TSTP Solution File: ITP104^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP104^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n003.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 : Sat May  4 08:06:58 EDT 2024

% Result   : Theorem 0.44s 0.75s
% Output   : CNFRefutation 0.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   26 (   8 unt;  12 typ;   0 def)
%            Number of atoms       :   20 (  11 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  118 (   8   ~;   4   |;   0   &; 104   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (   0   ^  18   !;   0   ?;  18   :)

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

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

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

thf(decl_41,type,
    listSl1174287072ice2_a: list_a > nat > list_list_a ).

thf(decl_46,type,
    listSl97544552lice_a: list_a > nat > list_list_a ).

thf(decl_81,type,
    nth_list_a: list_list_a > nat > list_a ).

thf(decl_96,type,
    size_size_list_a: list_a > nat ).

thf(decl_97,type,
    ord_less_nat: nat > nat > $o ).

thf(decl_105,type,
    divide_divide_nat: nat > nat > nat ).

thf(decl_114,type,
    k: nat ).

thf(decl_115,type,
    m: nat ).

thf(decl_116,type,
    xs: list_a ).

thf(conj_1,conjecture,
    ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
    = k ),
    file('/export/starexec/sandbox/tmp/tmp.5dmyFnzKp3/E---3.1_32510.p',conj_1) ).

thf(fact_19_list__slice2__list__slice__nth,axiom,
    ! [X48: nat,X52: list_a,X12: nat] :
      ( ( ord_less_nat @ X48 @ ( divide_divide_nat @ ( size_size_list_a @ X52 ) @ X12 ) )
     => ( ( nth_list_a @ ( listSl1174287072ice2_a @ X52 @ X12 ) @ X48 )
        = ( nth_list_a @ ( listSl97544552lice_a @ X52 @ X12 ) @ X48 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.5dmyFnzKp3/E---3.1_32510.p',fact_19_list__slice2__list__slice__nth) ).

thf(conj_0,hypothesis,
    ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ),
    file('/export/starexec/sandbox/tmp/tmp.5dmyFnzKp3/E---3.1_32510.p',conj_0) ).

thf(fact_30_list__slice__nth__length,axiom,
    ! [X48: nat,X77: list_a,X12: nat] :
      ( ( ord_less_nat @ X48 @ ( divide_divide_nat @ ( size_size_list_a @ X77 ) @ X12 ) )
     => ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X77 @ X12 ) @ X48 ) )
        = X12 ) ),
    file('/export/starexec/sandbox/tmp/tmp.5dmyFnzKp3/E---3.1_32510.p',fact_30_list__slice__nth__length) ).

thf(c_0_4,negated_conjecture,
    ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
   != k ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).

thf(c_0_5,negated_conjecture,
    ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
   != k ),
    inference(fof_nnf,[status(thm)],[c_0_4]) ).

thf(c_0_6,plain,
    ! [X1132: nat,X1133: list_a,X1134: nat] :
      ( ~ ( ord_less_nat @ X1132 @ ( divide_divide_nat @ ( size_size_list_a @ X1133 ) @ X1134 ) )
      | ( ( nth_list_a @ ( listSl1174287072ice2_a @ X1133 @ X1134 ) @ X1132 )
        = ( nth_list_a @ ( listSl97544552lice_a @ X1133 @ X1134 ) @ X1132 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_19_list__slice2__list__slice__nth])])]) ).

thf(c_0_7,negated_conjecture,
    ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
   != k ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_8,plain,
    ! [X3: nat,X10: list_a,X12: nat] :
      ( ( ( nth_list_a @ ( listSl1174287072ice2_a @ X10 @ X12 ) @ X3 )
        = ( nth_list_a @ ( listSl97544552lice_a @ X10 @ X12 ) @ X3 ) )
      | ~ ( ord_less_nat @ X3 @ ( divide_divide_nat @ ( size_size_list_a @ X10 ) @ X12 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_9,hypothesis,
    ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ),
    inference(split_conjunct,[status(thm)],[conj_0]) ).

