TSTP Solution File: SWC110+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC110+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 : n013.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 20:19:54 EDT 2023

% Result   : Theorem 0.54s 0.82s
% Output   : CNFRefutation 0.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   91
% Syntax   : Number of formulae    :  177 (  27 unt;  76 typ;   0 def)
%            Number of atoms       :  388 ( 103 equ)
%            Maximal formula atoms :   26 (   3 avg)
%            Number of connectives :  488 ( 201   ~; 198   |;  44   &)
%                                         (   5 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   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    :   57 (  57 usr;   8 con; 0-2 aty)
%            Number of variables   :  148 (   0 sgn;  71   !;  10   ?;   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 ).

fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ! [X5] :
                        ( ssList(X5)
                       => ( app(X3,X5) != X4
                          | ~ equalelemsP(X3)
                          | ? [X6] :
                              ( ssItem(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(cons(X6,nil),X7) = X5
                                  & ? [X8] :
                                      ( ssList(X8)
                                      & app(X8,cons(X6,nil)) = X3 ) ) ) ) )
                    | ( nil != X4
                      & nil = X3 )
                    | ( ( nil != X2
                        | nil = X1 )
                      & ( ~ neq(X2,nil)
                        | ( neq(X1,nil)
                          & segmentP(X2,X1) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

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

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

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(ax47,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( ( rearsegP(X1,X2)
                  & rearsegP(X2,X3) )
               => rearsegP(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax47) ).

fof(ax51,axiom,
    ! [X1] :
      ( ssList(X1)
     => rearsegP(X1,nil) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax51) ).

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(ax7,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( segmentP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,X2),X4) = X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).

fof(ax43,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( frontsegP(X1,X2)
               => frontsegP(app(X1,X3),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax43) ).

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

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)
                         => ( app(X3,X5) != X4
                            | ~ equalelemsP(X3)
                            | ? [X6] :
                                ( ssItem(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(cons(X6,nil),X7) = X5
                                    & ? [X8] :
                                        ( ssList(X8)
                                        & app(X8,cons(X6,nil)) = X3 ) ) ) ) )
                      | ( nil != X4
                        & nil = X3 )
                      | ( ( nil != X2
                          | nil = X1 )
                        & ( ~ neq(X2,nil)
                          | ( neq(X1,nil)
                            & segmentP(X2,X1) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_16,negated_conjecture,
    ! [X258,X259,X260] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & ssList(esk52_0)
      & app(esk50_0,esk52_0) = esk51_0
      & equalelemsP(esk50_0)
      & ( ~ ssItem(X258)
        | ~ ssList(X259)
        | app(cons(X258,nil),X259) != esk52_0
        | ~ ssList(X260)
        | app(X260,cons(X258,nil)) != esk50_0 )
      & ( nil = esk51_0
        | nil != esk50_0 )
      & ( neq(esk49_0,nil)
        | nil = esk49_0 )
      & ( ~ neq(esk48_0,nil)
        | ~ segmentP(esk49_0,esk48_0)
        | nil = esk49_0 )
      & ( neq(esk49_0,nil)
        | nil != esk48_0 )
      & ( ~ neq(esk48_0,nil)
        | ~ segmentP(esk49_0,esk48_0)
        | nil != esk48_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_15])])])])]) ).

fof(c_0_17,plain,
    ! [X224,X225,X226] :
      ( ~ ssList(X224)
      | ~ ssList(X225)
      | ~ ssList(X226)
      | app(app(X224,X225),X226) = app(X224,app(X225,X226)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).

cnf(c_0_18,negated_conjecture,
    app(esk50_0,esk52_0) = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_21,plain,
    ! [X26,X27,X29] :
      ( ( ssList(esk7_2(X26,X27))
        | ~ rearsegP(X26,X27)
        | ~ ssList(X27)
        | ~ ssList(X26) )
      & ( app(esk7_2(X26,X27),X27) = X26
        | ~ rearsegP(X26,X27)
        | ~ ssList(X27)
        | ~ ssList(X26) )
      & ( ~ ssList(X29)
        | app(X29,X27) != X26
        | rearsegP(X26,X27)
        | ~ ssList(X27)
        | ~ ssList(X26) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).

