TSTP Solution File: NUM478+2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM478+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n015.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  : 300s
% DateTime : Sat May  4 08:54:50 EDT 2024

% Result   : Theorem 0.21s 0.55s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   34 (  14 unt;   0 def)
%            Number of atoms       :  100 (  49 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  104 (  38   ~;  33   |;  21   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   32 (   0 sgn  19   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mMulCanc,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( X1 != sz00
       => ! [X2,X3] :
            ( ( aNaturalNumber0(X2)
              & aNaturalNumber0(X3) )
           => ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
                | sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
             => X2 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.FJYUYnnu3D/E---3.1_22763.p',mMulCanc) ).

fof(m__1524_04,hypothesis,
    ( xl != sz00
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & xm = sdtasdt0(xl,X1) )
    & doDivides0(xl,xm) ),
    file('/export/starexec/sandbox2/tmp/tmp.FJYUYnnu3D/E---3.1_22763.p',m__1524_04) ).

fof(m__,conjecture,
    ( ( aNaturalNumber0(sdtsldt0(xm,xl))
      & xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
   => ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
      | sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.FJYUYnnu3D/E---3.1_22763.p',m__) ).

fof(m__1524,hypothesis,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm) ),
    file('/export/starexec/sandbox2/tmp/tmp.FJYUYnnu3D/E---3.1_22763.p',m__1524) ).

fof(mMulAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
    file('/export/starexec/sandbox2/tmp/tmp.FJYUYnnu3D/E---3.1_22763.p',mMulAsso) ).

fof(mMulComm,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.FJYUYnnu3D/E---3.1_22763.p',mMulComm) ).

fof(m__1553,hypothesis,
    aNaturalNumber0(xn),
    file('/export/starexec/sandbox2/tmp/tmp.FJYUYnnu3D/E---3.1_22763.p',m__1553) ).

fof(c_0_7,plain,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( X1 != sz00
       => ! [X2,X3] :
            ( ( aNaturalNumber0(X2)
              & aNaturalNumber0(X3) )
           => ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
                | sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
             => X2 = X3 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mMulCanc]) ).

fof(c_0_8,hypothesis,
    ( xl != sz00
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & xm = sdtasdt0(xl,X1) )
    & doDivides0(xl,xm) ),
    inference(fof_simplification,[status(thm)],[m__1524_04]) ).

fof(c_0_9,plain,
    ! [X32,X33,X34] :
      ( ( sdtasdt0(X32,X33) != sdtasdt0(X32,X34)
        | X33 = X34
        | ~ aNaturalNumber0(X33)
        | ~ aNaturalNumber0(X34)
        | X32 = sz00
        | ~ aNaturalNumber0(X32) )
      & ( sdtasdt0(X33,X32) != sdtasdt0(X34,X32)
        | X33 = X34
        | ~ aNaturalNumber0(X33)
        | ~ aNaturalNumber0(X34)
        | X32 = sz00
        | ~ aNaturalNumber0(X32) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).

fof(c_0_10,hypothesis,
    ( xl != sz00
    & aNaturalNumber0(esk1_0)
    & xm = sdtasdt0(xl,esk1_0)
    & doDivides0(xl,xm) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_8])])]) ).

fof(c_0_11,negated_conjecture,
    ~ ( ( aNaturalNumber0(sdtsldt0(xm,xl))
        & xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
     => ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
        | sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_12,plain,
    ( X2 = X3
    | X1 = sz00
    | sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,hypothesis,
    xm = sdtasdt0(xl,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,hypothesis,
    aNaturalNumber0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,hypothesis,
    aNaturalNumber0(xl),
    inference(split_conjunct,[status(thm)],[m__1524]) ).

cnf(c_0_16,hypothesis,
    xl != sz00,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_17,negated_conjecture,
    ( aNaturalNumber0(sdtsldt0(xm,xl))
    & xm = sdtasdt0(xl,sdtsldt0(xm,xl))
    & sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
    & sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).

fof(c_0_18,plain,
    ! [X25,X26,X27] :
      ( ~ aNaturalNumber0(X25)
      | ~ aNaturalNumber0(X26)
      | ~ aNaturalNumber0(X27)
      | sdtasdt0(sdtasdt0(X25,X26),X27) = sdtasdt0(X25,sdtasdt0(X26,X27)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).

cnf(c_0_19,hypothesis,
    ( X1 = esk1_0
    | sdtasdt0(xl,X1) != xm
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    aNaturalNumber0(sdtsldt0(xm,xl)),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_23,plain,
    ! [X23,X24] :
      ( ~ aNaturalNumber0(X23)
      | ~ aNaturalNumber0(X24)
      | sdtasdt0(X23,X24) = sdtasdt0(X24,X23) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).

cnf(c_0_24,negated_conjecture,
    sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,negated_conjecture,
    sdtsldt0(xm,xl) = esk1_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_26,negated_conjecture,
    ( sdtasdt0(xl,sdtasdt0(sdtsldt0(xm,xl),X1)) = sdtasdt0(xm,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_21]),c_0_15])]) ).

cnf(c_0_27,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_28,negated_conjecture,
    sdtasdt0(xl,sdtasdt0(xn,esk1_0)) != sdtasdt0(xn,xm),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    ( sdtasdt0(xl,sdtasdt0(X1,esk1_0)) = sdtasdt0(xm,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_21])]),c_0_25]) ).

cnf(c_0_30,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1553]) ).

cnf(c_0_31,negated_conjecture,
    sdtasdt0(xn,xm) != sdtasdt0(xm,xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).

