↑ Up

CSE_E---1.7.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SEU277+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  5 05:11:20 PM UTC 2026

% Result   : Theorem 1.39s 1.78s
% Output   : CNFRefutation 1.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   69 (  12 unt;   0 def)
%            Number of atoms       :  509 ( 132 equ)
%            Maximal formula atoms :  231 (   7 avg)
%            Number of connectives :  741 ( 301   ~; 374   |;  58   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   52 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;   3 con; 0-4 aty)
%            Number of variables   :  159 (   0 sgn  26   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(s1_tarski__e6_21__wellord2__1,axiom,
    ! [X1,X2,X3] :
      ( ( relation(X2)
        & relation(X3)
        & function(X3) )
     => ( ! [X4,X5,X6] :
            ( ( X4 = X5
              & ? [X7,X8] :
                  ( X5 = ordered_pair(X7,X8)
                  & in(ordered_pair(apply(X3,X7),apply(X3,X8)),X2) )
              & X4 = X6
              & ? [X9,X10] :
                  ( X6 = ordered_pair(X9,X10)
                  & in(ordered_pair(apply(X3,X9),apply(X3,X10)),X2) ) )
           => X5 = X6 )
       => ? [X4] :
          ! [X5] :
            ( in(X5,X4)
          <=> ? [X6] :
                ( in(X6,cartesian_product2(X1,X1))
                & X6 = X5
                & ? [X11,X12] :
                    ( X5 = ordered_pair(X11,X12)
                    & in(ordered_pair(apply(X3,X11),apply(X3,X12)),X2) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).

fof(s1_xboole_0__e6_21__wellord2__1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X2)
        & relation(X3)
        & function(X3) )
     => ? [X4] :
        ! [X5] :
          ( in(X5,X4)
        <=> ( in(X5,cartesian_product2(X1,X1))
            & ? [X6,X7] :
                ( X5 = ordered_pair(X6,X7)
                & in(ordered_pair(apply(X3,X6),apply(X3,X7)),X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).

