TSTP Solution File: ALG219+3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG219+3 : TPTP v8.2.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n014.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 : Mon May 20 18:05:41 EDT 2024

% Result   : Theorem 37.43s 5.53s
% Output   : CNFRefutation 37.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   45 (  33 unt;   0 def)
%            Number of atoms       :  309 (  29 equ)
%            Maximal formula atoms :   26 (   6 avg)
%            Number of connectives :  383 ( 119   ~; 112   |; 130   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   20 (  18 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   40 (   0 sgn  28   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t13_rmod_5,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_rlvect_1(X1)
        & v4_rlvect_1(X1)
        & v5_rlvect_1(X1)
        & v6_rlvect_1(X1)
        & v4_group_1(X1)
        & v7_group_1(X1)
        & v6_vectsp_1(X1)
        & v7_vectsp_1(X1)
        & v8_vectsp_1(X1)
        & ~ v10_vectsp_1(X1)
        & v2_vectsp_2(X1)
        & l3_vectsp_1(X1) )
     => ! [X2] :
          ( ( ~ v3_struct_0(X2)
            & v3_rlvect_1(X2)
            & v4_rlvect_1(X2)
            & v5_rlvect_1(X2)
            & v6_rlvect_1(X2)
            & v5_vectsp_2(X2,X1)
            & l1_vectsp_2(X2,X1) )
         => ! [X3] :
              ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
             => ! [X4] :
                  ( ( v3_vectsp_2(X4,X1)
                    & m1_rmod_2(X4,X1,X2) )
                 => ( X3 = u1_struct_0(X4)
                   => ( k1_rlvect_1(X1) = k2_group_1(X1)
                      | k1_rmod_5(X1,X2,X3) = X4 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_rmod_5) ).

fof(t32_rmod_2,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_rlvect_1(X1)
        & v4_rlvect_1(X1)
        & v5_rlvect_1(X1)
        & v6_rlvect_1(X1)
        & v4_group_1(X1)
        & v6_vectsp_1(X1)
        & v7_vectsp_1(X1)
        & v8_vectsp_1(X1)
        & l3_vectsp_1(X1) )
     => ! [X2] :
          ( ( ~ v3_struct_0(X2)
            & v3_rlvect_1(X2)
            & v4_rlvect_1(X2)
            & v5_rlvect_1(X2)
            & v6_rlvect_1(X2)
            & v5_vectsp_2(X2,X1)
            & l1_vectsp_2(X2,X1) )
         => m1_rmod_2(X2,X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+278.ax',t32_rmod_2) ).

fof(t14_rmod_5,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_rlvect_1(X1)
        & v4_rlvect_1(X1)
        & v5_rlvect_1(X1)
        & v6_rlvect_1(X1)
        & v4_group_1(X1)
        & v7_group_1(X1)
        & v6_vectsp_1(X1)
        & v7_vectsp_1(X1)
        & v8_vectsp_1(X1)
        & ~ v10_vectsp_1(X1)
        & v2_vectsp_2(X1)
        & l3_vectsp_1(X1) )
     => ! [X2] :
          ( ( ~ v3_struct_0(X2)
            & v3_rlvect_1(X2)
            & v4_rlvect_1(X2)
            & v5_rlvect_1(X2)
            & v6_rlvect_1(X2)
            & v3_vectsp_2(X2,X1)
            & v5_vectsp_2(X2,X1)
            & l1_vectsp_2(X2,X1) )
         => ! [X3] :
              ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
             => ( X3 = u1_struct_0(X2)
               => ( k1_rlvect_1(X1) = k2_group_1(X1)
                  | k1_rmod_5(X1,X2,X3) = X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_rmod_5) ).

fof(dt_k2_subset_1,axiom,
    ! [X1] : m1_subset_1(k2_subset_1(X1),k1_zfmisc_1(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',dt_k2_subset_1) ).

fof(d4_subset_1,axiom,
    ! [X1] : k2_subset_1(X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',d4_subset_1) ).

