TSTP Solution File: SWC084+1 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SWC084+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% 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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:41:24 EDT 2023

% Result   : Theorem 16.58s 2.60s
% Output   : CNFRefutation 16.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  117 (  25 unt;   0 def)
%            Number of atoms       :  444 ( 138 equ)
%            Maximal formula atoms :   33 (   3 avg)
%            Number of connectives :  555 ( 228   ~; 234   |;  43   &)
%                                         (   4 <=>;  46  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :  173 (   0 sgn;  82   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ax79,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X3,X2) = app(X1,X2)
               => X3 = X1 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax79) ).

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/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax82) ).

fof(ax26,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax26) ).

fof(ax28,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax28) ).

fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ~ neq(X2,nil)
                    | ? [X5] :
                        ( ssList(X5)
                        & neq(X5,nil)
                        & segmentP(X2,X5)
                        & segmentP(X1,X5) )
                    | ( ! [X6] :
                          ( ssItem(X6)
                         => ( cons(X6,nil) != X3
                            | ~ memberP(X4,X6)
                            | ? [X7] :
                                ( ssItem(X7)
                                & X6 != X7
                                & memberP(X4,X7)
                                & leq(X6,X7) ) ) )
                      & ( nil != X4
                        | nil != X3 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',co1) ).

fof(ax17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax17) ).

fof(ax81,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax81) ).

fof(ax83,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax83) ).

fof(ax80,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X2,X3) = app(X2,X1)
               => X3 = X1 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax80) ).

fof(ax84,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax84) ).

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/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax7) ).

fof(ax56,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( segmentP(X1,X2)
                   => segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax56) ).

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/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax3) ).

fof(ax15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax15) ).

fof(ax18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax18) ).

fof(ax16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax16) ).

fof(ax21,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p',ax21) ).

fof(c_0_17,plain,
    ! [X92,X93,X94] :
      ( ~ ssList(X92)
      | ~ ssList(X93)
      | ~ ssList(X94)
      | app(X94,X93) != app(X92,X93)
      | X94 = X92 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).

fof(c_0_18,plain,
    ! [X98,X99,X100] :
      ( ~ ssList(X98)
      | ~ ssList(X99)
      | ~ ssList(X100)
      | app(app(X98,X99),X100) = app(X98,app(X99,X100)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).

fof(c_0_19,plain,
    ! [X89,X90] :
      ( ~ ssList(X89)
      | ~ ssList(X90)
      | ssList(app(X89,X90)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

fof(c_0_20,plain,
    ! [X91] :
      ( ~ ssList(X91)
      | app(nil,X91) = X91 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

fof(c_0_21,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ neq(X2,nil)
                      | ? [X5] :
                          ( ssList(X5)
                          & neq(X5,nil)
                          & segmentP(X2,X5)
                          & segmentP(X1,X5) )
                      | ( ! [X6] :
                            ( ssItem(X6)
                           => ( cons(X6,nil) != X3
                              | ~ memberP(X4,X6)
                              | ? [X7] :
                                  ( ssItem(X7)
                                  & X6 != X7
                                  & memberP(X4,X7)
                                  & leq(X6,X7) ) ) )
                        & ( nil != X4
                          | nil != X3 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

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

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_18]) ).

cnf(c_0_24,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

fof(c_0_27,negated_conjecture,
    ! [X12,X14] :
      ( ssList(esk1_0)
      & ssList(esk2_0)
      & ssList(esk3_0)
      & ssList(esk4_0)
      & esk2_0 = esk4_0
      & esk1_0 = esk3_0
      & neq(esk2_0,nil)
      & ( ~ ssList(X12)
        | ~ neq(X12,nil)
        | ~ segmentP(esk2_0,X12)
        | ~ segmentP(esk1_0,X12) )
      & ( nil = esk4_0
        | ssItem(esk5_0) )
      & ( nil = esk3_0
        | ssItem(esk5_0) )
      & ( nil = esk4_0
        | cons(esk5_0,nil) = esk3_0 )
      & ( nil = esk3_0
        | cons(esk5_0,nil) = esk3_0 )
      & ( nil = esk4_0
        | memberP(esk4_0,esk5_0) )
      & ( nil = esk3_0
        | memberP(esk4_0,esk5_0) )
      & ( nil = esk4_0
        | ~ ssItem(X14)
        | esk5_0 = X14
        | ~ memberP(esk4_0,X14)
        | ~ leq(esk5_0,X14) )
      & ( nil = esk3_0
        | ~ ssItem(X14)
        | esk5_0 = X14
        | ~ memberP(esk4_0,X14)
        | ~ leq(esk5_0,X14) ) ),
    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_21])])])])]) ).

