TSTP Solution File: SEU311+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU311+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% 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 : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 09:18:52 EDT 2022

% Result   : Theorem 0.23s 1.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   44 (   9 unt;   0 def)
%            Number of atoms       :  163 (   0 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  205 (  86   ~;  83   |;  22   &)
%                                         (   5 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-2 aty)
%            Number of variables   :   75 (   7 sgn  33   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(s3_subset_1__e2_37_1_1__pre_topc,conjecture,
    ! [X1,X2] :
      ( ( topological_space(X1)
        & top_str(X1)
        & element(X2,powerset(powerset(the_carrier(X1)))) )
     => ? [X3] :
          ( element(X3,powerset(powerset(the_carrier(X1))))
          & ! [X4] :
              ( element(X4,powerset(the_carrier(X1)))
             => ( in(X4,X3)
              <=> in(set_difference(cast_as_carrier_subset(X1),X4),X2) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',s3_subset_1__e2_37_1_1__pre_topc) ).

fof(d2_subset_1,axiom,
    ! [X1,X2] :
      ( ( ~ empty(X1)
       => ( element(X2,X1)
        <=> in(X2,X1) ) )
      & ( empty(X1)
       => ( element(X2,X1)
        <=> empty(X2) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_subset_1) ).

fof(t7_boole,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & empty(X2) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t7_boole) ).

fof(s1_xboole_0__e2_37_1_1__pre_topc__1,axiom,
    ! [X1,X2] :
      ( ( topological_space(X1)
        & top_str(X1)
        & element(X2,powerset(powerset(the_carrier(X1)))) )
     => ? [X3] :
        ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,powerset(the_carrier(X1)))
            & in(set_difference(cast_as_carrier_subset(X1),X4),X2) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',s1_xboole_0__e2_37_1_1__pre_topc__1) ).

fof(l71_subset_1,axiom,
    ! [X1,X2] :
      ( ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) )
     => element(X1,powerset(X2)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l71_subset_1) ).

fof(fc1_subset_1,axiom,
    ! [X1] : ~ empty(powerset(X1)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc1_subset_1) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( topological_space(X1)
          & top_str(X1)
          & element(X2,powerset(powerset(the_carrier(X1)))) )
       => ? [X3] :
            ( element(X3,powerset(powerset(the_carrier(X1))))
            & ! [X4] :
                ( element(X4,powerset(the_carrier(X1)))
               => ( in(X4,X3)
                <=> in(set_difference(cast_as_carrier_subset(X1),X4),X2) ) ) ) ),
    inference(assume_negation,[status(cth)],[s3_subset_1__e2_37_1_1__pre_topc]) ).

fof(c_0_7,plain,
    ! [X3,X4,X4,X3,X4,X4] :
      ( ( ~ element(X4,X3)
        | in(X4,X3)
        | empty(X3) )
      & ( ~ in(X4,X3)
        | element(X4,X3)
        | empty(X3) )
      & ( ~ element(X4,X3)
        | empty(X4)
        | ~ empty(X3) )
      & ( ~ empty(X4)
        | element(X4,X3)
        | ~ empty(X3) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_subset_1])])])])])]) ).

fof(c_0_8,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | ~ empty(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).

fof(c_0_9,plain,
    ! [X5,X6,X8,X8] :
      ( ( in(X8,powerset(the_carrier(X5)))
        | ~ in(X8,esk5_2(X5,X6))
        | ~ topological_space(X5)
        | ~ top_str(X5)
        | ~ element(X6,powerset(powerset(the_carrier(X5)))) )
      & ( in(set_difference(cast_as_carrier_subset(X5),X8),X6)
        | ~ in(X8,esk5_2(X5,X6))
        | ~ topological_space(X5)
        | ~ top_str(X5)
        | ~ element(X6,powerset(powerset(the_carrier(X5)))) )
      & ( ~ in(X8,powerset(the_carrier(X5)))
        | ~ in(set_difference(cast_as_carrier_subset(X5),X8),X6)
        | in(X8,esk5_2(X5,X6))
        | ~ topological_space(X5)
        | ~ top_str(X5)
        | ~ element(X6,powerset(powerset(the_carrier(X5)))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[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)],[s1_xboole_0__e2_37_1_1__pre_topc__1])])])])])])]) ).

fof(c_0_10,plain,
    ! [X4,X5] :
      ( ( in(esk4_2(X4,X5),X4)
        | element(X4,powerset(X5)) )
      & ( ~ in(esk4_2(X4,X5),X5)
        | element(X4,powerset(X5)) ) ),
    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)],[l71_subset_1])])])])])]) ).

