TSTP Solution File: ITP131^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP131^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n024.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   : ContradictoryAxioms 0.21s 0.56s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   32 (  17 unt;   9 typ;   0 def)
%            Number of atoms       :   35 (  10 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  149 (  11   ~;   8   |;   1   &; 126   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   24 (   2   ^  22   !;   0   ?;  24   :)

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

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

thf(decl_24,type,
    times_times_nat: nat > nat > nat ).

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

thf(decl_28,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(decl_29,type,
    i: nat ).

thf(decl_30,type,
    k: nat ).

thf(decl_31,type,
    n: nat ).

thf(decl_32,type,
    p: nat > nat ).

thf(fact_136_mult_Ocommute,axiom,
    ( times_times_nat
    = ( ^ [X17: nat,X18: nat] : ( times_times_nat @ X18 @ X17 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_mult_Ocommute) ).

thf(fact_193_less__or__eq__imp__le,axiom,
    ! [X5: nat,X3: nat] :
      ( ( ( ord_less_nat @ X5 @ X3 )
        | ( X5 = X3 ) )
     => ( ord_less_eq_nat @ X5 @ X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_less__or__eq__imp__le) ).

thf(fact_149_le__antisym,axiom,
    ! [X5: nat,X3: nat] :
      ( ( ord_less_eq_nat @ X5 @ X3 )
     => ( ( ord_less_eq_nat @ X3 @ X5 )
       => ( X5 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_le__antisym) ).

thf(fact_2_upper__bound,axiom,
    ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ) @ n,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_upper__bound) ).

thf(fact_3_lower__bound,axiom,
    ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_lower__bound) ).

thf(fact_142_less__irrefl__nat,axiom,
    ! [X3: nat] :
      ~ ( ord_less_nat @ X3 @ X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_less__irrefl__nat) ).

thf(c_0_6,plain,
    ! [X544: nat,X545: nat] :
      ( ( times_times_nat @ X544 @ X545 )
      = ( times_times_nat @ X545 @ X544 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_136_mult_Ocommute])]) ).

thf(c_0_7,plain,
    ! [X894: nat,X895: nat] :
      ( ( times_times_nat @ X894 @ X895 )
      = ( times_times_nat @ X895 @ X894 ) ),
    inference(variable_rename,[status(thm)],[c_0_6]) ).

thf(c_0_8,plain,
    ! [X1034: nat,X1035: nat] :
      ( ( ~ ( ord_less_nat @ X1034 @ X1035 )
        | ( ord_less_eq_nat @ X1034 @ X1035 ) )
      & ( ( X1034 != X1035 )
        | ( ord_less_eq_nat @ X1034 @ X1035 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_193_less__or__eq__imp__le])])])]) ).

thf(c_0_9,plain,
    ! [X928: nat,X929: nat] :
      ( ~ ( ord_less_eq_nat @ X928 @ X929 )
      | ~ ( ord_less_eq_nat @ X929 @ X928 )
      | ( X928 = X929 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_149_le__antisym])])]) ).

thf(c_0_10,plain,
    ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ) @ n,
    inference(split_conjunct,[status(thm)],[fact_2_upper__bound]) ).

thf(c_0_11,plain,
    ! [X3: nat,X2: nat] :
      ( ( times_times_nat @ X2 @ X3 )
      = ( times_times_nat @ X3 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_12,plain,
    ! [X2: nat,X3: nat] :
      ( ( ord_less_eq_nat @ X2 @ X3 )
      | ~ ( ord_less_nat @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_13,plain,
    ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ),
    inference(split_conjunct,[status(thm)],[fact_3_lower__bound]) ).

thf(c_0_14,plain,
    ! [X3: nat] :
      ~ ( ord_less_nat @ X3 @ X3 ),
    inference(fof_simplification,[status(thm)],[fact_142_less__irrefl__nat]) ).

thf(c_0_15,plain,
    ! [X3: nat,X2: nat] :
      ( ( X2 = X3 )
      | ~ ( ord_less_eq_nat @ X2 @ X3 )
      | ~ ( ord_less_eq_nat @ X3 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_16,plain,
    ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) ) @ n,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).

thf(c_0_17,plain,
    ord_less_eq_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11]),c_0_11]) ).

thf(c_0_18,plain,
    ! [X912: nat] :
      ~ ( ord_less_nat @ X912 @ X912 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_14])]) ).

thf(c_0_19,plain,
    ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_11]) ).

thf(c_0_20,plain,
    ( ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) )
    = n ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).