fof(c_0_28,plain,
    ! [X59,X60] :
      ( ~ ssList(X59)
      | ~ ssItem(X60)
      | cons(X60,X59) = app(cons(X60,nil),X59) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

fof(c_0_29,plain,
    ! [X101,X102] :
      ( ( nil = X102
        | nil != app(X101,X102)
        | ~ ssList(X102)
        | ~ ssList(X101) )
      & ( nil = X101
        | nil != app(X101,X102)
        | ~ ssList(X102)
        | ~ ssList(X101) )
      & ( nil != X102
        | nil != X101
        | nil = app(X101,X102)
        | ~ ssList(X102)
        | ~ ssList(X101) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_30,plain,
    ( X1 = app(X2,X3)
    | app(X1,X4) != app(X2,app(X3,X4))
    | ~ ssList(X4)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_31,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_23,c_0_25]),c_0_26])]) ).

cnf(c_0_32,negated_conjecture,
    ssList(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_33,negated_conjecture,
    esk2_0 = esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_34,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_35,negated_conjecture,
    ( nil = esk3_0
    | cons(esk5_0,nil) = esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_36,negated_conjecture,
    ( nil = esk3_0
    | ssItem(esk5_0) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

fof(c_0_37,plain,
    ! [X95,X96,X97] :
      ( ~ ssList(X95)
      | ~ ssList(X96)
      | ~ ssList(X97)
      | app(X96,X97) != app(X96,X95)
      | X97 = X95 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).

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

fof(c_0_39,plain,
    ! [X103] :
      ( ~ ssList(X103)
      | app(X103,nil) = X103 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

cnf(c_0_40,plain,
    ( X1 = app(nil,X2)
    | app(X1,X3) != app(X2,X3)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_26])]) ).

cnf(c_0_41,negated_conjecture,
    ssList(esk4_0),
    inference(rw,[status(thm)],[c_0_32,c_0_33]) ).

fof(c_0_42,plain,
    ! [X61,X62,X65,X66] :
      ( ( ssList(esk12_2(X61,X62))
        | ~ segmentP(X61,X62)
        | ~ ssList(X62)
        | ~ ssList(X61) )
      & ( ssList(esk13_2(X61,X62))
        | ~ segmentP(X61,X62)
        | ~ ssList(X62)
        | ~ ssList(X61) )
      & ( app(app(esk12_2(X61,X62),X62),esk13_2(X61,X62)) = X61
        | ~ segmentP(X61,X62)
        | ~ ssList(X62)
        | ~ ssList(X61) )
      & ( ~ ssList(X65)
        | ~ ssList(X66)
        | app(app(X65,X62),X66) != X61
        | segmentP(X61,X62)
        | ~ ssList(X62)
        | ~ ssList(X61) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).

cnf(c_0_43,negated_conjecture,
    ( cons(esk5_0,X1) = app(esk3_0,X1)
    | esk3_0 = nil
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_44,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X2,X3) != app(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_45,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_38])]),c_0_26])]) ).

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

cnf(c_0_47,plain,
    ( ssList(app(X1,app(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_24]) ).

cnf(c_0_48,negated_conjecture,
    ( X1 = app(nil,X2)
    | app(X1,esk4_0) != app(X2,esk4_0)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_49,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_42]) ).

fof(c_0_50,plain,
    ! [X73,X74,X75,X76] :
      ( ~ ssList(X73)
      | ~ ssList(X74)
      | ~ ssList(X75)
      | ~ ssList(X76)
      | ~ segmentP(X73,X74)
      | segmentP(app(app(X75,X73),X76),X74) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])]) ).

