TSTP Solution File: SWC181+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC181+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 20:20:30 EDT 2023

% Result   : Theorem 113.23s 113.27s
% Output   : CNFRefutation 113.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   84
% Syntax   : Number of formulae    :  130 (   8 unt;  77 typ;   0 def)
%            Number of atoms       :  354 (  45 equ)
%            Maximal formula atoms :   34 (   6 avg)
%            Number of connectives :  476 ( 175   ~; 195   |;  63   &)
%                                         (   3 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   7 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  68   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   58 (  58 usr;   9 con; 0-2 aty)
%            Number of variables   :  136 (   0 sgn;  67   !;  16   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    ssItem: $i > $o ).

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

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

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

tff(decl_26,type,
    cons: ( $i * $i ) > $i ).

tff(decl_27,type,
    app: ( $i * $i ) > $i ).

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

tff(decl_29,type,
    nil: $i ).

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

tff(decl_31,type,
    rearsegP: ( $i * $i ) > $o ).

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

tff(decl_33,type,
    cyclefreeP: $i > $o ).

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

tff(decl_35,type,
    totalorderP: $i > $o ).

tff(decl_36,type,
    strictorderP: $i > $o ).

tff(decl_37,type,
    lt: ( $i * $i ) > $o ).

tff(decl_38,type,
    totalorderedP: $i > $o ).

tff(decl_39,type,
    strictorderedP: $i > $o ).

tff(decl_40,type,
    duplicatefreeP: $i > $o ).

tff(decl_41,type,
    equalelemsP: $i > $o ).

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

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

tff(decl_44,type,
    geq: ( $i * $i ) > $o ).

tff(decl_45,type,
    gt: ( $i * $i ) > $o ).

tff(decl_46,type,
    esk1_0: $i ).

tff(decl_47,type,
    esk2_0: $i ).

tff(decl_48,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk5_1: $i > $i ).

tff(decl_51,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk10_1: $i > $i ).

tff(decl_56,type,
    esk11_1: $i > $i ).

tff(decl_57,type,
    esk12_1: $i > $i ).

tff(decl_58,type,
    esk13_1: $i > $i ).

tff(decl_59,type,
    esk14_1: $i > $i ).

tff(decl_60,type,
    esk15_1: $i > $i ).

tff(decl_61,type,
    esk16_1: $i > $i ).

tff(decl_62,type,
    esk17_1: $i > $i ).

tff(decl_63,type,
    esk18_1: $i > $i ).

tff(decl_64,type,
    esk19_1: $i > $i ).

tff(decl_65,type,
    esk20_1: $i > $i ).

tff(decl_66,type,
    esk21_1: $i > $i ).

tff(decl_67,type,
    esk22_1: $i > $i ).

tff(decl_68,type,
    esk23_1: $i > $i ).

tff(decl_69,type,
    esk24_1: $i > $i ).

tff(decl_70,type,
    esk25_1: $i > $i ).

tff(decl_71,type,
    esk26_1: $i > $i ).

tff(decl_72,type,
    esk27_1: $i > $i ).

tff(decl_73,type,
    esk28_1: $i > $i ).

tff(decl_74,type,
    esk29_1: $i > $i ).

tff(decl_75,type,
    esk30_1: $i > $i ).

tff(decl_76,type,
    esk31_1: $i > $i ).

tff(decl_77,type,
    esk32_1: $i > $i ).

tff(decl_78,type,
    esk33_1: $i > $i ).

tff(decl_79,type,
    esk34_1: $i > $i ).

tff(decl_80,type,
    esk35_1: $i > $i ).

tff(decl_81,type,
    esk36_1: $i > $i ).

tff(decl_82,type,
    esk37_1: $i > $i ).

tff(decl_83,type,
    esk38_1: $i > $i ).

tff(decl_84,type,
    esk39_1: $i > $i ).

tff(decl_85,type,
    esk40_1: $i > $i ).

tff(decl_86,type,
    esk41_1: $i > $i ).

tff(decl_87,type,
    esk42_1: $i > $i ).

tff(decl_88,type,
    esk43_1: $i > $i ).

tff(decl_89,type,
    esk44_1: $i > $i ).

tff(decl_90,type,
    esk45_1: $i > $i ).

tff(decl_91,type,
    esk46_1: $i > $i ).

