TSTP Solution File: SWC397+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC397+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 : n002.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 20:22:15 EDT 2023

% Result   : Theorem 0.64s 0.73s
% Output   : CNFRefutation 0.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   93
% Syntax   : Number of formulae    :  167 (  17 unt;  78 typ;   0 def)
%            Number of atoms       :  378 ( 103 equ)
%            Maximal formula atoms :   19 (   4 avg)
%            Number of connectives :  466 ( 177   ~; 201   |;  37   &)
%                                         (   6 <=>;  45  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Maximal term depth    :    4 (   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    :   59 (  59 usr;  10 con; 0-2 aty)
%            Number of variables   :  129 (   0 sgn;  77   !;   5   ?;   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 ).

tff(decl_99,type,
    esk54_0: $i ).

fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ! [X5] :
                        ( ssItem(X5)
                       => ( ~ memberP(X1,X5)
                          | memberP(X2,X5) ) )
                    | ( nil != X3
                      & nil = X4 )
                    | ( ! [X6] :
                          ( ssItem(X6)
                         => ! [X7] :
                              ( ssList(X7)
                             => ( app(cons(X6,nil),X7) != X3
                                | app(X7,cons(X6,nil)) != X4 ) ) )
                      & neq(X4,nil) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(ax15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).

fof(ax17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).

fof(ax81,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).

fof(ax27,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).

fof(ax5,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( frontsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X2,X3) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).

fof(ax26,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).

fof(ax36,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(app(X2,X3),X1)
              <=> ( memberP(X2,X1)
                  | memberP(X3,X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).

fof(ax16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).

fof(ax44,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( frontsegP(cons(X1,X3),cons(X2,X4))
                  <=> ( X1 = X2
                      & frontsegP(X3,X4) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax44) ).

fof(ax20,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).

fof(ax79,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X3,X2) = app(X1,X2)
               => X3 = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).

fof(ax28,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).

fof(ax3,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( memberP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).

fof(ax37,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(cons(X2,X3),X1)
              <=> ( X1 = X2
                  | memberP(X3,X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).

fof(c_0_15,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssItem(X5)
                         => ( ~ memberP(X1,X5)
                            | memberP(X2,X5) ) )
                      | ( nil != X3
                        & nil = X4 )
                      | ( ! [X6] :
                            ( ssItem(X6)
                           => ! [X7] :
                                ( ssList(X7)
                               => ( app(cons(X6,nil),X7) != X3
                                  | app(X7,cons(X6,nil)) != X4 ) ) )
                        & neq(X4,nil) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_16,negated_conjecture,
    ( ssList(esk48_0)
    & ssList(esk49_0)
    & ssList(esk50_0)
    & ssList(esk51_0)
    & esk49_0 = esk51_0
    & esk48_0 = esk50_0
    & ssItem(esk52_0)
    & memberP(esk48_0,esk52_0)
    & ~ memberP(esk49_0,esk52_0)
    & ( nil = esk50_0
      | nil != esk51_0 )
    & ( ssItem(esk53_0)
      | ~ neq(esk51_0,nil) )
    & ( ssList(esk54_0)
      | ~ neq(esk51_0,nil) )
    & ( app(cons(esk53_0,nil),esk54_0) = esk50_0
      | ~ neq(esk51_0,nil) )
    & ( app(esk54_0,cons(esk53_0,nil)) = esk51_0
      | ~ neq(esk51_0,nil) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).

fof(c_0_17,plain,
    ! [X110,X111] :
      ( ( ~ neq(X110,X111)
        | X110 != X111
        | ~ ssList(X111)
        | ~ ssList(X110) )
      & ( X110 = X111
        | neq(X110,X111)
        | ~ ssList(X111)
        | ~ ssList(X110) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

cnf(c_0_18,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    ( app(cons(esk53_0,nil),esk54_0) = esk50_0
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_23,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

fof(c_0_24,plain,
    ! [X221,X222] :
      ( ~ ssList(X221)
      | ~ ssItem(X222)
      | cons(X222,X221) = app(cons(X222,nil),X221) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_25,negated_conjecture,
    ( ssItem(esk53_0)
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_26,negated_conjecture,
    ( ssList(esk54_0)
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_27,plain,
    ! [X133,X134,X135] :
      ( ~ ssList(X133)
      | ~ ssList(X134)
      | ~ ssItem(X135)
      | cons(X135,app(X134,X133)) = app(cons(X135,X134),X133) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).

