TSTP Solution File: SEU161+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU161+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 : 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 16:22:56 EDT 2023

% Result   : Theorem 0.19s 0.56s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   61 (  12 unt;  38 typ;   0 def)
%            Number of atoms       :   36 (  16 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   26 (  13   ~;   7   |;   2   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   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   :   29 (   0 sgn;  18   !;   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_2: ( $i * $i ) > $i ).

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

tff(decl_58,type,
    esk22_0: $i ).

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

fof(t46_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( in(X1,X2)
     => set_union2(singleton(X1),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).

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

fof(commutativity_k2_xboole_0,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(t12_xboole_1,lemma,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_union2(X1,X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_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(c_0_5,negated_conjecture,
    ~ ! [X1,X2] :
        ( in(X1,X2)
       => set_union2(singleton(X1),X2) = X2 ),
    inference(assume_negation,[status(cth)],[t46_zfmisc_1]) ).

fof(c_0_6,negated_conjecture,
    ( in(esk21_0,esk22_0)
    & set_union2(singleton(esk21_0),esk22_0) != esk22_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_7,lemma,
    ! [X222] : unordered_pair(X222,X222) = singleton(X222),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

cnf(c_0_8,negated_conjecture,
    set_union2(singleton(esk21_0),esk22_0) != esk22_0,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,lemma,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,plain,
    ! [X13,X14] : set_union2(X13,X14) = set_union2(X14,X13),
    inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).

fof(c_0_11,lemma,
    ! [X153,X154] :
      ( ~ subset(X153,X154)
      | set_union2(X153,X154) = X154 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).

cnf(c_0_12,negated_conjecture,
    set_union2(unordered_pair(esk21_0,esk21_0),esk22_0) != esk22_0,
    inference(rw,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,lemma,
    ( set_union2(X1,X2) = X2
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_15,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])]) ).

cnf(c_0_16,negated_conjecture,
    set_union2(esk22_0,unordered_pair(esk21_0,esk21_0)) != esk22_0,
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,lemma,
    ( set_union2(X1,X2) = X1
    | ~ subset(X2,X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_13]) ).

cnf(c_0_18,lemma,
    ( subset(singleton(X1),X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    ~ subset(unordered_pair(esk21_0,esk21_0),esk22_0),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,lemma,
    ( subset(unordered_pair(X1,X1),X2)
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[c_0_18,c_0_9]) ).

cnf(c_0_21,negated_conjecture,
    in(esk21_0,esk22_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_22,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU161+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Wed Aug 23 20:04:07 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.53  start to proof: theBenchmark
% 0.19/0.56  % Version  : CSE_E---1.5
% 0.19/0.56  % Problem  : theBenchmark.p
% 0.19/0.56  % Proof found
% 0.19/0.56  % SZS status Theorem for theBenchmark.p
% 0.19/0.56  % SZS output start Proof
% See solution above
% 0.19/0.56  % Total time : 0.024000 s
% 0.19/0.56  % SZS output end Proof
% 0.19/0.56  % Total time : 0.028000 s
%------------------------------------------------------------------------------