tff(decl_92,type,
    esk47_1: $i > $i ).

tff(decl_93,type,
    esk48_0: $i ).

tff(decl_94,type,
    esk49_0: $i ).

tff(decl_95,type,
    esk50_0: $i ).

tff(decl_96,type,
    esk51_0: $i ).

tff(decl_97,type,
    esk52_0: $i ).

tff(decl_98,type,
    esk53_0: $i ).

fof(ax90,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ lt(X1,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax90) ).

fof(ax8,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( cyclefreeP(X1)
      <=> ! [X2] :
            ( ssItem(X2)
           => ! [X3] :
                ( ssItem(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
                             => ~ ( leq(X2,X3)
                                  & leq(X3,X2) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax8) ).

fof(ax91,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssItem(X3)
             => ( ( leq(X1,X2)
                  & lt(X2,X3) )
               => lt(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax91) ).

fof(ax13,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( duplicatefreeP(X1)
      <=> ! [X2] :
            ( ssItem(X2)
           => ! [X3] :
                ( ssItem(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
                             => X2 != X3 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax13) ).

fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X5,X3),X6) != X4
                              | ~ strictorderedP(X3)
                              | ? [X7] :
                                  ( ssItem(X7)
                                  & ? [X8] :
                                      ( ssList(X8)
                                      & app(X8,cons(X7,nil)) = X5
                                      & ? [X9] :
                                          ( ssItem(X9)
                                          & ? [X10] :
                                              ( ssList(X10)
                                              & app(cons(X9,nil),X10) = X3
                                              & lt(X7,X9) ) ) ) )
                              | ? [X11] :
                                  ( ssItem(X11)
                                  & ? [X12] :
                                      ( ssList(X12)
                                      & app(cons(X11,nil),X12) = X6
                                      & ? [X13] :
                                          ( ssItem(X13)
                                          & ? [X14] :
                                              ( ssList(X14)
                                              & app(X14,cons(X13,nil)) = X3
                                              & lt(X13,X11) ) ) ) ) ) ) )
                    | duplicatefreeP(X1)
                    | ( nil != X4
                      & nil = X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(ax31,axiom,
    ! [X1] :
      ( ssItem(X1)
     => leq(X1,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax31) ).

fof(ax12,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( strictorderedP(X1)
      <=> ! [X2] :
            ( ssItem(X2)
           => ! [X3] :
                ( ssItem(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
                             => lt(X2,X3) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax12) ).

fof(c_0_7,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ lt(X1,X1) ),
    inference(fof_simplification,[status(thm)],[ax90]) ).

fof(c_0_8,plain,
    ! [X42,X43,X44,X45,X46,X47] :
      ( ( ~ cyclefreeP(X42)
        | ~ ssItem(X43)
        | ~ ssItem(X44)
        | ~ ssList(X45)
        | ~ ssList(X46)
        | ~ ssList(X47)
        | app(app(X45,cons(X43,X46)),cons(X44,X47)) != X42
        | ~ leq(X43,X44)
        | ~ leq(X44,X43)
        | ~ ssList(X42) )
      & ( ssItem(esk10_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( ssItem(esk11_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( ssList(esk12_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( ssList(esk13_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( ssList(esk14_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( app(app(esk12_1(X42),cons(esk10_1(X42),esk13_1(X42))),cons(esk11_1(X42),esk14_1(X42))) = X42
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( leq(esk10_1(X42),esk11_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( leq(esk11_1(X42),esk10_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax8])])])])]) ).

fof(c_0_9,plain,
    ! [X246] :
      ( ~ ssItem(X246)
      | ~ lt(X246,X246) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).

fof(c_0_10,plain,
    ! [X247,X248,X249] :
      ( ~ ssItem(X247)
      | ~ ssItem(X248)
      | ~ ssItem(X249)
      | ~ leq(X247,X248)
      | ~ lt(X248,X249)
      | lt(X247,X249) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax91])])]) ).

