%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU158+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n025.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 16:22:53 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   41
% Syntax   : Number of formulae    :   57 (   6 unt;  38 typ;   0 def)
%            Number of atoms       :   36 (   3 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   31 (  14   ~;  12   |;   2   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   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   :   19 (   0 sgn;  10   !;   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(t37_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).

fof(l2_zfmisc_1,lemma,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).

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

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(singleton(X1),X2)
      <=> in(X1,X2) ),
    inference(assume_negation,[status(cth)],[t37_zfmisc_1]) ).

fof(c_0_4,lemma,
    ! [X129,X130] :
      ( ( ~ subset(singleton(X129),X130)
        | in(X129,X130) )
      & ( ~ in(X129,X130)
        | subset(singleton(X129),X130) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).

fof(c_0_5,lemma,
    ! [X215] : unordered_pair(X215,X215) = singleton(X215),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

fof(c_0_6,negated_conjecture,
    ( ( ~ subset(singleton(esk20_0),esk21_0)
      | ~ in(esk20_0,esk21_0) )
    & ( subset(singleton(esk20_0),esk21_0)
      | in(esk20_0,esk21_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_7,lemma,
    ( in(X1,X2)
    | ~ subset(singleton(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,lemma,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    ( subset(singleton(esk20_0),esk21_0)
    | in(esk20_0,esk21_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ( ~ subset(singleton(esk20_0),esk21_0)
    | ~ in(esk20_0,esk21_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,lemma,
    ( in(X1,X2)
    | ~ subset(unordered_pair(X1,X1),X2) ),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    ( in(esk20_0,esk21_0)
    | subset(unordered_pair(esk20_0,esk20_0),esk21_0) ),
    inference(rw,[status(thm)],[c_0_9,c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    ( ~ in(esk20_0,esk21_0)
    | ~ subset(unordered_pair(esk20_0,esk20_0),esk21_0) ),
    inference(rw,[status(thm)],[c_0_10,c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    in(esk20_0,esk21_0),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,lemma,
    ( subset(singleton(X1),X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_16,negated_conjecture,
    ~ subset(unordered_pair(esk20_0,esk20_0),esk21_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).

cnf(c_0_17,lemma,
    ( subset(unordered_pair(X1,X1),X2)
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[c_0_15,c_0_8]) ).

cnf(c_0_18,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU158+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n025.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Thu Aug 24 01:53:35 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.61  % Version  : CSE_E---1.5
% 0.20/0.61  % Problem  : theBenchmark.p
% 0.20/0.61  % Proof found
% 0.20/0.61  % SZS status Theorem for theBenchmark.p
% 0.20/0.61  % SZS output start Proof
% See solution above
% 0.20/0.61  % Total time : 0.021000 s
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  % Total time : 0.025000 s
%------------------------------------------------------------------------------