TSTP Solution File: ITP226^3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP226^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n032.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 08:07:35 EDT 2024

% Result   : Theorem 32.44s 12.61s
% Output   : CNFRefutation 32.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   42 (  12 unt;  12 typ;   0 def)
%            Number of atoms       :   65 (   4 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  197 (  26   ~;  24   |;   3   &; 137   @)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   32 (   3   ^  29   !;   0   ?;  32   :)

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

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

thf(decl_sort3,type,
    vEBT_VEBT: $tType ).

thf(decl_853,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(decl_952,type,
    vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).

thf(decl_964,type,
    vEBT_invar_vebt: vEBT_VEBT > nat > $o ).

thf(decl_965,type,
    vEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(decl_972,type,
    vEBT_vebt_member: vEBT_VEBT > nat > $o ).

thf(decl_993,type,
    member_nat: nat > set_nat > $o ).

thf(decl_1000,type,
    n: nat ).

thf(decl_1001,type,
    t: vEBT_VEBT ).

thf(decl_1002,type,
    x: nat ).

thf(conj_1,conjecture,
    ( ( vEBT_vebt_member @ t @ x )
  <=> ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.QE1H20wuUP/E---3.1_13683.p',conj_1) ).

thf(fact_8231_set__vebt__def,axiom,
    ( vEBT_set_vebt
    = ( ^ [X13: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ X13 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.QE1H20wuUP/E---3.1_13683.p',fact_8231_set__vebt__def) ).

thf(fact_4_both__member__options__equiv__member,axiom,
    ! [X1: vEBT_VEBT,X4: nat,X2: nat] :
      ( ( vEBT_invar_vebt @ X1 @ X4 )
     => ( ( vEBT_V8194947554948674370ptions @ X1 @ X2 )
      <=> ( vEBT_vebt_member @ X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.QE1H20wuUP/E---3.1_13683.p',fact_4_both__member__options__equiv__member) ).

thf(fact_48_mem__Collect__eq,axiom,
    ! [X54: nat,X40: nat > $o] :
      ( ( member_nat @ X54 @ ( collect_nat @ X40 ) )
    <=> ( X40 @ X54 ) ),
    file('/export/starexec/sandbox/tmp/tmp.QE1H20wuUP/E---3.1_13683.p',fact_48_mem__Collect__eq) ).

thf(conj_0,hypothesis,
    vEBT_invar_vebt @ t @ n,
    file('/export/starexec/sandbox/tmp/tmp.QE1H20wuUP/E---3.1_13683.p',conj_0) ).

thf(fact_5_valid__member__both__member__options,axiom,
    ! [X1: vEBT_VEBT,X4: nat,X2: nat] :
      ( ( vEBT_invar_vebt @ X1 @ X4 )
     => ( ( vEBT_V8194947554948674370ptions @ X1 @ X2 )
       => ( vEBT_vebt_member @ X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.QE1H20wuUP/E---3.1_13683.p',fact_5_valid__member__both__member__options) ).

thf(c_0_6,negated_conjecture,
    ~ ( ( vEBT_vebt_member @ t @ x )
    <=> ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ),
    inference(assume_negation,[status(cth)],[conj_1]) ).

thf(c_0_7,plain,
    ( vEBT_set_vebt
    = ( ^ [Z0: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ Z0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_8231_set__vebt__def]) ).

thf(c_0_8,negated_conjecture,
    ( ( ~ ( vEBT_vebt_member @ t @ x )
      | ~ ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) )
    & ( ( vEBT_vebt_member @ t @ x )
      | ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_6]) ).

thf(c_0_9,plain,
    ( vEBT_set_vebt
    = ( ^ [Z0: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ Z0 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_10,plain,
    ! [X23395: vEBT_VEBT,X23396: nat,X23397: nat] :
      ( ( ~ ( vEBT_V8194947554948674370ptions @ X23395 @ X23397 )
        | ( vEBT_vebt_member @ X23395 @ X23397 )
        | ~ ( vEBT_invar_vebt @ X23395 @ X23396 ) )
      & ( ~ ( vEBT_vebt_member @ X23395 @ X23397 )
        | ( vEBT_V8194947554948674370ptions @ X23395 @ X23397 )
        | ~ ( vEBT_invar_vebt @ X23395 @ X23396 ) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_both__member__options__equiv__member])])]) ).

