TSTP Solution File: SWC031-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC031-1 : 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 : 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 20:19:14 EDT 2023

% Result   : Unsatisfiable 0.52s 0.86s
% Output   : CNFRefutation 0.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :  114
% Syntax   : Number of formulae    :  199 (  49 unt;  72 typ;   0 def)
%            Number of atoms       :  311 (  89 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  363 ( 179   ~; 184   |;   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  :   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   :  142 (  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(co1_10,negated_conjecture,
    ( nil = sk2
    | nil = sk1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).

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_7,negated_conjecture,
    frontsegP(sk4,sk3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).

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

cnf(clause84,axiom,
    ( nil = X1
    | ~ frontsegP(nil,X1)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause84) ).

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

cnf(clause132,axiom,
    ( app(X2,skaf45(X1,X2)) = X1
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).

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

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

cnf(clause51,axiom,
    ssList(skaf45(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).

cnf(clause173,axiom,
    ( segmentP(X4,X2)
    | app(app(X1,X2),X3) != X4
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).

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

cnf(clause143,axiom,
    ( rearsegP(X3,X2)
    | app(X1,X2) != X3
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause143) ).

cnf(clause85,axiom,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).

cnf(clause168,axiom,
    ( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause168) ).

cnf(clause48,axiom,
    ssList(skaf48(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause48) ).

cnf(clause49,axiom,
    ssList(skaf47(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause49) ).

cnf(clause136,axiom,
    ( rearsegP(app(X3,X1),X2)
    | ~ rearsegP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause136) ).

cnf(clause58,axiom,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause58) ).

cnf(clause131,axiom,
    ( app(skaf46(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause131) ).

cnf(clause50,axiom,
    ssList(skaf46(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause50) ).

cnf(co1_13,negated_conjecture,
    ( nil != sk1
    | nil != sk2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).

cnf(clause104,axiom,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).

cnf(clause123,axiom,
    ( nil = X2
    | hd(app(X2,X1)) = hd(X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause123) ).

cnf(clause118,axiom,
    ( nil = X1
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).

cnf(clause171,axiom,
    ( X4 = X2
    | cons(X1,X2) != cons(X3,X4)
    | ~ ssItem(X3)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause171) ).

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

cnf(clause98,axiom,
    ( cons(X1,X2) != nil
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).

cnf(clause76,axiom,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).

cnf(clause75,axiom,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).

cnf(clause178,axiom,
    ( frontsegP(cons(X3,X1),cons(X4,X2))
    | ~ frontsegP(X1,X2)
    | X3 != X4
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause178) ).

cnf(clause97,axiom,
    ( hd(cons(X1,X2)) = X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).

cnf(clause60,axiom,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause60) ).

cnf(co1_9,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(sk3,X1)
    | ~ frontsegP(sk4,X1)
    | ~ segmentP(X1,sk3)
    | ~ totalorderedP(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).

cnf(clause56,axiom,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).

cnf(clause100,axiom,
    ( neq(X2,X1)
    | X2 = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).

cnf(clause67,axiom,
    ( totalorderedP(cons(X1,nil))
    | ~ ssItem(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause67) ).

cnf(clause99,axiom,
    ( cons(X1,X2) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause99) ).

cnf(c_0_42,negated_conjecture,
    ( nil = sk2
    | nil = sk1 ),
    co1_10 ).

cnf(c_0_43,negated_conjecture,
    sk1 = sk3,
    co1_6 ).

cnf(c_0_44,negated_conjecture,
    sk2 = sk4,
    co1_5 ).

cnf(c_0_45,negated_conjecture,
    frontsegP(sk4,sk3),
    co1_7 ).

cnf(c_0_46,negated_conjecture,
    ( sk4 = nil
    | sk3 = nil ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).

cnf(c_0_47,negated_conjecture,
    ssList(sk1),
    co1_1 ).

cnf(c_0_48,axiom,
    ( nil = X1
    | ~ frontsegP(nil,X1)
    | ~ ssList(X1) ),
    clause84 ).

cnf(c_0_49,negated_conjecture,
    ( sk3 = nil
    | frontsegP(nil,sk3) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_50,negated_conjecture,
    ssList(sk3),
    inference(rw,[status(thm)],[c_0_47,c_0_43]) ).

cnf(c_0_51,negated_conjecture,
    sk3 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).

cnf(c_0_52,negated_conjecture,
    ssList(sk2),
    co1_2 ).

cnf(c_0_53,axiom,
    ( app(X2,skaf45(X1,X2)) = X1
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause132 ).

cnf(c_0_54,negated_conjecture,
    frontsegP(sk4,nil),
    inference(rw,[status(thm)],[c_0_45,c_0_51]) ).

cnf(c_0_55,axiom,
    ssList(nil),
    clause8 ).

cnf(c_0_56,negated_conjecture,
    ssList(sk4),
    inference(rw,[status(thm)],[c_0_52,c_0_44]) ).

