TSTP Solution File: NUM566+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM566+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n011.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 : Tue May 21 01:14:43 EDT 2024

% Result   : Theorem 0.17s 0.49s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   45 (  16 unt;   0 def)
%            Number of atoms       :  118 (  13 equ)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :  126 (  53   ~;  48   |;  16   &)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-2 aty)
%            Number of variables   :   43 (   0 sgn  19   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__,conjecture,
    ? [X1] :
      ( aElementOf0(X1,xT)
      & ? [X2] :
          ( aSubsetOf0(X2,xS)
          & isCountable0(X2)
          & ! [X3] :
              ( aElementOf0(X3,slbdtsldtrb0(X2,xK))
             => sdtlpdtrp0(xc,X3) = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(m__3507,hypothesis,
    ! [X1] :
      ( aElementOf0(X1,slbdtsldtrb0(xS,sz00))
     => sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3507) ).

fof(m__3453,hypothesis,
    ( aFunction0(xc)
    & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
    & aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).

fof(m__3462,hypothesis,
    xK = sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).

fof(mDefSub,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aSubsetOf0(X2,X1)
        <=> ( aSet0(X2)
            & ! [X3] :
                ( aElementOf0(X3,X2)
               => aElementOf0(X3,X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).

fof(m__3435,hypothesis,
    ( aSubsetOf0(xS,szNzAzT0)
    & isCountable0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).

fof(m__3291,hypothesis,
    ( aSet0(xT)
    & isFinite0(xT) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).

fof(mImgRng,axiom,
    ! [X1] :
      ( aFunction0(X1)
     => ! [X2] :
          ( aElementOf0(X2,szDzozmdt0(X1))
         => aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).

fof(m__3476,hypothesis,
    aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3476) ).

fof(mSubRefl,axiom,
    ! [X1] :
      ( aSet0(X1)
     => aSubsetOf0(X1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).

fof(mNATSet,axiom,
    ( aSet0(szNzAzT0)
    & isCountable0(szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).

fof(c_0_11,negated_conjecture,
    ~ ? [X1] :
        ( aElementOf0(X1,xT)
        & ? [X2] :
            ( aSubsetOf0(X2,xS)
            & isCountable0(X2)
            & ! [X3] :
                ( aElementOf0(X3,slbdtsldtrb0(X2,xK))
               => sdtlpdtrp0(xc,X3) = X1 ) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_12,hypothesis,
    ! [X13] :
      ( ~ aElementOf0(X13,slbdtsldtrb0(xS,sz00))
      | sdtlpdtrp0(xc,X13) = sdtlpdtrp0(xc,slcrc0) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3507])])]) ).

cnf(c_0_13,hypothesis,
    szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
    inference(split_conjunct,[status(thm)],[m__3453]) ).

cnf(c_0_14,hypothesis,
    xK = sz00,
    inference(split_conjunct,[status(thm)],[m__3462]) ).

fof(c_0_15,negated_conjecture,
    ! [X14,X15] :
      ( ( aElementOf0(esk3_2(X14,X15),slbdtsldtrb0(X15,xK))
        | ~ aSubsetOf0(X15,xS)
        | ~ isCountable0(X15)
        | ~ aElementOf0(X14,xT) )
      & ( sdtlpdtrp0(xc,esk3_2(X14,X15)) != X14
        | ~ aSubsetOf0(X15,xS)
        | ~ isCountable0(X15)
        | ~ aElementOf0(X14,xT) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])]) ).

cnf(c_0_16,hypothesis,
    ( sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0)
    | ~ aElementOf0(X1,slbdtsldtrb0(xS,sz00)) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,hypothesis,
    slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    ( aElementOf0(esk3_2(X1,X2),slbdtsldtrb0(X2,xK))
    | ~ aSubsetOf0(X2,xS)
    | ~ isCountable0(X2)
    | ~ aElementOf0(X1,xT) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_19,plain,
    ! [X26,X27,X28,X29] :
      ( ( aSet0(X27)
        | ~ aSubsetOf0(X27,X26)
        | ~ aSet0(X26) )
      & ( ~ aElementOf0(X28,X27)
        | aElementOf0(X28,X26)
        | ~ aSubsetOf0(X27,X26)
        | ~ aSet0(X26) )
      & ( aElementOf0(esk4_2(X26,X29),X29)
        | ~ aSet0(X29)
        | aSubsetOf0(X29,X26)
        | ~ aSet0(X26) )
      & ( ~ aElementOf0(esk4_2(X26,X29),X26)
        | ~ aSet0(X29)
        | aSubsetOf0(X29,X26)
        | ~ aSet0(X26) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSub])])])])])])]) ).

