TSTP Solution File: NUM752^4 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM752^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n025.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 01:17:04 EDT 2024

% Result   : Theorem 0.83s 0.59s
% Output   : CNFRefutation 0.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   39 (  18 unt;  14 typ;   0 def)
%            Number of atoms       :   88 (  33 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  338 (  15   ~;  12   |;   4   &; 291   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 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   :   58 (  40   ^  18   !;   0   ?;  58   :)

% 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_124,type,
    n_is: $i > $i > $o ).

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

thf(decl_189,type,
    frac: $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_198,type,
    n_pf: $i > $i > $i ).

thf(decl_199,type,
    esk1_0: $i ).

thf(decl_200,type,
    esk2_0: $i ).

thf(decl_201,type,
    esk3_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(satz62e,conjecture,
    ( all_of
    @ ^ [X1: $i] : ( in @ X1 @ frac )
    @ ^ [X1: $i] :
        ( all_of
        @ ^ [X530: $i] : ( in @ X530 @ frac )
        @ ^ [X531: $i] :
            ( all_of
            @ ^ [X4: $i] : ( in @ X4 @ frac )
            @ ^ [X4: $i] :
                ( ( n_eq @ X1 @ X531 )
               => ( n_eq @ ( n_pf @ X4 @ X1 ) @ ( n_pf @ X4 @ X531 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62e) ).

thf(satz56,axiom,
    ( all_of
    @ ^ [X1: $i] : ( in @ X1 @ frac )
    @ ^ [X1: $i] :
        ( all_of
        @ ^ [X508: $i] : ( in @ X508 @ frac )
        @ ^ [X509: $i] :
            ( all_of
            @ ^ [X4: $i] : ( in @ X4 @ frac )
            @ ^ [X4: $i] :
                ( all_of
                @ ^ [X13: $i] : ( in @ X13 @ frac )
                @ ^ [X13: $i] :
                    ( ( n_eq @ X1 @ X509 )
                   => ( ( n_eq @ X4 @ X13 )
                     => ( n_eq @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X509 @ X13 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz56) ).

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,
    ~ ! [X574: $i] :
        ( ( in @ X574 @ frac )
       => ! [X573: $i] :
            ( ( in @ X573 @ frac )
           => ! [X572: $i] :
                ( ( in @ X572 @ frac )
               => ( ( ( n_ts @ ( num @ X574 ) @ ( den @ X573 ) )
                    = ( n_ts @ ( num @ X573 ) @ ( den @ X574 ) ) )
                 => ( ( n_ts @ ( num @ ( n_pf @ X572 @ X574 ) ) @ ( den @ ( n_pf @ X572 @ X573 ) ) )
                    = ( n_ts @ ( num @ ( n_pf @ X572 @ X573 ) ) @ ( den @ ( n_pf @ X572 @ X574 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz62e])]),c_0_12]),c_0_13]) ).

thf(c_0_15,plain,
    ! [X584: $i] :
      ( ( in @ X584 @ frac )
     => ! [X583: $i] :
          ( ( in @ X583 @ frac )
         => ! [X582: $i] :
              ( ( in @ X582 @ frac )
             => ! [X581: $i] :
                  ( ( in @ X581 @ frac )
                 => ( ( ( n_ts @ ( num @ X584 ) @ ( den @ X583 ) )
                      = ( n_ts @ ( num @ X583 ) @ ( den @ X584 ) ) )
                   => ( ( ( n_ts @ ( num @ X582 ) @ ( den @ X581 ) )
                        = ( n_ts @ ( num @ X581 ) @ ( den @ X582 ) ) )
                     => ( ( n_ts @ ( num @ ( n_pf @ X584 @ X582 ) ) @ ( den @ ( n_pf @ X583 @ X581 ) ) )
                        = ( n_ts @ ( num @ ( n_pf @ X583 @ X581 ) ) @ ( den @ ( n_pf @ X584 @ X582 ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz56]),c_0_12]),c_0_13]) ).