thf(c_0_11,plain,
    ! [X25546: nat,X25547: nat > $o] :
      ( ( ~ ( member_nat @ X25546 @ ( collect_nat @ X25547 ) )
        | ( X25547 @ X25546 ) )
      & ( ~ ( X25547 @ X25546 )
        | ( member_nat @ X25546 @ ( collect_nat @ X25547 ) ) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_48_mem__Collect__eq])]) ).

thf(c_0_12,negated_conjecture,
    ( ( vEBT_vebt_member @ t @ x )
    | ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_13,plain,
    ! [X1: vEBT_VEBT] :
      ( ( vEBT_set_vebt @ X1 )
      = ( collect_nat @ ( vEBT_V8194947554948674370ptions @ X1 ) ) ),
    inference(arg_cong,[status(thm)],[c_0_9]) ).

thf(c_0_14,negated_conjecture,
    ( ~ ( vEBT_vebt_member @ t @ x )
    | ~ ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_15,plain,
    ! [X1: vEBT_VEBT,X2: nat,X3: nat] :
      ( ( vEBT_V8194947554948674370ptions @ X1 @ X2 )
      | ~ ( vEBT_vebt_member @ X1 @ X2 )
      | ~ ( vEBT_invar_vebt @ X1 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_16,hypothesis,
    vEBT_invar_vebt @ t @ n,
    inference(split_conjunct,[status(thm)],[conj_0]) ).

thf(c_0_17,plain,
    ! [X2: nat,X40: nat > $o] :
      ( ( X40 @ X2 )
      | ~ ( member_nat @ X2 @ ( collect_nat @ X40 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_18,negated_conjecture,
    ( ( member_nat @ x @ ( collect_nat @ ( vEBT_V8194947554948674370ptions @ t ) ) )
    | ( vEBT_vebt_member @ t @ x ) ),
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_19,negated_conjecture,
    ( ~ ( member_nat @ x @ ( collect_nat @ ( vEBT_V8194947554948674370ptions @ t ) ) )
    | ~ ( vEBT_vebt_member @ t @ x ) ),
    inference(rw,[status(thm)],[c_0_14,c_0_13]) ).

thf(c_0_20,plain,
    ! [X40: nat > $o,X2: nat] :
      ( ( member_nat @ X2 @ ( collect_nat @ X40 ) )
      | ~ ( X40 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_21,hypothesis,
    ! [X2: nat] :
      ( ( vEBT_V8194947554948674370ptions @ t @ X2 )
      | ~ ( vEBT_vebt_member @ t @ X2 ) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

thf(c_0_22,negated_conjecture,
    ( ( vEBT_vebt_member @ t @ x )
    | ( vEBT_V8194947554948674370ptions @ t @ x ) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

thf(c_0_23,plain,
    ! [X23398: vEBT_VEBT,X23399: nat,X23400: nat] :
      ( ~ ( vEBT_invar_vebt @ X23398 @ X23399 )
      | ~ ( vEBT_V8194947554948674370ptions @ X23398 @ X23400 )
      | ( vEBT_vebt_member @ X23398 @ X23400 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_valid__member__both__member__options])]) ).

thf(c_0_24,negated_conjecture,
    ( ~ ( vEBT_vebt_member @ t @ x )
    | ~ ( vEBT_V8194947554948674370ptions @ t @ x ) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

thf(c_0_25,negated_conjecture,
    vEBT_V8194947554948674370ptions @ t @ x,
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_26,plain,
    ! [X1: vEBT_VEBT,X2: nat,X3: nat] :
      ( ( vEBT_vebt_member @ X1 @ X3 )
      | ~ ( vEBT_invar_vebt @ X1 @ X2 )
      | ~ ( vEBT_V8194947554948674370ptions @ X1 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

thf(c_0_27,negated_conjecture,
    ~ ( vEBT_vebt_member @ t @ x ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).

