TSTP Solution File: SEU326+2 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SEU326+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n022.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:31:39 EDT 2023

% Result   : Theorem 0.40s 0.98s
% Output   : CNFRefutation 0.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   26 (   8 unt;   0 def)
%            Number of atoms       :   63 (  33 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :   68 (  31   ~;  19   |;  12   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   34 (   2 sgn;  22   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t10_tops_2,conjecture,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => ( ~ ( X2 != empty_set
            & complements_of_subsets(X1,X2) = empty_set )
        & ~ ( complements_of_subsets(X1,X2) != empty_set
            & X2 = empty_set ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.3Z9p2TIhfC/E---3.1_29385.p',t10_tops_2) ).

fof(t46_setfam_1,lemma,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => ~ ( X2 != empty_set
          & complements_of_subsets(X1,X2) = empty_set ) ),
    file('/export/starexec/sandbox2/tmp/tmp.3Z9p2TIhfC/E---3.1_29385.p',t46_setfam_1) ).

fof(involutiveness_k7_setfam_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
    file('/export/starexec/sandbox2/tmp/tmp.3Z9p2TIhfC/E---3.1_29385.p',involutiveness_k7_setfam_1) ).

fof(dt_k7_setfam_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.3Z9p2TIhfC/E---3.1_29385.p',dt_k7_setfam_1) ).

fof(t3_subset,axiom,
    ! [X1,X2] :
      ( element(X1,powerset(X2))
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.3Z9p2TIhfC/E---3.1_29385.p',t3_subset) ).

fof(t2_xboole_1,lemma,
    ! [X1] : subset(empty_set,X1),
    file('/export/starexec/sandbox2/tmp/tmp.3Z9p2TIhfC/E---3.1_29385.p',t2_xboole_1) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( element(X2,powerset(powerset(X1)))
       => ( ~ ( X2 != empty_set
              & complements_of_subsets(X1,X2) = empty_set )
          & ~ ( complements_of_subsets(X1,X2) != empty_set
              & X2 = empty_set ) ) ),
    inference(assume_negation,[status(cth)],[t10_tops_2]) ).

fof(c_0_7,lemma,
    ! [X44,X45] :
      ( ~ element(X45,powerset(powerset(X44)))
      | X45 = empty_set
      | complements_of_subsets(X44,X45) != empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_setfam_1])]) ).

fof(c_0_8,negated_conjecture,
    ( element(esk2_0,powerset(powerset(esk1_0)))
    & ( complements_of_subsets(esk1_0,esk2_0) != empty_set
      | esk2_0 != empty_set )
    & ( esk2_0 = empty_set
      | esk2_0 != empty_set )
    & ( complements_of_subsets(esk1_0,esk2_0) != empty_set
      | complements_of_subsets(esk1_0,esk2_0) = empty_set )
    & ( esk2_0 = empty_set
      | complements_of_subsets(esk1_0,esk2_0) = empty_set ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

cnf(c_0_9,lemma,
    ( X1 = empty_set
    | ~ element(X1,powerset(powerset(X2)))
    | complements_of_subsets(X2,X1) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    ( esk2_0 = empty_set
    | complements_of_subsets(esk1_0,esk2_0) = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    element(esk2_0,powerset(powerset(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_12,plain,
    ! [X42,X43] :
      ( ~ element(X43,powerset(powerset(X42)))
      | complements_of_subsets(X42,complements_of_subsets(X42,X43)) = X43 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).

fof(c_0_13,plain,
    ! [X40,X41] :
      ( ~ element(X41,powerset(powerset(X40)))
      | element(complements_of_subsets(X40,X41),powerset(powerset(X40))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).

fof(c_0_14,plain,
    ! [X56,X57] :
      ( ( ~ element(X56,powerset(X57))
        | subset(X56,X57) )
      & ( ~ subset(X56,X57)
        | element(X56,powerset(X57)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).

fof(c_0_15,lemma,
    ! [X27] : subset(empty_set,X27),
    inference(variable_rename,[status(thm)],[t2_xboole_1]) ).

cnf(c_0_16,negated_conjecture,
    ( complements_of_subsets(esk1_0,esk2_0) != empty_set
    | esk2_0 != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_17,negated_conjecture,
    esk2_0 = empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).

cnf(c_0_18,plain,
    ( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    ( element(X1,powerset(X2))
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,lemma,
    subset(empty_set,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,negated_conjecture,
    complements_of_subsets(esk1_0,empty_set) != empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17])]) ).

cnf(c_0_23,lemma,
    ( complements_of_subsets(X1,X2) = empty_set
    | X2 != empty_set
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_18]),c_0_19]) ).

