TSTP Solution File: SWC420-1 by CSE

TSTP Solution File: SWC420-1 by CSE_E---1.5

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC420-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n017.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 20:22:27 EDT 2023

% Result   : Unsatisfiable 0.20s 0.71s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   88
% Syntax   : Number of formulae    :  119 (  22 unt;  72 typ;   0 def)
%            Number of atoms       :  102 (  40 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  114 (  59   ~;  55   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   82 (  65   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   53 (  53 usr;   7 con; 0-2 aty)
%            Number of variables   :   40 (   4 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    nil: $i ).

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

tff(decl_24,type,
    duplicatefreeP: $i > $o ).

tff(decl_25,type,
    strictorderedP: $i > $o ).

tff(decl_26,type,
    totalorderedP: $i > $o ).

tff(decl_27,type,
    strictorderP: $i > $o ).

tff(decl_28,type,
    totalorderP: $i > $o ).

tff(decl_29,type,
    cyclefreeP: $i > $o ).

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

tff(decl_31,type,
    skac3: $i ).

tff(decl_32,type,
    ssItem: $i > $o ).

tff(decl_33,type,
    skac2: $i ).

tff(decl_34,type,
    singletonP: $i > $o ).

tff(decl_35,type,
    skaf83: $i > $i ).

tff(decl_36,type,
    skaf82: $i > $i ).

tff(decl_37,type,
    skaf81: $i > $i ).

tff(decl_38,type,
    skaf80: $i > $i ).

tff(decl_39,type,
    skaf79: $i > $i ).

tff(decl_40,type,
    skaf78: $i > $i ).

tff(decl_41,type,
    skaf77: $i > $i ).

tff(decl_42,type,
    skaf76: $i > $i ).

tff(decl_43,type,
    skaf75: $i > $i ).

tff(decl_44,type,
    skaf74: $i > $i ).

tff(decl_45,type,
    skaf73: $i > $i ).

tff(decl_46,type,
    skaf72: $i > $i ).

tff(decl_47,type,
    skaf71: $i > $i ).

tff(decl_48,type,
    skaf70: $i > $i ).

tff(decl_49,type,
    skaf69: $i > $i ).

tff(decl_50,type,
    skaf68: $i > $i ).

tff(decl_51,type,
    skaf67: $i > $i ).

tff(decl_52,type,
    skaf66: $i > $i ).

tff(decl_53,type,
    skaf65: $i > $i ).

tff(decl_54,type,
    skaf64: $i > $i ).

tff(decl_55,type,
    skaf63: $i > $i ).

tff(decl_56,type,
    skaf62: $i > $i ).

tff(decl_57,type,
    skaf61: $i > $i ).

tff(decl_58,type,
    skaf60: $i > $i ).

tff(decl_59,type,
    skaf59: $i > $i ).

tff(decl_60,type,
    skaf58: $i > $i ).

tff(decl_61,type,
    skaf57: $i > $i ).

tff(decl_62,type,
    skaf56: $i > $i ).

tff(decl_63,type,
    skaf55: $i > $i ).

tff(decl_64,type,
    skaf54: $i > $i ).

tff(decl_65,type,
    skaf53: $i > $i ).

tff(decl_66,type,
    skaf52: $i > $i ).

tff(decl_67,type,
    skaf51: $i > $i ).

tff(decl_68,type,
    skaf50: $i > $i ).

tff(decl_69,type,
    skaf49: $i > $i ).

tff(decl_70,type,
    skaf44: $i > $i ).

tff(decl_71,type,
    skaf48: ( $i * $i ) > $i ).

tff(decl_72,type,
    skaf47: ( $i * $i ) > $i ).

tff(decl_73,type,
    skaf46: ( $i * $i ) > $i ).

tff(decl_74,type,
    skaf45: ( $i * $i ) > $i ).

tff(decl_75,type,
    skaf43: ( $i * $i ) > $i ).

tff(decl_76,type,
    skaf42: ( $i * $i ) > $i ).

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

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

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

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

tff(decl_81,type,
    leq: ( $i * $i ) > $o ).

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

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

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

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

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

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

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

tff(decl_89,type,
    gt: ( $i * $i ) > $o ).

tff(decl_90,type,
    sk1: $i ).

tff(decl_91,type,
    sk2: $i ).

tff(decl_92,type,
    sk3: $i ).

tff(decl_93,type,
    sk4: $i ).

cnf(co1_8,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X2,cons(X1,nil)),X3) != sk2
    | app(app(X3,cons(X1,nil)),X2) != sk1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).

cnf(co1_6,negated_conjecture,
    sk1 = sk3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).

cnf(co1_5,negated_conjecture,
    sk2 = sk4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).

cnf(co1_9,negated_conjecture,
    ( app(X2,cons(X1,nil)) = sk3
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(cons(X1,nil),X2) != sk4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).

cnf(clause120,axiom,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).

cnf(co1_2,negated_conjecture,
    ssList(sk2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).

cnf(clause73,axiom,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).

cnf(clause8,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).

