TSTP Solution File: NUM728^4 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM728^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n006.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 : Tue May 21 01:15:50 EDT 2024

% Result   : Theorem 0.88s 0.72s
% Output   : CNFRefutation 0.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   37 (  16 unt;  14 typ;   0 def)
%            Number of atoms       :   61 (  24 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  259 (   7   ~;   4   |;   2   &; 239   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   5 con; 0-3 aty)
%            Number of variables   :   45 (  34   ^  11   !;   0   ?;  45   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    is_of: $i > ( $i > $o ) > $o ).

thf(decl_23,type,
    all_of: ( $i > $o ) > ( $i > $o ) > $o ).

thf(decl_25,type,
    in: $i > $i > $o ).

thf(decl_77,type,
    e_is: $i > $i > $i > $o ).

thf(decl_123,type,
    nat: $i ).

thf(decl_124,type,
    n_is: $i > $i > $o ).

thf(decl_162,type,
    n_ts: $i > $i > $i ).

thf(decl_189,type,
    frac: $i ).

thf(decl_190,type,
    n_fr: $i > $i > $i ).

thf(decl_191,type,
    num: $i > $i ).

thf(decl_192,type,
    den: $i > $i ).

thf(decl_193,type,
    n_eq: $i > $i > $o ).

thf(decl_327,type,
    esk130_0: $i ).

thf(decl_328,type,
    esk131_0: $i ).

thf(def_e_is,axiom,
    ( e_is
    = ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_e_is) ).

thf(def_all_of,axiom,
    ( all_of
    = ( ^ [X3: $i > $o,X2: $i > $o] :
        ! [X4: $i] :
          ( ( is_of @ X4 @ X3 )
         => ( X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_all_of) ).

thf(def_is_of,axiom,
    ( is_of
    = ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_is_of) ).

thf(def_n_eq,axiom,
    ( n_eq
    = ( ^ [X1: $i,X436: $i] : ( n_is @ ( n_ts @ ( num @ X1 ) @ ( den @ X436 ) ) @ ( n_ts @ ( num @ X436 ) @ ( den @ X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_n_eq) ).

thf(def_n_is,axiom,
    ( n_is
    = ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_is) ).

thf(satz40a,conjecture,
    ( all_of
    @ ^ [X1: $i] : ( in @ X1 @ frac )
    @ ^ [X1: $i] :
        ( all_of
        @ ^ [X443: $i] : ( in @ X443 @ nat )
        @ ^ [X444: $i] : ( n_eq @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X444 ) @ ( n_ts @ ( den @ X1 ) @ X444 ) ) @ X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40a) ).

thf(satz40,axiom,
    ( all_of
    @ ^ [X1: $i] : ( in @ X1 @ frac )
    @ ^ [X1: $i] :
        ( all_of
        @ ^ [X441: $i] : ( in @ X441 @ nat )
        @ ^ [X442: $i] : ( n_eq @ X1 @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X442 ) @ ( n_ts @ ( den @ X1 ) @ X442 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40) ).

thf(c_0_7,plain,
    ( e_is
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
    inference(fof_simplification,[status(thm)],[def_e_is]) ).

thf(c_0_8,plain,
    ( all_of
    = ( ^ [Z0: $i > $o,Z1: $i > $o] :
        ! [X4: $i] :
          ( ( Z0 @ X4 )
         => ( Z1 @ X4 ) ) ) ),
    inference(fof_simplification,[status(thm)],[def_all_of]) ).

thf(c_0_9,plain,
    ( is_of
    = ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
    inference(fof_simplification,[status(thm)],[def_is_of]) ).

thf(c_0_10,plain,
    ( n_eq
    = ( ^ [Z0: $i,Z1: $i] :
          ( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
          = ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[def_n_eq]) ).

thf(c_0_11,axiom,
    ( n_is
    = ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
    inference(apply_def,[status(thm)],[def_n_is,c_0_7]) ).

