TSTP Solution File: ITP155^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP155^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n026.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 08:07:09 EDT 2024

% Result   : Theorem 0.38s 0.66s
% Output   : CNFRefutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   38 (  13 unt;  14 typ;   0 def)
%            Number of atoms       :   42 (   6 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  215 (  14   ~;  14   |;   0   &; 183   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :   18 (   0   ^  18   !;   0   ?;  18   :)

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

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

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

thf(decl_sort4,type,
    a: $tType ).

thf(decl_24,type,
    finite_card_a: set_a > nat ).

thf(decl_30,type,
    finite_finite_a: set_a > $o ).

thf(decl_45,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(decl_52,type,
    ord_less_eq_set_a: set_a > set_a > $o ).

thf(decl_61,type,
    prefer1676310729than_a: a > set_a > set_Product_prod_a_a > set_a ).

thf(decl_91,type,
    member_a: a > set_a > $o ).

thf(decl_92,type,
    carrier: set_a ).

thf(decl_93,type,
    relation: set_Product_prod_a_a ).

thf(decl_94,type,
    x: a ).

thf(decl_95,type,
    y: a ).

thf(fact_211_card__seteq,axiom,
    ! [X372: set_a,X82: set_a] :
      ( ( finite_finite_a @ X372 )
     => ( ( ord_less_eq_set_a @ X82 @ X372 )
       => ( ( ord_less_eq_nat @ ( finite_card_a @ X372 ) @ ( finite_card_a @ X82 ) )
         => ( X82 = X372 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.pQfbdTx1yo/E---3.1_15222.p',fact_211_card__seteq) ).

thf(conj_0,conjecture,
    ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ),
    file('/export/starexec/sandbox2/tmp/tmp.pQfbdTx1yo/E---3.1_15222.p',conj_0) ).

thf(fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062,axiom,
    ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
    file('/export/starexec/sandbox2/tmp/tmp.pQfbdTx1yo/E---3.1_15222.p',fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062) ).

thf(fact_4_nbt__nest,axiom,
    ! [X2: a,X1: a] :
      ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) )
      | ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.pQfbdTx1yo/E---3.1_15222.p',fact_4_nbt__nest) ).

thf(fact_15_fnt__carrier__fnt__nbt,axiom,
    ! [X3: a] :
      ( ( member_a @ X3 @ carrier )
     => ( finite_finite_a @ ( prefer1676310729than_a @ X3 @ carrier @ relation ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.pQfbdTx1yo/E---3.1_15222.p',fact_15_fnt__carrier__fnt__nbt) ).

thf(fact_1_assms_I1_J,axiom,
    member_a @ x @ carrier,
    file('/export/starexec/sandbox2/tmp/tmp.pQfbdTx1yo/E---3.1_15222.p',fact_1_assms_I1_J) ).

thf(fact_154_subset__refl,axiom,
    ! [X82: set_a] : ( ord_less_eq_set_a @ X82 @ X82 ),
    file('/export/starexec/sandbox2/tmp/tmp.pQfbdTx1yo/E---3.1_15222.p',fact_154_subset__refl) ).

thf(c_0_7,plain,
    ! [X1669: set_a,X1670: set_a] :
      ( ~ ( finite_finite_a @ X1669 )
      | ~ ( ord_less_eq_set_a @ X1670 @ X1669 )
      | ~ ( ord_less_eq_nat @ ( finite_card_a @ X1669 ) @ ( finite_card_a @ X1670 ) )
      | ( X1670 = X1669 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_211_card__seteq])])]) ).

thf(c_0_8,negated_conjecture,
    ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

thf(c_0_9,plain,
    ! [X6: set_a,X18: set_a] :
      ( ( X18 = X6 )
      | ~ ( finite_finite_a @ X6 )
      | ~ ( ord_less_eq_set_a @ X18 @ X6 )
      | ~ ( ord_less_eq_nat @ ( finite_card_a @ X6 ) @ ( finite_card_a @ X18 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_10,plain,
    ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
    inference(split_conjunct,[status(thm)],[fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062]) ).

thf(c_0_11,plain,
    ! [X1368: a,X1369: a] :
      ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X1368 @ carrier @ relation ) @ ( prefer1676310729than_a @ X1369 @ carrier @ relation ) )
      | ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X1369 @ carrier @ relation ) @ ( prefer1676310729than_a @ X1368 @ carrier @ relation ) ) ),
    inference(variable_rename,[status(thm)],[fact_4_nbt__nest]) ).

