TSTP Solution File: SEU319+2 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU319+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n010.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  : 600s
% DateTime : Tue Jul 19 09:18:57 EDT 2022

% Result   : Theorem 0.27s 1.48s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   34 (   5 unt;   0 def)
%            Number of atoms       :   96 (   7 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  108 (  46   ~;  43   |;   5   &)
%                                         (   3 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-3 aty)
%            Number of variables   :   40 (   0 sgn  22   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(dt_k2_pre_topc,axiom,
    ! [X1] :
      ( one_sorted_str(X1)
     => element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k2_pre_topc) ).

fof(dt_l1_pre_topc,axiom,
    ! [X1] :
      ( top_str(X1)
     => one_sorted_str(X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_l1_pre_topc) ).

fof(t29_tops_1,conjecture,
    ! [X1] :
      ( top_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => ( closed_subset(X2,X1)
          <=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t29_tops_1) ).

fof(redefinition_k6_subset_1,axiom,
    ! [X1,X2,X3] :
      ( ( element(X2,powerset(X1))
        & element(X3,powerset(X1)) )
     => subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k6_subset_1) ).

fof(t17_pre_topc,lemma,
    ! [X1] :
      ( one_sorted_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t17_pre_topc) ).

fof(d6_pre_topc,axiom,
    ! [X1] :
      ( top_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => ( closed_subset(X2,X1)
          <=> open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d6_pre_topc) ).

fof(c_0_6,plain,
    ! [X2] :
      ( ~ one_sorted_str(X2)
      | element(cast_as_carrier_subset(X2),powerset(the_carrier(X2))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_pre_topc])]) ).

fof(c_0_7,plain,
    ! [X2] :
      ( ~ top_str(X2)
      | one_sorted_str(X2) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_pre_topc])]) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1] :
        ( top_str(X1)
       => ! [X2] :
            ( element(X2,powerset(the_carrier(X1)))
           => ( closed_subset(X2,X1)
            <=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
    inference(assume_negation,[status(cth)],[t29_tops_1]) ).

fof(c_0_9,plain,
    ! [X4,X5,X6] :
      ( ~ element(X5,powerset(X4))
      | ~ element(X6,powerset(X4))
      | subset_difference(X4,X5,X6) = set_difference(X5,X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).

fof(c_0_10,lemma,
    ! [X3,X4] :
      ( ~ one_sorted_str(X3)
      | ~ element(X4,powerset(the_carrier(X3)))
      | subset_complement(the_carrier(X3),X4) = subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_pre_topc])])])])]) ).

fof(c_0_11,plain,
    ! [X3,X4] :
      ( ( ~ closed_subset(X4,X3)
        | open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3)
        | ~ element(X4,powerset(the_carrier(X3)))
        | ~ top_str(X3) )
      & ( ~ open_subset(subset_difference(the_carrier(X3),cast_as_carrier_subset(X3),X4),X3)
        | closed_subset(X4,X3)
        | ~ element(X4,powerset(the_carrier(X3)))
        | ~ top_str(X3) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_pre_topc])])])])])]) ).

cnf(c_0_12,plain,
    ( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_13,plain,
    ( one_sorted_str(X1)
    | ~ top_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_14,negated_conjecture,
    ( top_str(esk1_0)
    & element(esk2_0,powerset(the_carrier(esk1_0)))
    & ( ~ closed_subset(esk2_0,esk1_0)
      | ~ open_subset(subset_complement(the_carrier(esk1_0),esk2_0),esk1_0) )
    & ( closed_subset(esk2_0,esk1_0)
      | open_subset(subset_complement(the_carrier(esk1_0),esk2_0),esk1_0) ) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).