cnf(c_0_11,plain,
    ( ~ cyclefreeP(X1)
    | ~ ssItem(X2)
    | ~ ssItem(X3)
    | ~ ssList(X4)
    | ~ ssList(X5)
    | ~ ssList(X6)
    | app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
    | ~ leq(X2,X3)
    | ~ leq(X3,X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_12,plain,
    ! [X97,X98,X99,X100,X101,X102] :
      ( ( ~ duplicatefreeP(X97)
        | ~ ssItem(X98)
        | ~ ssItem(X99)
        | ~ ssList(X100)
        | ~ ssList(X101)
        | ~ ssList(X102)
        | app(app(X100,cons(X98,X101)),cons(X99,X102)) != X97
        | X98 != X99
        | ~ ssList(X97) )
      & ( ssItem(esk35_1(X97))
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( ssItem(esk36_1(X97))
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( ssList(esk37_1(X97))
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( ssList(esk38_1(X97))
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( ssList(esk39_1(X97))
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( app(app(esk37_1(X97),cons(esk35_1(X97),esk38_1(X97))),cons(esk36_1(X97),esk39_1(X97))) = X97
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( esk35_1(X97) = esk36_1(X97)
        | duplicatefreeP(X97)
        | ~ ssList(X97) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax13])])])])]) ).

cnf(c_0_13,plain,
    ( ~ ssItem(X1)
    | ~ lt(X1,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( lt(X1,X3)
    | ~ ssItem(X1)
    | ~ ssItem(X2)
    | ~ ssItem(X3)
    | ~ leq(X1,X2)
    | ~ lt(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_15,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssList(X5)
                         => ! [X6] :
                              ( ssList(X6)
                             => ( app(app(X5,X3),X6) != X4
                                | ~ strictorderedP(X3)
                                | ? [X7] :
                                    ( ssItem(X7)
                                    & ? [X8] :
                                        ( ssList(X8)
                                        & app(X8,cons(X7,nil)) = X5
                                        & ? [X9] :
                                            ( ssItem(X9)
                                            & ? [X10] :
                                                ( ssList(X10)
                                                & app(cons(X9,nil),X10) = X3
                                                & lt(X7,X9) ) ) ) )
                                | ? [X11] :
                                    ( ssItem(X11)
                                    & ? [X12] :
                                        ( ssList(X12)
                                        & app(cons(X11,nil),X12) = X6
                                        & ? [X13] :
                                            ( ssItem(X13)
                                            & ? [X14] :
                                                ( ssList(X14)
                                                & app(X14,cons(X13,nil)) = X3
                                                & lt(X13,X11) ) ) ) ) ) ) )
                      | duplicatefreeP(X1)
                      | ( nil != X4
                        & nil = X3 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

cnf(c_0_16,plain,
    ( ~ leq(X1,X2)
    | ~ leq(X2,X1)
    | ~ cyclefreeP(app(app(X3,cons(X2,X4)),cons(X1,X5)))
    | ~ ssList(app(app(X3,cons(X2,X4)),cons(X1,X5)))
    | ~ ssList(X5)
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssItem(X1)
    | ~ ssItem(X2) ),
    inference(er,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    ( app(app(esk37_1(X1),cons(esk35_1(X1),esk38_1(X1))),cons(esk36_1(X1),esk39_1(X1))) = X1
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( ssItem(esk35_1(X1))
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ( ssItem(esk36_1(X1))
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    ( ssList(esk37_1(X1))
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_21,plain,
    ( ssList(esk38_1(X1))
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_22,plain,
    ( ssList(esk39_1(X1))
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_23,plain,
    ( ~ lt(X1,X2)
    | ~ leq(X2,X1)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

fof(c_0_24,negated_conjecture,
    ! [X265,X266,X267,X268,X269,X270,X271,X272] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & ssList(esk52_0)
      & ssList(esk53_0)
      & app(app(esk52_0,esk50_0),esk53_0) = esk51_0
      & strictorderedP(esk50_0)
      & ( ~ ssItem(X265)
        | ~ ssList(X266)
        | app(X266,cons(X265,nil)) != esk52_0
        | ~ ssItem(X267)
        | ~ ssList(X268)
        | app(cons(X267,nil),X268) != esk50_0
        | ~ lt(X265,X267) )
      & ( ~ ssItem(X269)
        | ~ ssList(X270)
        | app(cons(X269,nil),X270) != esk53_0
        | ~ ssItem(X271)
        | ~ ssList(X272)
        | app(X272,cons(X271,nil)) != esk50_0
        | ~ lt(X271,X269) )
      & ~ duplicatefreeP(esk48_0)
      & ( nil = esk51_0
        | nil != esk50_0 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).

