TSTP Solution File: NUM461+2 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUM461+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n005.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 : Mon Jul 18 09:32:40 EDT 2022

% Result   : Theorem 0.21s 1.40s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   37 (   9 unt;   0 def)
%            Number of atoms       :  152 (  74 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  189 (  74   ~;  83   |;  27   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   51 (   0 sgn  22   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__,conjecture,
    ( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)
    & ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(sdtpldt0(xm,xl),X1) = sdtpldt0(xm,xn) )
      | sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )
    & sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
    & ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(sdtpldt0(xl,xm),X1) = sdtpldt0(xn,xm) )
      | sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).

fof(mAddAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mAddAsso) ).

fof(m__873,hypothesis,
    aNaturalNumber0(xm),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__873) ).

fof(m__840,hypothesis,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__840) ).

fof(mAddComm,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mAddComm) ).

fof(mSortsB,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsB) ).

fof(m__840_03,hypothesis,
    ( xl != xn
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xl,X1) = xn )
    & sdtlseqdt0(xl,xn) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__840_03) ).

fof(mAddCanc,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
          | sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
       => X2 = X3 ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mAddCanc) ).

fof(c_0_8,negated_conjecture,
    ~ ( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)
      & ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(sdtpldt0(xm,xl),X1) = sdtpldt0(xm,xn) )
        | sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )
      & sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
      & ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(sdtpldt0(xl,xm),X1) = sdtpldt0(xn,xm) )
        | sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_9,negated_conjecture,
    ! [X2,X3] :
      ( ( ~ aNaturalNumber0(X3)
        | sdtpldt0(sdtpldt0(xl,xm),X3) != sdtpldt0(xn,xm)
        | ~ aNaturalNumber0(X2)
        | sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
        | sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
        | sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
      & ( ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
        | ~ aNaturalNumber0(X2)
        | sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
        | sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
        | sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
      & ( ~ aNaturalNumber0(X3)
        | sdtpldt0(sdtpldt0(xl,xm),X3) != sdtpldt0(xn,xm)
        | ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
        | sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
        | sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
      & ( ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
        | ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
        | sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
        | sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ) ),
    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_8])])])])])]) ).

fof(c_0_10,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).

cnf(c_0_11,negated_conjecture,
    ( sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
    | sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
    | sdtpldt0(sdtpldt0(xm,xl),X1) != sdtpldt0(xm,xn)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(sdtpldt0(xl,xm),X2) != sdtpldt0(xn,xm)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_12,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_13,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__873]) ).

cnf(c_0_14,hypothesis,
    aNaturalNumber0(xl),
    inference(split_conjunct,[status(thm)],[m__840]) ).

fof(c_0_15,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | sdtpldt0(X3,X4) = sdtpldt0(X4,X3) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

fof(c_0_16,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtpldt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).

cnf(c_0_17,negated_conjecture,
    ( sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
    | sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
    | sdtpldt0(xl,sdtpldt0(xm,X1)) != sdtpldt0(xn,xm)
    | sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).

cnf(c_0_18,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    ( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
    | sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
    | sdtpldt0(xl,sdtpldt0(X1,xm)) != sdtpldt0(xn,xm)
    | sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_13])]) ).

cnf(c_0_21,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_12]),c_0_19]) ).

fof(c_0_22,hypothesis,
    ( xl != xn
    & aNaturalNumber0(esk1_0)
    & sdtpldt0(xl,esk1_0) = xn
    & sdtlseqdt0(xl,xn) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[m__840_03])])])]) ).

cnf(c_0_23,negated_conjecture,
    ( sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
    | sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
    | sdtpldt0(xm,sdtpldt0(xl,X1)) != sdtpldt0(xn,xm)
    | sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_13]),c_0_14])]) ).

cnf(c_0_24,hypothesis,
    sdtpldt0(xl,esk1_0) = xn,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_25,hypothesis,
    aNaturalNumber0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_26,hypothesis,
    ( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
    | sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
    | sdtpldt0(sdtpldt0(xm,xl),X1) != sdtpldt0(xm,xn)
    | sdtpldt0(xm,xn) != sdtpldt0(xn,xm)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

cnf(c_0_27,hypothesis,
    ( sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
    | sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
    | sdtpldt0(xm,sdtpldt0(xl,X1)) != sdtpldt0(xm,xn)
    | sdtpldt0(xm,xn) != sdtpldt0(xn,xm)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_12]),c_0_14]),c_0_13])]) ).

cnf(c_0_28,hypothesis,
    ( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
    | sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
    | sdtpldt0(xm,xn) != sdtpldt0(xn,xm) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_25])]) ).

cnf(c_0_29,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__840]) ).

fof(c_0_30,plain,
    ! [X4,X5,X6] :
      ( ( sdtpldt0(X4,X5) != sdtpldt0(X4,X6)
        | X5 = X6
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) )
      & ( sdtpldt0(X5,X4) != sdtpldt0(X6,X4)
        | X5 = X6
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).

