TSTP Solution File: ALG216+2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG216+2 : TPTP v8.2.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.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 27.83s 4.29s
% Output   : CNFRefutation 27.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   47 (  24 unt;   0 def)
%            Number of atoms       :  485 (  25 equ)
%            Maximal formula atoms :   44 (  10 avg)
%            Number of connectives :  679 ( 241   ~; 232   |; 180   &)
%                                         (   0 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (  10 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   17 (  15 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   60 (   0 sgn  39   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(dt_k3_rmod_4,axiom,
    ! [X1,X2] :
      ( ( ~ 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)
        & ~ 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_4(k3_rmod_4(X1,X2),X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+280.ax',dt_k3_rmod_4) ).

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(t41_rmod_4,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) )
         => k5_rmod_4(X1,X2,k3_rmod_4(X1,X2)) = k1_rlvect_1(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+280.ax',t41_rmod_4) ).

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(dt_k5_rmod_4,axiom,
    ! [X1,X2,X3] :
      ( ( ~ 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)
        & ~ 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_4(X3,X1,X2) )
     => m1_subset_1(k5_rmod_4(X1,X2,X3),u1_struct_0(X2)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+280.ax',dt_k5_rmod_4) ).

fof(c_0_5,plain,
    ! [X1,X2] :
      ( ( ~ 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)
        & ~ 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_4(k3_rmod_4(X1,X2),X1,X2) ),
    inference(fof_simplification,[status(thm)],[dt_k3_rmod_4]) ).

fof(c_0_6,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_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) )
         => k5_rmod_4(X1,X2,k3_rmod_4(X1,X2)) = k1_rlvect_1(X2) ) ),
    inference(fof_simplification,[status(thm)],[t41_rmod_4]) ).

fof(c_0_8,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_9,plain,
    ! [X1,X2,X3] :
      ( ( ~ 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)
        & ~ 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_4(X3,X1,X2) )
     => m1_subset_1(k5_rmod_4(X1,X2,X3),u1_struct_0(X2)) ),
    inference(fof_simplification,[status(thm)],[dt_k5_rmod_4]) ).

fof(c_0_10,plain,
    ! [X1307,X1308] :
      ( v3_struct_0(X1307)
      | ~ v3_rlvect_1(X1307)
      | ~ v4_rlvect_1(X1307)
      | ~ v5_rlvect_1(X1307)
      | ~ v6_rlvect_1(X1307)
      | ~ v4_group_1(X1307)
      | ~ v6_vectsp_1(X1307)
      | ~ v7_vectsp_1(X1307)
      | ~ v8_vectsp_1(X1307)
      | ~ l3_vectsp_1(X1307)
      | v3_struct_0(X1308)
      | ~ v3_rlvect_1(X1308)
      | ~ v4_rlvect_1(X1308)
      | ~ v5_rlvect_1(X1308)
      | ~ v6_rlvect_1(X1308)
      | ~ v5_vectsp_2(X1308,X1307)
      | ~ l1_vectsp_2(X1308,X1307)
      | m1_rmod_4(k3_rmod_4(X1307,X1308),X1307,X1308) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_11,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_6])])])]) ).

