TSTP Solution File: RNG095+1 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : RNG095+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:15:43 EDT 2023

% Result   : Theorem 4.76s 1.19s
% Output   : CNFRefutation 4.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   81 (  20 unt;   0 def)
%            Number of atoms       :  295 (  65 equ)
%            Maximal formula atoms :   52 (   3 avg)
%            Number of connectives :  359 ( 145   ~; 153   |;  42   &)
%                                         (   3 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   4 con; 0-4 aty)
%            Number of variables   :  127 (   1 sgn;  61   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
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/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mDefIdeal) ).

fof(m__1205_03,hypothesis,
    ! [X1] :
      ( aElement0(X1)
     => aElementOf0(X1,sdtpldt1(xI,xJ)) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',m__1205_03) ).

fof(mAddZero,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mAddZero) ).

fof(mAddInvr,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtpldt0(X1,smndt0(X1)) = sz00
        & sz00 = sdtpldt0(smndt0(X1),X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mAddInvr) ).

fof(mIdeSum,axiom,
    ! [X1,X2] :
      ( ( aIdeal0(X1)
        & aIdeal0(X2) )
     => aIdeal0(sdtpldt1(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mIdeSum) ).

fof(mSortsC,axiom,
    aElement0(sz00),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mSortsC) ).

fof(mSortsU,axiom,
    ! [X1] :
      ( aElement0(X1)
     => aElement0(smndt0(X1)) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mSortsU) ).

fof(m__1205,hypothesis,
    ( aIdeal0(xI)
    & aIdeal0(xJ) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',m__1205) ).

fof(mMulUnit,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtasdt0(X1,sz10) = X1
        & X1 = sdtasdt0(sz10,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mMulUnit) ).

fof(mMulAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aElement0(X1)
        & aElement0(X2)
        & aElement0(X3) )
     => sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mMulAsso) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => aElement0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mSortsB_02) ).

fof(mDefSSum,axiom,
    ! [X1,X2] :
      ( ( aSet0(X1)
        & aSet0(X2) )
     => ! [X3] :
          ( X3 = sdtpldt1(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ? [X5,X6] :
                    ( aElementOf0(X5,X1)
                    & aElementOf0(X6,X2)
                    & sdtpldt0(X5,X6) = X4 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mDefSSum) ).

fof(mSortsC_01,axiom,
    aElement0(sz10),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mSortsC_01) ).

fof(mMulZero,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtasdt0(X1,sz00) = sz00
        & sz00 = sdtasdt0(sz00,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mMulZero) ).

fof(mEOfElem,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mEOfElem) ).

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/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',mAMDistr) ).

fof(m__,conjecture,
    ? [X1,X2] :
      ( aElementOf0(X1,xI)
      & aElementOf0(X2,xJ)
      & sdtpldt0(X1,X2) = sz10 ),
    file('/export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p',m__) ).

fof(c_0_17,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_18,hypothesis,
    ! [X75] :
      ( ~ aElement0(X75)
      | aElementOf0(X75,sdtpldt1(xI,xJ)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1205_03])]) ).

fof(c_0_19,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])])]) ).

fof(c_0_20,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])])]) ).

cnf(c_0_21,plain,
    ( aElementOf0(sdtpldt0(X3,X1),X2)
    | ~ aElementOf0(X1,X2)
    | ~ aElementOf0(X3,X2)
    | ~ aIdeal0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,hypothesis,
    ( aElementOf0(X1,sdtpldt1(xI,xJ))
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_23,plain,
    ! [X68,X69] :
      ( ~ aIdeal0(X68)
      | ~ aIdeal0(X69)
      | aIdeal0(sdtpldt1(X68,X69)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIdeSum])]) ).

cnf(c_0_24,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,plain,
    ( sz00 = sdtpldt0(smndt0(X1),X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,plain,
    aElement0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

fof(c_0_27,plain,
    ! [X7] :
      ( ~ aElement0(X7)
      | aElement0(smndt0(X7)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).

