TSTP Solution File: NUM558+3 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : NUM558+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n007.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:07:42 EDT 2023

% Result   : Theorem 0.17s 0.46s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   25 (  11 unt;   0 def)
%            Number of atoms       :  188 (  32 equ)
%            Maximal formula atoms :   67 (   7 avg)
%            Number of connectives :  230 (  67   ~;  69   |;  75   &)
%                                         (   2 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   39 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;  10 con; 0-2 aty)
%            Number of variables   :   38 (   0 sgn;  30   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__2227,hypothesis,
    ( aSet0(slbdtsldtrb0(xS,xk))
    & ! [X1] :
        ( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
         => ( aSet0(X1)
            & ! [X2] :
                ( aElementOf0(X2,X1)
               => aElementOf0(X2,xS) )
            & aSubsetOf0(X1,xS)
            & sbrdtbr0(X1) = xk ) )
        & ( ( ( ( aSet0(X1)
                & ! [X2] :
                    ( aElementOf0(X2,X1)
                   => aElementOf0(X2,xS) ) )
              | aSubsetOf0(X1,xS) )
            & sbrdtbr0(X1) = xk )
         => aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X1] :
        ( ( aElementOf0(X1,slbdtsldtrb0(xT,xk))
         => ( aSet0(X1)
            & ! [X2] :
                ( aElementOf0(X2,X1)
               => aElementOf0(X2,xT) )
            & aSubsetOf0(X1,xT)
            & sbrdtbr0(X1) = xk ) )
        & ( ( ( ( aSet0(X1)
                & ! [X2] :
                    ( aElementOf0(X2,X1)
                   => aElementOf0(X2,xT) ) )
              | aSubsetOf0(X1,xT) )
            & sbrdtbr0(X1) = xk )
         => aElementOf0(X1,slbdtsldtrb0(xT,xk)) ) )
    & ! [X1] :
        ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
       => aElementOf0(X1,slbdtsldtrb0(xT,xk)) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ~ ( ! [X1] :
            ( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
             => ( aSet0(X1)
                & ! [X2] :
                    ( aElementOf0(X2,X1)
                   => aElementOf0(X2,xS) )
                & aSubsetOf0(X1,xS)
                & sbrdtbr0(X1) = xk ) )
            & ( ( ( ( aSet0(X1)
                    & ! [X2] :
                        ( aElementOf0(X2,X1)
                       => aElementOf0(X2,xS) ) )
                  | aSubsetOf0(X1,xS) )
                & sbrdtbr0(X1) = xk )
             => aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
       => ( ~ ? [X1] : aElementOf0(X1,slbdtsldtrb0(xS,xk))
          | slbdtsldtrb0(xS,xk) = slcrc0 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.uZmEpcqPpB/E---3.1_10287.p',m__2227) ).

fof(m__2378,hypothesis,
    ( ! [X1] :
        ( aElementOf0(X1,xP)
       => aElementOf0(X1,xS) )
    & aSubsetOf0(xP,xS)
    & sbrdtbr0(xP) = xk
    & aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
    file('/export/starexec/sandbox/tmp/tmp.uZmEpcqPpB/E---3.1_10287.p',m__2378) ).

fof(mEOfElem,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.uZmEpcqPpB/E---3.1_10287.p',mEOfElem) ).

fof(m__2357,hypothesis,
    ( aSet0(sdtmndt0(xQ,xy))
    & ! [X1] :
        ( aElementOf0(X1,sdtmndt0(xQ,xy))
      <=> ( aElement0(X1)
          & aElementOf0(X1,xQ)
          & X1 != xy ) )
    & aSet0(xP)
    & ! [X1] :
        ( aElementOf0(X1,xP)
      <=> ( aElement0(X1)
          & ( aElementOf0(X1,sdtmndt0(xQ,xy))
            | X1 = xx ) ) )
    & xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
    file('/export/starexec/sandbox/tmp/tmp.uZmEpcqPpB/E---3.1_10287.p',m__2357) ).

fof(m__2256,hypothesis,
    aElementOf0(xx,xS),
    file('/export/starexec/sandbox/tmp/tmp.uZmEpcqPpB/E---3.1_10287.p',m__2256) ).

fof(m__2202_02,hypothesis,
    ( aSet0(xS)
    & aSet0(xT)
    & xk != sz00 ),
    file('/export/starexec/sandbox/tmp/tmp.uZmEpcqPpB/E---3.1_10287.p',m__2202_02) ).