fof(c_0_12,plain,
    ! [X181,X182] :
      ( v3_struct_0(X181)
      | ~ v3_rlvect_1(X181)
      | ~ v4_rlvect_1(X181)
      | ~ v5_rlvect_1(X181)
      | ~ v6_rlvect_1(X181)
      | ~ v4_group_1(X181)
      | ~ v6_vectsp_1(X181)
      | ~ v7_vectsp_1(X181)
      | ~ v8_vectsp_1(X181)
      | ~ l3_vectsp_1(X181)
      | v3_struct_0(X182)
      | ~ v3_rlvect_1(X182)
      | ~ v4_rlvect_1(X182)
      | ~ v5_rlvect_1(X182)
      | ~ v6_rlvect_1(X182)
      | ~ v5_vectsp_2(X182,X181)
      | ~ l1_vectsp_2(X182,X181)
      | k5_rmod_4(X181,X182,k3_rmod_4(X181,X182)) = k1_rlvect_1(X182) ),
    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_13,plain,
    ! [X32,X33,X34,X35] :
      ( ( X34 != k1_rlvect_1(X33)
        | k1_rlvect_1(X32) = k2_group_1(X32)
        | ~ v1_rmod_5(k8_rlvect_2(X33,X34,X35),X32,X33)
        | ~ m1_subset_1(X35,u1_struct_0(X33))
        | ~ m1_subset_1(X34,u1_struct_0(X33))
        | v3_struct_0(X33)
        | ~ v3_rlvect_1(X33)
        | ~ v4_rlvect_1(X33)
        | ~ v5_rlvect_1(X33)
        | ~ v6_rlvect_1(X33)
        | ~ v5_vectsp_2(X33,X32)
        | ~ l1_vectsp_2(X33,X32)
        | v3_struct_0(X32)
        | ~ v3_rlvect_1(X32)
        | ~ v4_rlvect_1(X32)
        | ~ v5_rlvect_1(X32)
        | ~ v6_rlvect_1(X32)
        | ~ v4_group_1(X32)
        | ~ v6_vectsp_1(X32)
        | ~ v7_vectsp_1(X32)
        | ~ v8_vectsp_1(X32)
        | ~ l3_vectsp_1(X32) )
      & ( X35 != k1_rlvect_1(X33)
        | k1_rlvect_1(X32) = k2_group_1(X32)
        | ~ v1_rmod_5(k8_rlvect_2(X33,X34,X35),X32,X33)
        | ~ m1_subset_1(X35,u1_struct_0(X33))
        | ~ m1_subset_1(X34,u1_struct_0(X33))
        | v3_struct_0(X33)
        | ~ v3_rlvect_1(X33)
        | ~ v4_rlvect_1(X33)
        | ~ v5_rlvect_1(X33)
        | ~ v6_rlvect_1(X33)
        | ~ v5_vectsp_2(X33,X32)
        | ~ l1_vectsp_2(X33,X32)
        | v3_struct_0(X32)
        | ~ v3_rlvect_1(X32)
        | ~ v4_rlvect_1(X32)
        | ~ v5_rlvect_1(X32)
        | ~ v6_rlvect_1(X32)
        | ~ v4_group_1(X32)
        | ~ v6_vectsp_1(X32)
        | ~ v7_vectsp_1(X32)
        | ~ v8_vectsp_1(X32)
        | ~ l3_vectsp_1(X32) ) ),
    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_8])])])])]) ).

fof(c_0_14,plain,
    ! [X190,X191,X192] :
      ( v3_struct_0(X190)
      | ~ v3_rlvect_1(X190)
      | ~ v4_rlvect_1(X190)
      | ~ v5_rlvect_1(X190)
      | ~ v6_rlvect_1(X190)
      | ~ v4_group_1(X190)
      | ~ v6_vectsp_1(X190)
      | ~ v7_vectsp_1(X190)
      | ~ v8_vectsp_1(X190)
      | ~ l3_vectsp_1(X190)
      | v3_struct_0(X191)
      | ~ v3_rlvect_1(X191)
      | ~ v4_rlvect_1(X191)
      | ~ v5_rlvect_1(X191)
      | ~ v6_rlvect_1(X191)
      | ~ v5_vectsp_2(X191,X190)
      | ~ l1_vectsp_2(X191,X190)
      | ~ m1_rmod_4(X192,X190,X191)
      | m1_subset_1(k5_rmod_4(X190,X191,X192),u1_struct_0(X191)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

cnf(c_0_15,plain,
    ( v3_struct_0(X1)
    | v3_struct_0(X2)
    | m1_rmod_4(k3_rmod_4(X1,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_10]) ).

