TSTP Solution File: SWC297+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SWC297+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n008.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 : Tue May 21 04:28:54 EDT 2024

% Result   : Theorem 0.89s 0.61s
% Output   : CNFRefutation 0.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   95 (  23 unt;   0 def)
%            Number of atoms       :  329 ( 121 equ)
%            Maximal formula atoms :   27 (   3 avg)
%            Number of connectives :  382 ( 148   ~; 144   |;  30   &)
%                                         (   3 <=>;  57  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;  10 con; 0-2 aty)
%            Number of variables   :  108 (   0 sgn  78   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ! [X5] :
                        ( ssItem(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ! [X7] :
                                ( ssList(X7)
                               => ( app(app(X6,cons(X5,nil)),X7) != X1
                                  | ! [X8] :
                                      ( ssItem(X8)
                                     => ( ( ~ memberP(X6,X8)
                                          | lt(X8,X5) )
                                        & ( ~ memberP(X7,X8)
                                          | lt(X5,X8) ) ) ) ) ) ) )
                    | ( nil != X3
                      & nil = X4 )
                    | ( ! [X9] :
                          ( ssItem(X9)
                         => ( cons(X9,nil) != X3
                            | ~ memberP(X4,X9) ) )
                      & neq(X4,nil) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(ax83,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).

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

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

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

fof(ax38,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).

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

fof(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/benchmark/Axioms/SWC001+0.ax',ax82) ).

fof(ax86,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).

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

fof(ax25,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => tl(cons(X2,X1)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).

fof(ax24,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).

fof(ax21,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).

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

fof(ax19,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => ! [X4] :
                  ( ssItem(X4)
                 => ( cons(X3,X1) = cons(X4,X2)
                   => ( X3 = X4
                      & X2 = X1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax19) ).

fof(c_0_15,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssItem(X5)
                         => ! [X6] :
                              ( ssList(X6)
                             => ! [X7] :
                                  ( ssList(X7)
                                 => ( app(app(X6,cons(X5,nil)),X7) != X1
                                    | ! [X8] :
                                        ( ssItem(X8)
                                       => ( ( ~ memberP(X6,X8)
                                            | lt(X8,X5) )
                                          & ( ~ memberP(X7,X8)
                                            | lt(X5,X8) ) ) ) ) ) ) )
                      | ( nil != X3
                        & nil = X4 )
                      | ( ! [X9] :
                            ( ssItem(X9)
                           => ( cons(X9,nil) != X3
                              | ~ memberP(X4,X9) ) )
                        & neq(X4,nil) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_16,negated_conjecture,
    ( ssList(esk48_0)
    & ssList(esk49_0)
    & ssList(esk50_0)
    & ssList(esk51_0)
    & esk49_0 = esk51_0
    & esk48_0 = esk50_0
    & ssItem(esk52_0)
    & ssList(esk53_0)
    & ssList(esk54_0)
    & app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0
    & ssItem(esk55_0)
    & ( memberP(esk54_0,esk55_0)
      | memberP(esk53_0,esk55_0) )
    & ( ~ lt(esk52_0,esk55_0)
      | memberP(esk53_0,esk55_0) )
    & ( memberP(esk54_0,esk55_0)
      | ~ lt(esk55_0,esk52_0) )
    & ( ~ lt(esk52_0,esk55_0)
      | ~ lt(esk55_0,esk52_0) )
    & ( nil = esk50_0
      | nil != esk51_0 )
    & ( ssItem(esk56_0)
      | ~ neq(esk51_0,nil) )
    & ( cons(esk56_0,nil) = esk50_0
      | ~ neq(esk51_0,nil) )
    & ( memberP(esk51_0,esk56_0)
      | ~ neq(esk51_0,nil) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).

fof(c_0_17,plain,
    ! [X228,X229] :
      ( ( nil = X229
        | nil != app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) )
      & ( nil = X228
        | nil != app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) )
      & ( nil != X229
        | nil != X228
        | nil = app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).

