TSTP Solution File: SET909+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n023.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 00:55:22 EDT 2022

% Result   : Theorem 0.22s 1.41s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   30 (  13 unt;   0 def)
%            Number of atoms       :   92 (  48 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  104 (  42   ~;  46   |;  11   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :   70 (  20 sgn  39   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t50_zfmisc_1,conjecture,
    ! [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) != empty_set,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t50_zfmisc_1) ).

fof(commutativity_k2_xboole_0,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_xboole_0) ).

fof(d2_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_union2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            | in(X4,X2) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_xboole_0) ).

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(d2_tarski,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_tarski) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) != empty_set,
    inference(assume_negation,[status(cth)],[t50_zfmisc_1]) ).

fof(c_0_6,negated_conjecture,
    set_union2(unordered_pair(esk1_0,esk2_0),esk3_0) = empty_set,
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_7,plain,
    ! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).

fof(c_0_8,plain,
    ! [X5,X6,X7,X8,X8,X5,X6,X7] :
      ( ( ~ in(X8,X7)
        | in(X8,X5)
        | in(X8,X6)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(X8,X5)
        | in(X8,X7)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(X8,X6)
        | in(X8,X7)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(esk6_3(X5,X6,X7),X5)
        | ~ in(esk6_3(X5,X6,X7),X7)
        | X7 = set_union2(X5,X6) )
      & ( ~ in(esk6_3(X5,X6,X7),X6)
        | ~ in(esk6_3(X5,X6,X7),X7)
        | X7 = set_union2(X5,X6) )
      & ( in(esk6_3(X5,X6,X7),X7)
        | in(esk6_3(X5,X6,X7),X5)
        | in(esk6_3(X5,X6,X7),X6)
        | X7 = set_union2(X5,X6) ) ),
    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)],[d2_xboole_0])])])])])])]) ).

cnf(c_0_9,negated_conjecture,
    set_union2(unordered_pair(esk1_0,esk2_0),esk3_0) = empty_set,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X3,X4,X3] :
      ( ( X3 != empty_set
        | ~ in(X4,X3) )
      & ( in(esk4_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_12,plain,
    ( in(X4,X1)
    | X1 != set_union2(X2,X3)
    | ~ in(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    set_union2(esk3_0,unordered_pair(esk1_0,esk2_0)) = empty_set,
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,plain,
    ( ~ in(X1,X2)
    | X2 != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    ( X1 != empty_set
    | ~ in(X2,esk3_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

cnf(c_0_16,plain,
    ( X1 = empty_set
    | in(esk4_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,negated_conjecture,
    ( empty_set = esk3_0
    | X1 != empty_set ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

fof(c_0_18,plain,
    ! [X5,X6,X7,X8,X8,X5,X6,X7] :
      ( ( ~ in(X8,X7)
        | X8 = X5
        | X8 = X6
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X5
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X6
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( esk5_3(X5,X6,X7) != X5
        | ~ in(esk5_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( esk5_3(X5,X6,X7) != X6
        | ~ in(esk5_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( in(esk5_3(X5,X6,X7),X7)
        | esk5_3(X5,X6,X7) = X5
        | esk5_3(X5,X6,X7) = X6
        | X7 = unordered_pair(X5,X6) ) ),
    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)],[d2_tarski])])])])])])]) ).

cnf(c_0_19,plain,
    ( in(X4,X1)
    | X1 != set_union2(X2,X3)
    | ~ in(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,negated_conjecture,
    empty_set = esk3_0,
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_21,plain,
    ( in(X4,X1)
    | X1 != unordered_pair(X2,X3)
    | X4 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_22,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    set_union2(esk3_0,unordered_pair(esk1_0,esk2_0)) = esk3_0,
    inference(rw,[status(thm)],[c_0_13,c_0_20]) ).

cnf(c_0_24,plain,
    ( in(X1,X2)
    | X2 != unordered_pair(X3,X1) ),
    inference(er,[status(thm)],[c_0_21]) ).

cnf(c_0_25,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(X1,unordered_pair(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,plain,
    in(X1,unordered_pair(X2,X1)),
    inference(er,[status(thm)],[c_0_24]) ).

