TSTP Solution File: ALG267^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG267^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n019.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 18:05:57 EDT 2024

% Result   : Theorem 0.15s 0.45s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   17 (   6 unt;   9 typ;   0 def)
%            Number of atoms       :   12 (   6 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   35 (   3   ~;   0   |;   0   &;  30   @)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    8 (   0   ^   5   !;   3   ?;   8   :)

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

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

thf(decl_22,type,
    one: term ).

thf(decl_25,type,
    sub: term > subst > term ).

thf(decl_27,type,
    sh: subst ).

thf(decl_28,type,
    push: term > subst > subst ).

thf(decl_70,type,
    hoasinduction_lem3b_lthm: $o ).

thf(decl_119,type,
    hoasinduction_lem3b: $o ).

thf(decl_144,type,
    esk1_0: term ).

thf(hoasinduction_lem3b_lthm,axiom,
    ( hoasinduction_lem3b_lthm
  <=> hoasinduction_lem3b ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3b_lthm) ).

thf(hoasinduction_lem3b,axiom,
    ( hoasinduction_lem3b
  <=> ! [X2: term] :
      ? [X12: subst > term > term] :
        ( ( sub @ X2 @ ( push @ one @ sh ) )
        = ( X12 @ sh @ one ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3b) ).

thf(thm,conjecture,
    hoasinduction_lem3b_lthm,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(c_0_3,axiom,
    ( hoasinduction_lem3b_lthm
    = ( ! [X30: term] :
        ? [X31: subst > term > term] :
          ( ( sub @ X30 @ ( push @ one @ sh ) )
          = ( X31 @ sh @ one ) ) ) ),
    inference(apply_def,[status(thm)],[hoasinduction_lem3b_lthm,hoasinduction_lem3b]) ).

thf(c_0_4,negated_conjecture,
    ~ ! [X32: term] :
      ? [X33: subst > term > term] :
        ( ( sub @ X32 @ ( push @ one @ sh ) )
        = ( X33 @ sh @ one ) ),
    inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_3]) ).

thf(c_0_5,negated_conjecture,
    ! [X35: subst > term > term] :
      ( ( sub @ esk1_0 @ ( push @ one @ sh ) )
     != ( X35 @ sh @ one ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