fof(c_0_2,plain,
    ! [X78,X79,X80,X89,X93,X94,X95,X96] :
      ( ( in(esk23_4(X78,X79,X80,X89),cartesian_product2(X78,X78))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk15_3(X78,X79,X80) = esk16_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( esk23_4(X78,X79,X80,X89) = X89
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk15_3(X78,X79,X80) = esk16_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( X89 = ordered_pair(esk24_4(X78,X79,X80,X89),esk25_4(X78,X79,X80,X89))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk15_3(X78,X79,X80) = esk16_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(ordered_pair(apply(X80,esk24_4(X78,X79,X80,X89)),apply(X80,esk25_4(X78,X79,X80,X89))),X79)
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk15_3(X78,X79,X80) = esk16_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( ~ in(X94,cartesian_product2(X78,X78))
        | X94 != X93
        | X93 != ordered_pair(X95,X96)
        | ~ in(ordered_pair(apply(X80,X95),apply(X80,X96)),X79)
        | in(X93,esk22_3(X78,X79,X80))
        | esk15_3(X78,X79,X80) = esk16_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(esk23_4(X78,X79,X80,X89),cartesian_product2(X78,X78))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk16_3(X78,X79,X80) = ordered_pair(esk18_3(X78,X79,X80),esk19_3(X78,X79,X80))
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( esk23_4(X78,X79,X80,X89) = X89
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk16_3(X78,X79,X80) = ordered_pair(esk18_3(X78,X79,X80),esk19_3(X78,X79,X80))
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( X89 = ordered_pair(esk24_4(X78,X79,X80,X89),esk25_4(X78,X79,X80,X89))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk16_3(X78,X79,X80) = ordered_pair(esk18_3(X78,X79,X80),esk19_3(X78,X79,X80))
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(ordered_pair(apply(X80,esk24_4(X78,X79,X80,X89)),apply(X80,esk25_4(X78,X79,X80,X89))),X79)
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk16_3(X78,X79,X80) = ordered_pair(esk18_3(X78,X79,X80),esk19_3(X78,X79,X80))
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( ~ in(X94,cartesian_product2(X78,X78))
        | X94 != X93
        | X93 != ordered_pair(X95,X96)
        | ~ in(ordered_pair(apply(X80,X95),apply(X80,X96)),X79)
        | in(X93,esk22_3(X78,X79,X80))
        | esk16_3(X78,X79,X80) = ordered_pair(esk18_3(X78,X79,X80),esk19_3(X78,X79,X80))
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(esk23_4(X78,X79,X80,X89),cartesian_product2(X78,X78))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | in(ordered_pair(apply(X80,esk18_3(X78,X79,X80)),apply(X80,esk19_3(X78,X79,X80))),X79)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( esk23_4(X78,X79,X80,X89) = X89
        | ~ in(X89,esk22_3(X78,X79,X80))
        | in(ordered_pair(apply(X80,esk18_3(X78,X79,X80)),apply(X80,esk19_3(X78,X79,X80))),X79)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( X89 = ordered_pair(esk24_4(X78,X79,X80,X89),esk25_4(X78,X79,X80,X89))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | in(ordered_pair(apply(X80,esk18_3(X78,X79,X80)),apply(X80,esk19_3(X78,X79,X80))),X79)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(ordered_pair(apply(X80,esk24_4(X78,X79,X80,X89)),apply(X80,esk25_4(X78,X79,X80,X89))),X79)
        | ~ in(X89,esk22_3(X78,X79,X80))
        | in(ordered_pair(apply(X80,esk18_3(X78,X79,X80)),apply(X80,esk19_3(X78,X79,X80))),X79)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( ~ in(X94,cartesian_product2(X78,X78))
        | X94 != X93
        | X93 != ordered_pair(X95,X96)
        | ~ in(ordered_pair(apply(X80,X95),apply(X80,X96)),X79)
        | in(X93,esk22_3(X78,X79,X80))
        | in(ordered_pair(apply(X80,esk18_3(X78,X79,X80)),apply(X80,esk19_3(X78,X79,X80))),X79)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(esk23_4(X78,X79,X80,X89),cartesian_product2(X78,X78))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk15_3(X78,X79,X80) = esk17_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( esk23_4(X78,X79,X80,X89) = X89
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk15_3(X78,X79,X80) = esk17_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( X89 = ordered_pair(esk24_4(X78,X79,X80,X89),esk25_4(X78,X79,X80,X89))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk15_3(X78,X79,X80) = esk17_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(ordered_pair(apply(X80,esk24_4(X78,X79,X80,X89)),apply(X80,esk25_4(X78,X79,X80,X89))),X79)
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk15_3(X78,X79,X80) = esk17_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( ~ in(X94,cartesian_product2(X78,X78))