cnf(c_0_28,hypothesis,
    ( aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ))
    | ~ aIdeal0(sdtpldt1(xI,xJ))
    | ~ aElementOf0(X2,sdtpldt1(xI,xJ))
    | ~ aElement0(X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_29,plain,
    ( aIdeal0(sdtpldt1(X1,X2))
    | ~ aIdeal0(X1)
    | ~ aIdeal0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_30,hypothesis,
    aIdeal0(xJ),
    inference(split_conjunct,[status(thm)],[m__1205]) ).

cnf(c_0_31,hypothesis,
    aIdeal0(xI),
    inference(split_conjunct,[status(thm)],[m__1205]) ).

cnf(c_0_32,plain,
    ( smndt0(sz00) = sz00
    | ~ aElement0(smndt0(sz00)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).

cnf(c_0_33,plain,
    ( aElement0(smndt0(X1))
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

fof(c_0_34,plain,
    ! [X24] :
      ( ( sdtasdt0(X24,sz10) = X24
        | ~ aElement0(X24) )
      & ( X24 = sdtasdt0(sz10,X24)
        | ~ aElement0(X24) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).

fof(c_0_35,plain,
    ! [X21,X22,X23] :
      ( ~ aElement0(X21)
      | ~ aElement0(X22)
      | ~ aElement0(X23)
      | sdtasdt0(sdtasdt0(X21,X22),X23) = sdtasdt0(X21,sdtasdt0(X22,X23)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).

fof(c_0_36,plain,
    ! [X10,X11] :
      ( ~ aElement0(X10)
      | ~ aElement0(X11)
      | aElement0(sdtasdt0(X10,X11)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

fof(c_0_37,plain,
    ! [X38,X39,X40,X41,X44,X45,X46,X47,X49,X50] :
      ( ( aSet0(X40)
        | X40 != sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( aElementOf0(esk3_4(X38,X39,X40,X41),X38)
        | ~ aElementOf0(X41,X40)
        | X40 != sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( aElementOf0(esk4_4(X38,X39,X40,X41),X39)
        | ~ aElementOf0(X41,X40)
        | X40 != sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( sdtpldt0(esk3_4(X38,X39,X40,X41),esk4_4(X38,X39,X40,X41)) = X41
        | ~ aElementOf0(X41,X40)
        | X40 != sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( ~ aElementOf0(X45,X38)
        | ~ aElementOf0(X46,X39)
        | sdtpldt0(X45,X46) != X44
        | aElementOf0(X44,X40)
        | X40 != sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( ~ aElementOf0(esk5_3(X38,X39,X47),X47)
        | ~ aElementOf0(X49,X38)
        | ~ aElementOf0(X50,X39)
        | sdtpldt0(X49,X50) != esk5_3(X38,X39,X47)
        | ~ aSet0(X47)
        | X47 = sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( aElementOf0(esk6_3(X38,X39,X47),X38)
        | aElementOf0(esk5_3(X38,X39,X47),X47)
        | ~ aSet0(X47)
        | X47 = sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( aElementOf0(esk7_3(X38,X39,X47),X39)
        | aElementOf0(esk5_3(X38,X39,X47),X47)
        | ~ aSet0(X47)
        | X47 = sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( sdtpldt0(esk6_3(X38,X39,X47),esk7_3(X38,X39,X47)) = esk5_3(X38,X39,X47)
        | aElementOf0(esk5_3(X38,X39,X47),X47)
        | ~ aSet0(X47)
        | X47 = sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ 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)],[mDefSSum])])])])])]) ).

cnf(c_0_38,hypothesis,
    ( aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ))
    | ~ aElementOf0(X2,sdtpldt1(xI,xJ))
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).

cnf(c_0_39,plain,
    smndt0(sz00) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_26])]) ).

cnf(c_0_40,plain,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_41,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_42,plain,
    aElement0(sz10),
    inference(split_conjunct,[status(thm)],[mSortsC_01]) ).

