TSTP Solution File: SET592+3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET592+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n007.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 02:54:26 EDT 2024

% Result   : Theorem 0.19s 0.48s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   24 (  11 unt;   0 def)
%            Number of atoms       :   60 (  13 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   58 (  22   ~;  17   |;  13   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   37 (   2 sgn  27   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_th51,conjecture,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X1,X3)
        & intersection(X2,X3) = empty_set )
     => X1 = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th51) ).

fof(intersection_of_subsets,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X1,X3) )
     => subset(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_subsets) ).

fof(empty_set_defn,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).

fof(subset_defn,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(equal_defn,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( subset(X1,X2)
          & subset(X1,X3)
          & intersection(X2,X3) = empty_set )
       => X1 = empty_set ),
    inference(assume_negation,[status(cth)],[prove_th51]) ).

fof(c_0_6,plain,
    ! [X9,X10,X11] :
      ( ~ subset(X9,X10)
      | ~ subset(X9,X11)
      | subset(X9,intersection(X10,X11)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_of_subsets])])]) ).

fof(c_0_7,negated_conjecture,
    ( subset(esk1_0,esk2_0)
    & subset(esk1_0,esk3_0)
    & intersection(esk2_0,esk3_0) = empty_set
    & esk1_0 != empty_set ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).

fof(c_0_8,plain,
    ! [X1] : ~ member(X1,empty_set),
    inference(fof_simplification,[status(thm)],[empty_set_defn]) ).

cnf(c_0_9,plain,
    ( subset(X1,intersection(X2,X3))
    | ~ subset(X1,X2)
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    intersection(esk2_0,esk3_0) = empty_set,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X8] : ~ member(X8,empty_set),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).

fof(c_0_12,plain,
    ! [X17,X18,X19,X20,X21] :
      ( ( ~ subset(X17,X18)
        | ~ member(X19,X17)
        | member(X19,X18) )
      & ( member(esk4_2(X20,X21),X20)
        | subset(X20,X21) )
      & ( ~ member(esk4_2(X20,X21),X21)
        | subset(X20,X21) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_defn])])])])])])]) ).

fof(c_0_13,plain,
    ! [X23,X24] :
      ( ( subset(X23,X24)
        | X23 != X24 )
      & ( subset(X24,X23)
        | X23 != X24 )
      & ( ~ subset(X23,X24)
        | ~ subset(X24,X23)
        | X23 = X24 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).

cnf(c_0_14,negated_conjecture,
    ( subset(X1,empty_set)
    | ~ subset(X1,esk3_0)
    | ~ subset(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    subset(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_16,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_17,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ( member(esk4_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,negated_conjecture,
    subset(esk1_0,empty_set),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).

