TSTP Solution File: GRP631+3 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : GRP631+3 : TPTP v8.2.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 20:58:16 EDT 2024

% Result   : Theorem 23.89s 4.03s
% Output   : CNFRefutation 23.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   57 (  12 unt;   0 def)
%            Number of atoms       :  376 (  86 equ)
%            Maximal formula atoms :   56 (   6 avg)
%            Number of connectives :  502 ( 183   ~; 185   |;  92   &)
%                                         (   4 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-5 aty)
%            Number of variables   :   90 (   1 sgn  60   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t24_autgroup,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v1_group_1(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(u1_struct_0(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_autgroup) ).

fof(t29_autgroup,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v1_group_1(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,X2)
            & k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,k2_group_1(X1))) = k6_autgroup(X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_autgroup) ).

fof(redefinition_k6_partfun1,axiom,
    ! [X1] : k6_partfun1(X1) = k6_relat_1(X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+17.ax',redefinition_k6_partfun1) ).

fof(t23_autgroup,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v1_group_1(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => k6_autgroup(X1,k1_group_1(X1,X2,X3)) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_autgroup) ).

fof(dt_k2_group_1,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_group_1(X1) )
     => m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+212.ax',dt_k2_group_1) ).

fof(t27_group_3,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => ( k2_group_3(X1,X2,X3) = X2
              <=> k1_group_1(X1,X2,X3) = k1_group_1(X1,X3,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+252.ax',t27_group_3) ).

fof(t24_group_3,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => k2_group_3(X1,X2,k2_group_1(X1)) = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+252.ax',t24_group_3) ).

fof(d6_group_1,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => ( X3 = k3_group_1(X1,X2)
              <=> ( k1_group_1(X1,X2,X3) = k2_group_1(X1)
                  & k1_group_1(X1,X3,X2) = k2_group_1(X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+212.ax',d6_group_1) ).

fof(dt_k3_group_1,axiom,
    ! [X1,X2] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1)
        & m1_subset_1(X2,u1_struct_0(X1)) )
     => m1_subset_1(k3_group_1(X1,X2),u1_struct_0(X1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+212.ax',dt_k3_group_1) ).

fof(t1_group_3,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => ( k1_group_1(X1,k1_group_1(X1,X2,X3),k3_group_1(X1,X3)) = X2
                & k1_group_1(X1,k1_group_1(X1,X2,k3_group_1(X1,X3)),X3) = X2
                & k1_group_1(X1,k1_group_1(X1,k3_group_1(X1,X3),X3),X2) = X2
                & k1_group_1(X1,k1_group_1(X1,X3,k3_group_1(X1,X3)),X2) = X2
                & k1_group_1(X1,X2,k1_group_1(X1,X3,k3_group_1(X1,X3))) = X2
                & k1_group_1(X1,X2,k1_group_1(X1,k3_group_1(X1,X3),X3)) = X2
                & k1_group_1(X1,k3_group_1(X1,X3),k1_group_1(X1,X3,X2)) = X2
                & k1_group_1(X1,X3,k1_group_1(X1,k3_group_1(X1,X3),X2)) = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+252.ax',t1_group_3) ).

fof(c_0_10,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v1_group_1(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[t24_autgroup]) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v1_group_1(X1)
          & v3_group_1(X1)
          & v4_group_1(X1)
          & l1_group_1(X1) )
       => ! [X2] :
            ( m1_subset_1(X2,u1_struct_0(X1))
           => ( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,X2)
              & k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,k2_group_1(X1))) = k6_autgroup(X1,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t29_autgroup])]) ).

fof(c_0_12,plain,
    ! [X27] :
      ( v3_struct_0(X27)
      | ~ v1_group_1(X27)
      | ~ v3_group_1(X27)
      | ~ v4_group_1(X27)
      | ~ l1_group_1(X27)
      | k6_autgroup(X27,k2_group_1(X27)) = k6_partfun1(u1_struct_0(X27)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_13,plain,
    ! [X277] : k6_partfun1(X277) = k6_relat_1(X277),
    inference(variable_rename,[status(thm)],[redefinition_k6_partfun1]) ).

fof(c_0_14,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v1_group_1(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => k6_autgroup(X1,k1_group_1(X1,X2,X3)) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,X3)) ) ) ),
    inference(fof_simplification,[status(thm)],[t23_autgroup]) ).

fof(c_0_15,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_group_1(X1) )
     => m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[dt_k2_group_1]) ).