cnf(c_0_31,hypothesis,
    ( sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
    | sdtpldt0(xm,xl) = sdtpldt0(xn,xm) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_29]),c_0_13])]) ).

cnf(c_0_32,plain,
    ( X2 = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtpldt0(X2,X3) != sdtpldt0(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_33,hypothesis,
    sdtpldt0(xn,xm) = sdtpldt0(xl,xm),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_31]),c_0_14]),c_0_13])]) ).

cnf(c_0_34,hypothesis,
    ( X1 = xn
    | sdtpldt0(X1,xm) != sdtpldt0(xl,xm)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_13]),c_0_29])]) ).

cnf(c_0_35,hypothesis,
    xl != xn,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_36,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_14])]),c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM461+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : run_ET %s %d
% 0.13/0.32  % Computer : n005.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 600
% 0.13/0.32  % DateTime : Tue Jul  5 18:49:37 EDT 2022
% 0.13/0.32  % CPUTime  : 
% 0.21/1.40  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.40  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.40  # Preprocessing time       : 0.017 s
% 0.21/1.40  
% 0.21/1.40  # Proof found!
% 0.21/1.40  # SZS status Theorem
% 0.21/1.40  # SZS output start CNFRefutation
% See solution above
% 0.21/1.40  # Proof object total steps             : 37
% 0.21/1.40  # Proof object clause steps            : 22
% 0.21/1.40  # Proof object formula steps           : 15
% 0.21/1.40  # Proof object conjectures             : 7
% 0.21/1.40  # Proof object clause conjectures      : 4
% 0.21/1.40  # Proof object formula conjectures     : 3
% 0.21/1.40  # Proof object initial clauses used    : 11
% 0.21/1.40  # Proof object initial formulas used   : 8
% 0.21/1.40  # Proof object generating inferences   : 11
% 0.21/1.40  # Proof object simplifying inferences  : 28
% 0.21/1.40  # Training examples: 0 positive, 0 negative
% 0.21/1.40  # Parsed axioms                        : 27
% 0.21/1.40  # Removed by relevancy pruning/SinE    : 3
% 0.21/1.40  # Initial clauses                      : 40
% 0.21/1.40  # Removed in clause preprocessing      : 1
% 0.21/1.40  # Initial clauses in saturation        : 39
% 0.21/1.40  # Processed clauses                    : 303
% 0.21/1.40  # ...of these trivial                  : 2
% 0.21/1.40  # ...subsumed                          : 140
% 0.21/1.40  # ...remaining for further processing  : 161
% 0.21/1.40  # Other redundant clauses eliminated   : 6
% 0.21/1.40  # Clauses deleted for lack of memory   : 0
% 0.21/1.40  # Backward-subsumed                    : 13
% 0.21/1.40  # Backward-rewritten                   : 20
% 0.21/1.40  # Generated clauses                    : 1798
% 0.21/1.40  # ...of the previous two non-trivial   : 1630
% 0.21/1.40  # Contextual simplify-reflections      : 32
% 0.21/1.40  # Paramodulations                      : 1783
% 0.21/1.40  # Factorizations                       : 0
% 0.21/1.40  # Equation resolutions                 : 15
% 0.21/1.40  # Current number of processed clauses  : 127
% 0.21/1.40  #    Positive orientable unit clauses  : 21
% 0.21/1.40  #    Positive unorientable unit clauses: 0
% 0.21/1.40  #    Negative unit clauses             : 4
% 0.21/1.40  #    Non-unit-clauses                  : 102
% 0.21/1.40  # Current number of unprocessed clauses: 1120
% 0.21/1.40  # ...number of literals in the above   : 5120
% 0.21/1.40  # Current number of archived formulas  : 0
% 0.21/1.40  # Current number of archived clauses   : 33
% 0.21/1.40  # Clause-clause subsumption calls (NU) : 3049
% 0.21/1.40  # Rec. Clause-clause subsumption calls : 822
% 0.21/1.40  # Non-unit clause-clause subsumptions  : 174
% 0.21/1.40  # Unit Clause-clause subsumption calls : 83
% 0.21/1.40  # Rewrite failures with RHS unbound    : 0
% 0.21/1.40  # BW rewrite match attempts            : 7
% 0.21/1.40  # BW rewrite match successes           : 2
% 0.21/1.40  # Condensation attempts                : 0
% 0.21/1.40  # Condensation successes               : 0
% 0.21/1.40  # Termbank termtop insertions          : 33712
% 0.21/1.40  
% 0.21/1.40  # -------------------------------------------------
% 0.21/1.40  # User time                : 0.100 s
% 0.21/1.40  # System time              : 0.001 s
% 0.21/1.40  # Total time               : 0.101 s
% 0.21/1.40  # Maximum resident set size: 4384 pages
%------------------------------------------------------------------------------