TSTP Solution File: NUM588+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM588+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n020.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 : Thu Aug 31 10:39:02 EDT 2023

% Result   : Theorem 6.23s 6.45s
% Output   : CNFRefutation 6.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   76
% Syntax   : Number of formulae    :   84 (   4 unt;  75 typ;   0 def)
%            Number of atoms       :  116 (  11 equ)
%            Maximal formula atoms :   44 (  12 avg)
%            Number of connectives :  134 (  27   ~;  22   |;  61   &)
%                                         (   4 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   35 (   9 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  122 (  61   >;  61   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :   64 (  64 usr;  14 con; 0-4 aty)
%            Number of variables   :   28 (   0 sgn;  26   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aSet0: $i > $o ).

tff(decl_23,type,
    aElement0: $i > $o ).

tff(decl_24,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(decl_25,type,
    isFinite0: $i > $o ).

tff(decl_26,type,
    slcrc0: $i ).

tff(decl_27,type,
    isCountable0: $i > $o ).

tff(decl_28,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff(decl_29,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_30,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff(decl_31,type,
    szNzAzT0: $i ).

tff(decl_32,type,
    sz00: $i ).

tff(decl_33,type,
    szszuzczcdt0: $i > $i ).

tff(decl_34,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(decl_35,type,
    iLess0: ( $i * $i ) > $o ).

tff(decl_36,type,
    sbrdtbr0: $i > $i ).

tff(decl_37,type,
    szmzizndt0: $i > $i ).

tff(decl_38,type,
    szmzazxdt0: $i > $i ).

tff(decl_39,type,
    slbdtrb0: $i > $i ).

tff(decl_40,type,
    slbdtsldtrb0: ( $i * $i ) > $i ).

tff(decl_41,type,
    aFunction0: $i > $o ).

tff(decl_42,type,
    szDzozmdt0: $i > $i ).

tff(decl_43,type,
    sdtlpdtrp0: ( $i * $i ) > $i ).

tff(decl_44,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

tff(decl_45,type,
    sdtlcdtrc0: ( $i * $i ) > $i ).

tff(decl_46,type,
    sdtexdt0: ( $i * $i ) > $i ).

tff(decl_47,type,
    szDzizrdt0: $i > $i ).

tff(decl_48,type,
    xT: $i ).

tff(decl_49,type,
    xK: $i ).

tff(decl_50,type,
    xS: $i ).

tff(decl_51,type,
    xc: $i ).

tff(decl_52,type,
    xk: $i ).

tff(decl_53,type,
    xN: $i ).

tff(decl_54,type,
    xC: $i ).

tff(decl_55,type,
    epred1_1: $i > $o ).

tff(decl_56,type,
    epred2_1: $i > $o ).

tff(decl_57,type,
    esk1_1: $i > $i ).

tff(decl_58,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_59,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_60,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_61,type,
    esk5_1: $i > $i ).

tff(decl_62,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_63,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_64,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_65,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_66,type,
    esk10_1: $i > $i ).

tff(decl_67,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_69,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_70,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_71,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_75,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_76,type,
    esk20_1: $i > $i ).

tff(decl_77,type,
    esk21_1: $i > $i ).

tff(decl_78,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_79,type,
    esk23_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk24_3: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk25_3: ( $i * $i * $i ) > $i ).

tff(decl_82,type,
    esk26_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_83,type,
    esk27_3: ( $i * $i * $i ) > $i ).

tff(decl_84,type,
    esk28_3: ( $i * $i * $i ) > $i ).

tff(decl_85,type,
    esk29_3: ( $i * $i * $i ) > $i ).

tff(decl_86,type,
    esk30_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk31_1: $i > $i ).

tff(decl_88,type,
    esk32_2: ( $i * $i ) > $i ).

tff(decl_89,type,
    esk33_2: ( $i * $i ) > $i ).

tff(decl_90,type,
    esk34_0: $i ).

tff(decl_91,type,
    esk35_0: $i ).

tff(decl_92,type,
    esk36_0: $i ).

tff(decl_93,type,
    esk37_0: $i ).

tff(decl_94,type,
    esk38_2: ( $i * $i ) > $i ).

tff(decl_95,type,
    esk39_2: ( $i * $i ) > $i ).

tff(decl_96,type,
    esk40_2: ( $i * $i ) > $i ).

