TSTP Solution File: SET787-2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET787-2 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n009.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 14:35:33 EDT 2023

% Result   : Unsatisfiable 0.42s 0.67s
% Output   : CNFRefutation 0.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   78
% Syntax   : Number of formulae    :   97 (   8 unt;  69 typ;   0 def)
%            Number of atoms       :   54 (   8 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   51 (  25   ~;  26   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  129 (  64   >;  65   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-8 aty)
%            Number of functors    :   61 (  61 usr;   5 con; 0-4 aty)
%            Number of variables   :   46 (   4 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    succ: $i > $i ).

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

tff(decl_27,type,
    inl: $i > $i ).

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

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

tff(decl_30,type,
    diff: ( $i * $i ) > $i ).

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

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

tff(decl_33,type,
    powI_sk1: ( $i * $i ) > $i ).

tff(decl_34,type,
    pow: $i > $i ).

tff(decl_35,type,
    interI_sk1: ( $i * $i ) > $i ).

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

tff(decl_37,type,
    card_Union_sk1: $i > $i ).

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

tff(decl_39,type,
    card: $i > $o ).

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

tff(decl_41,type,
    order_Inter_sk1: $i > $i ).

tff(decl_42,type,
    ord: $i > $o ).

tff(decl_43,type,
    order_Union_sk1: $i > $i ).

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

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

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

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

tff(decl_48,type,
    qInr: $i > $i ).

tff(decl_49,type,
    qInl: $i > $i ).

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

tff(decl_51,type,
    qsumE_sk1: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    qsumE_sk2: ( $i * $i * $i ) > $i ).

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

tff(decl_54,type,
    qconverseE_sk2: ( $i * $i ) > $i ).

tff(decl_55,type,
    qconverseE_sk1: ( $i * $i ) > $i ).

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

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

tff(decl_58,type,
    rmultE_c1: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).

tff(decl_59,type,
    rmultE_c2: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).

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

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

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

tff(decl_63,type,
    memrel: $i > $i ).

tff(decl_64,type,
    compE_sk1: ( $i * $i * $i ) > $i ).

tff(decl_65,type,
    compE_sk3: ( $i * $i * $i ) > $i ).

tff(decl_66,type,
    compE_sk2: ( $i * $i * $i ) > $i ).

tff(decl_67,type,
    id: $i > $i ).

tff(decl_68,type,
    idE_sk1: ( $i * $i ) > $i ).

tff(decl_69,type,
    sumE_sk1: ( $i * $i * $i ) > $i ).

tff(decl_70,type,
    sumE_sk2: ( $i * $i * $i ) > $i ).

tff(decl_71,type,
    unionE_sk1: ( $i * $i ) > $i ).

tff(decl_72,type,
    subsetD_sk1: ( $i * $i * $i ) > $i ).

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

tff(decl_74,type,
    field: $i > $i ).

tff(decl_75,type,
    subsetI_sk1: ( $i * $i ) > $i ).

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

tff(decl_77,type,
    sigma: ( $i * $i ) > $i ).

tff(decl_78,type,
    sigmaE_sk1x: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    sigmaE_sk1y: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    apply: ( $i * $i ) > $i ).

tff(decl_81,type,
    fst: $i > $i ).

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

tff(decl_83,type,
    converse: $i > $i ).

tff(decl_84,type,
    converseE_sk2: $i > $i ).

tff(decl_85,type,
    converseE_sk1: $i > $i ).

tff(decl_86,type,
    converse_sk1: $i > $i ).

tff(decl_87,type,
    converse_sk2: $i > $i ).

tff(decl_88,type,
    sk2: $i ).

tff(decl_89,type,
    a: $i ).

tff(decl_90,type,
    b: $i ).

cnf(clause112,axiom,
    ( X1 = X2
    | member(X1,X3)
    | ~ member(X1,cons(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).

cnf(clause120,axiom,
    ( member(unionE_sk1(X1,X2),X2)
    | ~ member(X1,union(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).

cnf(clause143,axiom,
    ( member(X3,union(X2))
    | ~ member(X1,X2)
    | ~ member(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause143) ).

cnf(clause119,axiom,
    ( member(X1,unionE_sk1(X1,X2))
    | ~ member(X1,union(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).