cnf(c_0_57,axiom,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    clause74 ).

cnf(c_0_58,negated_conjecture,
    app(nil,skaf45(sk4,nil)) = sk4,
    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_59,axiom,
    ssList(skaf45(X1,X2)),
    clause51 ).

cnf(c_0_60,axiom,
    ( segmentP(X4,X2)
    | app(app(X1,X2),X3) != X4
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X4) ),
    clause173 ).

cnf(c_0_61,negated_conjecture,
    skaf45(sk4,nil) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).

cnf(c_0_62,plain,
    ( segmentP(app(app(X1,X2),X3),X2)
    | ~ ssList(app(app(X1,X2),X3))
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[c_0_60]) ).

cnf(c_0_63,negated_conjecture,
    app(nil,sk4) = sk4,
    inference(rw,[status(thm)],[c_0_58,c_0_61]) ).

cnf(c_0_64,negated_conjecture,
    ( segmentP(app(sk4,X1),sk4)
    | ~ ssList(app(sk4,X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_56]),c_0_55])]) ).

cnf(c_0_65,axiom,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    clause73 ).

cnf(c_0_66,axiom,
    ( rearsegP(X3,X2)
    | app(X1,X2) != X3
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause143 ).

cnf(c_0_67,axiom,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause85 ).

cnf(c_0_68,axiom,
    ( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause168 ).

cnf(c_0_69,negated_conjecture,
    segmentP(sk4,sk4),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_56]),c_0_55])]) ).

cnf(c_0_70,plain,
    ( rearsegP(app(X1,X2),X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_66]),c_0_67]) ).

cnf(c_0_71,negated_conjecture,
    app(app(skaf47(sk4,sk4),sk4),skaf48(sk4,sk4)) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_56])]) ).

cnf(c_0_72,axiom,
    ssList(skaf48(X1,X2)),
    clause48 ).

cnf(c_0_73,negated_conjecture,
    ( rearsegP(sk4,skaf48(sk4,sk4))
    | ~ ssList(app(skaf47(sk4,sk4),sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).

cnf(c_0_74,axiom,
    ssList(skaf47(X1,X2)),
    clause49 ).

cnf(c_0_75,axiom,
    ( rearsegP(app(X3,X1),X2)
    | ~ rearsegP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause136 ).

cnf(c_0_76,axiom,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    clause58 ).

cnf(c_0_77,axiom,
    ( app(skaf46(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause131 ).

cnf(c_0_78,negated_conjecture,
    rearsegP(sk4,skaf48(sk4,sk4)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_67]),c_0_74]),c_0_56])]) ).

cnf(c_0_79,plain,
    ( rearsegP(app(X1,X2),nil)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_55])]) ).

cnf(c_0_80,negated_conjecture,
    app(skaf46(sk4,skaf48(sk4,sk4)),skaf48(sk4,sk4)) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_72]),c_0_56])]) ).

cnf(c_0_81,axiom,
    ssList(skaf46(X1,X2)),
    clause50 ).

cnf(c_0_82,negated_conjecture,
    rearsegP(sk4,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_72])]) ).

cnf(c_0_83,negated_conjecture,
    app(skaf46(sk4,nil),nil) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_82]),c_0_55]),c_0_56])]) ).

cnf(c_0_84,negated_conjecture,
    ( nil != sk1
    | nil != sk2 ),
    co1_13 ).

cnf(c_0_85,axiom,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause104 ).

cnf(c_0_86,axiom,
    ( nil = X2
    | hd(app(X2,X1)) = hd(X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause123 ).

cnf(c_0_87,axiom,
    ( nil = X1
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause118 ).

cnf(c_0_88,negated_conjecture,
    skaf46(sk4,nil) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_83]),c_0_81])]) ).

cnf(c_0_89,negated_conjecture,
    ( sk3 != nil
    | sk4 != nil ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_43]),c_0_44]) ).

cnf(c_0_90,axiom,
    ( X4 = X2
    | cons(X1,X2) != cons(X3,X4)
    | ~ ssItem(X3)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X2) ),
    clause171 ).

cnf(c_0_91,axiom,
    ( cons(skaf83(X1),skaf82(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause109 ).

cnf(c_0_92,axiom,
    ssItem(skaf83(X1)),
    clause12 ).

cnf(c_0_93,axiom,
    ssList(skaf82(X1)),
    clause13 ).

cnf(c_0_94,axiom,
    ( ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause86 ).

cnf(c_0_95,axiom,
    ( cons(X1,X2) != nil
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause98 ).

cnf(c_0_96,plain,
    ( cons(hd(X1),tl(app(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_85,c_0_86]),c_0_67]),c_0_87]) ).

cnf(c_0_97,negated_conjecture,
    app(sk4,nil) = sk4,
    inference(rw,[status(thm)],[c_0_83,c_0_88]) ).