fof(c_0_22,plain,
    ! [X132,X133] :
      ( ~ ssList(X132)
      | ~ ssList(X133)
      | ssList(app(X132,X133)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_23,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24,negated_conjecture,
    app(esk48_0,esk52_0) = esk49_0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    ssList(esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_26,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_27,plain,
    ! [X229] :
      ( ~ ssList(X229)
      | app(X229,nil) = X229 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

cnf(c_0_28,plain,
    ( rearsegP(X3,X2)
    | ~ ssList(X1)
    | app(X1,X2) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_29,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_30,plain,
    ! [X181,X182,X183] :
      ( ~ ssList(X181)
      | ~ ssList(X182)
      | ~ ssList(X183)
      | ~ rearsegP(X181,X182)
      | rearsegP(app(X183,X181),X182) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).

cnf(c_0_31,negated_conjecture,
    ( app(esk48_0,app(esk52_0,X1)) = app(esk49_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).

cnf(c_0_32,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_33,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

fof(c_0_34,plain,
    ! [X175,X176,X177] :
      ( ~ ssList(X175)
      | ~ ssList(X176)
      | ~ ssList(X177)
      | ~ rearsegP(X175,X176)
      | ~ rearsegP(X176,X177)
      | rearsegP(X175,X177) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax47])])]) ).

cnf(c_0_35,plain,
    ( rearsegP(app(X1,X2),X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_29]) ).

cnf(c_0_36,plain,
    ( rearsegP(app(X3,X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ rearsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_37,negated_conjecture,
    app(esk49_0,nil) = esk49_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_24]),c_0_33]),c_0_25])]) ).

cnf(c_0_38,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_39,plain,
    ( rearsegP(X1,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ rearsegP(X1,X2)
    | ~ rearsegP(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_40,negated_conjecture,
    rearsegP(esk49_0,esk52_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_24]),c_0_25]),c_0_26])]) ).

cnf(c_0_41,plain,
    ( rearsegP(app(X1,app(X2,X3)),X3)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_35]),c_0_29]) ).

cnf(c_0_42,negated_conjecture,
    ( app(esk49_0,app(nil,X1)) = app(esk49_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_37]),c_0_33]),c_0_38])]) ).

cnf(c_0_43,negated_conjecture,
    ( rearsegP(X1,esk52_0)
    | ~ rearsegP(X1,esk49_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25]),c_0_38])]) ).

cnf(c_0_44,negated_conjecture,
    ( rearsegP(app(esk49_0,X1),X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_38]),c_0_33])]) ).

cnf(c_0_45,negated_conjecture,
    ( rearsegP(app(esk49_0,esk49_0),esk52_0)
    | ~ ssList(app(esk49_0,esk49_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_38])]) ).

fof(c_0_46,plain,
    ! [X184] :
      ( ~ ssList(X184)
      | rearsegP(X184,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).

cnf(c_0_47,plain,
    ( app(esk7_2(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_48,negated_conjecture,
    rearsegP(app(esk49_0,esk49_0),esk52_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_29]),c_0_38])]) ).

cnf(c_0_49,plain,
    ( ssList(esk7_2(X1,X2))
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_50,plain,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_51,negated_conjecture,
    ( app(esk7_2(app(esk49_0,esk49_0),esk52_0),esk52_0) = app(esk49_0,esk49_0)
    | ~ ssList(app(esk49_0,esk49_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_25])]) ).

cnf(c_0_52,negated_conjecture,
    ( ssList(esk7_2(app(esk49_0,esk49_0),esk52_0))
    | ~ ssList(app(esk49_0,esk49_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_48]),c_0_25])]) ).