cnf(c_0_51,negated_conjecture,
    ( cons(esk5_0,nil) = app(esk3_0,nil)
    | esk3_0 = nil ),
    inference(spm,[status(thm)],[c_0_43,c_0_26]) ).

cnf(c_0_52,negated_conjecture,
    ssList(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_53,negated_conjecture,
    esk1_0 = esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_54,plain,
    ( X1 = nil
    | app(nil,X1) != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_26])]) ).

cnf(c_0_55,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_23]),c_0_26])]),c_0_24]) ).

cnf(c_0_56,plain,
    ( ssList(app(X1,nil))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_45]),c_0_26])]) ).

cnf(c_0_57,negated_conjecture,
    ( app(nil,X1) = esk4_0
    | app(esk4_0,esk4_0) != app(X1,esk4_0)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_41]) ).

cnf(c_0_58,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(X1,nil)
    | ~ segmentP(esk2_0,X1)
    | ~ segmentP(esk1_0,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_59,negated_conjecture,
    neq(esk2_0,nil),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_60,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_49]) ).

cnf(c_0_61,plain,
    ( segmentP(app(app(X3,X1),X4),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssList(X4)
    | ~ segmentP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_62,negated_conjecture,
    ( app(esk3_0,nil) = esk3_0
    | esk3_0 = nil ),
    inference(spm,[status(thm)],[c_0_35,c_0_51]) ).

cnf(c_0_63,negated_conjecture,
    ssList(esk3_0),
    inference(rw,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_64,plain,
    ( app(X1,nil) = nil
    | app(nil,X1) != nil
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_26])]),c_0_56]) ).

cnf(c_0_65,negated_conjecture,
    app(nil,esk4_0) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_57]),c_0_41])]) ).

cnf(c_0_66,negated_conjecture,
    ( ~ segmentP(esk3_0,X1)
    | ~ segmentP(esk4_0,X1)
    | ~ ssList(X1)
    | ~ neq(X1,nil) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_53]),c_0_33]) ).

cnf(c_0_67,negated_conjecture,
    neq(esk4_0,nil),
    inference(rw,[status(thm)],[c_0_59,c_0_33]) ).

cnf(c_0_68,plain,
    ( segmentP(app(X1,X2),X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_46]),c_0_26])]),c_0_24]) ).

cnf(c_0_69,plain,
    ( segmentP(app(nil,X1),X2)
    | ~ segmentP(nil,X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_45]),c_0_26])]) ).

cnf(c_0_70,negated_conjecture,
    ( app(nil,esk3_0) = esk3_0
    | esk3_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_62]),c_0_26]),c_0_63])]) ).

cnf(c_0_71,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_60,c_0_25]),c_0_26])]),c_0_24]) ).

cnf(c_0_72,negated_conjecture,
    ( app(esk4_0,nil) = nil
    | esk4_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_41])]) ).

cnf(c_0_73,negated_conjecture,
    ( ~ segmentP(esk3_0,esk4_0)
    | ~ segmentP(esk4_0,esk4_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_41])]) ).

cnf(c_0_74,negated_conjecture,
    segmentP(esk4_0,esk4_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_65]),c_0_41]),c_0_26])]) ).

cnf(c_0_75,negated_conjecture,
    ( esk3_0 = nil
    | segmentP(esk3_0,X1)
    | ~ segmentP(nil,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_63])]) ).

cnf(c_0_76,negated_conjecture,
    ( segmentP(nil,esk4_0)
    | esk4_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_41]),c_0_26])]) ).

cnf(c_0_77,negated_conjecture,
    ~ segmentP(esk3_0,esk4_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]) ).

cnf(c_0_78,negated_conjecture,
    ( nil = esk4_0
    | cons(esk5_0,nil) = esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_79,negated_conjecture,
    ( nil = esk4_0
    | ssItem(esk5_0) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

fof(c_0_80,plain,
    ! [X33,X34,X37,X38] :
      ( ( ssList(esk8_2(X33,X34))
        | ~ memberP(X33,X34)
        | ~ ssItem(X34)
        | ~ ssList(X33) )
      & ( ssList(esk9_2(X33,X34))
        | ~ memberP(X33,X34)
        | ~ ssItem(X34)
        | ~ ssList(X33) )
      & ( app(esk8_2(X33,X34),cons(X34,esk9_2(X33,X34))) = X33
        | ~ memberP(X33,X34)
        | ~ ssItem(X34)
        | ~ ssList(X33) )
      & ( ~ ssList(X37)
        | ~ ssList(X38)
        | app(X37,cons(X34,X38)) != X33
        | memberP(X33,X34)
        | ~ ssItem(X34)
        | ~ ssList(X33) ) ),
    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_81,negated_conjecture,
    ( esk3_0 = nil
    | esk4_0 != nil ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_41])]),c_0_77]) ).