thf(c_0_6,negated_conjecture,
    ! [X12: subst > term > term] :
      ( ( sub @ esk1_0 @ ( push @ one @ sh ) )
     != ( X12 @ sh @ one ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_7,negated_conjecture,
    $false,
    inference(er,[status(thm)],[c_0_6]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : ALG267^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.11/0.31  % Computer : n019.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Sat May 18 23:25:08 EDT 2024
% 0.11/0.31  % CPUTime    : 
% 0.15/0.43  Running higher-order theorem proving
% 0.15/0.43  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
% 0.15/0.45  # Version: 3.1.0-ho
% 0.15/0.45  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.15/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.15/0.45  # Starting post_as_ho1 with 300s (1) cores
% 0.15/0.45  # Starting post_as_ho5 with 300s (1) cores
% 0.15/0.45  # Starting post_as_ho10 with 300s (1) cores
% 0.15/0.45  # post_as_ho5 with pid 26630 completed with status 0
% 0.15/0.45  # Result found by post_as_ho5
% 0.15/0.45  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.15/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.15/0.45  # Starting post_as_ho1 with 300s (1) cores
% 0.15/0.45  # Starting post_as_ho5 with 300s (1) cores
% 0.15/0.45  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.15/0.45  # Search class: HUUPF-FFSF22-SHFMMMNN
% 0.15/0.45  # partial match(4): HUUPF-FFSF22-SFFFFFNN
% 0.15/0.45  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.45  # Starting new_ho_10 with 163s (1) cores
% 0.15/0.45  # new_ho_10 with pid 26632 completed with status 9
% 0.15/0.45  # Starting post_as_ho5 with 31s (1) cores
% 0.15/0.45  # post_as_ho5 with pid 26633 completed with status 0
% 0.15/0.45  # Result found by post_as_ho5
% 0.15/0.45  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.15/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.15/0.45  # Starting post_as_ho1 with 300s (1) cores
% 0.15/0.45  # Starting post_as_ho5 with 300s (1) cores
% 0.15/0.45  # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.15/0.45  # Search class: HUUPF-FFSF22-SHFMMMNN
% 0.15/0.45  # partial match(4): HUUPF-FFSF22-SFFFFFNN
% 0.15/0.45  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.45  # Starting new_ho_10 with 163s (1) cores
% 0.15/0.45  # new_ho_10 with pid 26632 completed with status 9
% 0.15/0.45  # Starting post_as_ho5 with 31s (1) cores
% 0.15/0.45  # Preprocessing time       : 0.003 s
% 0.15/0.45  # Presaturation interreduction done
% 0.15/0.45  
% 0.15/0.45  # Proof found!
% 0.15/0.45  # SZS status Theorem
% 0.15/0.45  # SZS output start CNFRefutation
% See solution above
% 0.15/0.45  # Parsed axioms                        : 238
% 0.15/0.45  # Removed by relevancy pruning/SinE    : 235
% 0.15/0.45  # Initial clauses                      : 1
% 0.15/0.45  # Removed in clause preprocessing      : 0
% 0.15/0.45  # Initial clauses in saturation        : 1
% 0.15/0.45  # Processed clauses                    : 2
% 0.15/0.45  # ...of these trivial                  : 0
% 0.15/0.45  # ...subsumed                          : 0
% 0.15/0.45  # ...remaining for further processing  : 2
% 0.15/0.45  # Other redundant clauses eliminated   : 0
% 0.15/0.45  # Clauses deleted for lack of memory   : 0
% 0.15/0.45  # Backward-subsumed                    : 0
% 0.15/0.45  # Backward-rewritten                   : 0
% 0.15/0.45  # Generated clauses                    : 1
% 0.15/0.45  # ...of the previous two non-redundant : 0
% 0.15/0.45  # ...aggressively subsumed             : 0
% 0.15/0.45  # Contextual simplify-reflections      : 0
% 0.15/0.45  # Paramodulations                      : 0
% 0.15/0.45  # Factorizations                       : 0
% 0.15/0.45  # NegExts                              : 0
% 0.15/0.45  # Equation resolutions                 : 1
% 0.15/0.45  # Disequality decompositions           : 0
% 0.15/0.45  # Total rewrite steps                  : 0
% 0.15/0.45  # ...of those cached                   : 0
% 0.15/0.45  # Propositional unsat checks           : 0
% 0.15/0.45  #    Propositional check models        : 0
% 0.15/0.45  #    Propositional check unsatisfiable : 0
% 0.15/0.45  #    Propositional clauses             : 0
% 0.15/0.45  #    Propositional clauses after purity: 0
% 0.15/0.45  #    Propositional unsat core size     : 0
% 0.15/0.45  #    Propositional preprocessing time  : 0.000
% 0.15/0.45  #    Propositional encoding time       : 0.000
% 0.15/0.45  #    Propositional solver time         : 0.000
% 0.15/0.45  #    Success case prop preproc time    : 0.000
% 0.15/0.45  #    Success case prop encoding time   : 0.000
% 0.15/0.45  #    Success case prop solver time     : 0.000
% 0.15/0.45  # Current number of processed clauses  : 1
% 0.15/0.45  #    Positive orientable unit clauses  : 0
% 0.15/0.45  #    Positive unorientable unit clauses: 0
% 0.15/0.45  #    Negative unit clauses             : 1
% 0.15/0.45  #    Non-unit-clauses                  : 0
% 0.15/0.45  # Current number of unprocessed clauses: 0
% 0.15/0.45  # ...number of literals in the above   : 0
% 0.15/0.45  # Current number of archived formulas  : 0
% 0.15/0.45  # Current number of archived clauses   : 1
% 0.15/0.45  # Clause-clause subsumption calls (NU) : 0
% 0.15/0.45  # Rec. Clause-clause subsumption calls : 0
% 0.15/0.45  # Non-unit clause-clause subsumptions  : 0
% 0.15/0.45  # Unit Clause-clause subsumption calls : 0
% 0.15/0.45  # Rewrite failures with RHS unbound    : 0
% 0.15/0.45  # BW rewrite match attempts            : 0
% 0.15/0.45  # BW rewrite match successes           : 0
% 0.15/0.45  # Condensation attempts                : 0
% 0.15/0.45  # Condensation successes               : 0
% 0.15/0.45  # Termbank termtop insertions          : 4914
% 0.15/0.45  # Search garbage collected termcells   : 1845
% 0.15/0.45  
% 0.15/0.45  # -------------------------------------------------
% 0.15/0.45  # User time                : 0.005 s
% 0.15/0.45  # System time              : 0.005 s
% 0.15/0.45  # Total time               : 0.010 s
% 0.15/0.45  # Maximum resident set size: 2400 pages
% 0.15/0.45  
% 0.15/0.45  # -------------------------------------------------
% 0.15/0.45  # User time                : 0.009 s
% 0.15/0.45  # System time              : 0.007 s
% 0.15/0.45  # Total time               : 0.016 s
% 0.15/0.45  # Maximum resident set size: 2076 pages
% 0.15/0.45  % E---3.1 exiting
% 0.15/0.45  % E exiting
%------------------------------------------------------------------------------