TSTP Solution File: LAT381+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT381+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 : n024.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 06:02:22 EDT 2023

% Result   : Theorem 0.15s 0.55s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   47 (  14 unt;  22 typ;   0 def)
%            Number of atoms       :  112 (   6 equ)
%            Maximal formula atoms :   27 (   4 avg)
%            Number of connectives :  114 (  27   ~;  30   |;  41   &)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   38 (  18   >;  20   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :   30 (   0 sgn;  24   !;   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,
    isEmpty0: $i > $o ).

tff(decl_26,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff(decl_27,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(decl_28,type,
    aLowerBoundOfIn0: ( $i * $i * $i ) > $o ).

tff(decl_29,type,
    aUpperBoundOfIn0: ( $i * $i * $i ) > $o ).

tff(decl_30,type,
    aInfimumOfIn0: ( $i * $i * $i ) > $o ).

tff(decl_31,type,
    aSupremumOfIn0: ( $i * $i * $i ) > $o ).

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

tff(decl_33,type,
    xS: $i ).

tff(decl_34,type,
    xu: $i ).

tff(decl_35,type,
    xv: $i ).

tff(decl_36,type,
    esk1_1: $i > $i ).

tff(decl_37,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_40,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_41,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_42,type,
    esk7_1: $i > $i ).

tff(decl_43,type,
    esk8_1: $i > $i ).

fof(m__744,hypothesis,
    ( aElementOf0(xu,xT)
    & aElementOf0(xu,xT)
    & ! [X1] :
        ( aElementOf0(X1,xS)
       => sdtlseqdt0(X1,xu) )
    & aUpperBoundOfIn0(xu,xS,xT)
    & ! [X1] :
        ( ( ( aElementOf0(X1,xT)
            & ! [X2] :
                ( aElementOf0(X2,xS)
               => sdtlseqdt0(X2,X1) ) )
          | aUpperBoundOfIn0(X1,xS,xT) )
       => sdtlseqdt0(xu,X1) )
    & aSupremumOfIn0(xu,xS,xT)
    & aElementOf0(xv,xT)
    & aElementOf0(xv,xT)
    & ! [X1] :
        ( aElementOf0(X1,xS)
       => sdtlseqdt0(X1,xv) )
    & aUpperBoundOfIn0(xv,xS,xT)
    & ! [X1] :
        ( ( ( aElementOf0(X1,xT)
            & ! [X2] :
                ( aElementOf0(X2,xS)
               => sdtlseqdt0(X2,X1) ) )
          | aUpperBoundOfIn0(X1,xS,xT) )
       => sdtlseqdt0(xv,X1) )
    & aSupremumOfIn0(xv,xS,xT) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__744) ).

fof(mEOfElem,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

fof(mASymm,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mASymm) ).

fof(m__725,hypothesis,
    aSet0(xT),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__725) ).

fof(m__,conjecture,
    xu = xv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(c_0_5,hypothesis,
    ( aElementOf0(xu,xT)
    & ! [X1] :
        ( aElementOf0(X1,xS)
       => sdtlseqdt0(X1,xu) )
    & aUpperBoundOfIn0(xu,xS,xT)
    & ! [X1] :
        ( ( ( aElementOf0(X1,xT)
            & ! [X2] :
                ( aElementOf0(X2,xS)
               => sdtlseqdt0(X2,X1) ) )
          | aUpperBoundOfIn0(X1,xS,xT) )
       => sdtlseqdt0(xu,X1) )
    & aSupremumOfIn0(xu,xS,xT)
    & aElementOf0(xv,xT)
    & aElementOf0(xv,xT)
    & ! [X1] :
        ( aElementOf0(X1,xS)
       => sdtlseqdt0(X1,xv) )
    & aUpperBoundOfIn0(xv,xS,xT)
    & ! [X1] :
        ( ( ( aElementOf0(X1,xT)
            & ! [X2] :
                ( aElementOf0(X2,xS)
               => sdtlseqdt0(X2,X1) ) )
          | aUpperBoundOfIn0(X1,xS,xT) )
       => sdtlseqdt0(xv,X1) )
    & aSupremumOfIn0(xv,xS,xT) ),
    inference(fof_simplification,[status(thm)],[m__744]) ).

