TSTP Solution File: SWV488+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SWV488+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n022.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 : Wed Jul 20 18:17:00 EDT 2022

% Result   : Theorem 0.26s 1.45s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   27 (  10 unt;   0 def)
%            Number of atoms       :  132 (  39 equ)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives :  150 (  45   ~;  42   |;  39   &)
%                                         (   2 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   56 (   3 sgn  42   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(qii,hypothesis,
    ! [X1,X2] :
      ( ( int_leq(int_one,X1)
        & int_leq(X1,n)
        & int_leq(int_one,X2)
        & int_leq(X2,n) )
     => ( ! [X8] :
            ( ( int_less(int_zero,X8)
              & X1 = plus(X2,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X2) )
               => a(plus(X3,X8),X3) = real_zero ) )
        & ! [X3] :
            ( ( int_leq(int_one,X3)
              & int_leq(X3,X2) )
           => a(X3,X3) = real_one )
        & ! [X8] :
            ( ( int_less(int_zero,X8)
              & X2 = plus(X1,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X1) )
               => a(X3,plus(X3,X8)) = real_zero ) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',qii) ).

fof(uti,conjecture,
    ! [X1,X2] :
      ( ( int_leq(int_one,X2)
        & int_leq(X2,X1)
        & int_leq(X1,n) )
     => ( X1 = X2
       => a(X1,X2) != real_zero ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',uti) ).

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

fof(real_constants,axiom,
    real_zero != real_one,
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',real_constants) ).

fof(c_0_4,plain,
    ! [X2,X1] :
      ( epred1_2(X1,X2)
    <=> ( ! [X8] :
            ( ( int_less(int_zero,X8)
              & X1 = plus(X2,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X2) )
               => a(plus(X3,X8),X3) = real_zero ) )
        & ! [X3] :
            ( ( int_leq(int_one,X3)
              & int_leq(X3,X2) )
           => a(X3,X3) = real_one )
        & ! [X8] :
            ( ( int_less(int_zero,X8)
              & X2 = plus(X1,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X1) )
               => a(X3,plus(X3,X8)) = real_zero ) ) ) ),
    introduced(definition) ).

fof(c_0_5,plain,
    ! [X2,X1] :
      ( epred1_2(X1,X2)
     => ( ! [X8] :
            ( ( int_less(int_zero,X8)
              & X1 = plus(X2,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X2) )
               => a(plus(X3,X8),X3) = real_zero ) )
        & ! [X3] :
            ( ( int_leq(int_one,X3)
              & int_leq(X3,X2) )
           => a(X3,X3) = real_one )
        & ! [X8] :
            ( ( int_less(int_zero,X8)
              & X2 = plus(X1,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X1) )
               => a(X3,plus(X3,X8)) = real_zero ) ) ) ),
    inference(split_equiv,[status(thm)],[c_0_4]) ).

fof(c_0_6,hypothesis,
    ! [X1,X2] :
      ( ( int_leq(int_one,X1)
        & int_leq(X1,n)
        & int_leq(int_one,X2)
        & int_leq(X2,n) )
     => epred1_2(X1,X2) ),
    inference(apply_def,[status(thm)],[qii,c_0_4]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( int_leq(int_one,X2)
          & int_leq(X2,X1)
          & int_leq(X1,n) )
       => ( X1 = X2
         => a(X1,X2) != real_zero ) ),
    inference(assume_negation,[status(cth)],[uti]) ).

fof(c_0_8,plain,
    ! [X9,X10,X11,X12,X13,X14,X15] :
      ( ( ~ int_less(int_zero,X11)
        | X10 != plus(X9,X11)
        | ~ int_leq(int_one,X12)
        | ~ int_leq(X12,X9)
        | a(plus(X12,X11),X12) = real_zero
        | ~ epred1_2(X10,X9) )
      & ( ~ int_leq(int_one,X13)
        | ~ int_leq(X13,X9)
        | a(X13,X13) = real_one
        | ~ epred1_2(X10,X9) )
      & ( ~ int_less(int_zero,X14)
        | X9 != plus(X10,X14)
        | ~ int_leq(int_one,X15)
        | ~ int_leq(X15,X10)
        | a(X15,plus(X15,X14)) = real_zero
        | ~ epred1_2(X10,X9) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).

fof(c_0_9,hypothesis,
    ! [X3,X4] :
      ( ~ int_leq(int_one,X3)
      | ~ int_leq(X3,n)
      | ~ int_leq(int_one,X4)
      | ~ int_leq(X4,n)
      | epred1_2(X3,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).

fof(c_0_10,negated_conjecture,
    ( int_leq(int_one,esk2_0)
    & int_leq(esk2_0,esk1_0)
    & int_leq(esk1_0,n)
    & esk1_0 = esk2_0
    & a(esk1_0,esk2_0) = real_zero ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_11,plain,
    ( a(X3,X3) = real_one
    | ~ epred1_2(X1,X2)
    | ~ int_leq(X3,X2)
    | ~ int_leq(int_one,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,hypothesis,
    ( epred1_2(X1,X2)
    | ~ int_leq(X2,n)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(X1,n)
    | ~ int_leq(int_one,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    int_leq(int_one,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    esk1_0 = esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,hypothesis,
    ( a(X1,X1) = real_one
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X2,n)
    | ~ int_leq(X3,n)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(int_one,X3)
    | ~ int_leq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,negated_conjecture,
    int_leq(esk1_0,n),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,negated_conjecture,
    int_leq(int_one,esk1_0),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

fof(c_0_18,plain,
    ! [X3,X4,X3,X4] :
      ( ( ~ int_leq(X3,X4)
        | int_less(X3,X4)
        | X3 = X4 )
      & ( ~ int_less(X3,X4)
        | int_leq(X3,X4) )
      & ( X3 != X4
        | int_leq(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)],[int_leq])])])])]) ).

