TSTP Solution File: RNG096+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG096+1 : 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 : 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 : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 13:49:06 EDT 2023

% Result   : Theorem 0.55s 0.73s
% Output   : CNFRefutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  129 (  34 unt;  30 typ;   0 def)
%            Number of atoms       :  279 (  51 equ)
%            Maximal formula atoms :   29 (   2 avg)
%            Number of connectives :  326 ( 146   ~; 135   |;  29   &)
%                                         (   1 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   44 (  21   >;  23   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   25 (  25 usr;   9 con; 0-4 aty)
%            Number of variables   :   87 (   0 sgn;  49   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aElement0: $i > $o ).

tff(decl_23,type,
    sz00: $i ).

tff(decl_24,type,
    sz10: $i ).

tff(decl_25,type,
    smndt0: $i > $i ).

tff(decl_26,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_27,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(decl_28,type,
    aSet0: $i > $o ).

tff(decl_29,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(decl_30,type,
    sdtpldt1: ( $i * $i ) > $i ).

tff(decl_31,type,
    sdtasasdt0: ( $i * $i ) > $i ).

tff(decl_32,type,
    aIdeal0: $i > $o ).

tff(decl_33,type,
    sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).

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

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

tff(decl_36,type,
    xx: $i ).

tff(decl_37,type,
    xy: $i ).

tff(decl_38,type,
    xa: $i ).

tff(decl_39,type,
    xb: $i ).

tff(decl_40,type,
    xw: $i ).

tff(decl_41,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_42,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_43,type,
    esk3_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk4_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_47,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk9_1: $i > $i ).

tff(decl_50,type,
    esk10_1: $i > $i ).

tff(decl_51,type,
    esk11_1: $i > $i ).

fof(mDefIdeal,axiom,
    ! [X1] :
      ( aIdeal0(X1)
    <=> ( aSet0(X1)
        & ! [X2] :
            ( aElementOf0(X2,X1)
           => ( ! [X3] :
                  ( aElementOf0(X3,X1)
                 => aElementOf0(sdtpldt0(X2,X3),X1) )
              & ! [X3] :
                  ( aElement0(X3)
                 => aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).

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

fof(m__1205,hypothesis,
    ( aIdeal0(xI)
    & aIdeal0(xJ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1205) ).

fof(mAddAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aElement0(X1)
        & aElement0(X2)
        & aElement0(X3) )
     => sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).

fof(m__1294,hypothesis,
    ( aElementOf0(xa,xI)
    & aElementOf0(xb,xJ)
    & sdtpldt0(xa,xb) = sz10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1294) ).

fof(mAddInvr,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtpldt0(X1,smndt0(X1)) = sz00
        & sz00 = sdtpldt0(smndt0(X1),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).

fof(mSortsU,axiom,
    ! [X1] :
      ( aElement0(X1)
     => aElement0(smndt0(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).

fof(mAddZero,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).

fof(mAddComm,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

fof(mSortsC,axiom,
    aElement0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

fof(mSortsB,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => aElement0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

fof(mSortsC_01,axiom,
    aElement0(sz10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).

fof(m__,conjecture,
    aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(m__1319,hypothesis,
    xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1319) ).

fof(mMulMnOne,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
        & smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).

fof(m__1217,hypothesis,
    ( aElement0(xx)
    & aElement0(xy) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1217) ).

fof(mMulComm,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).

fof(mAMDistr,axiom,
    ! [X1,X2,X3] :
      ( ( aElement0(X1)
        & aElement0(X2)
        & aElement0(X3) )
     => ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
        & sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => aElement0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

fof(c_0_19,plain,
    ! [X60,X61,X62,X63,X64] :
      ( ( aSet0(X60)
        | ~ aIdeal0(X60) )
      & ( ~ aElementOf0(X62,X60)
        | aElementOf0(sdtpldt0(X61,X62),X60)
        | ~ aElementOf0(X61,X60)
        | ~ aIdeal0(X60) )
      & ( ~ aElement0(X63)
        | aElementOf0(sdtasdt0(X63,X61),X60)
        | ~ aElementOf0(X61,X60)
        | ~ aIdeal0(X60) )
      & ( aElementOf0(esk9_1(X64),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( aElement0(esk11_1(X64))
        | aElementOf0(esk10_1(X64),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
        | aElementOf0(esk10_1(X64),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( aElement0(esk11_1(X64))
        | ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
        | ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) ) ),
    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)],[mDefIdeal])])])])])]) ).

