TSTP Solution File: ALG216+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG216+1 : TPTP v8.2.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% 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 : Mon May 20 18:05:39 EDT 2024

% Result   : Theorem 0.16s 0.45s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   51 (  23 unt;   0 def)
%            Number of atoms       :  266 (  18 equ)
%            Maximal formula atoms :   44 (   5 avg)
%            Number of connectives :  336 ( 121   ~; 105   |;  86   &)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   20 (  18 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   46 (   0 sgn  30   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t5_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)
        & 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) )
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X2))
             => ! [X4] :
                  ( m1_subset_1(X4,u1_struct_0(X2))
                 => ( v1_rmod_5(k8_rlvect_2(X2,X3,X4),X1,X2)
                   => ( k1_rlvect_1(X1) = k2_group_1(X1)
                      | ( X3 != k1_rlvect_1(X2)
                        & X4 != k1_rlvect_1(X2) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_rmod_5) ).

fof(t6_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)
        & 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) )
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X2))
             => ( k1_rlvect_1(X1) != k2_group_1(X1)
               => ( ~ v1_rmod_5(k8_rlvect_2(X2,X3,k1_rlvect_1(X2)),X1,X2)
                  & ~ v1_rmod_5(k8_rlvect_2(X2,k1_rlvect_1(X2),X3),X1,X2) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_rmod_5) ).

fof(dt_l1_rlvect_1,axiom,
    ! [X1] :
      ( l1_rlvect_1(X1)
     => l2_struct_0(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).

fof(dt_l3_vectsp_1,axiom,
    ! [X1] :
      ( l3_vectsp_1(X1)
     => ( l1_rlvect_1(X1)
        & l2_vectsp_1(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).

fof(dt_l1_vectsp_2,axiom,
    ! [X1] :
      ( l1_struct_0(X1)
     => ! [X2] :
          ( l1_vectsp_2(X2,X1)
         => l1_rlvect_1(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_2) ).

fof(dt_k1_rlvect_1,axiom,
    ! [X1] :
      ( l2_struct_0(X1)
     => m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_rlvect_1) ).

fof(dt_l2_struct_0,axiom,
    ! [X1] :
      ( l2_struct_0(X1)
     => l1_struct_0(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).

fof(c_0_7,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) )
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X2))
             => ! [X4] :
                  ( m1_subset_1(X4,u1_struct_0(X2))
                 => ( v1_rmod_5(k8_rlvect_2(X2,X3,X4),X1,X2)
                   => ( k1_rlvect_1(X1) = k2_group_1(X1)
                      | ( X3 != k1_rlvect_1(X2)
                        & X4 != k1_rlvect_1(X2) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[t5_rmod_5]) ).

fof(c_0_8,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)
          & 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) )
           => ! [X3] :
                ( m1_subset_1(X3,u1_struct_0(X2))
               => ( k1_rlvect_1(X1) != k2_group_1(X1)
                 => ( ~ v1_rmod_5(k8_rlvect_2(X2,X3,k1_rlvect_1(X2)),X1,X2)
                    & ~ v1_rmod_5(k8_rlvect_2(X2,k1_rlvect_1(X2),X3),X1,X2) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t6_rmod_5])]) ).

fof(c_0_9,plain,
    ! [X78,X79,X80,X81] :
      ( ( X80 != k1_rlvect_1(X79)
        | k1_rlvect_1(X78) = k2_group_1(X78)
        | ~ v1_rmod_5(k8_rlvect_2(X79,X80,X81),X78,X79)
        | ~ m1_subset_1(X81,u1_struct_0(X79))
        | ~ m1_subset_1(X80,u1_struct_0(X79))
        | v3_struct_0(X79)
        | ~ v3_rlvect_1(X79)
        | ~ v4_rlvect_1(X79)
        | ~ v5_rlvect_1(X79)
        | ~ v6_rlvect_1(X79)
        | ~ v5_vectsp_2(X79,X78)
        | ~ l1_vectsp_2(X79,X78)
        | v3_struct_0(X78)
        | ~ v3_rlvect_1(X78)
        | ~ v4_rlvect_1(X78)
        | ~ v5_rlvect_1(X78)
        | ~ v6_rlvect_1(X78)
        | ~ v4_group_1(X78)
        | ~ v6_vectsp_1(X78)
        | ~ v7_vectsp_1(X78)
        | ~ v8_vectsp_1(X78)
        | ~ l3_vectsp_1(X78) )
      & ( X81 != k1_rlvect_1(X79)
        | k1_rlvect_1(X78) = k2_group_1(X78)
        | ~ v1_rmod_5(k8_rlvect_2(X79,X80,X81),X78,X79)
        | ~ m1_subset_1(X81,u1_struct_0(X79))
        | ~ m1_subset_1(X80,u1_struct_0(X79))
        | v3_struct_0(X79)
        | ~ v3_rlvect_1(X79)
        | ~ v4_rlvect_1(X79)
        | ~ v5_rlvect_1(X79)
        | ~ v6_rlvect_1(X79)
        | ~ v5_vectsp_2(X79,X78)
        | ~ l1_vectsp_2(X79,X78)
        | v3_struct_0(X78)
        | ~ v3_rlvect_1(X78)
        | ~ v4_rlvect_1(X78)
        | ~ v5_rlvect_1(X78)
        | ~ v6_rlvect_1(X78)
        | ~ v4_group_1(X78)
        | ~ v6_vectsp_1(X78)
        | ~ v7_vectsp_1(X78)
        | ~ v8_vectsp_1(X78)
        | ~ l3_vectsp_1(X78) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).

