TSTP Solution File: SWC181+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SWC181+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n019.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 04:28:09 EDT 2024

% Result   : Theorem 26.48s 3.86s
% Output   : CNFRefutation 26.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   54 (   8 unt;   0 def)
%            Number of atoms       :  363 (  47 equ)
%            Maximal formula atoms :   34 (   6 avg)
%            Number of connectives :  485 ( 176   ~; 195   |;  63   &)
%                                         (   4 <=>;  47  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   7 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;   7 con; 0-2 aty)
%            Number of variables   :  142 (   0 sgn  73   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ax90,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ lt(X1,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax90) ).

fof(ax8,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( cyclefreeP(X1)
      <=> ! [X2] :
            ( ssItem(X2)
           => ! [X3] :
                ( ssItem(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
                             => ~ ( leq(X2,X3)
                                  & leq(X3,X2) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax8) ).

fof(ax13,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( duplicatefreeP(X1)
      <=> ! [X2] :
            ( ssItem(X2)
           => ! [X3] :
                ( ssItem(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
                             => X2 != X3 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax13) ).

fof(ax91,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssItem(X3)
             => ( ( leq(X1,X2)
                  & lt(X2,X3) )
               => lt(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax91) ).

fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X5,X3),X6) != X4
                              | ~ strictorderedP(X3)
                              | ? [X7] :
                                  ( ssItem(X7)
                                  & ? [X8] :
                                      ( ssList(X8)
                                      & app(X8,cons(X7,nil)) = X5
                                      & ? [X9] :
                                          ( ssItem(X9)
                                          & ? [X10] :
                                              ( ssList(X10)
                                              & app(cons(X9,nil),X10) = X3
                                              & lt(X7,X9) ) ) ) )
                              | ? [X11] :
                                  ( ssItem(X11)
                                  & ? [X12] :
                                      ( ssList(X12)
                                      & app(cons(X11,nil),X12) = X6
                                      & ? [X13] :
                                          ( ssItem(X13)
                                          & ? [X14] :
                                              ( ssList(X14)
                                              & app(X14,cons(X13,nil)) = X3
                                              & lt(X13,X11) ) ) ) ) ) ) )
                    | duplicatefreeP(X1)
                    | ( nil != X4
                      & nil = X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(ax31,axiom,
    ! [X1] :
      ( ssItem(X1)
     => leq(X1,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax31) ).

fof(ax12,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( strictorderedP(X1)
      <=> ! [X2] :
            ( ssItem(X2)
           => ! [X3] :
                ( ssItem(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
                             => lt(X2,X3) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax12) ).

fof(c_0_7,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ lt(X1,X1) ),
    inference(fof_simplification,[status(thm)],[ax90]) ).

fof(c_0_8,plain,
    ! [X42,X43,X44,X45,X46,X47] :
      ( ( ~ cyclefreeP(X42)
        | ~ ssItem(X43)
        | ~ ssItem(X44)
        | ~ ssList(X45)
        | ~ ssList(X46)
        | ~ ssList(X47)
        | app(app(X45,cons(X43,X46)),cons(X44,X47)) != X42
        | ~ leq(X43,X44)
        | ~ leq(X44,X43)
        | ~ ssList(X42) )
      & ( ssItem(esk10_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( ssItem(esk11_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( ssList(esk12_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( ssList(esk13_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( ssList(esk14_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( app(app(esk12_1(X42),cons(esk10_1(X42),esk13_1(X42))),cons(esk11_1(X42),esk14_1(X42))) = X42
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( leq(esk10_1(X42),esk11_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) )
      & ( leq(esk11_1(X42),esk10_1(X42))
        | cyclefreeP(X42)
        | ~ ssList(X42) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax8])])])])])]) ).

fof(c_0_9,plain,
    ! [X1] :
      ( ssList(X1)
     => ( duplicatefreeP(X1)
      <=> ! [X2] :
            ( ssItem(X2)
           => ! [X3] :
                ( ssItem(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
                             => X2 != X3 ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ax13]) ).

