TSTP Solution File: SWC410-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC410-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : Thu Aug 31 20:22:22 EDT 2023

% Result   : Unsatisfiable 0.56s 1.03s
% Output   : CNFRefutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :  113
% Syntax   : Number of formulae    :  211 (  37 unt;  73 typ;   0 def)
%            Number of atoms       :  413 ( 119 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  537 ( 262   ~; 275   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    6 (   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    :   54 (  54 usr;   8 con; 0-2 aty)
%            Number of variables   :  185 (  20 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 ).

tff(decl_94,type,
    sk5: $i ).

cnf(clause99,axiom,
    ( cons(X1,X2) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).

cnf(clause104,axiom,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).

cnf(clause75,axiom,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).

cnf(clause76,axiom,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).

cnf(co1_12,negated_conjecture,
    ( sk4 = X1
    | ~ neq(sk4,nil)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | tl(sk3) != X2
    | app(X2,X3) != X1
    | ~ ssItem(X4)
    | cons(X4,nil) != X3
    | hd(sk3) != X4
    | ~ neq(nil,sk3)
    | ~ neq(nil,sk3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).

cnf(clause116,axiom,
    ( singletonP(X2)
    | cons(X1,nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).

cnf(clause133,axiom,
    ( nil = X2
    | tl(app(X2,X1)) = app(tl(X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause133) ).

cnf(clause85,axiom,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).

cnf(clause118,axiom,
    ( nil = X1
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).

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

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

cnf(clause96,axiom,
    ( tl(cons(X1,X2)) = X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).

cnf(clause101,axiom,
    ( cons(skaf44(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).

cnf(clause47,axiom,
    ssItem(skaf44(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).

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

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

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

cnf(clause100,axiom,
    ( neq(X2,X1)
    | X2 = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).

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

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

cnf(clause98,axiom,
    ( cons(X1,X2) != nil
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).

cnf(co1_10,negated_conjecture,
    ( nil = sk3
    | nil != sk4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).

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

cnf(clause179,axiom,
    ( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ duplicatefreeP(X5)
    | ~ ssList(X5) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).

cnf(co1_8,negated_conjecture,
    memberP(sk2,sk5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

cnf(clause72,axiom,
    ( duplicatefreeP(X1)
    | ssItem(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).

cnf(clause169,axiom,
    ( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).

cnf(co1_7,negated_conjecture,
    ssItem(sk5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

cnf(clause52,axiom,
    ssList(skaf43(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).

cnf(clause53,axiom,
    ssList(skaf42(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).

cnf(clause97,axiom,
    ( hd(cons(X1,X2)) = X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).

cnf(clause139,axiom,
    ( memberP(cons(X3,X1),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X1)
    | ~ ssItem(X3)
    | ~ ssItem(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause139) ).

cnf(clause170,axiom,
    ( X1 = X3
    | cons(X1,X2) != cons(X3,X4)
    | ~ ssItem(X3)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause170) ).

cnf(clause161,axiom,
    ( memberP(X2,X3)
    | X3 = X1
    | ~ memberP(cons(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssItem(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause161) ).

cnf(clause71,axiom,
    ( ~ memberP(nil,X1)
    | ~ ssItem(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).

cnf(clause158,axiom,
    ( memberP(X2,X3)
    | memberP(X1,X3)
    | ~ memberP(app(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause158) ).

cnf(co1_9,negated_conjecture,
    ~ memberP(sk1,sk5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

cnf(clause138,axiom,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause138) ).

cnf(clause117,axiom,
    ( X1 != X2
    | ~ neq(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause117) ).

cnf(co1_11,negated_conjecture,
    ( neq(sk3,nil)
    | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).

cnf(c_0_40,axiom,
    ( cons(X1,X2) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause99 ).

cnf(c_0_41,axiom,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause104 ).

cnf(c_0_42,axiom,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause75 ).

cnf(c_0_43,axiom,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause76 ).

cnf(c_0_44,negated_conjecture,
    ( sk4 = X1
    | ~ neq(sk4,nil)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | tl(sk3) != X2
    | app(X2,X3) != X1
    | ~ ssItem(X4)
    | cons(X4,nil) != X3
    | hd(sk3) != X4
    | ~ neq(nil,sk3)
    | ~ neq(nil,sk3) ),
    co1_12 ).

cnf(c_0_45,axiom,
    ( singletonP(X2)
    | cons(X1,nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause116 ).

cnf(c_0_46,plain,
    ( nil = X1
    | tl(X1) != X1
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]) ).