cnf(c_0_43,plain,
    ( aElement0(sdtasdt0(X1,X2))
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_44,plain,
    ( X1 = sdtasdt0(sz10,X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_45,plain,
    ( aElementOf0(esk4_4(X1,X2,X3,X4),X2)
    | ~ aElementOf0(X4,X3)
    | X3 != sdtpldt1(X1,X2)
    | ~ aSet0(X1)
    | ~ aSet0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_46,hypothesis,
    ( aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ))
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(spm,[status(thm)],[c_0_38,c_0_22]) ).

cnf(c_0_47,plain,
    sdtpldt0(sz00,sz00) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_39]),c_0_26])]) ).

cnf(c_0_48,plain,
    ( aSet0(X1)
    | ~ aIdeal0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_49,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),c_0_43]) ).

cnf(c_0_50,plain,
    ( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_44]),c_0_42])]) ).

fof(c_0_51,plain,
    ! [X29] :
      ( ( sdtasdt0(X29,sz00) = sz00
        | ~ aElement0(X29) )
      & ( sz00 = sdtasdt0(sz00,X29)
        | ~ aElement0(X29) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).

fof(c_0_52,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_53,plain,
    ( aElementOf0(esk4_4(X1,X2,sdtpldt1(X1,X2),X3),X2)
    | ~ aElementOf0(X3,sdtpldt1(X1,X2))
    | ~ aSet0(X2)
    | ~ aSet0(X1) ),
    inference(er,[status(thm)],[c_0_45]) ).

cnf(c_0_54,hypothesis,
    aElementOf0(sz00,sdtpldt1(xI,xJ)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_26])]) ).

cnf(c_0_55,hypothesis,
    aSet0(xJ),
    inference(spm,[status(thm)],[c_0_48,c_0_30]) ).

cnf(c_0_56,hypothesis,
    aSet0(xI),
    inference(spm,[status(thm)],[c_0_48,c_0_31]) ).

fof(c_0_57,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_58,plain,
    ( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_42])]) ).

cnf(c_0_59,plain,
    ( sz00 = sdtasdt0(sz00,X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_60,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_61,hypothesis,
    aElementOf0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),sz00),xJ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_56])]) ).

cnf(c_0_62,plain,
    ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_63,plain,
    sdtasdt0(sz10,sz10) = sz10,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_58]),c_0_42])]) ).

cnf(c_0_64,plain,
    ( sdtasdt0(sz10,sz00) = sz00
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_59]),c_0_26])]) ).

cnf(c_0_65,hypothesis,
    aElement0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),sz00)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_55])]) ).

cnf(c_0_66,plain,
    ( sdtasdt0(sz10,sdtpldt0(sz10,X1)) = sdtpldt0(sz10,sdtasdt0(sz10,X1))
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_42])]) ).

cnf(c_0_67,hypothesis,
    sdtasdt0(sz10,sz00) = sz00,
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

fof(c_0_68,negated_conjecture,
    ~ ? [X1,X2] :
        ( aElementOf0(X1,xI)
        & aElementOf0(X2,xJ)
        & sdtpldt0(X1,X2) = sz10 ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_69,plain,
    ( sdtpldt0(esk3_4(X1,X2,X3,X4),esk4_4(X1,X2,X3,X4)) = X4
    | ~ aElementOf0(X4,X3)
    | X3 != sdtpldt1(X1,X2)
    | ~ aSet0(X1)
    | ~ aSet0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_70,plain,
    sdtpldt0(sz10,sz00) = sz10,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_24]),c_0_63]),c_0_67]),c_0_26]),c_0_42])]) ).

cnf(c_0_71,plain,
    ( aElementOf0(esk3_4(X1,X2,X3,X4),X1)
    | ~ aElementOf0(X4,X3)
    | X3 != sdtpldt1(X1,X2)
    | ~ aSet0(X1)
    | ~ aSet0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

fof(c_0_72,negated_conjecture,
    ! [X76,X77] :
      ( ~ aElementOf0(X76,xI)
      | ~ aElementOf0(X77,xJ)
      | sdtpldt0(X76,X77) != sz10 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])]) ).