fof(c_0_10,plain,
    ! [X246] :
      ( ~ ssItem(X246)
      | ~ lt(X246,X246) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_11,plain,
    ! [X247,X248,X249] :
      ( ~ ssItem(X247)
      | ~ ssItem(X248)
      | ~ ssItem(X249)
      | ~ leq(X247,X248)
      | ~ lt(X248,X249)
      | lt(X247,X249) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax91])])])]) ).

cnf(c_0_12,plain,
    ( ~ cyclefreeP(X1)
    | ~ ssItem(X2)
    | ~ ssItem(X3)
    | ~ ssList(X4)
    | ~ ssList(X5)
    | ~ ssList(X6)
    | app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
    | ~ leq(X2,X3)
    | ~ leq(X3,X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_13,plain,
    ! [X97,X98,X99,X100,X101,X102] :
      ( ( ~ duplicatefreeP(X97)
        | ~ ssItem(X98)
        | ~ ssItem(X99)
        | ~ ssList(X100)
        | ~ ssList(X101)
        | ~ ssList(X102)
        | app(app(X100,cons(X98,X101)),cons(X99,X102)) != X97
        | X98 != X99
        | ~ ssList(X97) )
      & ( ssItem(esk35_1(X97))
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( ssItem(esk36_1(X97))
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( ssList(esk37_1(X97))
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( ssList(esk38_1(X97))
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( ssList(esk39_1(X97))
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( app(app(esk37_1(X97),cons(esk35_1(X97),esk38_1(X97))),cons(esk36_1(X97),esk39_1(X97))) = X97
        | duplicatefreeP(X97)
        | ~ ssList(X97) )
      & ( esk35_1(X97) = esk36_1(X97)
        | duplicatefreeP(X97)
        | ~ ssList(X97) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])])]) ).

cnf(c_0_14,plain,
    ( ~ ssItem(X1)
    | ~ lt(X1,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,plain,
    ( lt(X1,X3)
    | ~ ssItem(X1)
    | ~ ssItem(X2)
    | ~ ssItem(X3)
    | ~ leq(X1,X2)
    | ~ lt(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_16,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssList(X5)
                         => ! [X6] :
                              ( ssList(X6)
                             => ( app(app(X5,X3),X6) != X4
                                | ~ strictorderedP(X3)
                                | ? [X7] :
                                    ( ssItem(X7)
                                    & ? [X8] :
                                        ( ssList(X8)
                                        & app(X8,cons(X7,nil)) = X5
                                        & ? [X9] :
                                            ( ssItem(X9)
                                            & ? [X10] :
                                                ( ssList(X10)
                                                & app(cons(X9,nil),X10) = X3
                                                & lt(X7,X9) ) ) ) )
                                | ? [X11] :
                                    ( ssItem(X11)
                                    & ? [X12] :
                                        ( ssList(X12)
                                        & app(cons(X11,nil),X12) = X6
                                        & ? [X13] :
                                            ( ssItem(X13)
                                            & ? [X14] :
                                                ( ssList(X14)
                                                & app(X14,cons(X13,nil)) = X3
                                                & lt(X13,X11) ) ) ) ) ) ) )
                      | duplicatefreeP(X1)
                      | ( nil != X4
                        & nil = X3 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

cnf(c_0_17,plain,
    ( ~ leq(X1,X2)
    | ~ leq(X2,X1)
    | ~ cyclefreeP(app(app(X3,cons(X2,X4)),cons(X1,X5)))
    | ~ ssList(app(app(X3,cons(X2,X4)),cons(X1,X5)))
    | ~ ssList(X5)
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssItem(X1)
    | ~ ssItem(X2) ),
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( app(app(esk37_1(X1),cons(esk35_1(X1),esk38_1(X1))),cons(esk36_1(X1),esk39_1(X1))) = X1
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    ( ssItem(esk35_1(X1))
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    ( ssItem(esk36_1(X1))
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    ( ssList(esk37_1(X1))
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,plain,
    ( ssList(esk38_1(X1))
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_23,plain,
    ( ssList(esk39_1(X1))
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_24,plain,
    ( ~ lt(X1,X2)
    | ~ leq(X2,X1)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