cnf(c_0_16,negated_conjecture,
    l1_vectsp_2(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,negated_conjecture,
    v5_vectsp_2(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    v8_vectsp_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,negated_conjecture,
    v7_vectsp_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_20,negated_conjecture,
    v6_vectsp_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_21,negated_conjecture,
    l3_vectsp_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_22,negated_conjecture,
    v4_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_23,negated_conjecture,
    v6_rlvect_1(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_24,negated_conjecture,
    v6_rlvect_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_25,negated_conjecture,
    v5_rlvect_1(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_26,negated_conjecture,
    v5_rlvect_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_27,negated_conjecture,
    v4_rlvect_1(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_28,negated_conjecture,
    v4_rlvect_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_29,negated_conjecture,
    v3_rlvect_1(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_30,negated_conjecture,
    v3_rlvect_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_31,negated_conjecture,
    ~ v3_struct_0(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_32,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_33,plain,
    ( v3_struct_0(X1)
    | v3_struct_0(X2)
    | k5_rmod_4(X1,X2,k3_rmod_4(X1,X2)) = k1_rlvect_1(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_12]) ).

cnf(c_0_34,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_13]) ).

cnf(c_0_35,plain,
    ( v3_struct_0(X1)
    | v3_struct_0(X2)
    | m1_subset_1(k5_rmod_4(X1,X2,X3),u1_struct_0(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)
    | ~ m1_rmod_4(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_36,negated_conjecture,
    m1_rmod_4(k3_rmod_4(esk1_0,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_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]),c_0_32]) ).

cnf(c_0_37,negated_conjecture,
    k5_rmod_4(esk1_0,esk2_0,k3_rmod_4(esk1_0,esk2_0)) = k1_rlvect_1(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_33,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]),c_0_32]) ).

cnf(c_0_38,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_13]) ).

cnf(c_0_39,plain,
    ( k2_group_1(X1) = k1_rlvect_1(X1)
    | v3_struct_0(X1)
    | v3_struct_0(X2)
    | ~ v1_rmod_5(k8_rlvect_2(X2,k1_rlvect_1(X2),X3),X1,X2)
    | ~ v5_vectsp_2(X2,X1)
    | ~ l1_vectsp_2(X2,X1)
    | ~ v8_vectsp_1(X1)
    | ~ v7_vectsp_1(X1)
    | ~ v6_vectsp_1(X1)
    | ~ l3_vectsp_1(X1)
    | ~ v4_group_1(X1)
    | ~ v6_rlvect_1(X1)
    | ~ v6_rlvect_1(X2)
    | ~ v5_rlvect_1(X1)
    | ~ v5_rlvect_1(X2)
    | ~ v4_rlvect_1(X1)
    | ~ v4_rlvect_1(X2)
    | ~ v3_rlvect_1(X1)
    | ~ v3_rlvect_1(X2)
    | ~ m1_subset_1(k1_rlvect_1(X2),u1_struct_0(X2))
    | ~ m1_subset_1(X3,u1_struct_0(X2)) ),
    inference(er,[status(thm)],[c_0_34]) ).

cnf(c_0_40,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_11]) ).

cnf(c_0_41,negated_conjecture,
    m1_subset_1(k1_rlvect_1(esk2_0),u1_struct_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_17]),c_0_16]),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]),c_0_32]) ).

cnf(c_0_42,negated_conjecture,
    m1_subset_1(esk3_0,u1_struct_0(esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_43,negated_conjecture,
    k1_rlvect_1(esk1_0) != k2_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_44,plain,
    ( k2_group_1(X1) = k1_rlvect_1(X1)
    | v3_struct_0(X1)
    | v3_struct_0(X2)
    | ~ v1_rmod_5(k8_rlvect_2(X2,X3,k1_rlvect_1(X2)),X1,X2)
    | ~ v5_vectsp_2(X2,X1)
    | ~ l1_vectsp_2(X2,X1)
    | ~ v8_vectsp_1(X1)
    | ~ v7_vectsp_1(X1)
    | ~ v6_vectsp_1(X1)
    | ~ l3_vectsp_1(X1)
    | ~ v4_group_1(X1)
    | ~ v6_rlvect_1(X1)
    | ~ v6_rlvect_1(X2)
    | ~ v5_rlvect_1(X1)
    | ~ v5_rlvect_1(X2)
    | ~ v4_rlvect_1(X1)
    | ~ v4_rlvect_1(X2)
    | ~ v3_rlvect_1(X1)
    | ~ v3_rlvect_1(X2)
    | ~ m1_subset_1(k1_rlvect_1(X2),u1_struct_0(X2))
    | ~ m1_subset_1(X3,u1_struct_0(X2)) ),
    inference(er,[status(thm)],[c_0_38]) ).

