TSTP Solution File: SEU147+2 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU147+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n005.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 09:17:09 EDT 2022

% Result   : Theorem 0.24s 1.42s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   42 (  15 unt;   0 def)
%            Number of atoms       :   99 (  26 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   94 (  37   ~;  41   |;   9   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   76 (  17 sgn  36   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
    ! [X1,X2] :
      ( X2 = powerset(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> subset(X3,X1) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_zfmisc_1) ).

fof(t2_xboole_1,lemma,
    ! [X1] : subset(empty_set,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_xboole_1) ).

fof(l2_zfmisc_1,lemma,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l2_zfmisc_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d3_tarski) ).

fof(t3_xboole_1,lemma,
    ! [X1] :
      ( subset(X1,empty_set)
     => X1 = empty_set ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t3_xboole_1) ).

fof(d10_xboole_0,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d10_xboole_0) ).

fof(reflexivity_r1_tarski,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',reflexivity_r1_tarski) ).

fof(t1_zfmisc_1,conjecture,
    powerset(empty_set) = singleton(empty_set),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t1_zfmisc_1) ).

fof(c_0_8,plain,
    ! [X4,X5,X6,X6,X4,X5] :
      ( ( ~ in(X6,X5)
        | subset(X6,X4)
        | X5 != powerset(X4) )
      & ( ~ subset(X6,X4)
        | in(X6,X5)
        | X5 != powerset(X4) )
      & ( ~ in(esk3_2(X4,X5),X5)
        | ~ subset(esk3_2(X4,X5),X4)
        | X5 = powerset(X4) )
      & ( in(esk3_2(X4,X5),X5)
        | subset(esk3_2(X4,X5),X4)
        | X5 = powerset(X4) ) ),
    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)],[d1_zfmisc_1])])])])])])]) ).

fof(c_0_9,lemma,
    ! [X2] : subset(empty_set,X2),
    inference(variable_rename,[status(thm)],[t2_xboole_1]) ).

fof(c_0_10,lemma,
    ! [X3,X4,X3,X4] :
      ( ( ~ subset(singleton(X3),X4)
        | in(X3,X4) )
      & ( ~ in(X3,X4)
        | subset(singleton(X3),X4) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])])])]) ).

cnf(c_0_11,plain,
    ( in(X3,X1)
    | X1 != powerset(X2)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,lemma,
    subset(empty_set,X1),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,lemma,
    ( subset(singleton(X1),X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,lemma,
    ( in(empty_set,X1)
    | X1 != powerset(X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,lemma,
    ( in(singleton(X1),X2)
    | X2 != powerset(X3)
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[c_0_11,c_0_13]) ).

cnf(c_0_16,lemma,
    in(empty_set,powerset(X1)),
    inference(er,[status(thm)],[c_0_14]) ).

fof(c_0_17,plain,
    ! [X4,X5,X6,X4,X5] :
      ( ( ~ subset(X4,X5)
        | ~ in(X6,X4)
        | in(X6,X5) )
      & ( in(esk5_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk5_2(X4,X5),X5)
        | subset(X4,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)],[d3_tarski])])])])])])]) ).

cnf(c_0_18,lemma,
    ( in(singleton(empty_set),X1)
    | X1 != powerset(powerset(X2)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,plain,
    ( subset(X3,X2)
    | X1 != powerset(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,plain,
    ( subset(X1,X2)
    | in(esk5_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_21,lemma,
    in(singleton(empty_set),powerset(powerset(X1))),
    inference(er,[status(thm)],[c_0_18]) ).

fof(c_0_22,lemma,
    ! [X2] :
      ( ~ subset(X2,empty_set)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).

cnf(c_0_23,plain,
    ( subset(esk5_2(X1,X2),X3)
    | subset(X1,X2)
    | X1 != powerset(X3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

fof(c_0_24,plain,
    ! [X3,X4,X3,X4] :
      ( ( subset(X3,X4)
        | X3 != X4 )
      & ( subset(X4,X3)
        | X3 != X4 )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])])]) ).

cnf(c_0_25,lemma,
    ( subset(singleton(empty_set),X1)
    | powerset(powerset(X2)) != powerset(X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_21]) ).

cnf(c_0_26,lemma,
    ( X1 = empty_set
    | ~ subset(X1,empty_set) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,plain,
    ( subset(esk5_2(powerset(X1),X2),X1)
    | subset(powerset(X1),X2) ),
    inference(er,[status(thm)],[c_0_23]) ).

fof(c_0_28,plain,
    ! [X3] : subset(X3,X3),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[reflexivity_r1_tarski])]) ).

fof(c_0_29,negated_conjecture,
    powerset(empty_set) != singleton(empty_set),
    inference(assume_negation,[status(cth)],[t1_zfmisc_1]) ).