cnf(c_0_47,axiom,
    ( nil = X2
    | tl(app(X2,X1)) = app(tl(X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause133 ).

cnf(c_0_48,axiom,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause85 ).

cnf(c_0_49,axiom,
    ( nil = X1
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause118 ).

cnf(c_0_50,negated_conjecture,
    ( sk4 = X1
    | tl(sk3) != X2
    | hd(sk3) != X4
    | app(X2,X3) != X1
    | cons(X4,nil) != X3
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X4)
    | ~ neq(nil,sk3)
    | ~ neq(sk4,nil) ),
    inference(cn,[status(thm)],[c_0_44]) ).

cnf(c_0_51,negated_conjecture,
    ssList(sk1),
    co1_1 ).

cnf(c_0_52,negated_conjecture,
    sk1 = sk3,
    co1_6 ).

cnf(c_0_53,axiom,
    ( tl(cons(X1,X2)) = X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause96 ).

cnf(c_0_54,axiom,
    ( cons(skaf44(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    clause101 ).

cnf(c_0_55,axiom,
    ssItem(skaf44(X1)),
    clause47 ).

cnf(c_0_56,axiom,
    ssList(nil),
    clause8 ).

cnf(c_0_57,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(er,[status(thm)],[c_0_45]) ).

cnf(c_0_58,axiom,
    ( ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause86 ).

cnf(c_0_59,plain,
    ( nil = X1
    | app(tl(X1),X2) != app(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49]) ).

cnf(c_0_60,axiom,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    clause73 ).

cnf(c_0_61,negated_conjecture,
    ( app(tl(sk3),cons(hd(sk3),nil)) = sk4
    | ~ neq(nil,sk3)
    | ~ neq(sk4,nil)
    | ~ ssItem(hd(sk3))
    | ~ ssList(cons(hd(sk3),nil))
    | ~ ssList(tl(sk3)) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_50])])])]),c_0_48]) ).

cnf(c_0_62,axiom,
    ( neq(X2,X1)
    | X2 = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause100 ).

cnf(c_0_63,negated_conjecture,
    ssList(sk3),
    inference(rw,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_64,negated_conjecture,
    ssList(sk2),
    co1_2 ).

cnf(c_0_65,negated_conjecture,
    sk2 = sk4,
    co1_5 ).

cnf(c_0_66,plain,
    ( tl(X1) = nil
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_56])]) ).

cnf(c_0_67,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_56])]) ).

cnf(c_0_68,plain,
    ( nil = X1
    | tl(X1) != app(X1,nil)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_56])]),c_0_42]) ).

cnf(c_0_69,axiom,
    ( cons(X1,X2) != nil
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause98 ).

cnf(c_0_70,negated_conjecture,
    ( app(tl(sk3),cons(hd(sk3),nil)) = sk4
    | sk3 = nil
    | ~ neq(sk4,nil)
    | ~ ssItem(hd(sk3))
    | ~ ssList(cons(hd(sk3),nil))
    | ~ ssList(tl(sk3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_56]),c_0_63])]) ).

cnf(c_0_71,negated_conjecture,
    ssList(sk4),
    inference(rw,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_72,negated_conjecture,
    ( nil = sk3
    | nil != sk4 ),
    co1_10 ).

cnf(c_0_73,plain,
    ( tl(cons(X1,nil)) = nil
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_74,plain,
    ( app(cons(X1,X2),nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_53]),c_0_58]),c_0_69]) ).

cnf(c_0_75,axiom,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause120 ).

cnf(c_0_76,negated_conjecture,
    ( app(tl(sk3),cons(hd(sk3),nil)) = sk4
    | sk3 = nil
    | ~ ssItem(hd(sk3))
    | ~ ssList(cons(hd(sk3),nil))
    | ~ ssList(tl(sk3)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_62]),c_0_71]),c_0_56])]),c_0_72]) ).

cnf(c_0_77,axiom,
    ( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ duplicatefreeP(X5)
    | ~ ssList(X5) ),
    clause179 ).

cnf(c_0_78,negated_conjecture,
    memberP(sk2,sk5),
    co1_8 ).

cnf(c_0_79,plain,
    ( tl(cons(X1,nil)) = nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_58]),c_0_56])]) ).

cnf(c_0_80,plain,
    ( cons(X1,nil) != nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_56])]) ).

