TSTP Solution File: NUM541+2 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : NUM541+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 19:07:38 EDT 2023

% Result   : Theorem 0.20s 0.55s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   60 (   7 unt;   0 def)
%            Number of atoms       :  239 (  42 equ)
%            Maximal formula atoms :   50 (   3 avg)
%            Number of connectives :  286 ( 107   ~; 128   |;  36   &)
%                                         (   1 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :   49 (   0 sgn;  26   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__,conjecture,
    ( ( ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
        & aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
     => ( sdtlseqdt0(szszuzczcdt0(xm),xn)
        | aElementOf0(xm,slbdtrb0(xn))
        | xm = xn ) )
    & ( ( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
          & aElementOf0(xm,slbdtrb0(xn)) )
        | xm = xn )
     => ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
        | aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.3muj9ZyBcR/E---3.1_15662.p',m__) ).

fof(mLessTotal,axiom,
    ! [X1,X2] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X2,szNzAzT0) )
     => ( sdtlseqdt0(X1,X2)
        | sdtlseqdt0(szszuzczcdt0(X2),X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.3muj9ZyBcR/E---3.1_15662.p',mLessTotal) ).

fof(mSuccLess,axiom,
    ! [X1,X2] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X2,szNzAzT0) )
     => ( sdtlseqdt0(X1,X2)
      <=> sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.3muj9ZyBcR/E---3.1_15662.p',mSuccLess) ).

fof(m__1936,hypothesis,
    ( aElementOf0(xm,szNzAzT0)
    & aElementOf0(xn,szNzAzT0) ),
    file('/export/starexec/sandbox/tmp/tmp.3muj9ZyBcR/E---3.1_15662.p',m__1936) ).

fof(mLessASymm,axiom,
    ! [X1,X2] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X2,szNzAzT0) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox/tmp/tmp.3muj9ZyBcR/E---3.1_15662.p',mLessASymm) ).

fof(mLessTrans,axiom,
    ! [X1,X2,X3] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X2,szNzAzT0)
        & aElementOf0(X3,szNzAzT0) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X3) )
       => sdtlseqdt0(X1,X3) ) ),
    file('/export/starexec/sandbox/tmp/tmp.3muj9ZyBcR/E---3.1_15662.p',mLessTrans) ).

fof(mLessSucc,axiom,
    ! [X1] :
      ( aElementOf0(X1,szNzAzT0)
     => sdtlseqdt0(X1,szszuzczcdt0(X1)) ),
    file('/export/starexec/sandbox/tmp/tmp.3muj9ZyBcR/E---3.1_15662.p',mLessSucc) ).

fof(mSuccNum,axiom,
    ! [X1] :
      ( aElementOf0(X1,szNzAzT0)
     => ( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
        & szszuzczcdt0(X1) != sz00 ) ),
    file('/export/starexec/sandbox/tmp/tmp.3muj9ZyBcR/E---3.1_15662.p',mSuccNum) ).

fof(mNatNSucc,axiom,
    ! [X1] :
      ( aElementOf0(X1,szNzAzT0)
     => X1 != szszuzczcdt0(X1) ),
    file('/export/starexec/sandbox/tmp/tmp.3muj9ZyBcR/E---3.1_15662.p',mNatNSucc) ).

fof(mLessRefl,axiom,
    ! [X1] :
      ( aElementOf0(X1,szNzAzT0)
     => sdtlseqdt0(X1,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.3muj9ZyBcR/E---3.1_15662.p',mLessRefl) ).

fof(c_0_10,negated_conjecture,
    ~ ( ( ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
          & aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
       => ( sdtlseqdt0(szszuzczcdt0(xm),xn)
          | aElementOf0(xm,slbdtrb0(xn))
          | xm = xn ) )
      & ( ( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
            & aElementOf0(xm,slbdtrb0(xn)) )
          | xm = xn )
       => ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
          | aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_11,plain,
    ! [X18,X19] :
      ( ~ aElementOf0(X18,szNzAzT0)
      | ~ aElementOf0(X19,szNzAzT0)
      | sdtlseqdt0(X18,X19)
      | sdtlseqdt0(szszuzczcdt0(X19),X18) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessTotal])]) ).