cnf(c_0_45,negated_conjecture,
    v1_rmod_5(k8_rlvect_2(esk2_0,esk3_0,k1_rlvect_1(esk2_0)),esk1_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_17]),c_0_16]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_24]),c_0_23]),c_0_26]),c_0_25]),c_0_28]),c_0_27]),c_0_30]),c_0_29]),c_0_41]),c_0_42])]),c_0_43]),c_0_31]),c_0_32]) ).

cnf(c_0_46,negated_conjecture,
    $false,
    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(spm,[status(thm)],[c_0_44,c_0_45]),c_0_17]),c_0_16]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_24]),c_0_23]),c_0_26]),c_0_25]),c_0_28]),c_0_27]),c_0_30]),c_0_29]),c_0_41]),c_0_42])]),c_0_43]),c_0_31]),c_0_32]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem    : ALG216+2 : TPTP v8.2.0. Released v3.4.0.
% 0.04/0.15  % Command    : run_E %s %d THM
% 0.15/0.37  % Computer : n004.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Sat May 18 22:58:53 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.23/0.53  Running first-order theorem proving
% 0.23/0.53  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
% 27.83/4.29  # Version: 3.1.0
% 27.83/4.29  # Preprocessing class: FMLMSMSLSSSNFFN.
% 27.83/4.29  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.83/4.29  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 27.83/4.29  # Starting new_bool_3 with 600s (2) cores
% 27.83/4.29  # Starting new_bool_1 with 600s (2) cores
% 27.83/4.29  # Starting sh5l with 300s (1) cores
% 27.83/4.29  # new_bool_3 with pid 17026 completed with status 0
% 27.83/4.29  # Result found by new_bool_3
% 27.83/4.29  # Preprocessing class: FMLMSMSLSSSNFFN.
% 27.83/4.29  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.83/4.29  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 27.83/4.29  # Starting new_bool_3 with 600s (2) cores
% 27.83/4.29  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 27.83/4.29  # Search class: FGHSM-SMLM32-MFFFFFNN
% 27.83/4.29  # Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 27.83/4.29  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 45s (1) cores
% 27.83/4.29  # Starting new_bool_3 with 61s (1) cores
% 27.83/4.29  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 17031 completed with status 0
% 27.83/4.29  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 27.83/4.29  # Preprocessing class: FMLMSMSLSSSNFFN.
% 27.83/4.29  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.83/4.29  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 27.83/4.29  # Starting new_bool_3 with 600s (2) cores
% 27.83/4.29  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 27.83/4.29  # Search class: FGHSM-SMLM32-MFFFFFNN
% 27.83/4.29  # Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 27.83/4.29  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 45s (1) cores
% 27.83/4.29  # Preprocessing time       : 0.022 s
% 27.83/4.29  # Presaturation interreduction done
% 27.83/4.29  
% 27.83/4.29  # Proof found!
% 27.83/4.29  # SZS status Theorem
% 27.83/4.29  # SZS output start CNFRefutation
% See solution above
% 27.83/4.29  # Parsed axioms                        : 3449
% 27.83/4.29  # Removed by relevancy pruning/SinE    : 2509
% 27.83/4.29  # Initial clauses                      : 1814
% 27.83/4.29  # Removed in clause preprocessing      : 75
% 27.83/4.29  # Initial clauses in saturation        : 1739
% 27.83/4.29  # Processed clauses                    : 15110
% 27.83/4.29  # ...of these trivial                  : 134
% 27.83/4.29  # ...subsumed                          : 6898
