TSTP Solution File: SWC418-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC418-1 : 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 : n004.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 20:22:26 EDT 2023

% Result   : Unsatisfiable 0.19s 0.68s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   97
% Syntax   : Number of formulae    :  162 (  23 unt;  72 typ;   0 def)
%            Number of atoms       :  281 (  86 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  379 ( 188   ~; 191   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 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   :  131 (  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 ).

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

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

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(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(co1_10,negated_conjecture,
    ( sk3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | tl(sk4) != X2
    | app(X2,X3) != X1
    | ~ ssItem(X4)
    | cons(X4,nil) != X3
    | hd(sk4) != X4
    | ~ neq(nil,sk4)
    | ~ neq(nil,sk4)
    | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).

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

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

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

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

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

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

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

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

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

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

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/sandbox/benchmark/theBenchmark.p',co1_8) ).

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

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

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

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

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

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

cnf(c_0_25,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_26,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_25]) ).

cnf(c_0_27,axiom,
    ( duplicatefreeP(X1)
    | ssItem(X2)
    | ~ ssList(X1) ),
    clause72 ).

cnf(c_0_28,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_26,c_0_27]) ).

cnf(c_0_29,axiom,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    clause74 ).

cnf(c_0_30,axiom,
    ssList(nil),
    clause8 ).

cnf(c_0_31,axiom,
    ( ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause86 ).

cnf(c_0_32,plain,
    ( ssItem(X1)
    | ~ ssItem(X2)
    | ~ ssList(app(cons(X2,X3),cons(X2,X4)))
    | ~ ssList(X4)
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),c_0_31]) ).

cnf(c_0_33,axiom,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause120 ).

cnf(c_0_34,negated_conjecture,
    ( sk3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | tl(sk4) != X2
    | app(X2,X3) != X1
    | ~ ssItem(X4)
    | cons(X4,nil) != X3
    | hd(sk4) != X4
    | ~ neq(nil,sk4)
    | ~ neq(nil,sk4)
    | ~ neq(sk4,nil) ),
    co1_10 ).

cnf(c_0_35,negated_conjecture,
    neq(sk2,nil),
    co1_7 ).

cnf(c_0_36,negated_conjecture,
    sk2 = sk4,
    co1_5 ).

cnf(c_0_37,plain,
    ( ssItem(X1)
    | ~ ssItem(X2)
    | ~ ssList(cons(X2,cons(X2,X3)))
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_30])]),c_0_31]) ).

cnf(c_0_38,negated_conjecture,
    ( sk3 = X1
    | tl(sk4) != X2
    | hd(sk4) != X4
    | app(X2,X3) != X1
    | cons(X4,nil) != X3
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X4)
    | ~ neq(nil,sk4)
    | ~ neq(sk4,nil) ),
    inference(cn,[status(thm)],[c_0_34]) ).

cnf(c_0_39,negated_conjecture,
    neq(sk4,nil),
    inference(rw,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_40,axiom,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause85 ).

cnf(c_0_41,negated_conjecture,
    ssList(sk2),
    co1_2 ).

cnf(c_0_42,plain,
    ( ssItem(X1)
    | ~ ssItem(X2)
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_31]),c_0_31]) ).

cnf(c_0_43,axiom,
    ssList(skaf42(X1,X2)),
    clause53 ).

cnf(c_0_44,negated_conjecture,
    ( app(tl(sk4),cons(hd(sk4),nil)) = sk3
    | ~ neq(nil,sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(tl(sk4)) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])])])])])]),c_0_40]) ).

cnf(c_0_45,axiom,
    ( neq(X2,X1)
    | X2 = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause100 ).

cnf(c_0_46,negated_conjecture,
    ssList(sk4),
    inference(rw,[status(thm)],[c_0_41,c_0_36]) ).

cnf(c_0_47,plain,
    ( ssItem(X1)
    | ~ ssItem(X2) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_48,axiom,
    ssItem(skaf44(X1)),
    clause47 ).

cnf(c_0_49,negated_conjecture,
    ( app(tl(sk4),cons(hd(sk4),nil)) = sk3
    | sk4 = nil
    | ~ ssItem(hd(sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(tl(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_30]),c_0_46])]) ).

cnf(c_0_50,axiom,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause76 ).

cnf(c_0_51,axiom,
    ( hd(cons(X1,X2)) = X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause97 ).

cnf(c_0_52,plain,
    ssItem(X1),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_53,axiom,
    ( singletonP(X2)
    | cons(X1,nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause116 ).

cnf(c_0_54,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_55,negated_conjecture,
    sk1 = sk3,
    co1_6 ).

cnf(c_0_56,negated_conjecture,
    ( app(tl(sk4),cons(hd(sk4),nil)) = sk3
    | sk4 = nil
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(tl(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_46])]) ).

