TSTP Solution File: SEU107+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU107+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 : n003.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 16:22:27 EDT 2023

% Result   : Theorem 0.23s 0.68s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   74 (  18 unt;  31 typ;   0 def)
%            Number of atoms       :  106 (  17 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  101 (  38   ~;  37   |;  17   &)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  25   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   6 con; 0-3 aty)
%            Number of variables   :   59 (   1 sgn;  35   !;   2   ?;   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_difference: ( $i * $i * $i ) > $i ).

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

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,
    subset: ( $i * $i ) > $o ).

tff(decl_42,type,
    esk1_1: $i > $i ).

tff(decl_43,type,
    esk2_0: $i ).

tff(decl_44,type,
    esk3_0: $i ).

tff(decl_45,type,
    esk4_1: $i > $i ).

tff(decl_46,type,
    esk5_0: $i ).

tff(decl_47,type,
    esk6_1: $i > $i ).

tff(decl_48,type,
    esk7_1: $i > $i ).

tff(decl_49,type,
    esk8_0: $i ).

tff(decl_50,type,
    esk9_1: $i > $i ).

tff(decl_51,type,
    esk10_1: $i > $i ).

tff(decl_52,type,
    esk11_0: $i ).

fof(t6_boole,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(rc1_xboole_0,axiom,
    ? [X1] : empty(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

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(t37_xboole_1,axiom,
    ! [X1,X2] :
      ( set_difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).

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(existence_m1_subset_1,axiom,
    ! [X1] :
    ? [X2] : element(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(reflexivity_r1_tarski,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(t18_finsub_1,conjecture,
    ! [X1] :
      ( ( ~ empty(X1)
        & preboolean(X1) )
     => in(empty_set,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finsub_1) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(c_0_9,plain,
    ! [X54] :
      ( ~ empty(X54)
      | X54 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(c_0_10,plain,
    empty(esk5_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).

fof(c_0_11,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_12,plain,
    ! [X42,X43] :
      ( ( set_difference(X42,X43) != empty_set
        | subset(X42,X43) )
      & ( ~ subset(X42,X43)
        | set_difference(X42,X43) = empty_set ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).

cnf(c_0_13,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    empty(esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_15,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_16,plain,
    ! [X33,X34,X35] :
      ( empty(X33)
      | ~ preboolean(X33)
      | ~ element(X34,X33)
      | ~ element(X35,X33)
      | prebool_difference(X33,X34,X35) = set_difference(X34,X35) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).

fof(c_0_17,plain,
    ! [X14] : element(esk1_1(X14),X14),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).

cnf(c_0_18,plain,
    ( set_difference(X1,X2) = empty_set
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    empty_set = esk5_0,
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

fof(c_0_20,plain,
    ! [X36] : subset(X36,X36),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).

fof(c_0_21,plain,
    ! [X11,X12,X13] :
      ( empty(X11)
      | ~ preboolean(X11)
      | ~ element(X12,X11)
      | ~ element(X13,X11)
      | element(prebool_difference(X11,X12,X13),X11) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).

cnf(c_0_22,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_16]) ).

cnf(c_0_23,plain,
    element(esk1_1(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24,plain,
    ( set_difference(X1,X2) = esk5_0
    | ~ subset(X1,X2) ),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_25,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_26,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty(X1)
          & preboolean(X1) )
       => in(empty_set,X1) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t18_finsub_1])]) ).

cnf(c_0_27,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_21]) ).

cnf(c_0_28,plain,
    ( prebool_difference(X1,X2,esk1_1(X1)) = set_difference(X2,esk1_1(X1))
    | empty(X1)
    | ~ element(X2,X1)
    | ~ preboolean(X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_29,plain,
    set_difference(X1,X1) = esk5_0,
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

fof(c_0_30,negated_conjecture,
    ( ~ empty(esk11_0)
    & preboolean(esk11_0)
    & ~ in(empty_set,esk11_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).

cnf(c_0_31,plain,
    ( element(prebool_difference(X1,X2,esk1_1(X1)),X1)
    | empty(X1)
    | ~ element(X2,X1)
    | ~ preboolean(X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_23]) ).

cnf(c_0_32,plain,
    ( prebool_difference(X1,esk1_1(X1),esk1_1(X1)) = esk5_0
    | empty(X1)
    | ~ preboolean(X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    preboolean(esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    ~ empty(esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

fof(c_0_35,plain,
    ! [X40,X41] :
      ( ~ element(X40,X41)
      | empty(X41)
      | in(X40,X41) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

cnf(c_0_36,plain,
    ( element(prebool_difference(X1,esk1_1(X1),esk1_1(X1)),X1)
    | empty(X1)
    | ~ preboolean(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_23]) ).

cnf(c_0_37,negated_conjecture,
    prebool_difference(esk11_0,esk1_1(esk11_0),esk1_1(esk11_0)) = esk5_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).

cnf(c_0_38,negated_conjecture,
    ~ in(empty_set,esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_39,plain,
    ( empty(X2)
    | in(X1,X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_40,negated_conjecture,
    element(esk5_0,esk11_0),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_37]),c_0_34]) ).

cnf(c_0_41,negated_conjecture,
    ~ in(esk5_0,esk11_0),
    inference(rw,[status(thm)],[c_0_38,c_0_19]) ).

cnf(c_0_42,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_34]),c_0_41]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SEU107+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36  % Computer : n003.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Wed Aug 23 18:17:52 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.23/0.60  start to proof: theBenchmark
% 0.23/0.68  % Version  : CSE_E---1.5
% 0.23/0.68  % Problem  : theBenchmark.p
% 0.23/0.68  % Proof found
% 0.23/0.68  % SZS status Theorem for theBenchmark.p
% 0.23/0.68  % SZS output start Proof
% See solution above
% 0.23/0.69  % Total time : 0.074000 s
% 0.23/0.69  % SZS output end Proof
% 0.23/0.69  % Total time : 0.077000 s
%------------------------------------------------------------------------------