TSTP Solution File: SEU281+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SEU281+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% 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 : Sat May  4 09:31:10 EDT 2024

% Result   : Theorem 0.17s 0.55s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   67 (   5 unt;   0 def)
%            Number of atoms       :  429 ( 199 equ)
%            Maximal formula atoms :  198 (   6 avg)
%            Number of connectives :  557 ( 195   ~; 283   |;  74   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   68 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;   2 con; 0-3 aty)
%            Number of variables   :  158 (   1 sgn  22   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(s1_tarski__e16_22__wellord2__2,axiom,
    ! [X1,X2] :
      ( ! [X3,X4,X5] :
          ( ( X3 = X4
            & ? [X6,X7] :
                ( ordered_pair(X6,X7) = X4
                & in(X6,X1)
                & X7 = singleton(X6) )
            & X3 = X5
            & ? [X8,X9] :
                ( ordered_pair(X8,X9) = X5
                & in(X8,X1)
                & X9 = singleton(X8) ) )
         => X4 = X5 )
     => ? [X3] :
        ! [X4] :
          ( in(X4,X3)
        <=> ? [X5] :
              ( in(X5,cartesian_product2(X1,X2))
              & X5 = X4
              & ? [X10,X11] :
                  ( ordered_pair(X10,X11) = X4
                  & in(X10,X1)
                  & X11 = singleton(X10) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bfX0Z7QPAh/E---3.1_24002.p',s1_tarski__e16_22__wellord2__2) ).

fof(s1_xboole_0__e16_22__wellord2__1,conjecture,
    ! [X1,X2] :
    ? [X3] :
    ! [X4] :
      ( in(X4,X3)
    <=> ( in(X4,cartesian_product2(X1,X2))
        & ? [X5,X6] :
            ( ordered_pair(X5,X6) = X4
            & in(X5,X1)
            & X6 = singleton(X5) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bfX0Z7QPAh/E---3.1_24002.p',s1_xboole_0__e16_22__wellord2__1) ).

