TSTP Solution File: SET764+4 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET764+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n009.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 00:53:49 EDT 2022

% Result   : Theorem 0.26s 1.42s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   21 (   9 unt;   0 def)
%            Number of atoms       :   52 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   53 (  22   ~;  16   |;   9   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   46 (  13 sgn  32   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(thIIa14,conjecture,
    ! [X6,X1,X2] :
      ( maps(X6,X1,X2)
     => equal_set(inverse_image2(X6,empty_set),empty_set) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thIIa14) ).

fof(empty_set,axiom,
    ! [X3] : ~ member(X3,empty_set),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).

fof(subset,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).

fof(inverse_image2,axiom,
    ! [X6,X2,X3] :
      ( member(X3,inverse_image2(X6,X2))
    <=> ? [X5] :
          ( member(X5,X2)
          & apply(X6,X3,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_image2) ).

fof(equal_set,axiom,
    ! [X1,X2] :
      ( equal_set(X1,X2)
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X6,X1,X2] :
        ( maps(X6,X1,X2)
       => equal_set(inverse_image2(X6,empty_set),empty_set) ),
    inference(assume_negation,[status(cth)],[thIIa14]) ).

fof(c_0_6,plain,
    ! [X4] : ~ member(X4,empty_set),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[empty_set])]) ).

fof(c_0_7,plain,
    ! [X4,X5,X6,X4,X5] :
      ( ( ~ subset(X4,X5)
        | ~ member(X6,X4)
        | member(X6,X5) )
      & ( member(esk10_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk10_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)],[subset])])])])])])]) ).

fof(c_0_8,plain,
    ! [X7,X8,X9,X7,X8,X9,X11] :
      ( ( member(esk4_3(X7,X8,X9),X8)
        | ~ member(X9,inverse_image2(X7,X8)) )
      & ( apply(X7,X9,esk4_3(X7,X8,X9))
        | ~ member(X9,inverse_image2(X7,X8)) )
      & ( ~ member(X11,X8)
        | ~ apply(X7,X9,X11)
        | member(X9,inverse_image2(X7,X8)) ) ),
    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)],[inverse_image2])])])])])])]) ).

fof(c_0_9,negated_conjecture,
    ( maps(esk1_0,esk2_0,esk3_0)
    & ~ equal_set(inverse_image2(esk1_0,empty_set),empty_set) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).

fof(c_0_10,plain,
    ! [X3,X4,X3,X4] :
      ( ( subset(X3,X4)
        | ~ equal_set(X3,X4) )
      & ( subset(X4,X3)
        | ~ equal_set(X3,X4) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | equal_set(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)],[equal_set])])])])]) ).

cnf(c_0_11,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,plain,
    ( subset(X1,X2)
    | member(esk10_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( member(esk4_3(X2,X3,X1),X3)
    | ~ member(X1,inverse_image2(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    ~ equal_set(inverse_image2(esk1_0,empty_set),empty_set),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

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

cnf(c_0_16,plain,
    subset(empty_set,X1),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,plain,
    ~ member(X1,inverse_image2(X2,empty_set)),
    inference(spm,[status(thm)],[c_0_11,c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    ~ subset(inverse_image2(esk1_0,empty_set),empty_set),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).

cnf(c_0_19,plain,
    subset(inverse_image2(X1,empty_set),X2),
    inference(spm,[status(thm)],[c_0_17,c_0_12]) ).

cnf(c_0_20,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET764+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jul 11 02:48:07 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.26/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.26/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.26/1.42  # Preprocessing time       : 0.017 s
% 0.26/1.42  
% 0.26/1.42  # Proof found!
% 0.26/1.42  # SZS status Theorem
% 0.26/1.42  # SZS output start CNFRefutation
% See solution above
% 0.26/1.42  # Proof object total steps             : 21
% 0.26/1.42  # Proof object clause steps            : 10
% 0.26/1.42  # Proof object formula steps           : 11
% 0.26/1.42  # Proof object conjectures             : 6
% 0.26/1.42  # Proof object clause conjectures      : 3
% 0.26/1.42  # Proof object formula conjectures     : 3
% 0.26/1.42  # Proof object initial clauses used    : 5
% 0.26/1.42  # Proof object initial formulas used   : 5
% 0.26/1.42  # Proof object generating inferences   : 4
% 0.26/1.42  # Proof object simplifying inferences  : 4
% 0.26/1.42  # Training examples: 0 positive, 0 negative
% 0.26/1.42  # Parsed axioms                        : 29
% 0.26/1.42  # Removed by relevancy pruning/SinE    : 23
% 0.26/1.42  # Initial clauses                      : 27
% 0.26/1.42  # Removed in clause preprocessing      : 0
% 0.26/1.42  # Initial clauses in saturation        : 27
% 0.26/1.42  # Processed clauses                    : 34
% 0.26/1.42  # ...of these trivial                  : 0
% 0.26/1.42  # ...subsumed                          : 1
% 0.26/1.42  # ...remaining for further processing  : 33
% 0.26/1.42  # Other redundant clauses eliminated   : 0
% 0.26/1.42  # Clauses deleted for lack of memory   : 0
% 0.26/1.42  # Backward-subsumed                    : 0
% 0.26/1.42  # Backward-rewritten                   : 1
% 0.26/1.42  # Generated clauses                    : 39
% 0.26/1.42  # ...of the previous two non-trivial   : 35
% 0.26/1.42  # Contextual simplify-reflections      : 0
% 0.26/1.42  # Paramodulations                      : 39
% 0.26/1.42  # Factorizations                       : 0
% 0.26/1.42  # Equation resolutions                 : 0
% 0.26/1.42  # Current number of processed clauses  : 32
% 0.26/1.42  #    Positive orientable unit clauses  : 5
% 0.26/1.42  #    Positive unorientable unit clauses: 0
% 0.26/1.42  #    Negative unit clauses             : 3
% 0.26/1.42  #    Non-unit-clauses                  : 24
% 0.26/1.42  # Current number of unprocessed clauses: 28
% 0.26/1.42  # ...number of literals in the above   : 114
% 0.26/1.42  # Current number of archived formulas  : 0
% 0.26/1.42  # Current number of archived clauses   : 1
% 0.26/1.42  # Clause-clause subsumption calls (NU) : 41
% 0.26/1.42  # Rec. Clause-clause subsumption calls : 20
% 0.26/1.42  # Non-unit clause-clause subsumptions  : 0
% 0.26/1.42  # Unit Clause-clause subsumption calls : 30
% 0.26/1.42  # Rewrite failures with RHS unbound    : 0
% 0.26/1.42  # BW rewrite match attempts            : 5
% 0.26/1.42  # BW rewrite match successes           : 1
% 0.26/1.42  # Condensation attempts                : 0
% 0.26/1.42  # Condensation successes               : 0
% 0.26/1.42  # Termbank termtop insertions          : 2586
% 0.26/1.42  
% 0.26/1.42  # -------------------------------------------------
% 0.26/1.42  # User time                : 0.015 s
% 0.26/1.42  # System time              : 0.004 s
% 0.26/1.42  # Total time               : 0.019 s
% 0.26/1.42  # Maximum resident set size: 3048 pages
%------------------------------------------------------------------------------