TSTP Solution File: SWC045-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC045-1 : 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 : n022.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 20:19:21 EDT 2023

% Result   : Unsatisfiable 194.40s 196.01s
% Output   : CNFRefutation 194.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :  105
% Syntax   : Number of formulae    :  184 (  35 unt;  73 typ;   0 def)
%            Number of atoms       :  294 (  76 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  371 ( 188   ~; 183   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   83 (  66   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   54 (  54 usr;   7 con; 0-2 aty)
%            Number of variables   :  163 (  28 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 > $i ).

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

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

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

cnf(co1_7,negated_conjecture,
    sk1 = sk3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

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

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

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

cnf(co1_8,negated_conjecture,
    nil != sk1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

cnf(clause157,axiom,
    ( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause157) ).

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

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

cnf(clause145,axiom,
    ( app(X1,X2) = nil
    | nil != X1
    | nil != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause145) ).

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

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

cnf(co1_6,negated_conjecture,
    sk2 = sk4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).

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

cnf(co1_11,negated_conjecture,
    ( segmentP(sk4,app(app(cons(X1,nil),sk5(X1)),cons(X1,nil)))
    | ~ ssItem(X1)
    | ~ memberP(sk3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).

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

cnf(clause127,axiom,
    ( X2 = X1
    | ~ segmentP(X1,X2)
    | ~ segmentP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause127) ).

cnf(clause56,axiom,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).

cnf(clause149,axiom,
    ( app(app(X3,X2),X1) = app(X3,app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).

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

cnf(clause119,axiom,
    ( nil = X2
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).

cnf(co1_10,negated_conjecture,
    ( ssList(sk5(X1))
    | ~ ssItem(X1)
    | ~ memberP(sk3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).

cnf(c_0_32,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_33,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_32]) ).

cnf(c_0_34,axiom,
    ( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    clause169 ).

cnf(c_0_35,axiom,
    ssList(skaf43(X1,X2)),
    clause52 ).

cnf(c_0_36,axiom,
    ssList(skaf42(X1,X2)),
    clause53 ).

cnf(c_0_37,axiom,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    clause138 ).

cnf(c_0_38,axiom,
    ( duplicatefreeP(X1)
    | ssItem(X2)
    | ~ ssList(X1) ),
    clause72 ).

cnf(c_0_39,axiom,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause85 ).

cnf(c_0_40,negated_conjecture,
    ssList(sk1),
    co1_1 ).

cnf(c_0_41,negated_conjecture,
    sk1 = sk3,
    co1_7 ).

cnf(c_0_42,plain,
    ( ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(app(X1,cons(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ duplicatefreeP(app(X1,cons(X2,X3))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]) ).

cnf(c_0_43,axiom,
    ( cons(skaf83(X1),skaf82(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause109 ).

cnf(c_0_44,axiom,
    ssItem(skaf83(X1)),
    clause12 ).

cnf(c_0_45,axiom,
    ssList(skaf82(X1)),
    clause13 ).

cnf(c_0_46,plain,
    ( memberP(cons(X1,X2),X1)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(er,[status(thm)],[c_0_37]) ).

cnf(c_0_47,plain,
    ( ssItem(X1)
    | duplicatefreeP(app(X2,X3))
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_48,negated_conjecture,
    ssList(sk3),
    inference(rw,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_49,plain,
    ( nil = X1
    | ~ memberP(X2,skaf83(X1))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ duplicatefreeP(app(X2,X1)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]),c_0_39]) ).

cnf(c_0_50,plain,
    ( nil = X1
    | memberP(X1,skaf83(X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_44]),c_0_45])]) ).

cnf(c_0_51,negated_conjecture,
    ( ssItem(X1)
    | duplicatefreeP(app(sk3,X2))
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_52,negated_conjecture,
    nil != sk1,
    co1_8 ).

cnf(c_0_53,plain,
    ( nil = X1
    | ~ ssList(X1)
    | ~ duplicatefreeP(app(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_54,negated_conjecture,
    ( ssItem(X1)
    | duplicatefreeP(app(sk3,sk3)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_48]) ).

cnf(c_0_55,negated_conjecture,
    sk3 != nil,
    inference(rw,[status(thm)],[c_0_52,c_0_41]) ).

cnf(c_0_56,axiom,
    ( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause157 ).

cnf(c_0_57,negated_conjecture,
    ssItem(X1),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_48])]),c_0_55]) ).