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)
    & v6_vectsp_1(esk1_0)
    & v7_vectsp_1(esk1_0)
    & v8_vectsp_1(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)
    & v5_vectsp_2(esk2_0,esk1_0)
    & l1_vectsp_2(esk2_0,esk1_0)
    & m1_subset_1(esk3_0,u1_struct_0(esk2_0))
    & k1_rlvect_1(esk1_0) != k2_group_1(esk1_0)
    & ( v1_rmod_5(k8_rlvect_2(esk2_0,esk3_0,k1_rlvect_1(esk2_0)),esk1_0,esk2_0)
      | v1_rmod_5(k8_rlvect_2(esk2_0,k1_rlvect_1(esk2_0),esk3_0),esk1_0,esk2_0) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).

cnf(c_0_11,plain,
    ( k1_rlvect_1(X3) = k2_group_1(X3)
    | v3_struct_0(X2)
    | v3_struct_0(X3)
    | X1 != k1_rlvect_1(X2)
    | ~ v1_rmod_5(k8_rlvect_2(X2,X1,X4),X3,X2)
    | ~ m1_subset_1(X4,u1_struct_0(X2))
    | ~ m1_subset_1(X1,u1_struct_0(X2))
    | ~ v3_rlvect_1(X2)
    | ~ v4_rlvect_1(X2)
    | ~ v5_rlvect_1(X2)
    | ~ v6_rlvect_1(X2)
    | ~ v5_vectsp_2(X2,X3)
    | ~ l1_vectsp_2(X2,X3)
    | ~ v3_rlvect_1(X3)
    | ~ v4_rlvect_1(X3)
    | ~ v5_rlvect_1(X3)
    | ~ v6_rlvect_1(X3)
    | ~ v4_group_1(X3)
    | ~ v6_vectsp_1(X3)
    | ~ v7_vectsp_1(X3)
    | ~ v8_vectsp_1(X3)
    | ~ l3_vectsp_1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    ( v1_rmod_5(k8_rlvect_2(esk2_0,esk3_0,k1_rlvect_1(esk2_0)),esk1_0,esk2_0)
    | v1_rmod_5(k8_rlvect_2(esk2_0,k1_rlvect_1(esk2_0),esk3_0),esk1_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    m1_subset_1(esk3_0,u1_struct_0(esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    l1_vectsp_2(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    v5_vectsp_2(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    l3_vectsp_1(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,
    v4_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_21,negated_conjecture,
    v6_rlvect_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,
    v5_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,
    v4_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,
    v3_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,
    k1_rlvect_1(esk1_0) != k2_group_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]) ).

fof(c_0_32,plain,
    ! [X46] :
      ( ~ l1_rlvect_1(X46)
      | l2_struct_0(X46) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_rlvect_1])])]) ).

fof(c_0_33,plain,
    ! [X77] :
      ( ( l1_rlvect_1(X77)
        | ~ l3_vectsp_1(X77) )
      & ( l2_vectsp_1(X77)
        | ~ l3_vectsp_1(X77) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_vectsp_1])])])]) ).

fof(c_0_34,plain,
    ! [X75,X76] :
      ( ~ l1_struct_0(X75)
      | ~ l1_vectsp_2(X76,X75)
      | l1_rlvect_1(X76) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_vectsp_2])])])]) ).