        | X94 != X93
        | X93 != ordered_pair(X95,X96)
        | ~ in(ordered_pair(apply(X80,X95),apply(X80,X96)),X79)
        | in(X93,esk22_3(X78,X79,X80))
        | esk15_3(X78,X79,X80) = esk17_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(esk23_4(X78,X79,X80,X89),cartesian_product2(X78,X78))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk17_3(X78,X79,X80) = ordered_pair(esk20_3(X78,X79,X80),esk21_3(X78,X79,X80))
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( esk23_4(X78,X79,X80,X89) = X89
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk17_3(X78,X79,X80) = ordered_pair(esk20_3(X78,X79,X80),esk21_3(X78,X79,X80))
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( X89 = ordered_pair(esk24_4(X78,X79,X80,X89),esk25_4(X78,X79,X80,X89))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk17_3(X78,X79,X80) = ordered_pair(esk20_3(X78,X79,X80),esk21_3(X78,X79,X80))
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(ordered_pair(apply(X80,esk24_4(X78,X79,X80,X89)),apply(X80,esk25_4(X78,X79,X80,X89))),X79)
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk17_3(X78,X79,X80) = ordered_pair(esk20_3(X78,X79,X80),esk21_3(X78,X79,X80))
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( ~ in(X94,cartesian_product2(X78,X78))
        | X94 != X93
        | X93 != ordered_pair(X95,X96)
        | ~ in(ordered_pair(apply(X80,X95),apply(X80,X96)),X79)
        | in(X93,esk22_3(X78,X79,X80))
        | esk17_3(X78,X79,X80) = ordered_pair(esk20_3(X78,X79,X80),esk21_3(X78,X79,X80))
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(esk23_4(X78,X79,X80,X89),cartesian_product2(X78,X78))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | in(ordered_pair(apply(X80,esk20_3(X78,X79,X80)),apply(X80,esk21_3(X78,X79,X80))),X79)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( esk23_4(X78,X79,X80,X89) = X89
        | ~ in(X89,esk22_3(X78,X79,X80))
        | in(ordered_pair(apply(X80,esk20_3(X78,X79,X80)),apply(X80,esk21_3(X78,X79,X80))),X79)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( X89 = ordered_pair(esk24_4(X78,X79,X80,X89),esk25_4(X78,X79,X80,X89))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | in(ordered_pair(apply(X80,esk20_3(X78,X79,X80)),apply(X80,esk21_3(X78,X79,X80))),X79)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(ordered_pair(apply(X80,esk24_4(X78,X79,X80,X89)),apply(X80,esk25_4(X78,X79,X80,X89))),X79)
        | ~ in(X89,esk22_3(X78,X79,X80))
        | in(ordered_pair(apply(X80,esk20_3(X78,X79,X80)),apply(X80,esk21_3(X78,X79,X80))),X79)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( ~ in(X94,cartesian_product2(X78,X78))
        | X94 != X93
        | X93 != ordered_pair(X95,X96)
        | ~ in(ordered_pair(apply(X80,X95),apply(X80,X96)),X79)
        | in(X93,esk22_3(X78,X79,X80))
        | in(ordered_pair(apply(X80,esk20_3(X78,X79,X80)),apply(X80,esk21_3(X78,X79,X80))),X79)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(esk23_4(X78,X79,X80,X89),cartesian_product2(X78,X78))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk16_3(X78,X79,X80) != esk17_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( esk23_4(X78,X79,X80,X89) = X89
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk16_3(X78,X79,X80) != esk17_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( X89 = ordered_pair(esk24_4(X78,X79,X80,X89),esk25_4(X78,X79,X80,X89))
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk16_3(X78,X79,X80) != esk17_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( in(ordered_pair(apply(X80,esk24_4(X78,X79,X80,X89)),apply(X80,esk25_4(X78,X79,X80,X89))),X79)
        | ~ in(X89,esk22_3(X78,X79,X80))
        | esk16_3(X78,X79,X80) != esk17_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) )
      & ( ~ in(X94,cartesian_product2(X78,X78))
        | X94 != X93
        | X93 != ordered_pair(X95,X96)
        | ~ in(ordered_pair(apply(X80,X95),apply(X80,X96)),X79)
        | in(X93,esk22_3(X78,X79,X80))
        | esk16_3(X78,X79,X80) != esk17_3(X78,X79,X80)
        | ~ relation(X79)
        | ~ relation(X80)
        | ~ function(X80) ) ),
    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)],[s1_tarski__e6_21__wellord2__1])])])])])]) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X2)
          & relation(X3)
          & function(X3) )
       => ? [X4] :
          ! [X5] :
            ( in(X5,X4)
          <=> ( in(X5,cartesian_product2(X1,X1))
              & ? [X6,X7] :
                  ( X5 = ordered_pair(X6,X7)
                  & in(ordered_pair(apply(X3,X6),apply(X3,X7)),X2) ) ) ) ),
    inference(assume_negation,[status(cth)],[s1_xboole_0__e6_21__wellord2__1]) ).