fof(c_0_2,plain,
    ! [X32,X40,X42,X46,X47,X48,X49] :
      ( ( in(esk18_3(X32,X40,X42),cartesian_product2(X32,X40))
        | ~ in(X42,esk17_2(X32,X40))
        | esk10_1(X32) = esk11_1(X32) )
      & ( esk18_3(X32,X40,X42) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | esk10_1(X32) = esk11_1(X32) )
      & ( ordered_pair(esk19_3(X32,X40,X42),esk20_3(X32,X40,X42)) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | esk10_1(X32) = esk11_1(X32) )
      & ( in(esk19_3(X32,X40,X42),X32)
        | ~ in(X42,esk17_2(X32,X40))
        | esk10_1(X32) = esk11_1(X32) )
      & ( esk20_3(X32,X40,X42) = singleton(esk19_3(X32,X40,X42))
        | ~ in(X42,esk17_2(X32,X40))
        | esk10_1(X32) = esk11_1(X32) )
      & ( ~ in(X47,cartesian_product2(X32,X40))
        | X47 != X46
        | ordered_pair(X48,X49) != X46
        | ~ in(X48,X32)
        | X49 != singleton(X48)
        | in(X46,esk17_2(X32,X40))
        | esk10_1(X32) = esk11_1(X32) )
      & ( in(esk18_3(X32,X40,X42),cartesian_product2(X32,X40))
        | ~ in(X42,esk17_2(X32,X40))
        | ordered_pair(esk13_1(X32),esk14_1(X32)) = esk11_1(X32) )
      & ( esk18_3(X32,X40,X42) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | ordered_pair(esk13_1(X32),esk14_1(X32)) = esk11_1(X32) )
      & ( ordered_pair(esk19_3(X32,X40,X42),esk20_3(X32,X40,X42)) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | ordered_pair(esk13_1(X32),esk14_1(X32)) = esk11_1(X32) )
      & ( in(esk19_3(X32,X40,X42),X32)
        | ~ in(X42,esk17_2(X32,X40))
        | ordered_pair(esk13_1(X32),esk14_1(X32)) = esk11_1(X32) )
      & ( esk20_3(X32,X40,X42) = singleton(esk19_3(X32,X40,X42))
        | ~ in(X42,esk17_2(X32,X40))
        | ordered_pair(esk13_1(X32),esk14_1(X32)) = esk11_1(X32) )
      & ( ~ in(X47,cartesian_product2(X32,X40))
        | X47 != X46
        | ordered_pair(X48,X49) != X46
        | ~ in(X48,X32)
        | X49 != singleton(X48)
        | in(X46,esk17_2(X32,X40))
        | ordered_pair(esk13_1(X32),esk14_1(X32)) = esk11_1(X32) )
      & ( in(esk18_3(X32,X40,X42),cartesian_product2(X32,X40))
        | ~ in(X42,esk17_2(X32,X40))
        | in(esk13_1(X32),X32) )
      & ( esk18_3(X32,X40,X42) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | in(esk13_1(X32),X32) )
      & ( ordered_pair(esk19_3(X32,X40,X42),esk20_3(X32,X40,X42)) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | in(esk13_1(X32),X32) )
      & ( in(esk19_3(X32,X40,X42),X32)
        | ~ in(X42,esk17_2(X32,X40))
        | in(esk13_1(X32),X32) )
      & ( esk20_3(X32,X40,X42) = singleton(esk19_3(X32,X40,X42))
        | ~ in(X42,esk17_2(X32,X40))
        | in(esk13_1(X32),X32) )
      & ( ~ in(X47,cartesian_product2(X32,X40))
        | X47 != X46
        | ordered_pair(X48,X49) != X46
        | ~ in(X48,X32)
        | X49 != singleton(X48)
        | in(X46,esk17_2(X32,X40))
        | in(esk13_1(X32),X32) )
      & ( in(esk18_3(X32,X40,X42),cartesian_product2(X32,X40))
        | ~ in(X42,esk17_2(X32,X40))
        | esk14_1(X32) = singleton(esk13_1(X32)) )
      & ( esk18_3(X32,X40,X42) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | esk14_1(X32) = singleton(esk13_1(X32)) )
      & ( ordered_pair(esk19_3(X32,X40,X42),esk20_3(X32,X40,X42)) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | esk14_1(X32) = singleton(esk13_1(X32)) )
      & ( in(esk19_3(X32,X40,X42),X32)
        | ~ in(X42,esk17_2(X32,X40))
        | esk14_1(X32) = singleton(esk13_1(X32)) )
      & ( esk20_3(X32,X40,X42) = singleton(esk19_3(X32,X40,X42))
        | ~ in(X42,esk17_2(X32,X40))
        | esk14_1(X32) = singleton(esk13_1(X32)) )
      & ( ~ in(X47,cartesian_product2(X32,X40))
        | X47 != X46
        | ordered_pair(X48,X49) != X46
        | ~ in(X48,X32)
        | X49 != singleton(X48)
        | in(X46,esk17_2(X32,X40))
        | esk14_1(X32) = singleton(esk13_1(X32)) )
      & ( in(esk18_3(X32,X40,X42),cartesian_product2(X32,X40))
        | ~ in(X42,esk17_2(X32,X40))
        | esk10_1(X32) = esk12_1(X32) )
      & ( esk18_3(X32,X40,X42) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | esk10_1(X32) = esk12_1(X32) )
      & ( ordered_pair(esk19_3(X32,X40,X42),esk20_3(X32,X40,X42)) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | esk10_1(X32) = esk12_1(X32) )
      & ( in(esk19_3(X32,X40,X42),X32)
        | ~ in(X42,esk17_2(X32,X40))
        | esk10_1(X32) = esk12_1(X32) )
      & ( esk20_3(X32,X40,X42) = singleton(esk19_3(X32,X40,X42))
        | ~ in(X42,esk17_2(X32,X40))
        | esk10_1(X32) = esk12_1(X32) )
