TSTP Solution File: SEU361+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU361+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 16:25:07 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   58 (  10 unt;  28 typ;   0 def)
%            Number of atoms       :  159 (  11 equ)
%            Maximal formula atoms :   50 (   5 avg)
%            Number of connectives :  209 (  80   ~;  76   |;  35   &)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   32 (  19   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  14 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   9 con; 0-3 aty)
%            Number of variables   :   40 (   1 sgn;  27   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    bottom_of_relstr: $i > $i ).

tff(decl_27,type,
    empty_set: $i ).

tff(decl_28,type,
    join_on_relstr: ( $i * $i ) > $i ).

tff(decl_29,type,
    the_carrier: $i > $i ).

tff(decl_30,type,
    element: ( $i * $i ) > $o ).

tff(decl_31,type,
    one_sorted_str: $i > $o ).

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

tff(decl_33,type,
    antisymmetric_relstr: $i > $o ).

tff(decl_34,type,
    ex_sup_of_relstr_set: ( $i * $i ) > $o ).

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

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

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

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

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

tff(decl_40,type,
    esk1_0: $i ).

tff(decl_41,type,
    esk2_0: $i ).

tff(decl_42,type,
    esk3_1: $i > $i ).

tff(decl_43,type,
    esk4_0: $i ).

tff(decl_44,type,
    esk5_0: $i ).

tff(decl_45,type,
    esk6_0: $i ).

tff(decl_46,type,
    esk7_0: $i ).

tff(decl_47,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk9_0: $i ).

tff(decl_49,type,
    esk10_0: $i ).

fof(t44_yellow_0,conjecture,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & antisymmetric_relstr(X1)
        & lower_bounded_relstr(X1)
        & rel_str(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => related(X1,bottom_of_relstr(X1),X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_yellow_0) ).

fof(t42_yellow_0,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & antisymmetric_relstr(X1)
        & lower_bounded_relstr(X1)
        & rel_str(X1) )
     => ( ex_sup_of_relstr_set(X1,empty_set)
        & ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_yellow_0) ).

fof(d11_yellow_0,axiom,
    ! [X1] :
      ( rel_str(X1)
     => bottom_of_relstr(X1) = join_on_relstr(X1,empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_yellow_0) ).

fof(t30_yellow_0,axiom,
    ! [X1] :
      ( ( antisymmetric_relstr(X1)
        & rel_str(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ! [X3] :
              ( ( ( X2 = join_on_relstr(X1,X3)
                  & ex_sup_of_relstr_set(X1,X3) )
               => ( relstr_set_smaller(X1,X3,X2)
                  & ! [X4] :
                      ( element(X4,the_carrier(X1))
                     => ( relstr_set_smaller(X1,X3,X4)
                       => related(X1,X2,X4) ) ) ) )
              & ( ( relstr_set_smaller(X1,X3,X2)
                  & ! [X4] :
                      ( element(X4,the_carrier(X1))
                     => ( relstr_set_smaller(X1,X3,X4)
                       => related(X1,X2,X4) ) ) )
               => ( X2 = join_on_relstr(X1,X3)
                  & ex_sup_of_relstr_set(X1,X3) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_yellow_0) ).

fof(dt_k1_yellow_0,axiom,
    ! [X1,X2] :
      ( rel_str(X1)
     => element(join_on_relstr(X1,X2),the_carrier(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_0) ).

fof(t6_yellow_0,axiom,
    ! [X1] :
      ( rel_str(X1)
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ( relstr_set_smaller(X1,empty_set,X2)
            & relstr_element_smaller(X1,empty_set,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & antisymmetric_relstr(X1)
          & lower_bounded_relstr(X1)
          & rel_str(X1) )
       => ! [X2] :
            ( element(X2,the_carrier(X1))
           => related(X1,bottom_of_relstr(X1),X2) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t44_yellow_0])]) ).

fof(c_0_7,plain,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & antisymmetric_relstr(X1)
        & lower_bounded_relstr(X1)
        & rel_str(X1) )
     => ( ex_sup_of_relstr_set(X1,empty_set)
        & ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
    inference(fof_simplification,[status(thm)],[t42_yellow_0]) ).

fof(c_0_8,negated_conjecture,
    ( ~ empty_carrier(esk9_0)
    & antisymmetric_relstr(esk9_0)
    & lower_bounded_relstr(esk9_0)
    & rel_str(esk9_0)
    & element(esk10_0,the_carrier(esk9_0))
    & ~ related(esk9_0,bottom_of_relstr(esk9_0),esk10_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_9,plain,
    ! [X8] :
      ( ~ rel_str(X8)
      | bottom_of_relstr(X8) = join_on_relstr(X8,empty_set) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_yellow_0])]) ).