thf(c_0_16,negated_conjecture,
    ( ( in @ esk1_0 @ frac )
    & ( in @ esk2_0 @ frac )
    & ( in @ esk3_0 @ frac )
    & ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) )
      = ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) )
    & ( ( n_ts @ ( num @ ( n_pf @ esk3_0 @ esk1_0 ) ) @ ( den @ ( n_pf @ esk3_0 @ esk2_0 ) ) )
     != ( n_ts @ ( num @ ( n_pf @ esk3_0 @ esk2_0 ) ) @ ( den @ ( n_pf @ esk3_0 @ esk1_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,
    ! [X845: $i,X846: $i,X847: $i,X848: $i] :
      ( ~ ( in @ X845 @ frac )
      | ~ ( in @ X846 @ frac )
      | ~ ( in @ X847 @ frac )
      | ~ ( in @ X848 @ frac )
      | ( ( n_ts @ ( num @ X845 ) @ ( den @ X846 ) )
       != ( n_ts @ ( num @ X846 ) @ ( den @ X845 ) ) )
      | ( ( n_ts @ ( num @ X847 ) @ ( den @ X848 ) )
       != ( n_ts @ ( num @ X848 ) @ ( den @ X847 ) ) )
      | ( ( n_ts @ ( num @ ( n_pf @ X845 @ X847 ) ) @ ( den @ ( n_pf @ X846 @ X848 ) ) )
        = ( n_ts @ ( num @ ( n_pf @ X846 @ X848 ) ) @ ( den @ ( n_pf @ X845 @ X847 ) ) ) ) ),
    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_pf @ esk3_0 @ esk1_0 ) ) @ ( den @ ( n_pf @ esk3_0 @ esk2_0 ) ) )
   != ( n_ts @ ( num @ ( n_pf @ esk3_0 @ esk2_0 ) ) @ ( den @ ( n_pf @ esk3_0 @ esk1_0 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_19,plain,
    ! [X1: $i,X4: $i,X6: $i,X5: $i] :
      ( ( ( n_ts @ ( num @ ( n_pf @ X1 @ X5 ) ) @ ( den @ ( n_pf @ X4 @ X6 ) ) )
        = ( n_ts @ ( num @ ( n_pf @ X4 @ X6 ) ) @ ( den @ ( n_pf @ X1 @ X5 ) ) ) )
      | ~ ( in @ X1 @ frac )
      | ~ ( in @ X4 @ frac )
      | ~ ( in @ X5 @ frac )
      | ~ ( in @ X6 @ frac )
      | ( ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) )
       != ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) )
      | ( ( n_ts @ ( num @ X5 ) @ ( den @ X6 ) )
       != ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_20,negated_conjecture,
    ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) )
    = ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_21,negated_conjecture,
    in @ esk2_0 @ frac,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_22,negated_conjecture,
    in @ esk1_0 @ frac,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_23,negated_conjecture,
    in @ esk3_0 @ frac,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_24,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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]),c_0_22]),c_0_23])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : NUM752^4 : TPTP v8.2.0. Released v7.1.0.
% 0.12/0.13  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n025.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   : Mon May 20 04:09:53 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
% 0.83/0.59  # Version: 3.1.0-ho
% 0.83/0.59  # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.83/0.59  # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.83/0.59  # Starting pre_casc_4 with 1200s (4) cores
% 0.83/0.59  # Starting full_lambda_6 with 300s (1) cores
% 0.83/0.59  # Starting sh10 with 300s (1) cores
% 0.83/0.59  # Starting post_as_ho9 with 300s (1) cores
% 0.83/0.59  # Starting post_as_ho8 with 300s (1) cores
% 0.83/0.59  # pre_casc_4 with pid 24352 completed with status 0
% 0.83/0.59  # Result found by pre_casc_4
% 0.83/0.59  # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.83/0.59  # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.83/0.59  # Starting pre_casc_4 with 1200s (4) cores
% 0.83/0.59  # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.83/0.59  # Search class: HGUSM-FSLM31-DHSMMFBN
% 0.83/0.59  # partial match(2): HGUSM-FSLM31-DHSFFFBN
% 0.83/0.59  # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 0.83/0.59  # Starting new_bool_5 with 540s (1) cores
% 0.83/0.59  # Starting pre_casc_4 with 121s (1) cores
% 0.83/0.59  # Starting ehoh_best8_lambda with 135s (1) cores
% 0.83/0.59  # Starting new_bool_1 with 135s (1) cores
% 0.83/0.59  # new_bool_5 with pid 24357 completed with status 0
% 0.83/0.59  # Result found by new_bool_5
% 0.83/0.59  # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.83/0.59  # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.83/0.59  # Starting pre_casc_4 with 1200s (4) cores
% 0.83/0.59  # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.83/0.59  # Search class: HGUSM-FSLM31-DHSMMFBN
