TSTP Solution File: ITP100^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP100^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n013.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 22:16:18 EDT 2024

% Result   : Theorem 0.43s 0.53s
% Output   : CNFRefutation 0.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   21 (  11 unt;  10 typ;   0 def)
%            Number of atoms       :   11 (  10 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   85 (   3   ~;   0   |;   0   &;  82   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    3 (   3 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   15 (   0   ^  15   !;   0   ?;  15   :)

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

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

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

thf(decl_31,type,
    listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).

thf(decl_35,type,
    append_a: list_a > list_a > list_a ).

thf(decl_55,type,
    cons_a: a > list_a > list_a ).

thf(decl_59,type,
    nil_a: list_a ).

thf(decl_104,type,
    f: nat > a ).

thf(decl_105,type,
    x: a ).

thf(decl_106,type,
    xs: list_a ).

thf(conj_0,conjecture,
    ( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
    = ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(fact_151_i__append__assoc,axiom,
    ! [X441: list_a,X442: list_a,X443: nat > a] :
      ( ( listIn1312259492pend_a @ X441 @ ( listIn1312259492pend_a @ X442 @ X443 ) )
      = ( listIn1312259492pend_a @ ( append_a @ X441 @ X442 ) @ X443 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_i__append__assoc) ).

thf(fact_186_append__eq__Cons,axiom,
    ! [X511: a,X512: list_a] :
      ( ( append_a @ ( cons_a @ X511 @ nil_a ) @ X512 )
      = ( cons_a @ X511 @ X512 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_append__eq__Cons) ).

thf(c_0_3,negated_conjecture,
    ( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
   != ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

thf(c_0_4,negated_conjecture,
    ( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
   != ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_3]) ).

thf(c_0_5,plain,
    ! [X1529: list_a,X1530: list_a,X1531: nat > a] :
      ( ( listIn1312259492pend_a @ X1529 @ ( listIn1312259492pend_a @ X1530 @ X1531 ) )
      = ( listIn1312259492pend_a @ ( append_a @ X1529 @ X1530 ) @ X1531 ) ),
    inference(variable_rename,[status(thm)],[fact_151_i__append__assoc]) ).

thf(c_0_6,plain,
    ! [X1723: a,X1724: list_a] :
      ( ( append_a @ ( cons_a @ X1723 @ nil_a ) @ X1724 )
      = ( cons_a @ X1723 @ X1724 ) ),
    inference(variable_rename,[status(thm)],[fact_186_append__eq__Cons]) ).

