TSTP Solution File: SEU177+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU177+2 : 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 : n016.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 16:23:06 EDT 2023

% Result   : Theorem 0.59s 0.79s
% Output   : CNFRefutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   75
% Syntax   : Number of formulae    :  102 (  17 unt;  69 typ;   0 def)
%            Number of atoms       :   99 (  28 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  112 (  46   ~;  46   |;  10   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  126 (  62   >;  64   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   61 (  61 usr;   7 con; 0-4 aty)
%            Number of variables   :   71 (   4 sgn;  36   !;   2   ?;   0   :)

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

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

tff(decl_24,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_25,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_26,type,
    set_intersection2: ( $i * $i ) > $i ).

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

tff(decl_28,type,
    empty_set: $i ).

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

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

tff(decl_31,type,
    powerset: $i > $i ).

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

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

tff(decl_34,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

tff(decl_37,type,
    relation_dom: $i > $i ).

tff(decl_38,type,
    cast_to_subset: $i > $i ).

tff(decl_39,type,
    union: $i > $i ).

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

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

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

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

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

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

tff(decl_46,type,
    meet_of_subsets: ( $i * $i ) > $i ).

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

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

tff(decl_49,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk5_1: $i > $i ).

tff(decl_54,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_57,type,
    esk9_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_58,type,
    esk10_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_59,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_60,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_61,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_62,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_63,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_66,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_67,type,
    esk19_3: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk20_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk22_3: ( $i * $i * $i ) > $i ).

tff(decl_71,type,
    esk23_3: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_73,type,
    esk25_2: ( $i * $i ) > $i ).

tff(decl_74,type,
    esk26_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk27_1: $i > $i ).

tff(decl_76,type,
    esk28_2: ( $i * $i ) > $i ).

tff(decl_77,type,
    esk29_0: $i ).

tff(decl_78,type,
    esk30_1: $i > $i ).

tff(decl_79,type,
    esk31_0: $i ).

tff(decl_80,type,
    esk32_1: $i > $i ).

tff(decl_81,type,
    esk33_0: $i ).

tff(decl_82,type,
    esk34_1: $i > $i ).

tff(decl_83,type,
    esk35_0: $i ).

tff(decl_84,type,
    esk36_0: $i ).

tff(decl_85,type,
    esk37_0: $i ).

tff(decl_86,type,
    esk38_2: ( $i * $i ) > $i ).

tff(decl_87,type,
    esk39_2: ( $i * $i ) > $i ).

tff(decl_88,type,
    esk40_2: ( $i * $i ) > $i ).

tff(decl_89,type,
    esk41_1: $i > $i ).

tff(decl_90,type,
    esk42_2: ( $i * $i ) > $i ).

fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

fof(t69_enumset1,lemma,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).

fof(t20_relat_1,conjecture,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(ordered_pair(X1,X2),X3)
       => ( in(X1,relation_dom(X3))
          & in(X2,relation_rng(X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).

fof(d5_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( X2 = relation_rng(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(d4_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( X2 = relation_dom(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).

fof(c_0_6,plain,
    ! [X145,X146] : ordered_pair(X145,X146) = unordered_pair(unordered_pair(X145,X146),singleton(X145)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_7,lemma,
    ! [X354] : unordered_pair(X354,X354) = singleton(X354),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( relation(X3)
       => ( in(ordered_pair(X1,X2),X3)
         => ( in(X1,relation_dom(X3))
            & in(X2,relation_rng(X3)) ) ) ),
    inference(assume_negation,[status(cth)],[t20_relat_1]) ).

fof(c_0_9,plain,
    ! [X133,X134,X135,X137,X138,X139,X141] :
      ( ( ~ in(X135,X134)
        | in(ordered_pair(esk23_3(X133,X134,X135),X135),X133)
        | X134 != relation_rng(X133)
        | ~ relation(X133) )
      & ( ~ in(ordered_pair(X138,X137),X133)
        | in(X137,X134)
        | X134 != relation_rng(X133)
        | ~ relation(X133) )
      & ( ~ in(esk24_2(X133,X139),X139)
        | ~ in(ordered_pair(X141,esk24_2(X133,X139)),X133)
        | X139 = relation_rng(X133)
        | ~ relation(X133) )
      & ( in(esk24_2(X133,X139),X139)
        | in(ordered_pair(esk25_2(X133,X139),esk24_2(X133,X139)),X133)
        | X139 = relation_rng(X133)
        | ~ relation(X133) ) ),
    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_relat_1])])])])])]) ).