cnf(c_0_27,plain,
    ( X1 != esk3_0
    | ~ in(X2,X1) ),
    inference(rw,[status(thm)],[c_0_14,c_0_20]) ).

cnf(c_0_28,negated_conjecture,
    in(esk2_0,esk3_0),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_27,c_0_28]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n023.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 : Sun Jul 10 16:59:55 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.22/1.41  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41  # Preprocessing time       : 0.015 s
% 0.22/1.41  
% 0.22/1.41  # Proof found!
% 0.22/1.41  # SZS status Theorem
% 0.22/1.41  # SZS output start CNFRefutation
% See solution above
% 0.22/1.41  # Proof object total steps             : 30
% 0.22/1.41  # Proof object clause steps            : 19
% 0.22/1.41  # Proof object formula steps           : 11
% 0.22/1.41  # Proof object conjectures             : 12
% 0.22/1.41  # Proof object clause conjectures      : 9
% 0.22/1.41  # Proof object formula conjectures     : 3
% 0.22/1.41  # Proof object initial clauses used    : 7
% 0.22/1.41  # Proof object initial formulas used   : 5
% 0.22/1.41  # Proof object generating inferences   : 8
% 0.22/1.41  # Proof object simplifying inferences  : 5
% 0.22/1.41  # Training examples: 0 positive, 0 negative
% 0.22/1.41  # Parsed axioms                        : 13
% 0.22/1.41  # Removed by relevancy pruning/SinE    : 0
% 0.22/1.41  # Initial clauses                      : 24
% 0.22/1.41  # Removed in clause preprocessing      : 0
% 0.22/1.41  # Initial clauses in saturation        : 24
% 0.22/1.41  # Processed clauses                    : 58
% 0.22/1.41  # ...of these trivial                  : 2
% 0.22/1.41  # ...subsumed                          : 9
% 0.22/1.41  # ...remaining for further processing  : 47
% 0.22/1.41  # Other redundant clauses eliminated   : 5
% 0.22/1.41  # Clauses deleted for lack of memory   : 0
% 0.22/1.41  # Backward-subsumed                    : 0
% 0.22/1.41  # Backward-rewritten                   : 8
% 0.22/1.41  # Generated clauses                    : 134
% 0.22/1.41  # ...of the previous two non-trivial   : 114
% 0.22/1.41  # Contextual simplify-reflections      : 1
% 0.22/1.41  # Paramodulations                      : 114
% 0.22/1.41  # Factorizations                       : 8
% 0.22/1.41  # Equation resolutions                 : 12
% 0.22/1.41  # Current number of processed clauses  : 37
% 0.22/1.41  #    Positive orientable unit clauses  : 9
% 0.22/1.41  #    Positive unorientable unit clauses: 2
% 0.22/1.41  #    Negative unit clauses             : 4
% 0.22/1.41  #    Non-unit-clauses                  : 22
% 0.22/1.41  # Current number of unprocessed clauses: 69
% 0.22/1.41  # ...number of literals in the above   : 204
% 0.22/1.41  # Current number of archived formulas  : 0
% 0.22/1.41  # Current number of archived clauses   : 8
% 0.22/1.41  # Clause-clause subsumption calls (NU) : 160
% 0.22/1.41  # Rec. Clause-clause subsumption calls : 139
% 0.22/1.41  # Non-unit clause-clause subsumptions  : 10
% 0.22/1.41  # Unit Clause-clause subsumption calls : 37
% 0.22/1.41  # Rewrite failures with RHS unbound    : 0
% 0.22/1.41  # BW rewrite match attempts            : 10
% 0.22/1.41  # BW rewrite match successes           : 7
% 0.22/1.41  # Condensation attempts                : 0
% 0.22/1.41  # Condensation successes               : 0
% 0.22/1.41  # Termbank termtop insertions          : 2239
% 0.22/1.41  
% 0.22/1.41  # -------------------------------------------------
% 0.22/1.41  # User time                : 0.017 s
% 0.22/1.41  # System time              : 0.002 s
% 0.22/1.41  # Total time               : 0.019 s
% 0.22/1.41  # Maximum resident set size: 2776 pages
%------------------------------------------------------------------------------