TSTP Solution File: ALG260^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG260^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n007.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 18:05:55 EDT 2024

% Result   : Theorem 0.18s 0.53s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   38 (  15 unt;  16 typ;   0 def)
%            Number of atoms       :   49 (  19 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  184 (  12   ~;   0   |;   3   &; 153   @)
%                                         (   5 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   35 (  35   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   8 con; 0-3 aty)
%            Number of variables   :   57 (  16   ^  41   !;   0   ?;  57   :)

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

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

thf(decl_22,type,
    one: term ).

thf(decl_24,type,
    lam: term > term ).

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

thf(decl_26,type,
    id: subst ).

thf(decl_27,type,
    sh: subst ).

thf(decl_29,type,
    comp: subst > subst > subst ).

thf(decl_30,type,
    var: term > $o ).

thf(decl_68,type,
    hoaslamnotvar_lthm: $o ).

thf(decl_93,type,
    hoaslam: subst > ( subst > term > term ) > term ).

thf(decl_110,type,
    hoaslamnotvar: $o ).

thf(decl_121,type,
    lamnotvar: $o ).

thf(decl_127,type,
    hoasvar: subst > term > subst > $o ).

thf(decl_142,type,
    axvarid: $o ).

thf(decl_144,type,
    esk1_0: subst > term > term ).

thf(hoaslamnotvar,axiom,
    ( hoaslamnotvar
  <=> ! [X12: subst > term > term] :
        ( ! [X3: subst,X1: term,X4: subst] :
            ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
            = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
       => ~ ( hoasvar @ id
            @ ( hoaslam @ id
              @ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
            @ id ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslamnotvar) ).

thf(hoasvar,axiom,
    ( hoasvar
    = ( ^ [X3: subst,X1: term,X4: subst] : ( var @ ( sub @ X1 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasvar) ).

thf(hoaslamnotvar_lthm,axiom,
    ( hoaslamnotvar_lthm
  <=> ( axvarid
     => ( lamnotvar
       => hoaslamnotvar ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslamnotvar_lthm) ).

thf(axvarid,axiom,
    ( axvarid
  <=> ! [X1: term] :
        ( ( sub @ X1 @ id )
        = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axvarid) ).

thf(lamnotvar,axiom,
    ( lamnotvar
  <=> ! [X1: term] :
        ~ ( var @ ( lam @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',lamnotvar) ).

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

thf(hoaslam,axiom,
    ( hoaslam
    = ( ^ [X3: subst,X12: subst > term > term] : ( lam @ ( X12 @ sh @ one ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslam) ).

thf(c_0_7,plain,
    ( hoaslamnotvar
  <=> ! [X12: subst > term > term] :
        ( ! [X3: subst,X1: term,X4: subst] :
            ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
            = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
       => ~ ( hoasvar @ id
            @ ( hoaslam @ id
              @ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
            @ id ) ) ),
    inference(fof_simplification,[status(thm)],[hoaslamnotvar]) ).

thf(c_0_8,plain,
    ( hoasvar
    = ( ^ [Z0: subst,Z1: term,Z2: subst] : ( var @ ( sub @ Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[hoasvar]) ).

thf(c_0_9,plain,
    ( hoaslamnotvar
    = ( ! [X12: subst > term > term] :
          ( ! [X3: subst,X1: term,X4: subst] :
              ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
              = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
         => ~ ( var
              @ ( sub
                @ ( hoaslam @ id
                  @ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
                @ id ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_7,c_0_8]) ).

thf(c_0_10,axiom,
    ( hoaslamnotvar_lthm
    = ( ! [X1205: term] :
          ( ( sub @ X1205 @ id )
          = X1205 )
     => ( ! [X1206: term] :
            ~ ( var @ ( lam @ X1206 ) )
       => ! [X1207: subst > term > term] :
            ( ! [X1208: subst,X1209: term,X1210: subst] :
                ( ( sub @ ( X1207 @ X1208 @ X1209 ) @ X1210 )
                = ( X1207 @ ( comp @ X1208 @ X1210 ) @ ( sub @ X1209 @ X1210 ) ) )
           => ~ ( var
                @ ( sub
                  @ ( hoaslam @ id
                    @ ^ [Z0: subst,Z1: term] : ( X1207 @ Z0 @ Z1 ) )
                  @ id ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoaslamnotvar_lthm,axvarid]),lamnotvar]),c_0_8]),c_0_9]) ).