cnf(c_0_4,plain,
    ( in(X3,esk22_3(X2,X7,X6))
    | esk15_3(X2,X7,X6) = esk16_3(X2,X7,X6)
    | ~ in(X1,cartesian_product2(X2,X2))
    | X1 != X3
    | X3 != ordered_pair(X4,X5)
    | ~ in(ordered_pair(apply(X6,X4),apply(X6,X5)),X7)
    | ~ relation(X7)
    | ~ relation(X6)
    | ~ function(X6) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

fof(c_0_5,negated_conjecture,
    ! [X55,X57,X58] :
      ( relation(esk2_0)
      & relation(esk3_0)
      & function(esk3_0)
      & ( ~ in(esk4_1(X55),X55)
        | ~ in(esk4_1(X55),cartesian_product2(esk1_0,esk1_0))
        | esk4_1(X55) != ordered_pair(X57,X58)
        | ~ in(ordered_pair(apply(esk3_0,X57),apply(esk3_0,X58)),esk2_0) )
      & ( in(esk4_1(X55),cartesian_product2(esk1_0,esk1_0))
        | in(esk4_1(X55),X55) )
      & ( esk4_1(X55) = ordered_pair(esk5_1(X55),esk6_1(X55))
        | in(esk4_1(X55),X55) )
      & ( in(ordered_pair(apply(esk3_0,esk5_1(X55)),apply(esk3_0,esk6_1(X55))),esk2_0)
        | in(esk4_1(X55),X55) ) ),
    inference(distribute,[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,
    ( esk15_3(X1,X2,X3) = esk16_3(X1,X2,X3)
    | in(ordered_pair(X4,X5),esk22_3(X1,X2,X3))
    | ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
    | ~ in(ordered_pair(X4,X5),cartesian_product2(X1,X1))
    | ~ function(X3)
    | ~ relation(X2)
    | ~ relation(X3) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_4])]) ).

cnf(c_0_7,negated_conjecture,
    ( esk4_1(X1) = ordered_pair(esk5_1(X1),esk6_1(X1))
    | in(esk4_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    ( esk15_3(X1,X2,X3) = esk16_3(X1,X2,X3)
    | in(esk4_1(X4),esk22_3(X1,X2,X3))
    | in(esk4_1(X4),X4)
    | ~ in(ordered_pair(apply(X3,esk5_1(X4)),apply(X3,esk6_1(X4))),X2)
    | ~ in(esk4_1(X4),cartesian_product2(X1,X1))
    | ~ function(X3)
    | ~ relation(X2)
    | ~ relation(X3) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_9,negated_conjecture,
    ( in(esk4_1(X1),cartesian_product2(esk1_0,esk1_0))
    | in(esk4_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    ( in(X3,esk22_3(X2,X7,X6))
    | esk15_3(X2,X7,X6) = esk17_3(X2,X7,X6)
    | ~ in(X1,cartesian_product2(X2,X2))
    | X1 != X3
    | X3 != ordered_pair(X4,X5)
    | ~ in(ordered_pair(apply(X6,X4),apply(X6,X5)),X7)
    | ~ relation(X7)
    | ~ relation(X6)
    | ~ function(X6) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_11,negated_conjecture,
    ( esk15_3(esk1_0,X1,X2) = esk16_3(esk1_0,X1,X2)
    | in(esk4_1(X3),esk22_3(esk1_0,X1,X2))
    | in(esk4_1(X3),X3)
    | ~ in(ordered_pair(apply(X2,esk5_1(X3)),apply(X2,esk6_1(X3))),X1)
    | ~ function(X2)
    | ~ relation(X1)
    | ~ relation(X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    ( in(ordered_pair(apply(esk3_0,esk5_1(X1)),apply(esk3_0,esk6_1(X1))),esk2_0)
    | in(esk4_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_13,negated_conjecture,
    function(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_14,negated_conjecture,
    relation(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_15,negated_conjecture,
    relation(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_16,plain,
    ( esk15_3(X1,X2,X3) = esk17_3(X1,X2,X3)
    | in(ordered_pair(X4,X5),esk22_3(X1,X2,X3))
    | ~ in(ordered_pair(apply(X3,X4),apply(X3,X5)),X2)
    | ~ in(ordered_pair(X4,X5),cartesian_product2(X1,X1))
    | ~ function(X3)
    | ~ relation(X2)
    | ~ relation(X3) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).