fof(c_0_25,negated_conjecture,
    ! [X265,X266,X267,X268,X269,X270,X271,X272] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & ssList(esk52_0)
      & ssList(esk53_0)
      & app(app(esk52_0,esk50_0),esk53_0) = esk51_0
      & strictorderedP(esk50_0)
      & ( ~ ssItem(X265)
        | ~ ssList(X266)
        | app(X266,cons(X265,nil)) != esk52_0
        | ~ ssItem(X267)
        | ~ ssList(X268)
        | app(cons(X267,nil),X268) != esk50_0
        | ~ lt(X265,X267) )
      & ( ~ ssItem(X269)
        | ~ ssList(X270)
        | app(cons(X269,nil),X270) != esk53_0
        | ~ ssItem(X271)
        | ~ ssList(X272)
        | app(X272,cons(X271,nil)) != esk50_0
        | ~ lt(X271,X269) )
      & ~ duplicatefreeP(esk48_0)
      & ( nil = esk51_0
        | nil != esk50_0 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).

cnf(c_0_26,plain,
    ( duplicatefreeP(X1)
    | ~ leq(esk36_1(X1),esk35_1(X1))
    | ~ leq(esk35_1(X1),esk36_1(X1))
    | ~ cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_23]) ).

cnf(c_0_27,plain,
    ( esk35_1(X1) = esk36_1(X1)
    | duplicatefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_28,plain,
    ! [X149] :
      ( ~ ssItem(X149)
      | leq(X149,X149) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax31])])]) ).

fof(c_0_29,plain,
    ! [X86,X87,X88,X89,X90,X91] :
      ( ( ~ strictorderedP(X86)
        | ~ ssItem(X87)
        | ~ ssItem(X88)
        | ~ ssList(X89)
        | ~ ssList(X90)
        | ~ ssList(X91)
        | app(app(X89,cons(X87,X90)),cons(X88,X91)) != X86
        | lt(X87,X88)
        | ~ ssList(X86) )
      & ( ssItem(esk30_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( ssItem(esk31_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( ssList(esk32_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( ssList(esk33_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( ssList(esk34_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( app(app(esk32_1(X86),cons(esk30_1(X86),esk33_1(X86))),cons(esk31_1(X86),esk34_1(X86))) = X86
        | strictorderedP(X86)
        | ~ ssList(X86) )
      & ( ~ lt(esk30_1(X86),esk31_1(X86))
        | strictorderedP(X86)
        | ~ ssList(X86) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])])])])]) ).

cnf(c_0_30,plain,
    ( ~ lt(X1,X2)
    | ~ leq(X2,X3)
    | ~ leq(X3,X1)
    | ~ ssItem(X2)
    | ~ ssItem(X3)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_15]) ).

cnf(c_0_31,plain,
    ( leq(esk11_1(X1),esk10_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_32,plain,
    ( ssItem(esk10_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_33,plain,
    ( ssItem(esk11_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_34,negated_conjecture,
    ~ duplicatefreeP(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_35,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_36,plain,
    ( duplicatefreeP(X1)
    | ~ leq(esk36_1(X1),esk36_1(X1))
    | ~ cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_37,plain,
    ( leq(X1,X1)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_38,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_39,plain,
    ( lt(X2,X3)
    | ~ strictorderedP(X1)
    | ~ ssItem(X2)
    | ~ ssItem(X3)
    | ~ ssList(X4)
    | ~ ssList(X5)
    | ~ ssList(X6)
    | app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_40,plain,
    ( cyclefreeP(X1)
    | ~ lt(esk10_1(X1),X2)
    | ~ leq(X2,esk11_1(X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33]) ).