      & ( ~ in(X47,cartesian_product2(X32,X40))
        | X47 != X46
        | ordered_pair(X48,X49) != X46
        | ~ in(X48,X32)
        | X49 != singleton(X48)
        | in(X46,esk17_2(X32,X40))
        | esk10_1(X32) = esk12_1(X32) )
      & ( in(esk18_3(X32,X40,X42),cartesian_product2(X32,X40))
        | ~ in(X42,esk17_2(X32,X40))
        | ordered_pair(esk15_1(X32),esk16_1(X32)) = esk12_1(X32) )
      & ( esk18_3(X32,X40,X42) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | ordered_pair(esk15_1(X32),esk16_1(X32)) = esk12_1(X32) )
      & ( ordered_pair(esk19_3(X32,X40,X42),esk20_3(X32,X40,X42)) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | ordered_pair(esk15_1(X32),esk16_1(X32)) = esk12_1(X32) )
      & ( in(esk19_3(X32,X40,X42),X32)
        | ~ in(X42,esk17_2(X32,X40))
        | ordered_pair(esk15_1(X32),esk16_1(X32)) = esk12_1(X32) )
      & ( esk20_3(X32,X40,X42) = singleton(esk19_3(X32,X40,X42))
        | ~ in(X42,esk17_2(X32,X40))
        | ordered_pair(esk15_1(X32),esk16_1(X32)) = esk12_1(X32) )
      & ( ~ in(X47,cartesian_product2(X32,X40))
        | X47 != X46
        | ordered_pair(X48,X49) != X46
        | ~ in(X48,X32)
        | X49 != singleton(X48)
        | in(X46,esk17_2(X32,X40))
        | ordered_pair(esk15_1(X32),esk16_1(X32)) = esk12_1(X32) )
      & ( in(esk18_3(X32,X40,X42),cartesian_product2(X32,X40))
        | ~ in(X42,esk17_2(X32,X40))
        | in(esk15_1(X32),X32) )
      & ( esk18_3(X32,X40,X42) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | in(esk15_1(X32),X32) )
      & ( ordered_pair(esk19_3(X32,X40,X42),esk20_3(X32,X40,X42)) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | in(esk15_1(X32),X32) )
      & ( in(esk19_3(X32,X40,X42),X32)
        | ~ in(X42,esk17_2(X32,X40))
        | in(esk15_1(X32),X32) )
      & ( esk20_3(X32,X40,X42) = singleton(esk19_3(X32,X40,X42))
        | ~ in(X42,esk17_2(X32,X40))
        | in(esk15_1(X32),X32) )
      & ( ~ in(X47,cartesian_product2(X32,X40))
        | X47 != X46
        | ordered_pair(X48,X49) != X46
        | ~ in(X48,X32)
        | X49 != singleton(X48)
        | in(X46,esk17_2(X32,X40))
        | in(esk15_1(X32),X32) )
      & ( in(esk18_3(X32,X40,X42),cartesian_product2(X32,X40))
        | ~ in(X42,esk17_2(X32,X40))
        | esk16_1(X32) = singleton(esk15_1(X32)) )
      & ( esk18_3(X32,X40,X42) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | esk16_1(X32) = singleton(esk15_1(X32)) )
      & ( ordered_pair(esk19_3(X32,X40,X42),esk20_3(X32,X40,X42)) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | esk16_1(X32) = singleton(esk15_1(X32)) )
      & ( in(esk19_3(X32,X40,X42),X32)
        | ~ in(X42,esk17_2(X32,X40))
        | esk16_1(X32) = singleton(esk15_1(X32)) )
      & ( esk20_3(X32,X40,X42) = singleton(esk19_3(X32,X40,X42))
        | ~ in(X42,esk17_2(X32,X40))
        | esk16_1(X32) = singleton(esk15_1(X32)) )
      & ( ~ in(X47,cartesian_product2(X32,X40))
        | X47 != X46
        | ordered_pair(X48,X49) != X46
        | ~ in(X48,X32)
        | X49 != singleton(X48)
        | in(X46,esk17_2(X32,X40))
        | esk16_1(X32) = singleton(esk15_1(X32)) )
      & ( in(esk18_3(X32,X40,X42),cartesian_product2(X32,X40))
        | ~ in(X42,esk17_2(X32,X40))
        | esk11_1(X32) != esk12_1(X32) )
      & ( esk18_3(X32,X40,X42) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | esk11_1(X32) != esk12_1(X32) )
      & ( ordered_pair(esk19_3(X32,X40,X42),esk20_3(X32,X40,X42)) = X42
        | ~ in(X42,esk17_2(X32,X40))
        | esk11_1(X32) != esk12_1(X32) )
      & ( in(esk19_3(X32,X40,X42),X32)
        | ~ in(X42,esk17_2(X32,X40))
        | esk11_1(X32) != esk12_1(X32) )
      & ( esk20_3(X32,X40,X42) = singleton(esk19_3(X32,X40,X42))
        | ~ in(X42,esk17_2(X32,X40))
        | esk11_1(X32) != esk12_1(X32) )
      & ( ~ in(X47,cartesian_product2(X32,X40))
        | X47 != X46
        | ordered_pair(X48,X49) != X46
        | ~ in(X48,X32)
        | X49 != singleton(X48)
        | in(X46,esk17_2(X32,X40))
        | esk11_1(X32) != esk12_1(X32) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[s1_tarski__e16_22__wellord2__2])])])])])])]) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
      ? [X3] :
      ! [X4] :
        ( in(X4,X3)
      <=> ( in(X4,cartesian_product2(X1,X2))
          & ? [X5,X6] :
              ( ordered_pair(X5,X6) = X4
              & in(X5,X1)
              & X6 = singleton(X5) ) ) ),
    inference(assume_negation,[status(cth)],[s1_xboole_0__e16_22__wellord2__1]) ).