cnf(c_0_18,negated_conjecture,
    app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_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,plain,
    ( nil = X1
    | nil != app(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk50_0,
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_22,negated_conjecture,
    ssList(esk54_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_23,plain,
    ! [X133,X134] :
      ( ~ ssList(X133)
      | ~ ssList(X134)
      | ssList(app(X133,X134)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).

cnf(c_0_24,plain,
    ( nil = X1
    | nil != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,negated_conjecture,
    ( esk54_0 = nil
    | esk50_0 != nil
    | ~ ssList(app(esk53_0,cons(esk52_0,nil))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).

cnf(c_0_26,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    ssList(esk53_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_28,plain,
    ! [X114,X115] :
      ( ~ ssList(X114)
      | ~ ssItem(X115)
      | ssList(cons(X115,X114)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).

cnf(c_0_29,negated_conjecture,
    ( app(esk53_0,cons(esk52_0,nil)) = nil
    | esk50_0 != nil
    | ~ ssList(app(esk53_0,cons(esk52_0,nil))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_22])]) ).

cnf(c_0_30,negated_conjecture,
    ( esk54_0 = nil
    | esk50_0 != nil
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).

cnf(c_0_31,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_32,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_33,negated_conjecture,
    ssItem(esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_34,negated_conjecture,
    ( app(esk53_0,cons(esk52_0,nil)) = nil
    | esk50_0 != nil
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_27])]) ).

fof(c_0_35,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[ax38]) ).

cnf(c_0_36,negated_conjecture,
    ( memberP(esk54_0,esk55_0)
    | memberP(esk53_0,esk55_0) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_37,negated_conjecture,
    ( esk54_0 = nil
    | esk50_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]) ).

cnf(c_0_38,negated_conjecture,
    ( esk53_0 = nil
    | esk50_0 != nil
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_34]),c_0_27])]) ).

fof(c_0_39,plain,
    ! [X160] :
      ( ~ ssItem(X160)
      | ~ memberP(nil,X160) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).

cnf(c_0_40,negated_conjecture,
    ( memberP(nil,esk55_0)
    | memberP(esk53_0,esk55_0)
    | esk50_0 != nil ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_41,negated_conjecture,
    ( esk53_0 = nil
    | esk50_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_31]),c_0_32]),c_0_33])]) ).

fof(c_0_42,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    inference(fof_simplification,[status(thm)],[ax15]) ).

cnf(c_0_43,plain,
    ( ~ ssItem(X1)
    | ~ memberP(nil,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_44,negated_conjecture,
    ( memberP(nil,esk55_0)
    | esk50_0 != nil ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_45,negated_conjecture,
    ssItem(esk55_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_46,plain,
    ! [X225,X226,X227] :
      ( ~ ssList(X225)
      | ~ ssList(X226)
      | ~ ssList(X227)
      | app(app(X225,X226),X227) = app(X225,app(X226,X227)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).

fof(c_0_47,plain,
    ! [X112,X113] :
      ( ( ~ neq(X112,X113)
        | X112 != X113
        | ~ ssList(X113)
        | ~ ssList(X112) )
      & ( X112 = X113
        | neq(X112,X113)
        | ~ ssList(X113)
        | ~ ssList(X112) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])])]) ).

cnf(c_0_48,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_49,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_50,negated_conjecture,
    esk50_0 != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).

cnf(c_0_51,negated_conjecture,
    ( nil = esk50_0
    | nil != esk51_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_52,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
    inference(fof_simplification,[status(thm)],[ax86]) ).

cnf(c_0_53,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

fof(c_0_54,plain,
    ! [X223,X224] :
      ( ~ ssList(X223)
      | ~ ssItem(X224)
      | cons(X224,X223) = app(cons(X224,nil),X223) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).