fof(c_0_5,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_rlvect_1(X1)
        & v4_rlvect_1(X1)
        & v5_rlvect_1(X1)
        & v6_rlvect_1(X1)
        & v4_group_1(X1)
        & v7_group_1(X1)
        & v6_vectsp_1(X1)
        & v7_vectsp_1(X1)
        & v8_vectsp_1(X1)
        & ~ v10_vectsp_1(X1)
        & v2_vectsp_2(X1)
        & l3_vectsp_1(X1) )
     => ! [X2] :
          ( ( ~ v3_struct_0(X2)
            & v3_rlvect_1(X2)
            & v4_rlvect_1(X2)
            & v5_rlvect_1(X2)
            & v6_rlvect_1(X2)
            & v5_vectsp_2(X2,X1)
            & l1_vectsp_2(X2,X1) )
         => ! [X3] :
              ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
             => ! [X4] :
                  ( ( v3_vectsp_2(X4,X1)
                    & m1_rmod_2(X4,X1,X2) )
                 => ( X3 = u1_struct_0(X4)
                   => ( k1_rlvect_1(X1) = k2_group_1(X1)
                      | k1_rmod_5(X1,X2,X3) = X4 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[t13_rmod_5]) ).

fof(c_0_6,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_rlvect_1(X1)
        & v4_rlvect_1(X1)
        & v5_rlvect_1(X1)
        & v6_rlvect_1(X1)
        & v4_group_1(X1)
        & v6_vectsp_1(X1)
        & v7_vectsp_1(X1)
        & v8_vectsp_1(X1)
        & l3_vectsp_1(X1) )
     => ! [X2] :
          ( ( ~ v3_struct_0(X2)
            & v3_rlvect_1(X2)
            & v4_rlvect_1(X2)
            & v5_rlvect_1(X2)
            & v6_rlvect_1(X2)
            & v5_vectsp_2(X2,X1)
            & l1_vectsp_2(X2,X1) )
         => m1_rmod_2(X2,X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[t32_rmod_2]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v3_rlvect_1(X1)
          & v4_rlvect_1(X1)
          & v5_rlvect_1(X1)
          & v6_rlvect_1(X1)
          & v4_group_1(X1)
          & v7_group_1(X1)
          & v6_vectsp_1(X1)
          & v7_vectsp_1(X1)
          & v8_vectsp_1(X1)
          & ~ v10_vectsp_1(X1)
          & v2_vectsp_2(X1)
          & l3_vectsp_1(X1) )
       => ! [X2] :
            ( ( ~ v3_struct_0(X2)
              & v3_rlvect_1(X2)
              & v4_rlvect_1(X2)
              & v5_rlvect_1(X2)
              & v6_rlvect_1(X2)
              & v3_vectsp_2(X2,X1)
              & v5_vectsp_2(X2,X1)
              & l1_vectsp_2(X2,X1) )
           => ! [X3] :
                ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
               => ( X3 = u1_struct_0(X2)
                 => ( k1_rlvect_1(X1) = k2_group_1(X1)
                    | k1_rmod_5(X1,X2,X3) = X2 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t14_rmod_5])]) ).

fof(c_0_8,plain,
    ! [X36,X37,X38,X39] :
      ( v3_struct_0(X36)
      | ~ v3_rlvect_1(X36)
      | ~ v4_rlvect_1(X36)
      | ~ v5_rlvect_1(X36)
      | ~ v6_rlvect_1(X36)
      | ~ v4_group_1(X36)
      | ~ v7_group_1(X36)
      | ~ v6_vectsp_1(X36)
      | ~ v7_vectsp_1(X36)
      | ~ v8_vectsp_1(X36)
      | v10_vectsp_1(X36)
      | ~ v2_vectsp_2(X36)
      | ~ l3_vectsp_1(X36)
      | v3_struct_0(X37)
      | ~ v3_rlvect_1(X37)
      | ~ v4_rlvect_1(X37)
      | ~ v5_rlvect_1(X37)
      | ~ v6_rlvect_1(X37)
      | ~ v5_vectsp_2(X37,X36)
      | ~ l1_vectsp_2(X37,X36)
      | ~ m1_subset_1(X38,k1_zfmisc_1(u1_struct_0(X37)))
      | ~ v3_vectsp_2(X39,X36)
      | ~ m1_rmod_2(X39,X36,X37)
      | X38 != u1_struct_0(X39)
      | k1_rlvect_1(X36) = k2_group_1(X36)
      | k1_rmod_5(X36,X37,X38) = X39 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).

