TSTP Solution File: SET927+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n019.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 00:55:32 EDT 2022

% Result   : Theorem 0.24s 1.41s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   30 (   8 unt;   0 def)
%            Number of atoms       :   87 (  47 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :   92 (  35   ~;  45   |;   9   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   44 (   5 sgn  19   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t70_zfmisc_1,conjecture,
    ! [X1,X2,X3] :
      ( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
    <=> ( ~ in(X1,X3)
        & ( in(X2,X3)
          | X1 = X2 ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t70_zfmisc_1) ).

fof(l39_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
    <=> ( ~ in(X1,X3)
        & ( in(X2,X3)
          | X1 = X2 ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l39_zfmisc_1) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_tarski) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
      <=> ( ~ in(X1,X3)
          & ( in(X2,X3)
            | X1 = X2 ) ) ),
    inference(assume_negation,[status(cth)],[t70_zfmisc_1]) ).

fof(c_0_4,plain,
    ! [X4,X5,X6,X4,X5,X6] :
      ( ( ~ in(X4,X6)
        | set_difference(unordered_pair(X4,X5),X6) != singleton(X4) )
      & ( in(X5,X6)
        | X4 = X5
        | set_difference(unordered_pair(X4,X5),X6) != singleton(X4) )
      & ( ~ in(X5,X6)
        | in(X4,X6)
        | set_difference(unordered_pair(X4,X5),X6) = singleton(X4) )
      & ( X4 != X5
        | in(X4,X6)
        | set_difference(unordered_pair(X4,X5),X6) = singleton(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)],[inference(fof_simplification,[status(thm)],[l39_zfmisc_1])])])])])]) ).

fof(c_0_5,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

fof(c_0_6,negated_conjecture,
    ( ( ~ in(esk2_0,esk3_0)
      | in(esk1_0,esk3_0)
      | set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk1_0) )
    & ( esk1_0 != esk2_0
      | in(esk1_0,esk3_0)
      | set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk1_0) )
    & ( ~ in(esk1_0,esk3_0)
      | set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) = singleton(esk1_0) )
    & ( in(esk2_0,esk3_0)
      | esk1_0 = esk2_0
      | set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) = singleton(esk1_0) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3])])])])]) ).

cnf(c_0_7,plain,
    ( set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
    | ~ in(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    ( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) = singleton(esk1_0)
    | ~ in(esk1_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( X1 = X2
    | in(X2,X3)
    | set_difference(unordered_pair(X1,X2),X3) != singleton(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_11,negated_conjecture,
    ( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) = singleton(esk1_0)
    | esk1_0 = esk2_0
    | in(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,negated_conjecture,
    ( in(esk1_0,esk3_0)
    | set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk1_0)
    | ~ in(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_13,plain,
    ( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
    | in(X1,X3)
    | ~ in(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_14,plain,
    ( set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
    | ~ in(X2,X3) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    ( set_difference(unordered_pair(esk2_0,esk1_0),esk3_0) = singleton(esk1_0)
    | ~ in(esk1_0,esk3_0) ),
    inference(rw,[status(thm)],[c_0_9,c_0_8]) ).

cnf(c_0_16,plain,
    ( X1 = X2
    | in(X2,X3)
    | set_difference(unordered_pair(X2,X1),X3) != singleton(X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_8]) ).

cnf(c_0_17,negated_conjecture,
    ( set_difference(unordered_pair(esk2_0,esk1_0),esk3_0) = singleton(esk1_0)
    | esk1_0 = esk2_0
    | in(esk2_0,esk3_0) ),
    inference(rw,[status(thm)],[c_0_11,c_0_8]) ).

cnf(c_0_18,negated_conjecture,
    ( in(esk1_0,esk3_0)
    | set_difference(unordered_pair(esk2_0,esk1_0),esk3_0) != singleton(esk1_0)
    | ~ in(esk2_0,esk3_0) ),
    inference(rw,[status(thm)],[c_0_12,c_0_8]) ).

cnf(c_0_19,plain,
    ( set_difference(unordered_pair(X1,X2),X3) = singleton(X2)
    | in(X2,X3)
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[c_0_13,c_0_8]) ).

cnf(c_0_20,negated_conjecture,
    ~ in(esk1_0,esk3_0),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    ( esk1_0 = esk2_0
    | in(esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    ~ in(esk2_0,esk3_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

cnf(c_0_23,plain,
    ( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
    | in(X1,X3)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_24,negated_conjecture,
    ( in(esk1_0,esk3_0)
    | set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk1_0)
    | esk1_0 != esk2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_25,negated_conjecture,
    esk1_0 = esk2_0,
    inference(sr,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,plain,
    ( set_difference(unordered_pair(X1,X1),X2) = singleton(X1)
    | in(X1,X2) ),
    inference(er,[status(thm)],[c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    ( in(esk1_0,esk3_0)
    | set_difference(unordered_pair(esk2_0,esk1_0),esk3_0) != singleton(esk1_0)
    | esk1_0 != esk2_0 ),
    inference(rw,[status(thm)],[c_0_24,c_0_8]) ).

