TSTP Solution File: SWC392+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC392+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 : n021.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 20:22:12 EDT 2023

% Result   : Theorem 0.54s 0.72s
% Output   : CNFRefutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   92
% Syntax   : Number of formulae    :  169 (  20 unt;  77 typ;   0 def)
%            Number of atoms       :  355 ( 110 equ)
%            Maximal formula atoms :   31 (   3 avg)
%            Number of connectives :  428 ( 165   ~; 179   |;  40   &)
%                                         (   7 <=>;  37  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   5 avg)
%            Maximal term depth    :    3 (   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   :  111 (   0 sgn;  63   !;   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 ).

fof(ax52,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( rearsegP(nil,X1)
      <=> nil = X1 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax52) ).

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) ) )
                    | ( ! [X6] :
                          ( ssItem(X6)
                         => ( cons(X6,nil) != X3
                            | ~ memberP(X4,X6)
                            | ? [X7] :
                                ( ssItem(X7)
                                & X6 != X7
                                & memberP(X4,X7)
                                & leq(X7,X6) ) ) )
                      & ( nil != X4
                        | nil != X3 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(ax50,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( rearsegP(X1,X2)
               => rearsegP(app(X3,X1),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax50) ).

fof(ax17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).

fof(ax6,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( rearsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).

fof(ax84,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).

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

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

fof(ax38,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).

fof(ax4,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( singletonP(X1)
      <=> ? [X2] :
            ( ssItem(X2)
            & cons(X2,nil) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).

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/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).

fof(ax46,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( frontsegP(nil,X1)
      <=> nil = X1 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).

fof(ax18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).

fof(ax83,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).

fof(c_0_15,plain,
    ! [X184] :
      ( ( ~ rearsegP(nil,X184)
        | nil = X184
        | ~ ssList(X184) )
      & ( nil != X184
        | rearsegP(nil,X184)
        | ~ ssList(X184) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax52])])]) ).

fof(c_0_16,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) ) )
                      | ( ! [X6] :
                            ( ssItem(X6)
                           => ( cons(X6,nil) != X3
                              | ~ memberP(X4,X6)
                              | ? [X7] :
                                  ( ssItem(X7)
                                  & X6 != X7
                                  & memberP(X4,X7)
                                  & leq(X7,X6) ) ) )
                        & ( nil != X4
                          | nil != X3 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_17,plain,
    ! [X180,X181,X182] :
      ( ~ ssList(X180)
      | ~ ssList(X181)
      | ~ ssList(X182)
      | ~ rearsegP(X180,X181)
      | rearsegP(app(X182,X180),X181) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).

cnf(c_0_18,plain,
    ( rearsegP(nil,X1)
    | nil != X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

fof(c_0_20,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])])]) ).

fof(c_0_21,negated_conjecture,
    ! [X258] :
      ( 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 = esk51_0
        | ssItem(esk53_0) )
      & ( nil = esk50_0
        | ssItem(esk53_0) )
      & ( nil = esk51_0
        | cons(esk53_0,nil) = esk50_0 )
      & ( nil = esk50_0
        | cons(esk53_0,nil) = esk50_0 )
      & ( nil = esk51_0
        | memberP(esk51_0,esk53_0) )
      & ( nil = esk50_0
        | memberP(esk51_0,esk53_0) )
      & ( nil = esk51_0
        | ~ ssItem(X258)
        | esk53_0 = X258
        | ~ memberP(esk51_0,X258)
        | ~ leq(X258,esk53_0) )
      & ( nil = esk50_0
        | ~ ssItem(X258)
        | esk53_0 = X258
        | ~ memberP(esk51_0,X258)
        | ~ leq(X258,esk53_0) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).

cnf(c_0_22,plain,
    ( rearsegP(app(X3,X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ rearsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,plain,
    rearsegP(nil,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19])]) ).

cnf(c_0_24,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    ( nil = esk51_0
    | cons(esk53_0,nil) = esk50_0 ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    ( nil = esk51_0
    | ssItem(esk53_0) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_29,plain,
    ( rearsegP(app(X1,nil),nil)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19])]) ).