fof(c_0_20,plain,
    ! [X32,X33] :
      ( ~ aSet0(X32)
      | ~ aElementOf0(X33,X32)
      | aElement0(X33) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).

cnf(c_0_21,plain,
    ( aSet0(X1)
    | ~ aIdeal0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_22,hypothesis,
    aIdeal0(xJ),
    inference(split_conjunct,[status(thm)],[m__1205]) ).

cnf(c_0_23,hypothesis,
    aIdeal0(xI),
    inference(split_conjunct,[status(thm)],[m__1205]) ).

fof(c_0_24,plain,
    ! [X14,X15,X16] :
      ( ~ aElement0(X14)
      | ~ aElement0(X15)
      | ~ aElement0(X16)
      | sdtpldt0(sdtpldt0(X14,X15),X16) = sdtpldt0(X14,sdtpldt0(X15,X16)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).

cnf(c_0_25,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,hypothesis,
    aElementOf0(xb,xJ),
    inference(split_conjunct,[status(thm)],[m__1294]) ).

cnf(c_0_27,hypothesis,
    aSet0(xJ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,hypothesis,
    aElementOf0(xa,xI),
    inference(split_conjunct,[status(thm)],[m__1294]) ).

cnf(c_0_29,hypothesis,
    aSet0(xI),
    inference(spm,[status(thm)],[c_0_21,c_0_23]) ).

fof(c_0_30,plain,
    ! [X18] :
      ( ( sdtpldt0(X18,smndt0(X18)) = sz00
        | ~ aElement0(X18) )
      & ( sz00 = sdtpldt0(smndt0(X18),X18)
        | ~ aElement0(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).

fof(c_0_31,plain,
    ! [X7] :
      ( ~ aElement0(X7)
      | aElement0(smndt0(X7)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).

cnf(c_0_32,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_33,hypothesis,
    sdtpldt0(xa,xb) = sz10,
    inference(split_conjunct,[status(thm)],[m__1294]) ).

cnf(c_0_34,hypothesis,
    aElement0(xb),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).

cnf(c_0_35,hypothesis,
    aElement0(xa),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_28]),c_0_29])]) ).

fof(c_0_36,plain,
    ! [X17] :
      ( ( sdtpldt0(X17,sz00) = X17
        | ~ aElement0(X17) )
      & ( X17 = sdtpldt0(sz00,X17)
        | ~ aElement0(X17) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).

cnf(c_0_37,plain,
    ( sz00 = sdtpldt0(smndt0(X1),X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_38,plain,
    ( aElement0(smndt0(X1))
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_39,plain,
    ! [X12,X13] :
      ( ~ aElement0(X12)
      | ~ aElement0(X13)
      | sdtpldt0(X12,X13) = sdtpldt0(X13,X12) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

cnf(c_0_40,hypothesis,
    ( sdtpldt0(xa,sdtpldt0(xb,X1)) = sdtpldt0(sz10,X1)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35])]) ).

cnf(c_0_41,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_42,plain,
    aElement0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

fof(c_0_43,plain,
    ! [X8,X9] :
      ( ~ aElement0(X8)
      | ~ aElement0(X9)
      | aElement0(sdtpldt0(X8,X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).

cnf(c_0_44,plain,
    ( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_38]) ).