cnf(c_0_17,negated_conjecture,
    ( esk15_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0)
    | in(esk4_1(X1),esk22_3(esk1_0,esk2_0,esk3_0))
    | in(esk4_1(X1),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14]),c_0_15])]) ).

cnf(c_0_18,negated_conjecture,
    ( esk15_3(X1,X2,X3) = esk17_3(X1,X2,X3)
    | in(esk4_1(X4),esk22_3(X1,X2,X3))
    | in(esk4_1(X4),X4)
    | ~ in(ordered_pair(apply(X3,esk5_1(X4)),apply(X3,esk6_1(X4))),X2)
    | ~ in(esk4_1(X4),cartesian_product2(X1,X1))
    | ~ function(X3)
    | ~ relation(X2)
    | ~ relation(X3) ),
    inference(spm,[status(thm)],[c_0_16,c_0_7]) ).

cnf(c_0_19,plain,
    ( X1 = ordered_pair(esk24_4(X2,X3,X4,X1),esk25_4(X2,X3,X4,X1))
    | esk15_3(X2,X3,X4) = esk16_3(X2,X3,X4)
    | ~ in(X1,esk22_3(X2,X3,X4))
    | ~ relation(X3)
    | ~ relation(X4)
    | ~ function(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_20,negated_conjecture,
    ( esk15_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0)
    | in(esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)),esk22_3(esk1_0,esk2_0,esk3_0)) ),
    inference(ef,[status(thm)],[c_0_17]) ).

cnf(c_0_21,plain,
    ( in(ordered_pair(apply(X1,esk24_4(X2,X3,X1,X4)),apply(X1,esk25_4(X2,X3,X1,X4))),X3)
    | esk15_3(X2,X3,X1) = esk16_3(X2,X3,X1)
    | ~ in(X4,esk22_3(X2,X3,X1))
    | ~ relation(X3)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_22,plain,
    ( in(esk23_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
    | esk15_3(X1,X2,X3) = esk16_3(X1,X2,X3)
    | ~ in(X4,esk22_3(X1,X2,X3))
    | ~ relation(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_23,plain,
    ( esk23_4(X1,X2,X3,X4) = X4
    | esk15_3(X1,X2,X3) = esk16_3(X1,X2,X3)
    | ~ in(X4,esk22_3(X1,X2,X3))
    | ~ relation(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_24,negated_conjecture,
    ( esk15_3(esk1_0,X1,X2) = esk17_3(esk1_0,X1,X2)
    | in(esk4_1(X3),esk22_3(esk1_0,X1,X2))
    | in(esk4_1(X3),X3)
    | ~ in(ordered_pair(apply(X2,esk5_1(X3)),apply(X2,esk6_1(X3))),X1)
    | ~ function(X2)
    | ~ relation(X1)
    | ~ relation(X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_9]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ in(esk4_1(X1),X1)
    | ~ in(esk4_1(X1),cartesian_product2(esk1_0,esk1_0))
    | esk4_1(X1) != ordered_pair(X2,X3)
    | ~ in(ordered_pair(apply(esk3_0,X2),apply(esk3_0,X3)),esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_26,negated_conjecture,
    ( ordered_pair(esk24_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))),esk25_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)))) = esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))
    | esk15_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_13]),c_0_15]),c_0_14])]) ).

cnf(c_0_27,negated_conjecture,
    ( esk15_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0)
    | in(ordered_pair(apply(esk3_0,esk24_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)))),apply(esk3_0,esk25_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))))),esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_13]),c_0_14]),c_0_15])]) ).

cnf(c_0_28,negated_conjecture,
    ( esk15_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0)
    | in(esk23_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))),cartesian_product2(esk1_0,esk1_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_13]),c_0_15]),c_0_14])]) ).

cnf(c_0_29,negated_conjecture,
    ( esk23_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))) = esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))
    | esk15_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_13]),c_0_15]),c_0_14])]) ).

