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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : LAT313+1 : TPTP v9.2.1. Released v3.4.0.
% 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 : n019.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 04:38:03 PM UTC 2026

% Result   : Theorem 1.30s 1.72s
% Output   : CNFRefutation 1.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   58 (  19 unt;   0 def)
%            Number of atoms       :  234 (  23 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  276 ( 100   ~;  90   |;  54   &)
%                                         (   2 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :   67 (   1 sgn  47   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d8_filter_2,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => k17_filter_2(X1) = u1_struct_0(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_2) ).

fof(t43_filter_2,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m2_filter_2(X2,X1)
         => ( ( v14_lattices(X1)
              & r2_hidden(k6_lattices(X1),X2) )
           => ( r1_filter_2(u1_struct_0(X1),X2,k17_filter_2(X1))
              & X2 = u1_struct_0(X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_filter_2) ).

fof(dt_m2_filter_2,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m2_filter_2(X2,X1)
         => ( ~ v1_xboole_0(X2)
            & m2_lattice4(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).

fof(dt_k17_filter_2,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => m2_filter_2(k17_filter_2(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_filter_2) ).

fof(t42_filter_2,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( ( ~ v1_xboole_0(X2)
            & m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
         => ( ( v14_lattices(X1)
              & r2_hidden(k6_lattices(X1),X2) )
           => ( r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),k17_filter_2(X1))
              & k19_filter_2(X1,X2) = u1_struct_0(X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_2) ).

fof(dt_m2_lattice4,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m2_lattice4(X2,X1)
         => m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).

fof(t38_filter_2,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m2_filter_2(X2,X1)
         => r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_2) ).

fof(t7_boole,axiom,
    ! [X1,X2] :
      ~ ( r2_hidden(X1,X2)
        & v1_xboole_0(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

fof(redefinition_r1_filter_2,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X1)
        & m1_subset_1(X2,k1_zfmisc_1(X1))
        & m1_subset_1(X3,k1_zfmisc_1(X1)) )
     => ( r1_filter_2(X1,X2,X3)
      <=> X2 = X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).

fof(c_0_9,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => k17_filter_2(X1) = u1_struct_0(X1) ),
    inference(fof_simplification,[status(thm)],[d8_filter_2]) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v10_lattices(X1)
          & l3_lattices(X1) )
       => ! [X2] :
            ( m2_filter_2(X2,X1)
           => ( ( v14_lattices(X1)
                & r2_hidden(k6_lattices(X1),X2) )
             => ( r1_filter_2(u1_struct_0(X1),X2,k17_filter_2(X1))
                & X2 = u1_struct_0(X1) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t43_filter_2])]) ).

fof(c_0_11,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m2_filter_2(X2,X1)
         => ( ~ v1_xboole_0(X2)
            & m2_lattice4(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[dt_m2_filter_2]) ).

fof(c_0_12,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => m2_filter_2(k17_filter_2(X1),X1) ),
    inference(fof_simplification,[status(thm)],[dt_k17_filter_2]) ).

fof(c_0_13,plain,
    ! [X85] :
      ( v3_struct_0(X85)
      | ~ v10_lattices(X85)
      | ~ l3_lattices(X85)
      | k17_filter_2(X85) = u1_struct_0(X85) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).

fof(c_0_14,negated_conjecture,
    ( ~ v3_struct_0(esk1_0)
    & v10_lattices(esk1_0)
    & l3_lattices(esk1_0)
    & m2_filter_2(esk2_0,esk1_0)
    & v14_lattices(esk1_0)
    & r2_hidden(k6_lattices(esk1_0),esk2_0)
    & ( ~ r1_filter_2(u1_struct_0(esk1_0),esk2_0,k17_filter_2(esk1_0))
      | esk2_0 != u1_struct_0(esk1_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_15,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( ( ~ v1_xboole_0(X2)
            & m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
         => ( ( v14_lattices(X1)
              & r2_hidden(k6_lattices(X1),X2) )
           => ( r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),k17_filter_2(X1))
              & k19_filter_2(X1,X2) = u1_struct_0(X1) ) ) ) ),
    inference(fof_simplification,[status(thm)],[t42_filter_2]) ).

fof(c_0_16,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m2_lattice4(X2,X1)
         => m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
    inference(fof_simplification,[status(thm)],[dt_m2_lattice4]) ).

fof(c_0_17,plain,
    ! [X93,X94] :
      ( ( ~ v1_xboole_0(X94)
        | ~ m2_filter_2(X94,X93)
        | v3_struct_0(X93)
        | ~ v10_lattices(X93)
        | ~ l3_lattices(X93) )
      & ( m2_lattice4(X94,X93)
        | ~ m2_filter_2(X94,X93)
        | v3_struct_0(X93)
        | ~ v10_lattices(X93)
        | ~ l3_lattices(X93) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).