cnf(c_0_28,negated_conjecture,
    ( app(cons(esk53_0,nil),esk54_0) = esk50_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).

cnf(c_0_29,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_30,negated_conjecture,
    ( esk51_0 = nil
    | ssItem(esk53_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_21]),c_0_22]),c_0_23])]) ).

cnf(c_0_31,negated_conjecture,
    ( esk51_0 = nil
    | ssList(esk54_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_22]),c_0_23])]) ).

fof(c_0_32,plain,
    ! [X21,X22,X24] :
      ( ( ssList(esk6_2(X21,X22))
        | ~ frontsegP(X21,X22)
        | ~ ssList(X22)
        | ~ ssList(X21) )
      & ( app(X22,esk6_2(X21,X22)) = X21
        | ~ frontsegP(X21,X22)
        | ~ ssList(X22)
        | ~ ssList(X21) )
      & ( ~ ssList(X24)
        | app(X22,X24) != X21
        | frontsegP(X21,X22)
        | ~ ssList(X22)
        | ~ ssList(X21) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).

fof(c_0_33,plain,
    ! [X131,X132] :
      ( ~ ssList(X131)
      | ~ ssList(X132)
      | ssList(app(X131,X132)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_34,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_35,negated_conjecture,
    ( cons(esk53_0,esk54_0) = esk50_0
    | esk51_0 = nil ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    ( app(esk54_0,cons(esk53_0,nil)) = esk51_0
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_37,plain,
    ( frontsegP(X3,X2)
    | ~ ssList(X1)
    | app(X2,X1) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_38,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

fof(c_0_39,plain,
    ! [X152,X153,X154] :
      ( ( ~ memberP(app(X153,X154),X152)
        | memberP(X153,X152)
        | memberP(X154,X152)
        | ~ ssList(X154)
        | ~ ssList(X153)
        | ~ ssItem(X152) )
      & ( ~ memberP(X153,X152)
        | memberP(app(X153,X154),X152)
        | ~ ssList(X154)
        | ~ ssList(X153)
        | ~ ssItem(X152) )
      & ( ~ memberP(X154,X152)
        | memberP(app(X153,X154),X152)
        | ~ ssList(X154)
        | ~ ssList(X153)
        | ~ ssItem(X152) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).

cnf(c_0_40,negated_conjecture,
    memberP(esk48_0,esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_41,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_42,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_43,negated_conjecture,
    ( cons(esk53_0,app(esk54_0,X1)) = app(esk50_0,X1)
    | esk51_0 = nil
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_30]),c_0_31]) ).

cnf(c_0_44,negated_conjecture,
    ( app(esk54_0,cons(esk53_0,nil)) = esk51_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_21]),c_0_22]),c_0_23])]) ).

fof(c_0_45,plain,
    ! [X112,X113] :
      ( ~ ssList(X112)
      | ~ ssItem(X113)
      | ssList(cons(X113,X112)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

fof(c_0_46,plain,
    ! [X168,X169,X170,X171] :
      ( ( X168 = X169
        | ~ frontsegP(cons(X168,X170),cons(X169,X171))
        | ~ ssList(X171)
        | ~ ssList(X170)
        | ~ ssItem(X169)
        | ~ ssItem(X168) )
      & ( frontsegP(X170,X171)
        | ~ frontsegP(cons(X168,X170),cons(X169,X171))
        | ~ ssList(X171)
        | ~ ssList(X170)
        | ~ ssItem(X169)
        | ~ ssItem(X168) )
      & ( X168 != X169
        | ~ frontsegP(X170,X171)
        | frontsegP(cons(X168,X170),cons(X169,X171))
        | ~ ssList(X171)
        | ~ ssList(X170)
        | ~ ssItem(X169)
        | ~ ssItem(X168) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).