cnf(c_0_15,plain,
    ( subset_difference(X1,X2,X3) = set_difference(X2,X3)
    | ~ element(X3,powerset(X1))
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,lemma,
    ( subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    ( closed_subset(X2,X1)
    | ~ top_str(X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
    | ~ top_str(X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    ( open_subset(subset_complement(the_carrier(esk1_0),esk2_0),esk1_0)
    | closed_subset(esk2_0,esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,lemma,
    ( subset_complement(the_carrier(X1),X2) = set_difference(cast_as_carrier_subset(X1),X2)
    | ~ one_sorted_str(X1)
    | ~ element(X2,powerset(the_carrier(X1))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12]) ).

cnf(c_0_21,negated_conjecture,
    element(esk2_0,powerset(the_carrier(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    ( closed_subset(X1,X2)
    | ~ open_subset(set_difference(cast_as_carrier_subset(X2),X1),X2)
    | ~ top_str(X2)
    | ~ element(X1,powerset(the_carrier(X2))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    ( closed_subset(esk2_0,esk1_0)
    | open_subset(set_difference(cast_as_carrier_subset(esk1_0),esk2_0),esk1_0)
    | ~ one_sorted_str(esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_24,negated_conjecture,
    top_str(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ open_subset(subset_complement(the_carrier(esk1_0),esk2_0),esk1_0)
    | ~ closed_subset(esk2_0,esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_26,negated_conjecture,
    ( closed_subset(esk2_0,esk1_0)
    | ~ one_sorted_str(esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_21])]) ).

cnf(c_0_27,negated_conjecture,
    ( ~ closed_subset(esk2_0,esk1_0)
    | ~ one_sorted_str(esk1_0)
    | ~ open_subset(set_difference(cast_as_carrier_subset(esk1_0),esk2_0),esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_21])]) ).

cnf(c_0_28,negated_conjecture,
    closed_subset(esk2_0,esk1_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_13]),c_0_24])]) ).

cnf(c_0_29,plain,
    ( open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1)
    | ~ top_str(X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ closed_subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_30,negated_conjecture,
    ( ~ one_sorted_str(esk1_0)
    | ~ open_subset(set_difference(cast_as_carrier_subset(esk1_0),esk2_0),esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).

cnf(c_0_31,plain,
    ( open_subset(set_difference(cast_as_carrier_subset(X1),X2),X1)
    | ~ closed_subset(X2,X1)
    | ~ top_str(X1)
    | ~ element(X2,powerset(the_carrier(X1))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_15]),c_0_18]) ).

