TSTP Solution File: SEU324+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n015.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 09:19:00 EDT 2022

% Result   : Theorem 0.22s 1.40s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   37 (   9 unt;   0 def)
%            Number of atoms       :  128 (  27 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  143 (  52   ~;  49   |;  18   &)
%                                         (   1 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   50 (   0 sgn  32   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d1_tops_1,axiom,
    ! [X1] :
      ( top_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_tops_1) ).

fof(involutiveness_k3_subset_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => subset_complement(X1,subset_complement(X1,X2)) = X2 ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',involutiveness_k3_subset_1) ).

fof(dt_k3_subset_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => element(subset_complement(X1,X2),powerset(X1)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k3_subset_1) ).

fof(t55_tops_1,conjecture,
    ! [X1] :
      ( ( topological_space(X1)
        & top_str(X1) )
     => ! [X2] :
          ( top_str(X2)
         => ! [X3] :
              ( element(X3,powerset(the_carrier(X1)))
             => ! [X4] :
                  ( element(X4,powerset(the_carrier(X2)))
                 => ( ( open_subset(X4,X2)
                     => interior(X2,X4) = X4 )
                    & ( interior(X1,X3) = X3
                     => open_subset(X3,X1) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t55_tops_1) ).

fof(t52_pre_topc,axiom,
    ! [X1] :
      ( top_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => ( ( closed_subset(X2,X1)
             => topstr_closure(X1,X2) = X2 )
            & ( ( topological_space(X1)
                & topstr_closure(X1,X2) = X2 )
             => closed_subset(X2,X1) ) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t52_pre_topc) ).

fof(fc6_tops_1,axiom,
    ! [X1,X2] :
      ( ( topological_space(X1)
        & top_str(X1)
        & element(X2,powerset(the_carrier(X1))) )
     => open_subset(interior(X1,X2),X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc6_tops_1) ).

fof(t30_tops_1,axiom,
    ! [X1] :
      ( top_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => ( open_subset(X2,X1)
          <=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t30_tops_1) ).

fof(c_0_7,plain,
    ! [X3,X4] :
      ( ~ top_str(X3)
      | ~ element(X4,powerset(the_carrier(X3)))
      | interior(X3,X4) = subset_complement(the_carrier(X3),topstr_closure(X3,subset_complement(the_carrier(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)],[d1_tops_1])])])])]) ).

fof(c_0_8,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(X3))
      | subset_complement(X3,subset_complement(X3,X4)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).

fof(c_0_9,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(X3))
      | element(subset_complement(X3,X4),powerset(X3)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1] :
        ( ( topological_space(X1)
          & top_str(X1) )
       => ! [X2] :
            ( top_str(X2)
           => ! [X3] :
                ( element(X3,powerset(the_carrier(X1)))
               => ! [X4] :
                    ( element(X4,powerset(the_carrier(X2)))
                   => ( ( open_subset(X4,X2)
                       => interior(X2,X4) = X4 )
                      & ( interior(X1,X3) = X3
                       => open_subset(X3,X1) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[t55_tops_1]) ).

cnf(c_0_11,plain,
    ( interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2)))
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ top_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ( subset_complement(X1,subset_complement(X1,X2)) = X2
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( element(subset_complement(X1,X2),powerset(X1))
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_14,plain,
    ! [X3,X4] :
      ( ( ~ closed_subset(X4,X3)
        | topstr_closure(X3,X4) = X4
        | ~ element(X4,powerset(the_carrier(X3)))
        | ~ top_str(X3) )
      & ( ~ topological_space(X3)
        | topstr_closure(X3,X4) != X4
        | 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)],[t52_pre_topc])])])])])]) ).

fof(c_0_15,plain,
    ! [X3,X4] :
      ( ~ topological_space(X3)
      | ~ top_str(X3)
      | ~ element(X4,powerset(the_carrier(X3)))
      | open_subset(interior(X3,X4),X3) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc6_tops_1])]) ).

fof(c_0_16,negated_conjecture,
    ( topological_space(esk1_0)
    & top_str(esk1_0)
    & top_str(esk2_0)
    & element(esk3_0,powerset(the_carrier(esk1_0)))
    & element(esk4_0,powerset(the_carrier(esk2_0)))
    & ( interior(esk1_0,esk3_0) = esk3_0
      | open_subset(esk4_0,esk2_0) )
    & ( ~ open_subset(esk3_0,esk1_0)
      | open_subset(esk4_0,esk2_0) )
    & ( interior(esk1_0,esk3_0) = esk3_0
      | interior(esk2_0,esk4_0) != esk4_0 )
    & ( ~ open_subset(esk3_0,esk1_0)
      | interior(esk2_0,esk4_0) != esk4_0 ) ),
    inference(distribute,[status(thm)],[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_10])])])])])]) ).

cnf(c_0_17,plain,
    ( subset_complement(the_carrier(X1),topstr_closure(X1,X2)) = interior(X1,subset_complement(the_carrier(X1),X2))
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ top_str(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).

cnf(c_0_18,plain,
    ( topstr_closure(X1,X2) = X2
    | ~ top_str(X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ closed_subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    ( open_subset(interior(X1,X2),X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ top_str(X1)
    | ~ topological_space(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    ( interior(esk1_0,esk3_0) = esk3_0
    | interior(esk2_0,esk4_0) != esk4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    topological_space(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    element(esk3_0,powerset(the_carrier(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,negated_conjecture,
    top_str(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,negated_conjecture,
    ( interior(esk2_0,esk4_0) != esk4_0
    | ~ open_subset(esk3_0,esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,plain,
    ( interior(X1,subset_complement(the_carrier(X1),X2)) = subset_complement(the_carrier(X1),X2)
    | ~ closed_subset(X2,X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ top_str(X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_26,negated_conjecture,
    interior(esk2_0,esk4_0) != esk4_0,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).

