TSTP Solution File: ALG261^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG261^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n016.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 0.19s 0.52s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   34 (  14 unt;  14 typ;   0 def)
%            Number of atoms       :   40 (  13 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  128 (  10   ~;   0   |;   2   &; 106   @)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   8 con; 0-4 aty)
%            Number of variables   :   45 (  10   ^  35   !;   0   ?;  45   :)

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

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

thf(decl_23,type,
    ap: term > term > term ).

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

thf(decl_26,type,
    id: subst ).

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

thf(decl_38,type,
    hoasap: subst > term > subst > term > term ).

thf(decl_48,type,
    apnotvar: $o ).

thf(decl_63,type,
    hoasapnotvar: $o ).

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

thf(decl_139,type,
    hoasapnotvar_lthm: $o ).

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

thf(decl_144,type,
    esk1_0: term ).

thf(decl_145,type,
    esk2_0: term ).

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

thf(hoasapnotvar,axiom,
    ( hoasapnotvar
  <=> ! [X1: term,X2: term] :
        ~ ( hoasvar @ id @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasapnotvar) ).

thf(hoasapnotvar_lthm,axiom,
    ( hoasapnotvar_lthm
  <=> ( axvarid
     => ( apnotvar
       => hoasapnotvar ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasapnotvar_lthm) ).

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

thf(apnotvar,axiom,
    ( apnotvar
  <=> ! [X1: term,X2: term] :
        ~ ( var @ ( ap @ X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',apnotvar) ).

thf(thm,conjecture,
    hoasapnotvar_lthm,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(hoasap,axiom,
    ( hoasap
    = ( ^ [X3: subst,X1: term,X4: subst,X2: term] : ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasap) ).

thf(c_0_7,plain,
    ( hoasvar
    = ( ^ [Z0: subst,Z1: term,Z2: subst] : ( var @ ( sub @ Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[hoasvar]) ).

thf(c_0_8,axiom,
    ( hoasapnotvar
    = ( ! [X1: term,X2: term] :
          ~ ( var @ ( sub @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ) ) ),
    inference(apply_def,[status(thm)],[hoasapnotvar,c_0_7]) ).

thf(c_0_9,axiom,
    ( hoasapnotvar_lthm
    = ( ! [X3304: term] :
          ( ( sub @ X3304 @ id )
          = X3304 )
     => ( ! [X3305: term,X3306: term] :
            ~ ( var @ ( ap @ X3305 @ X3306 ) )
       => ! [X3307: term,X3308: term] :
            ~ ( var @ ( sub @ ( hoasap @ id @ X3307 @ id @ X3308 ) @ id ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoasapnotvar_lthm,axvarid]),apnotvar]),c_0_8]) ).

thf(c_0_10,negated_conjecture,
    ~ ( ! [X3373: term] :
          ( ( sub @ X3373 @ id )
          = X3373 )
     => ( ! [X3374: term,X3375: term] :
            ~ ( var @ ( ap @ X3374 @ X3375 ) )
       => ! [X3376: term,X3377: term] :
            ~ ( var @ ( sub @ ( hoasap @ id @ X3376 @ id @ X3377 ) @ id ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_9])]) ).

thf(c_0_11,negated_conjecture,
    ! [X3390: term,X3391: term,X3392: term] :
      ( ( ( sub @ X3390 @ id )
        = X3390 )
      & ~ ( var @ ( ap @ X3391 @ X3392 ) )
      & ( var @ ( sub @ ( hoasap @ id @ esk1_0 @ id @ esk2_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_10])])])])]) ).

thf(c_0_12,plain,
    ! [X3378: subst,X3379: term,X3380: subst,X3381: term] :
      ( ( hoasap @ X3378 @ X3379 @ X3380 @ X3381 )
      = ( ap @ ( sub @ X3379 @ X3380 ) @ X3381 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoasap])]) ).

thf(c_0_13,negated_conjecture,
    var @ ( sub @ ( hoasap @ id @ esk1_0 @ id @ esk2_0 ) @ id ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: term] :
      ( ( sub @ X1 @ id )
      = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_15,plain,
    ! [X3384: subst,X3385: term,X3386: subst,X3387: term] :
      ( ( hoasap @ X3384 @ X3385 @ X3386 @ X3387 )
      = ( ap @ ( sub @ X3385 @ X3386 ) @ X3387 ) ),
    inference(variable_rename,[status(thm)],[c_0_12]) ).