cnf(c_0_4,plain,
    ( in(X4,esk17_2(X2,X3))
    | esk10_1(X2) = esk11_1(X2)
    | ~ in(X1,cartesian_product2(X2,X3))
    | X1 != X4
    | ordered_pair(X5,X6) != X4
    | ~ in(X5,X2)
    | X6 != singleton(X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

fof(c_0_5,negated_conjecture,
    ! [X14,X16,X17] :
      ( ( ~ in(esk3_1(X14),X14)
        | ~ in(esk3_1(X14),cartesian_product2(esk1_0,esk2_0))
        | ordered_pair(X16,X17) != esk3_1(X14)
        | ~ in(X16,esk1_0)
        | X17 != singleton(X16) )
      & ( in(esk3_1(X14),cartesian_product2(esk1_0,esk2_0))
        | in(esk3_1(X14),X14) )
      & ( ordered_pair(esk4_1(X14),esk5_1(X14)) = esk3_1(X14)
        | in(esk3_1(X14),X14) )
      & ( in(esk4_1(X14),esk1_0)
        | in(esk3_1(X14),X14) )
      & ( esk5_1(X14) = singleton(esk4_1(X14))
        | in(esk3_1(X14),X14) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])])]) ).

cnf(c_0_6,plain,
    ( esk10_1(X1) = esk11_1(X1)
    | in(ordered_pair(X2,singleton(X2)),esk17_2(X1,X3))
    | ~ in(ordered_pair(X2,singleton(X2)),cartesian_product2(X1,X3))
    | ~ in(X2,X1) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_4])])]) ).

cnf(c_0_7,negated_conjecture,
    ( esk5_1(X1) = singleton(esk4_1(X1))
    | in(esk3_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    ( esk10_1(X1) = esk11_1(X1)
    | in(ordered_pair(esk4_1(X2),esk5_1(X2)),esk17_2(X1,X3))
    | in(esk3_1(X2),X2)
    | ~ in(ordered_pair(esk4_1(X2),esk5_1(X2)),cartesian_product2(X1,X3))
    | ~ in(esk4_1(X2),X1) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_9,negated_conjecture,
    ( ordered_pair(esk4_1(X1),esk5_1(X1)) = esk3_1(X1)
    | in(esk3_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,negated_conjecture,
    ( esk10_1(X1) = esk11_1(X1)
    | in(esk3_1(X2),esk17_2(X1,X3))
    | in(esk3_1(X2),X2)
    | ~ in(esk3_1(X2),cartesian_product2(X1,X3))
    | ~ in(esk4_1(X2),X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,negated_conjecture,
    ( in(esk3_1(X1),cartesian_product2(esk1_0,esk2_0))
    | in(esk3_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,negated_conjecture,
    ( in(esk4_1(X1),esk1_0)
    | in(esk3_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_13,negated_conjecture,
    ( esk10_1(esk1_0) = esk11_1(esk1_0)
    | in(esk3_1(X1),esk17_2(esk1_0,esk2_0))
    | in(esk3_1(X1),X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).

cnf(c_0_14,plain,
    ( in(esk18_3(X1,X2,X3),cartesian_product2(X1,X2))
    | esk10_1(X1) = esk11_1(X1)
    | ~ in(X3,esk17_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_15,negated_conjecture,
    ( esk10_1(esk1_0) = esk11_1(esk1_0)
    | in(esk3_1(esk17_2(esk1_0,esk2_0)),esk17_2(esk1_0,esk2_0)) ),
    inference(ef,[status(thm)],[c_0_13]) ).

cnf(c_0_16,plain,
    ( esk18_3(X1,X2,X3) = X3
    | esk10_1(X1) = esk11_1(X1)
    | ~ in(X3,esk17_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_17,negated_conjecture,
    ( ~ in(esk3_1(X1),X1)
    | ~ in(esk3_1(X1),cartesian_product2(esk1_0,esk2_0))
    | ordered_pair(X2,X3) != esk3_1(X1)
    | ~ in(X2,esk1_0)
    | X3 != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_18,negated_conjecture,
    ( esk10_1(esk1_0) = esk11_1(esk1_0)
    | in(esk18_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),cartesian_product2(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    ( esk18_3(X1,X2,esk3_1(esk17_2(X1,X2))) = esk3_1(esk17_2(X1,X2))
    | esk10_1(X1) = esk11_1(X1)
    | in(esk3_1(esk17_2(X1,X2)),cartesian_product2(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_16,c_0_11]) ).