fof(c_0_9,plain,
    ! [X220,X221] :
      ( v3_struct_0(X220)
      | ~ v3_rlvect_1(X220)
      | ~ v4_rlvect_1(X220)
      | ~ v5_rlvect_1(X220)
      | ~ v6_rlvect_1(X220)
      | ~ v4_group_1(X220)
      | ~ v6_vectsp_1(X220)
      | ~ v7_vectsp_1(X220)
      | ~ v8_vectsp_1(X220)
      | ~ l3_vectsp_1(X220)
      | v3_struct_0(X221)
      | ~ v3_rlvect_1(X221)
      | ~ v4_rlvect_1(X221)
      | ~ v5_rlvect_1(X221)
      | ~ v6_rlvect_1(X221)
      | ~ v5_vectsp_2(X221,X220)
      | ~ l1_vectsp_2(X221,X220)
      | m1_rmod_2(X221,X220,X221) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

fof(c_0_10,negated_conjecture,
    ( ~ v3_struct_0(esk1_0)
    & v3_rlvect_1(esk1_0)
    & v4_rlvect_1(esk1_0)
    & v5_rlvect_1(esk1_0)
    & v6_rlvect_1(esk1_0)
    & v4_group_1(esk1_0)
    & v7_group_1(esk1_0)
    & v6_vectsp_1(esk1_0)
    & v7_vectsp_1(esk1_0)
    & v8_vectsp_1(esk1_0)
    & ~ v10_vectsp_1(esk1_0)
    & v2_vectsp_2(esk1_0)
    & l3_vectsp_1(esk1_0)
    & ~ v3_struct_0(esk2_0)
    & v3_rlvect_1(esk2_0)
    & v4_rlvect_1(esk2_0)
    & v5_rlvect_1(esk2_0)
    & v6_rlvect_1(esk2_0)
    & v3_vectsp_2(esk2_0,esk1_0)
    & v5_vectsp_2(esk2_0,esk1_0)
    & l1_vectsp_2(esk2_0,esk1_0)
    & m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0)))
    & esk3_0 = u1_struct_0(esk2_0)
    & k1_rlvect_1(esk1_0) != k2_group_1(esk1_0)
    & k1_rmod_5(esk1_0,esk2_0,esk3_0) != esk2_0 ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).

fof(c_0_11,plain,
    ! [X1703] : m1_subset_1(k2_subset_1(X1703),k1_zfmisc_1(X1703)),
    inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).

fof(c_0_12,plain,
    ! [X1696] : k2_subset_1(X1696) = X1696,
    inference(variable_rename,[status(thm)],[d4_subset_1]) ).