cnf(c_0_41,negated_conjecture,
    ~ duplicatefreeP(esk50_0),
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_42,plain,
    ( duplicatefreeP(X1)
    | ~ cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_20]) ).

cnf(c_0_43,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_38,c_0_35]) ).

cnf(c_0_44,plain,
    ( lt(X1,X2)
    | ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
    | ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
    | ~ ssList(X5)
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_39]) ).

cnf(c_0_45,plain,
    ( app(app(esk12_1(X1),cons(esk10_1(X1),esk13_1(X1))),cons(esk11_1(X1),esk14_1(X1))) = X1
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_46,plain,
    ( ssList(esk12_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_47,plain,
    ( ssList(esk13_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_48,plain,
    ( ssList(esk14_1(X1))
    | cyclefreeP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_49,plain,
    ( cyclefreeP(X1)
    | ~ lt(esk10_1(X1),esk11_1(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_37]),c_0_33]) ).

cnf(c_0_50,negated_conjecture,
    ~ cyclefreeP(esk50_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).

cnf(c_0_51,plain,
    ( cyclefreeP(X1)
    | ~ strictorderedP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_32]),c_0_33]),c_0_46]),c_0_47]),c_0_48]),c_0_49]) ).

cnf(c_0_52,negated_conjecture,
    strictorderedP(esk50_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_53,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_43])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : SWC181+1 : TPTP v8.2.0. Released v2.4.0.
% 0.08/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 02:37:08 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running first-order model finding
% 0.19/0.47  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
% 26.48/3.86  # Version: 3.1.0
% 26.48/3.86  # Preprocessing class: FSLSSMSSSSSNFFN.
% 26.48/3.86  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.48/3.86  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 26.48/3.86  # Starting new_bool_3 with 300s (1) cores
% 26.48/3.86  # Starting new_bool_1 with 300s (1) cores
% 26.48/3.86  # Starting sh5l with 300s (1) cores
% 26.48/3.86  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 8921 completed with status 0
% 26.48/3.86  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 26.48/3.86  # Preprocessing class: FSLSSMSSSSSNFFN.
% 26.48/3.86  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.48/3.86  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 26.48/3.86  # No SInE strategy applied
% 26.48/3.86  # Search class: FGHSF-FSLM21-MFFFFFNN
% 26.48/3.86  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 26.48/3.86  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 26.48/3.86  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 26.48/3.86  # Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 26.48/3.86  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 26.48/3.86  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2o with 136s (1) cores
% 26.48/3.86  # G-E--_208_C18_F1_SE_CS_SP_PS_S2o with pid 8932 completed with status 0
% 26.48/3.86  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S2o
% 26.48/3.86  # Preprocessing class: FSLSSMSSSSSNFFN.
% 26.48/3.86  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.48/3.86  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 26.48/3.86  # No SInE strategy applied
% 26.48/3.86  # Search class: FGHSF-FSLM21-MFFFFFNN
% 26.48/3.86  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 26.48/3.86  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 26.48/3.86  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 26.48/3.86  # Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 26.48/3.86  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 26.48/3.86  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2o with 136s (1) cores
% 26.48/3.86  # Preprocessing time       : 0.004 s
% 26.48/3.86  # Presaturation interreduction done
% 26.48/3.86  
% 26.48/3.86  # Proof found!