fof(c_0_12,negated_conjecture,
    ( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
      | xm = xn
      | sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
    & ( aElementOf0(xm,slbdtrb0(xn))
      | xm = xn
      | sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
    & ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
      | sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
    & ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
      | sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
    & ( sdtlseqdt0(szszuzczcdt0(xm),xn)
      | xm = xn
      | aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
    & ( aElementOf0(xm,slbdtrb0(xn))
      | xm = xn
      | aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
    & ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
      | aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
    & ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
      | aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
    & ( sdtlseqdt0(szszuzczcdt0(xm),xn)
      | xm = xn
      | ~ sdtlseqdt0(szszuzczcdt0(xm),xn) )
    & ( aElementOf0(xm,slbdtrb0(xn))
      | xm = xn
      | ~ sdtlseqdt0(szszuzczcdt0(xm),xn) )
    & ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
      | ~ sdtlseqdt0(szszuzczcdt0(xm),xn) )
    & ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
      | ~ sdtlseqdt0(szszuzczcdt0(xm),xn) )
    & ( sdtlseqdt0(szszuzczcdt0(xm),xn)
      | xm = xn
      | ~ aElementOf0(xm,slbdtrb0(xn)) )
    & ( aElementOf0(xm,slbdtrb0(xn))
      | xm = xn
      | ~ aElementOf0(xm,slbdtrb0(xn)) )
    & ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
      | ~ aElementOf0(xm,slbdtrb0(xn)) )
    & ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
      | ~ aElementOf0(xm,slbdtrb0(xn)) )
    & ( sdtlseqdt0(szszuzczcdt0(xm),xn)
      | xm = xn
      | xm != xn )
    & ( aElementOf0(xm,slbdtrb0(xn))
      | xm = xn
      | xm != xn )
    & ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
      | xm != xn )
    & ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
      | xm != xn ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).

fof(c_0_13,plain,
    ! [X15,X16] :
      ( ( ~ sdtlseqdt0(X15,X16)
        | sdtlseqdt0(szszuzczcdt0(X15),szszuzczcdt0(X16))
        | ~ aElementOf0(X15,szNzAzT0)
        | ~ aElementOf0(X16,szNzAzT0) )
      & ( ~ sdtlseqdt0(szszuzczcdt0(X15),szszuzczcdt0(X16))
        | sdtlseqdt0(X15,X16)
        | ~ aElementOf0(X15,szNzAzT0)
        | ~ aElementOf0(X16,szNzAzT0) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccLess])])]) ).

cnf(c_0_14,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(szszuzczcdt0(X2),X1)
    | ~ aElementOf0(X1,szNzAzT0)
    | ~ aElementOf0(X2,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,hypothesis,
    aElementOf0(xm,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__1936]) ).

fof(c_0_16,plain,
    ! [X21,X22] :
      ( ~ aElementOf0(X21,szNzAzT0)
      | ~ aElementOf0(X22,szNzAzT0)
      | ~ sdtlseqdt0(X21,X22)
      | ~ sdtlseqdt0(X22,X21)
      | X21 = X22 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])]) ).

cnf(c_0_17,negated_conjecture,
    ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
    | ~ sdtlseqdt0(szszuzczcdt0(xm),xn) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
    | ~ sdtlseqdt0(X1,X2)
    | ~ aElementOf0(X1,szNzAzT0)
    | ~ aElementOf0(X2,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,hypothesis,
    aElementOf0(xn,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__1936]) ).

cnf(c_0_20,hypothesis,
    ( sdtlseqdt0(szszuzczcdt0(xm),X1)
    | sdtlseqdt0(X1,xm)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,plain,
    ( X1 = X2
    | ~ aElementOf0(X1,szNzAzT0)
    | ~ aElementOf0(X2,szNzAzT0)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    ( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
    | ~ sdtlseqdt0(xm,xn) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_15])]) ).

