TSTP Solution File: SEU110+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU110+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 16:22:28 EDT 2023

% Result   : Theorem 0.69s 0.84s
% Output   : CNFRefutation 0.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   62 (   6 unt;  33 typ;   0 def)
%            Number of atoms       :   96 (  10 equ)
%            Maximal formula atoms :   26 (   3 avg)
%            Number of connectives :  109 (  42   ~;  49   |;  10   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  26   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   7 con; 0-2 aty)
%            Number of variables   :   57 (   3 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,
    preboolean: $i > $o ).

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

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

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

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

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

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

tff(decl_32,type,
    empty_set: $i ).

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

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

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

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

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

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

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

tff(decl_40,type,
    natural: $i > $o ).

tff(decl_41,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_42,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_43,type,
    esk3_1: $i > $i ).

tff(decl_44,type,
    esk4_0: $i ).

tff(decl_45,type,
    esk5_0: $i ).

tff(decl_46,type,
    esk6_1: $i > $i ).

tff(decl_47,type,
    esk7_0: $i ).

tff(decl_48,type,
    esk8_1: $i > $i ).

tff(decl_49,type,
    esk9_1: $i > $i ).

tff(decl_50,type,
    esk10_0: $i ).

tff(decl_51,type,
    esk11_1: $i > $i ).

tff(decl_52,type,
    esk12_1: $i > $i ).

tff(decl_53,type,
    esk13_0: $i ).

tff(decl_54,type,
    esk14_0: $i ).

fof(t23_finsub_1,conjecture,
    ! [X1,X2] :
      ( subset(X1,X2)
     => subset(finite_subsets(X1),finite_subsets(X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).

fof(d5_finsub_1,axiom,
    ! [X1,X2] :
      ( preboolean(X2)
     => ( X2 = finite_subsets(X1)
      <=> ! [X3] :
            ( in(X3,X2)
          <=> ( subset(X3,X1)
              & finite(X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).

fof(dt_k5_finsub_1,axiom,
    ! [X1] : preboolean(finite_subsets(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).

fof(t1_xboole_1,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X2,X3) )
     => subset(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,X2)
       => subset(finite_subsets(X1),finite_subsets(X2)) ),
    inference(assume_negation,[status(cth)],[t23_finsub_1]) ).

fof(c_0_6,plain,
    ! [X19,X20,X21,X22] :
      ( ( subset(X21,X19)
        | ~ in(X21,X20)
        | X20 != finite_subsets(X19)
        | ~ preboolean(X20) )
      & ( finite(X21)
        | ~ in(X21,X20)
        | X20 != finite_subsets(X19)
        | ~ preboolean(X20) )
      & ( ~ subset(X22,X19)
        | ~ finite(X22)
        | in(X22,X20)
        | X20 != finite_subsets(X19)
        | ~ preboolean(X20) )
      & ( ~ in(esk2_2(X19,X20),X20)
        | ~ subset(esk2_2(X19,X20),X19)
        | ~ finite(esk2_2(X19,X20))
        | X20 = finite_subsets(X19)
        | ~ preboolean(X20) )
      & ( subset(esk2_2(X19,X20),X19)
        | in(esk2_2(X19,X20),X20)
        | X20 = finite_subsets(X19)
        | ~ preboolean(X20) )
      & ( finite(esk2_2(X19,X20))
        | in(esk2_2(X19,X20),X20)
        | X20 = finite_subsets(X19)
        | ~ preboolean(X20) ) ),
    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)],[d5_finsub_1])])])])])]) ).

fof(c_0_7,plain,
    ! [X24] : preboolean(finite_subsets(X24)),
    inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).

fof(c_0_8,plain,
    ! [X47,X48,X49] :
      ( ~ subset(X47,X48)
      | ~ subset(X48,X49)
      | subset(X47,X49) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).

fof(c_0_9,negated_conjecture,
    ( subset(esk13_0,esk14_0)
    & ~ subset(finite_subsets(esk13_0),finite_subsets(esk14_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

cnf(c_0_10,plain,
    ( subset(X1,X2)
    | ~ in(X1,X3)
    | X3 != finite_subsets(X2)
    | ~ preboolean(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    preboolean(finite_subsets(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_12,plain,
    ! [X13,X14,X15,X16,X17] :
      ( ( ~ subset(X13,X14)
        | ~ in(X15,X13)
        | in(X15,X14) )
      & ( in(esk1_2(X16,X17),X16)
        | subset(X16,X17) )
      & ( ~ in(esk1_2(X16,X17),X17)
        | subset(X16,X17) ) ),
    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)],[d3_tarski])])])])])]) ).

cnf(c_0_13,plain,
    ( subset(X1,X3)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    subset(esk13_0,esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( subset(X1,X2)
    | ~ in(X1,finite_subsets(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_10]),c_0_11])]) ).

cnf(c_0_16,plain,
    ( in(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    ( finite(X1)
    | ~ in(X1,X2)
    | X2 != finite_subsets(X3)
    | ~ preboolean(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_18,plain,
    ( in(X1,X3)
    | ~ subset(X1,X2)
    | ~ finite(X1)
    | X3 != finite_subsets(X2)
    | ~ preboolean(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_19,negated_conjecture,
    ( subset(X1,esk14_0)
    | ~ subset(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_20,plain,
    ( subset(esk1_2(finite_subsets(X1),X2),X1)
    | subset(finite_subsets(X1),X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,plain,
    ( finite(X1)
    | ~ in(X1,finite_subsets(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_11])]) ).

cnf(c_0_22,plain,
    ( in(X1,finite_subsets(X2))
    | ~ subset(X1,X2)
    | ~ finite(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_11])]) ).

cnf(c_0_23,negated_conjecture,
    ( subset(esk1_2(finite_subsets(esk13_0),X1),esk14_0)
    | subset(finite_subsets(esk13_0),X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,plain,
    ( subset(finite_subsets(X1),X2)
    | finite(esk1_2(finite_subsets(X1),X2)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_16]) ).

cnf(c_0_25,plain,
    ( subset(X1,X2)
    | ~ in(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_26,negated_conjecture,
    ( subset(finite_subsets(esk13_0),X1)
    | in(esk1_2(finite_subsets(esk13_0),X1),finite_subsets(esk14_0)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_27,negated_conjecture,
    ~ subset(finite_subsets(esk13_0),finite_subsets(esk14_0)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU110+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Wed Aug 23 18:51:16 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.69/0.84  % Version  : CSE_E---1.5
% 0.69/0.84  % Problem  : theBenchmark.p
% 0.69/0.84  % Proof found
% 0.69/0.84  % SZS status Theorem for theBenchmark.p
% 0.69/0.84  % SZS output start Proof
% See solution above
% 0.82/0.85  % Total time : 0.263000 s
% 0.82/0.85  % SZS output end Proof
% 0.82/0.85  % Total time : 0.266000 s
%------------------------------------------------------------------------------