fof(c_0_55,plain,
    ! [X131,X132] :
      ( ~ ssList(X131)
      | ~ ssItem(X132)
      | tl(cons(X132,X131)) = X131 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).

cnf(c_0_56,negated_conjecture,
    ( cons(esk56_0,nil) = esk50_0
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_57,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_58,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_59,negated_conjecture,
    esk51_0 != nil,
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_60,negated_conjecture,
    ( ssItem(esk56_0)
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_61,plain,
    ! [X233,X234] :
      ( ~ ssList(X233)
      | ~ ssList(X234)
      | nil = X233
      | tl(app(X233,X234)) = app(tl(X233),X234) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).

cnf(c_0_62,negated_conjecture,
    ( app(esk53_0,app(cons(esk52_0,nil),esk54_0)) = esk50_0
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_53]),c_0_22]),c_0_27])]) ).

cnf(c_0_63,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_64,plain,
    ( tl(cons(X2,X1)) = X1
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_65,negated_conjecture,
    cons(esk56_0,nil) = esk50_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_32]),c_0_58])]),c_0_59]) ).

cnf(c_0_66,negated_conjecture,
    ssItem(esk56_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_57]),c_0_32]),c_0_58])]),c_0_59]) ).

cnf(c_0_67,plain,
    ( nil = X1
    | tl(app(X1,X2)) = app(tl(X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_68,negated_conjecture,
    ( app(esk53_0,cons(esk52_0,esk54_0)) = esk50_0
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_22]),c_0_33])]) ).

cnf(c_0_69,negated_conjecture,
    tl(esk50_0) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_32]),c_0_66])]) ).

fof(c_0_70,plain,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    inference(fof_simplification,[status(thm)],[ax24]) ).

cnf(c_0_71,negated_conjecture,
    ( app(tl(esk53_0),cons(esk52_0,esk54_0)) = nil
    | esk53_0 = nil
    | ~ ssList(cons(esk52_0,esk54_0))
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_27])]) ).

fof(c_0_72,plain,
    ! [X130] :
      ( ~ ssList(X130)
      | nil = X130
      | ssList(tl(X130)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])]) ).

cnf(c_0_73,negated_conjecture,
    ( cons(esk52_0,esk54_0) = nil
    | esk53_0 = nil
    | ~ ssList(cons(esk52_0,esk54_0))
    | ~ ssList(cons(esk52_0,nil))
    | ~ ssList(tl(esk53_0)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_71]) ).

cnf(c_0_74,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_72]) ).

fof(c_0_75,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[ax21]) ).

cnf(c_0_76,negated_conjecture,
    ( cons(esk52_0,esk54_0) = nil
    | esk53_0 = nil
    | ~ ssList(cons(esk52_0,esk54_0))
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_27])]) ).

fof(c_0_77,plain,
    ! [X125,X126] :
      ( ~ ssList(X125)
      | ~ ssItem(X126)
      | nil != cons(X126,X125) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])]) ).

cnf(c_0_78,negated_conjecture,
    ( cons(esk52_0,esk54_0) = nil
    | esk53_0 = nil
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_31]),c_0_22]),c_0_33])]) ).

cnf(c_0_79,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_77]) ).

cnf(c_0_80,negated_conjecture,
    ( cons(esk52_0,esk54_0) = nil
    | esk53_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_31]),c_0_32]),c_0_33])]) ).

cnf(c_0_81,negated_conjecture,
    esk53_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_22]),c_0_33])]) ).

fof(c_0_82,plain,
    ! [X138] :
      ( ~ ssList(X138)
      | app(nil,X138) = X138 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).

cnf(c_0_83,negated_conjecture,
    app(app(nil,cons(esk52_0,nil)),esk54_0) = esk50_0,
    inference(spm,[status(thm)],[c_0_21,c_0_81]) ).

cnf(c_0_84,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_82]) ).