cnf(c_0_32,negated_conjecture,
    ~ one_sorted_str(esk1_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28]),c_0_24]),c_0_21])]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_13]),c_0_24])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU319+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14  % Command  : run_ET %s %d
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jun 20 02:03:37 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.27/1.48  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.27/1.48  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.27/1.48  # Preprocessing time       : 0.052 s
% 0.27/1.48  
% 0.27/1.48  # Proof found!
% 0.27/1.48  # SZS status Theorem
% 0.27/1.48  # SZS output start CNFRefutation
% See solution above
% 0.27/1.48  # Proof object total steps             : 34
% 0.27/1.48  # Proof object clause steps            : 21
% 0.27/1.48  # Proof object formula steps           : 13
% 0.27/1.48  # Proof object conjectures             : 14
% 0.27/1.48  # Proof object clause conjectures      : 11
% 0.27/1.48  # Proof object formula conjectures     : 3
% 0.27/1.48  # Proof object initial clauses used    : 10
% 0.27/1.48  # Proof object initial formulas used   : 6
% 0.27/1.48  # Proof object generating inferences   : 10
% 0.27/1.48  # Proof object simplifying inferences  : 20
% 0.27/1.48  # Training examples: 0 positive, 0 negative
% 0.27/1.48  # Parsed axioms                        : 521
% 0.27/1.48  # Removed by relevancy pruning/SinE    : 420
% 0.27/1.48  # Initial clauses                      : 419
% 0.27/1.48  # Removed in clause preprocessing      : 1
% 0.27/1.48  # Initial clauses in saturation        : 418
% 0.27/1.48  # Processed clauses                    : 3671
% 0.27/1.48  # ...of these trivial                  : 19
% 0.27/1.48  # ...subsumed                          : 2410
% 0.27/1.48  # ...remaining for further processing  : 1242
% 0.27/1.48  # Other redundant clauses eliminated   : 127
% 0.27/1.48  # Clauses deleted for lack of memory   : 0
% 0.27/1.48  # Backward-subsumed                    : 54
% 0.27/1.48  # Backward-rewritten                   : 197
% 0.27/1.48  # Generated clauses                    : 15320
% 0.27/1.48  # ...of the previous two non-trivial   : 13285
% 0.27/1.48  # Contextual simplify-reflections      : 1514
% 0.27/1.48  # Paramodulations                      : 15178
% 0.27/1.48  # Factorizations                       : 4
% 0.27/1.48  # Equation resolutions                 : 149
% 0.27/1.48  # Current number of processed clauses  : 935
% 0.27/1.48  #    Positive orientable unit clauses  : 47
% 0.27/1.48  #    Positive unorientable unit clauses: 0
% 0.27/1.48  #    Negative unit clauses             : 39
% 0.27/1.48  #    Non-unit-clauses                  : 849
% 0.27/1.48  # Current number of unprocessed clauses: 9138
% 0.27/1.48  # ...number of literals in the above   : 45834
% 0.27/1.48  # Current number of archived formulas  : 0
% 0.27/1.48  # Current number of archived clauses   : 252
% 0.27/1.48  # Clause-clause subsumption calls (NU) : 398125
% 0.27/1.48  # Rec. Clause-clause subsumption calls : 223975
% 0.27/1.48  # Non-unit clause-clause subsumptions  : 3454
% 0.27/1.48  # Unit Clause-clause subsumption calls : 12891
% 0.27/1.48  # Rewrite failures with RHS unbound    : 0
% 0.27/1.48  # BW rewrite match attempts            : 86
% 0.27/1.48  # BW rewrite match successes           : 8
% 0.27/1.48  # Condensation attempts                : 0
% 0.27/1.48  # Condensation successes               : 0
% 0.27/1.48  # Termbank termtop insertions          : 262602
% 0.27/1.48  
% 0.27/1.48  # -------------------------------------------------
% 0.27/1.48  # User time                : 0.572 s
% 0.27/1.48  # System time              : 0.011 s
% 0.27/1.48  # Total time               : 0.583 s
% 0.27/1.48  # Maximum resident set size: 14208 pages
% 0.31/23.47  eprover: CPU time limit exceeded, terminating
% 0.31/23.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.48  eprover: No such file or directory
% 0.31/23.49  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.49  eprover: No such file or directory
% 0.31/23.49  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.49  eprover: No such file or directory
% 0.31/23.50  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.50  eprover: No such file or directory
% 0.31/23.51  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.51  eprover: No such file or directory
% 0.31/23.51  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.51  eprover: No such file or directory
% 0.31/23.52  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.52  eprover: No such file or directory
% 0.31/23.52  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.52  eprover: No such file or directory
% 0.31/23.53  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.53  eprover: No such file or directory
% 0.31/23.53  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.53  eprover: No such file or directory
% 0.31/23.54  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.54  eprover: No such file or directory
% 0.31/23.61  eprover: CPU time limit exceeded, terminating
% 0.31/23.62  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.62  eprover: No such file or directory
% 0.31/23.63  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.63  eprover: No such file or directory
% 0.31/23.63  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.63  eprover: No such file or directory
% 0.31/23.64  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.64  eprover: No such file or directory
% 0.31/23.64  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.64  eprover: No such file or directory
% 0.31/23.65  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.65  eprover: No such file or directory
% 0.31/23.65  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.65  eprover: No such file or directory
% 0.31/23.66  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.66  eprover: No such file or directory
% 0.31/23.67  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.67  eprover: No such file or directory
% 0.31/23.67  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.67  eprover: No such file or directory
% 0.31/23.68  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.68  eprover: No such file or directory
%------------------------------------------------------------------------------