cnf(c_0_25,plain,
    ( duplicatefreeP(X1)
    | ~ leq(esk36_1(X1),esk35_1(X1))
    | ~ leq(esk35_1(X1),esk36_1(X1))
    | ~ cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]) ).

cnf(c_0_26,plain,
    ( esk35_1(X1) = esk36_1(X1)
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_27,plain,
    ! [X149] :
      ( ~ ssItem(X149)
      | leq(X149,X149) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax31])]) ).

fof(c_0_28,plain,
    ! [X86,X87,X88,X89,X90,X91] :
      ( ( ~ strictorderedP(X86)
        | ~ ssItem(X87)
        | ~ ssItem(X88)
        | ~ ssList(X89)
        | ~ ssList(X90)
        | ~ ssList(X91)
        | app(app(X89,cons(X87,X90)),cons(X88,X91)) != X86
        | lt(X87,X88)
        | ~ ssList(X86) )
      & ( ssItem(esk30_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( ssItem(esk31_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( ssList(esk32_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( ssList(esk33_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( ssList(esk34_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( app(app(esk32_1(X86),cons(esk30_1(X86),esk33_1(X86))),cons(esk31_1(X86),esk34_1(X86))) = X86
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( ~ lt(esk30_1(X86),esk31_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])])])]) ).

cnf(c_0_29,plain,
    ( ~ lt(X1,X2)
    | ~ leq(X2,X3)
    | ~ leq(X3,X1)
    | ~ ssItem(X2)
    | ~ ssItem(X3)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_14]) ).

cnf(c_0_30,plain,
    ( leq(esk11_1(X1),esk10_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_31,plain,
    ( ssItem(esk10_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_32,plain,
    ( ssItem(esk11_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_33,negated_conjecture,
    ~ duplicatefreeP(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_35,plain,
    ( duplicatefreeP(X1)
    | ~ leq(esk36_1(X1),esk36_1(X1))
    | ~ cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_36,plain,
    ( leq(X1,X1)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_37,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_38,plain,
    ( lt(X2,X3)
    | ~ strictorderedP(X1)
    | ~ ssItem(X2)
    | ~ ssItem(X3)
    | ~ ssList(X4)
    | ~ ssList(X5)
    | ~ ssList(X6)
    | app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_39,plain,
    ( cyclefreeP(X1)
    | ~ lt(esk10_1(X1),X2)
    | ~ leq(X2,esk11_1(X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]) ).

cnf(c_0_40,negated_conjecture,
    ~ duplicatefreeP(esk50_0),
    inference(rw,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_41,plain,
    ( duplicatefreeP(X1)
    | ~ cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_19]) ).

cnf(c_0_42,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_37,c_0_34]) ).

cnf(c_0_43,plain,
    ( lt(X1,X2)
    | ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
    | ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
    | ~ ssList(X5)
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_38]) ).

cnf(c_0_44,plain,
    ( app(app(esk12_1(X1),cons(esk10_1(X1),esk13_1(X1))),cons(esk11_1(X1),esk14_1(X1))) = X1
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_45,plain,
    ( ssList(esk12_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_46,plain,
    ( ssList(esk13_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_47,plain,
    ( ssList(esk14_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_48,plain,
    ( cyclefreeP(X1)
    | ~ lt(esk10_1(X1),esk11_1(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_36]),c_0_32]) ).

cnf(c_0_49,negated_conjecture,
    ~ cyclefreeP(esk50_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).

cnf(c_0_50,plain,
    ( cyclefreeP(X1)
    | ~ strictorderedP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_31]),c_0_32]),c_0_45]),c_0_46]),c_0_47]),c_0_48]) ).

cnf(c_0_51,negated_conjecture,
    strictorderedP(esk50_0),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_52,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_42])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SWC181+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n004.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Aug 28 14:29:52 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 113.23/113.27  % Version  : CSE_E---1.5
% 113.23/113.27  % Problem  : theBenchmark.p
% 113.23/113.27  % Proof found
% 113.23/113.27  % SZS status Theorem for theBenchmark.p
% 113.23/113.27  % SZS output start Proof
% See solution above
% 113.23/113.28  % Total time : 112.716000 s
% 113.23/113.28  % SZS output end Proof
% 113.23/113.28  % Total time : 112.726000 s
%------------------------------------------------------------------------------