↑ Up

CSE_E---1.7.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SET644+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n027.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 05:08:13 PM UTC 2026

% Result   : Theorem 1.33s 1.73s
% Output   : CNFRefutation 1.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   59 (  15 unt;   0 def)
%            Number of atoms       :  269 (  12 equ)
%            Maximal formula atoms :   26 (   4 avg)
%            Number of connectives :  347 ( 137   ~; 133   |;  35   &)
%                                         (   6 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   5 con; 0-2 aty)
%            Number of variables   :  124 (  10 sgn  59   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(p5,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X1,X2)))
               => ilf_type(X3,relation_type(X1,X2)) )
            & ! [X4] :
                ( ilf_type(X4,relation_type(X1,X2))
               => ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).

fof(p27,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).

fof(prove_relset_1_6,conjecture,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,relation_type(X1,X2))
                 => ( member(X3,X4)
                   => ? [X5] :
                        ( ilf_type(X5,set_type)
                        & ? [X6] :
                            ( ilf_type(X6,set_type)
                            & X3 = ordered_pair(X5,X6)
                            & member(X5,X1)
                            & member(X6,X2) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_6) ).

fof(p24,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,subset_type(cross_product(X1,X2)))
             => relation_like(X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).

fof(p21,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ( ilf_type(X1,member_type(X2))
          <=> member(X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).

fof(p14,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ilf_type(X2,subset_type(X1))
          <=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).

fof(p20,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( ~ empty(power_set(X1))
        & ilf_type(power_set(X1),set_type) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).

fof(p23,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( relation_like(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ( member(X2,X1)
             => ? [X3] :
                  ( ilf_type(X3,set_type)
                  & ? [X4] :
                      ( ilf_type(X4,set_type)
                      & X2 = ordered_pair(X3,X4) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).

fof(p19,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( member(X1,power_set(X2))
          <=> ! [X3] :
                ( ilf_type(X3,set_type)
               => ( member(X3,X1)
                 => member(X3,X2) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).

fof(p2,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,set_type)
                 => ( member(ordered_pair(X1,X2),cross_product(X3,X4))
                  <=> ( member(X1,X3)
                      & member(X2,X4) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

fof(c_0_10,plain,
    ! [X91,X92,X93,X94] :
      ( ( ~ ilf_type(X93,subset_type(cross_product(X91,X92)))
        | ilf_type(X93,relation_type(X91,X92))
        | ~ ilf_type(X92,set_type)
        | ~ ilf_type(X91,set_type) )
      & ( ~ ilf_type(X94,relation_type(X91,X92))
        | ilf_type(X94,subset_type(cross_product(X91,X92)))
        | ~ ilf_type(X92,set_type)
        | ~ ilf_type(X91,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])]) ).

fof(c_0_11,plain,
    ! [X145] : ilf_type(X145,set_type),
    inference(variable_rename,[status(thm)],[p27]) ).

fof(c_0_12,negated_conjecture,
    ~ ! [X1] :
        ( ilf_type(X1,set_type)
       => ! [X2] :
            ( ilf_type(X2,set_type)
           => ! [X3] :
                ( ilf_type(X3,set_type)
               => ! [X4] :
                    ( ilf_type(X4,relation_type(X1,X2))
                   => ( member(X3,X4)
                     => ? [X5] :
                          ( ilf_type(X5,set_type)
                          & ? [X6] :
                              ( ilf_type(X6,set_type)
                              & X3 = ordered_pair(X5,X6)
                              & member(X5,X1)
                              & member(X6,X2) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[prove_relset_1_6]) ).

fof(c_0_13,plain,
    ! [X138,X139,X140] :
      ( ~ ilf_type(X138,set_type)
      | ~ ilf_type(X139,set_type)
      | ~ ilf_type(X140,subset_type(cross_product(X138,X139)))
      | relation_like(X140) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p24])])]) ).

cnf(c_0_14,plain,
    ( ilf_type(X1,subset_type(cross_product(X2,X3)))
    | ~ ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_16,negated_conjecture,
    ! [X150,X151] :
      ( ilf_type(esk14_0,set_type)
      & ilf_type(esk15_0,set_type)
      & ilf_type(esk16_0,set_type)
      & ilf_type(esk17_0,relation_type(esk14_0,esk15_0))
      & member(esk16_0,esk17_0)
      & ( ~ ilf_type(X150,set_type)
        | ~ ilf_type(X151,set_type)
        | esk16_0 != ordered_pair(X150,X151)
        | ~ member(X150,esk14_0)
        | ~ member(X151,esk15_0) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).

fof(c_0_17,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ( ilf_type(X1,member_type(X2))
          <=> member(X1,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[p21]) ).