fof(c_0_16,negated_conjecture,
    ( ~ v3_struct_0(esk1_0)
    & v1_group_1(esk1_0)
    & v3_group_1(esk1_0)
    & v4_group_1(esk1_0)
    & l1_group_1(esk1_0)
    & m1_subset_1(esk2_0,u1_struct_0(esk1_0))
    & ( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k2_group_1(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0)
      | k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_autgroup(esk1_0,k2_group_1(esk1_0))) != k6_autgroup(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_11])])])]) ).

cnf(c_0_17,plain,
    ( v3_struct_0(X1)
    | k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(u1_struct_0(X1))
    | ~ v1_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    k6_partfun1(X1) = k6_relat_1(X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_19,plain,
    ! [X24,X25,X26] :
      ( v3_struct_0(X24)
      | ~ v1_group_1(X24)
      | ~ v3_group_1(X24)
      | ~ v4_group_1(X24)
      | ~ l1_group_1(X24)
      | ~ m1_subset_1(X25,u1_struct_0(X24))
      | ~ m1_subset_1(X26,u1_struct_0(X24))
      | k6_autgroup(X24,k1_group_1(X24,X25,X26)) = k7_funct_2(u1_struct_0(X24),u1_struct_0(X24),u1_struct_0(X24),k6_autgroup(X24,X25),k6_autgroup(X24,X26)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).

fof(c_0_20,plain,
    ! [X70] :
      ( v3_struct_0(X70)
      | ~ l1_group_1(X70)
      | m1_subset_1(k2_group_1(X70),u1_struct_0(X70)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).

cnf(c_0_21,negated_conjecture,
    ( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k2_group_1(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0)
    | k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_autgroup(esk1_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    ( k6_autgroup(X1,k2_group_1(X1)) = k6_relat_1(u1_struct_0(X1))
    | v3_struct_0(X1)
    | ~ l1_group_1(X1)
    | ~ v1_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1) ),
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    v4_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,negated_conjecture,
    v3_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,negated_conjecture,
    v1_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_26,negated_conjecture,
    l1_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_27,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_28,plain,
    ( v3_struct_0(X1)
    | k6_autgroup(X1,k1_group_1(X1,X2,X3)) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,X3))
    | ~ v1_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ m1_subset_1(X3,u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_29,plain,
    ( v3_struct_0(X1)
    | m1_subset_1(k2_group_1(X1),u1_struct_0(X1))
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_30,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => ( k2_group_3(X1,X2,X3) = X2
              <=> k1_group_1(X1,X2,X3) = k1_group_1(X1,X3,X2) ) ) ) ),
    inference(fof_simplification,[status(thm)],[t27_group_3]) ).

fof(c_0_31,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => k2_group_3(X1,X2,k2_group_1(X1)) = X2 ) ),
    inference(fof_simplification,[status(thm)],[t24_group_3]) ).

cnf(c_0_32,negated_conjecture,
    ( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_relat_1(u1_struct_0(esk1_0))) != k6_autgroup(esk1_0,esk2_0)
    | k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_relat_1(u1_struct_0(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_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_21,c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26])]),c_0_27]) ).

cnf(c_0_33,plain,
    ( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_relat_1(u1_struct_0(X1))) = k6_autgroup(X1,k1_group_1(X1,X2,k2_group_1(X1)))
    | v3_struct_0(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v1_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_29]) ).

cnf(c_0_34,negated_conjecture,
    m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_35,plain,
    ! [X154,X155,X156] :
      ( ( k2_group_3(X154,X155,X156) != X155
        | k1_group_1(X154,X155,X156) = k1_group_1(X154,X156,X155)
        | ~ m1_subset_1(X156,u1_struct_0(X154))
        | ~ m1_subset_1(X155,u1_struct_0(X154))
        | v3_struct_0(X154)
        | ~ v3_group_1(X154)
        | ~ v4_group_1(X154)
        | ~ l1_group_1(X154) )
      & ( k1_group_1(X154,X155,X156) != k1_group_1(X154,X156,X155)
        | k2_group_3(X154,X155,X156) = X155
        | ~ m1_subset_1(X156,u1_struct_0(X154))
        | ~ m1_subset_1(X155,u1_struct_0(X154))
        | v3_struct_0(X154)
        | ~ v3_group_1(X154)
        | ~ v4_group_1(X154)
        | ~ l1_group_1(X154) ) ),
    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_30])])])])]) ).