cnf(c_0_30,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,lemma,
    subset(singleton(empty_set),powerset(X1)),
    inference(er,[status(thm)],[c_0_25]) ).

cnf(c_0_32,plain,
    ( subset(X1,X2)
    | ~ in(esk5_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_33,lemma,
    ( esk5_2(powerset(empty_set),X1) = empty_set
    | subset(powerset(empty_set),X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_34,lemma,
    ( in(X1,X2)
    | ~ subset(singleton(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_35,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_36,negated_conjecture,
    powerset(empty_set) != singleton(empty_set),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

cnf(c_0_37,lemma,
    ( powerset(X1) = singleton(empty_set)
    | ~ subset(powerset(X1),singleton(empty_set)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_38,lemma,
    ( subset(powerset(empty_set),X1)
    | ~ in(empty_set,X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,lemma,
    in(X1,singleton(X1)),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,negated_conjecture,
    powerset(empty_set) != singleton(empty_set),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_41,lemma,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]),c_0_40]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU147+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 20 05:01:08 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.24/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42  # Preprocessing time       : 0.019 s
% 0.24/1.42  
% 0.24/1.42  # Proof found!
% 0.24/1.42  # SZS status Theorem
% 0.24/1.42  # SZS output start CNFRefutation
% See solution above
% 0.24/1.42  # Proof object total steps             : 42
% 0.24/1.42  # Proof object clause steps            : 25
% 0.24/1.42  # Proof object formula steps           : 17
% 0.24/1.42  # Proof object conjectures             : 4
% 0.24/1.42  # Proof object clause conjectures      : 1
% 0.24/1.42  # Proof object formula conjectures     : 3
% 0.24/1.42  # Proof object initial clauses used    : 11
% 0.24/1.42  # Proof object initial formulas used   : 8
% 0.24/1.42  # Proof object generating inferences   : 14
% 0.24/1.42  # Proof object simplifying inferences  : 3
% 0.24/1.42  # Training examples: 0 positive, 0 negative
% 0.24/1.42  # Parsed axioms                        : 70
% 0.24/1.42  # Removed by relevancy pruning/SinE    : 28
% 0.24/1.42  # Initial clauses                      : 74
% 0.24/1.42  # Removed in clause preprocessing      : 1
% 0.24/1.42  # Initial clauses in saturation        : 73
% 0.24/1.42  # Processed clauses                    : 4519
% 0.24/1.42  # ...of these trivial                  : 242
% 0.24/1.42  # ...subsumed                          : 3324
% 0.24/1.42  # ...remaining for further processing  : 953
% 0.24/1.42  # Other redundant clauses eliminated   : 284
% 0.24/1.42  # Clauses deleted for lack of memory   : 0
% 0.24/1.42  # Backward-subsumed                    : 28
% 0.24/1.42  # Backward-rewritten                   : 18
% 0.24/1.42  # Generated clauses                    : 46650
% 0.24/1.42  # ...of the previous two non-trivial   : 37670
% 0.24/1.42  # Contextual simplify-reflections      : 401
% 0.24/1.42  # Paramodulations                      : 46175
% 0.24/1.42  # Factorizations                       : 64
% 0.24/1.42  # Equation resolutions                 : 411
% 0.24/1.42  # Current number of processed clauses  : 904
% 0.24/1.42  #    Positive orientable unit clauses  : 118
% 0.24/1.42  #    Positive unorientable unit clauses: 2
% 0.24/1.42  #    Negative unit clauses             : 76
% 0.24/1.42  #    Non-unit-clauses                  : 708
% 0.24/1.42  # Current number of unprocessed clauses: 29891
% 0.24/1.42  # ...number of literals in the above   : 100110
% 0.24/1.42  # Current number of archived formulas  : 0
% 0.24/1.42  # Current number of archived clauses   : 47
% 0.24/1.42  # Clause-clause subsumption calls (NU) : 207327
% 0.24/1.42  # Rec. Clause-clause subsumption calls : 142177
% 0.24/1.42  # Non-unit clause-clause subsumptions  : 2093
% 0.24/1.42  # Unit Clause-clause subsumption calls : 12081
% 0.24/1.42  # Rewrite failures with RHS unbound    : 0
% 0.24/1.42  # BW rewrite match attempts            : 157
% 0.24/1.42  # BW rewrite match successes           : 22
% 0.24/1.42  # Condensation attempts                : 0
% 0.24/1.42  # Condensation successes               : 0
% 0.24/1.42  # Termbank termtop insertions          : 509636
% 0.24/1.42  
% 0.24/1.42  # -------------------------------------------------
% 0.24/1.42  # User time                : 0.645 s
% 0.24/1.42  # System time              : 0.019 s
% 0.24/1.42  # Total time               : 0.664 s
% 0.24/1.42  # Maximum resident set size: 27916 pages
%------------------------------------------------------------------------------