cnf(un_eq_Union_2_c1,negated_conjecture,
    member(sk2,union(cons(a,cons(b,eptset)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c1) ).

cnf(clause111,axiom,
    ( X1 = X2
    | ~ member(X1,cons(X2,eptset)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).

cnf(un_eq_Union_2_c2,negated_conjecture,
    ~ member(sk2,un(a,b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c2) ).

cnf(clause20,axiom,
    ( member(X1,un(X2,X3))
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).

cnf(clause19,axiom,
    ( member(X1,un(X3,X2))
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).

cnf(c_0_9,axiom,
    ( X1 = X2
    | member(X1,X3)
    | ~ member(X1,cons(X2,X3)) ),
    clause112 ).

cnf(c_0_10,axiom,
    ( member(unionE_sk1(X1,X2),X2)
    | ~ member(X1,union(X2)) ),
    clause120 ).

cnf(c_0_11,axiom,
    ( member(X3,union(X2))
    | ~ member(X1,X2)
    | ~ member(X3,X1) ),
    clause143 ).

cnf(c_0_12,axiom,
    ( member(X1,unionE_sk1(X1,X2))
    | ~ member(X1,union(X2)) ),
    clause119 ).

cnf(c_0_13,plain,
    ( unionE_sk1(X1,cons(X2,X3)) = X2
    | member(unionE_sk1(X1,cons(X2,X3)),X3)
    | ~ member(X1,union(cons(X2,X3))) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    member(sk2,union(cons(a,cons(b,eptset)))),
    un_eq_Union_2_c1 ).

cnf(c_0_15,axiom,
    ( X1 = X2
    | ~ member(X1,cons(X2,eptset)) ),
    clause111 ).

cnf(c_0_16,plain,
    ( member(X1,union(X2))
    | ~ member(unionE_sk1(X1,X3),X2)
    | ~ member(X1,union(X3)) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,negated_conjecture,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    ~ member(sk2,un(a,b)),
    un_eq_Union_2_c2 ).

cnf(c_0_19,axiom,
    ( member(X1,un(X2,X3))
    | ~ member(X1,X2) ),
    clause20 ).

cnf(c_0_20,plain,
    ( unionE_sk1(X1,cons(X2,eptset)) = X2
    | ~ member(X1,union(cons(X2,eptset))) ),
    inference(spm,[status(thm)],[c_0_15,c_0_10]) ).

cnf(c_0_21,negated_conjecture,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
    | member(sk2,union(cons(b,eptset))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14])]) ).

cnf(c_0_22,negated_conjecture,
    ~ member(sk2,a),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,axiom,
    ( member(X1,un(X3,X2))
    | ~ member(X1,X2) ),
    clause19 ).

cnf(c_0_24,plain,
    ( member(X1,X2)
    | ~ member(X1,union(cons(X2,eptset))) ),
    inference(spm,[status(thm)],[c_0_12,c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    member(sk2,union(cons(b,eptset))),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_21]),c_0_14])]),c_0_22]) ).

cnf(c_0_26,negated_conjecture,
    ~ member(sk2,b),
    inference(spm,[status(thm)],[c_0_18,c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : SET787-2 : TPTP v8.1.2. Released v2.7.0.
% 0.07/0.15  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.36  % Computer : n009.cluster.edu
% 0.11/0.36  % Model    : x86_64 x86_64
% 0.11/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36  % Memory   : 8042.1875MB
% 0.11/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.36  % CPULimit   : 300
% 0.11/0.36  % WCLimit    : 300
% 0.11/0.36  % DateTime   : Sat Aug 26 13:17:05 EDT 2023
% 0.11/0.36  % CPUTime  : 
% 0.16/0.57  start to proof: theBenchmark
% 0.42/0.67  % Version  : CSE_E---1.5
% 0.42/0.67  % Problem  : theBenchmark.p
% 0.42/0.67  % Proof found
% 0.42/0.67  % SZS status Theorem for theBenchmark.p
% 0.42/0.67  % SZS output start Proof
% See solution above
% 0.42/0.67  % Total time : 0.086000 s
% 0.42/0.67  % SZS output end Proof
% 0.42/0.67  % Total time : 0.089000 s
%------------------------------------------------------------------------------