fof(c_0_36,plain,
    ! [X148,X149] :
      ( v3_struct_0(X148)
      | ~ v3_group_1(X148)
      | ~ v4_group_1(X148)
      | ~ l1_group_1(X148)
      | ~ m1_subset_1(X149,u1_struct_0(X148))
      | k2_group_3(X148,X149,k2_group_1(X148)) = X149 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).

fof(c_0_37,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => ( X3 = k3_group_1(X1,X2)
              <=> ( k1_group_1(X1,X2,X3) = k2_group_1(X1)
                  & k1_group_1(X1,X3,X2) = k2_group_1(X1) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[d6_group_1]) ).

fof(c_0_38,plain,
    ! [X1,X2] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1)
        & m1_subset_1(X2,u1_struct_0(X1)) )
     => m1_subset_1(k3_group_1(X1,X2),u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[dt_k3_group_1]) ).

cnf(c_0_39,negated_conjecture,
    ( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_relat_1(u1_struct_0(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0)
    | k6_autgroup(esk1_0,k1_group_1(esk1_0,esk2_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_34])]),c_0_27]) ).

cnf(c_0_40,plain,
    ( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_relat_1(u1_struct_0(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,k1_group_1(X1,k2_group_1(X1),X2))
    | v3_struct_0(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v1_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_29]) ).

cnf(c_0_41,plain,
    ( k1_group_1(X1,X2,X3) = k1_group_1(X1,X3,X2)
    | v3_struct_0(X1)
    | k2_group_3(X1,X2,X3) != X2
    | ~ m1_subset_1(X3,u1_struct_0(X1))
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_42,plain,
    ( v3_struct_0(X1)
    | k2_group_3(X1,X2,k2_group_1(X1)) = X2
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

fof(c_0_43,plain,
    ! [X292,X293,X294] :
      ( ( k1_group_1(X292,X293,X294) = k2_group_1(X292)
        | X294 != k3_group_1(X292,X293)
        | ~ m1_subset_1(X294,u1_struct_0(X292))
        | ~ m1_subset_1(X293,u1_struct_0(X292))
        | v3_struct_0(X292)
        | ~ v3_group_1(X292)
        | ~ v4_group_1(X292)
        | ~ l1_group_1(X292) )
      & ( k1_group_1(X292,X294,X293) = k2_group_1(X292)
        | X294 != k3_group_1(X292,X293)
        | ~ m1_subset_1(X294,u1_struct_0(X292))
        | ~ m1_subset_1(X293,u1_struct_0(X292))
        | v3_struct_0(X292)
        | ~ v3_group_1(X292)
        | ~ v4_group_1(X292)
        | ~ l1_group_1(X292) )
      & ( k1_group_1(X292,X293,X294) != k2_group_1(X292)
        | k1_group_1(X292,X294,X293) != k2_group_1(X292)
        | X294 = k3_group_1(X292,X293)
        | ~ m1_subset_1(X294,u1_struct_0(X292))
        | ~ m1_subset_1(X293,u1_struct_0(X292))
        | v3_struct_0(X292)
        | ~ v3_group_1(X292)
        | ~ v4_group_1(X292)
        | ~ l1_group_1(X292) ) ),
    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_37])])])])]) ).

fof(c_0_44,plain,
    ! [X335,X336] :
      ( v3_struct_0(X335)
      | ~ v3_group_1(X335)
      | ~ v4_group_1(X335)
      | ~ l1_group_1(X335)
      | ~ m1_subset_1(X336,u1_struct_0(X335))
      | m1_subset_1(k3_group_1(X335,X336),u1_struct_0(X335)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).

cnf(c_0_45,negated_conjecture,
    ( k6_autgroup(esk1_0,k1_group_1(esk1_0,k2_group_1(esk1_0),esk2_0)) != k6_autgroup(esk1_0,esk2_0)
    | k6_autgroup(esk1_0,k1_group_1(esk1_0,esk2_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_34])]),c_0_27]) ).

cnf(c_0_46,plain,
    ( k1_group_1(X1,X2,k2_group_1(X1)) = k1_group_1(X1,k2_group_1(X1),X2)
    | v3_struct_0(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_29]) ).