cnf(c_0_32,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1524]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_32]),c_0_30])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : NUM478+2 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14  % Command    : run_E %s %d THM
% 0.15/0.35  % Computer : n015.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 09:36:06 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.FJYUYnnu3D/E---3.1_22763.p
% 0.21/0.55  # Version: 3.1.0
% 0.21/0.55  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.55  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.55  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.55  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.55  # Starting sh5l with 300s (1) cores
% 0.21/0.55  # new_bool_1 with pid 22920 completed with status 0
% 0.21/0.55  # Result found by new_bool_1
% 0.21/0.55  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.55  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.55  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.55  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.55  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.55  # Search class: FGUSF-FFMM22-MFFFFFNN
% 0.21/0.55  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.55  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.21/0.55  # SAT001_MinMin_p005000_rr_RG with pid 22923 completed with status 0
% 0.21/0.55  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.21/0.55  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.55  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.55  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.55  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.55  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.55  # Search class: FGUSF-FFMM22-MFFFFFNN
% 0.21/0.55  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.55  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.21/0.55  # Preprocessing time       : 0.002 s
% 0.21/0.55  # Presaturation interreduction done
% 0.21/0.55  
% 0.21/0.55  # Proof found!
% 0.21/0.55  # SZS status Theorem
% 0.21/0.55  # SZS output start CNFRefutation
% See solution above
% 0.21/0.55  # Parsed axioms                        : 39
% 0.21/0.55  # Removed by relevancy pruning/SinE    : 6
% 0.21/0.55  # Initial clauses                      : 59
% 0.21/0.55  # Removed in clause preprocessing      : 1
% 0.21/0.55  # Initial clauses in saturation        : 58
% 0.21/0.55  # Processed clauses                    : 242
% 0.21/0.55  # ...of these trivial                  : 6
% 0.21/0.55  # ...subsumed                          : 49
% 0.21/0.55  # ...remaining for further processing  : 187
% 0.21/0.55  # Other redundant clauses eliminated   : 26
% 0.21/0.55  # Clauses deleted for lack of memory   : 0
% 0.21/0.55  # Backward-subsumed                    : 24
% 0.21/0.55  # Backward-rewritten                   : 14
% 0.21/0.55  # Generated clauses                    : 533
% 0.21/0.55  # ...of the previous two non-redundant : 449
% 0.21/0.55  # ...aggressively subsumed             : 0
% 0.21/0.55  # Contextual simplify-reflections      : 4
% 0.21/0.55  # Paramodulations                      : 502
% 0.21/0.55  # Factorizations                       : 0
% 0.21/0.55  # NegExts                              : 0
% 0.21/0.55  # Equation resolutions                 : 30
% 0.21/0.55  # Disequality decompositions           : 0
% 0.21/0.55  # Total rewrite steps                  : 556
% 0.21/0.55  # ...of those cached                   : 538
% 0.21/0.55  # Propositional unsat checks           : 0
% 0.21/0.55  #    Propositional check models        : 0
% 0.21/0.55  #    Propositional check unsatisfiable : 0
% 0.21/0.55  #    Propositional clauses             : 0
% 0.21/0.55  #    Propositional clauses after purity: 0
% 0.21/0.55  #    Propositional unsat core size     : 0
% 0.21/0.55  #    Propositional preprocessing time  : 0.000
% 0.21/0.55  #    Propositional encoding time       : 0.000
% 0.21/0.55  #    Propositional solver time         : 0.000
% 0.21/0.55  #    Success case prop preproc time    : 0.000
% 0.21/0.55  #    Success case prop encoding time   : 0.000
% 0.21/0.55  #    Success case prop solver time     : 0.000
% 0.21/0.55  # Current number of processed clauses  : 89
% 0.21/0.55  #    Positive orientable unit clauses  : 20
% 0.21/0.55  #    Positive unorientable unit clauses: 0
% 0.21/0.55  #    Negative unit clauses             : 8
% 0.21/0.55  #    Non-unit-clauses                  : 61
% 0.21/0.55  # Current number of unprocessed clauses: 298
% 0.21/0.55  # ...number of literals in the above   : 1355
% 0.21/0.55  # Current number of archived formulas  : 0
% 0.21/0.55  # Current number of archived clauses   : 92
% 0.21/0.55  # Clause-clause subsumption calls (NU) : 919
% 0.21/0.55  # Rec. Clause-clause subsumption calls : 406
% 0.21/0.55  # Non-unit clause-clause subsumptions  : 50
% 0.21/0.55  # Unit Clause-clause subsumption calls : 97
% 0.21/0.55  # Rewrite failures with RHS unbound    : 0
% 0.21/0.55  # BW rewrite match attempts            : 6
% 0.21/0.55  # BW rewrite match successes           : 6
% 0.21/0.55  # Condensation attempts                : 0
% 0.21/0.55  # Condensation successes               : 0
% 0.21/0.55  # Termbank termtop insertions          : 13149
% 0.21/0.55  # Search garbage collected termcells   : 1023
% 0.21/0.55  
% 0.21/0.55  # -------------------------------------------------
% 0.21/0.55  # User time                : 0.026 s
% 0.21/0.55  # System time              : 0.005 s
% 0.21/0.55  # Total time               : 0.031 s
% 0.21/0.55  # Maximum resident set size: 1880 pages
% 0.21/0.55  
% 0.21/0.55  # -------------------------------------------------
% 0.21/0.55  # User time                : 0.029 s
% 0.21/0.55  # System time              : 0.009 s
% 0.21/0.55  # Total time               : 0.038 s
% 0.21/0.55  # Maximum resident set size: 1740 pages
% 0.21/0.55  % E---3.1 exiting
% 0.21/0.55  % E exiting
%------------------------------------------------------------------------------