TSTP Solution File: GRP643+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP643+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n013.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 : Thu Aug 31 00:22:24 EDT 2023

% Result   : Theorem 0.19s 0.65s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   50
% Syntax   : Number of formulae    :   81 (  14 unt;  46 typ;   0 def)
%            Number of atoms       :  184 (   0 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  230 (  81   ~;  76   |;  43   &)
%                                         (   2 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   58 (  36   >;  22   *;   0   +;   0  <<)
%            Number of predicates  :   19 (  18 usr;   1 prp; 0-3 aty)
%            Number of functors    :   28 (  28 usr;  10 con; 0-3 aty)
%            Number of variables   :   59 (   0 sgn;  38   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    v3_struct_0: $i > $o ).

tff(decl_23,type,
    v3_group_1: $i > $o ).

tff(decl_24,type,
    v4_group_1: $i > $o ).

tff(decl_25,type,
    l1_group_1: $i > $o ).

tff(decl_26,type,
    v1_group_1: $i > $o ).

tff(decl_27,type,
    m1_group_2: ( $i * $i ) > $o ).

tff(decl_28,type,
    u1_struct_0: $i > $i ).

tff(decl_29,type,
    m1_subset_1: ( $i * $i ) > $o ).

tff(decl_30,type,
    k1_latsubgr: $i > $i ).

tff(decl_31,type,
    k1_funct_1: ( $i * $i ) > $i ).

tff(decl_32,type,
    r2_hidden: ( $i * $i ) > $o ).

tff(decl_33,type,
    k1_group_1: ( $i * $i * $i ) > $i ).

tff(decl_34,type,
    u1_group_1: $i > $i ).

tff(decl_35,type,
    g1_group_1: ( $i * $i ) > $i ).

tff(decl_36,type,
    m1_relset_1: ( $i * $i * $i ) > $o ).

tff(decl_37,type,
    v1_funct_1: $i > $o ).

tff(decl_38,type,
    v1_partfun1: ( $i * $i * $i ) > $o ).

tff(decl_39,type,
    v1_funct_2: ( $i * $i * $i ) > $o ).

tff(decl_40,type,
    k2_zfmisc_1: ( $i * $i ) > $i ).

tff(decl_41,type,
    k1_zfmisc_1: $i > $i ).

tff(decl_42,type,
    v1_relat_1: $i > $o ).

tff(decl_43,type,
    v1_xboole_0: $i > $o ).

tff(decl_44,type,
    k1_group_3: $i > $i ).

tff(decl_45,type,
    m2_relset_1: ( $i * $i * $i ) > $o ).

tff(decl_46,type,
    l1_struct_0: $i > $o ).

tff(decl_47,type,
    k1_xboole_0: $i ).

tff(decl_48,type,
    r1_tarski: ( $i * $i ) > $o ).

tff(decl_49,type,
    r1_rlvect_1: ( $i * $i ) > $o ).

tff(decl_50,type,
    esk1_0: $i ).

tff(decl_51,type,
    esk2_0: $i ).

tff(decl_52,type,
    esk3_0: $i ).

tff(decl_53,type,
    esk4_0: $i ).

tff(decl_54,type,
    esk5_0: $i ).

tff(decl_55,type,
    esk6_0: $i ).

tff(decl_56,type,
    esk7_1: $i > $i ).

tff(decl_57,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_58,type,
    esk9_1: $i > $i ).

tff(decl_59,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_60,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_61,type,
    esk12_1: $i > $i ).

tff(decl_62,type,
    esk13_0: $i ).

tff(decl_63,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_64,type,
    esk15_1: $i > $i ).

tff(decl_65,type,
    esk16_0: $i ).

tff(decl_66,type,
    esk17_0: $i ).

tff(decl_67,type,
    esk18_1: $i > $i ).

fof(dt_k1_group_1,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & l1_group_1(X1)
        & m1_subset_1(X2,u1_struct_0(X1))
        & m1_subset_1(X3,u1_struct_0(X1)) )
     => m1_subset_1(k1_group_1(X1,X2,X3),u1_struct_0(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_group_1) ).

fof(t21_latsubgr,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( ( v1_group_1(X2)
            & m1_group_2(X2,X1) )
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => ! [X4] :
                  ( m1_subset_1(X4,u1_struct_0(X1))
                 => ( ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X1),X2))
                      & r2_hidden(X4,k1_funct_1(k1_latsubgr(X1),X2)) )
                   => r2_hidden(k1_group_1(X1,X3,X4),k1_funct_1(k1_latsubgr(X1),X2)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_latsubgr) ).

fof(t18_latsubgr,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( ( v1_group_1(X2)
            & m1_group_2(X2,X1) )
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X1),X2))
              <=> r1_rlvect_1(X2,X3) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_latsubgr) ).