fof(c_0_10,plain,
    ! [X26,X27,X28,X29,X30] :
      ( ( relstr_set_smaller(X26,X28,X27)
        | X27 != join_on_relstr(X26,X28)
        | ~ ex_sup_of_relstr_set(X26,X28)
        | ~ element(X27,the_carrier(X26))
        | ~ antisymmetric_relstr(X26)
        | ~ rel_str(X26) )
      & ( ~ element(X29,the_carrier(X26))
        | ~ relstr_set_smaller(X26,X28,X29)
        | related(X26,X27,X29)
        | X27 != join_on_relstr(X26,X28)
        | ~ ex_sup_of_relstr_set(X26,X28)
        | ~ element(X27,the_carrier(X26))
        | ~ antisymmetric_relstr(X26)
        | ~ rel_str(X26) )
      & ( X27 = join_on_relstr(X26,X30)
        | element(esk8_3(X26,X27,X30),the_carrier(X26))
        | ~ relstr_set_smaller(X26,X30,X27)
        | ~ element(X27,the_carrier(X26))
        | ~ antisymmetric_relstr(X26)
        | ~ rel_str(X26) )
      & ( ex_sup_of_relstr_set(X26,X30)
        | element(esk8_3(X26,X27,X30),the_carrier(X26))
        | ~ relstr_set_smaller(X26,X30,X27)
        | ~ element(X27,the_carrier(X26))
        | ~ antisymmetric_relstr(X26)
        | ~ rel_str(X26) )
      & ( X27 = join_on_relstr(X26,X30)
        | relstr_set_smaller(X26,X30,esk8_3(X26,X27,X30))
        | ~ relstr_set_smaller(X26,X30,X27)
        | ~ element(X27,the_carrier(X26))
        | ~ antisymmetric_relstr(X26)
        | ~ rel_str(X26) )
      & ( ex_sup_of_relstr_set(X26,X30)
        | relstr_set_smaller(X26,X30,esk8_3(X26,X27,X30))
        | ~ relstr_set_smaller(X26,X30,X27)
        | ~ element(X27,the_carrier(X26))
        | ~ antisymmetric_relstr(X26)
        | ~ rel_str(X26) )
      & ( X27 = join_on_relstr(X26,X30)
        | ~ related(X26,X27,esk8_3(X26,X27,X30))
        | ~ relstr_set_smaller(X26,X30,X27)
        | ~ element(X27,the_carrier(X26))
        | ~ antisymmetric_relstr(X26)
        | ~ rel_str(X26) )
      & ( ex_sup_of_relstr_set(X26,X30)
        | ~ related(X26,X27,esk8_3(X26,X27,X30))
        | ~ relstr_set_smaller(X26,X30,X27)
        | ~ element(X27,the_carrier(X26))
        | ~ antisymmetric_relstr(X26)
        | ~ rel_str(X26) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[t30_yellow_0])])])])])]) ).

fof(c_0_11,plain,
    ! [X9,X10] :
      ( ~ rel_str(X9)
      | element(join_on_relstr(X9,X10),the_carrier(X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_yellow_0])]) ).

fof(c_0_12,plain,
    ! [X32] :
      ( ( ex_sup_of_relstr_set(X32,empty_set)
        | empty_carrier(X32)
        | ~ antisymmetric_relstr(X32)
        | ~ lower_bounded_relstr(X32)
        | ~ rel_str(X32) )
      & ( ex_inf_of_relstr_set(X32,the_carrier(X32))
        | empty_carrier(X32)
        | ~ antisymmetric_relstr(X32)
        | ~ lower_bounded_relstr(X32)
        | ~ rel_str(X32) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_13,negated_conjecture,
    ~ related(esk9_0,bottom_of_relstr(esk9_0),esk10_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( bottom_of_relstr(X1) = join_on_relstr(X1,empty_set)
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    rel_str(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_16,plain,
    ( related(X2,X4,X1)
    | ~ element(X1,the_carrier(X2))
    | ~ relstr_set_smaller(X2,X3,X1)
    | X4 != join_on_relstr(X2,X3)
    | ~ ex_sup_of_relstr_set(X2,X3)
    | ~ element(X4,the_carrier(X2))
    | ~ antisymmetric_relstr(X2)
    | ~ rel_str(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    ( element(join_on_relstr(X1,X2),the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ( ex_sup_of_relstr_set(X1,empty_set)
    | empty_carrier(X1)
    | ~ antisymmetric_relstr(X1)
    | ~ lower_bounded_relstr(X1)
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,negated_conjecture,
    lower_bounded_relstr(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,negated_conjecture,
    antisymmetric_relstr(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_21,negated_conjecture,
    ~ empty_carrier(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_22,negated_conjecture,
    ~ related(esk9_0,join_on_relstr(esk9_0,empty_set),esk10_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

cnf(c_0_23,plain,
    ( related(X1,join_on_relstr(X1,X2),X3)
    | ~ relstr_set_smaller(X1,X2,X3)
    | ~ ex_sup_of_relstr_set(X1,X2)
    | ~ antisymmetric_relstr(X1)
    | ~ element(X3,the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]) ).

cnf(c_0_24,negated_conjecture,
    ex_sup_of_relstr_set(esk9_0,empty_set),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_15])]),c_0_21]) ).

cnf(c_0_25,negated_conjecture,
    element(esk10_0,the_carrier(esk9_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_26,plain,
    ! [X36,X37] :
      ( ( relstr_set_smaller(X36,empty_set,X37)
        | ~ element(X37,the_carrier(X36))
        | ~ rel_str(X36) )
      & ( relstr_element_smaller(X36,empty_set,X37)
        | ~ element(X37,the_carrier(X36))
        | ~ rel_str(X36) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_yellow_0])])])]) ).

cnf(c_0_27,negated_conjecture,
    ~ relstr_set_smaller(esk9_0,empty_set,esk10_0),
    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_22,c_0_23]),c_0_24]),c_0_20]),c_0_25]),c_0_15])]) ).

cnf(c_0_28,plain,
    ( relstr_set_smaller(X1,empty_set,X2)
    | ~ element(X2,the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25]),c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU361+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34  % Computer : n011.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Wed Aug 23 19:10:07 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.012000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.015000 s
%------------------------------------------------------------------------------