TSTP Solution File: LAT381+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT381+1 : 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 : n026.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 06:02:21 EDT 2023

% Result   : Theorem 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   52 (  18 unt;  20 typ;   0 def)
%            Number of atoms       :   93 (   6 equ)
%            Maximal formula atoms :   25 (   2 avg)
%            Number of connectives :  107 (  46   ~;  44   |;   9   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   36 (  16   >;  20   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   33 (   0 sgn;  17   !;   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 ).

fof(mDefSup,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aSubsetOf0(X2,X1)
         => ! [X3] :
              ( aSupremumOfIn0(X3,X2,X1)
            <=> ( aElementOf0(X3,X1)
                & aUpperBoundOfIn0(X3,X2,X1)
                & ! [X4] :
                    ( aUpperBoundOfIn0(X4,X2,X1)
                   => sdtlseqdt0(X3,X4) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSup) ).

fof(m__744,hypothesis,
    ( aSupremumOfIn0(xu,xS,xT)
    & aSupremumOfIn0(xv,xS,xT) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__744) ).

fof(m__725_01,hypothesis,
    aSubsetOf0(xS,xT),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__725_01) ).

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

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

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

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

fof(c_0_7,plain,
    ! [X39,X40,X41,X42,X43] :
      ( ( aElementOf0(X41,X39)
        | ~ aSupremumOfIn0(X41,X40,X39)
        | ~ aSubsetOf0(X40,X39)
        | ~ aSet0(X39) )
      & ( aUpperBoundOfIn0(X41,X40,X39)
        | ~ aSupremumOfIn0(X41,X40,X39)
        | ~ aSubsetOf0(X40,X39)
        | ~ aSet0(X39) )
      & ( ~ aUpperBoundOfIn0(X42,X40,X39)
        | sdtlseqdt0(X41,X42)
        | ~ aSupremumOfIn0(X41,X40,X39)
        | ~ aSubsetOf0(X40,X39)
        | ~ aSet0(X39) )
      & ( aUpperBoundOfIn0(esk6_3(X39,X40,X43),X40,X39)
        | ~ aElementOf0(X43,X39)
        | ~ aUpperBoundOfIn0(X43,X40,X39)
        | aSupremumOfIn0(X43,X40,X39)
        | ~ aSubsetOf0(X40,X39)
        | ~ aSet0(X39) )
      & ( ~ sdtlseqdt0(X43,esk6_3(X39,X40,X43))
        | ~ aElementOf0(X43,X39)
        | ~ aUpperBoundOfIn0(X43,X40,X39)
        | aSupremumOfIn0(X43,X40,X39)
        | ~ aSubsetOf0(X40,X39)
        | ~ aSet0(X39) ) ),
    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)],[mDefSup])])])])])]) ).

cnf(c_0_8,plain,
    ( sdtlseqdt0(X4,X1)
    | ~ aUpperBoundOfIn0(X1,X2,X3)
    | ~ aSupremumOfIn0(X4,X2,X3)
    | ~ aSubsetOf0(X2,X3)
    | ~ aSet0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_9,hypothesis,
    aSupremumOfIn0(xv,xS,xT),
    inference(split_conjunct,[status(thm)],[m__744]) ).

cnf(c_0_10,hypothesis,
    aSubsetOf0(xS,xT),
    inference(split_conjunct,[status(thm)],[m__725_01]) ).

cnf(c_0_11,hypothesis,
    aSet0(xT),
    inference(split_conjunct,[status(thm)],[m__725]) ).

cnf(c_0_12,plain,
    ( aUpperBoundOfIn0(X1,X2,X3)
    | ~ aSupremumOfIn0(X1,X2,X3)
    | ~ aSubsetOf0(X2,X3)
    | ~ aSet0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,hypothesis,
    aSupremumOfIn0(xu,xS,xT),
    inference(split_conjunct,[status(thm)],[m__744]) ).

fof(c_0_14,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])])]) ).

cnf(c_0_15,plain,
    ( aElementOf0(X1,X2)
    | ~ aSupremumOfIn0(X1,X3,X2)
    | ~ aSubsetOf0(X3,X2)
    | ~ aSet0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_16,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_17,hypothesis,
    ( sdtlseqdt0(xv,X1)
    | ~ aUpperBoundOfIn0(X1,xS,xT) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11])]) ).

cnf(c_0_18,hypothesis,
    aUpperBoundOfIn0(xu,xS,xT),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10]),c_0_11])]) ).

cnf(c_0_19,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,hypothesis,
    aElementOf0(xv,xT),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_9]),c_0_10]),c_0_11])]) ).

cnf(c_0_21,hypothesis,
    aElementOf0(xu,xT),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_10]),c_0_11])]) ).

fof(c_0_22,negated_conjecture,
    xu != xv,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_23,plain,
    ( X1 = X2
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,hypothesis,
    sdtlseqdt0(xv,xu),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_25,hypothesis,
    aElement0(xv),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_11])]) ).

cnf(c_0_26,hypothesis,
    aElement0(xu),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_21]),c_0_11])]) ).

cnf(c_0_27,negated_conjecture,
    xu != xv,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_28,hypothesis,
    ( sdtlseqdt0(xu,X1)
    | ~ aUpperBoundOfIn0(X1,xS,xT) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_13]),c_0_10]),c_0_11])]) ).

cnf(c_0_29,hypothesis,
    aUpperBoundOfIn0(xv,xS,xT),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_9]),c_0_10]),c_0_11])]) ).

cnf(c_0_30,hypothesis,
    ~ sdtlseqdt0(xu,xv),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]),c_0_27]) ).

cnf(c_0_31,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT381+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n026.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Thu Aug 24 07:56:31 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.012000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.015000 s
%------------------------------------------------------------------------------