% 27.83/4.29  # ...remaining for further processing  : 8078
% 27.83/4.29  # Other redundant clauses eliminated   : 253
% 27.83/4.29  # Clauses deleted for lack of memory   : 0
% 27.83/4.29  # Backward-subsumed                    : 138
% 27.83/4.29  # Backward-rewritten                   : 68
% 27.83/4.29  # Generated clauses                    : 99910
% 27.83/4.29  # ...of the previous two non-redundant : 95074
% 27.83/4.29  # ...aggressively subsumed             : 0
% 27.83/4.29  # Contextual simplify-reflections      : 94
% 27.83/4.29  # Paramodulations                      : 99600
% 27.83/4.29  # Factorizations                       : 24
% 27.83/4.29  # NegExts                              : 0
% 27.83/4.29  # Equation resolutions                 : 299
% 27.83/4.29  # Disequality decompositions           : 0
% 27.83/4.29  # Total rewrite steps                  : 35292
% 27.83/4.29  # ...of those cached                   : 32494
% 27.83/4.29  # Propositional unsat checks           : 1
% 27.83/4.29  #    Propositional check models        : 0
% 27.83/4.29  #    Propositional check unsatisfiable : 0
% 27.83/4.29  #    Propositional clauses             : 0
% 27.83/4.29  #    Propositional clauses after purity: 0
% 27.83/4.29  #    Propositional unsat core size     : 0
% 27.83/4.29  #    Propositional preprocessing time  : 0.000
% 27.83/4.29  #    Propositional encoding time       : 0.028
% 27.83/4.29  #    Propositional solver time         : 0.023
% 27.83/4.29  #    Success case prop preproc time    : 0.000
% 27.83/4.29  #    Success case prop encoding time   : 0.000
% 27.83/4.29  #    Success case prop solver time     : 0.000
% 27.83/4.29  # Current number of processed clauses  : 6097
% 27.83/4.29  #    Positive orientable unit clauses  : 907
% 27.83/4.29  #    Positive unorientable unit clauses: 3
% 27.83/4.29  #    Negative unit clauses             : 955
% 27.83/4.29  #    Non-unit-clauses                  : 4232
% 27.83/4.29  # Current number of unprocessed clauses: 83219
% 27.83/4.29  # ...number of literals in the above   : 250273
% 27.83/4.29  # Current number of archived formulas  : 0
% 27.83/4.29  # Current number of archived clauses   : 1815
% 27.83/4.29  # Clause-clause subsumption calls (NU) : 6619927
% 27.83/4.29  # Rec. Clause-clause subsumption calls : 1611116
% 27.83/4.29  # Non-unit clause-clause subsumptions  : 2264
% 27.83/4.29  # Unit Clause-clause subsumption calls : 497567
% 27.83/4.29  # Rewrite failures with RHS unbound    : 0
% 27.83/4.29  # BW rewrite match attempts            : 3521
% 27.83/4.29  # BW rewrite match successes           : 214
% 27.83/4.29  # Condensation attempts                : 0
% 27.83/4.29  # Condensation successes               : 0
% 27.83/4.29  # Termbank termtop insertions          : 1865429
% 27.83/4.29  # Search garbage collected termcells   : 60715
% 27.83/4.29  
% 27.83/4.29  # -------------------------------------------------
% 27.83/4.29  # User time                : 3.488 s
% 27.83/4.29  # System time              : 0.105 s
% 27.83/4.29  # Total time               : 3.593 s
% 27.83/4.29  # Maximum resident set size: 12936 pages
% 27.83/4.29  
% 27.83/4.29  # -------------------------------------------------
% 27.83/4.29  # User time                : 7.024 s
% 27.83/4.29  # System time              : 0.120 s
% 27.83/4.29  # Total time               : 7.144 s
% 27.83/4.29  # Maximum resident set size: 5780 pages
% 27.83/4.29  % E---3.1 exiting
% 27.83/4.29  % E exiting
%------------------------------------------------------------------------------