cnf(c_0_19,negated_conjecture,
    a(esk1_0,esk2_0) = real_zero,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_20,negated_conjecture,
    ( a(X1,X1) = real_one
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X2,n)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(X1,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).

cnf(c_0_21,plain,
    ( int_leq(X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    a(esk1_0,esk1_0) = real_zero,
    inference(rw,[status(thm)],[c_0_19,c_0_14]) ).

cnf(c_0_23,negated_conjecture,
    ( a(X1,X1) = real_one
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X1,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_17])]) ).

cnf(c_0_24,plain,
    int_leq(X1,X1),
    inference(er,[status(thm)],[c_0_21]) ).

cnf(c_0_25,plain,
    real_zero != real_one,
    inference(split_conjunct,[status(thm)],[real_constants]) ).

cnf(c_0_26,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_17]),c_0_24])]),c_0_25]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SWV488+3 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.15  % Command  : run_ET %s %d
% 0.14/0.36  % Computer : n022.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Thu Jun 16 00:37:02 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.26/1.45  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.26/1.45  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.26/1.45  # Preprocessing time       : 0.015 s
% 0.26/1.45  
% 0.26/1.45  # Proof found!
% 0.26/1.45  # SZS status Theorem
% 0.26/1.45  # SZS output start CNFRefutation
% See solution above
% 0.26/1.45  # Proof object total steps             : 27
% 0.26/1.45  # Proof object clause steps            : 15
% 0.26/1.45  # Proof object formula steps           : 12
% 0.26/1.45  # Proof object conjectures             : 12
% 0.26/1.45  # Proof object clause conjectures      : 9
% 0.26/1.45  # Proof object formula conjectures     : 3
% 0.26/1.45  # Proof object initial clauses used    : 8
% 0.26/1.45  # Proof object initial formulas used   : 4
% 0.26/1.45  # Proof object generating inferences   : 4
% 0.26/1.45  # Proof object simplifying inferences  : 11
% 0.26/1.45  # Training examples: 0 positive, 0 negative
% 0.26/1.45  # Parsed axioms                        : 13
% 0.26/1.45  # Removed by relevancy pruning/SinE    : 0
% 0.26/1.45  # Initial clauses                      : 25
% 0.26/1.45  # Removed in clause preprocessing      : 0
% 0.26/1.45  # Initial clauses in saturation        : 25
% 0.26/1.45  # Processed clauses                    : 415
% 0.26/1.45  # ...of these trivial                  : 1
% 0.26/1.45  # ...subsumed                          : 234
% 0.26/1.45  # ...remaining for further processing  : 180
% 0.26/1.45  # Other redundant clauses eliminated   : 20
% 0.26/1.45  # Clauses deleted for lack of memory   : 0
% 0.26/1.45  # Backward-subsumed                    : 6
% 0.26/1.45  # Backward-rewritten                   : 2
% 0.26/1.45  # Generated clauses                    : 2117
% 0.26/1.45  # ...of the previous two non-trivial   : 1801
% 0.26/1.45  # Contextual simplify-reflections      : 116
% 0.26/1.45  # Paramodulations                      : 2065
% 0.26/1.45  # Factorizations                       : 26
% 0.26/1.45  # Equation resolutions                 : 26
% 0.26/1.45  # Current number of processed clauses  : 170
% 0.26/1.45  #    Positive orientable unit clauses  : 10
% 0.26/1.45  #    Positive unorientable unit clauses: 1
% 0.26/1.45  #    Negative unit clauses             : 4
% 0.26/1.45  #    Non-unit-clauses                  : 155
% 0.26/1.45  # Current number of unprocessed clauses: 1367
% 0.26/1.45  # ...number of literals in the above   : 5962
% 0.26/1.45  # Current number of archived formulas  : 0
% 0.26/1.45  # Current number of archived clauses   : 8
% 0.26/1.45  # Clause-clause subsumption calls (NU) : 3694
% 0.26/1.45  # Rec. Clause-clause subsumption calls : 2327
% 0.26/1.45  # Non-unit clause-clause subsumptions  : 334
% 0.26/1.45  # Unit Clause-clause subsumption calls : 20
% 0.26/1.45  # Rewrite failures with RHS unbound    : 0
% 0.26/1.45  # BW rewrite match attempts            : 19
% 0.26/1.45  # BW rewrite match successes           : 4
% 0.26/1.45  # Condensation attempts                : 0
% 0.26/1.45  # Condensation successes               : 0
% 0.26/1.45  # Termbank termtop insertions          : 24769
% 0.26/1.45  
% 0.26/1.45  # -------------------------------------------------
% 0.26/1.45  # User time                : 0.065 s
% 0.26/1.45  # System time              : 0.003 s
% 0.26/1.45  # Total time               : 0.068 s
% 0.26/1.45  # Maximum resident set size: 4104 pages
%------------------------------------------------------------------------------