cnf(c_0_47,plain,
    ( k1_group_1(X1,X2,X3) = k2_group_1(X1)
    | v3_struct_0(X1)
    | X3 != k3_group_1(X1,X2)
    | ~ m1_subset_1(X3,u1_struct_0(X1))
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_48,plain,
    ( v3_struct_0(X1)
    | m1_subset_1(k3_group_1(X1,X2),u1_struct_0(X1))
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

fof(c_0_49,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => ( k1_group_1(X1,k1_group_1(X1,X2,X3),k3_group_1(X1,X3)) = X2
                & k1_group_1(X1,k1_group_1(X1,X2,k3_group_1(X1,X3)),X3) = X2
                & k1_group_1(X1,k1_group_1(X1,k3_group_1(X1,X3),X3),X2) = X2
                & k1_group_1(X1,k1_group_1(X1,X3,k3_group_1(X1,X3)),X2) = X2
                & k1_group_1(X1,X2,k1_group_1(X1,X3,k3_group_1(X1,X3))) = X2
                & k1_group_1(X1,X2,k1_group_1(X1,k3_group_1(X1,X3),X3)) = X2
                & k1_group_1(X1,k3_group_1(X1,X3),k1_group_1(X1,X3,X2)) = X2
                & k1_group_1(X1,X3,k1_group_1(X1,k3_group_1(X1,X3),X2)) = X2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[t1_group_3]) ).

cnf(c_0_50,negated_conjecture,
    k6_autgroup(esk1_0,k1_group_1(esk1_0,esk2_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_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_45,c_0_46]),c_0_23]),c_0_24]),c_0_26]),c_0_34])]),c_0_27]) ).

cnf(c_0_51,plain,
    ( k1_group_1(X1,X2,k3_group_1(X1,X2)) = k2_group_1(X1)
    | v3_struct_0(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1)) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_47]),c_0_48]) ).

fof(c_0_52,plain,
    ! [X350,X351,X352] :
      ( ( k1_group_1(X350,k1_group_1(X350,X351,X352),k3_group_1(X350,X352)) = X351
        | ~ m1_subset_1(X352,u1_struct_0(X350))
        | ~ m1_subset_1(X351,u1_struct_0(X350))
        | v3_struct_0(X350)
        | ~ v3_group_1(X350)
        | ~ v4_group_1(X350)
        | ~ l1_group_1(X350) )
      & ( k1_group_1(X350,k1_group_1(X350,X351,k3_group_1(X350,X352)),X352) = X351
        | ~ m1_subset_1(X352,u1_struct_0(X350))
        | ~ m1_subset_1(X351,u1_struct_0(X350))
        | v3_struct_0(X350)
        | ~ v3_group_1(X350)
        | ~ v4_group_1(X350)
        | ~ l1_group_1(X350) )
      & ( k1_group_1(X350,k1_group_1(X350,k3_group_1(X350,X352),X352),X351) = X351
        | ~ m1_subset_1(X352,u1_struct_0(X350))
        | ~ m1_subset_1(X351,u1_struct_0(X350))
        | v3_struct_0(X350)
        | ~ v3_group_1(X350)
        | ~ v4_group_1(X350)
        | ~ l1_group_1(X350) )
      & ( k1_group_1(X350,k1_group_1(X350,X352,k3_group_1(X350,X352)),X351) = X351
        | ~ m1_subset_1(X352,u1_struct_0(X350))
        | ~ m1_subset_1(X351,u1_struct_0(X350))
        | v3_struct_0(X350)
        | ~ v3_group_1(X350)
        | ~ v4_group_1(X350)
        | ~ l1_group_1(X350) )
      & ( k1_group_1(X350,X351,k1_group_1(X350,X352,k3_group_1(X350,X352))) = X351
        | ~ m1_subset_1(X352,u1_struct_0(X350))
        | ~ m1_subset_1(X351,u1_struct_0(X350))
        | v3_struct_0(X350)
        | ~ v3_group_1(X350)
        | ~ v4_group_1(X350)
        | ~ l1_group_1(X350) )
      & ( k1_group_1(X350,X351,k1_group_1(X350,k3_group_1(X350,X352),X352)) = X351
        | ~ m1_subset_1(X352,u1_struct_0(X350))
        | ~ m1_subset_1(X351,u1_struct_0(X350))
        | v3_struct_0(X350)
        | ~ v3_group_1(X350)
        | ~ v4_group_1(X350)
        | ~ l1_group_1(X350) )
      & ( k1_group_1(X350,k3_group_1(X350,X352),k1_group_1(X350,X352,X351)) = X351
        | ~ m1_subset_1(X352,u1_struct_0(X350))
        | ~ m1_subset_1(X351,u1_struct_0(X350))
        | v3_struct_0(X350)
        | ~ v3_group_1(X350)
        | ~ v4_group_1(X350)
        | ~ l1_group_1(X350) )
      & ( k1_group_1(X350,X352,k1_group_1(X350,k3_group_1(X350,X352),X351)) = X351
        | ~ m1_subset_1(X352,u1_struct_0(X350))
        | ~ m1_subset_1(X351,u1_struct_0(X350))
        | v3_struct_0(X350)
        | ~ v3_group_1(X350)
        | ~ v4_group_1(X350)
        | ~ l1_group_1(X350) ) ),
    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_49])])])])]) ).