fof(m__,conjecture,
    aElementOf0(xx,xT),
    file('/export/starexec/sandbox/tmp/tmp.uZmEpcqPpB/E---3.1_10287.p',m__) ).

fof(c_0_7,hypothesis,
    ! [X5,X6,X7,X9,X10,X11,X13,X14,X15,X16] :
      ( aSet0(slbdtsldtrb0(xS,xk))
      & ( aSet0(X5)
        | ~ aElementOf0(X5,slbdtsldtrb0(xS,xk)) )
      & ( ~ aElementOf0(X6,X5)
        | aElementOf0(X6,xS)
        | ~ aElementOf0(X5,slbdtsldtrb0(xS,xk)) )
      & ( aSubsetOf0(X5,xS)
        | ~ aElementOf0(X5,slbdtsldtrb0(xS,xk)) )
      & ( sbrdtbr0(X5) = xk
        | ~ aElementOf0(X5,slbdtsldtrb0(xS,xk)) )
      & ( aElementOf0(esk1_1(X7),X7)
        | ~ aSet0(X7)
        | sbrdtbr0(X7) != xk
        | aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
      & ( ~ aElementOf0(esk1_1(X7),xS)
        | ~ aSet0(X7)
        | sbrdtbr0(X7) != xk
        | aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
      & ( ~ aSubsetOf0(X7,xS)
        | sbrdtbr0(X7) != xk
        | aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
      & aSet0(slbdtsldtrb0(xT,xk))
      & ( aSet0(X9)
        | ~ aElementOf0(X9,slbdtsldtrb0(xT,xk)) )
      & ( ~ aElementOf0(X10,X9)
        | aElementOf0(X10,xT)
        | ~ aElementOf0(X9,slbdtsldtrb0(xT,xk)) )
      & ( aSubsetOf0(X9,xT)
        | ~ aElementOf0(X9,slbdtsldtrb0(xT,xk)) )
      & ( sbrdtbr0(X9) = xk
        | ~ aElementOf0(X9,slbdtsldtrb0(xT,xk)) )
      & ( aElementOf0(esk2_1(X11),X11)
        | ~ aSet0(X11)
        | sbrdtbr0(X11) != xk
        | aElementOf0(X11,slbdtsldtrb0(xT,xk)) )
      & ( ~ aElementOf0(esk2_1(X11),xT)
        | ~ aSet0(X11)
        | sbrdtbr0(X11) != xk
        | aElementOf0(X11,slbdtsldtrb0(xT,xk)) )
      & ( ~ aSubsetOf0(X11,xT)
        | sbrdtbr0(X11) != xk
        | aElementOf0(X11,slbdtsldtrb0(xT,xk)) )
      & ( ~ aElementOf0(X13,slbdtsldtrb0(xS,xk))
        | aElementOf0(X13,slbdtsldtrb0(xT,xk)) )
      & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
      & ( aSet0(X14)
        | ~ aElementOf0(X14,slbdtsldtrb0(xS,xk)) )
      & ( ~ aElementOf0(X15,X14)
        | aElementOf0(X15,xS)
        | ~ aElementOf0(X14,slbdtsldtrb0(xS,xk)) )
      & ( aSubsetOf0(X14,xS)
        | ~ aElementOf0(X14,slbdtsldtrb0(xS,xk)) )
      & ( sbrdtbr0(X14) = xk
        | ~ aElementOf0(X14,slbdtsldtrb0(xS,xk)) )
      & ( aElementOf0(esk3_1(X16),X16)
        | ~ aSet0(X16)
        | sbrdtbr0(X16) != xk
        | aElementOf0(X16,slbdtsldtrb0(xS,xk)) )
      & ( ~ aElementOf0(esk3_1(X16),xS)
        | ~ aSet0(X16)
        | sbrdtbr0(X16) != xk
        | aElementOf0(X16,slbdtsldtrb0(xS,xk)) )
      & ( ~ aSubsetOf0(X16,xS)
        | sbrdtbr0(X16) != xk
        | aElementOf0(X16,slbdtsldtrb0(xS,xk)) )
      & aElementOf0(esk4_0,slbdtsldtrb0(xS,xk))
      & slbdtsldtrb0(xS,xk) != slcrc0 ),
    inference(distribute,[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)],[m__2227])])])])])]) ).

