TSTP Solution File: SWC045+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC045+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 : n015.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 20:19:21 EDT 2023

% Result   : Theorem 93.94s 94.16s
% Output   : CNFRefutation 93.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   91
% Syntax   : Number of formulae    :  154 (  13 unt;  76 typ;   0 def)
%            Number of atoms       :  306 (  88 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  391 ( 163   ~; 160   |;  28   &)
%                                         (   2 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   86 (  69   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   57 (  57 usr;   7 con; 0-2 aty)
%            Number of variables   :  135 (   0 sgn;  64   !;   6   ?;   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_1: $i > $i ).

fof(ax82,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).

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

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

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

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

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

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/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).

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

fof(ax21,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).

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

fof(ax54,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( ( segmentP(X1,X2)
              & segmentP(X2,X1) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).

fof(ax57,axiom,
    ! [X1] :
      ( ssList(X1)
     => segmentP(X1,nil) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).

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

fof(c_0_15,plain,
    ! [X222,X223,X224] :
      ( ~ ssList(X222)
      | ~ ssList(X223)
      | ~ ssList(X224)
      | app(app(X222,X223),X224) = app(X222,app(X223,X224)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).

fof(c_0_16,plain,
    ! [X227] :
      ( ~ ssList(X227)
      | app(X227,nil) = X227 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

fof(c_0_17,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( nil != X2
                      | X2 != X4
                      | X1 != X3
                      | nil = X1
                      | ? [X5] :
                          ( ssItem(X5)
                          & ( ( ~ memberP(X3,X5)
                              & ? [X6] :
                                  ( ssList(X6)
                                  & segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) )
                            | ( ! [X6] :
                                  ( ssList(X6)
                                 => ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
                              & memberP(X3,X5) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_18,plain,
    ! [X214,X215,X216] :
      ( ~ ssList(X214)
      | ~ ssList(X215)
      | ~ ssList(X216)
      | app(X216,X215) != app(X214,X215)
      | X216 = X214 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).

fof(c_0_19,plain,
    ! [X135] :
      ( ~ ssList(X135)
      | app(nil,X135) = X135 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

fof(c_0_20,plain,
    ! [X225,X226] :
      ( ( nil = X226
        | nil != app(X225,X226)
        | ~ ssList(X226)
        | ~ ssList(X225) )
      & ( nil = X225
        | nil != app(X225,X226)
        | ~ ssList(X226)
        | ~ ssList(X225) )
      & ( nil != X226
        | nil != X225
        | nil = app(X225,X226)
        | ~ ssList(X226)
        | ~ ssList(X225) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_21,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

fof(c_0_24,negated_conjecture,
    ! [X255,X256] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & nil = esk49_0
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & nil != esk48_0
      & ( memberP(esk50_0,X255)
        | ~ ssList(X256)
        | ~ segmentP(esk51_0,app(app(cons(X255,nil),X256),cons(X255,nil)))
        | ~ ssItem(X255) )
      & ( ssList(esk52_1(X255))
        | ~ memberP(esk50_0,X255)
        | ~ ssItem(X255) )
      & ( segmentP(esk51_0,app(app(cons(X255,nil),esk52_1(X255)),cons(X255,nil)))
        | ~ memberP(esk50_0,X255)
        | ~ ssItem(X255) ) ),
    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_17])])])])]) ).

cnf(c_0_25,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X3,X2) != app(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_27,plain,
    ! [X132,X133,X134] :
      ( ~ ssList(X132)
      | ~ ssList(X133)
      | ~ ssItem(X134)
      | cons(X134,app(X133,X132)) = app(cons(X134,X133),X132) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).

fof(c_0_28,plain,
    ! [X111,X112] :
      ( ~ ssList(X111)
      | ~ ssItem(X112)
      | ssList(cons(X112,X111)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

fof(c_0_29,plain,
    ! [X122,X123] :
      ( ~ ssList(X122)
      | ~ ssItem(X123)
      | nil != cons(X123,X122) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).

cnf(c_0_30,plain,
    ( nil = X1
    | nil != app(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_31,plain,
    ( app(X1,app(nil,X2)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).

fof(c_0_32,plain,
    ! [X130,X131] :
      ( ~ ssList(X130)
      | ~ ssList(X131)
      | ssList(app(X130,X131)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_33,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,negated_conjecture,
    nil = esk49_0,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_35,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_25,c_0_26]),c_0_23])]) ).

cnf(c_0_36,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_37,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_38,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_39,plain,
    ( app(nil,X1) = nil
    | app(X2,X1) != nil
    | ~ ssList(app(nil,X1))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_40,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_41,plain,
    ( nil = app(X2,X1)
    | nil != X1
    | nil != X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_42,plain,
    ! [X187,X188] :
      ( ~ ssList(X187)
      | ~ ssList(X188)
      | ~ segmentP(X187,X188)
      | ~ segmentP(X188,X187)
      | X187 = X188 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])]) ).