fof(c_0_47,plain,
    ! [X120] :
      ( ( ssList(esk44_1(X120))
        | nil = X120
        | ~ ssList(X120) )
      & ( ssItem(esk45_1(X120))
        | nil = X120
        | ~ ssList(X120) )
      & ( cons(esk45_1(X120),esk44_1(X120)) = X120
        | nil = X120
        | ~ ssList(X120) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).

cnf(c_0_48,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_37]),c_0_38]) ).

cnf(c_0_49,plain,
    ( memberP(app(X1,X3),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_50,negated_conjecture,
    memberP(esk50_0,esk52_0),
    inference(rw,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_51,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_42,c_0_41]) ).

cnf(c_0_52,negated_conjecture,
    ssItem(esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_53,negated_conjecture,
    ( app(esk50_0,cons(esk53_0,nil)) = cons(esk53_0,esk51_0)
    | esk51_0 = nil
    | ~ ssList(cons(esk53_0,nil)) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_54,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

fof(c_0_55,plain,
    ! [X215,X216,X217] :
      ( ~ ssList(X215)
      | ~ ssList(X216)
      | ~ ssList(X217)
      | app(X217,X216) != app(X215,X216)
      | X217 = X215 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).

fof(c_0_56,plain,
    ! [X136] :
      ( ~ ssList(X136)
      | app(nil,X136) = X136 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_57,plain,
    ( X1 = X2
    | ~ frontsegP(cons(X1,X3),cons(X2,X4))
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_58,plain,
    ( cons(esk45_1(X1),esk44_1(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_59,plain,
    ( ssItem(esk45_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_60,plain,
    ( ssList(esk44_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_61,negated_conjecture,
    ( esk51_0 = nil
    | frontsegP(esk50_0,cons(esk53_0,nil))
    | ~ ssList(cons(esk53_0,nil)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_28]),c_0_31]) ).

fof(c_0_62,plain,
    ! [X12,X13,X16,X17] :
      ( ( ssList(esk3_2(X12,X13))
        | ~ memberP(X12,X13)
        | ~ ssItem(X13)
        | ~ ssList(X12) )
      & ( ssList(esk4_2(X12,X13))
        | ~ memberP(X12,X13)
        | ~ ssItem(X13)
        | ~ ssList(X12) )
      & ( app(esk3_2(X12,X13),cons(X13,esk4_2(X12,X13))) = X12
        | ~ memberP(X12,X13)
        | ~ ssItem(X13)
        | ~ ssList(X12) )
      & ( ~ ssList(X16)
        | ~ ssList(X17)
        | app(X16,cons(X13,X17)) != X12
        | memberP(X12,X13)
        | ~ ssItem(X13)
        | ~ ssList(X12) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).

cnf(c_0_63,negated_conjecture,
    ( memberP(app(esk50_0,X1),esk52_0)
    | ~ ssList(X1) ),
    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_52])]) ).

cnf(c_0_64,negated_conjecture,
    ( app(esk50_0,cons(esk53_0,nil)) = cons(esk53_0,esk51_0)
    | esk51_0 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_22])]),c_0_30]) ).

cnf(c_0_65,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X3,X2) != app(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_66,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_67,plain,
    ( esk45_1(X1) = X2
    | nil = X1
    | ~ frontsegP(X1,cons(X2,X3))
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60]) ).

cnf(c_0_68,negated_conjecture,
    ( esk51_0 = nil
    | frontsegP(esk50_0,cons(esk53_0,nil)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_54]),c_0_22])]),c_0_30]) ).