cnf(c_0_98,negated_conjecture,
    sk4 != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_51])]) ).

cnf(c_0_99,plain,
    ( skaf82(cons(X1,X2)) = X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[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_90,c_0_91]),c_0_92]),c_0_93])])]),c_0_94]),c_0_95]) ).

cnf(c_0_100,negated_conjecture,
    cons(hd(sk4),tl(sk4)) = sk4,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_56]),c_0_55])]),c_0_98]) ).

cnf(c_0_101,negated_conjecture,
    ( skaf82(sk4) = tl(sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(tl(sk4)) ),
    inference(spm,[status(thm)],[c_0_99,c_0_100]) ).

cnf(c_0_102,axiom,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause76 ).

cnf(c_0_103,negated_conjecture,
    ( skaf82(sk4) = tl(sk4)
    | ~ ssList(tl(sk4)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_56])]),c_0_98]) ).

cnf(c_0_104,axiom,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause75 ).

cnf(c_0_105,negated_conjecture,
    skaf82(sk4) = tl(sk4),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_56])]),c_0_98]) ).

cnf(c_0_106,axiom,
    ( frontsegP(cons(X3,X1),cons(X4,X2))
    | ~ frontsegP(X1,X2)
    | X3 != X4
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3) ),
    clause178 ).

cnf(c_0_107,axiom,
    ( hd(cons(X1,X2)) = X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause97 ).

cnf(c_0_108,negated_conjecture,
    cons(skaf83(sk4),tl(sk4)) = sk4,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_105]),c_0_56])]),c_0_98]) ).

cnf(c_0_109,negated_conjecture,
    ssList(tl(sk4)),
    inference(spm,[status(thm)],[c_0_93,c_0_105]) ).

cnf(c_0_110,plain,
    ( frontsegP(cons(X1,X2),cons(X1,X3))
    | ~ frontsegP(X2,X3)
    | ~ ssItem(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(er,[status(thm)],[c_0_106]) ).

cnf(c_0_111,axiom,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    clause60 ).

cnf(c_0_112,negated_conjecture,
    skaf83(sk4) = hd(sk4),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_92]),c_0_109])]) ).

cnf(c_0_113,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(sk3,X1)
    | ~ frontsegP(sk4,X1)
    | ~ segmentP(X1,sk3)
    | ~ totalorderedP(X1) ),
    co1_9 ).

cnf(c_0_114,axiom,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    clause56 ).

cnf(c_0_115,plain,
    ( frontsegP(cons(X1,X2),cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_55])]) ).

cnf(c_0_116,negated_conjecture,
    ssItem(hd(sk4)),
    inference(spm,[status(thm)],[c_0_92,c_0_112]) ).

cnf(c_0_117,negated_conjecture,
    ( ~ neq(nil,X1)
    | ~ frontsegP(sk4,X1)
    | ~ ssList(X1)
    | ~ totalorderedP(X1) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_51]),c_0_51]),c_0_114]) ).

cnf(c_0_118,negated_conjecture,
    frontsegP(sk4,cons(hd(sk4),nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_100]),c_0_116]),c_0_109])]) ).

cnf(c_0_119,negated_conjecture,
    ( ~ neq(nil,cons(hd(sk4),nil))
    | ~ ssList(cons(hd(sk4),nil))
    | ~ totalorderedP(cons(hd(sk4),nil)) ),
    inference(spm,[status(thm)],[c_0_117,c_0_118]) ).

cnf(c_0_120,axiom,
    ( neq(X2,X1)
    | X2 = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause100 ).

cnf(c_0_121,negated_conjecture,
    ( cons(hd(sk4),nil) = nil
    | ~ ssList(cons(hd(sk4),nil))
    | ~ totalorderedP(cons(hd(sk4),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_55])]) ).

cnf(c_0_122,negated_conjecture,
    ( cons(hd(sk4),nil) = nil
    | ~ totalorderedP(cons(hd(sk4),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_94]),c_0_116]),c_0_55])]) ).

cnf(c_0_123,axiom,
    ( totalorderedP(cons(X1,nil))
    | ~ ssItem(X1) ),
    clause67 ).

cnf(c_0_124,axiom,
    ( cons(X1,X2) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause99 ).

cnf(c_0_125,negated_conjecture,
    cons(hd(sk4),nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_116])]) ).

cnf(c_0_126,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_116]),c_0_55])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SWC031-1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n022.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % 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 16:43:54 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.52/0.86  % Version  : CSE_E---1.5
% 0.52/0.86  % Problem  : theBenchmark.p
% 0.52/0.86  % Proof found
% 0.52/0.86  % SZS status Theorem for theBenchmark.p
% 0.52/0.86  % SZS output start Proof
% See solution above
% 0.52/0.87  % Total time : 0.289000 s
% 0.52/0.87  % SZS output end Proof
% 0.52/0.87  % Total time : 0.295000 s
%------------------------------------------------------------------------------