cnf(c_0_28,negated_conjecture,
    set_difference(unordered_pair(esk2_0,esk2_0),esk3_0) = singleton(esk2_0),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_25]),c_0_25]),c_0_25]),c_0_26]) ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_25]),c_0_25]),c_0_25]),c_0_25])]),c_0_22]),c_0_28])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % Command  : run_ET %s %d
% 0.14/0.34  % Computer : n019.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 04:59:53 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.24/1.41  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.41  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.41  # Preprocessing time       : 0.014 s
% 0.24/1.41  
% 0.24/1.41  # Proof found!
% 0.24/1.41  # SZS status Theorem
% 0.24/1.41  # SZS output start CNFRefutation
% See solution above
% 0.24/1.41  # Proof object total steps             : 30
% 0.24/1.41  # Proof object clause steps            : 23
% 0.24/1.41  # Proof object formula steps           : 7
% 0.24/1.41  # Proof object conjectures             : 17
% 0.24/1.41  # Proof object clause conjectures      : 14
% 0.24/1.41  # Proof object formula conjectures     : 3
% 0.24/1.41  # Proof object initial clauses used    : 9
% 0.24/1.41  # Proof object initial formulas used   : 3
% 0.24/1.41  # Proof object generating inferences   : 6
% 0.24/1.41  # Proof object simplifying inferences  : 19
% 0.24/1.41  # Training examples: 0 positive, 0 negative
% 0.24/1.41  # Parsed axioms                        : 6
% 0.24/1.41  # Removed by relevancy pruning/SinE    : 2
% 0.24/1.41  # Initial clauses                      : 10
% 0.24/1.41  # Removed in clause preprocessing      : 0
% 0.24/1.41  # Initial clauses in saturation        : 10
% 0.24/1.41  # Processed clauses                    : 35
% 0.24/1.41  # ...of these trivial                  : 0
% 0.24/1.41  # ...subsumed                          : 9
% 0.24/1.41  # ...remaining for further processing  : 25
% 0.24/1.41  # Other redundant clauses eliminated   : 1
% 0.24/1.41  # Clauses deleted for lack of memory   : 0
% 0.24/1.41  # Backward-subsumed                    : 2
% 0.24/1.41  # Backward-rewritten                   : 8
% 0.24/1.41  # Generated clauses                    : 50
% 0.24/1.41  # ...of the previous two non-trivial   : 37
% 0.24/1.41  # Contextual simplify-reflections      : 2
% 0.24/1.41  # Paramodulations                      : 48
% 0.24/1.41  # Factorizations                       : 0
% 0.24/1.41  # Equation resolutions                 : 1
% 0.24/1.41  # Current number of processed clauses  : 13
% 0.24/1.41  #    Positive orientable unit clauses  : 2
% 0.24/1.41  #    Positive unorientable unit clauses: 1
% 0.24/1.41  #    Negative unit clauses             : 1
% 0.24/1.41  #    Non-unit-clauses                  : 9
% 0.24/1.41  # Current number of unprocessed clauses: 10
% 0.24/1.41  # ...number of literals in the above   : 28
% 0.24/1.41  # Current number of archived formulas  : 0
% 0.24/1.41  # Current number of archived clauses   : 11
% 0.24/1.41  # Clause-clause subsumption calls (NU) : 47
% 0.24/1.41  # Rec. Clause-clause subsumption calls : 40
% 0.24/1.41  # Non-unit clause-clause subsumptions  : 10
% 0.24/1.41  # Unit Clause-clause subsumption calls : 7
% 0.24/1.41  # Rewrite failures with RHS unbound    : 0
% 0.24/1.41  # BW rewrite match attempts            : 3
% 0.24/1.41  # BW rewrite match successes           : 3
% 0.24/1.41  # Condensation attempts                : 0
% 0.24/1.41  # Condensation successes               : 0
% 0.24/1.41  # Termbank termtop insertions          : 1223
% 0.24/1.41  
% 0.24/1.41  # -------------------------------------------------
% 0.24/1.41  # User time                : 0.013 s
% 0.24/1.41  # System time              : 0.003 s
% 0.24/1.41  # Total time               : 0.017 s
% 0.24/1.41  # Maximum resident set size: 2768 pages
%------------------------------------------------------------------------------