cnf(c_0_23,hypothesis,
    ( sdtlseqdt0(szszuzczcdt0(xm),xn)
    | sdtlseqdt0(xn,xm) ),
    inference(spm,[status(thm)],[c_0_20,c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
    | xm != xn ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_25,plain,
    ! [X23,X24,X25] :
      ( ~ aElementOf0(X23,szNzAzT0)
      | ~ aElementOf0(X24,szNzAzT0)
      | ~ aElementOf0(X25,szNzAzT0)
      | ~ sdtlseqdt0(X23,X24)
      | ~ sdtlseqdt0(X24,X25)
      | sdtlseqdt0(X23,X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessTrans])]) ).

cnf(c_0_26,hypothesis,
    ( sdtlseqdt0(szszuzczcdt0(xn),X1)
    | sdtlseqdt0(X1,xn)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_19]) ).

cnf(c_0_27,hypothesis,
    ( X1 = xn
    | ~ sdtlseqdt0(xn,X1)
    | ~ sdtlseqdt0(X1,xn)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(spm,[status(thm)],[c_0_21,c_0_19]) ).

cnf(c_0_28,negated_conjecture,
    ( sdtlseqdt0(xn,xm)
    | ~ sdtlseqdt0(xm,xn) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    ( xn != xm
    | ~ sdtlseqdt0(xm,xn) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_18]),c_0_19]),c_0_15])]) ).

cnf(c_0_30,plain,
    ( sdtlseqdt0(X1,X3)
    | ~ aElementOf0(X1,szNzAzT0)
    | ~ aElementOf0(X2,szNzAzT0)
    | ~ aElementOf0(X3,szNzAzT0)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_31,hypothesis,
    ( sdtlseqdt0(szszuzczcdt0(xn),xm)
    | sdtlseqdt0(xm,xn) ),
    inference(spm,[status(thm)],[c_0_26,c_0_15]) ).

cnf(c_0_32,hypothesis,
    ~ sdtlseqdt0(xm,xn),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_15])]),c_0_29]) ).

cnf(c_0_33,hypothesis,
    ( sdtlseqdt0(X1,xm)
    | ~ sdtlseqdt0(X2,xm)
    | ~ sdtlseqdt0(X1,X2)
    | ~ aElementOf0(X2,szNzAzT0)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(spm,[status(thm)],[c_0_30,c_0_15]) ).

cnf(c_0_34,hypothesis,
    sdtlseqdt0(szszuzczcdt0(xn),xm),
    inference(sr,[status(thm)],[c_0_31,c_0_32]) ).

fof(c_0_35,plain,
    ! [X17] :
      ( ~ aElementOf0(X17,szNzAzT0)
      | sdtlseqdt0(X17,szszuzczcdt0(X17)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessSucc])]) ).

cnf(c_0_36,hypothesis,
    ( sdtlseqdt0(X1,xm)
    | ~ sdtlseqdt0(X1,szszuzczcdt0(xn))
    | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_37,plain,
    ( sdtlseqdt0(X1,szszuzczcdt0(X1))
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_38,plain,
    ( sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
    | ~ aElementOf0(X1,szNzAzT0)
    | ~ aElementOf0(X2,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_39,negated_conjecture,
    ( sdtlseqdt0(szszuzczcdt0(xm),xn)
    | xm = xn
    | sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_40,hypothesis,
    ( sdtlseqdt0(xn,xm)
    | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_19])]) ).

cnf(c_0_41,negated_conjecture,
    ( xn = xm
    | sdtlseqdt0(szszuzczcdt0(xm),xn)
    | sdtlseqdt0(xm,xn) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_19]),c_0_15])]) ).

cnf(c_0_42,hypothesis,
    ( sdtlseqdt0(X1,xm)
    | ~ sdtlseqdt0(X1,xn)
    | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_19])]) ).