fof(t59_group_2,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))
             => ! [X4] :
                  ( m1_group_2(X4,X1)
                 => ( ( r1_rlvect_1(X4,X2)
                      & r1_rlvect_1(X4,X3) )
                   => r1_rlvect_1(X4,k1_group_1(X1,X2,X3)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_group_2) ).

fof(c_0_4,plain,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & l1_group_1(X1)
        & m1_subset_1(X2,u1_struct_0(X1))
        & m1_subset_1(X3,u1_struct_0(X1)) )
     => m1_subset_1(k1_group_1(X1,X2,X3),u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[dt_k1_group_1]) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v3_group_1(X1)
          & v4_group_1(X1)
          & l1_group_1(X1) )
       => ! [X2] :
            ( ( v1_group_1(X2)
              & m1_group_2(X2,X1) )
           => ! [X3] :
                ( m1_subset_1(X3,u1_struct_0(X1))
               => ! [X4] :
                    ( m1_subset_1(X4,u1_struct_0(X1))
                   => ( ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X1),X2))
                        & r2_hidden(X4,k1_funct_1(k1_latsubgr(X1),X2)) )
                     => r2_hidden(k1_group_1(X1,X3,X4),k1_funct_1(k1_latsubgr(X1),X2)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t21_latsubgr])]) ).

fof(c_0_6,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( ( v1_group_1(X2)
            & m1_group_2(X2,X1) )
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X1),X2))
              <=> r1_rlvect_1(X2,X3) ) ) ) ),
    inference(fof_simplification,[status(thm)],[t18_latsubgr]) ).

fof(c_0_7,plain,
    ! [X26,X27,X28] :
      ( v3_struct_0(X26)
      | ~ l1_group_1(X26)
      | ~ m1_subset_1(X27,u1_struct_0(X26))
      | ~ m1_subset_1(X28,u1_struct_0(X26))
      | m1_subset_1(k1_group_1(X26,X27,X28),u1_struct_0(X26)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).

fof(c_0_8,negated_conjecture,
    ( ~ v3_struct_0(esk1_0)
    & v3_group_1(esk1_0)
    & v4_group_1(esk1_0)
    & l1_group_1(esk1_0)
    & v1_group_1(esk2_0)
    & m1_group_2(esk2_0,esk1_0)
    & m1_subset_1(esk3_0,u1_struct_0(esk1_0))
    & m1_subset_1(esk4_0,u1_struct_0(esk1_0))
    & r2_hidden(esk3_0,k1_funct_1(k1_latsubgr(esk1_0),esk2_0))
    & r2_hidden(esk4_0,k1_funct_1(k1_latsubgr(esk1_0),esk2_0))
    & ~ r2_hidden(k1_group_1(esk1_0,esk3_0,esk4_0),k1_funct_1(k1_latsubgr(esk1_0),esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_9,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))
             => ! [X4] :
                  ( m1_group_2(X4,X1)
                 => ( ( r1_rlvect_1(X4,X2)
                      & r1_rlvect_1(X4,X3) )
                   => r1_rlvect_1(X4,k1_group_1(X1,X2,X3)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[t59_group_2]) ).

fof(c_0_10,plain,
    ! [X77,X78,X79] :
      ( ( ~ r2_hidden(X79,k1_funct_1(k1_latsubgr(X77),X78))
        | r1_rlvect_1(X78,X79)
        | ~ m1_subset_1(X79,u1_struct_0(X77))
        | ~ v1_group_1(X78)
        | ~ m1_group_2(X78,X77)
        | v3_struct_0(X77)
        | ~ v3_group_1(X77)
        | ~ v4_group_1(X77)
        | ~ l1_group_1(X77) )
      & ( ~ r1_rlvect_1(X78,X79)
        | r2_hidden(X79,k1_funct_1(k1_latsubgr(X77),X78))
        | ~ m1_subset_1(X79,u1_struct_0(X77))
        | ~ v1_group_1(X78)
        | ~ m1_group_2(X78,X77)
        | v3_struct_0(X77)
        | ~ v3_group_1(X77)
        | ~ v4_group_1(X77)
        | ~ l1_group_1(X77) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

cnf(c_0_11,plain,
    ( v3_struct_0(X1)
    | m1_subset_1(k1_group_1(X1,X2,X3),u1_struct_0(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_7]) ).

cnf(c_0_12,negated_conjecture,
    m1_subset_1(esk4_0,u1_struct_0(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    l1_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_15,plain,
    ! [X89,X90,X91,X92] :
      ( v3_struct_0(X89)
      | ~ v3_group_1(X89)
      | ~ v4_group_1(X89)
      | ~ l1_group_1(X89)
      | ~ m1_subset_1(X90,u1_struct_0(X89))
      | ~ m1_subset_1(X91,u1_struct_0(X89))
      | ~ m1_group_2(X92,X89)
      | ~ r1_rlvect_1(X92,X90)
      | ~ r1_rlvect_1(X92,X91)
      | r1_rlvect_1(X92,k1_group_1(X89,X90,X91)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