cnf(clause109,axiom,
    ( cons(skaf83(X1),skaf82(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).

cnf(clause12,axiom,
    ssItem(skaf83(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).

cnf(clause13,axiom,
    ssList(skaf82(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).

cnf(co1_1,negated_conjecture,
    ssList(sk1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).

cnf(clause74,axiom,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).

cnf(co1_7,negated_conjecture,
    neq(sk2,nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).

cnf(clause86,axiom,
    ( ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).

cnf(clause115,axiom,
    ( X1 != X2
    | ~ neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause115) ).

cnf(c_0_16,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X2,cons(X1,nil)),X3) != sk2
    | app(app(X3,cons(X1,nil)),X2) != sk1 ),
    co1_8 ).

cnf(c_0_17,negated_conjecture,
    sk1 = sk3,
    co1_6 ).

cnf(c_0_18,negated_conjecture,
    sk2 = sk4,
    co1_5 ).

cnf(c_0_19,negated_conjecture,
    ( app(X2,cons(X1,nil)) = sk3
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(cons(X1,nil),X2) != sk4 ),
    co1_9 ).

cnf(c_0_20,axiom,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause120 ).

cnf(c_0_21,negated_conjecture,
    ssList(sk2),
    co1_2 ).

cnf(c_0_22,negated_conjecture,
    ( app(app(X1,cons(X2,nil)),X3) != sk3
    | app(app(X3,cons(X2,nil)),X1) != sk4
    | ~ ssItem(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

cnf(c_0_23,axiom,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    clause73 ).

cnf(c_0_24,axiom,
    ssList(nil),
    clause8 ).

cnf(c_0_25,negated_conjecture,
    ( app(X1,cons(X2,nil)) = sk3
    | cons(X2,X1) != sk4
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,axiom,
    ( cons(skaf83(X1),skaf82(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause109 ).

cnf(c_0_27,axiom,
    ssItem(skaf83(X1)),
    clause12 ).

cnf(c_0_28,axiom,
    ssList(skaf82(X1)),
    clause13 ).

cnf(c_0_29,negated_conjecture,
    ssList(sk4),
    inference(rw,[status(thm)],[c_0_21,c_0_18]) ).

cnf(c_0_30,negated_conjecture,
    ssList(sk1),
    co1_1 ).

cnf(c_0_31,negated_conjecture,
    ( app(app(nil,cons(X1,nil)),X2) != sk4
    | app(X2,cons(X1,nil)) != sk3
    | ~ ssItem(X1)
    | ~ ssList(app(X2,cons(X1,nil)))
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_32,negated_conjecture,
    ( app(skaf82(sk4),cons(skaf83(sk4),nil)) = sk3
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])])]),c_0_29])]) ).

cnf(c_0_33,negated_conjecture,
    ssList(sk3),
    inference(rw,[status(thm)],[c_0_30,c_0_17]) ).

cnf(c_0_34,negated_conjecture,
    ( sk4 = nil
    | app(app(nil,cons(skaf83(sk4),nil)),skaf82(sk4)) != sk4 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_27]),c_0_33]),c_0_28])]) ).

cnf(c_0_35,axiom,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    clause74 ).

cnf(c_0_36,negated_conjecture,
    ( sk4 = nil
    | app(cons(skaf83(sk4),nil),skaf82(sk4)) != sk4
    | ~ ssList(cons(skaf83(sk4),nil)) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_37,negated_conjecture,
    ( sk4 = nil
    | cons(skaf83(sk4),skaf82(sk4)) != sk4
    | ~ ssList(cons(skaf83(sk4),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_20]),c_0_27]),c_0_28])]) ).

cnf(c_0_38,negated_conjecture,
    neq(sk2,nil),
    co1_7 ).

cnf(c_0_39,negated_conjecture,
    ( sk4 = nil
    | ~ ssList(cons(skaf83(sk4),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_26]),c_0_29])]) ).

cnf(c_0_40,axiom,
    ( ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause86 ).

cnf(c_0_41,axiom,
    ( X1 != X2
    | ~ neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause115 ).

cnf(c_0_42,negated_conjecture,
    neq(sk4,nil),
    inference(rw,[status(thm)],[c_0_38,c_0_18]) ).

cnf(c_0_43,negated_conjecture,
    sk4 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_27]),c_0_24])]) ).

cnf(c_0_44,plain,
    ( ~ neq(X1,X1)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[c_0_41]) ).

cnf(c_0_45,negated_conjecture,
    neq(nil,nil),
    inference(rw,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_46,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_24])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC420-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 17:39:28 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.71  % Version  : CSE_E---1.5
% 0.20/0.71  % Problem  : theBenchmark.p
% 0.20/0.71  % Proof found
% 0.20/0.71  % SZS status Theorem for theBenchmark.p
% 0.20/0.71  % SZS output start Proof
% See solution above
% 0.20/0.72  % Total time : 0.134000 s
% 0.20/0.72  % SZS output end Proof
% 0.20/0.72  % Total time : 0.140000 s
%------------------------------------------------------------------------------