cnf(c_0_20,plain,
    ( in(X4,esk17_2(X2,X3))
    | ~ in(X1,cartesian_product2(X2,X3))
    | X1 != X4
    | ordered_pair(X5,X6) != X4
    | ~ in(X5,X2)
    | X6 != singleton(X5)
    | esk11_1(X2) != esk12_1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_21,plain,
    ( in(X4,esk17_2(X2,X3))
    | esk10_1(X2) = esk12_1(X2)
    | ~ in(X1,cartesian_product2(X2,X3))
    | X1 != X4
    | ordered_pair(X5,X6) != X4
    | ~ in(X5,X2)
    | X6 != singleton(X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_22,negated_conjecture,
    ( ordered_pair(X1,singleton(X1)) != esk3_1(X2)
    | ~ in(esk3_1(X2),cartesian_product2(esk1_0,esk2_0))
    | ~ in(esk3_1(X2),X2)
    | ~ in(X1,esk1_0) ),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    ( esk10_1(esk1_0) = esk11_1(esk1_0)
    | in(esk3_1(esk17_2(esk1_0,esk2_0)),cartesian_product2(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,plain,
    ( esk20_3(X1,X2,X3) = singleton(esk19_3(X1,X2,X3))
    | esk10_1(X1) = esk11_1(X1)
    | ~ in(X3,esk17_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_25,plain,
    ( in(esk19_3(X1,X2,X3),X1)
    | esk10_1(X1) = esk11_1(X1)
    | ~ in(X3,esk17_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_26,plain,
    ( in(ordered_pair(X1,singleton(X1)),esk17_2(X2,X3))
    | esk12_1(X2) != esk11_1(X2)
    | ~ in(ordered_pair(X1,singleton(X1)),cartesian_product2(X2,X3))
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_20])])]) ).

cnf(c_0_27,plain,
    ( esk10_1(X1) = esk12_1(X1)
    | in(ordered_pair(X2,singleton(X2)),esk17_2(X1,X3))
    | ~ in(ordered_pair(X2,singleton(X2)),cartesian_product2(X1,X3))
    | ~ in(X2,X1) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])])]) ).

cnf(c_0_28,negated_conjecture,
    ( esk10_1(esk1_0) = esk11_1(esk1_0)
    | ordered_pair(X1,singleton(X1)) != esk3_1(esk17_2(esk1_0,esk2_0))
    | ~ in(X1,esk1_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_15]) ).

cnf(c_0_29,negated_conjecture,
    ( singleton(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))) = esk20_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))
    | esk10_1(esk1_0) = esk11_1(esk1_0) ),
    inference(spm,[status(thm)],[c_0_24,c_0_15]) ).

cnf(c_0_30,negated_conjecture,
    ( esk10_1(esk1_0) = esk11_1(esk1_0)
    | in(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),esk1_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_15]) ).

cnf(c_0_31,negated_conjecture,
    ( in(ordered_pair(esk4_1(X1),esk5_1(X1)),esk17_2(X2,X3))
    | in(esk3_1(X1),X1)
    | esk12_1(X2) != esk11_1(X2)
    | ~ in(ordered_pair(esk4_1(X1),esk5_1(X1)),cartesian_product2(X2,X3))
    | ~ in(esk4_1(X1),X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_7]) ).

cnf(c_0_32,negated_conjecture,
    ( esk10_1(X1) = esk12_1(X1)
    | in(ordered_pair(esk4_1(X2),esk5_1(X2)),esk17_2(X1,X3))
    | in(esk3_1(X2),X2)
    | ~ in(ordered_pair(esk4_1(X2),esk5_1(X2)),cartesian_product2(X1,X3))
    | ~ in(esk4_1(X2),X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_7]) ).

cnf(c_0_33,plain,
    ( ordered_pair(esk19_3(X1,X2,X3),esk20_3(X1,X2,X3)) = X3
    | esk10_1(X1) = esk11_1(X1)
    | ~ in(X3,esk17_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_34,negated_conjecture,
    ( esk10_1(esk1_0) = esk11_1(esk1_0)
    | ordered_pair(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),esk20_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))) != esk3_1(esk17_2(esk1_0,esk2_0)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

cnf(c_0_35,negated_conjecture,
    ( in(esk3_1(X1),esk17_2(X2,X3))
    | in(esk3_1(X1),X1)
    | esk12_1(X2) != esk11_1(X2)
    | ~ in(esk3_1(X1),cartesian_product2(X2,X3))
    | ~ in(esk4_1(X1),X2) ),
    inference(spm,[status(thm)],[c_0_31,c_0_9]) ).