cnf(c_0_30,negated_conjecture,
    ( esk15_3(esk1_0,esk2_0,esk3_0) = esk17_3(esk1_0,esk2_0,esk3_0)
    | in(esk4_1(X1),esk22_3(esk1_0,esk2_0,esk3_0))
    | in(esk4_1(X1),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_12]),c_0_13]),c_0_14]),c_0_15])]) ).

cnf(c_0_31,negated_conjecture,
    ( esk15_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0)
    | esk4_1(X1) != esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))
    | ~ in(esk4_1(X1),cartesian_product2(esk1_0,esk1_0))
    | ~ in(esk4_1(X1),X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

cnf(c_0_32,negated_conjecture,
    ( esk15_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0)
    | in(esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)),cartesian_product2(esk1_0,esk1_0)) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    ( esk15_3(esk1_0,esk2_0,esk3_0) = esk17_3(esk1_0,esk2_0,esk3_0)
    | in(esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)),esk22_3(esk1_0,esk2_0,esk3_0)) ),
    inference(ef,[status(thm)],[c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    esk15_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_31]),c_0_32]),c_0_20]) ).

cnf(c_0_35,plain,
    ( in(ordered_pair(apply(X1,esk24_4(X2,X3,X1,X4)),apply(X1,esk25_4(X2,X3,X1,X4))),X3)
    | esk15_3(X2,X3,X1) = esk17_3(X2,X3,X1)
    | ~ in(X4,esk22_3(X2,X3,X1))
    | ~ relation(X3)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_36,plain,
    ( in(esk23_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
    | esk15_3(X1,X2,X3) = esk17_3(X1,X2,X3)
    | ~ in(X4,esk22_3(X1,X2,X3))
    | ~ relation(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_37,plain,
    ( esk23_4(X1,X2,X3,X4) = X4
    | esk15_3(X1,X2,X3) = esk17_3(X1,X2,X3)
    | ~ in(X4,esk22_3(X1,X2,X3))
    | ~ relation(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_38,plain,
    ( X1 = ordered_pair(esk24_4(X2,X3,X4,X1),esk25_4(X2,X3,X4,X1))
    | esk15_3(X2,X3,X4) = esk17_3(X2,X3,X4)
    | ~ in(X1,esk22_3(X2,X3,X4))
    | ~ relation(X3)
    | ~ relation(X4)
    | ~ function(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_39,negated_conjecture,
    ( esk17_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0)
    | in(esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)),esk22_3(esk1_0,esk2_0,esk3_0)) ),
    inference(rw,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_40,negated_conjecture,
    ( esk15_3(esk1_0,esk2_0,esk3_0) = esk17_3(esk1_0,esk2_0,esk3_0)
    | in(ordered_pair(apply(esk3_0,esk24_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)))),apply(esk3_0,esk25_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))))),esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_13]),c_0_14]),c_0_15])]) ).

cnf(c_0_41,negated_conjecture,
    ( esk15_3(esk1_0,esk2_0,esk3_0) = esk17_3(esk1_0,esk2_0,esk3_0)
    | in(esk23_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))),cartesian_product2(esk1_0,esk1_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_13]),c_0_15]),c_0_14])]) ).

cnf(c_0_42,negated_conjecture,
    ( esk23_4(X1,X2,X3,esk4_1(esk22_3(X1,X2,X3))) = esk4_1(esk22_3(X1,X2,X3))
    | esk15_3(X1,X2,X3) = esk17_3(X1,X2,X3)
    | in(esk4_1(esk22_3(X1,X2,X3)),cartesian_product2(esk1_0,esk1_0))
    | ~ function(X3)
    | ~ relation(X3)
    | ~ relation(X2) ),
    inference(spm,[status(thm)],[c_0_37,c_0_9]) ).

cnf(c_0_43,negated_conjecture,
    ( ordered_pair(esk24_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))),esk25_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)))) = esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))
    | esk17_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0) ),
    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_38,c_0_39]),c_0_34]),c_0_13]),c_0_15]),c_0_14])]) ).