cnf(c_0_30,negated_conjecture,
    ( app(esk50_0,X1) = cons(esk53_0,X1)
    | esk51_0 = nil
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_27,c_0_28]) ).

fof(c_0_32,plain,
    ! [X25,X26,X28] :
      ( ( ssList(esk7_2(X25,X26))
        | ~ rearsegP(X25,X26)
        | ~ ssList(X26)
        | ~ ssList(X25) )
      & ( app(esk7_2(X25,X26),X26) = X25
        | ~ rearsegP(X25,X26)
        | ~ ssList(X26)
        | ~ ssList(X25) )
      & ( ~ ssList(X28)
        | app(X28,X26) != X25
        | rearsegP(X25,X26)
        | ~ ssList(X26)
        | ~ ssList(X25) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).

cnf(c_0_33,negated_conjecture,
    ( esk51_0 = nil
    | rearsegP(cons(esk53_0,nil),nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_19])]) ).

fof(c_0_34,plain,
    ! [X228] :
      ( ~ ssList(X228)
      | app(X228,nil) = X228 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

cnf(c_0_35,plain,
    ( app(esk7_2(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    ( esk51_0 = nil
    | rearsegP(esk50_0,nil) ),
    inference(spm,[status(thm)],[c_0_33,c_0_25]) ).

cnf(c_0_37,plain,
    ( ssList(esk7_2(X1,X2))
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_38,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_39,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_40,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_41,negated_conjecture,
    ( app(esk7_2(esk50_0,nil),nil) = esk50_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_19]),c_0_31])]) ).

cnf(c_0_42,negated_conjecture,
    ( esk51_0 = nil
    | ssList(esk7_2(esk50_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_36]),c_0_19]),c_0_31])]) ).

fof(c_0_43,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[ax38]) ).

fof(c_0_44,plain,
    ! [X18,X20] :
      ( ( ssItem(esk5_1(X18))
        | ~ singletonP(X18)
        | ~ ssList(X18) )
      & ( cons(esk5_1(X18),nil) = X18
        | ~ singletonP(X18)
        | ~ ssList(X18) )
      & ( ~ ssItem(X20)
        | cons(X20,nil) != X18
        | singletonP(X18)
        | ~ ssList(X18) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).

cnf(c_0_45,plain,
    ( frontsegP(X3,X2)
    | ~ ssList(X1)
    | app(X2,X1) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_46,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_47,negated_conjecture,
    ( esk7_2(esk50_0,nil) = esk50_0
    | esk51_0 = nil ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).

fof(c_0_48,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])])])]) ).

fof(c_0_49,plain,
    ! [X158] :
      ( ~ ssItem(X158)
      | ~ memberP(nil,X158) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])]) ).

fof(c_0_50,plain,
    ! [X173] :
      ( ( ~ frontsegP(nil,X173)
        | nil = X173
        | ~ ssList(X173) )
      & ( nil != X173
        | frontsegP(nil,X173)
        | ~ ssList(X173) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])]) ).

fof(c_0_51,plain,
    ! [X114,X115] :
      ( ~ ssList(X114)
      | ~ ssItem(X115)
      | cons(X115,X114) != X114 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).

cnf(c_0_52,plain,
    ( cons(esk5_1(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_53,plain,
    ( ssItem(esk5_1(X1))
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_54,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_45]),c_0_46]) ).

cnf(c_0_55,negated_conjecture,
    ( app(esk50_0,nil) = esk50_0
    | esk51_0 = nil ),
    inference(spm,[status(thm)],[c_0_41,c_0_47]) ).

cnf(c_0_56,plain,
    ( singletonP(X2)
    | ~ ssItem(X1)
    | cons(X1,nil) != X2
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_57,plain,
    ( X3 = X1
    | memberP(X2,X3)
    | ~ memberP(cons(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_58,negated_conjecture,
    ( nil = esk50_0
    | cons(esk53_0,nil) = esk50_0 ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_59,negated_conjecture,
    ( nil = esk50_0
    | ssItem(esk53_0) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_60,plain,
    ( ~ ssItem(X1)
    | ~ memberP(nil,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_61,negated_conjecture,
    memberP(esk48_0,esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_62,plain,
    ( frontsegP(nil,X1)
    | nil != X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_63,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_64,plain,
    ( cons(esk5_1(X1),X2) = app(X1,X2)
    | ~ singletonP(X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_52]),c_0_53]) ).