thf(c_0_12,negated_conjecture,
    ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
    inference(fof_nnf,[status(thm)],[c_0_8]) ).

thf(c_0_13,plain,
    ( ( ( prefer1676310729than_a @ y @ carrier @ relation )
      = ( prefer1676310729than_a @ x @ carrier @ relation ) )
    | ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
    | ~ ( finite_finite_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

thf(c_0_14,plain,
    ! [X2: a,X1: a] :
      ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) )
      | ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_15,negated_conjecture,
    ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_16,plain,
    ! [X1552: a] :
      ( ~ ( member_a @ X1552 @ carrier )
      | ( finite_finite_a @ ( prefer1676310729than_a @ X1552 @ carrier @ relation ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_15_fnt__carrier__fnt__nbt])])]) ).

thf(c_0_17,plain,
    ( ( ( prefer1676310729than_a @ y @ carrier @ relation )
      = ( prefer1676310729than_a @ x @ carrier @ relation ) )
    | ~ ( finite_finite_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).

thf(c_0_18,plain,
    ! [X1: a] :
      ( ( finite_finite_a @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) )
      | ~ ( member_a @ X1 @ carrier ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_19,plain,
    member_a @ x @ carrier,
    inference(split_conjunct,[status(thm)],[fact_1_assms_I1_J]) ).

thf(c_0_20,plain,
    ! [X1427: set_a] : ( ord_less_eq_set_a @ X1427 @ X1427 ),
    inference(variable_rename,[status(thm)],[fact_154_subset__refl]) ).

thf(c_0_21,plain,
    ( ( prefer1676310729than_a @ y @ carrier @ relation )
    = ( prefer1676310729than_a @ x @ carrier @ relation ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).