thf(c_0_21,plain,
    ! [X2: nat] :
      ~ ( ord_less_nat @ X2 @ X2 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_22,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : ITP131^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat May 18 17:01:08 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  Running higher-order theorem proving
% 0.21/0.49  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
% 0.21/0.56  # Version: 3.1.0-ho
% 0.21/0.56  # Preprocessing class: HSLSSMSSSSSNSFA.
% 0.21/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56  # Starting new_ho_11 with 1500s (5) cores
% 0.21/0.56  # Starting post_as_ho6 with 300s (1) cores
% 0.21/0.56  # Starting sh9 with 300s (1) cores
% 0.21/0.56  # Starting sh5l with 300s (1) cores
% 0.21/0.56  # sh5l with pid 24428 completed with status 8
% 0.21/0.56  # post_as_ho6 with pid 24426 completed with status 8
% 0.21/0.56  # sh9 with pid 24427 completed with status 0
% 0.21/0.56  # Result found by sh9
% 0.21/0.56  # Preprocessing class: HSLSSMSSSSSNSFA.
% 0.21/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56  # Starting new_ho_11 with 1500s (5) cores
% 0.21/0.56  # Starting post_as_ho6 with 300s (1) cores
% 0.21/0.56  # Starting sh9 with 300s (1) cores
% 0.21/0.56  # No SInE strategy applied
% 0.21/0.56  # Search class: HGHSM-FSLM31-MSFFFFBN
% 0.21/0.56  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.56  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.56  # new_ho_10 with pid 24457 completed with status 0
% 0.21/0.56  # Result found by new_ho_10
% 0.21/0.56  # Preprocessing class: HSLSSMSSSSSNSFA.
% 0.21/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56  # Starting new_ho_11 with 1500s (5) cores
% 0.21/0.56  # Starting post_as_ho6 with 300s (1) cores
% 0.21/0.56  # Starting sh9 with 300s (1) cores
% 0.21/0.56  # No SInE strategy applied
% 0.21/0.56  # Search class: HGHSM-FSLM31-MSFFFFBN
% 0.21/0.56  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.56  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.56  # Preprocessing time       : 0.005 s
% 0.21/0.56  # Presaturation interreduction done
% 0.21/0.56  
% 0.21/0.56  # Proof found!
% 0.21/0.56  # SZS status ContradictoryAxioms
% 0.21/0.56  # SZS output start CNFRefutation
% See solution above
% 0.21/0.56  # Parsed axioms                        : 225
% 0.21/0.56  # Removed by relevancy pruning/SinE    : 0
% 0.21/0.56  # Initial clauses                      : 327
% 0.21/0.56  # Removed in clause preprocessing      : 22
% 0.21/0.56  # Initial clauses in saturation        : 305
% 0.21/0.56  # Processed clauses                    : 434
% 0.21/0.56  # ...of these trivial                  : 22
% 0.21/0.56  # ...subsumed                          : 109
% 0.21/0.56  # ...remaining for further processing  : 303
% 0.21/0.56  # Other redundant clauses eliminated   : 56
% 0.21/0.56  # Clauses deleted for lack of memory   : 0
% 0.21/0.56  # Backward-subsumed                    : 2
% 0.21/0.56  # Backward-rewritten                   : 3
% 0.21/0.56  # Generated clauses                    : 464
% 0.21/0.56  # ...of the previous two non-redundant : 274
% 0.21/0.56  # ...aggressively subsumed             : 0
% 0.21/0.56  # Contextual simplify-reflections      : 0
% 0.21/0.56  # Paramodulations                      : 407
% 0.21/0.56  # Factorizations                       : 0
% 0.21/0.56  # NegExts                              : 0
% 0.21/0.56  # Equation resolutions                 : 60
% 0.21/0.56  # Disequality decompositions           : 0
% 0.21/0.56  # Total rewrite steps                  : 215
% 0.21/0.56  # ...of those cached                   : 149
% 0.21/0.56  # Propositional unsat checks           : 0
% 0.21/0.56  #    Propositional check models        : 0
% 0.21/0.56  #    Propositional check unsatisfiable : 0
% 0.21/0.56  #    Propositional clauses             : 0
% 0.21/0.56  #    Propositional clauses after purity: 0
% 0.21/0.56  #    Propositional unsat core size     : 0
% 0.21/0.56  #    Propositional preprocessing time  : 0.000
% 0.21/0.56  #    Propositional encoding time       : 0.000
% 0.21/0.56  #    Propositional solver time         : 0.000
% 0.21/0.56  #    Success case prop preproc time    : 0.000
% 0.21/0.56  #    Success case prop encoding time   : 0.000
% 0.21/0.56  #    Success case prop solver time     : 0.000
% 0.21/0.56  # Current number of processed clauses  : 84
% 0.21/0.56  #    Positive orientable unit clauses  : 31
% 0.21/0.56  #    Positive unorientable unit clauses: 2
% 0.21/0.56  #    Negative unit clauses             : 6
% 0.21/0.56  #    Non-unit-clauses                  : 45
% 0.21/0.56  # Current number of unprocessed clauses: 312
% 0.21/0.56  # ...number of literals in the above   : 665
% 0.21/0.56  # Current number of archived formulas  : 0
% 0.21/0.56  # Current number of archived clauses   : 172
% 0.21/0.56  # Clause-clause subsumption calls (NU) : 1923
% 0.21/0.56  # Rec. Clause-clause subsumption calls : 1828
% 0.21/0.56  # Non-unit clause-clause subsumptions  : 73
% 0.21/0.56  # Unit Clause-clause subsumption calls : 16
% 0.21/0.56  # Rewrite failures with RHS unbound    : 0
% 0.21/0.56  # BW rewrite match attempts            : 79
% 0.21/0.56  # BW rewrite match successes           : 53
% 0.21/0.56  # Condensation attempts                : 434
% 0.21/0.56  # Condensation successes               : 0
% 0.21/0.56  # Termbank termtop insertions          : 26852
% 0.21/0.56  # Search garbage collected termcells   : 5431
% 0.21/0.56  
% 0.21/0.56  # -------------------------------------------------
% 0.21/0.56  # User time                : 0.044 s
% 0.21/0.56  # System time              : 0.007 s
% 0.21/0.56  # Total time               : 0.051 s
% 0.21/0.56  # Maximum resident set size: 3044 pages
% 0.21/0.56  
% 0.21/0.56  # -------------------------------------------------
% 0.21/0.56  # User time                : 0.079 s
% 0.21/0.56  # System time              : 0.025 s
% 0.21/0.56  # Total time               : 0.105 s
% 0.21/0.56  # Maximum resident set size: 1960 pages
% 0.21/0.56  % E---3.1 exiting
% 0.21/0.56  % E exiting
%------------------------------------------------------------------------------