cnf(c_0_36,negated_conjecture,
    ( esk10_1(X1) = esk12_1(X1)
    | in(esk3_1(X2),esk17_2(X1,X3))
    | in(esk3_1(X2),X2)
    | ~ in(esk3_1(X2),cartesian_product2(X1,X3))
    | ~ in(esk4_1(X2),X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_9]) ).

cnf(c_0_37,negated_conjecture,
    esk10_1(esk1_0) = esk11_1(esk1_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_15]),c_0_34]) ).

cnf(c_0_38,negated_conjecture,
    ( in(esk3_1(X1),esk17_2(esk1_0,esk2_0))
    | in(esk3_1(X1),X1)
    | esk12_1(esk1_0) != esk11_1(esk1_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_11]),c_0_12]) ).

cnf(c_0_39,negated_conjecture,
    ( in(esk3_1(X1),esk17_2(esk1_0,esk2_0))
    | in(esk3_1(X1),X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_11]),c_0_37]),c_0_12]),c_0_38]) ).

cnf(c_0_40,plain,
    ( in(esk18_3(X1,X2,X3),cartesian_product2(X1,X2))
    | esk10_1(X1) = esk12_1(X1)
    | ~ in(X3,esk17_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_41,negated_conjecture,
    in(esk3_1(esk17_2(esk1_0,esk2_0)),esk17_2(esk1_0,esk2_0)),
    inference(ef,[status(thm)],[c_0_39]) ).

cnf(c_0_42,plain,
    ( esk18_3(X1,X2,X3) = X3
    | esk10_1(X1) = esk12_1(X1)
    | ~ in(X3,esk17_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_43,negated_conjecture,
    ( esk12_1(esk1_0) = esk11_1(esk1_0)
    | in(esk18_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),cartesian_product2(esk1_0,esk2_0)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_37]) ).

cnf(c_0_44,negated_conjecture,
    ( esk18_3(X1,X2,esk3_1(esk17_2(X1,X2))) = esk3_1(esk17_2(X1,X2))
    | esk10_1(X1) = esk12_1(X1)
    | in(esk3_1(esk17_2(X1,X2)),cartesian_product2(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_42,c_0_11]) ).

cnf(c_0_45,plain,
    ( in(esk18_3(X1,X2,X3),cartesian_product2(X1,X2))
    | ~ in(X3,esk17_2(X1,X2))
    | esk11_1(X1) != esk12_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_46,plain,
    ( esk18_3(X1,X2,X3) = X3
    | ~ in(X3,esk17_2(X1,X2))
    | esk11_1(X1) != esk12_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_47,negated_conjecture,
    ( esk12_1(esk1_0) = esk11_1(esk1_0)
    | in(esk3_1(esk17_2(esk1_0,esk2_0)),cartesian_product2(esk1_0,esk2_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_37])]) ).

cnf(c_0_48,plain,
    ( esk20_3(X1,X2,X3) = singleton(esk19_3(X1,X2,X3))
    | esk10_1(X1) = esk12_1(X1)
    | ~ in(X3,esk17_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_49,plain,
    ( in(esk19_3(X1,X2,X3),X1)
    | esk10_1(X1) = esk12_1(X1)
    | ~ in(X3,esk17_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_50,plain,
    ( ordered_pair(esk19_3(X1,X2,X3),esk20_3(X1,X2,X3)) = X3
    | esk10_1(X1) = esk12_1(X1)
    | ~ in(X3,esk17_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_51,plain,
    ( in(X1,cartesian_product2(X2,X3))
    | esk12_1(X2) != esk11_1(X2)
    | ~ in(X1,esk17_2(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_52,negated_conjecture,
    ( esk12_1(esk1_0) = esk11_1(esk1_0)
    | ordered_pair(X1,singleton(X1)) != esk3_1(esk17_2(esk1_0,esk2_0))
    | ~ in(X1,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_47]),c_0_41])]) ).

cnf(c_0_53,negated_conjecture,
    ( singleton(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))) = esk20_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))
    | esk12_1(esk1_0) = esk11_1(esk1_0) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_41]),c_0_37]) ).

cnf(c_0_54,negated_conjecture,
    ( esk12_1(esk1_0) = esk11_1(esk1_0)
    | in(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),esk1_0) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_41]),c_0_37]) ).

cnf(c_0_55,negated_conjecture,
    ( ordered_pair(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),esk20_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))) = esk3_1(esk17_2(esk1_0,esk2_0))
    | esk12_1(esk1_0) = esk11_1(esk1_0) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_41]),c_0_37]) ).