cnf(c_0_81,negated_conjecture,
    ( app(tl(sk3),cons(hd(sk3),nil)) = sk4
    | sk3 = nil
    | ~ ssList(cons(hd(sk3),nil))
    | ~ ssList(tl(sk3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_43]),c_0_63])]) ).

cnf(c_0_82,plain,
    ( ~ ssItem(X1)
    | ~ ssList(app(app(X2,cons(X1,X3)),cons(X1,X4)))
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ duplicatefreeP(app(app(X2,cons(X1,X3)),cons(X1,X4))) ),
    inference(er,[status(thm)],[c_0_77]) ).

cnf(c_0_83,axiom,
    ( duplicatefreeP(X1)
    | ssItem(X2)
    | ~ ssList(X1) ),
    clause72 ).

cnf(c_0_84,axiom,
    ( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    clause169 ).

cnf(c_0_85,negated_conjecture,
    memberP(sk4,sk5),
    inference(rw,[status(thm)],[c_0_78,c_0_65]) ).

cnf(c_0_86,negated_conjecture,
    ssItem(sk5),
    co1_7 ).

cnf(c_0_87,plain,
    ( cons(hd(cons(X1,nil)),nil) = cons(X1,nil)
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_79]),c_0_80]) ).

cnf(c_0_88,negated_conjecture,
    ( app(tl(sk3),cons(hd(sk3),nil)) = sk4
    | sk3 = nil
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_42]),c_0_63])]) ).

cnf(c_0_89,plain,
    ( ssItem(X1)
    | ~ ssItem(X2)
    | ~ ssList(app(app(X3,cons(X2,X4)),cons(X2,X5)))
    | ~ ssList(X5)
    | ~ ssList(X4)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

cnf(c_0_90,negated_conjecture,
    app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]),c_0_71])]) ).

cnf(c_0_91,axiom,
    ssList(skaf43(X1,X2)),
    clause52 ).

cnf(c_0_92,axiom,
    ssList(skaf42(X1,X2)),
    clause53 ).

cnf(c_0_93,plain,
    ( cons(hd(cons(X1,nil)),nil) = cons(X1,nil)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_58]),c_0_56])]) ).

cnf(c_0_94,negated_conjecture,
    ( app(tl(sk3),cons(hd(sk3),nil)) = sk4
    | sk3 = nil
    | ~ ssItem(hd(sk3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_58]),c_0_56])]) ).

cnf(c_0_95,negated_conjecture,
    ( ssItem(X1)
    | ~ ssList(app(sk4,cons(sk5,X2)))
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_86]),c_0_91]),c_0_92])]) ).

cnf(c_0_96,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(hd(cons(X1,nil)))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_93]),c_0_56])]) ).

cnf(c_0_97,axiom,
    ( hd(cons(X1,X2)) = X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause97 ).

cnf(c_0_98,plain,
    ( cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2)
    | nil = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_47]),c_0_48]),c_0_49]) ).

cnf(c_0_99,negated_conjecture,
    ( app(tl(sk3),cons(hd(sk3),nil)) = sk4
    | sk3 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_43]),c_0_63])]) ).

cnf(c_0_100,axiom,
    ( memberP(cons(X3,X1),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X1)
    | ~ ssItem(X3)
    | ~ ssItem(X2) ),
    clause139 ).

cnf(c_0_101,negated_conjecture,
    ( ssItem(X1)
    | ~ ssList(cons(sk5,X2))
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_48]),c_0_71])]) ).

cnf(c_0_102,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_56])]) ).

cnf(c_0_103,negated_conjecture,
    ( cons(hd(app(sk3,cons(hd(sk3),nil))),sk4) = app(sk3,cons(hd(sk3),nil))
    | sk3 = nil
    | ~ ssList(cons(hd(sk3),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_63])]) ).

cnf(c_0_104,negated_conjecture,
    ( memberP(cons(X1,sk4),sk5)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_85]),c_0_86]),c_0_71])]) ).

cnf(c_0_105,negated_conjecture,
    ssItem(X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_56]),c_0_86])]) ).

cnf(c_0_106,negated_conjecture,
    ( cons(hd(app(sk3,cons(hd(sk3),nil))),sk4) = app(sk3,cons(hd(sk3),nil))
    | sk3 = nil
    | ~ ssItem(hd(sk3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_58]),c_0_56])]) ).

cnf(c_0_107,axiom,
    ( X1 = X3
    | cons(X1,X2) != cons(X3,X4)
    | ~ ssItem(X3)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X2) ),
    clause170 ).

cnf(c_0_108,axiom,
    ( memberP(X2,X3)
    | X3 = X1
    | ~ memberP(cons(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssItem(X3) ),
    clause161 ).