cnf(c_0_20,negated_conjecture,
    ( sdtlpdtrp0(xc,esk3_2(X1,X2)) != X1
    | ~ aSubsetOf0(X2,xS)
    | ~ isCountable0(X2)
    | ~ aElementOf0(X1,xT) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,hypothesis,
    ( sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0)
    | ~ aElementOf0(X1,szDzozmdt0(xc)) ),
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    ( aElementOf0(esk3_2(X1,X2),slbdtsldtrb0(X2,sz00))
    | ~ aSubsetOf0(X2,xS)
    | ~ isCountable0(X2)
    | ~ aElementOf0(X1,xT) ),
    inference(rw,[status(thm)],[c_0_18,c_0_14]) ).

cnf(c_0_23,hypothesis,
    isCountable0(xS),
    inference(split_conjunct,[status(thm)],[m__3435]) ).

cnf(c_0_24,plain,
    ( aElementOf0(X1,X3)
    | ~ aElementOf0(X1,X2)
    | ~ aSubsetOf0(X2,X3)
    | ~ aSet0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,hypothesis,
    aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
    inference(split_conjunct,[status(thm)],[m__3453]) ).

cnf(c_0_26,hypothesis,
    aSet0(xT),
    inference(split_conjunct,[status(thm)],[m__3291]) ).

fof(c_0_27,plain,
    ! [X48,X49] :
      ( ~ aFunction0(X48)
      | ~ aElementOf0(X49,szDzozmdt0(X48))
      | aElementOf0(sdtlpdtrp0(X48,X49),sdtlcdtrc0(X48,szDzozmdt0(X48))) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])])]) ).

cnf(c_0_28,negated_conjecture,
    ( ~ aSubsetOf0(X1,xS)
    | ~ isCountable0(X1)
    | ~ aElementOf0(esk3_2(sdtlpdtrp0(xc,slcrc0),X1),szDzozmdt0(xc))
    | ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]) ).

cnf(c_0_29,hypothesis,
    ( aElementOf0(esk3_2(X1,xS),szDzozmdt0(xc))
    | ~ aSubsetOf0(xS,xS)
    | ~ aElementOf0(X1,xT) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_17]),c_0_23])]) ).

cnf(c_0_30,hypothesis,
    ( aElementOf0(X1,xT)
    | ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).

cnf(c_0_31,plain,
    ( aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1)))
    | ~ aFunction0(X1)
    | ~ aElementOf0(X2,szDzozmdt0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_32,hypothesis,
    aFunction0(xc),
    inference(split_conjunct,[status(thm)],[m__3453]) ).

cnf(c_0_33,hypothesis,
    aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    inference(split_conjunct,[status(thm)],[m__3476]) ).

cnf(c_0_34,negated_conjecture,
    ( ~ aSubsetOf0(xS,xS)
    | ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_23])]) ).

cnf(c_0_35,hypothesis,
    ( aElementOf0(sdtlpdtrp0(xc,X1),xT)
    | ~ aElementOf0(X1,szDzozmdt0(xc)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).

cnf(c_0_36,hypothesis,
    aElementOf0(slcrc0,szDzozmdt0(xc)),
    inference(rw,[status(thm)],[c_0_33,c_0_17]) ).

fof(c_0_37,plain,
    ! [X31] :
      ( ~ aSet0(X31)
      | aSubsetOf0(X31,X31) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])])]) ).

cnf(c_0_38,plain,
    ( aSet0(X1)
    | ~ aSubsetOf0(X1,X2)
    | ~ aSet0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_39,hypothesis,
    aSubsetOf0(xS,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__3435]) ).

cnf(c_0_40,plain,
    aSet0(szNzAzT0),
    inference(split_conjunct,[status(thm)],[mNATSet]) ).

cnf(c_0_41,negated_conjecture,
    ~ aSubsetOf0(xS,xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).