thf(c_0_11,negated_conjecture,
    ~ ( ! [X3373: term] :
          ( ( sub @ X3373 @ id )
          = X3373 )
     => ( ! [X3374: term] :
            ~ ( var @ ( lam @ X3374 ) )
       => ! [X3375: subst > term > term] :
            ( ! [X3376: subst,X3377: term,X3378: subst] :
                ( ( sub @ ( X3375 @ X3376 @ X3377 ) @ X3378 )
                = ( X3375 @ ( comp @ X3376 @ X3378 ) @ ( sub @ X3377 @ X3378 ) ) )
           => ~ ( var @ ( sub @ ( hoaslam @ id @ X3375 ) @ id ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_10])])]) ).

thf(c_0_12,plain,
    ! [X3383: subst,X3384: subst > term > term] :
      ( ( hoaslam @ X3383 @ X3384 )
      = ( lam @ ( X3384 @ sh @ one ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoaslam])]) ).

thf(c_0_13,negated_conjecture,
    ! [X3391: term,X3392: term,X3394: subst,X3395: term,X3396: subst] :
      ( ( ( sub @ X3391 @ id )
        = X3391 )
      & ~ ( var @ ( lam @ X3392 ) )
      & ( ( sub @ ( esk1_0 @ X3394 @ X3395 ) @ X3396 )
        = ( esk1_0 @ ( comp @ X3394 @ X3396 ) @ ( sub @ X3395 @ X3396 ) ) )
      & ( var @ ( sub @ ( hoaslam @ id @ esk1_0 ) @ id ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).

thf(c_0_14,plain,
    ! [X3389: subst,X3390: subst > term > term] :
      ( ( hoaslam @ X3389 @ X3390 )
      = ( lam @ ( X3390 @ sh @ one ) ) ),
    inference(variable_rename,[status(thm)],[c_0_12]) ).

thf(c_0_15,negated_conjecture,
    var @ ( sub @ ( hoaslam @ id @ esk1_0 ) @ id ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_16,negated_conjecture,
    ! [X1: term] :
      ( ( sub @ X1 @ id )
      = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_17,negated_conjecture,
    ! [X1: term] :
      ~ ( var @ ( lam @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_18,plain,
    ! [X3: subst,X12: subst > term > term] :
      ( ( hoaslam @ X3 @ X12 )
      = ( lam @ ( X12 @ sh @ one ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_19,negated_conjecture,
    var @ ( hoaslam @ id @ esk1_0 ),
    inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