fof(c_0_18,plain,
    ! [X86] :
      ( v3_struct_0(X86)
      | ~ v10_lattices(X86)
      | ~ l3_lattices(X86)
      | m2_filter_2(k17_filter_2(X86),X86) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).

cnf(c_0_19,plain,
    ( v3_struct_0(X1)
    | k17_filter_2(X1) = u1_struct_0(X1)
    | ~ v10_lattices(X1)
    | ~ l3_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,negated_conjecture,
    l3_lattices(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,negated_conjecture,
    v10_lattices(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_23,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m2_filter_2(X2,X1)
         => r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),X2) ) ),
    inference(fof_simplification,[status(thm)],[t38_filter_2]) ).

fof(c_0_24,plain,
    ! [X138,X139] :
      ( ( r1_filter_2(u1_struct_0(X138),k19_filter_2(X138,X139),k17_filter_2(X138))
        | ~ v14_lattices(X138)
        | ~ r2_hidden(k6_lattices(X138),X139)
        | v1_xboole_0(X139)
        | ~ m1_subset_1(X139,k1_zfmisc_1(u1_struct_0(X138)))
        | v3_struct_0(X138)
        | ~ v10_lattices(X138)
        | ~ l3_lattices(X138) )
      & ( k19_filter_2(X138,X139) = u1_struct_0(X138)
        | ~ v14_lattices(X138)
        | ~ r2_hidden(k6_lattices(X138),X139)
        | v1_xboole_0(X139)
        | ~ m1_subset_1(X139,k1_zfmisc_1(u1_struct_0(X138)))
        | v3_struct_0(X138)
        | ~ v10_lattices(X138)
        | ~ l3_lattices(X138) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).

fof(c_0_25,plain,
    ! [X147,X148] :
      ( ~ r2_hidden(X147,X148)
      | ~ v1_xboole_0(X148) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).

fof(c_0_26,plain,
    ! [X95,X96] :
      ( v3_struct_0(X95)
      | ~ v10_lattices(X95)
      | ~ l3_lattices(X95)
      | ~ m2_lattice4(X96,X95)
      | m1_subset_1(X96,k1_zfmisc_1(u1_struct_0(X95))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).

cnf(c_0_27,plain,
    ( m2_lattice4(X1,X2)
    | v3_struct_0(X2)
    | ~ m2_filter_2(X1,X2)
    | ~ v10_lattices(X2)
    | ~ l3_lattices(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_28,negated_conjecture,
    m2_filter_2(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_29,plain,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X1)
        & m1_subset_1(X2,k1_zfmisc_1(X1))
        & m1_subset_1(X3,k1_zfmisc_1(X1)) )
     => ( r1_filter_2(X1,X2,X3)
      <=> X2 = X3 ) ),
    inference(fof_simplification,[status(thm)],[redefinition_r1_filter_2]) ).

cnf(c_0_30,plain,
    ( v3_struct_0(X1)
    | m2_filter_2(k17_filter_2(X1),X1)
    | ~ v10_lattices(X1)
    | ~ l3_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_31,negated_conjecture,
    k17_filter_2(esk1_0) = u1_struct_0(esk1_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_22]) ).

fof(c_0_32,plain,
    ! [X134,X135] :
      ( v3_struct_0(X134)
      | ~ v10_lattices(X134)
      | ~ l3_lattices(X134)
      | ~ m2_filter_2(X135,X134)
      | r1_filter_2(u1_struct_0(X134),k19_filter_2(X134,X135),X135) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).

cnf(c_0_33,plain,
    ( k19_filter_2(X1,X2) = u1_struct_0(X1)
    | v1_xboole_0(X2)
    | v3_struct_0(X1)
    | ~ v14_lattices(X1)
    | ~ r2_hidden(k6_lattices(X1),X2)
    | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ v10_lattices(X1)
    | ~ l3_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,plain,
    ( ~ r2_hidden(X1,X2)
    | ~ v1_xboole_0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_35,plain,
    ( v3_struct_0(X1)
    | m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ v10_lattices(X1)
    | ~ l3_lattices(X1)
    | ~ m2_lattice4(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_36,negated_conjecture,
    m2_lattice4(esk2_0,esk1_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]),c_0_21])]),c_0_22]) ).