thf(c_0_7,negated_conjecture,
    ( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
   != ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_8,plain,
    ! [X5: list_a,X3: list_a,X2: nat > a] :
      ( ( listIn1312259492pend_a @ X3 @ ( listIn1312259492pend_a @ X5 @ X2 ) )
      = ( listIn1312259492pend_a @ ( append_a @ X3 @ X5 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_9,plain,
    ! [X7: a,X3: list_a] :
      ( ( append_a @ ( cons_a @ X7 @ nil_a ) @ X3 )
      = ( cons_a @ X7 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_10,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_9])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : ITP100^1 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.12  % Command    : run_E %s %d THM
% 0.12/0.32  % Computer : n013.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Sat May 18 18:07:38 EDT 2024
% 0.12/0.32  % CPUTime    : 
% 0.17/0.44  Running higher-order theorem proving
% 0.17/0.44  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
% 0.43/0.53  # Version: 3.1.0-ho
% 0.43/0.53  # Preprocessing class: HSLSSMSSSSMNHSA.
% 0.43/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.53  # Starting sh1 with 1500s (5) cores
% 0.43/0.53  # Starting new_ho_8 with 300s (1) cores
% 0.43/0.53  # Starting new_ho_11 with 300s (1) cores
% 0.43/0.53  # Starting sh5l with 300s (1) cores
% 0.43/0.53  # new_ho_8 with pid 21528 completed with status 0
% 0.43/0.53  # Result found by new_ho_8
% 0.43/0.53  # Preprocessing class: HSLSSMSSSSMNHSA.
% 0.43/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.53  # Starting sh1 with 1500s (5) cores
% 0.43/0.53  # Starting new_ho_8 with 300s (1) cores
% 0.43/0.53  # SinE strategy is GSinE(CountTerms,hypos,10,,2,20000,1.0,true)
% 0.43/0.53  # Search class: HGHSM-FSLF31-MHSFFSBN
% 0.43/0.53  # partial match(1): HGHSM-FSLM31-MHSFFSBN
% 0.43/0.53  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.43/0.53  # Starting almost_fo_1 with 163s (1) cores
% 0.43/0.53  # almost_fo_1 with pid 21531 completed with status 0
% 0.43/0.53  # Result found by almost_fo_1
% 0.43/0.53  # Preprocessing class: HSLSSMSSSSMNHSA.
% 0.43/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.53  # Starting sh1 with 1500s (5) cores
% 0.43/0.53  # Starting new_ho_8 with 300s (1) cores
% 0.43/0.53  # SinE strategy is GSinE(CountTerms,hypos,10,,2,20000,1.0,true)
% 0.43/0.53  # Search class: HGHSM-FSLF31-MHSFFSBN
% 0.43/0.53  # partial match(1): HGHSM-FSLM31-MHSFFSBN
% 0.43/0.53  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.43/0.53  # Starting almost_fo_1 with 163s (1) cores
% 0.43/0.53  # Preprocessing time       : 0.009 s
% 0.43/0.53  # Presaturation interreduction done
% 0.43/0.53  
% 0.43/0.53  # Proof found!
% 0.43/0.53  # SZS status Theorem
% 0.43/0.53  # SZS output start CNFRefutation
% See solution above
% 0.43/0.53  # Parsed axioms                        : 450
% 0.43/0.53  # Removed by relevancy pruning/SinE    : 281
% 0.43/0.53  # Initial clauses                      : 497
% 0.43/0.53  # Removed in clause preprocessing      : 12
% 0.43/0.53  # Initial clauses in saturation        : 485
% 0.43/0.53  # Processed clauses                    : 157
% 0.43/0.53  # ...of these trivial                  : 6
% 0.43/0.53  # ...subsumed                          : 21
% 0.43/0.53  # ...remaining for further processing  : 130
% 0.43/0.53  # Other redundant clauses eliminated   : 58
% 0.43/0.53  # Clauses deleted for lack of memory   : 0
% 0.43/0.53  # Backward-subsumed                    : 0
% 0.43/0.53  # Backward-rewritten                   : 3
% 0.43/0.53  # Generated clauses                    : 49
% 0.43/0.53  # ...of the previous two non-redundant : 21
% 0.43/0.53  # ...aggressively subsumed             : 0
% 0.43/0.53  # Contextual simplify-reflections      : 0
% 0.43/0.53  # Paramodulations                      : 0
% 0.43/0.53  # Factorizations                       : 0
% 0.43/0.53  # NegExts                              : 0
% 0.43/0.53  # Equation resolutions                 : 58
% 0.43/0.53  # Disequality decompositions           : 0
% 0.43/0.53  # Total rewrite steps                  : 41
% 0.43/0.53  # ...of those cached                   : 24
% 0.43/0.53  # Propositional unsat checks           : 0
% 0.43/0.53  #    Propositional check models        : 0
% 0.43/0.53  #    Propositional check unsatisfiable : 0
% 0.43/0.53  #    Propositional clauses             : 0
% 0.43/0.53  #    Propositional clauses after purity: 0
% 0.43/0.53  #    Propositional unsat core size     : 0
% 0.43/0.53  #    Propositional preprocessing time  : 0.000
% 0.43/0.53  #    Propositional encoding time       : 0.000
% 0.43/0.53  #    Propositional solver time         : 0.000
% 0.43/0.53  #    Success case prop preproc time    : 0.000
% 0.43/0.53  #    Success case prop encoding time   : 0.000
% 0.43/0.53  #    Success case prop solver time     : 0.000
% 0.43/0.53  # Current number of processed clauses  : 78
% 0.43/0.53  #    Positive orientable unit clauses  : 24
% 0.43/0.53  #    Positive unorientable unit clauses: 0
% 0.43/0.53  #    Negative unit clauses             : 7
% 0.43/0.53  #    Non-unit-clauses                  : 47
% 0.43/0.53  # Current number of unprocessed clauses: 349
% 0.43/0.53  # ...number of literals in the above   : 1267
% 0.43/0.53  # Current number of archived formulas  : 0
% 0.43/0.53  # Current number of archived clauses   : 3
% 0.43/0.53  # Clause-clause subsumption calls (NU) : 458
% 0.43/0.53  # Rec. Clause-clause subsumption calls : 406
% 0.43/0.53  # Non-unit clause-clause subsumptions  : 17
% 0.43/0.53  # Unit Clause-clause subsumption calls : 66
% 0.43/0.53  # Rewrite failures with RHS unbound    : 0
% 0.43/0.53  # BW rewrite match attempts            : 2
% 0.43/0.53  # BW rewrite match successes           : 2
% 0.43/0.53  # Condensation attempts                : 0
% 0.43/0.53  # Condensation successes               : 0
% 0.43/0.53  # Termbank termtop insertions          : 40401
% 0.43/0.53  # Search garbage collected termcells   : 14428
% 0.43/0.53  
% 0.43/0.53  # -------------------------------------------------
% 0.43/0.53  # User time                : 0.037 s
% 0.43/0.53  # System time              : 0.010 s
% 0.43/0.53  # Total time               : 0.047 s
% 0.43/0.53  # Maximum resident set size: 4676 pages
% 0.43/0.53  
% 0.43/0.53  # -------------------------------------------------
% 0.43/0.53  # User time                : 0.054 s
% 0.43/0.53  # System time              : 0.013 s
% 0.43/0.53  # Total time               : 0.066 s
% 0.43/0.53  # Maximum resident set size: 2872 pages
% 0.43/0.53  % E---3.1 exiting
% 0.43/0.53  % E exiting
%------------------------------------------------------------------------------