cnf(c_0_35,plain,
    ( k1_rlvect_1(X3) = k2_group_1(X3)
    | v3_struct_0(X2)
    | v3_struct_0(X3)
    | X1 != k1_rlvect_1(X2)
    | ~ v1_rmod_5(k8_rlvect_2(X2,X4,X1),X3,X2)
    | ~ m1_subset_1(X1,u1_struct_0(X2))
    | ~ m1_subset_1(X4,u1_struct_0(X2))
    | ~ v3_rlvect_1(X2)
    | ~ v4_rlvect_1(X2)
    | ~ v5_rlvect_1(X2)
    | ~ v6_rlvect_1(X2)
    | ~ v5_vectsp_2(X2,X3)
    | ~ l1_vectsp_2(X2,X3)
    | ~ v3_rlvect_1(X3)
    | ~ v4_rlvect_1(X3)
    | ~ v5_rlvect_1(X3)
    | ~ v6_rlvect_1(X3)
    | ~ v4_group_1(X3)
    | ~ v6_vectsp_1(X3)
    | ~ v7_vectsp_1(X3)
    | ~ v8_vectsp_1(X3)
    | ~ l3_vectsp_1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_36,negated_conjecture,
    ( v1_rmod_5(k8_rlvect_2(esk2_0,esk3_0,k1_rlvect_1(esk2_0)),esk1_0,esk2_0)
    | ~ m1_subset_1(k1_rlvect_1(esk2_0),u1_struct_0(esk2_0)) ),
    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(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),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]) ).

fof(c_0_37,plain,
    ! [X70] :
      ( ~ l2_struct_0(X70)
      | m1_subset_1(k1_rlvect_1(X70),u1_struct_0(X70)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_rlvect_1])])]) ).

fof(c_0_38,plain,
    ! [X47] :
      ( ~ l2_struct_0(X47)
      | l1_struct_0(X47) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_struct_0])])]) ).

cnf(c_0_39,plain,
    ( l2_struct_0(X1)
    | ~ l1_rlvect_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_40,plain,
    ( l1_rlvect_1(X1)
    | ~ l3_vectsp_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_41,plain,
    ( l1_rlvect_1(X2)
    | ~ l1_struct_0(X1)
    | ~ l1_vectsp_2(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_42,negated_conjecture,
    ~ m1_subset_1(k1_rlvect_1(esk2_0),u1_struct_0(esk2_0)),
    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(spm,[status(thm)],[c_0_35,c_0_36]),c_0_13]),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_43,plain,
    ( m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
    | ~ l2_struct_0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_44,plain,
    ( l1_struct_0(X1)
    | ~ l2_struct_0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_45,plain,
    ( l2_struct_0(X1)
    | ~ l3_vectsp_1(X1) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_46,negated_conjecture,
    ( l1_rlvect_1(esk2_0)
    | ~ l1_struct_0(esk1_0) ),
    inference(spm,[status(thm)],[c_0_41,c_0_14]) ).

cnf(c_0_47,negated_conjecture,
    ~ l2_struct_0(esk2_0),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_48,plain,
    ( l1_struct_0(X1)
    | ~ l3_vectsp_1(X1) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_49,negated_conjecture,
    ~ l1_struct_0(esk1_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_46]),c_0_47]) ).