cnf(c_0_44,negated_conjecture,
    ( esk17_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0)
    | in(ordered_pair(apply(esk3_0,esk24_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)))),apply(esk3_0,esk25_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))))),esk2_0) ),
    inference(rw,[status(thm)],[c_0_40,c_0_34]) ).

cnf(c_0_45,negated_conjecture,
    ( esk15_3(esk1_0,esk2_0,esk3_0) = esk17_3(esk1_0,esk2_0,esk3_0)
    | in(esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)),cartesian_product2(esk1_0,esk1_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_13]),c_0_15]),c_0_14])]) ).

cnf(c_0_46,plain,
    ( in(X3,esk22_3(X2,X7,X6))
    | ~ in(X1,cartesian_product2(X2,X2))
    | X1 != X3
    | X3 != ordered_pair(X4,X5)
    | ~ in(ordered_pair(apply(X6,X4),apply(X6,X5)),X7)
    | esk16_3(X2,X7,X6) != esk17_3(X2,X7,X6)
    | ~ relation(X7)
    | ~ relation(X6)
    | ~ function(X6) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_47,negated_conjecture,
    ( esk17_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0)
    | esk4_1(X1) != esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))
    | ~ in(esk4_1(X1),cartesian_product2(esk1_0,esk1_0))
    | ~ in(esk4_1(X1),X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_43]),c_0_44]) ).

cnf(c_0_48,negated_conjecture,
    ( esk17_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0)
    | in(esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)),cartesian_product2(esk1_0,esk1_0)) ),
    inference(rw,[status(thm)],[c_0_45,c_0_34]) ).

cnf(c_0_49,plain,
    ( in(ordered_pair(X1,X2),esk22_3(X3,X4,X5))
    | esk17_3(X3,X4,X5) != esk16_3(X3,X4,X5)
    | ~ in(ordered_pair(apply(X5,X1),apply(X5,X2)),X4)
    | ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X3))
    | ~ function(X5)
    | ~ relation(X4)
    | ~ relation(X5) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_46])]) ).

cnf(c_0_50,negated_conjecture,
    esk17_3(esk1_0,esk2_0,esk3_0) = esk16_3(esk1_0,esk2_0,esk3_0),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_47]),c_0_48]),c_0_39]) ).

cnf(c_0_51,negated_conjecture,
    ( in(ordered_pair(X1,X2),esk22_3(esk1_0,esk2_0,esk3_0))
    | ~ in(ordered_pair(apply(esk3_0,X1),apply(esk3_0,X2)),esk2_0)
    | ~ in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk1_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_13]),c_0_14]),c_0_15])]) ).

cnf(c_0_52,plain,
    ( X1 = ordered_pair(esk24_4(X2,X3,X4,X1),esk25_4(X2,X3,X4,X1))
    | ~ in(X1,esk22_3(X2,X3,X4))
    | esk16_3(X2,X3,X4) != esk17_3(X2,X3,X4)
    | ~ relation(X3)
    | ~ relation(X4)
    | ~ function(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_53,negated_conjecture,
    ( in(esk4_1(X1),esk22_3(esk1_0,esk2_0,esk3_0))
    | in(esk4_1(X1),X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_7]),c_0_9]),c_0_12]) ).

cnf(c_0_54,plain,
    ( in(ordered_pair(apply(X1,esk24_4(X2,X3,X1,X4)),apply(X1,esk25_4(X2,X3,X1,X4))),X3)
    | ~ in(X4,esk22_3(X2,X3,X1))
    | esk16_3(X2,X3,X1) != esk17_3(X2,X3,X1)
    | ~ relation(X3)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_55,plain,
    ( in(esk23_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
    | ~ in(X4,esk22_3(X1,X2,X3))
    | esk16_3(X1,X2,X3) != esk17_3(X1,X2,X3)
    | ~ relation(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_56,plain,
    ( esk23_4(X1,X2,X3,X4) = X4
    | ~ in(X4,esk22_3(X1,X2,X3))
    | esk16_3(X1,X2,X3) != esk17_3(X1,X2,X3)
    | ~ relation(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_57,negated_conjecture,
    ( ordered_pair(esk24_4(esk1_0,esk2_0,esk3_0,X1),esk25_4(esk1_0,esk2_0,esk3_0,X1)) = X1
    | ~ in(X1,esk22_3(esk1_0,esk2_0,esk3_0)) ),
    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_13]),c_0_15]),c_0_14])]) ).