thf(c_0_20,negated_conjecture,
    ! [X3: subst,X12: subst > term > term] :
      ~ ( var @ ( hoaslam @ X3 @ X12 ) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : ALG260^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat May 18 22:45:23 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.18/0.47  Running higher-order theorem proving
% 0.18/0.47  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
% 0.18/0.53  # Version: 3.1.0-ho
% 0.18/0.53  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.53  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.53  # Starting post_as_ho5 with 300s (1) cores
% 0.18/0.53  # Starting post_as_ho10 with 300s (1) cores
% 0.18/0.53  # post_as_ho1 with pid 18460 completed with status 0
% 0.18/0.53  # Result found by post_as_ho1
% 0.18/0.53  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.53  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.53  # No SInE strategy applied
% 0.18/0.53  # Search class: HUUSM-FFSF32-SHFMMFNN
% 0.18/0.53  # partial match(2): HHUSS-FFSF32-SHFMMFNN
% 0.18/0.53  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.53  # Starting new_ho_10 with 163s (1) cores
% 0.18/0.53  # new_ho_10 with pid 18469 completed with status 0
% 0.18/0.53  # Result found by new_ho_10
% 0.18/0.53  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.53  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.53  # No SInE strategy applied
% 0.18/0.53  # Search class: HUUSM-FFSF32-SHFMMFNN
% 0.18/0.53  # partial match(2): HHUSS-FFSF32-SHFMMFNN
% 0.18/0.53  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.53  # Starting new_ho_10 with 163s (1) cores
% 0.18/0.53  # Preprocessing time       : 0.003 s
% 0.18/0.53  # Presaturation interreduction done
% 0.18/0.53  
% 0.18/0.53  # Proof found!
% 0.18/0.53  # SZS status Theorem
% 0.18/0.53  # SZS output start CNFRefutation
% See solution above
% 0.18/0.53  # Parsed axioms                        : 238
% 0.18/0.53  # Removed by relevancy pruning/SinE    : 0
% 0.30/0.53  # Initial clauses                      : 130
% 0.30/0.53  # Removed in clause preprocessing      : 124
% 0.30/0.53  # Initial clauses in saturation        : 6
% 0.30/0.53  # Processed clauses                    : 12
% 0.30/0.53  # ...of these trivial                  : 0
% 0.30/0.53  # ...subsumed                          : 0
% 0.30/0.53  # ...remaining for further processing  : 12
% 0.30/0.53  # Other redundant clauses eliminated   : 0
% 0.30/0.53  # Clauses deleted for lack of memory   : 0
% 0.30/0.53  # Backward-subsumed                    : 0
% 0.30/0.53  # Backward-rewritten                   : 1
% 0.30/0.53  # Generated clauses                    : 4
% 0.30/0.53  # ...of the previous two non-redundant : 3
% 0.30/0.53  # ...aggressively subsumed             : 0
% 0.30/0.53  # Contextual simplify-reflections      : 0
% 0.30/0.53  # Paramodulations                      : 3
% 0.30/0.53  # Factorizations                       : 0
% 0.30/0.53  # NegExts                              : 0
% 0.30/0.53  # Equation resolutions                 : 0
% 0.30/0.53  # Disequality decompositions           : 0
% 0.30/0.53  # Total rewrite steps                  : 1
% 0.30/0.53  # ...of those cached                   : 0
% 0.30/0.53  # Propositional unsat checks           : 0
% 0.30/0.53  #    Propositional check models        : 0
% 0.30/0.53  #    Propositional check unsatisfiable : 0
% 0.30/0.53  #    Propositional clauses             : 0
% 0.30/0.53  #    Propositional clauses after purity: 0
% 0.30/0.53  #    Propositional unsat core size     : 0
% 0.30/0.53  #    Propositional preprocessing time  : 0.000
% 0.30/0.53  #    Propositional encoding time       : 0.000
% 0.30/0.53  #    Propositional solver time         : 0.000
% 0.30/0.53  #    Success case prop preproc time    : 0.000
% 0.30/0.53  #    Success case prop encoding time   : 0.000
% 0.30/0.53  #    Success case prop solver time     : 0.000
% 0.30/0.53  # Current number of processed clauses  : 4
% 0.30/0.53  #    Positive orientable unit clauses  : 1
% 0.30/0.53  #    Positive unorientable unit clauses: 1
% 0.30/0.53  #    Negative unit clauses             : 2
% 0.30/0.53  #    Non-unit-clauses                  : 0
% 0.30/0.53  # Current number of unprocessed clauses: 3
% 0.30/0.53  # ...number of literals in the above   : 3
% 0.30/0.53  # Current number of archived formulas  : 0
% 0.30/0.53  # Current number of archived clauses   : 8
% 0.30/0.53  # Clause-clause subsumption calls (NU) : 0
% 0.30/0.53  # Rec. Clause-clause subsumption calls : 0
% 0.30/0.53  # Non-unit clause-clause subsumptions  : 0
% 0.30/0.53  # Unit Clause-clause subsumption calls : 1
% 0.30/0.53  # Rewrite failures with RHS unbound    : 0
% 0.30/0.53  # BW rewrite match attempts            : 4
% 0.30/0.53  # BW rewrite match successes           : 3
% 0.30/0.53  # Condensation attempts                : 12
% 0.30/0.53  # Condensation successes               : 0
% 0.30/0.53  # Termbank termtop insertions          : 26338
% 0.30/0.53  # Search garbage collected termcells   : 1715
% 0.30/0.53  
% 0.30/0.53  # -------------------------------------------------
% 0.30/0.53  # User time                : 0.027 s
% 0.30/0.53  # System time              : 0.012 s
% 0.30/0.53  # Total time               : 0.039 s
% 0.30/0.53  # Maximum resident set size: 5788 pages
% 0.30/0.53  
% 0.30/0.53  # -------------------------------------------------
% 0.30/0.53  # User time                : 0.034 s
% 0.30/0.53  # System time              : 0.015 s
% 0.30/0.53  # Total time               : 0.049 s
% 0.30/0.53  # Maximum resident set size: 2072 pages
% 0.30/0.53  % E---3.1 exiting
% 0.30/0.53  % E exiting
%------------------------------------------------------------------------------