cnf(c_0_45,plain,
    ( sdtpldt0(X1,smndt0(X1)) = sz00
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_46,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_47,hypothesis,
    sdtpldt0(sz10,sz00) = sz10,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_33]),c_0_42]),c_0_34])]) ).

cnf(c_0_48,plain,
    aElement0(sz10),
    inference(split_conjunct,[status(thm)],[mSortsC_01]) ).

cnf(c_0_49,plain,
    ( aElement0(sdtpldt0(X1,X2))
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_50,hypothesis,
    sdtpldt0(smndt0(xa),sz10) = sdtpldt0(sz00,xb),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_33]),c_0_34]),c_0_35])]) ).

fof(c_0_51,negated_conjecture,
    ~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_52,plain,
    ( sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_45]),c_0_38]) ).

cnf(c_0_53,hypothesis,
    sdtpldt0(sz00,sz10) = sz10,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42]),c_0_48])]) ).

cnf(c_0_54,hypothesis,
    ( aElement0(sdtpldt0(sz00,xb))
    | ~ aElement0(smndt0(xa)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_48])]) ).

cnf(c_0_55,negated_conjecture,
    ~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_56,hypothesis,
    xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
    inference(split_conjunct,[status(thm)],[m__1319]) ).

cnf(c_0_57,hypothesis,
    sdtpldt0(xa,sdtpldt0(sz00,xb)) = sz10,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_50]),c_0_53]),c_0_48]),c_0_35])]) ).

cnf(c_0_58,hypothesis,
    aElement0(sdtpldt0(sz00,xb)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_38]),c_0_35])]) ).

cnf(c_0_59,negated_conjecture,
    ~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_60,hypothesis,
    sdtpldt0(sz00,sdtpldt0(sz00,xb)) = sdtpldt0(sz00,xb),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_57]),c_0_50]),c_0_58]),c_0_35])]) ).

cnf(c_0_61,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_62,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),xI)
    | ~ aElement0(sdtasdt0(xx,xb))
    | ~ aElement0(sdtasdt0(xy,xa))
    | ~ aElement0(smndt0(xx)) ),
    inference(spm,[status(thm)],[c_0_59,c_0_32]) ).

cnf(c_0_63,plain,
    ( aElementOf0(sdtpldt0(X3,X1),X2)
    | ~ aElementOf0(X1,X2)
    | ~ aElementOf0(X3,X2)
    | ~ aIdeal0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_64,plain,
    ! [X28] :
      ( ( sdtasdt0(smndt0(sz10),X28) = smndt0(X28)
        | ~ aElement0(X28) )
      & ( smndt0(X28) = sdtasdt0(X28,smndt0(sz10))
        | ~ aElement0(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])]) ).

cnf(c_0_65,hypothesis,
    ( sdtpldt0(sz10,smndt0(xa)) = sdtpldt0(sz00,xb)
    | ~ aElement0(smndt0(xa)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_50]),c_0_48])]) ).

cnf(c_0_66,hypothesis,
    sdtpldt0(sz00,xb) = xb,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_34])]) ).

cnf(c_0_67,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(sdtasdt0(xx,xb),smndt0(xx)),xI)
    | ~ aElementOf0(sdtasdt0(xy,xa),xI)
    | ~ aElement0(sdtasdt0(xx,xb))
    | ~ aElement0(sdtasdt0(xy,xa))
    | ~ aElement0(smndt0(xx)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_23])]) ).

cnf(c_0_68,plain,
    ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_69,hypothesis,
    aElement0(xx),
    inference(split_conjunct,[status(thm)],[m__1217]) ).

cnf(c_0_70,hypothesis,
    ( sdtpldt0(sz10,smndt0(xa)) = xb
    | ~ aElement0(smndt0(xa)) ),
    inference(rw,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_71,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(sdtasdt0(xx,xb),sdtasdt0(smndt0(sz10),xx)),xI)
    | ~ aElementOf0(sdtasdt0(xy,xa),xI)
    | ~ aElement0(sdtasdt0(smndt0(sz10),xx))
    | ~ aElement0(sdtasdt0(xx,xb))
    | ~ aElement0(sdtasdt0(xy,xa)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]) ).

