TSTP Solution File: COL100-2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : COL100-2 : 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 : n021.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 : Wed Aug 30 18:22:38 EDT 2023

% Result   : Unsatisfiable 1.14s 1.22s
% Output   : CNFRefutation 1.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   91
% Syntax   : Number of formulae    :  110 (  11 unt;  80 typ;   0 def)
%            Number of atoms       :   63 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   71 (  38   ~;  33   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  147 (  71   >;  76   *;   0   +;   0  <<)
%            Number of predicates  :   11 (  10 usr;   1 prp; 0-8 aty)
%            Number of functors    :   70 (  70 usr;   9 con; 0-4 aty)
%            Number of variables   :   47 (   2 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,
    cons_subsetI_sk1: ( $i * $i * $i ) > $i ).

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

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

tff(decl_32,type,
    converse: $i > $i ).

tff(decl_33,type,
    eptset: $i ).

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

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

tff(decl_36,type,
    un: ( $i * $i ) > $i ).

tff(decl_37,type,
    powI_sk1: ( $i * $i ) > $i ).

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

tff(decl_39,type,
    interI_sk1: ( $i * $i ) > $i ).

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

tff(decl_41,type,
    card_Union_sk1: $i > $i ).

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

tff(decl_43,type,
    card: $i > $o ).

tff(decl_44,type,
    fin: $i > $i ).

tff(decl_45,type,
    order_Inter_sk1: $i > $i ).

tff(decl_46,type,
    ord: $i > $o ).

tff(decl_47,type,
    order_Union_sk1: $i > $i ).

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

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

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

tff(decl_51,type,
    qInr: $i > $i ).

tff(decl_52,type,
    qInl: $i > $i ).

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

tff(decl_54,type,
    qsumE_sk1: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    qsumE_sk2: ( $i * $i * $i ) > $i ).

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

tff(decl_57,type,
    qconverseE_sk2: ( $i * $i ) > $i ).

tff(decl_58,type,
    qconverseE_sk1: ( $i * $i ) > $i ).

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

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

tff(decl_61,type,
    rmultE_c1: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).

tff(decl_62,type,
    rmultE_c2: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).

tff(decl_63,type,
    radd: ( $i * $i * $i * $i ) > $i ).

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

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

tff(decl_66,type,
    memrel: $i > $i ).

tff(decl_67,type,
    compE_sk1: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    compE_sk3: ( $i * $i * $i ) > $i ).

tff(decl_69,type,
    compE_sk2: ( $i * $i * $i ) > $i ).

tff(decl_70,type,
    id: $i > $i ).

tff(decl_71,type,
    idE_sk1: ( $i * $i ) > $i ).

tff(decl_72,type,
    sumE_sk1: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    sumE_sk2: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    vimageE_sk1: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    imageE_sk1: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    field: $i > $i ).

tff(decl_77,type,
    fieldE_sk1: ( $i * $i ) > $i ).

tff(decl_78,type,
    fieldE_sk2: ( $i * $i ) > $i ).

tff(decl_79,type,
    range: $i > $i ).

tff(decl_80,type,
    rangeE_sk1: ( $i * $i ) > $i ).

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

tff(decl_82,type,
    domainE_sk1: ( $i * $i ) > $i ).

tff(decl_83,type,
    cons_subsetE_sk1: ( $i * $i * $i ) > $i ).

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

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

tff(decl_86,type,
    unionE_sk1: ( $i * $i ) > $i ).

tff(decl_87,type,
    subsetD_sk1: ( $i * $i * $i ) > $i ).

tff(decl_88,type,
    subsetI_sk1: ( $i * $i ) > $i ).

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

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

tff(decl_91,type,
    comb_app: ( $i * $i ) > $i ).

tff(decl_92,type,
    trancl: $i > $i ).

tff(decl_93,type,
    trans: $i > $o ).

tff(decl_94,type,
    diamond: $i > $o ).

tff(decl_95,type,
    diamond_strip_lemmaD_sk1: ( $i * $i * $i * $i ) > $i ).

tff(decl_96,type,
    r: $i ).

tff(decl_97,type,
    y: $i ).

tff(decl_98,type,
    ya: $i ).

tff(decl_99,type,
    z: $i ).

tff(decl_100,type,
    sk1: $i > $i ).

tff(decl_101,type,
    yp: $i ).

cnf(transD,axiom,
    ( member(pair(X2,X4),X1)
    | ~ trans(X1)
    | ~ member(pair(X2,X3),X1)
    | ~ member(pair(X3,X4),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transD) ).