cnf(c_0_50,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_16]),c_0_49]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : ALG216+1 : TPTP v8.2.0. Released v3.4.0.
% 0.10/0.11  % Command    : run_E %s %d THM
% 0.10/0.31  % Computer : n026.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Sat May 18 23:50:23 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.16/0.45  # Version: 3.1.0
% 0.16/0.45  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.45  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.45  # Starting new_bool_3 with 300s (1) cores
% 0.16/0.45  # Starting new_bool_1 with 300s (1) cores
% 0.16/0.45  # Starting sh5l with 300s (1) cores
% 0.16/0.45  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 7226 completed with status 0
% 0.16/0.45  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/0.45  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.45  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.45  # No SInE strategy applied
% 0.16/0.45  # Search class: FGHSM-FFMM31-SFFFFFNN
% 0.16/0.45  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.45  # Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/0.45  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.45  # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.16/0.45  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/0.45  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 136s (1) cores
% 0.16/0.45  # G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 7235 completed with status 0
% 0.16/0.45  # Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y
% 0.16/0.45  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.45  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.45  # No SInE strategy applied
% 0.16/0.45  # Search class: FGHSM-FFMM31-SFFFFFNN
% 0.16/0.45  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.45  # Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/0.45  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.45  # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.16/0.45  # Preprocessing time       : 0.004 s
% 0.16/0.45  
% 0.16/0.45  # Proof found!
% 0.16/0.45  # SZS status Theorem
% 0.16/0.45  # SZS output start CNFRefutation
% See solution above
% 0.16/0.45  # Parsed axioms                        : 53
% 0.16/0.45  # Removed by relevancy pruning/SinE    : 0
% 0.16/0.45  # Initial clauses                      : 85
% 0.16/0.45  # Removed in clause preprocessing      : 6
% 0.16/0.45  # Initial clauses in saturation        : 79
% 0.16/0.45  # Processed clauses                    : 127
% 0.16/0.45  # ...of these trivial                  : 1
% 0.16/0.45  # ...subsumed                          : 11
% 0.16/0.45  # ...remaining for further processing  : 115
% 0.16/0.45  # Other redundant clauses eliminated   : 0
% 0.16/0.45  # Clauses deleted for lack of memory   : 0
% 0.16/0.45  # Backward-subsumed                    : 2
% 0.16/0.45  # Backward-rewritten                   : 3
% 0.16/0.45  # Generated clauses                    : 96
% 0.16/0.45  # ...of the previous two non-redundant : 89
% 0.16/0.45  # ...aggressively subsumed             : 0
% 0.16/0.45  # Contextual simplify-reflections      : 0
% 0.16/0.45  # Paramodulations                      : 96
% 0.16/0.45  # Factorizations                       : 0
% 0.16/0.45  # NegExts                              : 0
% 0.16/0.45  # Equation resolutions                 : 0
% 0.16/0.45  # Disequality decompositions           : 0
% 0.16/0.45  # Total rewrite steps                  : 75
% 0.16/0.45  # ...of those cached                   : 54
% 0.16/0.45  # Propositional unsat checks           : 0
% 0.16/0.45  #    Propositional check models        : 0
% 0.16/0.45  #    Propositional check unsatisfiable : 0
% 0.16/0.45  #    Propositional clauses             : 0
% 0.16/0.45  #    Propositional clauses after purity: 0
% 0.16/0.45  #    Propositional unsat core size     : 0
% 0.16/0.45  #    Propositional preprocessing time  : 0.000
% 0.16/0.45  #    Propositional encoding time       : 0.000
% 0.16/0.45  #    Propositional solver time         : 0.000
% 0.16/0.45  #    Success case prop preproc time    : 0.000
% 0.16/0.45  #    Success case prop encoding time   : 0.000
% 0.16/0.45  #    Success case prop solver time     : 0.000
% 0.16/0.45  # Current number of processed clauses  : 110
% 0.16/0.45  #    Positive orientable unit clauses  : 42
% 0.16/0.45  #    Positive unorientable unit clauses: 1
% 0.16/0.45  #    Negative unit clauses             : 12
% 0.16/0.45  #    Non-unit-clauses                  : 55
% 0.16/0.45  # Current number of unprocessed clauses: 35
% 0.16/0.45  # ...number of literals in the above   : 261
% 0.16/0.45  # Current number of archived formulas  : 0
% 0.16/0.45  # Current number of archived clauses   : 5
% 0.16/0.45  # Clause-clause subsumption calls (NU) : 2150
% 0.16/0.45  # Rec. Clause-clause subsumption calls : 557
% 0.16/0.45  # Non-unit clause-clause subsumptions  : 6
% 0.16/0.45  # Unit Clause-clause subsumption calls : 341
% 0.16/0.45  # Rewrite failures with RHS unbound    : 0
% 0.16/0.45  # BW rewrite match attempts            : 12
% 0.16/0.45  # BW rewrite match successes           : 4
% 0.16/0.45  # Condensation attempts                : 0
% 0.16/0.45  # Condensation successes               : 0
% 0.16/0.45  # Termbank termtop insertions          : 6478
% 0.16/0.45  # Search garbage collected termcells   : 977
% 0.16/0.45  
% 0.16/0.45  # -------------------------------------------------
% 0.16/0.45  # User time                : 0.015 s
% 0.16/0.45  # System time              : 0.004 s
% 0.16/0.45  # Total time               : 0.019 s
% 0.16/0.45  # Maximum resident set size: 1904 pages
% 0.16/0.45  
% 0.16/0.45  # -------------------------------------------------
% 0.16/0.45  # User time                : 0.059 s
% 0.16/0.45  # System time              : 0.020 s
% 0.16/0.45  # Total time               : 0.078 s
% 0.16/0.45  # Maximum resident set size: 1736 pages
% 0.16/0.45  % E---3.1 exiting
% 0.16/0.45  % E exiting
%------------------------------------------------------------------------------