fof(c_0_72,plain,
    ! [X19,X20] :
      ( ~ aElement0(X19)
      | ~ aElement0(X20)
      | sdtasdt0(X19,X20) = sdtasdt0(X20,X19) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).

cnf(c_0_73,hypothesis,
    ( sdtpldt0(sz00,smndt0(xa)) = sdtpldt0(smndt0(sz10),xb)
    | ~ aElement0(smndt0(xa)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_70]),c_0_48])]) ).

cnf(c_0_74,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(sdtasdt0(smndt0(sz10),xx),sdtasdt0(xx,xb)),xI)
    | ~ aElementOf0(sdtasdt0(xy,xa),xI)
    | ~ aElement0(sdtasdt0(smndt0(sz10),xx))
    | ~ aElement0(sdtasdt0(xx,xb))
    | ~ aElement0(sdtasdt0(xy,xa)) ),
    inference(spm,[status(thm)],[c_0_71,c_0_46]) ).

cnf(c_0_75,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_72]) ).

fof(c_0_76,plain,
    ! [X25,X26,X27] :
      ( ( sdtasdt0(X25,sdtpldt0(X26,X27)) = sdtpldt0(sdtasdt0(X25,X26),sdtasdt0(X25,X27))
        | ~ aElement0(X25)
        | ~ aElement0(X26)
        | ~ aElement0(X27) )
      & ( sdtasdt0(sdtpldt0(X26,X27),X25) = sdtpldt0(sdtasdt0(X26,X25),sdtasdt0(X27,X25))
        | ~ aElement0(X25)
        | ~ aElement0(X26)
        | ~ aElement0(X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).

cnf(c_0_77,hypothesis,
    ( smndt0(xa) = sdtpldt0(smndt0(sz10),xb)
    | ~ aElement0(smndt0(xa)) ),
    inference(spm,[status(thm)],[c_0_61,c_0_73]) ).

cnf(c_0_78,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(sdtasdt0(smndt0(sz10),xx),sdtasdt0(xb,xx)),xI)
    | ~ aElementOf0(sdtasdt0(xy,xa),xI)
    | ~ aElement0(sdtasdt0(smndt0(sz10),xx))
    | ~ aElement0(sdtasdt0(xb,xx))
    | ~ aElement0(sdtasdt0(xy,xa)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_34]),c_0_69])]) ).

cnf(c_0_79,plain,
    ( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
    | ~ aElement0(X3)
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

cnf(c_0_80,plain,
    ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_81,hypothesis,
    smndt0(xa) = sdtpldt0(smndt0(sz10),xb),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_38]),c_0_35])]) ).

cnf(c_0_82,negated_conjecture,
    ( ~ aElementOf0(sdtasdt0(sdtpldt0(smndt0(sz10),xb),xx),xI)
    | ~ aElementOf0(sdtasdt0(xy,xa),xI)
    | ~ aElement0(sdtasdt0(smndt0(sz10),xx))
    | ~ aElement0(sdtasdt0(xb,xx))
    | ~ aElement0(sdtasdt0(xy,xa))
    | ~ aElement0(smndt0(sz10)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_69]),c_0_34])]) ).

cnf(c_0_83,hypothesis,
    sdtpldt0(smndt0(sz10),xb) = sdtasdt0(xa,smndt0(sz10)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_35])]) ).

cnf(c_0_84,plain,
    ( aElementOf0(sdtasdt0(X1,X2),X3)
    | ~ aElement0(X1)
    | ~ aElementOf0(X2,X3)
    | ~ aIdeal0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_85,hypothesis,
    aElement0(sdtpldt0(smndt0(sz10),xb)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_81]),c_0_35])]) ).