% 26.48/3.86  # SZS status Theorem
% 26.48/3.86  # SZS output start CNFRefutation
% See solution above
% 26.48/3.86  # Parsed axioms                        : 96
% 26.48/3.86  # Removed by relevancy pruning/SinE    : 0
% 26.48/3.86  # Initial clauses                      : 204
% 26.48/3.86  # Removed in clause preprocessing      : 2
% 26.48/3.86  # Initial clauses in saturation        : 202
% 26.48/3.86  # Processed clauses                    : 10071
% 26.48/3.86  # ...of these trivial                  : 60
% 26.48/3.86  # ...subsumed                          : 6492
% 26.48/3.86  # ...remaining for further processing  : 3519
% 26.48/3.86  # Other redundant clauses eliminated   : 1983
% 26.48/3.86  # Clauses deleted for lack of memory   : 0
% 26.48/3.86  # Backward-subsumed                    : 319
% 26.48/3.86  # Backward-rewritten                   : 185
% 26.48/3.86  # Generated clauses                    : 67220
% 26.48/3.86  # ...of the previous two non-redundant : 62815
% 26.48/3.86  # ...aggressively subsumed             : 0
% 26.48/3.86  # Contextual simplify-reflections      : 1446
% 26.48/3.86  # Paramodulations                      : 65224
% 26.48/3.86  # Factorizations                       : 0
% 26.48/3.86  # NegExts                              : 0
% 26.48/3.86  # Equation resolutions                 : 1998
% 26.48/3.86  # Disequality decompositions           : 0
% 26.48/3.86  # Total rewrite steps                  : 39491
% 26.48/3.86  # ...of those cached                   : 39346
% 26.48/3.86  # Propositional unsat checks           : 0
% 26.48/3.86  #    Propositional check models        : 0
% 26.48/3.86  #    Propositional check unsatisfiable : 0
% 26.48/3.86  #    Propositional clauses             : 0
% 26.48/3.86  #    Propositional clauses after purity: 0
% 26.48/3.86  #    Propositional unsat core size     : 0
% 26.48/3.86  #    Propositional preprocessing time  : 0.000
% 26.48/3.86  #    Propositional encoding time       : 0.000
% 26.48/3.86  #    Propositional solver time         : 0.000
% 26.48/3.86  #    Success case prop preproc time    : 0.000
% 26.48/3.86  #    Success case prop encoding time   : 0.000
% 26.48/3.86  #    Success case prop solver time     : 0.000
% 26.48/3.86  # Current number of processed clauses  : 2796
% 26.48/3.86  #    Positive orientable unit clauses  : 153
% 26.48/3.86  #    Positive unorientable unit clauses: 0
% 26.48/3.86  #    Negative unit clauses             : 4
% 26.48/3.86  #    Non-unit-clauses                  : 2639
% 26.48/3.86  # Current number of unprocessed clauses: 52666
% 26.48/3.86  # ...number of literals in the above   : 413071
% 26.48/3.86  # Current number of archived formulas  : 0
% 26.48/3.86  # Current number of archived clauses   : 700
% 26.48/3.86  # Clause-clause subsumption calls (NU) : 1413823
% 26.48/3.86  # Rec. Clause-clause subsumption calls : 261872
% 26.48/3.86  # Non-unit clause-clause subsumptions  : 7518
% 26.48/3.86  # Unit Clause-clause subsumption calls : 10847
% 26.48/3.86  # Rewrite failures with RHS unbound    : 0
% 26.48/3.86  # BW rewrite match attempts            : 76
% 26.48/3.86  # BW rewrite match successes           : 73
% 26.48/3.86  # Condensation attempts                : 0
% 26.48/3.86  # Condensation successes               : 0
% 26.48/3.86  # Termbank termtop insertions          : 1503740
% 26.48/3.86  # Search garbage collected termcells   : 4469
% 26.48/3.86  
% 26.48/3.86  # -------------------------------------------------
% 26.48/3.86  # User time                : 3.229 s
% 26.48/3.86  # System time              : 0.069 s
% 26.48/3.86  # Total time               : 3.298 s
% 26.48/3.86  # Maximum resident set size: 2496 pages
% 26.48/3.86  
% 26.48/3.86  # -------------------------------------------------
% 26.48/3.86  # User time                : 16.030 s
% 26.48/3.86  # System time              : 0.330 s
% 26.48/3.86  # Total time               : 16.360 s
% 26.48/3.86  # Maximum resident set size: 1828 pages
% 26.48/3.86  % E---3.1 exiting
%------------------------------------------------------------------------------