TSTP Solution File: NUM800^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM800^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n029.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 08:58:02 EDT 2024

% Result   : Theorem 0.17s 0.45s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   35 (  23 unt;   7 typ;   0 def)
%            Number of atoms       :   33 (  32 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  144 (   8   ~;   3   |;   2   &; 131   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :  148 ( 148   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   1 con; 0-4 aty)
%            Number of variables   :   55 (  12   ^  41   !;   2   ?;  55   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_23,type,
    one: ( $i > $i ) > $i > $i ).

thf(decl_24,type,
    two: ( $i > $i ) > $i > $i ).

thf(decl_25,type,
    three: ( $i > $i ) > $i > $i ).

thf(decl_28,type,
    six: ( $i > $i ) > $i > $i ).

thf(decl_35,type,
    mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(decl_36,type,
    esk1_2: ( ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > $i > $i ).

thf(decl_37,type,
    esk2_1: ( ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > $i ).

thf(thm,conjecture,
    ? [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
      ( ( ( X5 @ two @ three )
        = six )
      & ( ( X5 @ one @ two )
        = two ) ),
    file('/export/starexec/sandbox/tmp/tmp.pAnxqbjvcb/E---3.1_17279.p',thm) ).

thf(mult_ax,axiom,
    ( mult
    = ( ^ [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X4 @ ( X3 @ X1 ) @ X2 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.pAnxqbjvcb/E---3.1_17279.p',mult_ax) ).

thf(one_ax,axiom,
    ( one
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.pAnxqbjvcb/E---3.1_17279.p',one_ax) ).

thf(six_ax,axiom,
    ( six
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.pAnxqbjvcb/E---3.1_17279.p',six_ax) ).

thf(three_ax,axiom,
    ( three
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.pAnxqbjvcb/E---3.1_17279.p',three_ax) ).

thf(two_ax,axiom,
    ( two
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.pAnxqbjvcb/E---3.1_17279.p',two_ax) ).

thf(c_0_6,negated_conjecture,
    ~ ? [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
        ( ( ( X5 @ two @ three )
          = six )
        & ( ( X5 @ one @ two )
          = two ) ),
    inference(assume_negation,[status(cth)],[thm]) ).

thf(c_0_7,negated_conjecture,
    ! [X73: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
      ( ( ( X73 @ two @ three )
       != six )
      | ( ( X73 @ one @ two )
       != two ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

thf(c_0_8,plain,
    ! [X36: ( $i > $i ) > $i > $i,X37: ( $i > $i ) > $i > $i,X38: $i > $i,X39: $i] :
      ( ( mult @ X36 @ X37 @ X38 @ X39 )
      = ( X36 @ ( X37 @ X38 ) @ X39 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[mult_ax])]) ).

thf(c_0_9,plain,
    ! [X9: $i > $i,X10: $i] :
      ( ( one @ X9 @ X10 )
      = ( X9 @ X10 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[one_ax])]) ).

thf(c_0_10,plain,
    ! [X19: $i > $i,X20: $i] :
      ( ( six @ X19 @ X20 )
      = ( X19 @ ( X19 @ ( X19 @ ( X19 @ ( X19 @ ( X19 @ X20 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[six_ax])]) ).

thf(c_0_11,plain,
    ! [X13: $i > $i,X14: $i] :
      ( ( three @ X13 @ X14 )
      = ( X13 @ ( X13 @ ( X13 @ X14 ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[three_ax])]) ).

thf(c_0_12,plain,
    ! [X11: $i > $i,X12: $i] :
      ( ( two @ X11 @ X12 )
      = ( X11 @ ( X11 @ X12 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[two_ax])]) ).

thf(c_0_13,negated_conjecture,
    ! [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
      ( ( ( X5 @ two @ three )
       != six )
      | ( ( X5 @ one @ two )
       != two ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_14,plain,
    ! [X69: ( $i > $i ) > $i > $i,X70: ( $i > $i ) > $i > $i,X71: $i > $i,X72: $i] :
      ( ( mult @ X69 @ X70 @ X71 @ X72 )
      = ( X69 @ ( X70 @ X71 ) @ X72 ) ),
    inference(variable_rename,[status(thm)],[c_0_8]) ).

thf(c_0_15,plain,
    ! [X42: $i > $i,X43: $i] :
      ( ( one @ X42 @ X43 )
      = ( X42 @ X43 ) ),
    inference(variable_rename,[status(thm)],[c_0_9]) ).

