TSTP Solution File: SET060+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET060+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 14:32:36 EDT 2023

% Result   : Theorem 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   55 (   7 unt;  40 typ;   0 def)
%            Number of atoms       :   36 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   38 (  17   ~;  11   |;   7   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   47 (  31   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   35 (  35 usr;   9 con; 0-3 aty)
%            Number of variables   :   24 (   2 sgn;  16   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    universal_class: $i ).

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

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

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

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

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

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

tff(decl_31,type,
    element_relation: $i ).

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

tff(decl_33,type,
    complement: $i > $i ).

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

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

tff(decl_36,type,
    domain_of: $i > $i ).

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

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

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

tff(decl_40,type,
    successor: $i > $i ).

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

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

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

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

tff(decl_45,type,
    inductive: $i > $o ).

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

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

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

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

tff(decl_50,type,
    function: $i > $o ).

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

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

tff(decl_53,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk2_0: $i ).

tff(decl_55,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk4_1: $i > $i ).

tff(decl_57,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_58,type,
    esk6_1: $i > $i ).

tff(decl_59,type,
    esk7_0: $i ).

tff(decl_60,type,
    esk8_0: $i ).

tff(decl_61,type,
    esk9_0: $i ).

fof(special_classes_lemma,conjecture,
    ! [X1,X2] : ~ member(X2,intersection(complement(X1),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',special_classes_lemma) ).

fof(complement,axiom,
    ! [X1,X5] :
      ( member(X5,complement(X1))
    <=> ( member(X5,universal_class)
        & ~ member(X5,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',complement) ).

fof(intersection,axiom,
    ! [X1,X2,X5] :
      ( member(X5,intersection(X1,X2))
    <=> ( member(X5,X1)
        & member(X5,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',intersection) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] : ~ member(X2,intersection(complement(X1),X1)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[special_classes_lemma])]) ).

fof(c_0_4,plain,
    ! [X1,X5] :
      ( member(X5,complement(X1))
    <=> ( member(X5,universal_class)
        & ~ member(X5,X1) ) ),
    inference(fof_simplification,[status(thm)],[complement]) ).

fof(c_0_5,plain,
    ! [X38,X39,X40] :
      ( ( member(X40,X38)
        | ~ member(X40,intersection(X38,X39)) )
      & ( member(X40,X39)
        | ~ member(X40,intersection(X38,X39)) )
      & ( ~ member(X40,X38)
        | ~ member(X40,X39)
        | member(X40,intersection(X38,X39)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).

fof(c_0_6,negated_conjecture,
    member(esk9_0,intersection(complement(esk8_0),esk8_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_7,plain,
    ! [X41,X42] :
      ( ( member(X42,universal_class)
        | ~ member(X42,complement(X41)) )
      & ( ~ member(X42,X41)
        | ~ member(X42,complement(X41)) )
      & ( ~ member(X42,universal_class)
        | member(X42,X41)
        | member(X42,complement(X41)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_8,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    member(esk9_0,intersection(complement(esk8_0),esk8_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,plain,
    ( ~ member(X1,X2)
    | ~ member(X1,complement(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    member(esk9_0,complement(esk8_0)),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    member(esk9_0,esk8_0),
    inference(spm,[status(thm)],[c_0_10,c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET060+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n003.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   : Sat Aug 26 08:17:39 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.60  % Version  : CSE_E---1.5
% 0.20/0.60  % Problem  : theBenchmark.p
% 0.20/0.60  % Proof found
% 0.20/0.60  % SZS status Theorem for theBenchmark.p
% 0.20/0.60  % SZS output start Proof
% See solution above
% 0.20/0.60  % Total time : 0.014000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.018000 s
%------------------------------------------------------------------------------