% 0.83/0.59  # partial match(2): HGUSM-FSLM31-DHSFFFBN
% 0.83/0.59  # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 0.83/0.59  # Starting new_bool_5 with 540s (1) cores
% 0.83/0.59  # Preprocessing time       : 0.005 s
% 0.83/0.59  # Presaturation interreduction done
% 0.83/0.59  
% 0.83/0.59  # Proof found!
% 0.83/0.59  # SZS status Theorem
% 0.83/0.59  # SZS output start CNFRefutation
% See solution above
% 0.83/0.59  # Parsed axioms                        : 586
% 0.83/0.59  # Removed by relevancy pruning/SinE    : 446
% 0.83/0.59  # Initial clauses                      : 141
% 0.83/0.59  # Removed in clause preprocessing      : 12
% 0.83/0.59  # Initial clauses in saturation        : 129
% 0.83/0.59  # Processed clauses                    : 280
% 0.83/0.59  # ...of these trivial                  : 3
% 0.83/0.59  # ...subsumed                          : 52
% 0.83/0.59  # ...remaining for further processing  : 225
% 0.83/0.59  # Other redundant clauses eliminated   : 16
% 0.83/0.59  # Clauses deleted for lack of memory   : 0
% 0.83/0.59  # Backward-subsumed                    : 0
% 0.83/0.59  # Backward-rewritten                   : 6
% 0.83/0.59  # Generated clauses                    : 741
% 0.83/0.59  # ...of the previous two non-redundant : 683
% 0.83/0.59  # ...aggressively subsumed             : 0
% 0.83/0.59  # Contextual simplify-reflections      : 0
% 0.83/0.59  # Paramodulations                      : 681
% 0.83/0.59  # Factorizations                       : 0
% 0.83/0.59  # NegExts                              : 1
% 0.83/0.59  # Equation resolutions                 : 22
% 0.83/0.59  # Disequality decompositions           : 0
% 0.83/0.59  # Total rewrite steps                  : 304
% 0.83/0.59  # ...of those cached                   : 262
% 0.83/0.59  # Propositional unsat checks           : 0
% 0.83/0.59  #    Propositional check models        : 0
% 0.83/0.59  #    Propositional check unsatisfiable : 0
% 0.83/0.59  #    Propositional clauses             : 0
% 0.83/0.59  #    Propositional clauses after purity: 0
% 0.83/0.59  #    Propositional unsat core size     : 0
% 0.83/0.59  #    Propositional preprocessing time  : 0.000
% 0.83/0.59  #    Propositional encoding time       : 0.000
% 0.83/0.59  #    Propositional solver time         : 0.000
% 0.83/0.59  #    Success case prop preproc time    : 0.000
% 0.83/0.59  #    Success case prop encoding time   : 0.000
% 0.83/0.59  #    Success case prop solver time     : 0.000
% 0.83/0.59  # Current number of processed clauses  : 117
% 0.83/0.59  #    Positive orientable unit clauses  : 48
% 0.83/0.59  #    Positive unorientable unit clauses: 0
% 0.83/0.59  #    Negative unit clauses             : 9
% 0.83/0.59  #    Non-unit-clauses                  : 60
% 0.83/0.59  # Current number of unprocessed clauses: 602
% 0.83/0.59  # ...number of literals in the above   : 2897
% 0.83/0.59  # Current number of archived formulas  : 0
% 0.83/0.59  # Current number of archived clauses   : 100
% 0.83/0.59  # Clause-clause subsumption calls (NU) : 6627
% 0.83/0.59  # Rec. Clause-clause subsumption calls : 1139
% 0.83/0.59  # Non-unit clause-clause subsumptions  : 41
% 0.83/0.59  # Unit Clause-clause subsumption calls : 24
% 0.83/0.59  # Rewrite failures with RHS unbound    : 0
% 0.83/0.59  # BW rewrite match attempts            : 20
% 0.83/0.59  # BW rewrite match successes           : 6
% 0.83/0.59  # Condensation attempts                : 280
% 0.83/0.59  # Condensation successes               : 0
% 0.83/0.59  # Termbank termtop insertions          : 67386
% 0.83/0.59  # Search garbage collected termcells   : 16863
% 0.83/0.59  
% 0.83/0.59  # -------------------------------------------------
% 0.83/0.59  # User time                : 0.069 s
% 0.83/0.59  # System time              : 0.008 s
% 0.83/0.59  # Total time               : 0.077 s
% 0.83/0.59  # Maximum resident set size: 5336 pages
% 0.83/0.59  
% 0.83/0.59  # -------------------------------------------------
% 0.83/0.59  # User time                : 0.260 s
% 0.83/0.59  # System time              : 0.029 s
% 0.83/0.59  # Total time               : 0.289 s
% 0.83/0.59  # Maximum resident set size: 2796 pages
% 0.83/0.59  % E---3.1 exiting
% 0.83/0.59  % E exiting
%------------------------------------------------------------------------------