thf(c_0_16,plain,
    ! [X52: $i > $i,X53: $i] :
      ( ( six @ X52 @ X53 )
      = ( X52 @ ( X52 @ ( X52 @ ( X52 @ ( X52 @ ( X52 @ X53 ) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_10]) ).

thf(c_0_17,plain,
    ! [X46: $i > $i,X47: $i] :
      ( ( three @ X46 @ X47 )
      = ( X46 @ ( X46 @ ( X46 @ X47 ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_11]) ).

thf(c_0_18,plain,
    ! [X44: $i > $i,X45: $i] :
      ( ( two @ X44 @ X45 )
      = ( X44 @ ( X44 @ X45 ) ) ),
    inference(variable_rename,[status(thm)],[c_0_12]) ).

thf(c_0_19,negated_conjecture,
    ! [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
      ( ( ( X5 @ one @ two @ ( esk1_2 @ X5 ) @ ( esk2_1 @ X5 ) )
       != ( two @ ( esk1_2 @ X5 ) @ ( esk2_1 @ X5 ) ) )
      | ( ( X5 @ two @ three )
       != six ) ),
    inference(neg_ext,[status(thm)],[c_0_13]) ).

thf(c_0_20,plain,
    ! [X1: $i > $i,X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
      ( ( mult @ X3 @ X4 @ X1 @ X2 )
      = ( X3 @ ( X4 @ X1 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_21,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( one @ X1 @ X2 )
      = ( X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_22,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( six @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_23,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( three @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_24,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( two @ X1 @ X2 )
      = ( X1 @ ( X1 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_25,negated_conjecture,
    ( ( mult @ two @ three )
   != six ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

thf(c_0_26,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( six @ X1 @ X2 )
      = ( two @ ( three @ X1 ) @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_24]) ).