cnf(c_0_69,negated_conjecture,
    ( nil = esk50_0
    | nil != esk51_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_70,plain,
    ( memberP(X4,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(X1,cons(X3,X2)) != X4
    | ~ ssItem(X3)
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

fof(c_0_71,plain,
    ! [X155,X156,X157] :
      ( ( ~ memberP(cons(X156,X157),X155)
        | X155 = X156
        | memberP(X157,X155)
        | ~ ssList(X157)
        | ~ ssItem(X156)
        | ~ ssItem(X155) )
      & ( X155 != X156
        | memberP(cons(X156,X157),X155)
        | ~ ssList(X157)
        | ~ ssItem(X156)
        | ~ ssItem(X155) )
      & ( ~ memberP(X157,X155)
        | memberP(cons(X156,X157),X155)
        | ~ ssList(X157)
        | ~ ssItem(X156)
        | ~ ssItem(X155) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).

cnf(c_0_72,negated_conjecture,
    ( esk51_0 = nil
    | memberP(cons(esk53_0,esk51_0),esk52_0)
    | ~ ssList(cons(esk53_0,nil)) ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_73,negated_conjecture,
    ~ memberP(esk49_0,esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_74,plain,
    ( X1 = nil
    | app(X1,X2) != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_22])]) ).

cnf(c_0_75,negated_conjecture,
    ( esk45_1(esk50_0) = esk53_0
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_22]),c_0_51])]),c_0_30]),c_0_69]) ).

cnf(c_0_76,plain,
    ( memberP(app(X1,cons(X2,X3)),X2)
    | ~ ssList(app(X1,cons(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(er,[status(thm)],[c_0_70]) ).

cnf(c_0_77,plain,
    ( X3 = X1
    | memberP(X2,X3)
    | ~ memberP(cons(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

cnf(c_0_78,negated_conjecture,
    ( esk51_0 = nil
    | memberP(cons(esk53_0,esk51_0),esk52_0) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_54]),c_0_22])]),c_0_30]) ).

cnf(c_0_79,negated_conjecture,
    ~ memberP(esk51_0,esk52_0),
    inference(rw,[status(thm)],[c_0_73,c_0_19]) ).

cnf(c_0_80,negated_conjecture,
    ( esk50_0 = nil
    | cons(esk53_0,esk51_0) != cons(esk53_0,nil)
    | ~ ssList(cons(esk53_0,nil)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_64]),c_0_51])]),c_0_69]) ).

cnf(c_0_81,negated_conjecture,
    ( esk50_0 = nil
    | ssItem(esk53_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_75]),c_0_51])]) ).

cnf(c_0_82,negated_conjecture,
    ( esk51_0 = nil
    | memberP(esk51_0,esk53_0) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_44]),c_0_23]),c_0_22])]),c_0_30]),c_0_31]) ).

cnf(c_0_83,negated_conjecture,
    ( esk51_0 = nil
    | esk53_0 = esk52_0 ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_23]),c_0_52])]),c_0_79]),c_0_30]) ).

cnf(c_0_84,negated_conjecture,
    ( esk50_0 = nil
    | cons(esk53_0,esk51_0) != cons(esk53_0,nil) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_54]),c_0_22])]),c_0_81]) ).

cnf(c_0_85,negated_conjecture,
    esk51_0 = nil,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_79]) ).

cnf(c_0_86,negated_conjecture,
    esk50_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).

cnf(c_0_87,negated_conjecture,
    ~ memberP(nil,esk52_0),
    inference(rw,[status(thm)],[c_0_79,c_0_85]) ).

cnf(c_0_88,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_86]),c_0_87]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWC397+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n002.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 16:41:04 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.64/0.73  % Version  : CSE_E---1.5
% 0.64/0.73  % Problem  : theBenchmark.p
% 0.64/0.73  % Proof found
% 0.64/0.73  % SZS status Theorem for theBenchmark.p
% 0.64/0.73  % SZS output start Proof
% See solution above
% 0.64/0.74  % Total time : 0.165000 s
% 0.64/0.74  % SZS output end Proof
% 0.64/0.74  % Total time : 0.170000 s
%------------------------------------------------------------------------------