fof(c_0_8,hypothesis,
    ! [X22] :
      ( ( ~ aElementOf0(X22,xP)
        | aElementOf0(X22,xS) )
      & aSubsetOf0(xP,xS)
      & sbrdtbr0(xP) = xk
      & aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2378])])]) ).

fof(c_0_9,plain,
    ! [X67,X68] :
      ( ~ aSet0(X67)
      | ~ aElementOf0(X68,X67)
      | aElement0(X68) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).

cnf(c_0_10,hypothesis,
    ( aElementOf0(X1,slbdtsldtrb0(xT,xk))
    | ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,hypothesis,
    aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_12,hypothesis,
    ! [X20,X21] :
      ( aSet0(sdtmndt0(xQ,xy))
      & ( aElement0(X20)
        | ~ aElementOf0(X20,sdtmndt0(xQ,xy)) )
      & ( aElementOf0(X20,xQ)
        | ~ aElementOf0(X20,sdtmndt0(xQ,xy)) )
      & ( X20 != xy
        | ~ aElementOf0(X20,sdtmndt0(xQ,xy)) )
      & ( ~ aElement0(X20)
        | ~ aElementOf0(X20,xQ)
        | X20 = xy
        | aElementOf0(X20,sdtmndt0(xQ,xy)) )
      & aSet0(xP)
      & ( aElement0(X21)
        | ~ aElementOf0(X21,xP) )
      & ( aElementOf0(X21,sdtmndt0(xQ,xy))
        | X21 = xx
        | ~ aElementOf0(X21,xP) )
      & ( ~ aElementOf0(X21,sdtmndt0(xQ,xy))
        | ~ aElement0(X21)
        | aElementOf0(X21,xP) )
      & ( X21 != xx
        | ~ aElement0(X21)
        | aElementOf0(X21,xP) )
      & xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2357])])])]) ).

cnf(c_0_13,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,hypothesis,
    aElementOf0(xx,xS),
    inference(split_conjunct,[status(thm)],[m__2256]) ).

cnf(c_0_15,hypothesis,
    aSet0(xS),
    inference(split_conjunct,[status(thm)],[m__2202_02]) ).

cnf(c_0_16,hypothesis,
    ( aElementOf0(X1,xT)
    | ~ aElementOf0(X1,X2)
    | ~ aElementOf0(X2,slbdtsldtrb0(xT,xk)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_17,hypothesis,
    aElementOf0(xP,slbdtsldtrb0(xT,xk)),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_18,hypothesis,
    ( aElementOf0(X1,xP)
    | X1 != xx
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,hypothesis,
    aElement0(xx),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

fof(c_0_20,negated_conjecture,
    ~ aElementOf0(xx,xT),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_21,hypothesis,
    ( aElementOf0(X1,xT)
    | ~ aElementOf0(X1,xP) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,hypothesis,
    aElementOf0(xx,xP),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19])]) ).