cnf(c_0_53,negated_conjecture,
    ( k6_autgroup(esk1_0,k1_group_1(esk1_0,esk2_0,k1_group_1(esk1_0,X1,k3_group_1(esk1_0,X1)))) != k6_autgroup(esk1_0,esk2_0)
    | ~ m1_subset_1(X1,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(spm,[status(thm)],[c_0_50,c_0_51]),c_0_23]),c_0_24]),c_0_26])]),c_0_27]) ).

cnf(c_0_54,plain,
    ( k1_group_1(X1,X2,k1_group_1(X1,X3,k3_group_1(X1,X3))) = X2
    | v3_struct_0(X1)
    | ~ m1_subset_1(X3,u1_struct_0(X1))
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_55,negated_conjecture,
    ~ m1_subset_1(X1,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_53,c_0_54]),c_0_23]),c_0_24]),c_0_26]),c_0_34])]),c_0_27]) ).

cnf(c_0_56,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_34,c_0_55]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : GRP631+3 : TPTP v8.2.0. Released v3.4.0.
% 0.09/0.11  % Command    : run_E %s %d THM
% 0.10/0.31  % Computer : n028.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   : Sun May 19 05:14:39 EDT 2024
% 0.16/0.31  % CPUTime    : 
% 0.16/0.42  Running first-order model finding
% 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 --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.29/4.03  # Version: 3.1.0
% 23.29/4.03  # Preprocessing class: FMLLSMLLSSSNFFN.
% 23.29/4.03  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.29/4.03  # Starting new_bool_3 with 900s (3) cores
% 23.29/4.03  # Starting new_bool_1 with 900s (3) cores
% 23.29/4.03  # Starting sh5l with 300s (1) cores
% 23.29/4.03  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 23.29/4.03  # G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with pid 32205 completed with status 0
% 23.29/4.03  # Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y
% 23.29/4.03  # Preprocessing class: FMLLSMLLSSSNFFN.
% 23.29/4.03  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.29/4.03  # Starting new_bool_3 with 900s (3) cores
% 23.29/4.03  # Starting new_bool_1 with 900s (3) cores
% 23.29/4.03  # Starting sh5l with 300s (1) cores
% 23.29/4.03  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 23.29/4.03  # SinE strategy is gf120_gu_R02_F100_L20000
% 23.29/4.03  # Search class: FGHSM-FSLM32-MFFFFFNN
% 23.29/4.03  # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 23.29/4.03  # Starting G-E--_303_C18_F1_URBAN_S0Y with 25s (1) cores
% 23.29/4.03  # G-E--_303_C18_F1_URBAN_S0Y with pid 32206 completed with status 0
% 23.29/4.03  # Result found by G-E--_303_C18_F1_URBAN_S0Y
% 23.89/4.03  # Preprocessing class: FMLLSMLLSSSNFFN.
% 23.89/4.03  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.89/4.03  # Starting new_bool_3 with 900s (3) cores
% 23.89/4.03  # Starting new_bool_1 with 900s (3) cores
% 23.89/4.03  # Starting sh5l with 300s (1) cores
% 23.89/4.03  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 23.89/4.03  # SinE strategy is gf120_gu_R02_F100_L20000
% 23.89/4.03  # Search class: FGHSM-FSLM32-MFFFFFNN
% 23.89/4.03  # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 23.89/4.03  # Starting G-E--_303_C18_F1_URBAN_S0Y with 25s (1) cores
% 23.89/4.03  # Preprocessing time       : 0.041 s
% 23.89/4.03  
% 23.89/4.03  # Proof found!
% 23.89/4.03  # SZS status Theorem
% 23.89/4.03  # SZS output start CNFRefutation
% See solution above
% 23.89/4.03  # Parsed axioms                        : 12910
% 23.89/4.03  # Removed by relevancy pruning/SinE    : 12693
% 23.89/4.03  # Initial clauses                      : 523
% 23.89/4.03  # Removed in clause preprocessing      : 21
% 23.89/4.03  # Initial clauses in saturation        : 502
% 23.89/4.03  # Processed clauses                    : 3825
