TSTP Solution File: SEU160+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU160+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 : n011.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 16:22:55 EDT 2023

% Result   : Theorem 0.17s 0.59s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   67 (  11 unt;  38 typ;   0 def)
%            Number of atoms       :   66 (  41 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   60 (  23   ~;  28   |;   5   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   73 (  33   >;  40   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   33 (  33 usr;   5 con; 0-4 aty)
%            Number of variables   :   28 (   2 sgn;  19   !;   0   ?;   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,
    singleton: $i > $i ).

tff(decl_29,type,
    empty_set: $i ).

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

tff(decl_31,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

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

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

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

tff(decl_37,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk2_1: $i > $i ).

tff(decl_39,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_41,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_42,type,
    esk6_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk7_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_47,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_48,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk17_0: $i ).

tff(decl_54,type,
    esk18_0: $i ).

tff(decl_55,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk20_0: $i ).

tff(decl_57,type,
    esk21_0: $i ).

tff(decl_58,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_59,type,
    esk23_2: ( $i * $i ) > $i ).

fof(t39_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( subset(X1,singleton(X2))
    <=> ( X1 = empty_set
        | X1 = singleton(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).

fof(l4_zfmisc_1,lemma,
    ! [X1,X2] :
      ( subset(X1,singleton(X2))
    <=> ( X1 = empty_set
        | X1 = singleton(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).

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

fof(l32_xboole_1,lemma,
    ! [X1,X2] :
      ( set_difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).

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

fof(t4_boole,axiom,
    ! [X1] : set_difference(empty_set,X1) = empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,singleton(X2))
      <=> ( X1 = empty_set
          | X1 = singleton(X2) ) ),
    inference(assume_negation,[status(cth)],[t39_zfmisc_1]) ).

fof(c_0_7,lemma,
    ! [X136,X137] :
      ( ( ~ subset(X136,singleton(X137))
        | X136 = empty_set
        | X136 = singleton(X137) )
      & ( X136 != empty_set
        | subset(X136,singleton(X137)) )
      & ( X136 != singleton(X137)
        | subset(X136,singleton(X137)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).

fof(c_0_8,lemma,
    ! [X220] : unordered_pair(X220,X220) = singleton(X220),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

fof(c_0_9,negated_conjecture,
    ( ( esk20_0 != empty_set
      | ~ subset(esk20_0,singleton(esk21_0)) )
    & ( esk20_0 != singleton(esk21_0)
      | ~ subset(esk20_0,singleton(esk21_0)) )
    & ( subset(esk20_0,singleton(esk21_0))
      | esk20_0 = empty_set
      | esk20_0 = singleton(esk21_0) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

cnf(c_0_10,lemma,
    ( X1 = empty_set
    | X1 = singleton(X2)
    | ~ subset(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,lemma,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    ( subset(esk20_0,singleton(esk21_0))
    | esk20_0 = empty_set
    | esk20_0 = singleton(esk21_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    ( esk20_0 != empty_set
    | ~ subset(esk20_0,singleton(esk21_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_14,lemma,
    ! [X131,X132] :
      ( ( set_difference(X131,X132) != empty_set
        | subset(X131,X132) )
      & ( ~ subset(X131,X132)
        | set_difference(X131,X132) = empty_set ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).

cnf(c_0_15,negated_conjecture,
    ( esk20_0 != singleton(esk21_0)
    | ~ subset(esk20_0,singleton(esk21_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,lemma,
    ( X1 = empty_set
    | X1 = unordered_pair(X2,X2)
    | ~ subset(X1,unordered_pair(X2,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).

cnf(c_0_17,negated_conjecture,
    ( esk20_0 = empty_set
    | esk20_0 = unordered_pair(esk21_0,esk21_0)
    | subset(esk20_0,unordered_pair(esk21_0,esk21_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_11]) ).

fof(c_0_18,plain,
    ! [X146] : subset(X146,X146),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).

cnf(c_0_19,negated_conjecture,
    ( esk20_0 != empty_set
    | ~ subset(esk20_0,unordered_pair(esk21_0,esk21_0)) ),
    inference(rw,[status(thm)],[c_0_13,c_0_11]) ).

cnf(c_0_20,lemma,
    ( subset(X1,X2)
    | set_difference(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,negated_conjecture,
    ( esk20_0 != unordered_pair(esk21_0,esk21_0)
    | ~ subset(esk20_0,unordered_pair(esk21_0,esk21_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_11]),c_0_11]) ).

cnf(c_0_22,negated_conjecture,
    ( unordered_pair(esk21_0,esk21_0) = esk20_0
    | esk20_0 = empty_set ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_23,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_24,plain,
    ! [X208] : set_difference(empty_set,X208) = empty_set,
    inference(variable_rename,[status(thm)],[t4_boole]) ).

cnf(c_0_25,negated_conjecture,
    ( set_difference(esk20_0,unordered_pair(esk21_0,esk21_0)) != empty_set
    | esk20_0 != empty_set ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    esk20_0 = empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).

cnf(c_0_27,plain,
    set_difference(empty_set,X1) = empty_set,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SEU160+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.32  % Computer : n011.cluster.edu
% 0.15/0.32  % Model    : x86_64 x86_64
% 0.15/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32  % Memory   : 8042.1875MB
% 0.15/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32  % CPULimit   : 300
% 0.15/0.32  % WCLimit    : 300
% 0.15/0.32  % DateTime   : Wed Aug 23 13:56:52 EDT 2023
% 0.15/0.33  % CPUTime  : 
% 0.17/0.55  start to proof: theBenchmark
% 0.17/0.59  % Version  : CSE_E---1.5
% 0.17/0.59  % Problem  : theBenchmark.p
% 0.17/0.59  % Proof found
% 0.17/0.59  % SZS status Theorem for theBenchmark.p
% 0.17/0.59  % SZS output start Proof
% See solution above
% 0.17/0.59  % Total time : 0.029000 s
% 0.17/0.59  % SZS output end Proof
% 0.17/0.59  % Total time : 0.033000 s
%------------------------------------------------------------------------------