cnf(c_0_73,plain,
    ( sdtpldt0(esk3_4(X1,X2,sdtpldt1(X1,X2),X3),esk4_4(X1,X2,sdtpldt1(X1,X2),X3)) = X3
    | ~ aElementOf0(X3,sdtpldt1(X1,X2))
    | ~ aSet0(X2)
    | ~ aSet0(X1) ),
    inference(er,[status(thm)],[c_0_69]) ).

cnf(c_0_74,hypothesis,
    aElementOf0(sz10,sdtpldt1(xI,xJ)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_70]),c_0_42]),c_0_26])]) ).

cnf(c_0_75,plain,
    ( aElementOf0(esk3_4(X1,X2,sdtpldt1(X1,X2),X3),X1)
    | ~ aElementOf0(X3,sdtpldt1(X1,X2))
    | ~ aSet0(X2)
    | ~ aSet0(X1) ),
    inference(er,[status(thm)],[c_0_71]) ).

cnf(c_0_76,negated_conjecture,
    ( ~ aElementOf0(X1,xI)
    | ~ aElementOf0(X2,xJ)
    | sdtpldt0(X1,X2) != sz10 ),
    inference(split_conjunct,[status(thm)],[c_0_72]) ).

cnf(c_0_77,hypothesis,
    ( sdtpldt0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),X1),esk4_4(xI,xJ,sdtpldt1(xI,xJ),X1)) = X1
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_22]),c_0_55]),c_0_56])]) ).

cnf(c_0_78,hypothesis,
    aElementOf0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),sz10),xJ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_74]),c_0_55]),c_0_56])]) ).

cnf(c_0_79,hypothesis,
    aElementOf0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),sz10),xI),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_74]),c_0_55]),c_0_56])]) ).