thf(c_0_28,hypothesis,
    ! [X2: nat] :
      ( ( vEBT_vebt_member @ t @ X2 )
      | ~ ( vEBT_V8194947554948674370ptions @ t @ X2 ) ),
    inference(spm,[status(thm)],[c_0_26,c_0_16]) ).

thf(c_0_29,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.33/2.35  % Problem    : ITP226^3 : TPTP v8.1.2. Released v8.1.0.
% 2.35/2.36  % Command    : run_E %s %d THM
% 2.35/2.55  % Computer : n032.cluster.edu
% 2.35/2.55  % Model    : x86_64 x86_64
% 2.35/2.55  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.35/2.55  % Memory   : 8042.1875MB
% 2.35/2.55  % OS       : Linux 3.10.0-693.el7.x86_64
% 2.35/2.55  % CPULimit   : 300
% 2.35/2.55  % WCLimit    : 300
% 2.35/2.55  % DateTime   : Fri May  3 12:51:11 EDT 2024
% 2.35/2.55  % CPUTime    : 
% 4.89/5.06  Running higher-order theorem proving
% 4.89/5.06  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.QE1H20wuUP/E---3.1_13683.p
% 32.44/12.61  # Version: 3.1.0-ho
% 32.44/12.61  # partial match(1): HMLMSMSMSSLCHFA
% 32.44/12.61  # Preprocessing class: HMLMSMLMSSLCHFA.
% 32.44/12.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 32.44/12.61  # Starting new_ho_10 with 1500s (5) cores
% 32.44/12.61  # Starting sh5l with 300s (1) cores
% 32.44/12.61  # Starting new_bool_1 with 300s (1) cores
% 32.44/12.61  # Starting new_bool_2 with 300s (1) cores
% 32.44/12.61  # new_bool_2 with pid 13765 completed with status 0
% 32.44/12.61  # Result found by new_bool_2
% 32.44/12.61  # partial match(1): HMLMSMSMSSLCHFA
% 32.44/12.61  # Preprocessing class: HMLMSMLMSSLCHFA.
% 32.44/12.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 32.44/12.61  # Starting new_ho_10 with 1500s (5) cores
% 32.44/12.61  # Starting sh5l with 300s (1) cores
% 32.44/12.61  # Starting new_bool_1 with 300s (1) cores
% 32.44/12.61  # Starting new_bool_2 with 300s (1) cores
% 32.44/12.61  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 32.44/12.61  # Search class: HGHSM-SMLM32-DHFFFSBN
% 32.44/12.61  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 32.44/12.61  # Starting new_ho_10 with 181s (1) cores
% 32.44/12.61  # new_ho_10 with pid 13766 completed with status 0
% 32.44/12.61  # Result found by new_ho_10
% 32.44/12.61  # partial match(1): HMLMSMSMSSLCHFA
% 32.44/12.61  # Preprocessing class: HMLMSMLMSSLCHFA.
% 32.44/12.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 32.44/12.61  # Starting new_ho_10 with 1500s (5) cores
% 32.44/12.61  # Starting sh5l with 300s (1) cores
% 32.44/12.61  # Starting new_bool_1 with 300s (1) cores
% 32.44/12.61  # Starting new_bool_2 with 300s (1) cores
% 32.44/12.61  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 32.44/12.61  # Search class: HGHSM-SMLM32-DHFFFSBN
% 32.44/12.61  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 32.44/12.61  # Starting new_ho_10 with 181s (1) cores
% 32.44/12.61  # Preprocessing time       : 0.115 s
% 32.44/12.61  # Presaturation interreduction done
% 32.44/12.61  
% 32.44/12.61  # Proof found!
% 32.44/12.61  # SZS status Theorem
% 32.44/12.61  # SZS output start CNFRefutation
% See solution above
% 32.44/12.61  # Parsed axioms                        : 11247
% 32.44/12.61  # Removed by relevancy pruning/SinE    : 8122
% 32.44/12.61  # Initial clauses                      : 8118
% 32.44/12.61  # Removed in clause preprocessing      : 1929
% 32.44/12.61  # Initial clauses in saturation        : 6189
% 32.44/12.61  # Processed clauses                    : 8554
% 32.44/12.61  # ...of these trivial                  : 259
% 32.44/12.61  # ...subsumed                          : 1665
% 32.44/12.61  # ...remaining for further processing  : 6630