cnf(c_0_43,negated_conjecture,
    ( xn = xm
    | sdtlseqdt0(szszuzczcdt0(xm),xn) ),
    inference(sr,[status(thm)],[c_0_41,c_0_32]) ).

fof(c_0_44,plain,
    ! [X34] :
      ( ( aElementOf0(szszuzczcdt0(X34),szNzAzT0)
        | ~ aElementOf0(X34,szNzAzT0) )
      & ( szszuzczcdt0(X34) != sz00
        | ~ aElementOf0(X34,szNzAzT0) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccNum])])]) ).

cnf(c_0_45,negated_conjecture,
    ( xn = xm
    | sdtlseqdt0(szszuzczcdt0(xm),xm)
    | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
    | ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_46,plain,
    ( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_47,hypothesis,
    ( X1 = xm
    | ~ sdtlseqdt0(xm,X1)
    | ~ sdtlseqdt0(X1,xm)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(spm,[status(thm)],[c_0_21,c_0_15]) ).

cnf(c_0_48,negated_conjecture,
    ( xn = xm
    | sdtlseqdt0(szszuzczcdt0(xm),xm)
    | ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_19])]) ).

cnf(c_0_49,hypothesis,
    ( szszuzczcdt0(xm) = xm
    | ~ sdtlseqdt0(szszuzczcdt0(xm),xm)
    | ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_37]),c_0_15])]) ).

cnf(c_0_50,negated_conjecture,
    ( xn = xm
    | sdtlseqdt0(szszuzczcdt0(xm),xm) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_46]),c_0_15])]) ).

fof(c_0_51,plain,
    ! [X14] :
      ( ~ aElementOf0(X14,szNzAzT0)
      | X14 != szszuzczcdt0(X14) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNatNSucc])]) ).

cnf(c_0_52,hypothesis,
    ( szszuzczcdt0(xm) = xm
    | xn = xm
    | ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_53,plain,
    ( ~ aElementOf0(X1,szNzAzT0)
    | X1 != szszuzczcdt0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_54,hypothesis,
    ( szszuzczcdt0(xm) = xm
    | xn = xm ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_46]),c_0_15])]) ).

cnf(c_0_55,hypothesis,
    xn = xm,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_15])]) ).

fof(c_0_56,plain,
    ! [X20] :
      ( ~ aElementOf0(X20,szNzAzT0)
      | sdtlseqdt0(X20,X20) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessRefl])]) ).

cnf(c_0_57,hypothesis,
    ~ sdtlseqdt0(xm,xm),
    inference(rw,[status(thm)],[c_0_32,c_0_55]) ).