fof(c_0_53,plain,
    ! [X22,X23,X25] :
      ( ( ssList(esk6_2(X22,X23))
        | ~ frontsegP(X22,X23)
        | ~ ssList(X23)
        | ~ ssList(X22) )
      & ( app(X23,esk6_2(X22,X23)) = X22
        | ~ frontsegP(X22,X23)
        | ~ ssList(X23)
        | ~ ssList(X22) )
      & ( ~ ssList(X25)
        | app(X23,X25) != X22
        | frontsegP(X22,X23)
        | ~ ssList(X23)
        | ~ ssList(X22) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).

cnf(c_0_54,plain,
    ( rearsegP(app(X1,X2),nil)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_50]),c_0_33])]) ).

cnf(c_0_55,negated_conjecture,
    app(esk7_2(app(esk49_0,esk49_0),esk52_0),esk52_0) = app(esk49_0,esk49_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_29]),c_0_38])]) ).

cnf(c_0_56,negated_conjecture,
    ssList(esk7_2(app(esk49_0,esk49_0),esk52_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_29]),c_0_38])]) ).

fof(c_0_57,plain,
    ! [X30,X31,X34,X35] :
      ( ( ssList(esk8_2(X30,X31))
        | ~ segmentP(X30,X31)
        | ~ ssList(X31)
        | ~ ssList(X30) )
      & ( ssList(esk9_2(X30,X31))
        | ~ segmentP(X30,X31)
        | ~ ssList(X31)
        | ~ ssList(X30) )
      & ( app(app(esk8_2(X30,X31),X31),esk9_2(X30,X31)) = X30
        | ~ segmentP(X30,X31)
        | ~ ssList(X31)
        | ~ ssList(X30) )
      & ( ~ ssList(X34)
        | ~ ssList(X35)
        | app(app(X34,X31),X35) != X30
        | segmentP(X30,X31)
        | ~ ssList(X31)
        | ~ ssList(X30) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).

fof(c_0_58,plain,
    ! [X166,X167,X168] :
      ( ~ ssList(X166)
      | ~ ssList(X167)
      | ~ ssList(X168)
      | ~ frontsegP(X166,X167)
      | frontsegP(app(X166,X168),X167) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).

cnf(c_0_59,plain,
    ( frontsegP(X3,X2)
    | ~ ssList(X1)
    | app(X2,X1) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_60,negated_conjecture,
    rearsegP(app(esk49_0,esk49_0),nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_25])]) ).

cnf(c_0_61,negated_conjecture,
    ssList(app(esk49_0,esk49_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_55]),c_0_25]),c_0_56])]) ).

cnf(c_0_62,plain,
    ( app(esk7_2(X1,nil),nil) = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_50]),c_0_33])]) ).

cnf(c_0_63,plain,
    ( ssList(esk7_2(X1,nil))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_33])]) ).

cnf(c_0_64,plain,
    ( segmentP(X4,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(app(X1,X3),X2) != X4
    | ~ ssList(X3)
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

fof(c_0_65,plain,
    ! [X137] :
      ( ~ ssList(X137)
      | app(nil,X137) = X137 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

fof(c_0_66,plain,
    ! [X227,X228] :
      ( ( nil = X228
        | nil != app(X227,X228)
        | ~ ssList(X228)
        | ~ ssList(X227) )
      & ( nil = X227
        | nil != app(X227,X228)
        | ~ ssList(X228)
        | ~ ssList(X227) )
      & ( nil != X228
        | nil != X227
        | nil = app(X227,X228)
        | ~ ssList(X228)
        | ~ ssList(X227) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_67,plain,
    ( frontsegP(app(X1,X3),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ frontsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_68,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_29]) ).

cnf(c_0_69,negated_conjecture,
    app(esk7_2(app(esk49_0,esk49_0),nil),nil) = app(esk49_0,esk49_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_60]),c_0_33]),c_0_61])]) ).

cnf(c_0_70,plain,
    ( esk7_2(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_62]),c_0_63]) ).

cnf(c_0_71,plain,
    ( segmentP(app(app(X1,X2),X3),X2)
    | ~ ssList(app(app(X1,X2),X3))
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[c_0_64]) ).

cnf(c_0_72,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_73,plain,
    ( nil = X1
    | nil != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_74,plain,
    ( frontsegP(app(app(X1,X2),X3),X1)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_29]) ).