thf(c_0_27,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_25]),c_0_20]),c_0_26])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem    : NUM800^1 : TPTP v8.1.2. Released v3.7.0.
% 0.09/0.12  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n029.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri May  3 09:39:52 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.17/0.43  Running higher-order theorem proving
% 0.17/0.43  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.pAnxqbjvcb/E---3.1_17279.p
% 0.17/0.45  # Version: 3.1.0-ho
% 0.17/0.45  # Preprocessing class: HSSSSMSSMSSNHHA.
% 0.17/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45  # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.45  # Starting ho_unfolding_6 with 300s (1) cores
% 0.17/0.45  # Starting sh4l with 300s (1) cores
% 0.17/0.45  # Starting ehoh_best_nonlift with 300s (1) cores
% 0.17/0.45  # ehoh_best_nonlift with pid 17361 completed with status 0
% 0.17/0.45  # Result found by ehoh_best_nonlift
% 0.17/0.45  # Preprocessing class: HSSSSMSSMSSNHHA.
% 0.17/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45  # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.45  # Starting ho_unfolding_6 with 300s (1) cores
% 0.17/0.45  # Starting sh4l with 300s (1) cores
% 0.17/0.45  # Starting ehoh_best_nonlift with 300s (1) cores
% 0.17/0.45  # No SInE strategy applied
% 0.17/0.45  # Search class: HUHPM-FFSF32-DHHSFMNN
% 0.17/0.45  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.45  # Starting new_ho_10 with 181s (1) cores
% 0.17/0.45  # new_ho_10 with pid 17365 completed with status 0
% 0.17/0.45  # Result found by new_ho_10
% 0.17/0.45  # Preprocessing class: HSSSSMSSMSSNHHA.
% 0.17/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45  # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.45  # Starting ho_unfolding_6 with 300s (1) cores
% 0.17/0.45  # Starting sh4l with 300s (1) cores
% 0.17/0.45  # Starting ehoh_best_nonlift with 300s (1) cores
% 0.17/0.45  # No SInE strategy applied
% 0.17/0.45  # Search class: HUHPM-FFSF32-DHHSFMNN
% 0.17/0.45  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.45  # Starting new_ho_10 with 181s (1) cores
% 0.17/0.45  # Preprocessing time       : 0.001 s
% 0.17/0.45  # Presaturation interreduction done
% 0.17/0.45  
% 0.17/0.45  # Proof found!
% 0.17/0.45  # SZS status Theorem
% 0.17/0.45  # SZS output start CNFRefutation
% See solution above
% 0.17/0.45  # Parsed axioms                        : 29
% 0.17/0.45  # Removed by relevancy pruning/SinE    : 0
% 0.17/0.45  # Initial clauses                      : 29
% 0.17/0.45  # Removed in clause preprocessing      : 14
% 0.17/0.45  # Initial clauses in saturation        : 15
% 0.17/0.45  # Processed clauses                    : 35
% 0.17/0.45  # ...of these trivial                  : 1
% 0.17/0.45  # ...subsumed                          : 0
% 0.17/0.45  # ...remaining for further processing  : 34
% 0.17/0.45  # Other redundant clauses eliminated   : 0
% 0.17/0.45  # Clauses deleted for lack of memory   : 0
% 0.17/0.45  # Backward-subsumed                    : 0
% 0.17/0.45  # Backward-rewritten                   : 0
% 0.17/0.45  # Generated clauses                    : 70
% 0.17/0.45  # ...of the previous two non-redundant : 61
% 0.17/0.45  # ...aggressively subsumed             : 0
% 0.17/0.45  # Contextual simplify-reflections      : 0
% 0.17/0.45  # Paramodulations                      : 43
% 0.17/0.45  # Factorizations                       : 0
% 0.17/0.45  # NegExts                              : 22
% 0.17/0.45  # Equation resolutions                 : 0
% 0.17/0.45  # Disequality decompositions           : 0
% 0.17/0.45  # Total rewrite steps                  : 103
% 0.17/0.45  # ...of those cached                   : 67
% 0.17/0.45  # Propositional unsat checks           : 0
% 0.17/0.45  #    Propositional check models        : 0
% 0.17/0.45  #    Propositional check unsatisfiable : 0
% 0.17/0.45  #    Propositional clauses             : 0
% 0.17/0.45  #    Propositional clauses after purity: 0
% 0.17/0.45  #    Propositional unsat core size     : 0
% 0.17/0.45  #    Propositional preprocessing time  : 0.000
% 0.17/0.45  #    Propositional encoding time       : 0.000
% 0.17/0.45  #    Propositional solver time         : 0.000
% 0.17/0.45  #    Success case prop preproc time    : 0.000
% 0.17/0.45  #    Success case prop encoding time   : 0.000
% 0.17/0.45  #    Success case prop solver time     : 0.000
% 0.17/0.45  # Current number of processed clauses  : 19
% 0.17/0.45  #    Positive orientable unit clauses  : 9
% 0.17/0.45  #    Positive unorientable unit clauses: 1
% 0.17/0.45  #    Negative unit clauses             : 1
% 0.17/0.45  #    Non-unit-clauses                  : 8
% 0.17/0.45  # Current number of unprocessed clauses: 55
% 0.17/0.45  # ...number of literals in the above   : 68
% 0.17/0.45  # Current number of archived formulas  : 0
% 0.17/0.45  # Current number of archived clauses   : 15
% 0.17/0.45  # Clause-clause subsumption calls (NU) : 37
% 0.17/0.45  # Rec. Clause-clause subsumption calls : 28
% 0.17/0.45  # Non-unit clause-clause subsumptions  : 0
% 0.17/0.45  # Unit Clause-clause subsumption calls : 10
% 0.17/0.45  # Rewrite failures with RHS unbound    : 0
% 0.17/0.45  # BW rewrite match attempts            : 281
% 0.17/0.45  # BW rewrite match successes           : 2
% 0.17/0.45  # Condensation attempts                : 35
% 0.17/0.45  # Condensation successes               : 0
% 0.17/0.45  # Termbank termtop insertions          : 2894
% 0.17/0.45  # Search garbage collected termcells   : 98
% 0.17/0.45  
% 0.17/0.45  # -------------------------------------------------
% 0.17/0.45  # User time                : 0.005 s
% 0.17/0.45  # System time              : 0.002 s
% 0.17/0.45  # Total time               : 0.007 s
% 0.17/0.45  # Maximum resident set size: 1748 pages
% 0.17/0.45  
% 0.17/0.45  # -------------------------------------------------
% 0.17/0.45  # User time                : 0.005 s
% 0.17/0.45  # System time              : 0.005 s
% 0.17/0.45  # Total time               : 0.009 s
% 0.17/0.45  # Maximum resident set size: 1744 pages
% 0.17/0.45  % E---3.1 exiting
% 0.17/0.45  % E exiting
%------------------------------------------------------------------------------