thf(c_0_12,plain,
    ( all_of
    = ( ^ [Z0: $i > $o,Z1: $i > $o] :
        ! [X4: $i] :
          ( ( Z0 @ X4 )
         => ( Z1 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).

thf(c_0_13,plain,
    ( n_eq
    = ( ^ [Z0: $i,Z1: $i] :
          ( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
          = ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_14,negated_conjecture,
    ~ ! [X1266: $i] :
        ( ( in @ X1266 @ frac )
       => ! [X1265: $i] :
            ( ( in @ X1265 @ nat )
           => ( ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X1266 ) @ X1265 ) @ ( n_ts @ ( den @ X1266 ) @ X1265 ) ) ) @ ( den @ X1266 ) )
              = ( n_ts @ ( num @ X1266 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X1266 ) @ X1265 ) @ ( n_ts @ ( den @ X1266 ) @ X1265 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz40a])]),c_0_12]),c_0_13]) ).

thf(c_0_15,plain,
    ! [X1264: $i] :
      ( ( in @ X1264 @ frac )
     => ! [X1263: $i] :
          ( ( in @ X1263 @ nat )
         => ( ( n_ts @ ( num @ X1264 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X1264 ) @ X1263 ) @ ( n_ts @ ( den @ X1264 ) @ X1263 ) ) ) )
            = ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X1264 ) @ X1263 ) @ ( n_ts @ ( den @ X1264 ) @ X1263 ) ) ) @ ( den @ X1264 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz40]),c_0_12]),c_0_13]) ).

thf(c_0_16,negated_conjecture,
    ( ( in @ esk130_0 @ frac )
    & ( in @ esk131_0 @ nat )
    & ( ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ esk130_0 ) @ esk131_0 ) @ ( n_ts @ ( den @ esk130_0 ) @ esk131_0 ) ) ) @ ( den @ esk130_0 ) )
     != ( n_ts @ ( num @ esk130_0 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ esk130_0 ) @ esk131_0 ) @ ( n_ts @ ( den @ esk130_0 ) @ esk131_0 ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).

thf(c_0_17,plain,
    ! [X2041: $i,X2042: $i] :
      ( ~ ( in @ X2041 @ frac )
      | ~ ( in @ X2042 @ nat )
      | ( ( n_ts @ ( num @ X2041 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X2041 ) @ X2042 ) @ ( n_ts @ ( den @ X2041 ) @ X2042 ) ) ) )
        = ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X2041 ) @ X2042 ) @ ( n_ts @ ( den @ X2041 ) @ X2042 ) ) ) @ ( den @ X2041 ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).

