TSTP Solution File: SEU144+2 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU144+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n029.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 09:17:07 EDT 2022

% Result   : Theorem 0.23s 1.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   35 (  11 unt;   0 def)
%            Number of atoms       :   84 (  28 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   83 (  34   ~;  35   |;   7   &)
%                                         (   6 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :   55 (   7 sgn  30   !;   0   ?)

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

fof(t69_enumset1,lemma,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t69_enumset1) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_tarski) ).

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

fof(l1_zfmisc_1,lemma,
    ! [X1] : singleton(X1) != empty_set,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l1_zfmisc_1) ).

fof(d1_xboole_0,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_xboole_0) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(singleton(X1),X2)
      <=> in(X1,X2) ),
    inference(assume_negation,[status(cth)],[l2_zfmisc_1]) ).

fof(c_0_7,negated_conjecture,
    ( ( ~ subset(singleton(esk1_0),esk2_0)
      | ~ in(esk1_0,esk2_0) )
    & ( subset(singleton(esk1_0),esk2_0)
      | in(esk1_0,esk2_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_8,lemma,
    ! [X2] : unordered_pair(X2,X2) = singleton(X2),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

fof(c_0_9,plain,
    ! [X4,X5,X6,X6,X4,X5] :
      ( ( ~ in(X6,X5)
        | X6 = X4
        | X5 != singleton(X4) )
      & ( X6 != X4
        | in(X6,X5)
        | X5 != singleton(X4) )
      & ( ~ in(esk9_2(X4,X5),X5)
        | esk9_2(X4,X5) != X4
        | X5 = singleton(X4) )
      & ( in(esk9_2(X4,X5),X5)
        | esk9_2(X4,X5) = X4
        | X5 = singleton(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_tarski])])])])])])]) ).

fof(c_0_10,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_11,negated_conjecture,
    ( in(esk1_0,esk2_0)
    | subset(singleton(esk1_0),esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,lemma,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_13,lemma,
    ! [X2] : singleton(X2) != empty_set,
    inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).

cnf(c_0_14,plain,
    ( X3 = X2
    | X1 != singleton(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    ( in(esk1_0,esk2_0)
    | subset(unordered_pair(esk1_0,esk1_0),esk2_0) ),
    inference(rw,[status(thm)],[c_0_11,c_0_12]) ).

fof(c_0_17,plain,
    ! [X3,X4,X3] :
      ( ( X3 != empty_set
        | ~ in(X4,X3) )
      & ( in(esk3_1(X3),X3)
        | X3 = empty_set ) ),
    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)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])]) ).

cnf(c_0_18,lemma,
    singleton(X1) != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    ( X2 = X3
    | X1 != unordered_pair(X2,X2)
    | ~ in(X3,X1) ),
    inference(rw,[status(thm)],[c_0_14,c_0_12]) ).

cnf(c_0_20,negated_conjecture,
    ( in(esk1_0,esk2_0)
    | in(X1,esk2_0)
    | ~ in(X1,unordered_pair(esk1_0,esk1_0)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,plain,
    ( X1 = empty_set
    | in(esk3_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,lemma,
    unordered_pair(X1,X1) != empty_set,
    inference(rw,[status(thm)],[c_0_18,c_0_12]) ).

cnf(c_0_23,plain,
    ( X1 = X2
    | ~ in(X2,unordered_pair(X1,X1)) ),
    inference(er,[status(thm)],[c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ in(esk1_0,esk2_0)
    | ~ subset(singleton(esk1_0),esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_25,negated_conjecture,
    ( in(esk3_1(unordered_pair(esk1_0,esk1_0)),esk2_0)
    | in(esk1_0,esk2_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

cnf(c_0_26,plain,
    esk3_1(unordered_pair(X1,X1)) = X1,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_22]) ).

cnf(c_0_27,plain,
    ( subset(X1,X2)
    | in(esk5_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_28,negated_conjecture,
    ( ~ in(esk1_0,esk2_0)
    | ~ subset(unordered_pair(esk1_0,esk1_0),esk2_0) ),
    inference(rw,[status(thm)],[c_0_24,c_0_12]) ).