fof(c_0_18,plain,
    ! [X109,X110] :
      ( ( ~ ilf_type(X110,subset_type(X109))
        | ilf_type(X110,member_type(power_set(X109)))
        | ~ ilf_type(X110,set_type)
        | ~ ilf_type(X109,set_type) )
      & ( ~ ilf_type(X110,member_type(power_set(X109)))
        | ilf_type(X110,subset_type(X109))
        | ~ ilf_type(X110,set_type)
        | ~ ilf_type(X109,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p14])])])]) ).

fof(c_0_19,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( ~ empty(power_set(X1))
        & ilf_type(power_set(X1),set_type) ) ),
    inference(fof_simplification,[status(thm)],[p20]) ).

fof(c_0_20,plain,
    ! [X131,X132,X136,X137] :
      ( ( ilf_type(esk10_2(X131,X132),set_type)
        | ~ member(X132,X131)
        | ~ ilf_type(X132,set_type)
        | ~ relation_like(X131)
        | ~ ilf_type(X131,set_type) )
      & ( ilf_type(esk11_2(X131,X132),set_type)
        | ~ member(X132,X131)
        | ~ ilf_type(X132,set_type)
        | ~ relation_like(X131)
        | ~ ilf_type(X131,set_type) )
      & ( X132 = ordered_pair(esk10_2(X131,X132),esk11_2(X131,X132))
        | ~ member(X132,X131)
        | ~ ilf_type(X132,set_type)
        | ~ relation_like(X131)
        | ~ ilf_type(X131,set_type) )
      & ( ilf_type(esk12_1(X131),set_type)
        | relation_like(X131)
        | ~ ilf_type(X131,set_type) )
      & ( member(esk12_1(X131),X131)
        | relation_like(X131)
        | ~ ilf_type(X131,set_type) )
      & ( ~ ilf_type(X136,set_type)
        | ~ ilf_type(X137,set_type)
        | esk12_1(X131) != ordered_pair(X136,X137)
        | relation_like(X131)
        | ~ ilf_type(X131,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])])])]) ).

cnf(c_0_21,plain,
    ( relation_like(X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,plain,
    ( ilf_type(X1,subset_type(cross_product(X2,X3)))
    | ~ ilf_type(X1,relation_type(X2,X3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15])]) ).

cnf(c_0_23,negated_conjecture,
    ilf_type(esk17_0,relation_type(esk14_0,esk15_0)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_24,plain,
    ! [X122,X123,X124] :
      ( ( ~ member(X122,power_set(X123))
        | ~ ilf_type(X124,set_type)
        | ~ member(X124,X122)
        | member(X124,X123)
        | ~ ilf_type(X123,set_type)
        | ~ ilf_type(X122,set_type) )
      & ( ilf_type(esk8_2(X122,X123),set_type)
        | member(X122,power_set(X123))
        | ~ ilf_type(X123,set_type)
        | ~ ilf_type(X122,set_type) )
      & ( member(esk8_2(X122,X123),X122)
        | member(X122,power_set(X123))
        | ~ ilf_type(X123,set_type)
        | ~ ilf_type(X122,set_type) )
      & ( ~ member(esk8_2(X122,X123),X123)
        | member(X122,power_set(X123))
        | ~ ilf_type(X123,set_type)
        | ~ ilf_type(X122,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p19])])])])]) ).

fof(c_0_25,plain,
    ! [X127,X128] :
      ( ( ~ ilf_type(X127,member_type(X128))
        | member(X127,X128)
        | empty(X128)
        | ~ ilf_type(X128,set_type)
        | ~ ilf_type(X127,set_type) )
      & ( ~ member(X127,X128)
        | ilf_type(X127,member_type(X128))
        | empty(X128)
        | ~ ilf_type(X128,set_type)
        | ~ ilf_type(X127,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).

cnf(c_0_26,plain,
    ( ilf_type(X1,member_type(power_set(X2)))
    | ~ ilf_type(X1,subset_type(X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_27,plain,
    ! [X126] :
      ( ( ~ empty(power_set(X126))
        | ~ ilf_type(X126,set_type) )
      & ( ilf_type(power_set(X126),set_type)
        | ~ ilf_type(X126,set_type) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).

fof(c_0_28,plain,
    ! [X80,X81,X82,X83] :
      ( ( member(X80,X82)
        | ~ member(ordered_pair(X80,X81),cross_product(X82,X83))
        | ~ ilf_type(X83,set_type)
        | ~ ilf_type(X82,set_type)
        | ~ ilf_type(X81,set_type)
        | ~ ilf_type(X80,set_type) )
      & ( member(X81,X83)
        | ~ member(ordered_pair(X80,X81),cross_product(X82,X83))
        | ~ ilf_type(X83,set_type)
        | ~ ilf_type(X82,set_type)
        | ~ ilf_type(X81,set_type)
        | ~ ilf_type(X80,set_type) )
      & ( ~ member(X80,X82)
        | ~ member(X81,X83)
        | member(ordered_pair(X80,X81),cross_product(X82,X83))
        | ~ ilf_type(X83,set_type)
        | ~ ilf_type(X82,set_type)
        | ~ ilf_type(X81,set_type)
        | ~ ilf_type(X80,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).