cnf(c_0_21,plain,
    subset(empty_set,X1),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    esk1_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_23,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_22]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : SET592+3 : TPTP v8.2.0. Released v2.2.0.
% 0.06/0.14  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n007.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 12:09:08 EDT 2024
% 0.12/0.35  % CPUTime    : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48  # Version: 3.1.0
% 0.19/0.48  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.48  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.48  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.48  # Starting sh5l with 300s (1) cores
% 0.19/0.48  # sh5l with pid 16628 completed with status 0
% 0.19/0.48  # Result found by sh5l
% 0.19/0.48  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.48  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.48  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.48  # Starting sh5l with 300s (1) cores
% 0.19/0.48  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.48  # Search class: FGHSS-FFSS21-SFFFFFNN
% 0.19/0.48  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.48  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.19/0.48  # SAT001_MinMin_p005000_rr_RG with pid 16629 completed with status 0
% 0.19/0.48  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.19/0.48  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.48  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.48  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.48  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.48  # Starting sh5l with 300s (1) cores
% 0.19/0.48  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.48  # Search class: FGHSS-FFSS21-SFFFFFNN
% 0.19/0.48  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.48  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.19/0.48  # Preprocessing time       : 0.001 s
% 0.19/0.48  # Presaturation interreduction done
% 0.19/0.48  
% 0.19/0.48  # Proof found!
% 0.19/0.48  # SZS status Theorem
% 0.19/0.48  # SZS output start CNFRefutation
% See solution above
% 0.19/0.48  # Parsed axioms                        : 11
% 0.19/0.48  # Removed by relevancy pruning/SinE    : 0
% 0.19/0.48  # Initial clauses                      : 24
% 0.19/0.48  # Removed in clause preprocessing      : 2
% 0.19/0.48  # Initial clauses in saturation        : 22
% 0.19/0.48  # Processed clauses                    : 49
% 0.19/0.48  # ...of these trivial                  : 0
% 0.19/0.48  # ...subsumed                          : 3
% 0.19/0.48  # ...remaining for further processing  : 46
% 0.19/0.48  # Other redundant clauses eliminated   : 2
% 0.19/0.48  # Clauses deleted for lack of memory   : 0
% 0.19/0.48  # Backward-subsumed                    : 0
% 0.19/0.48  # Backward-rewritten                   : 0
% 0.19/0.48  # Generated clauses                    : 35
% 0.19/0.48  # ...of the previous two non-redundant : 26
% 0.19/0.48  # ...aggressively subsumed             : 0
% 0.19/0.48  # Contextual simplify-reflections      : 0
% 0.19/0.48  # Paramodulations                      : 33
% 0.19/0.48  # Factorizations                       : 0
% 0.19/0.48  # NegExts                              : 0
% 0.19/0.48  # Equation resolutions                 : 2
% 0.19/0.48  # Disequality decompositions           : 0
% 0.19/0.48  # Total rewrite steps                  : 7
% 0.19/0.48  # ...of those cached                   : 2
% 0.19/0.48  # Propositional unsat checks           : 0
% 0.19/0.48  #    Propositional check models        : 0
% 0.19/0.48  #    Propositional check unsatisfiable : 0
% 0.19/0.48  #    Propositional clauses             : 0
% 0.19/0.48  #    Propositional clauses after purity: 0
% 0.19/0.48  #    Propositional unsat core size     : 0
% 0.19/0.48  #    Propositional preprocessing time  : 0.000
% 0.19/0.48  #    Propositional encoding time       : 0.000
% 0.19/0.48  #    Propositional solver time         : 0.000
% 0.19/0.48  #    Success case prop preproc time    : 0.000
% 0.19/0.48  #    Success case prop encoding time   : 0.000
% 0.19/0.48  #    Success case prop solver time     : 0.000
% 0.19/0.48  # Current number of processed clauses  : 24
% 0.19/0.48  #    Positive orientable unit clauses  : 7
% 0.19/0.48  #    Positive unorientable unit clauses: 1
% 0.19/0.48  #    Negative unit clauses             : 2
% 0.19/0.48  #    Non-unit-clauses                  : 14
% 0.19/0.48  # Current number of unprocessed clauses: 19
% 0.19/0.48  # ...number of literals in the above   : 46
% 0.19/0.48  # Current number of archived formulas  : 0
% 0.19/0.48  # Current number of archived clauses   : 20
% 0.19/0.48  # Clause-clause subsumption calls (NU) : 39
% 0.19/0.48  # Rec. Clause-clause subsumption calls : 33
% 0.19/0.48  # Non-unit clause-clause subsumptions  : 1
% 0.19/0.48  # Unit Clause-clause subsumption calls : 0
% 0.19/0.48  # Rewrite failures with RHS unbound    : 0
% 0.19/0.48  # BW rewrite match attempts            : 12
% 0.19/0.48  # BW rewrite match successes           : 8
% 0.19/0.48  # Condensation attempts                : 0
% 0.19/0.48  # Condensation successes               : 0
% 0.19/0.48  # Termbank termtop insertions          : 1661
% 0.19/0.48  # Search garbage collected termcells   : 378
% 0.19/0.48  
% 0.19/0.48  # -------------------------------------------------
% 0.19/0.48  # User time                : 0.006 s
% 0.19/0.48  # System time              : 0.001 s
% 0.19/0.48  # Total time               : 0.007 s
% 0.19/0.48  # Maximum resident set size: 1708 pages
% 0.19/0.48  
% 0.19/0.48  # -------------------------------------------------
% 0.19/0.48  # User time                : 0.009 s
% 0.19/0.48  # System time              : 0.002 s
% 0.19/0.48  # Total time               : 0.010 s
% 0.19/0.48  # Maximum resident set size: 1696 pages
% 0.19/0.48  % E---3.1 exiting
% 0.19/0.49  % E exiting
%------------------------------------------------------------------------------