TSTP Solution File: SEU103+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU103+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 : 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 : Thu Aug 31 16:22:26 EDT 2023

% Result   : Theorem 0.73s 0.79s
% Output   : CNFRefutation 0.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   75 (  11 unt;  36 typ;   0 def)
%            Number of atoms       :  127 (  14 equ)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  141 (  53   ~;  44   |;  32   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   38 (  28   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;   8 con; 0-3 aty)
%            Number of variables   :   72 (   0 sgn;  46   !;   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,
    prebool_union2: ( $i * $i * $i ) > $i ).

tff(decl_31,type,
    set_union2: ( $i * $i ) > $i ).

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

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

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

tff(decl_35,type,
    empty_set: $i ).

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

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

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

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

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

tff(decl_41,type,
    epsilon_connected: $i > $o ).

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

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

tff(decl_44,type,
    subset: ( $i * $i ) > $o ).

tff(decl_45,type,
    esk1_1: $i > $i ).

tff(decl_46,type,
    esk2_0: $i ).

tff(decl_47,type,
    esk3_0: $i ).

tff(decl_48,type,
    esk4_1: $i > $i ).

tff(decl_49,type,
    esk5_0: $i ).

tff(decl_50,type,
    esk6_1: $i > $i ).

tff(decl_51,type,
    esk7_1: $i > $i ).

tff(decl_52,type,
    esk8_0: $i ).

tff(decl_53,type,
    esk9_1: $i > $i ).

tff(decl_54,type,
    esk10_1: $i > $i ).

tff(decl_55,type,
    esk11_0: $i ).

tff(decl_56,type,
    esk12_0: $i ).

tff(decl_57,type,
    esk13_0: $i ).

fof(dt_k2_finsub_1,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => element(prebool_difference(X1,X2,X3),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_finsub_1) ).

fof(t14_finsub_1,conjecture,
    ! [X1,X2,X3] :
      ( ( ~ empty(X3)
        & preboolean(X3) )
     => ( ( element(X1,X3)
          & element(X2,X3) )
       => element(symmetric_difference(X1,X2),X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finsub_1) ).

fof(redefinition_k2_finsub_1,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).

fof(dt_k1_finsub_1,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => element(prebool_union2(X1,X2,X3),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_finsub_1) ).

fof(redefinition_k1_finsub_1,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => prebool_union2(X1,X2,X3) = set_union2(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_finsub_1) ).

fof(d6_xboole_0,axiom,
    ! [X1,X2] : symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).

fof(c_0_6,plain,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => element(prebool_difference(X1,X2,X3),X1) ),
    inference(fof_simplification,[status(thm)],[dt_k2_finsub_1]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( ~ empty(X3)
          & preboolean(X3) )
       => ( ( element(X1,X3)
            & element(X2,X3) )
         => element(symmetric_difference(X1,X2),X3) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t14_finsub_1])]) ).

fof(c_0_8,plain,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
    inference(fof_simplification,[status(thm)],[redefinition_k2_finsub_1]) ).

fof(c_0_9,plain,
    ! [X23,X24,X25] :
      ( empty(X23)
      | ~ preboolean(X23)
      | ~ element(X24,X23)
      | ~ element(X25,X23)
      | element(prebool_difference(X23,X24,X25),X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).

fof(c_0_10,negated_conjecture,
    ( ~ empty(esk13_0)
    & preboolean(esk13_0)
    & element(esk11_0,esk13_0)
    & element(esk12_0,esk13_0)
    & ~ element(symmetric_difference(esk11_0,esk12_0),esk13_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_11,plain,
    ! [X60,X61,X62] :
      ( empty(X60)
      | ~ preboolean(X60)
      | ~ element(X61,X60)
      | ~ element(X62,X60)
      | prebool_difference(X60,X61,X62) = set_difference(X61,X62) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).

fof(c_0_12,plain,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => element(prebool_union2(X1,X2,X3),X1) ),
    inference(fof_simplification,[status(thm)],[dt_k1_finsub_1]) ).

cnf(c_0_13,plain,
    ( empty(X1)
    | element(prebool_difference(X1,X2,X3),X1)
    | ~ preboolean(X1)
    | ~ element(X2,X1)
    | ~ element(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    element(esk11_0,esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    preboolean(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    ~ empty(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    ( empty(X1)
    | prebool_difference(X1,X2,X3) = set_difference(X2,X3)
    | ~ preboolean(X1)
    | ~ element(X2,X1)
    | ~ element(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_18,plain,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => prebool_union2(X1,X2,X3) = set_union2(X2,X3) ),
    inference(fof_simplification,[status(thm)],[redefinition_k1_finsub_1]) ).