cnf(c_0_57,axiom,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause75 ).

cnf(c_0_58,plain,
    ( hd(cons(X1,X2)) = X1
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).

cnf(c_0_59,axiom,
    ( cons(skaf44(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    clause101 ).

cnf(c_0_60,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(er,[status(thm)],[c_0_53]) ).

cnf(c_0_61,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_54,c_0_55]),c_0_36]) ).

cnf(c_0_62,negated_conjecture,
    ( app(tl(sk4),cons(hd(sk4),nil)) = sk3
    | sk4 = nil
    | ~ ssList(cons(hd(sk4),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_46])]) ).

cnf(c_0_63,plain,
    ( skaf44(X1) = hd(X1)
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_30])]) ).

cnf(c_0_64,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_31]),c_0_30])]) ).

cnf(c_0_65,negated_conjecture,
    ( app(app(X1,X2),X3) != sk3
    | app(app(X3,X2),X1) != sk4
    | ~ singletonP(X2)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_59]),c_0_48])]) ).

cnf(c_0_66,axiom,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    clause73 ).

cnf(c_0_67,negated_conjecture,
    ( app(tl(sk4),cons(hd(sk4),nil)) = sk3
    | sk4 = nil
    | ~ ssItem(hd(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_31]),c_0_30])]) ).

cnf(c_0_68,plain,
    ( cons(hd(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_59,c_0_63]) ).

cnf(c_0_69,plain,
    singletonP(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_52])]) ).

cnf(c_0_70,negated_conjecture,
    ( app(app(nil,X1),X2) != sk4
    | app(X2,X1) != sk3
    | ~ singletonP(X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_30])]),c_0_40]) ).

cnf(c_0_71,negated_conjecture,
    ( app(tl(sk4),cons(hd(sk4),nil)) = sk3
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_50]),c_0_46])]) ).

cnf(c_0_72,plain,
    ( cons(hd(cons(X1,nil)),nil) = cons(X1,nil)
    | ~ ssList(cons(X1,nil)) ),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_73,plain,
    ( ssList(cons(X1,X2))
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_52])]) ).

cnf(c_0_74,negated_conjecture,
    ( sk4 = nil
    | app(app(nil,cons(hd(sk4),nil)),tl(sk4)) != sk4
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(tl(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_69])]) ).

cnf(c_0_75,plain,
    cons(hd(cons(X1,nil)),nil) = cons(X1,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_30])]) ).

cnf(c_0_76,negated_conjecture,
    ( sk4 = nil
    | app(cons(hd(sk4),nil),tl(sk4)) != sk4
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(tl(sk4)) ),
    inference(spm,[status(thm)],[c_0_74,c_0_29]) ).

cnf(c_0_77,plain,
    ssList(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_75]),c_0_30])]) ).

cnf(c_0_78,axiom,
    ( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause157 ).

cnf(c_0_79,negated_conjecture,
    ( sk4 = nil
    | app(cons(hd(sk4),nil),tl(sk4)) != sk4
    | ~ ssList(tl(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).

cnf(c_0_80,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_78,c_0_52])]) ).

cnf(c_0_81,negated_conjecture,
    ( sk4 = nil
    | cons(hd(sk4),app(nil,tl(sk4))) != sk4
    | ~ ssList(tl(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_30])]) ).

cnf(c_0_82,negated_conjecture,
    ( sk4 = nil
    | cons(hd(sk4),tl(sk4)) != sk4
    | ~ ssList(tl(sk4)) ),
    inference(spm,[status(thm)],[c_0_81,c_0_29]) ).

cnf(c_0_83,axiom,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause104 ).

cnf(c_0_84,axiom,
    ( X1 != X2
    | ~ neq(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    clause117 ).

cnf(c_0_85,negated_conjecture,
    ( sk4 = nil
    | ~ ssList(tl(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_46])]) ).

cnf(c_0_86,plain,
    ( ~ neq(X1,X1)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_84]) ).

cnf(c_0_87,negated_conjecture,
    sk4 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_57]),c_0_46])]) ).

cnf(c_0_88,plain,
    ~ neq(X1,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_52])]) ).

cnf(c_0_89,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_87]),c_0_88]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWC418-1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n004.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 14:35:52 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.68  % Version  : CSE_E---1.5
% 0.19/0.68  % Problem  : theBenchmark.p
% 0.19/0.68  % Proof found
% 0.19/0.68  % SZS status Theorem for theBenchmark.p
% 0.19/0.68  % SZS output start Proof
% See solution above
% 0.19/0.69  % Total time : 0.116000 s
% 0.19/0.69  % SZS output end Proof
% 0.19/0.69  % Total time : 0.122000 s
%------------------------------------------------------------------------------