cnf(c_0_27,plain,
    ( interior(X1,X2) = X2
    | ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ top_str(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_12]),c_0_13]) ).

cnf(c_0_28,negated_conjecture,
    element(esk4_0,powerset(the_carrier(esk2_0))),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_29,negated_conjecture,
    top_str(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_30,plain,
    ! [X3,X4] :
      ( ( ~ open_subset(X4,X3)
        | closed_subset(subset_complement(the_carrier(X3),X4),X3)
        | ~ element(X4,powerset(the_carrier(X3)))
        | ~ top_str(X3) )
      & ( ~ closed_subset(subset_complement(the_carrier(X3),X4),X3)
        | open_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)],[t30_tops_1])])])])])]) ).

cnf(c_0_31,negated_conjecture,
    ( open_subset(esk4_0,esk2_0)
    | interior(esk1_0,esk3_0) = esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_32,negated_conjecture,
    ( open_subset(esk4_0,esk2_0)
    | ~ open_subset(esk3_0,esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_33,negated_conjecture,
    ~ closed_subset(subset_complement(the_carrier(esk2_0),esk4_0),esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).

cnf(c_0_34,plain,
    ( closed_subset(subset_complement(the_carrier(X1),X2),X1)
    | ~ top_str(X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ open_subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_35,negated_conjecture,
    open_subset(esk4_0,esk2_0),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_31]),c_0_21]),c_0_22]),c_0_23])]),c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_28]),c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jun 19 06:37:29 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.22/1.40  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40  # Preprocessing time       : 0.009 s
% 0.22/1.40  
% 0.22/1.40  # Proof found!
% 0.22/1.40  # SZS status Theorem
% 0.22/1.40  # SZS output start CNFRefutation
% See solution above
% 0.22/1.40  # Proof object total steps             : 37
% 0.22/1.40  # Proof object clause steps            : 22
% 0.22/1.40  # Proof object formula steps           : 15
% 0.22/1.40  # Proof object conjectures             : 16
% 0.22/1.40  # Proof object clause conjectures      : 13
% 0.22/1.40  # Proof object formula conjectures     : 3
% 0.22/1.40  # Proof object initial clauses used    : 15
% 0.22/1.40  # Proof object initial formulas used   : 7
% 0.22/1.40  # Proof object generating inferences   : 7
% 0.22/1.40  # Proof object simplifying inferences  : 19
% 0.22/1.40  # Training examples: 0 positive, 0 negative
% 0.22/1.40  # Parsed axioms                        : 25
% 0.22/1.40  # Removed by relevancy pruning/SinE    : 8
% 0.22/1.40  # Initial clauses                      : 31
% 0.22/1.40  # Removed in clause preprocessing      : 0
% 0.22/1.40  # Initial clauses in saturation        : 31
% 0.22/1.40  # Processed clauses                    : 45
% 0.22/1.40  # ...of these trivial                  : 0
% 0.22/1.40  # ...subsumed                          : 3
% 0.22/1.40  # ...remaining for further processing  : 42
% 0.22/1.40  # Other redundant clauses eliminated   : 0
% 0.22/1.40  # Clauses deleted for lack of memory   : 0
% 0.22/1.40  # Backward-subsumed                    : 2
% 0.22/1.40  # Backward-rewritten                   : 1
% 0.22/1.40  # Generated clauses                    : 52
% 0.22/1.40  # ...of the previous two non-trivial   : 39
% 0.22/1.40  # Contextual simplify-reflections      : 12
% 0.22/1.40  # Paramodulations                      : 52
% 0.22/1.40  # Factorizations                       : 0
% 0.22/1.40  # Equation resolutions                 : 0
% 0.22/1.40  # Current number of processed clauses  : 39
% 0.22/1.40  #    Positive orientable unit clauses  : 8
% 0.22/1.40  #    Positive unorientable unit clauses: 0
% 0.22/1.40  #    Negative unit clauses             : 2
% 0.22/1.40  #    Non-unit-clauses                  : 29
% 0.22/1.40  # Current number of unprocessed clauses: 22
% 0.22/1.40  # ...number of literals in the above   : 96
% 0.22/1.40  # Current number of archived formulas  : 0
% 0.22/1.40  # Current number of archived clauses   : 3
% 0.22/1.40  # Clause-clause subsumption calls (NU) : 130
% 0.22/1.40  # Rec. Clause-clause subsumption calls : 74
% 0.22/1.40  # Non-unit clause-clause subsumptions  : 16
% 0.22/1.40  # Unit Clause-clause subsumption calls : 10
% 0.22/1.40  # Rewrite failures with RHS unbound    : 0
% 0.22/1.40  # BW rewrite match attempts            : 1
% 0.22/1.40  # BW rewrite match successes           : 1
% 0.22/1.40  # Condensation attempts                : 0
% 0.22/1.40  # Condensation successes               : 0
% 0.22/1.40  # Termbank termtop insertions          : 3444
% 0.22/1.40  
% 0.22/1.40  # -------------------------------------------------
% 0.22/1.40  # User time                : 0.008 s
% 0.22/1.40  # System time              : 0.003 s
% 0.22/1.40  # Total time               : 0.011 s
% 0.22/1.40  # Maximum resident set size: 2980 pages
%------------------------------------------------------------------------------