fof(c_0_85,plain,
    ! [X118,X119,X120,X121] :
      ( ( X120 = X121
        | cons(X120,X118) != cons(X121,X119)
        | ~ ssItem(X121)
        | ~ ssItem(X120)
        | ~ ssList(X119)
        | ~ ssList(X118) )
      & ( X119 = X118
        | cons(X120,X118) != cons(X121,X119)
        | ~ ssItem(X121)
        | ~ ssItem(X120)
        | ~ ssList(X119)
        | ~ ssList(X118) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])])]) ).

cnf(c_0_86,negated_conjecture,
    ( app(cons(esk52_0,nil),esk54_0) = esk50_0
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(spm,[status(thm)],[c_0_83,c_0_84]) ).

cnf(c_0_87,plain,
    ( X1 = X2
    | cons(X3,X2) != cons(X4,X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_88,negated_conjecture,
    ( cons(esk52_0,esk54_0) = esk50_0
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_86]),c_0_22]),c_0_33])]) ).

cnf(c_0_89,negated_conjecture,
    ( nil = X1
    | cons(X2,X1) != esk50_0
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_65]),c_0_32]),c_0_66])]) ).

cnf(c_0_90,negated_conjecture,
    cons(esk52_0,esk54_0) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_31]),c_0_32]),c_0_33])]) ).

cnf(c_0_91,negated_conjecture,
    ( memberP(esk54_0,esk55_0)
    | memberP(nil,esk55_0) ),
    inference(rw,[status(thm)],[c_0_36,c_0_81]) ).

cnf(c_0_92,negated_conjecture,
    esk54_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_22]),c_0_33])]) ).

cnf(c_0_93,negated_conjecture,
    memberP(nil,esk55_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).