thf(c_0_10,plain,
    ! [X1332: nat,X1333: list_a,X1334: nat] :
      ( ~ ( ord_less_nat @ X1332 @ ( divide_divide_nat @ ( size_size_list_a @ X1333 ) @ X1334 ) )
      | ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X1333 @ X1334 ) @ X1332 ) )
        = X1334 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30_list__slice__nth__length])])]) ).

thf(c_0_11,negated_conjecture,
    ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m ) )
   != k ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]) ).

thf(c_0_12,plain,
    ! [X3: nat,X10: list_a,X12: nat] :
      ( ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X10 @ X12 ) @ X3 ) )
        = X12 )
      | ~ ( ord_less_nat @ X3 @ ( divide_divide_nat @ ( size_size_list_a @ X10 ) @ X12 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_13,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_9])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.18/0.18  % Problem    : ITP104^1 : TPTP v8.1.2. Released v7.5.0.
% 0.18/0.19  % Command    : run_E %s %d THM
% 0.19/0.40  % Computer : n003.cluster.edu
% 0.19/0.40  % Model    : x86_64 x86_64
% 0.19/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40  % Memory   : 8042.1875MB
% 0.19/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40  % CPULimit   : 300
% 0.19/0.40  % WCLimit    : 300
% 0.19/0.40  % DateTime   : Fri May  3 12:22:35 EDT 2024
% 0.19/0.40  % CPUTime    : 
% 0.42/0.59  Running higher-order theorem proving
% 0.42/0.59  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/tmp/tmp.5dmyFnzKp3/E---3.1_32510.p
% 0.44/0.75  # Version: 3.1.0-ho
% 0.44/0.75  # Preprocessing class: HSLSSMSSSSMNHFA.
% 0.44/0.75  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.75  # Starting pre_casc_2 with 1500s (5) cores
% 0.44/0.75  # Starting sh3 with 300s (1) cores
% 0.44/0.75  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.44/0.75  # Starting new_bool_3 with 300s (1) cores
% 0.44/0.75  # new_bool_3 with pid 32595 completed with status 0
% 0.44/0.75  # Result found by new_bool_3
% 0.44/0.75  # Preprocessing class: HSLSSMSSSSMNHFA.
% 0.44/0.75  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.75  # Starting pre_casc_2 with 1500s (5) cores
% 0.44/0.75  # Starting sh3 with 300s (1) cores
% 0.44/0.75  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.44/0.75  # Starting new_bool_3 with 300s (1) cores
% 0.44/0.75  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.44/0.75  # Search class: HGHSM-FSLM32-DHFFFSBN
% 0.44/0.75  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.44/0.75  # Starting new_ho_10 with 163s (1) cores
% 0.44/0.75  # new_ho_10 with pid 32596 completed with status 0
% 0.44/0.75  # Result found by new_ho_10
% 0.44/0.75  # Preprocessing class: HSLSSMSSSSMNHFA.
% 0.44/0.75  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.75  # Starting pre_casc_2 with 1500s (5) cores
% 0.44/0.75  # Starting sh3 with 300s (1) cores
% 0.44/0.75  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.44/0.75  # Starting new_bool_3 with 300s (1) cores
% 0.44/0.75  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.44/0.75  # Search class: HGHSM-FSLM32-DHFFFSBN
% 0.44/0.75  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.44/0.75  # Starting new_ho_10 with 163s (1) cores
% 0.44/0.75  # Preprocessing time       : 0.011 s
% 0.44/0.75  # Presaturation interreduction done
% 0.44/0.75  
% 0.44/0.75  # Proof found!
% 0.44/0.75  # SZS status Theorem
% 0.44/0.75  # SZS output start CNFRefutation
% See solution above
% 0.44/0.75  # Parsed axioms                        : 462
% 0.44/0.75  # Removed by relevancy pruning/SinE    : 313
% 0.44/0.75  # Initial clauses                      : 414