thf(c_0_18,negated_conjecture,
    ( ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ esk130_0 ) @ esk131_0 ) @ ( n_ts @ ( den @ esk130_0 ) @ esk131_0 ) ) ) @ ( den @ esk130_0 ) )
   != ( n_ts @ ( num @ esk130_0 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ esk130_0 ) @ esk131_0 ) @ ( n_ts @ ( den @ esk130_0 ) @ esk131_0 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_19,plain,
    ! [X1: $i,X4: $i] :
      ( ( ( n_ts @ ( num @ X1 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X4 ) @ ( n_ts @ ( den @ X1 ) @ X4 ) ) ) )
        = ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X4 ) @ ( n_ts @ ( den @ X1 ) @ X4 ) ) ) @ ( den @ X1 ) ) )
      | ~ ( in @ X1 @ frac )
      | ~ ( in @ X4 @ nat ) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_20,negated_conjecture,
    in @ esk131_0 @ nat,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_21,negated_conjecture,
    in @ esk130_0 @ frac,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_22,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem    : NUM728^4 : TPTP v8.2.0. Released v7.1.0.
% 0.07/0.12  % Command    : run_E %s %d THM
% 0.11/0.31  % Computer : n006.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   : Mon May 20 07:24:07 EDT 2024
% 0.16/0.31  % CPUTime    : 
% 0.16/0.44  Running higher-order theorem proving
% 0.16/0.44  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
% 0.58/0.61  # Type mismatch in argument #1 of indeq @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ (d_11_i @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1)) @ db(0): expected $i but got $o
% 0.58/0.61  eprover: Type error
% 0.58/0.62  # Type mismatch in argument #1 of indeq @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ (d_11_i @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1)) @ db(0): expected $i but got $o
% 0.58/0.62  eprover: Type error
% 0.83/0.64  # Type mismatch in argument #1 of indeq @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ (d_11_i @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1)) @ db(0): expected $i but got $o
% 0.83/0.64  eprover: Type error
% 0.88/0.72  # Version: 3.1.0-ho
% 0.88/0.72  # Preprocessing class: HSLMSMSMLMLCHSA.
% 0.88/0.72  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.88/0.72  # Starting new_ho_10 with 1500s (5) cores
% 0.88/0.72  # Starting ho_unfolding_6 with 300s (1) cores
% 0.88/0.72  # Starting sh4l with 300s (1) cores
% 0.88/0.72  # Starting ehoh_best_nonlift_nonlambdatoforall with 300s (1) cores
% 0.88/0.72  # ho_unfolding_6 with pid 9439 completed with status 0
% 0.88/0.72  # Result found by ho_unfolding_6
% 0.88/0.72  # Preprocessing class: HSLMSMSMLMLCHSA.
% 0.88/0.72  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.88/0.72  # Starting new_ho_10 with 1500s (5) cores
% 0.88/0.72  # Starting ho_unfolding_6 with 300s (1) cores
% 0.88/0.72  # No SInE strategy applied
% 0.88/0.72  # Search class: HGHSM-FSLM32-DHSMSSBN
% 0.88/0.72  # partial match(1): HGHSM-FSLM32-MHSMSSBN
% 0.88/0.72  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.88/0.72  # Starting new_ho_10 with 181s (1) cores
% 0.88/0.72  # new_ho_10 with pid 9492 completed with status 3
% 0.88/0.72  # Starting ho_unfolding_6 with 31s (1) cores
% 0.88/0.72  # ho_unfolding_6 with pid 9493 completed with status 0
% 0.88/0.72  # Result found by ho_unfolding_6
% 0.88/0.72  # Preprocessing class: HSLMSMSMLMLCHSA.
% 0.88/0.72  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.88/0.72  # Starting new_ho_10 with 1500s (5) cores
% 0.88/0.72  # Starting ho_unfolding_6 with 300s (1) cores
% 0.88/0.72  # No SInE strategy applied
% 0.88/0.72  # Search class: HGHSM-FSLM32-DHSMSSBN
% 0.88/0.72  # partial match(1): HGHSM-FSLM32-MHSMSSBN
% 0.88/0.72  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.88/0.72  # Starting new_ho_10 with 181s (1) cores
% 0.88/0.72  # new_ho_10 with pid 9492 completed with status 3
% 0.88/0.72  # Starting ho_unfolding_6 with 31s (1) cores
% 0.88/0.72  # Preprocessing time       : 0.012 s
% 0.88/0.72  