cnf(c_0_94,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_93]),c_0_45])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWC297+1 : TPTP v8.2.0. Released v2.4.0.
% 0.11/0.13  % Command    : run_E %s %d THM
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sun May 19 03:23:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.50  Running first-order model finding
% 0.21/0.51  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/benchmark/theBenchmark.p
% 0.89/0.61  # Version: 3.1.0
% 0.89/0.61  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.89/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.89/0.61  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.89/0.61  # Starting new_bool_3 with 300s (1) cores
% 0.89/0.61  # Starting new_bool_1 with 300s (1) cores
% 0.89/0.61  # Starting sh5l with 300s (1) cores
% 0.89/0.61  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4190 completed with status 0
% 0.89/0.61  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.89/0.61  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.89/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.89/0.61  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.89/0.61  # No SInE strategy applied
% 0.89/0.61  # Search class: FGHSF-FSLM21-MFFFFFNN
% 0.89/0.61  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.89/0.61  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.89/0.61  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.89/0.61  # Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.89/0.61  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.89/0.61  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2o with 136s (1) cores
% 0.89/0.61  # G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 4203 completed with status 0
% 0.89/0.61  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 0.89/0.61  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.89/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.89/0.61  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.89/0.61  # No SInE strategy applied
% 0.89/0.61  # Search class: FGHSF-FSLM21-MFFFFFNN
% 0.89/0.61  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.89/0.61  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.89/0.61  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.89/0.61  # Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.89/0.61  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.89/0.61  # Preprocessing time       : 0.002 s
% 0.89/0.61  # Presaturation interreduction done
% 0.89/0.61  
% 0.89/0.61  # Proof found!
% 0.89/0.61  # SZS status Theorem
% 0.89/0.61  # SZS output start CNFRefutation
% See solution above
% 0.89/0.61  # Parsed axioms                        : 96
% 0.89/0.61  # Removed by relevancy pruning/SinE    : 0
% 0.89/0.61  # Initial clauses                      : 209
% 0.89/0.61  # Removed in clause preprocessing      : 2
% 0.89/0.61  # Initial clauses in saturation        : 207
% 0.89/0.61  # Processed clauses                    : 834
% 0.89/0.61  # ...of these trivial                  : 7
% 0.89/0.61  # ...subsumed                          : 179
% 0.89/0.61  # ...remaining for further processing  : 648
% 0.89/0.61  # Other redundant clauses eliminated   : 98
% 0.89/0.61  # Clauses deleted for lack of memory   : 0
% 0.89/0.61  # Backward-subsumed                    : 50
% 0.89/0.61  # Backward-rewritten                   : 75
% 0.89/0.61  # Generated clauses                    : 2265
% 0.89/0.61  # ...of the previous two non-redundant : 2010
% 0.89/0.61  # ...aggressively subsumed             : 0
% 0.89/0.61  # Contextual simplify-reflections      : 51
% 0.89/0.61  # Paramodulations                      : 2164
% 0.89/0.61  # Factorizations                       : 0
% 0.89/0.61  # NegExts                              : 0
% 0.89/0.61  # Equation resolutions                 : 103
% 0.89/0.61  # Disequality decompositions           : 0
% 0.89/0.61  # Total rewrite steps                  : 1945
% 0.89/0.61  # ...of those cached                   : 1899
% 0.89/0.61  # Propositional unsat checks           : 0
% 0.89/0.61  #    Propositional check models        : 0
% 0.89/0.61  #    Propositional check unsatisfiable : 0
% 0.89/0.61  #    Propositional clauses             : 0
% 0.89/0.61  #    Propositional clauses after purity: 0
% 0.89/0.61  #    Propositional unsat core size     : 0
% 0.89/0.61  #    Propositional preprocessing time  : 0.000
% 0.89/0.61  #    Propositional encoding time       : 0.000
% 0.89/0.61  #    Propositional solver time         : 0.000
% 0.89/0.61  #    Success case prop preproc time    : 0.000
% 0.89/0.61  #    Success case prop encoding time   : 0.000
% 0.89/0.61  #    Success case prop solver time     : 0.000
% 0.89/0.61  # Current number of processed clauses  : 299
% 0.89/0.61  #    Positive orientable unit clauses  : 47
% 0.89/0.61  #    Positive unorientable unit clauses: 0
% 0.89/0.61  #    Negative unit clauses             : 7
% 0.89/0.61  #    Non-unit-clauses                  : 245
% 0.89/0.61  # Current number of unprocessed clauses: 1523
% 0.89/0.61  # ...number of literals in the above   : 9811
% 0.89/0.61  # Current number of archived formulas  : 0
% 0.89/0.61  # Current number of archived clauses   : 326
% 0.89/0.61  # Clause-clause subsumption calls (NU) : 25474
% 0.89/0.61  # Rec. Clause-clause subsumption calls : 6694
% 0.89/0.61  # Non-unit clause-clause subsumptions  : 197
% 0.89/0.61  # Unit Clause-clause subsumption calls : 507
% 0.89/0.61  # Rewrite failures with RHS unbound    : 0
% 0.89/0.61  # BW rewrite match attempts            : 13
% 0.89/0.61  # BW rewrite match successes           : 13
% 0.89/0.61  # Condensation attempts                : 0
% 0.89/0.61  # Condensation successes               : 0
% 0.89/0.61  # Termbank termtop insertions          : 60781
% 0.89/0.61  # Search garbage collected termcells   : 4403
% 0.89/0.61  
% 0.89/0.61  # -------------------------------------------------
% 0.89/0.61  # User time                : 0.079 s
% 0.89/0.61  # System time              : 0.007 s
% 0.89/0.61  # Total time               : 0.086 s
% 0.89/0.61  # Maximum resident set size: 2496 pages
% 0.89/0.61  
% 0.89/0.61  # -------------------------------------------------
% 0.89/0.61  # User time                : 0.355 s
% 0.89/0.61  # System time              : 0.028 s
% 0.89/0.61  # Total time               : 0.383 s
% 0.89/0.61  # Maximum resident set size: 1824 pages
% 0.89/0.61  % E---3.1 exiting
%------------------------------------------------------------------------------