cnf(c_0_86,negated_conjecture,
    ( ~ aElementOf0(sdtasdt0(sdtasdt0(xa,smndt0(sz10)),xx),xI)
    | ~ aElementOf0(sdtasdt0(xy,xa),xI)
    | ~ aElement0(sdtasdt0(smndt0(sz10),xx))
    | ~ aElement0(sdtasdt0(xb,xx))
    | ~ aElement0(sdtasdt0(xy,xa))
    | ~ aElement0(smndt0(sz10)) ),
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

cnf(c_0_87,plain,
    ( aElementOf0(sdtasdt0(X1,X2),X3)
    | ~ aIdeal0(X3)
    | ~ aElementOf0(X1,X3)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(spm,[status(thm)],[c_0_84,c_0_75]) ).

cnf(c_0_88,hypothesis,
    aElement0(sdtasdt0(xa,smndt0(sz10))),
    inference(rw,[status(thm)],[c_0_85,c_0_83]) ).

fof(c_0_89,plain,
    ! [X10,X11] :
      ( ~ aElement0(X10)
      | ~ aElement0(X11)
      | aElement0(sdtasdt0(X10,X11)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

cnf(c_0_90,negated_conjecture,
    ( ~ aElementOf0(sdtasdt0(xa,smndt0(sz10)),xI)
    | ~ aElementOf0(sdtasdt0(xy,xa),xI)
    | ~ aElement0(sdtasdt0(smndt0(sz10),xx))
    | ~ aElement0(sdtasdt0(xb,xx))
    | ~ aElement0(sdtasdt0(xy,xa))
    | ~ aElement0(smndt0(sz10)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_23]),c_0_69]),c_0_88])]) ).

cnf(c_0_91,plain,
    ( aElement0(sdtasdt0(X1,X2))
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_89]) ).

cnf(c_0_92,negated_conjecture,
    ( ~ aElementOf0(sdtasdt0(xa,smndt0(sz10)),xI)
    | ~ aElementOf0(sdtasdt0(xy,xa),xI)
    | ~ aElement0(sdtasdt0(xb,xx))
    | ~ aElement0(sdtasdt0(xy,xa))
    | ~ aElement0(smndt0(sz10)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_69])]) ).

cnf(c_0_93,negated_conjecture,
    ( ~ aElementOf0(sdtasdt0(xa,smndt0(sz10)),xI)
    | ~ aElementOf0(sdtasdt0(xy,xa),xI)
    | ~ aElement0(sdtasdt0(xy,xa))
    | ~ aElement0(smndt0(sz10)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_91]),c_0_69]),c_0_34])]) ).

cnf(c_0_94,negated_conjecture,
    ( ~ aElementOf0(sdtasdt0(xy,xa),xI)
    | ~ aElement0(sdtasdt0(xy,xa))
    | ~ aElement0(smndt0(sz10)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_87]),c_0_23]),c_0_28]),c_0_35])]) ).

cnf(c_0_95,hypothesis,
    aElement0(xy),
    inference(split_conjunct,[status(thm)],[m__1217]) ).

cnf(c_0_96,negated_conjecture,
    ( ~ aElement0(sdtasdt0(xy,xa))
    | ~ aElement0(smndt0(sz10)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_84]),c_0_23]),c_0_28]),c_0_95])]) ).

cnf(c_0_97,negated_conjecture,
    ~ aElement0(sdtasdt0(xy,xa)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_38]),c_0_48])]) ).

cnf(c_0_98,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_91]),c_0_35]),c_0_95])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : RNG096+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun Aug 27 02:39:12 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.55/0.73  % Version  : CSE_E---1.5
% 0.55/0.73  % Problem  : theBenchmark.p
% 0.55/0.73  % Proof found
% 0.55/0.73  % SZS status Theorem for theBenchmark.p
% 0.55/0.73  % SZS output start Proof
% See solution above
% 0.55/0.74  % Total time : 0.149000 s
% 0.55/0.74  % SZS output end Proof
% 0.55/0.74  % Total time : 0.153000 s
%------------------------------------------------------------------------------