cnf(c_0_58,negated_conjecture,
    in(esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)),esk22_3(esk1_0,esk2_0,esk3_0)),
    inference(ef,[status(thm)],[c_0_53]) ).

cnf(c_0_59,negated_conjecture,
    ( in(ordered_pair(apply(esk3_0,esk24_4(esk1_0,esk2_0,esk3_0,X1)),apply(esk3_0,esk25_4(esk1_0,esk2_0,esk3_0,X1))),esk2_0)
    | ~ in(X1,esk22_3(esk1_0,esk2_0,esk3_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_13]),c_0_14]),c_0_15])]) ).

cnf(c_0_60,negated_conjecture,
    ( in(esk23_4(esk1_0,esk2_0,esk3_0,X1),cartesian_product2(esk1_0,esk1_0))
    | ~ in(X1,esk22_3(esk1_0,esk2_0,esk3_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_50]),c_0_13]),c_0_15]),c_0_14])]) ).

cnf(c_0_61,negated_conjecture,
    ( esk23_4(esk1_0,esk2_0,esk3_0,X1) = X1
    | ~ in(X1,esk22_3(esk1_0,esk2_0,esk3_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_50]),c_0_13]),c_0_15]),c_0_14])]) ).

cnf(c_0_62,negated_conjecture,
    ordered_pair(esk24_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))),esk25_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)))) = esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_63,negated_conjecture,
    in(ordered_pair(apply(esk3_0,esk24_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)))),apply(esk3_0,esk25_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))))),esk2_0),
    inference(spm,[status(thm)],[c_0_59,c_0_58]) ).

cnf(c_0_64,negated_conjecture,
    in(esk23_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))),cartesian_product2(esk1_0,esk1_0)),
    inference(spm,[status(thm)],[c_0_60,c_0_58]) ).

cnf(c_0_65,negated_conjecture,
    esk23_4(esk1_0,esk2_0,esk3_0,esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))) = esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)),
    inference(spm,[status(thm)],[c_0_61,c_0_58]) ).

cnf(c_0_66,negated_conjecture,
    ( esk4_1(X1) != esk4_1(esk22_3(esk1_0,esk2_0,esk3_0))
    | ~ in(esk4_1(X1),cartesian_product2(esk1_0,esk1_0))
    | ~ in(esk4_1(X1),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_62]),c_0_63])]) ).

cnf(c_0_67,negated_conjecture,
    in(esk4_1(esk22_3(esk1_0,esk2_0,esk3_0)),cartesian_product2(esk1_0,esk1_0)),
    inference(rw,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_68,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_66]),c_0_67]),c_0_58])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU277+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32  % Computer : n026.cluster.edu
% 0.16/0.32  % Model    : x86_64 x86_64
% 0.16/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32  % Memory   : 8042.1875MB
% 0.16/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32  % CPULimit   : 300
% 0.16/0.32  % WCLimit    : 300
% 0.16/0.32  % DateTime   : Tue May  5 02:54:38 EDT 2026
% 0.16/0.33  % CPUTime    : 
% 0.16/0.34  % start to proof: theBenchmark
% 1.39/1.78  % Version  : CSE_E---1.7
% 1.39/1.78  % Problem  : theBenchmark.p
% 1.39/1.78  % SZS status Theorem for theBenchmark.p
% 1.39/1.78  % SZS output start CNFRefutation
% See solution above
% 1.39/1.79  % Total time : 1.371s
%------------------------------------------------------------------------------