fof(m__,conjecture,
    ! [X1] :
      ( aElementOf0(X1,szNzAzT0)
     => ! [X2] :
          ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
            & ! [X3] :
                ( aElementOf0(X3,sdtlpdtrp0(xN,X1))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
            & ! [X3] :
                ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
              <=> ( aElement0(X3)
                  & aElementOf0(X3,sdtlpdtrp0(xN,X1))
                  & X3 != szmzizndt0(sdtlpdtrp0(xN,X1)) ) )
            & aSet0(X2)
            & ! [X3] :
                ( aElementOf0(X3,X2)
               => aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
            & aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
            & isCountable0(X2) )
         => ! [X3] :
              ( ( aSet0(X3)
                & ! [X4] :
                    ( aElementOf0(X4,X3)
                   => aElementOf0(X4,X2) )
                & aSubsetOf0(X3,X2)
                & sbrdtbr0(X3) = xk
                & aElementOf0(X3,slbdtsldtrb0(X2,xk)) )
             => ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
                  & ! [X4] :
                      ( aElementOf0(X4,sdtlpdtrp0(xN,X1))
                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X4) ) )
               => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
                    & ! [X4] :
                        ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
                      <=> ( aElement0(X4)
                          & aElementOf0(X4,sdtlpdtrp0(xN,X1))
                          & X4 != szmzizndt0(sdtlpdtrp0(xN,X1)) ) ) )
                 => ( ! [X4] :
                        ( aElementOf0(X4,X3)
                       => aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
                    | aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
                    | aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(c_0_1,negated_conjecture,
    ~ ! [X1] :
        ( aElementOf0(X1,szNzAzT0)
       => ! [X2] :
            ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
              & ! [X3] :
                  ( aElementOf0(X3,sdtlpdtrp0(xN,X1))
                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
              & ! [X3] :
                  ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
                <=> ( aElement0(X3)
                    & aElementOf0(X3,sdtlpdtrp0(xN,X1))
                    & X3 != szmzizndt0(sdtlpdtrp0(xN,X1)) ) )
              & aSet0(X2)
              & ! [X3] :
                  ( aElementOf0(X3,X2)
                 => aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
              & aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
              & isCountable0(X2) )
           => ! [X3] :
                ( ( aSet0(X3)
                  & ! [X4] :
                      ( aElementOf0(X4,X3)
                     => aElementOf0(X4,X2) )
                  & aSubsetOf0(X3,X2)
                  & sbrdtbr0(X3) = xk
                  & aElementOf0(X3,slbdtsldtrb0(X2,xk)) )
               => ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
                    & ! [X4] :
                        ( aElementOf0(X4,sdtlpdtrp0(xN,X1))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X4) ) )
                 => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
                      & ! [X4] :
                          ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
                        <=> ( aElement0(X4)
                            & aElementOf0(X4,sdtlpdtrp0(xN,X1))
                            & X4 != szmzizndt0(sdtlpdtrp0(xN,X1)) ) ) )
                   => ( ! [X4] :
                          ( aElementOf0(X4,X3)
                         => aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
                      | aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
                      | aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_2,negated_conjecture,
    ! [X222,X223,X224,X226,X227,X228] :
      ( aElementOf0(esk34_0,szNzAzT0)
      & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk34_0)),sdtlpdtrp0(xN,esk34_0))
      & ( ~ aElementOf0(X222,sdtlpdtrp0(xN,esk34_0))
        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk34_0)),X222) )
      & aSet0(sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
      & ( aElement0(X223)
        | ~ aElementOf0(X223,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
      & ( aElementOf0(X223,sdtlpdtrp0(xN,esk34_0))
        | ~ aElementOf0(X223,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
      & ( X223 != szmzizndt0(sdtlpdtrp0(xN,esk34_0))
        | ~ aElementOf0(X223,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
      & ( ~ aElement0(X223)
        | ~ aElementOf0(X223,sdtlpdtrp0(xN,esk34_0))
        | X223 = szmzizndt0(sdtlpdtrp0(xN,esk34_0))
        | aElementOf0(X223,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
      & aSet0(esk35_0)
      & ( ~ aElementOf0(X224,esk35_0)
        | aElementOf0(X224,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
      & aSubsetOf0(esk35_0,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
      & isCountable0(esk35_0)
      & aSet0(esk36_0)
      & ( ~ aElementOf0(X226,esk36_0)
        | aElementOf0(X226,esk35_0) )
      & aSubsetOf0(esk36_0,esk35_0)
      & sbrdtbr0(esk36_0) = xk
      & aElementOf0(esk36_0,slbdtsldtrb0(esk35_0,xk))
      & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk34_0)),sdtlpdtrp0(xN,esk34_0))
      & ( ~ aElementOf0(X227,sdtlpdtrp0(xN,esk34_0))
        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk34_0)),X227) )
      & aSet0(sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
      & ( aElement0(X228)
        | ~ aElementOf0(X228,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
      & ( aElementOf0(X228,sdtlpdtrp0(xN,esk34_0))
        | ~ aElementOf0(X228,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
      & ( X228 != szmzizndt0(sdtlpdtrp0(xN,esk34_0))
        | ~ aElementOf0(X228,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
      & ( ~ aElement0(X228)
        | ~ aElementOf0(X228,sdtlpdtrp0(xN,esk34_0))
        | X228 = szmzizndt0(sdtlpdtrp0(xN,esk34_0))
        | aElementOf0(X228,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
      & aElementOf0(esk37_0,esk36_0)
      & ~ aElementOf0(esk37_0,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
      & ~ aSubsetOf0(esk36_0,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
      & ~ aElementOf0(esk36_0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))),xk)) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])]) ).

cnf(c_0_3,negated_conjecture,
    ( aElementOf0(X1,esk35_0)
    | ~ aElementOf0(X1,esk36_0) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4,negated_conjecture,
    aElementOf0(esk37_0,esk36_0),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_5,negated_conjecture,
    ( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
    | ~ aElementOf0(X1,esk35_0) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_6,negated_conjecture,
    aElementOf0(esk37_0,esk35_0),
    inference(spm,[status(thm)],[c_0_3,c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    ~ aElementOf0(esk37_0,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_8,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM588+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33  % Computer : n020.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Fri Aug 25 13:48:45 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.17/0.53  start to proof: theBenchmark
% 6.23/6.45  % Version  : CSE_E---1.5
% 6.23/6.45  % Problem  : theBenchmark.p
% 6.23/6.45  % Proof found
% 6.23/6.45  % SZS status Theorem for theBenchmark.p
% 6.23/6.45  % SZS output start Proof
% See solution above
% 6.23/6.45  % Total time : 5.811000 s
% 6.23/6.45  % SZS output end Proof
% 6.23/6.45  % Total time : 5.816000 s
%------------------------------------------------------------------------------