% 23.89/4.03  # ...of these trivial                  : 44
% 23.89/4.03  # ...subsumed                          : 1700
% 23.89/4.03  # ...remaining for further processing  : 2081
% 23.89/4.03  # Other redundant clauses eliminated   : 102
% 23.89/4.03  # Clauses deleted for lack of memory   : 0
% 23.89/4.03  # Backward-subsumed                    : 157
% 23.89/4.03  # Backward-rewritten                   : 68
% 23.89/4.03  # Generated clauses                    : 46436
% 23.89/4.03  # ...of the previous two non-redundant : 43999
% 23.89/4.03  # ...aggressively subsumed             : 0
% 23.89/4.03  # Contextual simplify-reflections      : 857
% 23.89/4.03  # Paramodulations                      : 46253
% 23.89/4.03  # Factorizations                       : 0
% 23.89/4.03  # NegExts                              : 0
% 23.89/4.03  # Equation resolutions                 : 182
% 23.89/4.03  # Disequality decompositions           : 0
% 23.89/4.03  # Total rewrite steps                  : 11045
% 23.89/4.03  # ...of those cached                   : 10853
% 23.89/4.03  # Propositional unsat checks           : 0
% 23.89/4.03  #    Propositional check models        : 0
% 23.89/4.03  #    Propositional check unsatisfiable : 0
% 23.89/4.03  #    Propositional clauses             : 0
% 23.89/4.03  #    Propositional clauses after purity: 0
% 23.89/4.03  #    Propositional unsat core size     : 0
% 23.89/4.03  #    Propositional preprocessing time  : 0.000
% 23.89/4.03  #    Propositional encoding time       : 0.000
% 23.89/4.03  #    Propositional solver time         : 0.000
% 23.89/4.03  #    Success case prop preproc time    : 0.000
% 23.89/4.03  #    Success case prop encoding time   : 0.000
% 23.89/4.03  #    Success case prop solver time     : 0.000
% 23.89/4.03  # Current number of processed clauses  : 1850
% 23.89/4.03  #    Positive orientable unit clauses  : 54
% 23.89/4.03  #    Positive unorientable unit clauses: 0
% 23.89/4.03  #    Negative unit clauses             : 9
% 23.89/4.03  #    Non-unit-clauses                  : 1787
% 23.89/4.03  # Current number of unprocessed clauses: 40443
% 23.89/4.03  # ...number of literals in the above   : 402453
% 23.89/4.03  # Current number of archived formulas  : 0
% 23.89/4.03  # Current number of archived clauses   : 228
% 23.89/4.03  # Clause-clause subsumption calls (NU) : 1295889
% 23.89/4.03  # Rec. Clause-clause subsumption calls : 78145
% 23.89/4.03  # Non-unit clause-clause subsumptions  : 2451
% 23.89/4.03  # Unit Clause-clause subsumption calls : 8253
% 23.89/4.03  # Rewrite failures with RHS unbound    : 20
% 23.89/4.03  # BW rewrite match attempts            : 25
% 23.89/4.03  # BW rewrite match successes           : 18
% 23.89/4.03  # Condensation attempts                : 0
% 23.89/4.03  # Condensation successes               : 0
% 23.89/4.03  # Termbank termtop insertions          : 1898158
% 23.89/4.03  # Search garbage collected termcells   : 119193
% 23.89/4.03  
% 23.89/4.03  # -------------------------------------------------
% 23.89/4.03  # User time                : 2.894 s
% 23.89/4.03  # System time              : 0.093 s
% 23.89/4.03  # Total time               : 2.987 s
% 23.89/4.03  # Maximum resident set size: 24572 pages
% 23.89/4.03  
% 23.89/4.03  # -------------------------------------------------
% 23.89/4.03  # User time                : 3.399 s
% 23.89/4.03  # System time              : 0.116 s
% 23.89/4.03  # Total time               : 3.515 s
% 23.89/4.03  # Maximum resident set size: 18960 pages
% 23.89/4.03  % E---3.1 exiting
%------------------------------------------------------------------------------