fof(c_0_11,negated_conjecture,
    ! [X7] :
      ( topological_space(esk1_0)
      & top_str(esk1_0)
      & element(esk2_0,powerset(powerset(the_carrier(esk1_0))))
      & ( element(esk3_1(X7),powerset(the_carrier(esk1_0)))
        | ~ element(X7,powerset(powerset(the_carrier(esk1_0)))) )
      & ( ~ in(esk3_1(X7),X7)
        | ~ in(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(X7)),esk2_0)
        | ~ element(X7,powerset(powerset(the_carrier(esk1_0)))) )
      & ( in(esk3_1(X7),X7)
        | in(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(X7)),esk2_0)
        | ~ element(X7,powerset(powerset(the_carrier(esk1_0)))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[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_6])])])])])])]) ).

cnf(c_0_12,plain,
    ( empty(X1)
    | element(X2,X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( ~ empty(X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( in(X3,powerset(the_carrier(X2)))
    | ~ element(X1,powerset(powerset(the_carrier(X2))))
    | ~ top_str(X2)
    | ~ topological_space(X2)
    | ~ in(X3,esk5_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( element(X1,powerset(X2))
    | in(esk4_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    ( in(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(X1)),esk2_0)
    | in(esk3_1(X1),X1)
    | ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    ( element(X1,X2)
    | ~ in(X1,X2) ),
    inference(csr,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_18,plain,
    ( element(X1,powerset(X2))
    | ~ in(esk4_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_19,plain,
    ( in(esk4_2(esk5_2(X1,X2),X3),powerset(the_carrier(X1)))
    | element(esk5_2(X1,X2),powerset(X3))
    | ~ element(X2,powerset(powerset(the_carrier(X1))))
    | ~ top_str(X1)
    | ~ topological_space(X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    ( in(esk3_1(X1),X1)
    | ~ empty(esk2_0)
    | ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
    inference(spm,[status(thm)],[c_0_13,c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    ( in(esk3_1(X1),X1)
    | element(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(X1)),esk2_0)
    | ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
    inference(spm,[status(thm)],[c_0_17,c_0_16]) ).

cnf(c_0_22,plain,
    ( element(esk5_2(X1,X2),powerset(powerset(the_carrier(X1))))
    | ~ element(X2,powerset(powerset(the_carrier(X1))))
    | ~ top_str(X1)
    | ~ topological_space(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    top_str(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_24,negated_conjecture,
    topological_space(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ empty(esk2_0)
    | ~ empty(X1)
    | ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
    inference(spm,[status(thm)],[c_0_13,c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    element(esk2_0,powerset(powerset(the_carrier(esk1_0)))),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_27,plain,
    ( in(set_difference(cast_as_carrier_subset(X2),X3),X1)
    | ~ element(X1,powerset(powerset(the_carrier(X2))))
    | ~ top_str(X2)
    | ~ topological_space(X2)
    | ~ in(X3,esk5_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_28,negated_conjecture,
    ( in(esk3_1(esk5_2(esk1_0,X1)),esk5_2(esk1_0,X1))
    | element(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(esk5_2(esk1_0,X1))),esk2_0)
    | ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]) ).

cnf(c_0_29,negated_conjecture,
    ( ~ element(X1,powerset(powerset(the_carrier(esk1_0))))
    | ~ in(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(X1)),esk2_0)
    | ~ in(esk3_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_30,plain,
    ( empty(X1)
    | in(X2,X1)
    | ~ element(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_31,negated_conjecture,
    ~ empty(esk2_0),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_32,negated_conjecture,
    ( in(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(esk5_2(esk1_0,X1))),X1)
    | element(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(esk5_2(esk1_0,X1))),esk2_0)
    | ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23]),c_0_24])]) ).

cnf(c_0_33,negated_conjecture,
    ( ~ in(esk3_1(X1),X1)
    | ~ element(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(X1)),esk2_0)
    | ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    ( element(set_difference(cast_as_carrier_subset(esk1_0),esk3_1(esk5_2(esk1_0,esk2_0))),esk2_0)
    | ~ element(esk5_2(esk1_0,esk2_0),powerset(powerset(the_carrier(esk1_0)))) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_26])]),c_0_21]) ).

cnf(c_0_35,plain,
    ( in(X3,esk5_2(X2,X1))
    | ~ element(X1,powerset(powerset(the_carrier(X2))))
    | ~ top_str(X2)
    | ~ topological_space(X2)
    | ~ in(set_difference(cast_as_carrier_subset(X2),X3),X1)
    | ~ in(X3,powerset(the_carrier(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_36,negated_conjecture,
    ( ~ in(esk3_1(esk5_2(esk1_0,esk2_0)),esk5_2(esk1_0,esk2_0))
    | ~ element(esk5_2(esk1_0,esk2_0),powerset(powerset(the_carrier(esk1_0)))) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_37,plain,
    ( empty(X1)
    | in(X2,esk5_2(X3,X1))
    | ~ in(X2,powerset(the_carrier(X3)))
    | ~ element(X1,powerset(powerset(the_carrier(X3))))
    | ~ element(set_difference(cast_as_carrier_subset(X3),X2),X1)
    | ~ top_str(X3)
    | ~ topological_space(X3) ),
    inference(spm,[status(thm)],[c_0_35,c_0_30]) ).