cnf(c_0_56,negated_conjecture,
    ( ordered_pair(X1,singleton(X1)) != esk3_1(X2)
    | esk12_1(esk1_0) != esk11_1(esk1_0)
    | ~ in(esk3_1(X2),esk17_2(esk1_0,esk2_0))
    | ~ in(esk3_1(X2),X2)
    | ~ in(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_22,c_0_51]) ).

cnf(c_0_57,negated_conjecture,
    esk12_1(esk1_0) = esk11_1(esk1_0),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55]) ).

cnf(c_0_58,negated_conjecture,
    ( ordered_pair(X1,singleton(X1)) != esk3_1(X2)
    | ~ in(esk3_1(X2),esk17_2(esk1_0,esk2_0))
    | ~ in(esk3_1(X2),X2)
    | ~ in(X1,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).

cnf(c_0_59,negated_conjecture,
    ( ordered_pair(X1,singleton(X1)) != esk3_1(esk17_2(esk1_0,esk2_0))
    | ~ in(X1,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_41]),c_0_41])]) ).

cnf(c_0_60,plain,
    ( esk20_3(X1,X2,X3) = singleton(esk19_3(X1,X2,X3))
    | ~ in(X3,esk17_2(X1,X2))
    | esk11_1(X1) != esk12_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_61,negated_conjecture,
    ( ordered_pair(esk19_3(X1,X2,X3),esk20_3(X1,X2,X3)) != esk3_1(esk17_2(esk1_0,esk2_0))
    | esk12_1(X1) != esk11_1(X1)
    | ~ in(esk19_3(X1,X2,X3),esk1_0)
    | ~ in(X3,esk17_2(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_62,plain,
    ( ordered_pair(esk19_3(X1,X2,X3),esk20_3(X1,X2,X3)) = X3
    | ~ in(X3,esk17_2(X1,X2))
    | esk11_1(X1) != esk12_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_63,negated_conjecture,
    ( esk12_1(X1) != esk11_1(X1)
    | ~ in(esk19_3(X1,X2,esk3_1(esk17_2(esk1_0,esk2_0))),esk1_0)
    | ~ in(esk3_1(esk17_2(esk1_0,esk2_0)),esk17_2(X1,X2)) ),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62])]) ).

cnf(c_0_64,plain,
    ( in(esk19_3(X1,X2,X3),X1)
    | ~ in(X3,esk17_2(X1,X2))
    | esk11_1(X1) != esk12_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_65,negated_conjecture,
    ~ in(esk3_1(esk17_2(esk1_0,esk2_0)),esk17_2(esk1_0,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_57])]) ).