% 0.88/0.72  # Proof found!
% 0.88/0.72  # SZS status Theorem
% 0.88/0.72  # SZS output start CNFRefutation
% See solution above
% 0.88/0.72  # Parsed axioms                        : 534
% 0.88/0.72  # Removed by relevancy pruning/SinE    : 0
% 0.88/0.72  # Initial clauses                      : 1635
% 0.88/0.72  # Removed in clause preprocessing      : 1101
% 0.88/0.72  # Initial clauses in saturation        : 534
% 0.88/0.72  # Processed clauses                    : 314
% 0.88/0.72  # ...of these trivial                  : 4
% 0.88/0.72  # ...subsumed                          : 19
% 0.88/0.72  # ...remaining for further processing  : 291
% 0.88/0.72  # Other redundant clauses eliminated   : 61
% 0.88/0.72  # Clauses deleted for lack of memory   : 0
% 0.88/0.72  # Backward-subsumed                    : 0
% 0.88/0.72  # Backward-rewritten                   : 0
% 0.88/0.72  # Generated clauses                    : 3090
% 0.88/0.72  # ...of the previous two non-redundant : 3028
% 0.88/0.72  # ...aggressively subsumed             : 0
% 0.88/0.72  # Contextual simplify-reflections      : 0
% 0.88/0.72  # Paramodulations                      : 2844
% 0.88/0.72  # Factorizations                       : 10
% 0.88/0.72  # NegExts                              : 0
% 0.88/0.72  # Equation resolutions                 : 63
% 0.88/0.72  # Disequality decompositions           : 0
% 0.88/0.72  # Total rewrite steps                  : 105
% 0.88/0.72  # ...of those cached                   : 82
% 0.88/0.72  # Propositional unsat checks           : 0
% 0.88/0.72  #    Propositional check models        : 0
% 0.88/0.72  #    Propositional check unsatisfiable : 0
% 0.88/0.72  #    Propositional clauses             : 0
% 0.88/0.72  #    Propositional clauses after purity: 0
% 0.88/0.72  #    Propositional unsat core size     : 0
% 0.88/0.72  #    Propositional preprocessing time  : 0.000
% 0.88/0.72  #    Propositional encoding time       : 0.000
% 0.88/0.72  #    Propositional solver time         : 0.000
% 0.88/0.72  #    Success case prop preproc time    : 0.000
% 0.88/0.72  #    Success case prop encoding time   : 0.000
% 0.88/0.72  #    Success case prop solver time     : 0.000
% 0.88/0.72  # Current number of processed clauses  : 246
% 0.88/0.72  #    Positive orientable unit clauses  : 73
% 0.88/0.72  #    Positive unorientable unit clauses: 0
% 0.88/0.72  #    Negative unit clauses             : 3
% 0.88/0.72  #    Non-unit-clauses                  : 170
% 0.88/0.72  # Current number of unprocessed clauses: 3235
% 0.88/0.72  # ...number of literals in the above   : 13929
% 0.88/0.72  # Current number of archived formulas  : 0
% 0.88/0.72  # Current number of archived clauses   : 0
% 0.88/0.72  # Clause-clause subsumption calls (NU) : 15929
% 0.88/0.72  # Rec. Clause-clause subsumption calls : 1966
% 0.88/0.72  # Non-unit clause-clause subsumptions  : 21
% 0.88/0.72  # Unit Clause-clause subsumption calls : 7
% 0.88/0.72  # Rewrite failures with RHS unbound    : 0
% 0.88/0.72  # BW rewrite match attempts            : 19
% 0.88/0.72  # BW rewrite match successes           : 0
% 0.88/0.72  # Condensation attempts                : 314
% 0.88/0.72  # Condensation successes               : 2
% 0.88/0.72  # Termbank termtop insertions          : 314348
% 0.88/0.72  # Search garbage collected termcells   : 69673
% 0.88/0.72  
% 0.88/0.72  # -------------------------------------------------
% 0.88/0.72  # User time                : 0.215 s
% 0.88/0.72  # System time              : 0.022 s
% 0.88/0.72  # Total time               : 0.237 s
% 0.88/0.72  # Maximum resident set size: 11112 pages
% 0.88/0.72  
% 0.88/0.72  # -------------------------------------------------
% 0.88/0.72  # User time                : 0.230 s
% 0.88/0.72  # System time              : 0.026 s
% 0.88/0.72  # Total time               : 0.256 s
% 0.88/0.72  # Maximum resident set size: 2620 pages
% 0.88/0.72  % E---3.1 exiting
% 0.88/0.72  % E exiting
%------------------------------------------------------------------------------