TSTP Solution File: ITP125^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP125^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n027.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 22:16:25 EDT 2024

% Result   : Theorem 1.18s 0.65s
% Output   : CNFRefutation 1.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   36 (  11 unt;  12 typ;   0 def)
%            Number of atoms       :   42 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  144 (  20   ~;  11   |;   1   &; 106   @)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :   36 (   0   ^  36   !;   0   ?;  36   :)

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

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

thf(decl_sort3,type,
    trace_1367752404list_a: $tType ).

thf(decl_sort4,type,
    prefix1027212443list_a: $tType ).

thf(decl_26,type,
    monito1457594016ress_a: trace_1367752404list_a > formula_a > nat > nat ).

thf(decl_27,type,
    ord_less_nat: nat > nat > $o ).

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

thf(decl_32,type,
    plen_P694648887list_a: prefix1027212443list_a > nat ).

thf(decl_36,type,
    phi_1: formula_a ).

thf(decl_38,type,
    pi: prefix1027212443list_a ).

thf(decl_39,type,
    sigma: trace_1367752404list_a ).

thf(decl_46,type,
    k: nat ).

thf(conj_0,conjecture,
    ord_less_nat @ k @ ( plen_P694648887list_a @ pi ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(fact_163_not__le,axiom,
    ! [X8: nat,X9: nat] :
      ( ~ ( ord_less_eq_nat @ X8 @ X9 )
    <=> ( ord_less_nat @ X9 @ X8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_not__le) ).

thf(fact_145_leD,axiom,
    ! [X9: nat,X8: nat] :
      ( ( ord_less_eq_nat @ X9 @ X8 )
     => ~ ( ord_less_nat @ X8 @ X9 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_leD) ).

thf(fact_194_dual__order_Ostrict__trans2,axiom,
    ! [X13: nat,X37: nat,X238: nat] :
      ( ( ord_less_nat @ X13 @ X37 )
     => ( ( ord_less_eq_nat @ X238 @ X13 )
       => ( ord_less_nat @ X238 @ X37 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_dual__order_Ostrict__trans2) ).

thf(fact_20_progress__le,axiom,
    ! [X17: trace_1367752404list_a,X18: formula_a,X11: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ X17 @ X18 @ X11 ) @ X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_progress__le) ).

thf(fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
    ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(c_0_6,negated_conjecture,
    ~ ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

thf(c_0_7,plain,
    ! [X8: nat,X9: nat] :
      ( ~ ( ord_less_eq_nat @ X8 @ X9 )
    <=> ( ord_less_nat @ X9 @ X8 ) ),
    inference(fof_simplification,[status(thm)],[fact_163_not__le]) ).

thf(c_0_8,negated_conjecture,
    ~ ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ),
    inference(fof_nnf,[status(thm)],[c_0_6]) ).

thf(c_0_9,plain,
    ! [X1673: nat,X1674: nat] :
      ( ( ( ord_less_eq_nat @ X1673 @ X1674 )
        | ( ord_less_nat @ X1674 @ X1673 ) )
      & ( ~ ( ord_less_nat @ X1674 @ X1673 )
        | ~ ( ord_less_eq_nat @ X1673 @ X1674 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

thf(c_0_10,plain,
    ! [X9: nat,X8: nat] :
      ( ( ord_less_eq_nat @ X9 @ X8 )
     => ~ ( ord_less_nat @ X8 @ X9 ) ),
    inference(fof_simplification,[status(thm)],[fact_145_leD]) ).

thf(c_0_11,plain,
    ! [X1746: nat,X1747: nat,X1748: nat] :
      ( ~ ( ord_less_nat @ X1746 @ X1747 )
      | ~ ( ord_less_eq_nat @ X1748 @ X1746 )
      | ( ord_less_nat @ X1748 @ X1747 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_194_dual__order_Ostrict__trans2])])]) ).