cnf(c_0_13,plain,
    ( v3_struct_0(X1)
    | v10_vectsp_1(X1)
    | v3_struct_0(X2)
    | k1_rlvect_1(X1) = k2_group_1(X1)
    | k1_rmod_5(X1,X2,X3) = X4
    | ~ v3_rlvect_1(X1)
    | ~ v4_rlvect_1(X1)
    | ~ v5_rlvect_1(X1)
    | ~ v6_rlvect_1(X1)
    | ~ v4_group_1(X1)
    | ~ v7_group_1(X1)
    | ~ v6_vectsp_1(X1)
    | ~ v7_vectsp_1(X1)
    | ~ v8_vectsp_1(X1)
    | ~ v2_vectsp_2(X1)
    | ~ l3_vectsp_1(X1)
    | ~ v3_rlvect_1(X2)
    | ~ v4_rlvect_1(X2)
    | ~ v5_rlvect_1(X2)
    | ~ v6_rlvect_1(X2)
    | ~ v5_vectsp_2(X2,X1)
    | ~ l1_vectsp_2(X2,X1)
    | ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
    | ~ v3_vectsp_2(X4,X1)
    | ~ m1_rmod_2(X4,X1,X2)
    | X3 != u1_struct_0(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( v3_struct_0(X1)
    | v3_struct_0(X2)
    | m1_rmod_2(X2,X1,X2)
    | ~ v3_rlvect_1(X1)
    | ~ v4_rlvect_1(X1)
    | ~ v5_rlvect_1(X1)
    | ~ v6_rlvect_1(X1)
    | ~ v4_group_1(X1)
    | ~ v6_vectsp_1(X1)
    | ~ v7_vectsp_1(X1)
    | ~ v8_vectsp_1(X1)
    | ~ l3_vectsp_1(X1)
    | ~ v3_rlvect_1(X2)
    | ~ v4_rlvect_1(X2)
    | ~ v5_rlvect_1(X2)
    | ~ v6_rlvect_1(X2)
    | ~ v5_vectsp_2(X2,X1)
    | ~ l1_vectsp_2(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    l1_vectsp_2(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    v5_vectsp_2(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,negated_conjecture,
    v8_vectsp_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,negated_conjecture,
    v7_vectsp_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_19,negated_conjecture,
    v6_vectsp_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_20,negated_conjecture,
    l3_vectsp_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_21,negated_conjecture,
    v4_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_22,negated_conjecture,
    v6_rlvect_1(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_23,negated_conjecture,
    v6_rlvect_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_24,negated_conjecture,
    v5_rlvect_1(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_25,negated_conjecture,
    v5_rlvect_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_26,negated_conjecture,
    v4_rlvect_1(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_27,negated_conjecture,
    v4_rlvect_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_28,negated_conjecture,
    v3_rlvect_1(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_29,negated_conjecture,
    v3_rlvect_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_30,negated_conjecture,
    ~ v3_struct_0(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_31,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_32,plain,
    m1_subset_1(k2_subset_1(X1),k1_zfmisc_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_33,plain,
    k2_subset_1(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_34,plain,
    ( k1_rmod_5(X1,X2,u1_struct_0(X3)) = X3
    | k2_group_1(X1) = k1_rlvect_1(X1)
    | v10_vectsp_1(X1)
    | v3_struct_0(X2)
    | v3_struct_0(X1)
    | ~ m1_rmod_2(X3,X1,X2)
    | ~ v5_vectsp_2(X2,X1)
    | ~ v3_vectsp_2(X3,X1)
    | ~ l1_vectsp_2(X2,X1)
    | ~ v2_vectsp_2(X1)
    | ~ v8_vectsp_1(X1)
    | ~ v7_vectsp_1(X1)
    | ~ v6_vectsp_1(X1)
    | ~ l3_vectsp_1(X1)
    | ~ v7_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ v6_rlvect_1(X2)
    | ~ v6_rlvect_1(X1)
    | ~ v5_rlvect_1(X2)
    | ~ v5_rlvect_1(X1)
    | ~ v4_rlvect_1(X2)
    | ~ v4_rlvect_1(X1)
    | ~ v3_rlvect_1(X2)
    | ~ v3_rlvect_1(X1)
    | ~ m1_subset_1(u1_struct_0(X3),k1_zfmisc_1(u1_struct_0(X2))) ),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_35,negated_conjecture,
    m1_rmod_2(esk2_0,esk1_0,esk2_0),
    inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]),c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    esk3_0 = u1_struct_0(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_37,negated_conjecture,
    v3_vectsp_2(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_38,negated_conjecture,
    v2_vectsp_2(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_39,negated_conjecture,
    v7_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_40,plain,
    m1_subset_1(X1,k1_zfmisc_1(X1)),
    inference(rw,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_41,negated_conjecture,
    k1_rmod_5(esk1_0,esk2_0,esk3_0) != esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_42,negated_conjecture,
    k1_rlvect_1(esk1_0) != k2_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_43,negated_conjecture,
    ~ v10_vectsp_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_16]),c_0_37]),c_0_15]),c_0_38]),c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_39]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_36]),c_0_36]),c_0_40])]),c_0_41]),c_0_42]),c_0_43]),c_0_31]),c_0_30]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : ALG219+3 : TPTP v8.2.0. Released v3.4.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.14/0.33  % Computer : n014.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Sat May 18 22:52:09 EDT 2024
% 0.14/0.33  % CPUTime    : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.43/5.53  # Version: 3.1.0
% 37.43/5.53  # Preprocessing class: FMLLSMLLSSSNFFN.
% 37.43/5.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.43/5.53  # Starting new_bool_3 with 900s (3) cores
% 37.43/5.53  # Starting new_bool_1 with 900s (3) cores
% 37.43/5.53  # Starting sh5l with 300s (1) cores
% 37.43/5.53  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 37.43/5.53  # new_bool_3 with pid 12544 completed with status 0