fof(c_0_37,plain,
    ! [X120,X121,X122] :
      ( ( ~ r1_filter_2(X120,X121,X122)
        | X121 = X122
        | v1_xboole_0(X120)
        | ~ m1_subset_1(X121,k1_zfmisc_1(X120))
        | ~ m1_subset_1(X122,k1_zfmisc_1(X120)) )
      & ( X121 != X122
        | r1_filter_2(X120,X121,X122)
        | v1_xboole_0(X120)
        | ~ m1_subset_1(X121,k1_zfmisc_1(X120))
        | ~ m1_subset_1(X122,k1_zfmisc_1(X120)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).

cnf(c_0_38,plain,
    ( v3_struct_0(X2)
    | ~ v1_xboole_0(X1)
    | ~ m2_filter_2(X1,X2)
    | ~ v10_lattices(X2)
    | ~ l3_lattices(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_39,negated_conjecture,
    m2_filter_2(u1_struct_0(esk1_0),esk1_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_31]),c_0_21])]),c_0_22]) ).

cnf(c_0_40,plain,
    ( v3_struct_0(X1)
    | r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),X2)
    | ~ v10_lattices(X1)
    | ~ l3_lattices(X1)
    | ~ m2_filter_2(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_41,plain,
    ( k19_filter_2(X1,X2) = u1_struct_0(X1)
    | v3_struct_0(X1)
    | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ r2_hidden(k6_lattices(X1),X2)
    | ~ v14_lattices(X1)
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1) ),
    inference(csr,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_42,negated_conjecture,
    m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_20]),c_0_21])]),c_0_22]) ).

cnf(c_0_43,negated_conjecture,
    r2_hidden(k6_lattices(esk1_0),esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_44,negated_conjecture,
    v14_lattices(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_45,plain,
    ( X2 = X3
    | v1_xboole_0(X1)
    | ~ r1_filter_2(X1,X2,X3)
    | ~ m1_subset_1(X2,k1_zfmisc_1(X1))
    | ~ m1_subset_1(X3,k1_zfmisc_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_46,negated_conjecture,
    ~ v1_xboole_0(u1_struct_0(esk1_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_20]),c_0_21])]),c_0_22]) ).

cnf(c_0_47,negated_conjecture,
    r1_filter_2(u1_struct_0(esk1_0),k19_filter_2(esk1_0,esk2_0),esk2_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_28]),c_0_20]),c_0_21])]),c_0_22]) ).

cnf(c_0_48,negated_conjecture,
    k19_filter_2(esk1_0,esk2_0) = u1_struct_0(esk1_0),
    inference(sr,[status(thm)],[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_41,c_0_42]),c_0_43]),c_0_44]),c_0_20]),c_0_21])]),c_0_22]) ).

cnf(c_0_49,negated_conjecture,
    m2_lattice4(u1_struct_0(esk1_0),esk1_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_39]),c_0_20]),c_0_21])]),c_0_22]) ).

cnf(c_0_50,negated_conjecture,
    ( X1 = esk2_0
    | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))
    | ~ r1_filter_2(u1_struct_0(esk1_0),X1,esk2_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_42]),c_0_46]) ).

cnf(c_0_51,negated_conjecture,
    r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk2_0),
    inference(rw,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_52,negated_conjecture,
    m1_subset_1(u1_struct_0(esk1_0),k1_zfmisc_1(u1_struct_0(esk1_0))),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_49]),c_0_20]),c_0_21])]),c_0_22]) ).

cnf(c_0_53,negated_conjecture,
    ( ~ r1_filter_2(u1_struct_0(esk1_0),esk2_0,k17_filter_2(esk1_0))
    | esk2_0 != u1_struct_0(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_54,negated_conjecture,
    u1_struct_0(esk1_0) = esk2_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).

cnf(c_0_55,negated_conjecture,
    ( u1_struct_0(esk1_0) != esk2_0
    | ~ r1_filter_2(u1_struct_0(esk1_0),esk2_0,u1_struct_0(esk1_0)) ),
    inference(rw,[status(thm)],[c_0_53,c_0_31]) ).

cnf(c_0_56,negated_conjecture,
    r1_filter_2(esk2_0,esk2_0,esk2_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_54]),c_0_54]) ).

cnf(c_0_57,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_54]),c_0_54]),c_0_54])]),c_0_56])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT313+1 : TPTP v9.2.1. Released v3.4.0.
% 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 : n019.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   : Mon May  4 21:12:44 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 1.30/1.72  % Version  : CSE_E---1.7
% 1.30/1.72  % Problem  : theBenchmark.p
% 1.30/1.72  % SZS status Theorem for theBenchmark.p
% 1.30/1.72  % SZS output start CNFRefutation
% See solution above
% 1.30/1.72  % Total time : 1.372s
%------------------------------------------------------------------------------