cnf(c_0_43,negated_conjecture,
    ( segmentP(esk51_0,app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)))
    | ~ memberP(esk50_0,X1)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_44,negated_conjecture,
    esk51_0 = nil,
    inference(rw,[status(thm)],[c_0_33,c_0_34]) ).

fof(c_0_45,plain,
    ! [X194] :
      ( ~ ssList(X194)
      | segmentP(X194,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).

cnf(c_0_46,plain,
    ( cons(X1,app(X2,X3)) != X3
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]) ).

cnf(c_0_47,plain,
    ( app(nil,X1) = nil
    | app(X2,X1) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_23])]) ).

cnf(c_0_48,plain,
    ( app(nil,app(X1,X2)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_23])]) ).

cnf(c_0_49,plain,
    ( ssList(cons(X1,app(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_37]) ).

cnf(c_0_50,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_41])]),c_0_23])]) ).

cnf(c_0_51,plain,
    ( X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ segmentP(X1,X2)
    | ~ segmentP(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_52,negated_conjecture,
    ( segmentP(nil,app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)))
    | ~ memberP(esk50_0,X1)
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_53,plain,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_54,plain,
    ( cons(X1,app(X2,app(X3,X4))) != X4
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_21]),c_0_40]) ).

cnf(c_0_55,plain,
    ( app(nil,app(X1,X2)) = nil
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_23])]),c_0_40]) ).

cnf(c_0_56,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_23])]) ).

cnf(c_0_57,negated_conjecture,
    ( app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)) = nil
    | ~ memberP(esk50_0,X1)
    | ~ ssList(app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)))
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_23])]),c_0_53]) ).

fof(c_0_58,plain,
    ! [X154,X155,X156] :
      ( ( ~ memberP(cons(X155,X156),X154)
        | X154 = X155
        | memberP(X156,X154)
        | ~ ssList(X156)
        | ~ ssItem(X155)
        | ~ ssItem(X154) )
      & ( X154 != X155
        | memberP(cons(X155,X156),X154)
        | ~ ssList(X156)
        | ~ ssItem(X155)
        | ~ ssItem(X154) )
      & ( ~ memberP(X156,X154)
        | memberP(cons(X155,X156),X154)
        | ~ ssList(X156)
        | ~ ssItem(X155)
        | ~ ssItem(X154) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).

cnf(c_0_59,plain,
    ( app(X1,cons(X2,nil)) != nil
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_23])])]),c_0_56]) ).

cnf(c_0_60,negated_conjecture,
    ( app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)) = nil
    | ~ memberP(esk50_0,X1)
    | ~ ssList(app(cons(X1,nil),esk52_1(X1)))
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_40]),c_0_56]) ).

cnf(c_0_61,plain,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

fof(c_0_62,plain,
    ! [X119] :
      ( ( ssList(esk44_1(X119))
        | nil = X119
        | ~ ssList(X119) )
      & ( ssItem(esk45_1(X119))
        | nil = X119
        | ~ ssList(X119) )
      & ( cons(esk45_1(X119),esk44_1(X119)) = X119
        | nil = X119
        | ~ ssList(X119) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).

cnf(c_0_63,negated_conjecture,
    ( ~ memberP(esk50_0,X1)
    | ~ ssList(app(cons(X1,nil),esk52_1(X1)))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_64,negated_conjecture,
    ( ssList(esk52_1(X1))
    | ~ memberP(esk50_0,X1)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_65,plain,
    ( memberP(cons(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_61]) ).

cnf(c_0_66,plain,
    ( cons(esk45_1(X1),esk44_1(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_67,plain,
    ( ssItem(esk45_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_68,plain,
    ( ssList(esk44_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_69,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_70,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_71,negated_conjecture,
    nil != esk48_0,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_72,negated_conjecture,
    ( ~ memberP(esk50_0,X1)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_40]),c_0_64]),c_0_56]) ).

cnf(c_0_73,plain,
    ( nil = X1
    | memberP(X1,esk45_1(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68]) ).

cnf(c_0_74,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_75,negated_conjecture,
    esk50_0 != nil,
    inference(rw,[status(thm)],[c_0_71,c_0_70]) ).

cnf(c_0_76,negated_conjecture,
    ~ ssItem(esk45_1(esk50_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]),c_0_75]) ).

cnf(c_0_77,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_67]),c_0_74])]),c_0_75]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SWC045+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32  % Computer : n015.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon Aug 28 17:27:55 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.18/0.57  start to proof: theBenchmark
% 93.94/94.16  % Version  : CSE_E---1.5
% 93.94/94.16  % Problem  : theBenchmark.p
% 93.94/94.16  % Proof found
% 93.94/94.16  % SZS status Theorem for theBenchmark.p
% 93.94/94.16  % SZS output start Proof
% See solution above
% 93.94/94.17  % Total time : 93.533000 s
% 93.94/94.17  % SZS output end Proof
% 93.94/94.17  % Total time : 93.542000 s
%------------------------------------------------------------------------------