cnf(c_0_42,plain,
    ( aSubsetOf0(X1,X1)
    | ~ aSet0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_43,hypothesis,
    aSet0(xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : NUM566+1 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n011.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon May 20 05:31:53 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.17/0.45  Running first-order theorem proving
% 0.17/0.45  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/benchmark/theBenchmark.p
% 0.17/0.49  # Version: 3.1.0
% 0.17/0.49  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.49  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.49  # Starting sh5l with 300s (1) cores
% 0.17/0.49  # new_bool_3 with pid 17995 completed with status 0
% 0.17/0.49  # Result found by new_bool_3
% 0.17/0.49  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.49  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.49  # Search class: FGHSF-FSLM32-MFFFFFNN
% 0.17/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.49  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 163s (1) cores
% 0.17/0.49  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 17999 completed with status 0
% 0.17/0.49  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.17/0.49  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.49  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.49  # Search class: FGHSF-FSLM32-MFFFFFNN
% 0.17/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.49  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 163s (1) cores
% 0.17/0.49  # Preprocessing time       : 0.003 s
% 0.17/0.49  # Presaturation interreduction done
% 0.17/0.49  
% 0.17/0.49  # Proof found!
% 0.17/0.49  # SZS status Theorem
% 0.17/0.49  # SZS output start CNFRefutation
% See solution above
% 0.17/0.49  # Parsed axioms                        : 81
% 0.17/0.49  # Removed by relevancy pruning/SinE    : 7
% 0.17/0.49  # Initial clauses                      : 137
% 0.17/0.49  # Removed in clause preprocessing      : 7
% 0.17/0.49  # Initial clauses in saturation        : 130
% 0.17/0.49  # Processed clauses                    : 312
% 0.17/0.49  # ...of these trivial                  : 1
% 0.17/0.49  # ...subsumed                          : 20
% 0.17/0.49  # ...remaining for further processing  : 291
% 0.17/0.49  # Other redundant clauses eliminated   : 38
% 0.17/0.49  # Clauses deleted for lack of memory   : 0
% 0.17/0.49  # Backward-subsumed                    : 6
% 0.17/0.49  # Backward-rewritten                   : 2
% 0.17/0.49  # Generated clauses                    : 304
% 0.17/0.49  # ...of the previous two non-redundant : 260
% 0.17/0.49  # ...aggressively subsumed             : 0
% 0.17/0.49  # Contextual simplify-reflections      : 12
% 0.17/0.49  # Paramodulations                      : 269
% 0.17/0.49  # Factorizations                       : 0
% 0.17/0.49  # NegExts                              : 0
% 0.17/0.49  # Equation resolutions                 : 39
% 0.17/0.49  # Disequality decompositions           : 0
% 0.17/0.49  # Total rewrite steps                  : 136
% 0.17/0.49  # ...of those cached                   : 117
% 0.17/0.49  # Propositional unsat checks           : 0
% 0.17/0.49  #    Propositional check models        : 0
% 0.17/0.49  #    Propositional check unsatisfiable : 0
% 0.17/0.49  #    Propositional clauses             : 0
% 0.17/0.49  #    Propositional clauses after purity: 0
% 0.17/0.49  #    Propositional unsat core size     : 0
% 0.17/0.49  #    Propositional preprocessing time  : 0.000
% 0.17/0.49  #    Propositional encoding time       : 0.000
% 0.17/0.49  #    Propositional solver time         : 0.000
% 0.17/0.49  #    Success case prop preproc time    : 0.000
% 0.17/0.49  #    Success case prop encoding time   : 0.000
% 0.17/0.49  #    Success case prop solver time     : 0.000
% 0.17/0.49  # Current number of processed clauses  : 127
% 0.17/0.49  #    Positive orientable unit clauses  : 26
% 0.17/0.49  #    Positive unorientable unit clauses: 0
% 0.17/0.49  #    Negative unit clauses             : 6
% 0.17/0.49  #    Non-unit-clauses                  : 95
% 0.17/0.49  # Current number of unprocessed clauses: 206
% 0.17/0.49  # ...number of literals in the above   : 1013
% 0.17/0.49  # Current number of archived formulas  : 0
% 0.17/0.49  # Current number of archived clauses   : 137
% 0.17/0.49  # Clause-clause subsumption calls (NU) : 6431
% 0.17/0.49  # Rec. Clause-clause subsumption calls : 1707
% 0.17/0.49  # Non-unit clause-clause subsumptions  : 26
% 0.17/0.49  # Unit Clause-clause subsumption calls : 44
% 0.17/0.49  # Rewrite failures with RHS unbound    : 0
% 0.17/0.49  # BW rewrite match attempts            : 2
% 0.17/0.49  # BW rewrite match successes           : 2
% 0.17/0.49  # Condensation attempts                : 0
% 0.17/0.49  # Condensation successes               : 0
% 0.17/0.49  # Termbank termtop insertions          : 17564
% 0.17/0.49  # Search garbage collected termcells   : 2886
% 0.17/0.49  
% 0.17/0.49  # -------------------------------------------------
% 0.17/0.49  # User time                : 0.030 s
% 0.17/0.49  # System time              : 0.002 s
% 0.17/0.49  # Total time               : 0.031 s
% 0.17/0.49  # Maximum resident set size: 2296 pages
% 0.17/0.49  
% 0.17/0.49  # -------------------------------------------------
% 0.17/0.49  # User time                : 0.031 s
% 0.17/0.49  # System time              : 0.005 s
% 0.17/0.49  # Total time               : 0.036 s
% 0.17/0.49  # Maximum resident set size: 1788 pages
% 0.17/0.49  % E---3.1 exiting
% 0.17/0.49  % E exiting
%------------------------------------------------------------------------------