% 32.44/12.61  # Other redundant clauses eliminated   : 1427
% 32.44/12.61  # Clauses deleted for lack of memory   : 0
% 32.44/12.61  # Backward-subsumed                    : 33
% 32.44/12.61  # Backward-rewritten                   : 73
% 32.44/12.61  # Generated clauses                    : 7246
% 32.44/12.61  # ...of the previous two non-redundant : 5187
% 32.44/12.61  # ...aggressively subsumed             : 0
% 32.44/12.61  # Contextual simplify-reflections      : 86
% 32.44/12.61  # Paramodulations                      : 6000
% 32.44/12.61  # Factorizations                       : 2
% 32.44/12.61  # NegExts                              : 0
% 32.44/12.61  # Equation resolutions                 : 1445
% 32.44/12.61  # Disequality decompositions           : 0
% 32.44/12.61  # Total rewrite steps                  : 6612
% 32.44/12.61  # ...of those cached                   : 5840
% 32.44/12.61  # Propositional unsat checks           : 0
% 32.44/12.61  #    Propositional check models        : 0
% 32.44/12.61  #    Propositional check unsatisfiable : 0
% 32.44/12.61  #    Propositional clauses             : 0
% 32.44/12.61  #    Propositional clauses after purity: 0
% 32.44/12.61  #    Propositional unsat core size     : 0
% 32.44/12.61  #    Propositional preprocessing time  : 0.000
% 32.44/12.61  #    Propositional encoding time       : 0.000
% 32.44/12.61  #    Propositional solver time         : 0.000
% 32.44/12.61  #    Success case prop preproc time    : 0.000
% 32.44/12.61  #    Success case prop encoding time   : 0.000
% 32.44/12.61  #    Success case prop solver time     : 0.000
% 32.44/12.61  # Current number of processed clauses  : 1114
% 32.44/12.61  #    Positive orientable unit clauses  : 416
% 32.44/12.61  #    Positive unorientable unit clauses: 4
% 32.44/12.61  #    Negative unit clauses             : 158
% 32.44/12.61  #    Non-unit-clauses                  : 536
% 32.44/12.61  # Current number of unprocessed clauses: 7260
% 32.44/12.61  # ...number of literals in the above   : 22500
% 32.44/12.61  # Current number of archived formulas  : 0
% 32.44/12.61  # Current number of archived clauses   : 4560
% 32.44/12.61  # Clause-clause subsumption calls (NU) : 13375700
% 32.44/12.61  # Rec. Clause-clause subsumption calls : 969479
% 32.44/12.61  # Non-unit clause-clause subsumptions  : 1175
% 32.44/12.61  # Unit Clause-clause subsumption calls : 50611
% 32.44/12.61  # Rewrite failures with RHS unbound    : 0
% 32.44/12.61  # BW rewrite match attempts            : 765
% 32.44/12.61  # BW rewrite match successes           : 233
% 32.44/12.61  # Condensation attempts                : 8554
% 32.44/12.61  # Condensation successes               : 1
% 32.44/12.61  # Termbank termtop insertions          : 2645516
% 32.44/12.61  # Search garbage collected termcells   : 162724
% 32.44/12.61  
% 32.44/12.61  # -------------------------------------------------
% 32.44/12.61  # User time                : 6.593 s
% 32.44/12.61  # System time              : 0.080 s
% 32.44/12.61  # Total time               : 6.673 s
% 32.44/12.61  # Maximum resident set size: 41652 pages
% 32.44/12.61  
% 32.44/12.61  # -------------------------------------------------
% 32.44/12.61  # User time                : 7.308 s
% 32.44/12.61  # System time              : 0.105 s
% 32.44/12.61  # Total time               : 7.412 s
% 32.44/12.61  # Maximum resident set size: 23900 pages
% 32.44/12.61  % E---3.1 exiting
% 32.44/12.61  % E exiting
%------------------------------------------------------------------------------