cnf(c_0_65,plain,
    ( app(X1,esk6_2(X2,X1)) = X2
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_66,negated_conjecture,
    ( esk51_0 = nil
    | frontsegP(esk50_0,esk50_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_31]),c_0_19])]) ).

cnf(c_0_67,plain,
    ( ssList(esk6_2(X1,X2))
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_68,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_56]) ).

cnf(c_0_69,negated_conjecture,
    ~ memberP(esk49_0,esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_70,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_71,negated_conjecture,
    ( esk50_0 = nil
    | esk53_0 = X1
    | ~ memberP(esk50_0,X1)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_19])]),c_0_59]),c_0_60]) ).

cnf(c_0_72,negated_conjecture,
    memberP(esk50_0,esk52_0),
    inference(rw,[status(thm)],[c_0_61,c_0_28]) ).

cnf(c_0_73,negated_conjecture,
    ssItem(esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_74,plain,
    ! [X226,X227] :
      ( ( nil = X227
        | nil != app(X226,X227)
        | ~ ssList(X227)
        | ~ ssList(X226) )
      & ( nil = X226
        | nil != app(X226,X227)
        | ~ ssList(X227)
        | ~ ssList(X226) )
      & ( nil != X227
        | nil != X226
        | nil = app(X226,X227)
        | ~ ssList(X227)
        | ~ ssList(X226) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_75,plain,
    frontsegP(nil,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_62]),c_0_19])]) ).

cnf(c_0_76,plain,
    ( app(X1,X2) != X2
    | ~ singletonP(X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_53]) ).

cnf(c_0_77,negated_conjecture,
    ( app(esk50_0,esk6_2(esk50_0,esk50_0)) = esk50_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_31])]) ).

cnf(c_0_78,negated_conjecture,
    ( esk51_0 = nil
    | ssList(esk6_2(esk50_0,esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_66]),c_0_31])]) ).

cnf(c_0_79,negated_conjecture,
    ( esk51_0 = nil
    | singletonP(esk50_0) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_25]),c_0_31])]),c_0_26]) ).

cnf(c_0_80,negated_conjecture,
    ~ memberP(esk51_0,esk52_0),
    inference(rw,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_81,negated_conjecture,
    ( esk52_0 = esk53_0
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).

cnf(c_0_82,negated_conjecture,
    ( nil = esk50_0
    | memberP(esk51_0,esk53_0) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_83,plain,
    ( nil = X1
    | nil != app(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

cnf(c_0_84,plain,
    app(nil,esk6_2(nil,nil)) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_75]),c_0_19])]) ).

cnf(c_0_85,plain,
    ssList(esk6_2(nil,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_75]),c_0_19])]) ).

cnf(c_0_86,negated_conjecture,
    ( esk51_0 = nil
    | esk6_2(esk50_0,esk50_0) != esk50_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_31])]),c_0_78]),c_0_79]) ).

cnf(c_0_87,negated_conjecture,
    esk50_0 = nil,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).

cnf(c_0_88,plain,
    esk6_2(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_19]),c_0_85])]) ).

cnf(c_0_89,negated_conjecture,
    esk51_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87]),c_0_87]),c_0_88]),c_0_87])]) ).

cnf(c_0_90,negated_conjecture,
    ~ memberP(nil,esk52_0),
    inference(rw,[status(thm)],[c_0_80,c_0_89]) ).

cnf(c_0_91,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_87]),c_0_90]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC392+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n021.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 16:14:28 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.54/0.72  % Version  : CSE_E---1.5
% 0.54/0.72  % Problem  : theBenchmark.p
% 0.54/0.72  % Proof found
% 0.54/0.72  % SZS status Theorem for theBenchmark.p
% 0.54/0.72  % SZS output start Proof
% See solution above
% 0.54/0.73  % Total time : 0.128000 s
% 0.54/0.73  % SZS output end Proof
% 0.54/0.73  % Total time : 0.132000 s
%------------------------------------------------------------------------------