cnf(c_0_75,negated_conjecture,
    app(app(esk49_0,esk49_0),nil) = app(esk49_0,esk49_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_61])]) ).

cnf(c_0_76,plain,
    ( segmentP(app(X1,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_33])]),c_0_29]) ).

cnf(c_0_77,negated_conjecture,
    ( esk48_0 = nil
    | app(esk49_0,X1) != nil
    | ~ ssList(app(esk52_0,X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_31]),c_0_26])]) ).

cnf(c_0_78,plain,
    ( app(X1,esk6_2(X2,X1)) = X2
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_79,negated_conjecture,
    frontsegP(app(esk49_0,esk49_0),esk49_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_33]),c_0_38])]) ).

cnf(c_0_80,plain,
    ( ssList(esk6_2(X1,X2))
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_81,negated_conjecture,
    ( nil = esk49_0
    | ~ neq(esk48_0,nil)
    | ~ segmentP(esk49_0,esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_82,negated_conjecture,
    segmentP(esk49_0,esk48_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_24]),c_0_26]),c_0_25])]) ).

fof(c_0_83,plain,
    ! [X111,X112] :
      ( ( ~ neq(X111,X112)
        | X111 != X112
        | ~ ssList(X112)
        | ~ ssList(X111) )
      & ( X111 = X112
        | neq(X111,X112)
        | ~ ssList(X112)
        | ~ ssList(X111) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

cnf(c_0_84,negated_conjecture,
    ( nil = esk51_0
    | nil != esk50_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_85,negated_conjecture,
    ( esk48_0 = nil
    | app(esk49_0,X1) != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_29]),c_0_25])]) ).

cnf(c_0_86,negated_conjecture,
    app(esk49_0,esk6_2(app(esk49_0,esk49_0),esk49_0)) = app(esk49_0,esk49_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_61]),c_0_38])]) ).

cnf(c_0_87,negated_conjecture,
    ssList(esk6_2(app(esk49_0,esk49_0),esk49_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_79]),c_0_38]),c_0_61])]) ).

cnf(c_0_88,negated_conjecture,
    ( esk49_0 = nil
    | ~ neq(esk48_0,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]) ).

cnf(c_0_89,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_83]) ).

cnf(c_0_90,negated_conjecture,
    ( esk49_0 = nil
    | esk48_0 != nil ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_20]),c_0_19]) ).

cnf(c_0_91,plain,
    ( nil = app(X2,X1)
    | nil != X1
    | nil != X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_92,negated_conjecture,
    ( ~ neq(esk48_0,nil)
    | ~ segmentP(esk49_0,esk48_0)
    | nil != esk48_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_93,negated_conjecture,
    ( esk48_0 = nil
    | app(esk49_0,esk49_0) != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).

cnf(c_0_94,negated_conjecture,
    esk49_0 = nil,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_33]),c_0_26])]),c_0_90]) ).

cnf(c_0_95,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_91])]),c_0_33])]) ).

cnf(c_0_96,negated_conjecture,
    ( esk48_0 != nil
    | ~ neq(esk48_0,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_82])]) ).

cnf(c_0_97,negated_conjecture,
    esk48_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_94]),c_0_95])]) ).

cnf(c_0_98,negated_conjecture,
    ( neq(esk49_0,nil)
    | nil != esk48_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_99,negated_conjecture,
    ~ neq(nil,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_97])]) ).

cnf(c_0_100,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_94]),c_0_97])]),c_0_99]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC110+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n013.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 18:33:16 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.54/0.82  % Version  : CSE_E---1.5
% 0.54/0.82  % Problem  : theBenchmark.p
% 0.54/0.82  % Proof found
% 0.54/0.82  % SZS status Theorem for theBenchmark.p
% 0.54/0.82  % SZS output start Proof
% See solution above
% 0.81/0.83  % Total time : 0.249000 s
% 0.81/0.83  % SZS output end Proof
% 0.81/0.83  % Total time : 0.255000 s
%------------------------------------------------------------------------------