cnf(c_0_80,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77])]),c_0_78]),c_0_79]),c_0_42])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15  % Problem    : RNG095+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.16  % Command    : run_E %s %d THM
% 0.16/0.38  % Computer : n021.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit   : 2400
% 0.16/0.38  % WCLimit    : 300
% 0.16/0.38  % DateTime   : Mon Oct  2 19:45:59 EDT 2023
% 0.16/0.38  % CPUTime    : 
% 0.24/0.54  Running first-order model finding
% 0.24/0.54  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.VIusn3QXJc/E---3.1_7846.p
% 4.76/1.19  # Version: 3.1pre001
% 4.76/1.19  # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.76/1.19  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.76/1.19  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.76/1.19  # Starting new_bool_3 with 300s (1) cores
% 4.76/1.19  # Starting new_bool_1 with 300s (1) cores
% 4.76/1.19  # Starting sh5l with 300s (1) cores
% 4.76/1.19  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 7923 completed with status 0
% 4.76/1.19  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 4.76/1.19  # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.76/1.19  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.76/1.19  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.76/1.19  # No SInE strategy applied
% 4.76/1.19  # Search class: FGHSF-FFMM32-SFFFFFNN
% 4.76/1.19  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.76/1.19  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SA with 811s (1) cores
% 4.76/1.19  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.76/1.19  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 4.76/1.19  # Starting G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 4.76/1.19  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 4.76/1.19  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 7933 completed with status 0
% 4.76/1.19  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 4.76/1.19  # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.76/1.19  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.76/1.19  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.76/1.19  # No SInE strategy applied
% 4.76/1.19  # Search class: FGHSF-FFMM32-SFFFFFNN
% 4.76/1.19  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.76/1.19  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SA with 811s (1) cores
% 4.76/1.19  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.76/1.19  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 4.76/1.19  # Starting G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 4.76/1.19  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 4.76/1.19  # Preprocessing time       : 0.002 s
% 4.76/1.19  # Presaturation interreduction done
% 4.76/1.19  
% 4.76/1.19  # Proof found!
% 4.76/1.19  # SZS status Theorem
% 4.76/1.19  # SZS output start CNFRefutation
% See solution above
% 4.76/1.19  # Parsed axioms                        : 31
% 4.76/1.19  # Removed by relevancy pruning/SinE    : 0
% 4.76/1.19  # Initial clauses                      : 64
% 4.76/1.19  # Removed in clause preprocessing      : 2
% 4.76/1.19  # Initial clauses in saturation        : 62
% 4.76/1.19  # Processed clauses                    : 5110
% 4.76/1.19  # ...of these trivial                  : 119
% 4.76/1.19  # ...subsumed                          : 4086
% 4.76/1.19  # ...remaining for further processing  : 905
% 4.76/1.19  # Other redundant clauses eliminated   : 174
% 4.76/1.19  # Clauses deleted for lack of memory   : 0
% 4.76/1.19  # Backward-subsumed                    : 41
% 4.76/1.19  # Backward-rewritten                   : 87
% 4.76/1.19  # Generated clauses                    : 37119
% 4.76/1.19  # ...of the previous two non-redundant : 34730
% 4.76/1.19  # ...aggressively subsumed             : 0
% 4.76/1.19  # Contextual simplify-reflections      : 234
% 4.76/1.19  # Paramodulations                      : 36926
% 4.76/1.19  # Factorizations                       : 20
% 4.76/1.19  # NegExts                              : 0
% 4.76/1.19  # Equation resolutions                 : 174
% 4.76/1.19  # Total rewrite steps                  : 30768
% 4.76/1.19  # Propositional unsat checks           : 0
% 4.76/1.19  #    Propositional check models        : 0
% 4.76/1.19  #    Propositional check unsatisfiable : 0
% 4.76/1.19  #    Propositional clauses             : 0
% 4.76/1.19  #    Propositional clauses after purity: 0
% 4.76/1.19  #    Propositional unsat core size     : 0
% 4.76/1.19  #    Propositional preprocessing time  : 0.000
% 4.76/1.19  #    Propositional encoding time       : 0.000
% 4.76/1.19  #    Propositional solver time         : 0.000
% 4.76/1.19  #    Success case prop preproc time    : 0.000
% 4.76/1.19  #    Success case prop encoding time   : 0.000
% 4.76/1.19  #    Success case prop solver time     : 0.000
% 4.76/1.19  # Current number of processed clauses  : 706
% 4.76/1.19  #    Positive orientable unit clauses  : 86
% 4.76/1.19  #    Positive unorientable unit clauses: 0
% 4.76/1.19  #    Negative unit clauses             : 4
% 4.76/1.19  #    Non-unit-clauses                  : 616
% 4.76/1.19  # Current number of unprocessed clauses: 29618
% 4.76/1.19  # ...number of literals in the above   : 193663
% 4.76/1.19  # Current number of archived formulas  : 0
% 4.76/1.19  # Current number of archived clauses   : 190
% 4.76/1.19  # Clause-clause subsumption calls (NU) : 131960
% 4.76/1.19  # Rec. Clause-clause subsumption calls : 13496
% 4.76/1.19  # Non-unit clause-clause subsumptions  : 3115
% 4.76/1.19  # Unit Clause-clause subsumption calls : 1096
% 4.76/1.19  # Rewrite failures with RHS unbound    : 0
% 4.76/1.19  # BW rewrite match attempts            : 91
% 4.76/1.19  # BW rewrite match successes           : 25
% 4.76/1.19  # Condensation attempts                : 0
% 4.76/1.19  # Condensation successes               : 0
% 4.76/1.19  # Termbank termtop insertions          : 860568
% 4.76/1.19  
% 4.76/1.19  # -------------------------------------------------
% 4.76/1.19  # User time                : 0.516 s
% 4.76/1.19  # System time              : 0.018 s
% 4.76/1.19  # Total time               : 0.534 s
% 4.76/1.19  # Maximum resident set size: 1892 pages
% 4.76/1.19  
% 4.76/1.19  # -------------------------------------------------
% 4.76/1.19  # User time                : 2.784 s
% 4.76/1.19  # System time              : 0.117 s
% 4.76/1.19  # Total time               : 2.901 s
% 4.76/1.19  # Maximum resident set size: 1728 pages
% 4.76/1.19  % E---3.1 exiting
%------------------------------------------------------------------------------