cnf(c_0_29,plain,
    ( X1 = ordered_pair(esk10_2(X2,X1),esk11_2(X2,X1))
    | ~ member(X1,X2)
    | ~ ilf_type(X1,set_type)
    | ~ relation_like(X2)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_30,plain,
    ( relation_like(X1)
    | ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_15]),c_0_15])]) ).

cnf(c_0_31,negated_conjecture,
    ilf_type(esk17_0,subset_type(cross_product(esk14_0,esk15_0))),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_32,plain,
    ( member(X3,X2)
    | ~ member(X1,power_set(X2))
    | ~ ilf_type(X3,set_type)
    | ~ member(X3,X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_33,plain,
    ( member(X1,X2)
    | empty(X2)
    | ~ ilf_type(X1,member_type(X2))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_34,plain,
    ( ilf_type(X1,member_type(power_set(X2)))
    | ~ ilf_type(X1,subset_type(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_15]),c_0_15])]) ).

cnf(c_0_35,plain,
    ( ~ empty(power_set(X1))
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_36,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X3,X1),cross_product(X4,X2))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X4,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_37,plain,
    ( ordered_pair(esk10_2(X1,X2),esk11_2(X1,X2)) = X2
    | ~ relation_like(X1)
    | ~ member(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_15]),c_0_15])]) ).

cnf(c_0_38,negated_conjecture,
    member(esk16_0,esk17_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_39,negated_conjecture,
    relation_like(esk17_0),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_40,plain,
    ( member(X1,X2)
    | ~ member(X3,power_set(X2))
    | ~ member(X1,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_15]),c_0_15]),c_0_15])]) ).

cnf(c_0_41,plain,
    ( empty(X1)
    | member(X2,X1)
    | ~ ilf_type(X2,member_type(X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_15]),c_0_15])]) ).

cnf(c_0_42,negated_conjecture,
    ilf_type(esk17_0,member_type(power_set(cross_product(esk14_0,esk15_0)))),
    inference(spm,[status(thm)],[c_0_34,c_0_31]) ).

cnf(c_0_43,plain,
    ~ empty(power_set(X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_15])]) ).

cnf(c_0_44,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_15]),c_0_15]),c_0_15]),c_0_15])]) ).

cnf(c_0_45,negated_conjecture,
    ordered_pair(esk10_2(esk17_0,esk16_0),esk11_2(esk17_0,esk16_0)) = esk16_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).

cnf(c_0_46,negated_conjecture,
    ( member(esk16_0,X1)
    | ~ member(esk17_0,power_set(X1)) ),
    inference(spm,[status(thm)],[c_0_40,c_0_38]) ).

cnf(c_0_47,negated_conjecture,
    member(esk17_0,power_set(cross_product(esk14_0,esk15_0))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).

cnf(c_0_48,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X1,X3),cross_product(X2,X4))
    | ~ ilf_type(X4,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_49,negated_conjecture,
    ( ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | esk16_0 != ordered_pair(X1,X2)
    | ~ member(X1,esk14_0)
    | ~ member(X2,esk15_0) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_50,negated_conjecture,
    ( member(esk11_2(esk17_0,esk16_0),X1)
    | ~ member(esk16_0,cross_product(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_51,negated_conjecture,
    member(esk16_0,cross_product(esk14_0,esk15_0)),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_52,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_15]),c_0_15]),c_0_15]),c_0_15])]) ).

cnf(c_0_53,negated_conjecture,
    ( ordered_pair(X1,X2) != esk16_0
    | ~ member(X2,esk15_0)
    | ~ member(X1,esk14_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_15]),c_0_15])]) ).

cnf(c_0_54,negated_conjecture,
    member(esk11_2(esk17_0,esk16_0),esk15_0),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_55,negated_conjecture,
    ( member(esk10_2(esk17_0,esk16_0),X1)
    | ~ member(esk16_0,cross_product(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_52,c_0_45]) ).

cnf(c_0_56,negated_conjecture,
    ( ordered_pair(X1,esk11_2(esk17_0,esk16_0)) != esk16_0
    | ~ member(X1,esk14_0) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_57,negated_conjecture,
    member(esk10_2(esk17_0,esk16_0),esk14_0),
    inference(spm,[status(thm)],[c_0_55,c_0_51]) ).

cnf(c_0_58,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_45])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET644+3 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.15/0.33  % Computer : n027.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Tue May  5 02:31:35 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 1.33/1.73  % Version  : CSE_E---1.7
% 1.33/1.73  % Problem  : theBenchmark.p
% 1.33/1.73  % SZS status Theorem for theBenchmark.p
% 1.33/1.73  % SZS output start CNFRefutation
% See solution above
% 1.33/1.73  % Total time : 1.368s
%------------------------------------------------------------------------------