fof(c_0_38,plain,
    ! [X2] : ~ empty(powerset(X2)),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_subset_1])]) ).

cnf(c_0_39,negated_conjecture,
    ( ~ in(esk3_1(esk5_2(esk1_0,esk2_0)),powerset(the_carrier(esk1_0)))
    | ~ element(esk5_2(esk1_0,esk2_0),powerset(powerset(the_carrier(esk1_0)))) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_26]),c_0_23]),c_0_24])]),c_0_31]),c_0_34]) ).

cnf(c_0_40,plain,
    ~ empty(powerset(X1)),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_41,negated_conjecture,
    ( element(esk3_1(X1),powerset(the_carrier(esk1_0)))
    | ~ element(X1,powerset(powerset(the_carrier(esk1_0)))) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_42,negated_conjecture,
    ~ element(esk5_2(esk1_0,esk2_0),powerset(powerset(the_carrier(esk1_0)))),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_30]),c_0_40]),c_0_41]) ).

cnf(c_0_43,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_42,c_0_22]),c_0_26]),c_0_23]),c_0_24])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU311+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n022.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  : 600
% 0.12/0.34  % DateTime : Mon Jun 20 12:41:16 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.23/1.41  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41  # Preprocessing time       : 0.018 s
% 0.23/1.41  
% 0.23/1.41  # Proof found!
% 0.23/1.41  # SZS status Theorem
% 0.23/1.41  # SZS output start CNFRefutation
% See solution above
% 0.23/1.41  # Proof object total steps             : 44
% 0.23/1.41  # Proof object clause steps            : 31
% 0.23/1.41  # Proof object formula steps           : 13
% 0.23/1.41  # Proof object conjectures             : 21
% 0.23/1.41  # Proof object clause conjectures      : 18
% 0.23/1.41  # Proof object formula conjectures     : 3
% 0.23/1.41  # Proof object initial clauses used    : 15
% 0.23/1.41  # Proof object initial formulas used   : 6
% 0.23/1.41  # Proof object generating inferences   : 15
% 0.23/1.41  # Proof object simplifying inferences  : 23
% 0.23/1.41  # Training examples: 0 positive, 0 negative
% 0.23/1.41  # Parsed axioms                        : 46
% 0.23/1.41  # Removed by relevancy pruning/SinE    : 17
% 0.23/1.41  # Initial clauses                      : 71
% 0.23/1.41  # Removed in clause preprocessing      : 0
% 0.23/1.41  # Initial clauses in saturation        : 71
% 0.23/1.41  # Processed clauses                    : 1455
% 0.23/1.41  # ...of these trivial                  : 13
% 0.23/1.41  # ...subsumed                          : 730
% 0.23/1.41  # ...remaining for further processing  : 712
% 0.23/1.41  # Other redundant clauses eliminated   : 0
% 0.23/1.41  # Clauses deleted for lack of memory   : 0
% 0.23/1.41  # Backward-subsumed                    : 159
% 0.23/1.41  # Backward-rewritten                   : 5
% 0.23/1.41  # Generated clauses                    : 3070
% 0.23/1.41  # ...of the previous two non-trivial   : 2834
% 0.23/1.41  # Contextual simplify-reflections      : 601
% 0.23/1.41  # Paramodulations                      : 3070
% 0.23/1.41  # Factorizations                       : 0
% 0.23/1.41  # Equation resolutions                 : 0
% 0.23/1.41  # Current number of processed clauses  : 548
% 0.23/1.41  #    Positive orientable unit clauses  : 45
% 0.23/1.41  #    Positive unorientable unit clauses: 0
% 0.23/1.41  #    Negative unit clauses             : 12
% 0.23/1.41  #    Non-unit-clauses                  : 491
% 0.23/1.41  # Current number of unprocessed clauses: 781
% 0.23/1.41  # ...number of literals in the above   : 4571
% 0.23/1.41  # Current number of archived formulas  : 0
% 0.23/1.41  # Current number of archived clauses   : 164
% 0.23/1.41  # Clause-clause subsumption calls (NU) : 255068
% 0.23/1.41  # Rec. Clause-clause subsumption calls : 147144
% 0.23/1.41  # Non-unit clause-clause subsumptions  : 1217
% 0.23/1.41  # Unit Clause-clause subsumption calls : 743
% 0.23/1.41  # Rewrite failures with RHS unbound    : 0
% 0.23/1.41  # BW rewrite match attempts            : 192
% 0.23/1.41  # BW rewrite match successes           : 5
% 0.23/1.41  # Condensation attempts                : 0
% 0.23/1.41  # Condensation successes               : 0
% 0.23/1.41  # Termbank termtop insertions          : 60140
% 0.23/1.41  
% 0.23/1.41  # -------------------------------------------------
% 0.23/1.41  # User time                : 0.192 s
% 0.23/1.41  # System time              : 0.003 s
% 0.23/1.41  # Total time               : 0.195 s
% 0.23/1.41  # Maximum resident set size: 5196 pages
%------------------------------------------------------------------------------