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

cnf(trans_trancl,axiom,
    trans(trancl(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_trancl) ).

cnf(diamond_trancl_2h5,hypothesis,
    ( member(pair(X1,sk1(X1)),trancl(r))
    | ~ member(pair(y,X1),trancl(r)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2h5) ).

cnf(diamond_trancl_2c1,negated_conjecture,
    member(pair(y,yp),trancl(r)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2c1) ).

cnf(diamond_trancl_2c2,negated_conjecture,
    ( ~ member(pair(z,X1),trancl(r))
    | ~ member(pair(yp,X1),trancl(r)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2c2) ).

cnf(diamond_strip_lemmaD1,axiom,
    ( member(pair(X4,diamond_strip_lemmaD_sk1(X2,X3,X4,X1)),trancl(X1))
    | ~ diamond(X1)
    | ~ member(pair(X2,X3),trancl(X1))
    | ~ member(pair(X2,X4),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD1) ).

cnf(diamond_trancl_2h1,hypothesis,
    diamond(r),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2h1) ).

cnf(diamond_strip_lemmaD2,axiom,
    ( member(pair(X3,diamond_strip_lemmaD_sk1(X2,X3,X4,X1)),X1)
    | ~ diamond(X1)
    | ~ member(pair(X2,X3),trancl(X1))
    | ~ member(pair(X2,X4),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD2) ).

cnf(diamond_trancl_2h4,hypothesis,
    ( member(pair(ya,sk1(X1)),trancl(r))
    | ~ member(pair(y,X1),trancl(r)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2h4) ).

cnf(diamond_trancl_2h3,hypothesis,
    member(pair(ya,z),r),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2h3) ).

cnf(c_0_11,axiom,
    ( member(pair(X2,X4),X1)
    | ~ trans(X1)
    | ~ member(pair(X2,X3),X1)
    | ~ member(pair(X3,X4),X1) ),
    transD ).

cnf(c_0_12,axiom,
    ( member(pair(X1,X2),trancl(X3))
    | ~ member(pair(X1,X2),X3) ),
    r_into_trancl ).

cnf(c_0_13,axiom,
    trans(trancl(X1)),
    trans_trancl ).

cnf(c_0_14,hypothesis,
    ( member(pair(X1,sk1(X1)),trancl(r))
    | ~ member(pair(y,X1),trancl(r)) ),
    diamond_trancl_2h5 ).

cnf(c_0_15,negated_conjecture,
    member(pair(y,yp),trancl(r)),
    diamond_trancl_2c1 ).

cnf(c_0_16,plain,
    ( member(pair(X1,X2),trancl(X3))
    | ~ member(pair(X1,X4),trancl(X3))
    | ~ member(pair(X4,X2),X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).

cnf(c_0_17,negated_conjecture,
    member(pair(yp,sk1(yp)),trancl(r)),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    ( ~ member(pair(z,X1),trancl(r))
    | ~ member(pair(yp,X1),trancl(r)) ),
    diamond_trancl_2c2 ).

cnf(c_0_19,negated_conjecture,
    ( member(pair(yp,X1),trancl(r))
    | ~ member(pair(sk1(yp),X1),r) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    ( ~ member(pair(z,X1),trancl(r))
    | ~ member(pair(sk1(yp),X1),r) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,axiom,
    ( member(pair(X4,diamond_strip_lemmaD_sk1(X2,X3,X4,X1)),trancl(X1))
    | ~ diamond(X1)
    | ~ member(pair(X2,X3),trancl(X1))
    | ~ member(pair(X2,X4),X1) ),
    diamond_strip_lemmaD1 ).

cnf(c_0_22,hypothesis,
    diamond(r),
    diamond_trancl_2h1 ).

cnf(c_0_23,negated_conjecture,
    ( ~ member(pair(sk1(yp),diamond_strip_lemmaD_sk1(X1,X2,z,r)),r)
    | ~ member(pair(X1,X2),trancl(r))
    | ~ member(pair(X1,z),r) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).

cnf(c_0_24,axiom,
    ( member(pair(X3,diamond_strip_lemmaD_sk1(X2,X3,X4,X1)),X1)
    | ~ diamond(X1)
    | ~ member(pair(X2,X3),trancl(X1))
    | ~ member(pair(X2,X4),X1) ),
    diamond_strip_lemmaD2 ).

cnf(c_0_25,hypothesis,
    ( member(pair(ya,sk1(X1)),trancl(r))
    | ~ member(pair(y,X1),trancl(r)) ),
    diamond_trancl_2h4 ).

cnf(c_0_26,negated_conjecture,
    ( ~ member(pair(X1,sk1(yp)),trancl(r))
    | ~ member(pair(X1,z),r) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_22])]) ).

cnf(c_0_27,negated_conjecture,
    member(pair(ya,sk1(yp)),trancl(r)),
    inference(spm,[status(thm)],[c_0_25,c_0_15]) ).

cnf(c_0_28,hypothesis,
    member(pair(ya,z),r),
    diamond_trancl_2h3 ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : COL100-2 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.16/0.33  % Computer : n021.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit   : 300
% 0.16/0.33  % WCLimit    : 300
% 0.16/0.33  % DateTime   : Sun Aug 27 04:12:12 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 1.14/1.22  % Version  : CSE_E---1.5
% 1.14/1.22  % Problem  : theBenchmark.p
% 1.14/1.22  % Proof found
% 1.14/1.22  % SZS status Theorem for theBenchmark.p
% 1.14/1.22  % SZS output start Proof
% See solution above
% 1.14/1.22  % Total time : 0.650000 s
% 1.14/1.22  % SZS output end Proof
% 1.14/1.22  % Total time : 0.655000 s
%------------------------------------------------------------------------------