thf(c_0_22,plain,
    ! [X6: set_a] : ( ord_less_eq_set_a @ X6 @ X6 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_23,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_21]),c_0_22])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.16  % Problem    : ITP155^1 : TPTP v8.1.2. Released v7.5.0.
% 0.16/0.17  % Command    : run_E %s %d THM
% 0.16/0.37  % Computer : n026.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Fri May  3 13:09:51 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.36/0.54  Running higher-order theorem proving
% 0.36/0.54  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.pQfbdTx1yo/E---3.1_15222.p
% 0.38/0.66  # Version: 3.1.0-ho
% 0.38/0.66  # Preprocessing class: HSLSSMSMSSMNSFA.
% 0.38/0.66  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.66  # Starting new_ho_3 with 1500s (5) cores
% 0.38/0.66  # Starting pre_casc_2 with 300s (1) cores
% 0.38/0.66  # Starting additional_ho_7 with 300s (1) cores
% 0.38/0.66  # Starting lpo8_s with 300s (1) cores
% 0.38/0.66  # additional_ho_7 with pid 15303 completed with status 0
% 0.38/0.66  # Result found by additional_ho_7
% 0.38/0.66  # Preprocessing class: HSLSSMSMSSMNSFA.
% 0.38/0.66  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.66  # Starting new_ho_3 with 1500s (5) cores
% 0.38/0.66  # Starting pre_casc_2 with 300s (1) cores
% 0.38/0.66  # Starting additional_ho_7 with 300s (1) cores
% 0.38/0.66  # SinE strategy is GSinE(CountFormulas,hypos,4.0,,2,20000,1.0)
% 0.38/0.66  # Search class: HGHSM-FSLM32-SSFFFSBN
% 0.38/0.66  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.38/0.66  # Starting new_ho_10 with 163s (1) cores
% 0.38/0.66  # new_ho_10 with pid 15305 completed with status 0
% 0.38/0.66  # Result found by new_ho_10
% 0.38/0.66  # Preprocessing class: HSLSSMSMSSMNSFA.
% 0.38/0.66  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.66  # Starting new_ho_3 with 1500s (5) cores
% 0.38/0.66  # Starting pre_casc_2 with 300s (1) cores
% 0.38/0.66  # Starting additional_ho_7 with 300s (1) cores
% 0.38/0.66  # SinE strategy is GSinE(CountFormulas,hypos,4.0,,2,20000,1.0)
% 0.38/0.66  # Search class: HGHSM-FSLM32-SSFFFSBN
% 0.38/0.66  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.38/0.66  # Starting new_ho_10 with 163s (1) cores
% 0.38/0.66  # Preprocessing time       : 0.008 s
% 0.38/0.66  # Presaturation interreduction done
% 0.38/0.66  
% 0.38/0.66  # Proof found!
% 0.38/0.66  # SZS status Theorem
% 0.38/0.66  # SZS output start CNFRefutation
% See solution above
% 0.38/0.66  # Parsed axioms                        : 443
% 0.38/0.66  # Removed by relevancy pruning/SinE    : 237
% 0.38/0.66  # Initial clauses                      : 486
% 0.38/0.66  # Removed in clause preprocessing      : 17
% 0.38/0.66  # Initial clauses in saturation        : 469
% 0.38/0.66  # Processed clauses                    : 634
% 0.38/0.66  # ...of these trivial                  : 10
% 0.38/0.66  # ...subsumed                          : 140
% 0.38/0.66  # ...remaining for further processing  : 484
% 0.38/0.66  # Other redundant clauses eliminated   : 57
% 0.38/0.66  # Clauses deleted for lack of memory   : 0
% 0.38/0.66  # Backward-subsumed                    : 1
% 0.38/0.66  # Backward-rewritten                   : 6
% 0.38/0.66  # Generated clauses                    : 292
% 0.38/0.66  # ...of the previous two non-redundant : 195
% 0.38/0.66  # ...aggressively subsumed             : 0
% 0.38/0.66  # Contextual simplify-reflections      : 6
% 0.38/0.66  # Paramodulations                      : 225
% 0.38/0.66  # Factorizations                       : 4
% 0.38/0.66  # NegExts                              : 0
% 0.38/0.66  # Equation resolutions                 : 59
% 0.38/0.66  # Disequality decompositions           : 0
% 0.38/0.66  # Total rewrite steps                  : 96
% 0.38/0.66  # ...of those cached                   : 66
% 0.38/0.66  # Propositional unsat checks           : 0
% 0.38/0.66  #    Propositional check models        : 0
% 0.38/0.66  #    Propositional check unsatisfiable : 0
% 0.38/0.66  #    Propositional clauses             : 0
% 0.38/0.66  #    Propositional clauses after purity: 0
% 0.38/0.66  #    Propositional unsat core size     : 0
% 0.38/0.66  #    Propositional preprocessing time  : 0.000
% 0.38/0.66  #    Propositional encoding time       : 0.000
% 0.38/0.66  #    Propositional solver time         : 0.000
% 0.38/0.66  #    Success case prop preproc time    : 0.000
% 0.38/0.66  #    Success case prop encoding time   : 0.000
% 0.38/0.66  #    Success case prop solver time     : 0.000
% 0.38/0.66  # Current number of processed clauses  : 125
% 0.38/0.66  #    Positive orientable unit clauses  : 25
% 0.38/0.66  #    Positive unorientable unit clauses: 0
% 0.38/0.66  #    Negative unit clauses             : 2
% 0.38/0.66  #    Non-unit-clauses                  : 98
% 0.38/0.66  # Current number of unprocessed clauses: 330
% 0.38/0.66  # ...number of literals in the above   : 1264
% 0.38/0.66  # Current number of archived formulas  : 0
% 0.38/0.66  # Current number of archived clauses   : 314
% 0.38/0.66  # Clause-clause subsumption calls (NU) : 25389
% 0.38/0.66  # Rec. Clause-clause subsumption calls : 9139
% 0.38/0.66  # Non-unit clause-clause subsumptions  : 157
% 0.38/0.66  # Unit Clause-clause subsumption calls : 375
% 0.38/0.66  # Rewrite failures with RHS unbound    : 0
% 0.38/0.66  # BW rewrite match attempts            : 9
% 0.38/0.66  # BW rewrite match successes           : 4
% 0.38/0.66  # Condensation attempts                : 634
% 0.38/0.66  # Condensation successes               : 15
% 0.38/0.66  # Termbank termtop insertions          : 56487
% 0.38/0.66  # Search garbage collected termcells   : 13600
% 0.38/0.66  
% 0.38/0.66  # -------------------------------------------------
% 0.38/0.66  # User time                : 0.081 s
% 0.38/0.66  # System time              : 0.011 s
% 0.38/0.66  # Total time               : 0.092 s
% 0.38/0.66  # Maximum resident set size: 4504 pages
% 0.38/0.66  
% 0.38/0.66  # -------------------------------------------------
% 0.38/0.66  # User time                : 0.097 s
% 0.38/0.66  # System time              : 0.013 s
% 0.38/0.66  # Total time               : 0.110 s
% 0.38/0.66  # Maximum resident set size: 2784 pages
% 0.38/0.66  % E---3.1 exiting
% 0.38/0.66  % E exiting
%------------------------------------------------------------------------------