_nat @ p2_a ) @ ( min_dist_capacity @ c @ s @ ua ) )
    = ( min_dist_capacity @ c @ s @ t ) ),
    inference(rw,[status(thm)],[c_0_17,c_0_27]) ).

thf(c_0_30,plain,
    ! [X1: nat] :
      ( ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p2_a ) @ X1 ) )
      | ~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ X1 ) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

thf(c_0_31,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_30]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : ITP048^1 : TPTP v8.2.0. Released v7.5.0.
% 0.03/0.13  % 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 16:09:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.49  Running higher-order theorem proving
% 0.20/0.49  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
% 1.10/0.68  # Version: 3.1.0-ho
% 1.10/0.68  # Preprocessing class: HSLSSMSMSSMCHSA.
% 1.10/0.68  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.10/0.68  # Starting post_as_ho6 with 1500s (5) cores
% 1.10/0.68  # Starting post_as_ho8 with 300s (1) cores
% 1.10/0.68  # Starting new_bool_3 with 300s (1) cores
% 1.10/0.68  # Starting new_bool_1 with 300s (1) cores
% 1.10/0.68  # post_as_ho6 with pid 14770 completed with status 0
% 1.10/0.68  # Result found by post_as_ho6
% 1.10/0.68  # Preprocessing class: HSLSSMSMSSMCHSA.
% 1.10/0.68  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.10/0.68  # Starting post_as_ho6 with 1500s (5) cores
% 1.10/0.68  # SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 1.10/0.68  # Search class: HGHSM-FSLM32-SHSFFSBC
% 1.10/0.68  # partial match(1): HGHSM-FSLM32-MHSFFSBC
% 1.10/0.68  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.10/0.68  # Starting ehoh_best4 with 728s (1) cores
% 1.10/0.68  # Starting post_as_ho6 with 151s (1) cores
% 1.10/0.68  # Starting sh1 with 136s (1) cores
% 1.10/0.68  # Starting almost_fo_4 with 136s (1) cores
% 1.10/0.68  # Starting new_bool_8 with 136s (1) cores
% 1.10/0.68  # post_as_ho6 with pid 14776 completed with status 0
% 1.10/0.68  # Result found by post_as_ho6
% 1.10/0.68  # Preprocessing class: HSLSSMSMSSMCHSA.
% 1.10/0.68  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.10/0.68  # Starting post_as_ho6 with 1500s (5) cores
% 1.10/0.68  # SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 1.10/0.68  # Search class: HGHSM-FSLM32-SHSFFSBC
% 1.10/0.68  # partial match(1): HGHSM-FSLM32-MHSFFSBC
% 1.10/0.68  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.10/0.68  # Starting ehoh_best4 with 728s (1) cores
% 1.10/0.68  # Starting post_as_ho6 with 151s (1) cores
% 1.10/0.68  # Preprocessing time       : 0.006 s
% 1.10/0.68  # Presaturation interreduction done
% 1.10/0.68  
% 1.10/0.68  # Proof found!
% 1.10/0.68  # SZS status Theorem
% 1.10/0.68  # SZS output start CNFRefutation
% See solution above
% 1.10/0.68  # Parsed axioms                        : 315
% 1.10/0.68  # Removed by relevancy pruning/SinE    : 107
% 1.10/0.68  # Initial clauses                      : 364
% 1.10/0.68  # Removed in clause preprocessing      : 17
% 1.10/0.68  # Initial clauses in saturation        : 347
% 1.10/0.68  # Processed clauses                    : 920
% 1.10/0.68  # ...of these trivial                  : 28
% 1.10/0.68  # ...subsumed                          : 360
% 1.10/0.68  # ...remaining for further processing  : 532
% 1.10/0.68  # Other redundant clauses eliminated   : 81
% 1.10/0.68  # Clauses deleted for lack of memory   : 0
% 1.10/0.68  # Backward-subsumed                    : 12
% 1.10/0.68  # Backward-rewritten                   : 32
% 1.10/0.68  # Generated clauses                    : 4454
% 1.10/0.68  # ...of the previous two non-redundant : 4202
% 1.10/0.68  # ...aggressively subsumed             : 0
% 1.10/0.68  # Contextual simplify-reflections      : 4
% 1.10/0.68  # Paramodulations                      : 4360
% 1.10/0.68  # Factorizations                       : 6
% 1.10/0.68  # NegExts                              : 0
% 1.10/0.68  # Equation resolutions                 : 86
% 1.10/0.68  # Disequality decompositions           : 0
% 1.10/0.68  # Total rewrite steps                  : 619
% 1.10/0.68  # ...of those cached                   : 463
% 1.10/0.68  # Propositional unsat checks           : 0
% 1.10/0.68  #    Propositional check models        : 0
% 1.10/0.68  #    Propositional check unsatisfiable : 0
% 1.10/0.68  #    Propositional clauses             : 0
% 1.10/0.68  #    Propositional clauses after purity: 0
% 1.10/0.68  #    Propositional unsat core size     : 0
% 1.10/0.68  #    Propositional preprocessing time  : 0.000
% 1.10/0.68  #    Propositional encoding time       : 0.000
% 1.10/0.68  #    Propositional solver time         : 0.000
% 1.10/0.68  #    Success case prop preproc time    : 0.000
% 1.10/0.68  #    Success case prop encoding time   : 0.000
% 1.10/0.68  #    Success case prop solver time     : 0.000
% 1.10/0.68  # Current number of processed clauses  : 279
% 1.10/0.68  #    Positive orientable unit clauses  : 46
% 1.10/0.68  #    Positive unorientable unit clauses: 2
% 1.10/0.68  #    Negative unit clauses             : 27
% 1.10/0.68  #    Non-unit-clauses                  : 204
% 1.10/0.68  # Current number of unprocessed clauses: 3773
% 1.10/0.68  # ...number of literals in the above   : 10087
% 1.10/0.68  # Current number of archived formulas  : 0
% 1.10/0.68  # Current number of archived clauses   : 200
% 1.10/0.68  # Clause-clause subsumption calls (NU) : 6438
% 1.10/0.68  # Rec. Clause-clause subsumption calls : 5215
% 1.10/0.68  # Non-unit clause-clause subsumptions  : 265
% 1.10/0.68  # Unit Clause-clause subsumption calls : 534
% 1.10/0.68  # Rewrite failures with RHS unbound    : 0
% 1.10/0.68  # BW rewrite match attempts            : 77
% 1.10/0.68  # BW rewrite match successes           : 43
% 1.10/0.68  # Condensation attempts                : 920
% 1.10/0.68  # Condensation successes               : 16
% 1.10/0.68  # Termbank termtop insertions          : 96598
% 1.10/0.68  # Search garbage collected termcells   : 8403
% 1.10/0.68  
% 1.10/0.68  # -------------------------------------------------
% 1.10/0.68  # User time                : 0.148 s
% 1.10/0.68  # System time              : 0.010 s
% 1.10/0.68  # Total time               : 0.158 s
% 1.10/0.68  # Maximum resident set size: 3708 pages
% 1.10/0.68  
% 1.10/0.68  # -------------------------------------------------
% 1.10/0.68  # User time                : 0.683 s
% 1.10/0.68  # System time              : 0.038 s
% 1.10/0.68  # Total time               : 0.720 s
% 1.10/0.68  # Maximum resident set size: 2160 pages
% 1.10/0.68  % E---3.1 exiting
% 1.10/0.68  % E exiting
%------------------------------------------------------------------------------