cnf(c_0_66,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_41,c_0_65]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem    : SEU281+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.12  % Command    : run_E %s %d THM
% 0.12/0.32  % Computer : n024.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Fri May  3 07:41:20 EDT 2024
% 0.12/0.32  % CPUTime    : 
% 0.17/0.44  Running first-order model finding
% 0.17/0.44  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.bfX0Z7QPAh/E---3.1_24002.p
% 0.17/0.55  # Version: 3.1.0
% 0.17/0.55  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.55  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.55  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.55  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.55  # Starting sh5l with 300s (1) cores
% 0.17/0.55  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 24079 completed with status 0
% 0.17/0.55  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.17/0.55  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.55  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.55  # No SInE strategy applied
% 0.17/0.55  # Search class: FGHSF-FFMM31-SFFFFFNN
% 0.17/0.55  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.55  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with 811s (1) cores
% 0.17/0.55  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.17/0.55  # Starting new_bool_3 with 136s (1) cores
% 0.17/0.55  # Starting new_bool_1 with 136s (1) cores
% 0.17/0.55  # Starting U----_212g_01_C10_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.17/0.55  # U----_212g_01_C10_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 24090 completed with status 0
% 0.17/0.55  # Result found by U----_212g_01_C10_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.17/0.55  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.55  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.55  # No SInE strategy applied
% 0.17/0.55  # Search class: FGHSF-FFMM31-SFFFFFNN
% 0.17/0.55  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.55  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with 811s (1) cores
% 0.17/0.55  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.17/0.55  # Starting new_bool_3 with 136s (1) cores
% 0.17/0.55  # Starting new_bool_1 with 136s (1) cores
% 0.17/0.55  # Starting U----_212g_01_C10_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.17/0.55  # Preprocessing time       : 0.002 s
% 0.17/0.55  # Presaturation interreduction done
% 0.17/0.55  
% 0.17/0.55  # Proof found!
% 0.17/0.55  # SZS status Theorem
% 0.17/0.55  # SZS output start CNFRefutation
% See solution above
% 0.17/0.55  # Parsed axioms                        : 15
% 0.17/0.55  # Removed by relevancy pruning/SinE    : 0
% 0.17/0.55  # Initial clauses                      : 80
% 0.17/0.55  # Removed in clause preprocessing      : 3
% 0.17/0.55  # Initial clauses in saturation        : 77
% 0.17/0.55  # Processed clauses                    : 899
% 0.17/0.55  # ...of these trivial                  : 3
% 0.17/0.55  # ...subsumed                          : 334
% 0.17/0.55  # ...remaining for further processing  : 562
% 0.17/0.55  # Other redundant clauses eliminated   : 33
% 0.17/0.55  # Clauses deleted for lack of memory   : 0
% 0.17/0.55  # Backward-subsumed                    : 23
% 0.17/0.55  # Backward-rewritten                   : 192
% 0.17/0.55  # Generated clauses                    : 4367
% 0.17/0.55  # ...of the previous two non-redundant : 3962
% 0.17/0.55  # ...aggressively subsumed             : 0
% 0.17/0.55  # Contextual simplify-reflections      : 58
% 0.17/0.55  # Paramodulations                      : 4331
% 0.17/0.55  # Factorizations                       : 10
% 0.17/0.55  # NegExts                              : 0
% 0.17/0.55  # Equation resolutions                 : 43
% 0.17/0.55  # Disequality decompositions           : 0
% 0.17/0.55  # Total rewrite steps                  : 844
% 0.17/0.55  # ...of those cached                   : 832
% 0.17/0.55  # Propositional unsat checks           : 0
% 0.17/0.55  #    Propositional check models        : 0
% 0.17/0.55  #    Propositional check unsatisfiable : 0
% 0.17/0.55  #    Propositional clauses             : 0
% 0.17/0.55  #    Propositional clauses after purity: 0
% 0.17/0.55  #    Propositional unsat core size     : 0
% 0.17/0.55  #    Propositional preprocessing time  : 0.000
% 0.17/0.55  #    Propositional encoding time       : 0.000
% 0.17/0.55  #    Propositional solver time         : 0.000
% 0.17/0.55  #    Success case prop preproc time    : 0.000
% 0.17/0.55  #    Success case prop encoding time   : 0.000
% 0.17/0.55  #    Success case prop solver time     : 0.000
% 0.17/0.55  # Current number of processed clauses  : 259
% 0.17/0.55  #    Positive orientable unit clauses  : 14
% 0.17/0.55  #    Positive unorientable unit clauses: 0
% 0.17/0.55  #    Negative unit clauses             : 10
% 0.17/0.55  #    Non-unit-clauses                  : 235
% 0.17/0.55  # Current number of unprocessed clauses: 3072
% 0.17/0.55  # ...number of literals in the above   : 13380
% 0.17/0.55  # Current number of archived formulas  : 0
% 0.17/0.55  # Current number of archived clauses   : 293
% 0.17/0.55  # Clause-clause subsumption calls (NU) : 13418
% 0.17/0.55  # Rec. Clause-clause subsumption calls : 7299
% 0.17/0.55  # Non-unit clause-clause subsumptions  : 407
% 0.17/0.55  # Unit Clause-clause subsumption calls : 392
% 0.17/0.55  # Rewrite failures with RHS unbound    : 0
% 0.17/0.55  # BW rewrite match attempts            : 6
% 0.17/0.55  # BW rewrite match successes           : 6
% 0.17/0.55  # Condensation attempts                : 0
% 0.17/0.55  # Condensation successes               : 0
% 0.17/0.55  # Termbank termtop insertions          : 115636
% 0.17/0.55  # Search garbage collected termcells   : 614
% 0.17/0.55  
% 0.17/0.55  # -------------------------------------------------
% 0.17/0.55  # User time                : 0.096 s
% 0.17/0.55  # System time              : 0.002 s
% 0.17/0.55  # Total time               : 0.098 s
% 0.17/0.55  # Maximum resident set size: 1844 pages
% 0.17/0.55  
% 0.17/0.55  # -------------------------------------------------
% 0.17/0.55  # User time                : 0.470 s
% 0.17/0.55  # System time              : 0.009 s
% 0.17/0.55  # Total time               : 0.479 s
% 0.17/0.55  # Maximum resident set size: 1700 pages
% 0.17/0.55  % E---3.1 exiting
%------------------------------------------------------------------------------