fof(c_0_82,plain,
    ! [X81,X82] :
      ( ( ~ neq(X81,X82)
        | X81 != X82
        | ~ ssList(X82)
        | ~ ssList(X81) )
      & ( X81 = X82
        | neq(X81,X82)
        | ~ ssList(X82)
        | ~ ssList(X81) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

cnf(c_0_83,negated_conjecture,
    ( cons(esk5_0,X1) = app(esk3_0,X1)
    | esk4_0 = nil
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_78]),c_0_79]) ).

cnf(c_0_84,plain,
    ( ssList(esk9_2(X1,X2))
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_80]) ).

fof(c_0_85,plain,
    ! [X50,X51] :
      ( ~ ssList(X50)
      | ~ ssItem(X51)
      | cons(X51,X50) != X50 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).

cnf(c_0_86,negated_conjecture,
    esk4_0 != nil,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_81]),c_0_76]) ).

cnf(c_0_87,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_82]) ).

fof(c_0_88,plain,
    ! [X48,X49] :
      ( ~ ssList(X48)
      | ~ ssItem(X49)
      | ssList(cons(X49,X48)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

fof(c_0_89,plain,
    ! [X18,X19] :
      ( ~ ssList(X18)
      | ~ ssItem(X19)
      | nil != cons(X19,X18) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).

cnf(c_0_90,negated_conjecture,
    ( cons(esk5_0,nil) = app(esk3_0,nil)
    | esk4_0 = nil ),
    inference(spm,[status(thm)],[c_0_83,c_0_26]) ).

cnf(c_0_91,negated_conjecture,
    ( cons(esk5_0,esk9_2(X1,X2)) = app(esk3_0,esk9_2(X1,X2))
    | esk3_0 = nil
    | ~ memberP(X1,X2)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(spm,[status(thm)],[c_0_43,c_0_84]) ).

cnf(c_0_92,negated_conjecture,
    ( nil = esk3_0
    | memberP(esk4_0,esk5_0) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_93,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_94,negated_conjecture,
    cons(esk5_0,nil) = esk3_0,
    inference(sr,[status(thm)],[c_0_78,c_0_86]) ).

cnf(c_0_95,negated_conjecture,
    ssItem(esk5_0),
    inference(sr,[status(thm)],[c_0_79,c_0_86]) ).

cnf(c_0_96,plain,
    ( X1 = nil
    | neq(X1,nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_87,c_0_26]) ).

cnf(c_0_97,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_88]) ).

cnf(c_0_98,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_89]) ).

cnf(c_0_99,negated_conjecture,
    ( app(esk3_0,nil) = esk3_0
    | esk4_0 = nil ),
    inference(spm,[status(thm)],[c_0_78,c_0_90]) ).

cnf(c_0_100,negated_conjecture,
    ( cons(esk5_0,esk9_2(esk4_0,esk5_0)) = app(esk3_0,esk9_2(esk4_0,esk5_0))
    | esk3_0 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_41])]),c_0_36]) ).

cnf(c_0_101,negated_conjecture,
    esk3_0 != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_26]),c_0_95])]) ).

cnf(c_0_102,negated_conjecture,
    ( nil = esk4_0
    | memberP(esk4_0,esk5_0) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_103,plain,
    ( neq(cons(X1,X2),nil)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]) ).

cnf(c_0_104,negated_conjecture,
    ( esk4_0 = nil
    | segmentP(esk3_0,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_99]),c_0_63]),c_0_26])]) ).

cnf(c_0_105,plain,
    ( app(esk8_2(X1,X2),cons(X2,esk9_2(X1,X2))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_80]) ).