thf(c_0_12,negated_conjecture,
    ~ ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_13,plain,
    ! [X2: nat,X1: nat] :
      ( ( ord_less_eq_nat @ X1 @ X2 )
      | ( ord_less_nat @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_14,plain,
    ! [X1589: nat,X1590: nat] :
      ( ~ ( ord_less_eq_nat @ X1589 @ X1590 )
      | ~ ( ord_less_nat @ X1590 @ X1589 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

thf(c_0_15,plain,
    ! [X3: nat,X2: nat,X1: nat] :
      ( ( ord_less_nat @ X3 @ X2 )
      | ~ ( ord_less_nat @ X1 @ X2 )
      | ~ ( ord_less_eq_nat @ X3 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_16,negated_conjecture,
    ord_less_eq_nat @ ( plen_P694648887list_a @ pi ) @ k,
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_17,plain,
    ! [X2: nat,X1: nat] :
      ( ~ ( ord_less_eq_nat @ X1 @ X2 )
      | ~ ( ord_less_nat @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_18,negated_conjecture,
    ! [X1: nat] :
      ( ( ord_less_nat @ ( plen_P694648887list_a @ pi ) @ X1 )
      | ~ ( ord_less_nat @ k @ X1 ) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

thf(c_0_19,plain,
    ! [X1172: trace_1367752404list_a,X1173: formula_a,X1174: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ X1172 @ X1173 @ X1174 ) @ X1174 ),
    inference(variable_rename,[status(thm)],[fact_20_progress__le]) ).

thf(c_0_20,negated_conjecture,
    ! [X1: nat] :
      ( ~ ( ord_less_eq_nat @ X1 @ ( plen_P694648887list_a @ pi ) )
      | ~ ( ord_less_nat @ k @ X1 ) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

thf(c_0_21,plain,
    ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
    inference(split_conjunct,[status(thm)],[fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062]) ).