fof(c_0_6,hypothesis,
    ! [X46,X47,X49,X50] :
      ( aElementOf0(xu,xT)
      & ( ~ aElementOf0(X46,xS)
        | sdtlseqdt0(X46,xu) )
      & aUpperBoundOfIn0(xu,xS,xT)
      & ( aElementOf0(esk7_1(X47),xS)
        | ~ aElementOf0(X47,xT)
        | sdtlseqdt0(xu,X47) )
      & ( ~ sdtlseqdt0(esk7_1(X47),X47)
        | ~ aElementOf0(X47,xT)
        | sdtlseqdt0(xu,X47) )
      & ( ~ aUpperBoundOfIn0(X47,xS,xT)
        | sdtlseqdt0(xu,X47) )
      & aSupremumOfIn0(xu,xS,xT)
      & aElementOf0(xv,xT)
      & aElementOf0(xv,xT)
      & ( ~ aElementOf0(X49,xS)
        | sdtlseqdt0(X49,xv) )
      & aUpperBoundOfIn0(xv,xS,xT)
      & ( aElementOf0(esk8_1(X50),xS)
        | ~ aElementOf0(X50,xT)
        | sdtlseqdt0(xv,X50) )
      & ( ~ sdtlseqdt0(esk8_1(X50),X50)
        | ~ aElementOf0(X50,xT)
        | sdtlseqdt0(xv,X50) )
      & ( ~ aUpperBoundOfIn0(X50,xS,xT)
        | sdtlseqdt0(xv,X50) )
      & aSupremumOfIn0(xv,xS,xT) ),
    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_5])])])])]) ).

fof(c_0_7,plain,
    ! [X5,X6] :
      ( ~ aSet0(X5)
      | ~ aElementOf0(X6,X5)
      | aElement0(X6) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).

fof(c_0_8,plain,
    ! [X16,X17] :
      ( ~ aElement0(X16)
      | ~ aElement0(X17)
      | ~ sdtlseqdt0(X16,X17)
      | ~ sdtlseqdt0(X17,X16)
      | X16 = X17 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mASymm])]) ).

cnf(c_0_9,hypothesis,
    ( sdtlseqdt0(xu,X1)
    | ~ aUpperBoundOfIn0(X1,xS,xT) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,hypothesis,
    aUpperBoundOfIn0(xv,xS,xT),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,hypothesis,
    aElementOf0(xu,xT),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_13,hypothesis,
    aSet0(xT),
    inference(split_conjunct,[status(thm)],[m__725]) ).

cnf(c_0_14,hypothesis,
    aElementOf0(xv,xT),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_15,negated_conjecture,
    xu != xv,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_16,plain,
    ( X1 = X2
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_17,hypothesis,
    sdtlseqdt0(xu,xv),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_18,hypothesis,
    aElement0(xu),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).

cnf(c_0_19,hypothesis,
    aElement0(xv),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_14]),c_0_13])]) ).

cnf(c_0_20,negated_conjecture,
    xu != xv,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,hypothesis,
    ( sdtlseqdt0(xv,X1)
    | ~ aUpperBoundOfIn0(X1,xS,xT) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_22,hypothesis,
    aUpperBoundOfIn0(xu,xS,xT),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_23,hypothesis,
    ~ sdtlseqdt0(xv,xu),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]),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
% 0.08/0.09  % Problem    : LAT381+3 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.10  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.30  % Computer : n024.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Thu Aug 24 04:17:09 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.15/0.53  start to proof: theBenchmark
% 0.15/0.55  % Version  : CSE_E---1.5
% 0.15/0.55  % Problem  : theBenchmark.p
% 0.15/0.55  % Proof found
% 0.15/0.55  % SZS status Theorem for theBenchmark.p
% 0.15/0.55  % SZS output start Proof
% See solution above
% 0.15/0.55  % Total time : 0.011000 s
% 0.15/0.55  % SZS output end Proof
% 0.15/0.55  % Total time : 0.013000 s
%------------------------------------------------------------------------------