cnf(c_0_106,negated_conjecture,
    cons(esk5_0,esk9_2(esk4_0,esk5_0)) = app(esk3_0,esk9_2(esk4_0,esk5_0)),
    inference(sr,[status(thm)],[c_0_100,c_0_101]) ).

cnf(c_0_107,negated_conjecture,
    memberP(esk4_0,esk5_0),
    inference(sr,[status(thm)],[c_0_102,c_0_86]) ).

cnf(c_0_108,negated_conjecture,
    ( ~ segmentP(esk3_0,cons(X1,X2))
    | ~ segmentP(esk4_0,cons(X1,X2))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_103]),c_0_97]) ).

cnf(c_0_109,negated_conjecture,
    segmentP(esk3_0,esk3_0),
    inference(sr,[status(thm)],[c_0_104,c_0_86]) ).

cnf(c_0_110,plain,
    ( segmentP(app(X1,app(X2,X3)),X2)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_23]),c_0_47]) ).

cnf(c_0_111,negated_conjecture,
    app(esk8_2(esk4_0,esk5_0),app(esk3_0,esk9_2(esk4_0,esk5_0))) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_41]),c_0_95])]) ).

cnf(c_0_112,negated_conjecture,
    ~ segmentP(esk4_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_94]),c_0_26]),c_0_95])]),c_0_109])]) ).

cnf(c_0_113,negated_conjecture,
    ( ~ ssList(esk9_2(esk4_0,esk5_0))
    | ~ ssList(esk8_2(esk4_0,esk5_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_63])]),c_0_112]) ).

cnf(c_0_114,negated_conjecture,
    ~ ssList(esk8_2(esk4_0,esk5_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_84]),c_0_107]),c_0_41]),c_0_95])]) ).

cnf(c_0_115,plain,
    ( ssList(esk8_2(X1,X2))
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_80]) ).