cnf(c_0_58,plain,
    ( sdtlseqdt0(X1,X1)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_59,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NUM541+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 2400
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Oct  2 15:18:21 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.50  Running first-order model finding
% 0.20/0.50  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.3muj9ZyBcR/E---3.1_15662.p
% 0.20/0.55  # Version: 3.1pre001
% 0.20/0.55  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.55  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.55  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.55  # Starting sh5l with 300s (1) cores
% 0.20/0.55  # new_bool_3 with pid 15740 completed with status 0
% 0.20/0.55  # Result found by new_bool_3
% 0.20/0.55  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.55  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.55  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.55  # Search class: FGHSF-FFMM21-MFFFFFNN
% 0.20/0.55  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.55  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.20/0.55  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 15743 completed with status 0
% 0.20/0.55  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.20/0.55  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.55  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.55  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.55  # Search class: FGHSF-FFMM21-MFFFFFNN
% 0.20/0.55  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.55  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.20/0.55  # Preprocessing time       : 0.002 s
% 0.20/0.55  # Presaturation interreduction done
% 0.20/0.55  
% 0.20/0.55  # Proof found!
% 0.20/0.55  # SZS status Theorem
% 0.20/0.55  # SZS output start CNFRefutation
% See solution above
% 0.20/0.55  # Parsed axioms                        : 54
% 0.20/0.55  # Removed by relevancy pruning/SinE    : 13
% 0.20/0.55  # Initial clauses                      : 79
% 0.20/0.55  # Removed in clause preprocessing      : 10
% 0.20/0.55  # Initial clauses in saturation        : 69
% 0.20/0.55  # Processed clauses                    : 324
% 0.20/0.55  # ...of these trivial                  : 3
% 0.20/0.55  # ...subsumed                          : 57
% 0.20/0.55  # ...remaining for further processing  : 264
% 0.20/0.55  # Other redundant clauses eliminated   : 9
% 0.20/0.55  # Clauses deleted for lack of memory   : 0
% 0.20/0.55  # Backward-subsumed                    : 17
% 0.20/0.55  # Backward-rewritten                   : 53
% 0.20/0.55  # Generated clauses                    : 502
% 0.20/0.55  # ...of the previous two non-redundant : 464
% 0.20/0.55  # ...aggressively subsumed             : 0
% 0.20/0.55  # Contextual simplify-reflections      : 23
% 0.20/0.55  # Paramodulations                      : 484
% 0.20/0.55  # Factorizations                       : 0
% 0.20/0.55  # NegExts                              : 0
% 0.20/0.55  # Equation resolutions                 : 10
% 0.20/0.55  # Total rewrite steps                  : 351
% 0.20/0.55  # Propositional unsat checks           : 0
% 0.20/0.55  #    Propositional check models        : 0
% 0.20/0.55  #    Propositional check unsatisfiable : 0
% 0.20/0.55  #    Propositional clauses             : 0
% 0.20/0.55  #    Propositional clauses after purity: 0
% 0.20/0.55  #    Propositional unsat core size     : 0
% 0.20/0.55  #    Propositional preprocessing time  : 0.000
% 0.20/0.55  #    Propositional encoding time       : 0.000
% 0.20/0.55  #    Propositional solver time         : 0.000
% 0.20/0.55  #    Success case prop preproc time    : 0.000
% 0.20/0.55  #    Success case prop encoding time   : 0.000
% 0.20/0.55  #    Success case prop solver time     : 0.000
% 0.20/0.55  # Current number of processed clauses  : 109
% 0.20/0.55  #    Positive orientable unit clauses  : 13
% 0.20/0.55  #    Positive unorientable unit clauses: 0
% 0.20/0.55  #    Negative unit clauses             : 5
% 0.20/0.55  #    Non-unit-clauses                  : 91
% 0.20/0.55  # Current number of unprocessed clauses: 265
% 0.20/0.55  # ...number of literals in the above   : 1065
% 0.20/0.55  # Current number of archived formulas  : 0
% 0.20/0.55  # Current number of archived clauses   : 147
% 0.20/0.55  # Clause-clause subsumption calls (NU) : 3390
% 0.20/0.55  # Rec. Clause-clause subsumption calls : 1476
% 0.20/0.55  # Non-unit clause-clause subsumptions  : 86
% 0.20/0.55  # Unit Clause-clause subsumption calls : 140
% 0.20/0.55  # Rewrite failures with RHS unbound    : 0
% 0.20/0.55  # BW rewrite match attempts            : 4
% 0.20/0.55  # BW rewrite match successes           : 4
% 0.20/0.55  # Condensation attempts                : 0
% 0.20/0.55  # Condensation successes               : 0
% 0.20/0.55  # Termbank termtop insertions          : 12481
% 0.20/0.55  
% 0.20/0.55  # -------------------------------------------------
% 0.20/0.55  # User time                : 0.031 s
% 0.20/0.55  # System time              : 0.001 s
% 0.20/0.55  # Total time               : 0.032 s
% 0.20/0.55  # Maximum resident set size: 2016 pages
% 0.20/0.55  
% 0.20/0.55  # -------------------------------------------------
% 0.20/0.55  # User time                : 0.034 s
% 0.20/0.55  # System time              : 0.002 s
% 0.20/0.55  # Total time               : 0.036 s
% 0.20/0.55  # Maximum resident set size: 1732 pages
% 0.20/0.55  % E---3.1 exiting
%------------------------------------------------------------------------------