cnf(c_0_16,plain,
    ( r2_hidden(X2,k1_funct_1(k1_latsubgr(X3),X1))
    | v3_struct_0(X3)
    | ~ r1_rlvect_1(X1,X2)
    | ~ m1_subset_1(X2,u1_struct_0(X3))
    | ~ v1_group_1(X1)
    | ~ m1_group_2(X1,X3)
    | ~ v3_group_1(X3)
    | ~ v4_group_1(X3)
    | ~ l1_group_1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,negated_conjecture,
    ( m1_subset_1(k1_group_1(esk1_0,X1,esk4_0),u1_struct_0(esk1_0))
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    v4_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_19,negated_conjecture,
    v3_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,plain,
    ( v3_struct_0(X1)
    | r1_rlvect_1(X4,k1_group_1(X1,X2,X3))
    | ~ 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))
    | ~ m1_group_2(X4,X1)
    | ~ r1_rlvect_1(X4,X2)
    | ~ r1_rlvect_1(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    ( r2_hidden(k1_group_1(esk1_0,X1,esk4_0),k1_funct_1(k1_latsubgr(esk1_0),X2))
    | ~ r1_rlvect_1(X2,k1_group_1(esk1_0,X1,esk4_0))
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0))
    | ~ m1_group_2(X2,esk1_0)
    | ~ v1_group_1(X2) ),
    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_16,c_0_17]),c_0_13]),c_0_18]),c_0_19])]),c_0_14]) ).

cnf(c_0_22,negated_conjecture,
    ( r1_rlvect_1(X1,k1_group_1(esk1_0,X2,esk4_0))
    | ~ r1_rlvect_1(X1,esk4_0)
    | ~ r1_rlvect_1(X1,X2)
    | ~ m1_subset_1(X2,u1_struct_0(esk1_0))
    | ~ m1_group_2(X1,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_20,c_0_12]),c_0_13]),c_0_18]),c_0_19])]),c_0_14]) ).

cnf(c_0_23,negated_conjecture,
    ( r2_hidden(k1_group_1(esk1_0,X1,esk4_0),k1_funct_1(k1_latsubgr(esk1_0),X2))
    | ~ r1_rlvect_1(X2,esk4_0)
    | ~ r1_rlvect_1(X2,X1)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0))
    | ~ m1_group_2(X2,esk1_0)
    | ~ v1_group_1(X2) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_24,negated_conjecture,
    m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_25,plain,
    ( r1_rlvect_1(X3,X1)
    | v3_struct_0(X2)
    | ~ r2_hidden(X1,k1_funct_1(k1_latsubgr(X2),X3))
    | ~ m1_subset_1(X1,u1_struct_0(X2))
    | ~ v1_group_1(X3)
    | ~ m1_group_2(X3,X2)
    | ~ v3_group_1(X2)
    | ~ v4_group_1(X2)
    | ~ l1_group_1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_26,negated_conjecture,
    r2_hidden(esk4_0,k1_funct_1(k1_latsubgr(esk1_0),esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_27,negated_conjecture,
    m1_group_2(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_28,negated_conjecture,
    v1_group_1(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_29,negated_conjecture,
    r2_hidden(esk3_0,k1_funct_1(k1_latsubgr(esk1_0),esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_30,negated_conjecture,
    ( r2_hidden(k1_group_1(esk1_0,esk3_0,esk4_0),k1_funct_1(k1_latsubgr(esk1_0),X1))
    | ~ r1_rlvect_1(X1,esk4_0)
    | ~ r1_rlvect_1(X1,esk3_0)
    | ~ m1_group_2(X1,esk1_0)
    | ~ v1_group_1(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_31,negated_conjecture,
    r1_rlvect_1(esk2_0,esk4_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_12]),c_0_27]),c_0_28]),c_0_13]),c_0_18]),c_0_19])]),c_0_14]) ).

cnf(c_0_32,negated_conjecture,
    r1_rlvect_1(esk2_0,esk3_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_29]),c_0_24]),c_0_27]),c_0_28]),c_0_13]),c_0_18]),c_0_19])]),c_0_14]) ).

cnf(c_0_33,negated_conjecture,
    ~ r2_hidden(k1_group_1(esk1_0,esk3_0,esk4_0),k1_funct_1(k1_latsubgr(esk1_0),esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_34,negated_conjecture,
    $false,
    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_30,c_0_31]),c_0_32]),c_0_27]),c_0_28])]),c_0_33]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP643+1 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Aug 28 22:15:31 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.65  % Version  : CSE_E---1.5
% 0.19/0.65  % Problem  : theBenchmark.p
% 0.19/0.65  % Proof found
% 0.19/0.65  % SZS status Theorem for theBenchmark.p
% 0.19/0.65  % SZS output start Proof
% See solution above
% 0.19/0.65  % Total time : 0.091000 s
% 0.19/0.65  % SZS output end Proof
% 0.19/0.65  % Total time : 0.095000 s
%------------------------------------------------------------------------------