%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM550+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n022.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 10:38:37 EDT 2023

% Result   : Theorem 0.19s 0.60s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   57 (   5 unt;  39 typ;   0 def)
%            Number of atoms       :   52 (  25 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   56 (  22   ~;  13   |;  17   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   48 (  30   >;  18   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   31 (  31 usr;   9 con; 0-3 aty)
%            Number of variables   :   15 (   0 sgn;   9   !;   3   ?;   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,
    xk: $i ).

tff(decl_42,type,
    xS: $i ).

tff(decl_43,type,
    xT: $i ).

tff(decl_44,type,
    xx: $i ).

tff(decl_45,type,
    xQ: $i ).

tff(decl_46,type,
    esk1_1: $i > $i ).

tff(decl_47,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_48,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk5_1: $i > $i ).

tff(decl_51,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk10_1: $i > $i ).

tff(decl_56,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_57,type,
    esk12_1: $i > $i ).

tff(decl_58,type,
    esk13_1: $i > $i ).

tff(decl_59,type,
    esk14_1: $i > $i ).

tff(decl_60,type,
    esk15_0: $i ).

fof(m__,conjecture,
    ~ ( ~ ? [X1] : aElementOf0(X1,xQ)
      & xQ = slcrc0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(mCardEmpty,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ( sbrdtbr0(X1) = sz00
      <=> X1 = slcrc0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).

fof(mDefEmp,axiom,
    ! [X1] :
      ( X1 = slcrc0
    <=> ( aSet0(X1)
        & ~ ? [X2] : aElementOf0(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).

fof(m__2270,hypothesis,
    ( aSet0(xQ)
    & ! [X1] :
        ( aElementOf0(X1,xQ)
       => aElementOf0(X1,xS) )
    & aSubsetOf0(xQ,xS)
    & sbrdtbr0(xQ) = xk
    & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).

fof(m__2202_02,hypothesis,
    ( aSet0(xS)
    & aSet0(xT)
    & xk != sz00 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).

fof(c_0_5,negated_conjecture,
    ~ ~ ( ~ ? [X1] : aElementOf0(X1,xQ)
        & xQ = slcrc0 ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_6,plain,
    ! [X74] :
      ( ( sbrdtbr0(X74) != sz00
        | X74 = slcrc0
        | ~ aSet0(X74) )
      & ( X74 != slcrc0
        | sbrdtbr0(X74) = sz00
        | ~ aSet0(X74) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])]) ).

fof(c_0_7,plain,
    ! [X7,X8,X9] :
      ( ( aSet0(X7)
        | X7 != slcrc0 )
      & ( ~ aElementOf0(X8,X7)
        | X7 != slcrc0 )
      & ( ~ aSet0(X9)
        | aElementOf0(esk1_1(X9),X9)
        | X9 = 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)],[mDefEmp])])])])])]) ).

fof(c_0_8,hypothesis,
    ! [X137] :
      ( aSet0(xQ)
      & ( ~ aElementOf0(X137,xQ)
        | aElementOf0(X137,xS) )
      & aSubsetOf0(xQ,xS)
      & sbrdtbr0(xQ) = xk
      & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2270])])]) ).

fof(c_0_9,negated_conjecture,
    ! [X138] :
      ( ~ aElementOf0(X138,xQ)
      & xQ = slcrc0 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

cnf(c_0_10,plain,
    ( sbrdtbr0(X1) = sz00
    | X1 != slcrc0
    | ~ aSet0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( aSet0(X1)
    | X1 != slcrc0 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,hypothesis,
    sbrdtbr0(xQ) = xk,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    xQ = slcrc0,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( sbrdtbr0(X1) = sz00
    | X1 != slcrc0 ),
    inference(csr,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,hypothesis,
    sbrdtbr0(slcrc0) = xk,
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,hypothesis,
    xk != sz00,
    inference(split_conjunct,[status(thm)],[m__2202_02]) ).

cnf(c_0_17,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_14]),c_0_15]),c_0_16]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM550+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.34  % Computer : n022.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit   : 300
% 0.16/0.34  % WCLimit    : 300
% 0.16/0.34  % DateTime   : Fri Aug 25 13:10:40 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.60  % Version  : CSE_E---1.5
% 0.19/0.60  % Problem  : theBenchmark.p
% 0.19/0.60  % Proof found
% 0.19/0.60  % SZS status Theorem for theBenchmark.p
% 0.19/0.60  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.022000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.026000 s
%------------------------------------------------------------------------------