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

cnf(c_0_59,axiom,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause120 ).

cnf(c_0_60,axiom,
    ( cons(skaf44(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    clause101 ).

cnf(c_0_61,axiom,
    ssItem(skaf44(X1)),
    clause47 ).

cnf(c_0_62,axiom,
    ( singletonP(X2)
    | cons(X1,nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause116 ).

cnf(c_0_63,plain,
    ( app(cons(X1,X2),X3) = cons(X1,app(X2,X3))
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).

cnf(c_0_64,plain,
    ( ssList(cons(X1,X2))
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_57])]) ).

cnf(c_0_65,axiom,
    ( app(X1,X2) = nil
    | nil != X1
    | nil != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause145 ).

cnf(c_0_66,axiom,
    ssList(nil),
    clause8 ).

cnf(c_0_67,plain,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_57])]) ).

cnf(c_0_68,plain,
    ( cons(skaf44(X1),X2) = app(X1,X2)
    | ~ singletonP(X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).

cnf(c_0_69,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(er,[status(thm)],[c_0_62]) ).

cnf(c_0_70,plain,
    ( ssList(cons(X1,app(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_63]),c_0_64]) ).

cnf(c_0_71,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_65])]),c_0_66])]) ).

cnf(c_0_72,axiom,
    ( hd(cons(X1,X2)) = X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause97 ).

cnf(c_0_73,negated_conjecture,
    sk2 = sk4,
    co1_6 ).

cnf(c_0_74,negated_conjecture,
    nil = sk2,
    co1_5 ).

cnf(c_0_75,plain,
    ( cons(skaf44(X1),X2) = app(app(X1,nil),X2)
    | ~ singletonP(X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_66])]) ).

cnf(c_0_76,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssList(cons(X1,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_57])]) ).

cnf(c_0_77,plain,
    ssList(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_66])]) ).

cnf(c_0_78,plain,
    ( skaf44(X1) = hd(X1)
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_60]),c_0_61]),c_0_66])]) ).

cnf(c_0_79,negated_conjecture,
    ( segmentP(sk4,app(app(cons(X1,nil),sk5(X1)),cons(X1,nil)))
    | ~ ssItem(X1)
    | ~ memberP(sk3,X1) ),
    co1_11 ).

cnf(c_0_80,negated_conjecture,
    sk4 = nil,
    inference(rw,[status(thm)],[c_0_73,c_0_74]) ).

cnf(c_0_81,plain,
    ( app(app(X1,nil),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_75]),c_0_66])]) ).

cnf(c_0_82,plain,
    singletonP(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).

cnf(c_0_83,axiom,
    ( cons(X1,X2) != nil
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause98 ).

cnf(c_0_84,plain,
    ( cons(hd(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_60,c_0_78]) ).

cnf(c_0_85,axiom,
    ( X2 = X1
    | ~ segmentP(X1,X2)
    | ~ segmentP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause127 ).

cnf(c_0_86,negated_conjecture,
    ( segmentP(nil,app(app(cons(X1,nil),sk5(X1)),cons(X1,nil)))
    | ~ memberP(sk3,X1)
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_87,axiom,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    clause56 ).

cnf(c_0_88,axiom,
    ( app(app(X3,X2),X1) = app(X3,app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause149 ).

cnf(c_0_89,axiom,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    clause74 ).

cnf(c_0_90,plain,
    app(app(cons(X1,nil),nil),nil) = cons(X1,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_77])]) ).

cnf(c_0_91,plain,
    ( cons(X1,X2) != nil
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_57])]) ).