thf(c_0_22,plain,
    ! [X18: formula_a,X17: trace_1367752404list_a,X1: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ X17 @ X18 @ X1 ) @ X1 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_23,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : ITP125^1 : TPTP v8.2.0. Released v7.5.0.
% 0.13/0.14  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n027.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 18:38:37 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.49  Running higher-order theorem proving
% 0.20/0.49  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
% 1.18/0.65  # Version: 3.1.0-ho
% 1.18/0.65  # Preprocessing class: HSLSSMSMSSSNHFA.
% 1.18/0.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.18/0.65  # Starting new_ho_10 with 1500s (5) cores
% 1.18/0.65  # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.18/0.65  # Starting full_lambda_6 with 300s (1) cores
% 1.18/0.65  # Starting full_lambda_9 with 300s (1) cores
% 1.18/0.65  # new_ho_10 with pid 24932 completed with status 0
% 1.18/0.65  # Result found by new_ho_10
% 1.18/0.65  # Preprocessing class: HSLSSMSMSSSNHFA.
% 1.18/0.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.18/0.65  # Starting new_ho_10 with 1500s (5) cores
% 1.18/0.65  # No SInE strategy applied
% 1.18/0.65  # Search class: HGHSM-FSLM32-MHFFFSBC
% 1.18/0.65  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.18/0.65  # Starting additional_ho_6 with 811s (1) cores
% 1.18/0.65  # Starting new_ho_10 with 151s (1) cores
% 1.18/0.65  # Starting new_ho_3 with 136s (1) cores
% 1.18/0.65  # Starting sh3 with 136s (1) cores
% 1.18/0.65  # Starting pre_casc_2 with 136s (1) cores
% 1.18/0.65  # pre_casc_2 with pid 24943 completed with status 0
% 1.18/0.65  # Result found by pre_casc_2
% 1.18/0.65  # Preprocessing class: HSLSSMSMSSSNHFA.
% 1.18/0.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.18/0.65  # Starting new_ho_10 with 1500s (5) cores
% 1.18/0.65  # No SInE strategy applied
% 1.18/0.65  # Search class: HGHSM-FSLM32-MHFFFSBC
% 1.18/0.65  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.18/0.65  # Starting additional_ho_6 with 811s (1) cores
% 1.18/0.65  # Starting new_ho_10 with 151s (1) cores
% 1.18/0.65  # Starting new_ho_3 with 136s (1) cores
% 1.18/0.65  # Starting sh3 with 136s (1) cores
% 1.18/0.65  # Starting pre_casc_2 with 136s (1) cores
% 1.18/0.65  # Preprocessing time       : 0.013 s
% 1.18/0.65  # Presaturation interreduction done
% 1.18/0.65  
% 1.18/0.65  # Proof found!
% 1.18/0.65  # SZS status Theorem
% 1.18/0.65  # SZS output start CNFRefutation
% See solution above
% 1.18/0.65  # Parsed axioms                        : 315
% 1.18/0.65  # Removed by relevancy pruning/SinE    : 0
% 1.18/0.65  # Initial clauses                      : 663
% 1.18/0.65  # Removed in clause preprocessing      : 46
% 1.18/0.65  # Initial clauses in saturation        : 617
% 1.18/0.65  # Processed clauses                    : 816
% 1.18/0.65  # ...of these trivial                  : 5
% 1.18/0.65  # ...subsumed                          : 234
% 1.18/0.65  # ...remaining for further processing  : 577
% 1.18/0.65  # Other redundant clauses eliminated   : 78
% 1.18/0.65  # Clauses deleted for lack of memory   : 0
% 1.18/0.65  # Backward-subsumed                    : 4
% 1.18/0.65  # Backward-rewritten                   : 3
% 1.18/0.65  # Generated clauses                    : 734
% 1.18/0.65  # ...of the previous two non-redundant : 635
% 1.18/0.65  # ...aggressively subsumed             : 0
% 1.18/0.65  # Contextual simplify-reflections      : 3
% 1.18/0.65  # Paramodulations                      : 646
% 1.18/0.65  # Factorizations                       : 4
% 1.18/0.65  # NegExts                              : 0
% 1.18/0.65  # Equation resolutions                 : 83
% 1.18/0.65  # Disequality decompositions           : 0
% 1.18/0.65  # Total rewrite steps                  : 117
% 1.18/0.65  # ...of those cached                   : 79
% 1.18/0.65  # Propositional unsat checks           : 0
% 1.18/0.65  #    Propositional check models        : 0
% 1.18/0.65  #    Propositional check unsatisfiable : 0
% 1.18/0.65  #    Propositional clauses             : 0
% 1.18/0.65  #    Propositional clauses after purity: 0
% 1.18/0.65  #    Propositional unsat core size     : 0
% 1.18/0.65  #    Propositional preprocessing time  : 0.000
% 1.18/0.65  #    Propositional encoding time       : 0.000
% 1.18/0.65  #    Propositional solver time         : 0.000
% 1.18/0.65  #    Success case prop preproc time    : 0.000
% 1.18/0.65  #    Success case prop encoding time   : 0.000
% 1.18/0.65  #    Success case prop solver time     : 0.000
% 1.18/0.65  # Current number of processed clauses  : 128
% 1.18/0.65  #    Positive orientable unit clauses  : 36
% 1.18/0.65  #    Positive unorientable unit clauses: 1
% 1.18/0.65  #    Negative unit clauses             : 26
% 1.18/0.65  #    Non-unit-clauses                  : 65
% 1.18/0.65  # Current number of unprocessed clauses: 787
% 1.18/0.65  # ...number of literals in the above   : 2519
% 1.18/0.65  # Current number of archived formulas  : 0
% 1.18/0.65  # Current number of archived clauses   : 371
% 1.18/0.65  # Clause-clause subsumption calls (NU) : 29426
% 1.18/0.65  # Rec. Clause-clause subsumption calls : 7326
% 1.18/0.65  # Non-unit clause-clause subsumptions  : 213
% 1.18/0.65  # Unit Clause-clause subsumption calls : 332
% 1.18/0.65  # Rewrite failures with RHS unbound    : 0
% 1.18/0.65  # BW rewrite match attempts            : 21
% 1.18/0.65  # BW rewrite match successes           : 17
% 1.18/0.65  # Condensation attempts                : 816
% 1.18/0.65  # Condensation successes               : 15
% 1.18/0.65  # Termbank termtop insertions          : 96503
% 1.18/0.65  # Search garbage collected termcells   : 12297
% 1.18/0.65  
% 1.18/0.65  # -------------------------------------------------
% 1.18/0.65  # User time                : 0.117 s
% 1.18/0.65  # System time              : 0.007 s
% 1.18/0.65  # Total time               : 0.124 s
% 1.18/0.65  # Maximum resident set size: 4652 pages
% 1.18/0.65  
% 1.18/0.65  # -------------------------------------------------
% 1.18/0.65  # User time                : 0.394 s
% 1.18/0.65  # System time              : 0.032 s
% 1.18/0.65  # Total time               : 0.425 s
% 1.18/0.65  # Maximum resident set size: 2292 pages
% 1.18/0.65  % E---3.1 exiting
% 1.18/0.66  % E exiting
%------------------------------------------------------------------------------