% 0.44/0.75  # Removed in clause preprocessing      : 10
% 0.44/0.75  # Initial clauses in saturation        : 404
% 0.44/0.75  # Processed clauses                    : 517
% 0.44/0.75  # ...of these trivial                  : 5
% 0.44/0.75  # ...subsumed                          : 129
% 0.44/0.75  # ...remaining for further processing  : 383
% 0.44/0.75  # Other redundant clauses eliminated   : 35
% 0.44/0.75  # Clauses deleted for lack of memory   : 0
% 0.44/0.75  # Backward-subsumed                    : 0
% 0.44/0.75  # Backward-rewritten                   : 0
% 0.44/0.75  # Generated clauses                    : 164
% 0.44/0.75  # ...of the previous two non-redundant : 145
% 0.44/0.75  # ...aggressively subsumed             : 0
% 0.44/0.75  # Contextual simplify-reflections      : 1
% 0.44/0.75  # Paramodulations                      : 99
% 0.44/0.75  # Factorizations                       : 2
% 0.44/0.75  # NegExts                              : 0
% 0.44/0.75  # Equation resolutions                 : 36
% 0.44/0.75  # Disequality decompositions           : 0
% 0.44/0.75  # Total rewrite steps                  : 16
% 0.44/0.75  # ...of those cached                   : 8
% 0.44/0.75  # Propositional unsat checks           : 0
% 0.44/0.75  #    Propositional check models        : 0
% 0.44/0.75  #    Propositional check unsatisfiable : 0
% 0.44/0.75  #    Propositional clauses             : 0
% 0.44/0.75  #    Propositional clauses after purity: 0
% 0.44/0.75  #    Propositional unsat core size     : 0
% 0.44/0.75  #    Propositional preprocessing time  : 0.000
% 0.44/0.75  #    Propositional encoding time       : 0.000
% 0.44/0.75  #    Propositional solver time         : 0.000
% 0.44/0.75  #    Success case prop preproc time    : 0.000
% 0.44/0.75  #    Success case prop encoding time   : 0.000
% 0.44/0.75  #    Success case prop solver time     : 0.000
% 0.44/0.75  # Current number of processed clauses  : 79
% 0.44/0.75  #    Positive orientable unit clauses  : 24
% 0.44/0.75  #    Positive unorientable unit clauses: 0
% 0.44/0.75  #    Negative unit clauses             : 16
% 0.44/0.75  #    Non-unit-clauses                  : 39
% 0.44/0.75  # Current number of unprocessed clauses: 303
% 0.44/0.75  # ...number of literals in the above   : 1471
% 0.44/0.75  # Current number of archived formulas  : 0
% 0.44/0.75  # Current number of archived clauses   : 271
% 0.44/0.75  # Clause-clause subsumption calls (NU) : 23131
% 0.44/0.75  # Rec. Clause-clause subsumption calls : 3314
% 0.44/0.75  # Non-unit clause-clause subsumptions  : 123
% 0.44/0.75  # Unit Clause-clause subsumption calls : 393
% 0.44/0.75  # Rewrite failures with RHS unbound    : 0
% 0.44/0.75  # BW rewrite match attempts            : 13
% 0.44/0.75  # BW rewrite match successes           : 4
% 0.44/0.75  # Condensation attempts                : 517
% 0.44/0.75  # Condensation successes               : 12
% 0.44/0.75  # Termbank termtop insertions          : 76134
% 0.44/0.75  # Search garbage collected termcells   : 9515
% 0.44/0.75  
% 0.44/0.75  # -------------------------------------------------
% 0.44/0.75  # User time                : 0.098 s
% 0.44/0.75  # System time              : 0.010 s
% 0.44/0.75  # Total time               : 0.108 s
% 0.44/0.75  # Maximum resident set size: 3948 pages
% 0.44/0.75  
% 0.44/0.75  # -------------------------------------------------
% 0.44/0.75  # User time                : 0.112 s
% 0.44/0.75  # System time              : 0.014 s
% 0.44/0.75  # Total time               : 0.126 s
% 0.44/0.75  # Maximum resident set size: 2672 pages
% 0.44/0.75  % E---3.1 exiting
% 0.44/0.75  % E exiting
%------------------------------------------------------------------------------