cnf(c_0_92,plain,
    ( cons(hd(cons(X1,nil)),nil) = cons(X1,nil)
    | ~ ssList(cons(X1,nil)) ),
    inference(spm,[status(thm)],[c_0_84,c_0_76]) ).

cnf(c_0_93,negated_conjecture,
    ( app(app(cons(X1,nil),sk5(X1)),cons(X1,nil)) = nil
    | ~ memberP(sk3,X1)
    | ~ ssItem(X1)
    | ~ ssList(app(app(cons(X1,nil),sk5(X1)),cons(X1,nil))) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_66])]),c_0_87]) ).

cnf(c_0_94,axiom,
    ( nil = X2
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause119 ).

cnf(c_0_95,plain,
    ( app(nil,app(X1,X2)) = app(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_66])]) ).

cnf(c_0_96,plain,
    app(cons(X1,nil),nil) = cons(X1,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_90]),c_0_71]),c_0_77]),c_0_66])]) ).

cnf(c_0_97,plain,
    ( cons(X1,nil) != nil
    | ~ ssList(cons(X1,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_66])]) ).

cnf(c_0_98,negated_conjecture,
    ( app(app(cons(X1,nil),sk5(X1)),cons(X1,nil)) = nil
    | ~ memberP(sk3,X1)
    | ~ ssList(app(app(cons(X1,nil),sk5(X1)),cons(X1,nil))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_57])]) ).

cnf(c_0_99,plain,
    ( nil = X1
    | app(X2,app(X3,X1)) != nil
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_88]),c_0_39]) ).

cnf(c_0_100,plain,
    app(nil,cons(X1,nil)) = cons(X1,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_77]),c_0_66])]) ).

cnf(c_0_101,plain,
    cons(X1,nil) != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_64]),c_0_66])]) ).

cnf(c_0_102,negated_conjecture,
    ( app(app(cons(X1,nil),sk5(X1)),cons(X1,nil)) = nil
    | ~ memberP(sk3,X1)
    | ~ ssList(app(cons(X1,nil),sk5(X1)))
    | ~ ssList(cons(X1,nil)) ),
    inference(spm,[status(thm)],[c_0_98,c_0_39]) ).

cnf(c_0_103,plain,
    ( app(X1,cons(X2,nil)) != nil
    | ~ ssList(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_77]),c_0_66])]),c_0_101]) ).

cnf(c_0_104,negated_conjecture,
    ( ssList(sk5(X1))
    | ~ ssItem(X1)
    | ~ memberP(sk3,X1) ),
    co1_10 ).

cnf(c_0_105,negated_conjecture,
    ( ~ memberP(sk3,X1)
    | ~ ssList(app(cons(X1,nil),sk5(X1))) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_77])]),c_0_103]) ).

cnf(c_0_106,negated_conjecture,
    ( ssList(sk5(X1))
    | ~ memberP(sk3,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_57])]) ).

cnf(c_0_107,plain,
    ( skaf83(X1) = hd(X1)
    | nil = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_43]),c_0_44]),c_0_45])]) ).

cnf(c_0_108,negated_conjecture,
    ~ memberP(sk3,X1),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_39]),c_0_77])]),c_0_106]) ).

cnf(c_0_109,plain,
    ( nil = X1
    | memberP(X1,hd(X1))
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_50,c_0_107]) ).

cnf(c_0_110,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_48])]),c_0_55]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC045-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n022.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 15:16:39 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 194.40/196.01  % Version  : CSE_E---1.5
% 194.40/196.01  % Problem  : theBenchmark.p
% 194.40/196.01  % Proof found
% 194.40/196.01  % SZS status Theorem for theBenchmark.p
% 194.40/196.01  % SZS output start Proof
% See solution above
% 194.45/196.02  % Total time : 193.783000 s
% 194.45/196.02  % SZS output end Proof
% 194.45/196.02  % Total time : 193.797000 s
%------------------------------------------------------------------------------