cnf(c_0_23,negated_conjecture,
    ~ aElementOf0(xx,xT),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_24,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : NUM558+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n007.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 2400
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Oct  2 14:51:54 EDT 2023
% 0.12/0.33  % CPUTime    : 
% 0.17/0.42  Running first-order model finding
% 0.17/0.42  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.uZmEpcqPpB/E---3.1_10287.p
% 0.17/0.46  # Version: 3.1pre001
% 0.17/0.46  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.46  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.46  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.46  # Starting sh5l with 300s (1) cores
% 0.17/0.46  # new_bool_1 with pid 10407 completed with status 0
% 0.17/0.46  # Result found by new_bool_1
% 0.17/0.46  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.46  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.46  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.46  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.46  # Search class: FGHSF-FSLM31-MFFFFFNN
% 0.17/0.46  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.46  # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 163s (1) cores
% 0.17/0.46  # G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with pid 10412 completed with status 0
% 0.17/0.46  # Result found by G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S
% 0.17/0.46  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/0.46  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.46  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.46  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.46  # Search class: FGHSF-FSLM31-MFFFFFNN
% 0.17/0.46  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.46  # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 163s (1) cores
% 0.17/0.46  # Preprocessing time       : 0.002 s
% 0.17/0.46  # Presaturation interreduction done
% 0.17/0.46  
% 0.17/0.46  # Proof found!
% 0.17/0.46  # SZS status Theorem
% 0.17/0.46  # SZS output start CNFRefutation
% See solution above
% 0.17/0.46  # Parsed axioms                        : 72
% 0.17/0.46  # Removed by relevancy pruning/SinE    : 5
% 0.17/0.46  # Initial clauses                      : 159
% 0.17/0.46  # Removed in clause preprocessing      : 5
% 0.17/0.46  # Initial clauses in saturation        : 154
% 0.17/0.46  # Processed clauses                    : 384
% 0.17/0.46  # ...of these trivial                  : 7
% 0.17/0.46  # ...subsumed                          : 21
% 0.17/0.46  # ...remaining for further processing  : 356
% 0.17/0.46  # Other redundant clauses eliminated   : 8
% 0.17/0.46  # Clauses deleted for lack of memory   : 0
% 0.17/0.46  # Backward-subsumed                    : 0
% 0.17/0.46  # Backward-rewritten                   : 3
% 0.17/0.46  # Generated clauses                    : 776
% 0.17/0.46  # ...of the previous two non-redundant : 708
% 0.17/0.46  # ...aggressively subsumed             : 0
% 0.17/0.46  # Contextual simplify-reflections      : 12
% 0.17/0.46  # Paramodulations                      : 741
% 0.17/0.46  # Factorizations                       : 4
% 0.17/0.46  # NegExts                              : 0
% 0.17/0.46  # Equation resolutions                 : 31
% 0.17/0.46  # Total rewrite steps                  : 573
% 0.17/0.46  # Propositional unsat checks           : 0
% 0.17/0.46  #    Propositional check models        : 0
% 0.17/0.46  #    Propositional check unsatisfiable : 0
% 0.17/0.46  #    Propositional clauses             : 0
% 0.17/0.46  #    Propositional clauses after purity: 0
% 0.17/0.46  #    Propositional unsat core size     : 0
% 0.17/0.46  #    Propositional preprocessing time  : 0.000
% 0.17/0.46  #    Propositional encoding time       : 0.000
% 0.17/0.46  #    Propositional solver time         : 0.000
% 0.17/0.46  #    Success case prop preproc time    : 0.000
% 0.17/0.46  #    Success case prop encoding time   : 0.000
% 0.17/0.46  #    Success case prop solver time     : 0.000
% 0.17/0.46  # Current number of processed clauses  : 204
% 0.17/0.46  #    Positive orientable unit clauses  : 60
% 0.17/0.46  #    Positive unorientable unit clauses: 0
% 0.17/0.46  #    Negative unit clauses             : 16
% 0.17/0.46  #    Non-unit-clauses                  : 128
% 0.17/0.46  # Current number of unprocessed clauses: 618
% 0.17/0.46  # ...number of literals in the above   : 2900
% 0.17/0.46  # Current number of archived formulas  : 0
% 0.17/0.46  # Current number of archived clauses   : 149
% 0.17/0.46  # Clause-clause subsumption calls (NU) : 7076
% 0.17/0.46  # Rec. Clause-clause subsumption calls : 1695
% 0.17/0.46  # Non-unit clause-clause subsumptions  : 28
% 0.17/0.46  # Unit Clause-clause subsumption calls : 1503
% 0.17/0.46  # Rewrite failures with RHS unbound    : 0
% 0.17/0.46  # BW rewrite match attempts            : 3
% 0.17/0.46  # BW rewrite match successes           : 3
% 0.17/0.46  # Condensation attempts                : 0
% 0.17/0.46  # Condensation successes               : 0
% 0.17/0.46  # Termbank termtop insertions          : 23283
% 0.17/0.46  
% 0.17/0.46  # -------------------------------------------------
% 0.17/0.46  # User time                : 0.022 s
% 0.17/0.46  # System time              : 0.005 s
% 0.17/0.46  # Total time               : 0.027 s
% 0.17/0.46  # Maximum resident set size: 2232 pages
% 0.17/0.46  
% 0.17/0.46  # -------------------------------------------------
% 0.17/0.46  # User time                : 0.023 s
% 0.17/0.46  # System time              : 0.009 s
% 0.17/0.46  # Total time               : 0.032 s
% 0.17/0.46  # Maximum resident set size: 1764 pages
% 0.17/0.46  % E---3.1 exiting
%------------------------------------------------------------------------------