cnf(c_0_29,negated_conjecture,
    in(esk1_0,esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).

cnf(c_0_30,plain,
    ( subset(X1,X2)
    | ~ in(esk5_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_31,plain,
    ( esk5_2(unordered_pair(X1,X1),X2) = X1
    | subset(unordered_pair(X1,X1),X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_27]) ).

cnf(c_0_32,negated_conjecture,
    ~ subset(unordered_pair(esk1_0,esk1_0),esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).

cnf(c_0_33,plain,
    ( subset(unordered_pair(X1,X1),X2)
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU144+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command  : run_ET %s %d
% 0.12/0.33  % Computer : n029.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 17:16:45 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             : 35
% 0.23/1.41  # Proof object clause steps            : 22
% 0.23/1.41  # Proof object formula steps           : 13
% 0.23/1.41  # Proof object conjectures             : 12
% 0.23/1.41  # Proof object clause conjectures      : 9
% 0.23/1.41  # Proof object formula conjectures     : 3
% 0.23/1.41  # Proof object initial clauses used    : 9
% 0.23/1.41  # Proof object initial formulas used   : 6
% 0.23/1.41  # Proof object generating inferences   : 7
% 0.23/1.41  # Proof object simplifying inferences  : 12
% 0.23/1.41  # Training examples: 0 positive, 0 negative
% 0.23/1.41  # Parsed axioms                        : 65
% 0.23/1.41  # Removed by relevancy pruning/SinE    : 24
% 0.23/1.41  # Initial clauses                      : 73
% 0.23/1.41  # Removed in clause preprocessing      : 2
% 0.23/1.41  # Initial clauses in saturation        : 71
% 0.23/1.41  # Processed clauses                    : 1258
% 0.23/1.41  # ...of these trivial                  : 82
% 0.23/1.41  # ...subsumed                          : 830
% 0.23/1.41  # ...remaining for further processing  : 346
% 0.23/1.41  # Other redundant clauses eliminated   : 172
% 0.23/1.41  # Clauses deleted for lack of memory   : 0
% 0.23/1.41  # Backward-subsumed                    : 3
% 0.23/1.41  # Backward-rewritten                   : 19
% 0.23/1.41  # Generated clauses                    : 8725
% 0.23/1.41  # ...of the previous two non-trivial   : 6315
% 0.23/1.41  # Contextual simplify-reflections      : 195
% 0.23/1.41  # Paramodulations                      : 8501
% 0.23/1.41  # Factorizations                       : 28
% 0.23/1.41  # Equation resolutions                 : 196
% 0.23/1.41  # Current number of processed clauses  : 319
% 0.23/1.41  #    Positive orientable unit clauses  : 61
% 0.23/1.41  #    Positive unorientable unit clauses: 3
% 0.23/1.41  #    Negative unit clauses             : 20
% 0.23/1.41  #    Non-unit-clauses                  : 235
% 0.23/1.41  # Current number of unprocessed clauses: 4747
% 0.23/1.41  # ...number of literals in the above   : 13045
% 0.23/1.41  # Current number of archived formulas  : 0
% 0.23/1.41  # Current number of archived clauses   : 24
% 0.23/1.41  # Clause-clause subsumption calls (NU) : 14660
% 0.23/1.41  # Rec. Clause-clause subsumption calls : 12231
% 0.23/1.41  # Non-unit clause-clause subsumptions  : 766
% 0.23/1.41  # Unit Clause-clause subsumption calls : 235
% 0.23/1.41  # Rewrite failures with RHS unbound    : 0
% 0.23/1.41  # BW rewrite match attempts            : 91
% 0.23/1.41  # BW rewrite match successes           : 26
% 0.23/1.41  # Condensation attempts                : 0
% 0.23/1.41  # Condensation successes               : 0
% 0.23/1.41  # Termbank termtop insertions          : 80655
% 0.23/1.41  
% 0.23/1.41  # -------------------------------------------------
% 0.23/1.41  # User time                : 0.156 s
% 0.23/1.41  # System time              : 0.009 s
% 0.23/1.41  # Total time               : 0.165 s
% 0.23/1.41  # Maximum resident set size: 7600 pages
%------------------------------------------------------------------------------