cnf(c_0_116,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_107]),c_0_41]),c_0_95])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : SWC084+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.11  % Command    : run_E %s %d THM
% 0.10/0.32  % Computer : n013.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit   : 2400
% 0.10/0.32  % WCLimit    : 300
% 0.10/0.32  % DateTime   : Tue Oct  3 01:57:14 EDT 2023
% 0.10/0.32  % CPUTime    : 
% 0.16/0.44  Running first-order model finding
% 0.16/0.44  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.WBfccRxpIe/E---3.1_31901.p
% 16.58/2.60  # Version: 3.1pre001
% 16.58/2.60  # Preprocessing class: FSLSSMSSSSSNFFN.
% 16.58/2.60  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.58/2.60  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.58/2.60  # Starting new_bool_3 with 300s (1) cores
% 16.58/2.60  # Starting new_bool_1 with 300s (1) cores
% 16.58/2.60  # Starting sh5l with 300s (1) cores
% 16.58/2.60  # new_bool_3 with pid 31979 completed with status 0
% 16.58/2.60  # Result found by new_bool_3
% 16.58/2.60  # Preprocessing class: FSLSSMSSSSSNFFN.
% 16.58/2.60  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.58/2.60  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.58/2.60  # Starting new_bool_3 with 300s (1) cores
% 16.58/2.60  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 16.58/2.60  # Search class: FGHSF-FFMM21-MFFFFFNN
% 16.58/2.60  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 16.58/2.60  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 16.58/2.60  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 31983 completed with status 0
% 16.58/2.60  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 16.58/2.60  # Preprocessing class: FSLSSMSSSSSNFFN.
% 16.58/2.60  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.58/2.60  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.58/2.60  # Starting new_bool_3 with 300s (1) cores
% 16.58/2.60  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 16.58/2.60  # Search class: FGHSF-FFMM21-MFFFFFNN
% 16.58/2.60  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 16.58/2.60  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 16.58/2.60  # Preprocessing time       : 0.002 s
% 16.58/2.60  # Presaturation interreduction done
% 16.58/2.60  
% 16.58/2.60  # Proof found!
% 16.58/2.60  # SZS status Theorem
% 16.58/2.60  # SZS output start CNFRefutation
% See solution above
% 16.58/2.60  # Parsed axioms                        : 96
% 16.58/2.60  # Removed by relevancy pruning/SinE    : 57
% 16.58/2.60  # Initial clauses                      : 76
% 16.58/2.60  # Removed in clause preprocessing      : 0
% 16.58/2.60  # Initial clauses in saturation        : 76
% 16.58/2.60  # Processed clauses                    : 11328
% 16.58/2.60  # ...of these trivial                  : 511
% 16.58/2.60  # ...subsumed                          : 7338
% 16.58/2.60  # ...remaining for further processing  : 3479
% 16.58/2.60  # Other redundant clauses eliminated   : 71
% 16.58/2.60  # Clauses deleted for lack of memory   : 0
% 16.58/2.60  # Backward-subsumed                    : 276
% 16.58/2.60  # Backward-rewritten                   : 298
% 16.58/2.60  # Generated clauses                    : 114229
% 16.58/2.60  # ...of the previous two non-redundant : 110959
% 16.58/2.60  # ...aggressively subsumed             : 0
% 16.58/2.60  # Contextual simplify-reflections      : 894
% 16.58/2.60  # Paramodulations                      : 113727
% 16.58/2.60  # Factorizations                       : 2
% 16.58/2.60  # NegExts                              : 0
% 16.58/2.60  # Equation resolutions                 : 103
% 16.58/2.60  # Total rewrite steps                  : 70457
% 16.58/2.60  # Propositional unsat checks           : 0
% 16.58/2.60  #    Propositional check models        : 0
% 16.58/2.60  #    Propositional check unsatisfiable : 0
% 16.58/2.60  #    Propositional clauses             : 0
% 16.58/2.60  #    Propositional clauses after purity: 0
% 16.58/2.60  #    Propositional unsat core size     : 0
% 16.58/2.60  #    Propositional preprocessing time  : 0.000
% 16.58/2.60  #    Propositional encoding time       : 0.000
% 16.58/2.60  #    Propositional solver time         : 0.000
% 16.58/2.60  #    Success case prop preproc time    : 0.000
% 16.58/2.60  #    Success case prop encoding time   : 0.000
% 16.58/2.60  #    Success case prop solver time     : 0.000
% 16.58/2.60  # Current number of processed clauses  : 2427
% 16.58/2.60  #    Positive orientable unit clauses  : 329
% 16.58/2.60  #    Positive unorientable unit clauses: 0
% 16.58/2.60  #    Negative unit clauses             : 267
% 16.58/2.60  #    Non-unit-clauses                  : 1831
% 16.58/2.60  # Current number of unprocessed clauses: 94216
% 16.58/2.60  # ...number of literals in the above   : 411219
% 16.58/2.60  # Current number of archived formulas  : 0
% 16.58/2.60  # Current number of archived clauses   : 1044
% 16.58/2.60  # Clause-clause subsumption calls (NU) : 327218
% 16.58/2.60  # Rec. Clause-clause subsumption calls : 107721
% 16.58/2.60  # Non-unit clause-clause subsumptions  : 5853
% 16.58/2.60  # Unit Clause-clause subsumption calls : 18406
% 16.58/2.60  # Rewrite failures with RHS unbound    : 0
% 16.58/2.60  # BW rewrite match attempts            : 1142
% 16.58/2.60  # BW rewrite match successes           : 32
% 16.58/2.60  # Condensation attempts                : 0
% 16.58/2.60  # Condensation successes               : 0
% 16.58/2.60  # Termbank termtop insertions          : 2701751
% 16.58/2.60  
% 16.58/2.60  # -------------------------------------------------
% 16.58/2.60  # User time                : 2.050 s
% 16.58/2.60  # System time              : 0.070 s
% 16.58/2.60  # Total time               : 2.120 s
% 16.58/2.60  # Maximum resident set size: 2044 pages
% 16.58/2.60  
% 16.58/2.60  # -------------------------------------------------
% 16.58/2.60  # User time                : 2.052 s
% 16.58/2.60  # System time              : 0.072 s
% 16.58/2.60  # Total time               : 2.124 s
% 16.58/2.60  # Maximum resident set size: 1800 pages
% 16.58/2.60  % E---3.1 exiting
%------------------------------------------------------------------------------