cnf(c_0_10,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,lemma,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_12,negated_conjecture,
    ( relation(esk37_0)
    & in(ordered_pair(esk35_0,esk36_0),esk37_0)
    & ( ~ in(esk35_0,relation_dom(esk37_0))
      | ~ in(esk36_0,relation_rng(esk37_0)) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

cnf(c_0_13,plain,
    ( in(X2,X4)
    | ~ in(ordered_pair(X1,X2),X3)
    | X4 != relation_rng(X3)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

fof(c_0_15,plain,
    ! [X11,X12] : unordered_pair(X11,X12) = unordered_pair(X12,X11),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_16,negated_conjecture,
    in(ordered_pair(esk35_0,esk36_0),esk37_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_17,plain,
    ! [X102,X103,X104,X106,X107,X108,X110] :
      ( ( ~ in(X104,X103)
        | in(ordered_pair(X104,esk16_3(X102,X103,X104)),X102)
        | X103 != relation_dom(X102)
        | ~ relation(X102) )
      & ( ~ in(ordered_pair(X106,X107),X102)
        | in(X106,X103)
        | X103 != relation_dom(X102)
        | ~ relation(X102) )
      & ( ~ in(esk17_2(X102,X108),X108)
        | ~ in(ordered_pair(esk17_2(X102,X108),X110),X102)
        | X108 = relation_dom(X102)
        | ~ relation(X102) )
      & ( in(esk17_2(X102,X108),X108)
        | in(ordered_pair(esk17_2(X102,X108),esk18_2(X102,X108)),X102)
        | X108 = relation_dom(X102)
        | ~ relation(X102) ) ),
    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)],[d4_relat_1])])])])])]) ).

cnf(c_0_18,plain,
    ( in(X2,X4)
    | X4 != relation_rng(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_19,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),esk37_0),
    inference(rw,[status(thm)],[c_0_16,c_0_14]) ).

cnf(c_0_21,plain,
    ( in(X1,X4)
    | ~ in(ordered_pair(X1,X2),X3)
    | X4 != relation_dom(X3)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,plain,
    ( in(X1,X2)
    | X2 != relation_rng(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,X1)),X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    in(unordered_pair(unordered_pair(esk35_0,esk35_0),unordered_pair(esk35_0,esk36_0)),esk37_0),
    inference(rw,[status(thm)],[c_0_20,c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    relation(esk37_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_25,plain,
    ( in(X1,X4)
    | X4 != relation_dom(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
    inference(rw,[status(thm)],[c_0_21,c_0_14]) ).

cnf(c_0_26,negated_conjecture,
    ( in(esk36_0,X1)
    | X1 != relation_rng(esk37_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_27,plain,
    ( in(X1,X2)
    | X2 != relation_dom(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X4)),X3) ),
    inference(spm,[status(thm)],[c_0_25,c_0_19]) ).

cnf(c_0_28,negated_conjecture,
    ( ~ in(esk35_0,relation_dom(esk37_0))
    | ~ in(esk36_0,relation_rng(esk37_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_29,negated_conjecture,
    in(esk36_0,relation_rng(esk37_0)),
    inference(er,[status(thm)],[c_0_26]) ).

cnf(c_0_30,negated_conjecture,
    ( in(esk35_0,X1)
    | X1 != relation_dom(esk37_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_23]),c_0_24])]) ).

cnf(c_0_31,negated_conjecture,
    ~ in(esk35_0,relation_dom(esk37_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).

cnf(c_0_32,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_30]),c_0_31]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU177+2 : 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
% 0.13/0.34  % Computer : n016.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   : Thu Aug 24 02:19:08 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.59/0.79  % Version  : CSE_E---1.5
% 0.59/0.79  % Problem  : theBenchmark.p
% 0.59/0.79  % Proof found
% 0.59/0.79  % SZS status Theorem for theBenchmark.p
% 0.59/0.79  % SZS output start Proof
% See solution above
% 0.59/0.79  % Total time : 0.206000 s
% 0.59/0.79  % SZS output end Proof
% 0.59/0.79  % Total time : 0.211000 s
%------------------------------------------------------------------------------