thf(c_0_16,negated_conjecture,
    var @ ( hoasap @ id @ esk1_0 @ id @ esk2_0 ),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_17,plain,
    ! [X1: term,X3: subst,X4: subst,X2: term] :
      ( ( hoasap @ X3 @ X1 @ X4 @ X2 )
      = ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_18,negated_conjecture,
    ! [X1: term,X2: term] :
      ~ ( var @ ( ap @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_19,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_14]),c_0_18]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : ALG261^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.10/0.13  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n016.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 23:52:08 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.19/0.47  Running higher-order theorem proving
% 0.19/0.47  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/benchmark/theBenchmark.p
% 0.19/0.52  # Version: 3.1.0-ho
% 0.19/0.52  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.19/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.19/0.52  # Starting post_as_ho1 with 300s (1) cores
% 0.19/0.52  # Starting post_as_ho5 with 300s (1) cores
% 0.19/0.52  # Starting post_as_ho10 with 300s (1) cores
% 0.19/0.52  # post_as_ho1 with pid 15591 completed with status 0
% 0.19/0.52  # Result found by post_as_ho1
% 0.19/0.52  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.19/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.19/0.52  # Starting post_as_ho1 with 300s (1) cores
% 0.19/0.52  # No SInE strategy applied
% 0.19/0.52  # Search class: HUUSS-FFSF32-SHFMMFNN
% 0.19/0.52  # partial match(1): HHUSS-FFSF32-SHFMMFNN
% 0.19/0.52  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.52  # Starting new_ho_10 with 163s (1) cores
% 0.19/0.52  # new_ho_10 with pid 15602 completed with status 0
% 0.19/0.52  # Result found by new_ho_10
% 0.19/0.52  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.19/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.19/0.52  # Starting post_as_ho1 with 300s (1) cores
% 0.19/0.52  # No SInE strategy applied
% 0.19/0.52  # Search class: HUUSS-FFSF32-SHFMMFNN
% 0.19/0.52  # partial match(1): HHUSS-FFSF32-SHFMMFNN
% 0.19/0.52  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.52  # Starting new_ho_10 with 163s (1) cores
% 0.19/0.52  # Preprocessing time       : 0.002 s
% 0.19/0.52  # Presaturation interreduction done
% 0.19/0.52  
% 0.19/0.52  # Proof found!
% 0.19/0.52  # SZS status Theorem
% 0.19/0.52  # SZS output start CNFRefutation
% See solution above
% 0.19/0.52  # Parsed axioms                        : 238
% 0.19/0.52  # Removed by relevancy pruning/SinE    : 0
% 0.19/0.52  # Initial clauses                      : 129
% 0.19/0.52  # Removed in clause preprocessing      : 124
% 0.19/0.52  # Initial clauses in saturation        : 5
% 0.19/0.52  # Processed clauses                    : 5
% 0.19/0.52  # ...of these trivial                  : 0
% 0.19/0.52  # ...subsumed                          : 0
% 0.19/0.52  # ...remaining for further processing  : 5
% 0.19/0.52  # Other redundant clauses eliminated   : 0
% 0.19/0.52  # Clauses deleted for lack of memory   : 0
% 0.19/0.52  # Backward-subsumed                    : 0
% 0.19/0.52  # Backward-rewritten                   : 2
% 0.19/0.52  # Generated clauses                    : 0
% 0.19/0.52  # ...of the previous two non-redundant : 1
% 0.19/0.52  # ...aggressively subsumed             : 0
% 0.19/0.52  # Contextual simplify-reflections      : 0
% 0.19/0.52  # Paramodulations                      : 0
% 0.19/0.52  # Factorizations                       : 0
% 0.19/0.52  # NegExts                              : 0
% 0.19/0.52  # Equation resolutions                 : 0
% 0.19/0.52  # Disequality decompositions           : 0
% 0.19/0.52  # Total rewrite steps                  : 3
% 0.19/0.52  # ...of those cached                   : 0
% 0.19/0.52  # Propositional unsat checks           : 0
% 0.19/0.52  #    Propositional check models        : 0
% 0.19/0.52  #    Propositional check unsatisfiable : 0
% 0.19/0.52  #    Propositional clauses             : 0
% 0.19/0.52  #    Propositional clauses after purity: 0
% 0.19/0.52  #    Propositional unsat core size     : 0
% 0.19/0.52  #    Propositional preprocessing time  : 0.000
% 0.19/0.52  #    Propositional encoding time       : 0.000
% 0.19/0.52  #    Propositional solver time         : 0.000
% 0.19/0.52  #    Success case prop preproc time    : 0.000
% 0.19/0.52  #    Success case prop encoding time   : 0.000
% 0.19/0.52  #    Success case prop solver time     : 0.000
% 0.19/0.52  # Current number of processed clauses  : 3
% 0.19/0.52  #    Positive orientable unit clauses  : 2
% 0.19/0.52  #    Positive unorientable unit clauses: 0
% 0.19/0.52  #    Negative unit clauses             : 1
% 0.19/0.52  #    Non-unit-clauses                  : 0
% 0.19/0.52  # Current number of unprocessed clauses: 1
% 0.19/0.52  # ...number of literals in the above   : 1
% 0.19/0.52  # Current number of archived formulas  : 0
% 0.19/0.52  # Current number of archived clauses   : 2
% 0.19/0.52  # Clause-clause subsumption calls (NU) : 0
% 0.19/0.52  # Rec. Clause-clause subsumption calls : 0
% 0.19/0.52  # Non-unit clause-clause subsumptions  : 0
% 0.19/0.52  # Unit Clause-clause subsumption calls : 0
% 0.19/0.52  # Rewrite failures with RHS unbound    : 0
% 0.19/0.52  # BW rewrite match attempts            : 2
% 0.19/0.52  # BW rewrite match successes           : 2
% 0.19/0.52  # Condensation attempts                : 5
% 0.19/0.52  # Condensation successes               : 0
% 0.19/0.52  # Termbank termtop insertions          : 26207
% 0.19/0.52  # Search garbage collected termcells   : 1675
% 0.19/0.52  
% 0.19/0.52  # -------------------------------------------------
% 0.19/0.52  # User time                : 0.024 s
% 0.19/0.52  # System time              : 0.010 s
% 0.19/0.52  # Total time               : 0.034 s
% 0.19/0.52  # Maximum resident set size: 5788 pages
% 0.19/0.52  
% 0.19/0.52  # -------------------------------------------------
% 0.19/0.52  # User time                : 0.033 s
% 0.19/0.52  # System time              : 0.013 s
% 0.19/0.52  # Total time               : 0.045 s
% 0.19/0.52  # Maximum resident set size: 2072 pages
% 0.19/0.52  % E---3.1 exiting
% 0.19/0.52  % E exiting
%------------------------------------------------------------------------------