cnf(c_0_109,axiom,
    ( ~ memberP(nil,X1)
    | ~ ssItem(X1) ),
    clause71 ).

cnf(c_0_110,axiom,
    ( memberP(X2,X3)
    | memberP(X1,X3)
    | ~ memberP(app(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X3) ),
    clause158 ).

cnf(c_0_111,negated_conjecture,
    memberP(cons(X1,sk4),sk5),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105])]) ).

cnf(c_0_112,negated_conjecture,
    ( cons(hd(app(sk3,cons(hd(sk3),nil))),sk4) = app(sk3,cons(hd(sk3),nil))
    | sk3 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_43]),c_0_63])]) ).

cnf(c_0_113,negated_conjecture,
    ~ memberP(sk1,sk5),
    co1_9 ).

cnf(c_0_114,plain,
    ( skaf44(cons(X1,X2)) = X1
    | ~ singletonP(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_54]),c_0_55]),c_0_56])])]),c_0_58]) ).

cnf(c_0_115,axiom,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    clause138 ).

cnf(c_0_116,plain,
    ( skaf44(X1) = X2
    | ~ memberP(X1,X2)
    | ~ singletonP(X1)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_54]),c_0_55]),c_0_56])]),c_0_109]) ).

cnf(c_0_117,plain,
    ( memberP(X1,X2)
    | memberP(X3,X2)
    | ~ memberP(app(X1,X3),X2)
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_105])]) ).

cnf(c_0_118,negated_conjecture,
    ( sk3 = nil
    | memberP(app(sk3,cons(hd(sk3),nil)),sk5) ),
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_119,plain,
    ssList(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_105])]) ).

cnf(c_0_120,negated_conjecture,
    ~ memberP(sk3,sk5),
    inference(rw,[status(thm)],[c_0_113,c_0_52]) ).

cnf(c_0_121,plain,
    ( skaf44(cons(X1,nil)) = X1
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_67]),c_0_56])]) ).

cnf(c_0_122,plain,
    ( memberP(cons(X1,X2),X1)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(er,[status(thm)],[c_0_115]) ).

cnf(c_0_123,plain,
    ( skaf44(X1) = X2
    | ~ memberP(X1,X2)
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_105])]) ).

cnf(c_0_124,negated_conjecture,
    ( sk3 = nil
    | memberP(cons(hd(sk3),nil),sk5) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]),c_0_63])]),c_0_120]) ).

cnf(c_0_125,plain,
    skaf44(cons(X1,nil)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_105])]) ).

cnf(c_0_126,plain,
    singletonP(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_105])]) ).

cnf(c_0_127,axiom,
    ( X1 != X2
    | ~ neq(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    clause117 ).

cnf(c_0_128,negated_conjecture,
    ( neq(sk3,nil)
    | ~ neq(sk4,nil) ),
    co1_11 ).

cnf(c_0_129,plain,
    ( nil = X1
    | memberP(X1,hd(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_41]),c_0_42]),c_0_43]) ).

cnf(c_0_130,negated_conjecture,
    ( hd(sk3) = sk5
    | sk3 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]),c_0_126]),c_0_119])]) ).

cnf(c_0_131,plain,
    ( ~ neq(X1,X1)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_127]) ).

cnf(c_0_132,negated_conjecture,
    ( sk4 = nil
    | neq(sk3,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_62]),c_0_71]),c_0_56])]) ).

cnf(c_0_133,negated_conjecture,
    sk3 = nil,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_63])]),c_0_120]) ).

cnf(c_0_134,plain,
    ~ neq(X1,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_105])]) ).

cnf(c_0_135,negated_conjecture,
    sk4 = nil,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133]),c_0_134]) ).

cnf(c_0_136,plain,
    ~ memberP(nil,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_105])]) ).

cnf(c_0_137,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_135]),c_0_136]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SWC410-1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n021.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   : Mon Aug 28 14:36:28 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.59  start to proof: theBenchmark
% 0.56/1.03  % Version  : CSE_E---1.5
% 0.56/1.03  % Problem  : theBenchmark.p
% 0.56/1.03  % Proof found
% 0.56/1.03  % SZS status Theorem for theBenchmark.p
% 0.56/1.03  % SZS output start Proof
% See solution above
% 0.56/1.04  % Total time : 0.426000 s
% 0.56/1.04  % SZS output end Proof
% 0.56/1.04  % Total time : 0.432000 s
%------------------------------------------------------------------------------