% 37.43/5.53  # Result found by new_bool_3
% 37.43/5.53  # Preprocessing class: FMLLSMLLSSSNFFN.
% 37.43/5.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.43/5.53  # Starting new_bool_3 with 900s (3) cores
% 37.43/5.53  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 37.43/5.53  # Search class: FGHSM-SMLM32-MFFFFFNN
% 37.43/5.53  # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 37.43/5.53  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 68s (1) cores
% 37.43/5.53  # Starting new_bool_3 with 91s (1) cores
% 37.43/5.53  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 68s (1) cores
% 37.43/5.53  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 12548 completed with status 0
% 37.43/5.53  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 37.43/5.53  # Preprocessing class: FMLLSMLLSSSNFFN.
% 37.43/5.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.43/5.53  # Starting new_bool_3 with 900s (3) cores
% 37.43/5.53  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 37.43/5.53  # Search class: FGHSM-SMLM32-MFFFFFNN
% 37.43/5.53  # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 37.43/5.53  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 68s (1) cores
% 37.43/5.53  # Preprocessing time       : 0.054 s
% 37.43/5.53  # Presaturation interreduction done
% 37.43/5.53  
% 37.43/5.53  # Proof found!
% 37.43/5.53  # SZS status Theorem
% 37.43/5.53  # SZS output start CNFRefutation
% See solution above
% 37.43/5.53  # Parsed axioms                        : 10005
% 37.43/5.53  # Removed by relevancy pruning/SinE    : 9060
% 37.43/5.53  # Initial clauses                      : 1989
% 37.43/5.53  # Removed in clause preprocessing      : 99
% 37.43/5.53  # Initial clauses in saturation        : 1890
% 37.43/5.53  # Processed clauses                    : 15813
% 37.43/5.53  # ...of these trivial                  : 206
% 37.43/5.53  # ...subsumed                          : 6321
% 37.43/5.53  # ...remaining for further processing  : 9286
% 37.43/5.53  # Other redundant clauses eliminated   : 239
% 37.43/5.53  # Clauses deleted for lack of memory   : 0
% 37.43/5.53  # Backward-subsumed                    : 252
% 37.43/5.53  # Backward-rewritten                   : 490
% 37.43/5.53  # Generated clauses                    : 84052
% 37.43/5.53  # ...of the previous two non-redundant : 80086
% 37.43/5.53  # ...aggressively subsumed             : 0
% 37.43/5.53  # Contextual simplify-reflections      : 132
% 37.43/5.53  # Paramodulations                      : 83768
% 37.43/5.53  # Factorizations                       : 8
% 37.43/5.53  # NegExts                              : 0
% 37.43/5.53  # Equation resolutions                 : 288
% 37.43/5.53  # Disequality decompositions           : 0
% 37.43/5.53  # Total rewrite steps                  : 65647
% 37.43/5.53  # ...of those cached                   : 63443
% 37.43/5.53  # Propositional unsat checks           : 1
% 37.43/5.53  #    Propositional check models        : 0
% 37.43/5.53  #    Propositional check unsatisfiable : 0
% 37.43/5.53  #    Propositional clauses             : 0
% 37.43/5.53  #    Propositional clauses after purity: 0
% 37.43/5.53  #    Propositional unsat core size     : 0
% 37.43/5.53  #    Propositional preprocessing time  : 0.000
% 37.43/5.53  #    Propositional encoding time       : 0.018
% 37.43/5.53  #    Propositional solver time         : 0.022
% 37.43/5.53  #    Success case prop preproc time    : 0.000
% 37.43/5.53  #    Success case prop encoding time   : 0.000
% 37.43/5.53  #    Success case prop solver time     : 0.000
% 37.43/5.53  # Current number of processed clauses  : 6598
% 37.43/5.53  #    Positive orientable unit clauses  : 2061
% 37.43/5.53  #    Positive unorientable unit clauses: 1
% 37.43/5.53  #    Negative unit clauses             : 1897
% 37.43/5.53  #    Non-unit-clauses                  : 2639
% 37.43/5.53  # Current number of unprocessed clauses: 67585
% 37.43/5.53  # ...number of literals in the above   : 280392
% 37.43/5.53  # Current number of archived formulas  : 0
% 37.43/5.53  # Current number of archived clauses   : 2534
% 37.43/5.53  # Clause-clause subsumption calls (NU) : 10825160
% 37.43/5.53  # Rec. Clause-clause subsumption calls : 490694
% 37.43/5.53  # Non-unit clause-clause subsumptions  : 498
% 37.43/5.53  # Unit Clause-clause subsumption calls : 1009534
% 37.43/5.53  # Rewrite failures with RHS unbound    : 0
% 37.43/5.53  # BW rewrite match attempts            : 4436
% 37.43/5.53  # BW rewrite match successes           : 420
% 37.43/5.53  # Condensation attempts                : 0
% 37.43/5.53  # Condensation successes               : 0
% 37.43/5.53  # Termbank termtop insertions          : 2738818
% 37.43/5.53  # Search garbage collected termcells   : 123947
% 37.43/5.53  
% 37.43/5.53  # -------------------------------------------------
% 37.43/5.53  # User time                : 4.654 s
% 37.43/5.53  # System time              : 0.100 s
% 37.43/5.53  # Total time               : 4.754 s
% 37.43/5.53  # Maximum resident set size: 23676 pages
% 37.43/5.53  
% 37.43/5.53  # -------------------------------------------------
% 37.43/5.53  # User time                : 13.807 s
% 37.43/5.53  # System time              : 0.206 s
% 37.43/5.53  # Total time               : 14.013 s
% 37.43/5.53  # Maximum resident set size: 14508 pages
% 37.43/5.53  % E---3.1 exiting
% 37.43/5.53  % E exiting
%------------------------------------------------------------------------------