fof(c_0_19,plain,
    ! [X20,X21,X22] :
      ( empty(X20)
      | ~ preboolean(X20)
      | ~ element(X21,X20)
      | ~ element(X22,X20)
      | element(prebool_union2(X20,X21,X22),X20) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).

cnf(c_0_20,negated_conjecture,
    ( element(prebool_difference(esk13_0,X1,esk11_0),esk13_0)
    | ~ element(X1,esk13_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    ( prebool_difference(esk13_0,X1,esk11_0) = set_difference(X1,esk11_0)
    | ~ element(X1,esk13_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15])]),c_0_16]) ).

fof(c_0_22,plain,
    ! [X57,X58,X59] :
      ( empty(X57)
      | ~ preboolean(X57)
      | ~ element(X58,X57)
      | ~ element(X59,X57)
      | prebool_union2(X57,X58,X59) = set_union2(X58,X59) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).

fof(c_0_23,plain,
    ! [X18,X19] : symmetric_difference(X18,X19) = set_union2(set_difference(X18,X19),set_difference(X19,X18)),
    inference(variable_rename,[status(thm)],[d6_xboole_0]) ).

cnf(c_0_24,plain,
    ( empty(X1)
    | element(prebool_union2(X1,X2,X3),X1)
    | ~ preboolean(X1)
    | ~ element(X2,X1)
    | ~ element(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,negated_conjecture,
    ( element(set_difference(X1,esk11_0),esk13_0)
    | ~ element(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    ( empty(X1)
    | prebool_union2(X1,X2,X3) = set_union2(X2,X3)
    | ~ preboolean(X1)
    | ~ element(X2,X1)
    | ~ element(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    ~ element(symmetric_difference(esk11_0,esk12_0),esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_28,plain,
    symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    ( element(prebool_union2(esk13_0,X1,set_difference(X2,esk11_0)),esk13_0)
    | ~ element(X1,esk13_0)
    | ~ element(X2,esk13_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15])]),c_0_16]) ).

cnf(c_0_30,negated_conjecture,
    ( prebool_union2(esk13_0,X1,set_difference(X2,esk11_0)) = set_union2(X1,set_difference(X2,esk11_0))
    | ~ element(X1,esk13_0)
    | ~ element(X2,esk13_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_25]),c_0_15])]),c_0_16]) ).

cnf(c_0_31,negated_conjecture,
    element(esk12_0,esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_32,negated_conjecture,
    ~ element(set_union2(set_difference(esk11_0,esk12_0),set_difference(esk12_0,esk11_0)),esk13_0),
    inference(rw,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_33,negated_conjecture,
    ( element(set_union2(X1,set_difference(X2,esk11_0)),esk13_0)
    | ~ element(X1,esk13_0)
    | ~ element(X2,esk13_0) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    ( element(prebool_difference(esk13_0,X1,esk12_0),esk13_0)
    | ~ element(X1,esk13_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_31]),c_0_15])]),c_0_16]) ).

cnf(c_0_35,negated_conjecture,
    ( prebool_difference(esk13_0,X1,esk12_0) = set_difference(X1,esk12_0)
    | ~ element(X1,esk13_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_31]),c_0_15])]),c_0_16]) ).

cnf(c_0_36,negated_conjecture,
    ~ element(set_difference(esk11_0,esk12_0),esk13_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_31])]) ).

cnf(c_0_37,negated_conjecture,
    ( element(set_difference(X1,esk12_0),esk13_0)
    | ~ element(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_38,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU103+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33  % Computer : n004.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Wed Aug 23 15:27:38 EDT 2023
% 0.14/0.33  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.73/0.79  % Version  : CSE_E---1.5
% 0.73/0.79  % Problem  : theBenchmark.p
% 0.73/0.79  % Proof found
% 0.73/0.79  % SZS status Theorem for theBenchmark.p
% 0.73/0.79  % SZS output start Proof
% See solution above
% 0.73/0.80  % Total time : 0.226000 s
% 0.73/0.80  % SZS output end Proof
% 0.73/0.80  % Total time : 0.230000 s
%------------------------------------------------------------------------------