cnf(c_0_24,lemma,
    element(empty_set,powerset(X1)),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem    : SEU326+2 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.15  % Command    : run_E %s %d THM
% 0.14/0.37  % Computer : n022.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 2400
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Mon Oct  2 08:29:39 EDT 2023
% 0.14/0.37  % CPUTime    : 
% 0.38/0.56  Running first-order model finding
% 0.38/0.56  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.3Z9p2TIhfC/E---3.1_29385.p
% 0.40/0.98  # Version: 3.1pre001
% 0.40/0.98  # Preprocessing class: FSLMSMSSSSSNFFN.
% 0.40/0.98  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.98  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.40/0.98  # Starting new_bool_3 with 600s (2) cores
% 0.40/0.98  # Starting new_bool_1 with 600s (2) cores
% 0.40/0.98  # Starting sh5l with 300s (1) cores
% 0.40/0.98  # new_bool_1 with pid 29465 completed with status 0
% 0.40/0.98  # Result found by new_bool_1
% 0.40/0.98  # Preprocessing class: FSLMSMSSSSSNFFN.
% 0.40/0.98  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.98  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.40/0.98  # Starting new_bool_3 with 600s (2) cores
% 0.40/0.98  # Starting new_bool_1 with 600s (2) cores
% 0.40/0.98  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.40/0.98  # Search class: FGHSM-FSLM32-MFFFFFNN
% 0.40/0.98  # Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 0.40/0.98  # Starting G-E--_303_C18_F1_URBAN_S0Y with 50s (1) cores
% 0.40/0.98  # Starting new_bool_1 with 61s (1) cores
% 0.40/0.98  # G-E--_303_C18_F1_URBAN_S0Y with pid 29467 completed with status 0
% 0.40/0.98  # Result found by G-E--_303_C18_F1_URBAN_S0Y
% 0.40/0.98  # Preprocessing class: FSLMSMSSSSSNFFN.
% 0.40/0.98  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.98  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.40/0.98  # Starting new_bool_3 with 600s (2) cores
% 0.40/0.98  # Starting new_bool_1 with 600s (2) cores
% 0.40/0.98  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.40/0.98  # Search class: FGHSM-FSLM32-MFFFFFNN
% 0.40/0.98  # Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 0.40/0.98  # Starting G-E--_303_C18_F1_URBAN_S0Y with 50s (1) cores
% 0.40/0.98  # Preprocessing time       : 0.017 s
% 0.40/0.98  
% 0.40/0.98  # Proof found!
% 0.40/0.98  # SZS status Theorem
% 0.40/0.98  # SZS output start CNFRefutation
% See solution above
% 0.40/0.98  # Parsed axioms                        : 539
% 0.40/0.98  # Removed by relevancy pruning/SinE    : 419
% 0.40/0.98  # Initial clauses                      : 657
% 0.40/0.98  # Removed in clause preprocessing      : 4
% 0.40/0.98  # Initial clauses in saturation        : 653
% 0.40/0.98  # Processed clauses                    : 840
% 0.40/0.98  # ...of these trivial                  : 6
% 0.40/0.98  # ...subsumed                          : 102
% 0.40/0.98  # ...remaining for further processing  : 732
% 0.40/0.98  # Other redundant clauses eliminated   : 76
% 0.40/0.98  # Clauses deleted for lack of memory   : 0
% 0.40/0.98  # Backward-subsumed                    : 9
% 0.40/0.98  # Backward-rewritten                   : 17
% 0.40/0.98  # Generated clauses                    : 10387
% 0.40/0.98  # ...of the previous two non-redundant : 10205
% 0.40/0.98  # ...aggressively subsumed             : 0
% 0.40/0.98  # Contextual simplify-reflections      : 116
% 0.40/0.98  # Paramodulations                      : 10262
% 0.40/0.98  # Factorizations                       : 4
% 0.40/0.98  # NegExts                              : 0
% 0.40/0.98  # Equation resolutions                 : 132
% 0.40/0.98  # Total rewrite steps                  : 254
% 0.40/0.98  # Propositional unsat checks           : 0
% 0.40/0.98  #    Propositional check models        : 0
% 0.40/0.98  #    Propositional check unsatisfiable : 0
% 0.40/0.98  #    Propositional clauses             : 0
% 0.40/0.98  #    Propositional clauses after purity: 0
% 0.40/0.98  #    Propositional unsat core size     : 0
% 0.40/0.98  #    Propositional preprocessing time  : 0.000
% 0.40/0.98  #    Propositional encoding time       : 0.000
% 0.40/0.98  #    Propositional solver time         : 0.000
% 0.40/0.98  #    Success case prop preproc time    : 0.000
% 0.40/0.98  #    Success case prop encoding time   : 0.000
% 0.40/0.98  #    Success case prop solver time     : 0.000
% 0.40/0.98  # Current number of processed clauses  : 648
% 0.40/0.98  #    Positive orientable unit clauses  : 37
% 0.40/0.98  #    Positive unorientable unit clauses: 0
% 0.40/0.98  #    Negative unit clauses             : 14
% 0.40/0.98  #    Non-unit-clauses                  : 597
% 0.40/0.98  # Current number of unprocessed clauses: 9979
% 0.40/0.98  # ...number of literals in the above   : 70496
% 0.40/0.98  # Current number of archived formulas  : 0
% 0.40/0.98  # Current number of archived clauses   : 26
% 0.40/0.98  # Clause-clause subsumption calls (NU) : 169387
% 0.40/0.98  # Rec. Clause-clause subsumption calls : 10080
% 0.40/0.98  # Non-unit clause-clause subsumptions  : 189
% 0.40/0.98  # Unit Clause-clause subsumption calls : 3825
% 0.40/0.98  # Rewrite failures with RHS unbound    : 0
% 0.40/0.98  # BW rewrite match attempts            : 62
% 0.40/0.98  # BW rewrite match successes           : 9
% 0.40/0.98  # Condensation attempts                : 0
% 0.40/0.98  # Condensation successes               : 0
% 0.40/0.98  # Termbank termtop insertions          : 288576
% 0.40/0.98  
% 0.40/0.98  # -------------------------------------------------
% 0.40/0.98  # User time                : 0.353 s
% 0.40/0.98  # System time              : 0.017 s
% 0.40/0.98  # Total time               : 0.369 s
% 0.40/0.98  # Maximum resident set size: 3724 pages
% 0.40/0.98  
% 0.40/0.98  # -------------------------------------------------
% 0.40/0.98  # User time                : 0.720 s
% 0.40/0.98  # System time              : 0.021 s
% 0.40/0.98  # Total time               : 0.742 s
% 0.40/0.98  # Maximum resident set size: 2396 pages
% 0.40/0.98  % E---3.1 exiting
%------------------------------------------------------------------------------