TSTP Solution File: SWC125+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SWC125+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n024.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 04:23:44 EDT 2024

% Result   : Theorem 28.27s 4.10s
% Output   : CNFRefutation 28.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   78 (  17 unt;   0 def)
%            Number of atoms       :  285 (  64 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  344 ( 137   ~; 137   |;  33   &)
%                                         (   4 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :  111 (   0 sgn  57   !;   6   ?)

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

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

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

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

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

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

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

fof(ax27,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).

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

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

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

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

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

fof(ax68,axiom,
    ! [X1] :
      ( ssItem(X1)
     => strictorderedP(cons(X1,nil)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax68) ).

fof(c_0_14,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    inference(fof_simplification,[status(thm)],[ax15]) ).

fof(c_0_15,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ neq(X2,nil)
                      | ~ segmentP(X4,X3)
                      | ~ strictorderedP(X3)
                      | ? [X5] :
                          ( ssList(X5)
                          & neq(X3,X5)
                          & segmentP(X4,X5)
                          & segmentP(X5,X3)
                          & strictorderedP(X5) )
                      | ( neq(X1,nil)
                        & segmentP(X2,X1) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_16,plain,
    ! [X32,X33] :
      ( ( ~ neq(X32,X33)
        | X32 != X33
        | ~ ssList(X33)
        | ~ ssList(X32) )
      & ( X32 = X33
        | neq(X32,X33)
        | ~ ssList(X33)
        | ~ ssList(X32) ) ),
    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_14])])])])]) ).

fof(c_0_17,negated_conjecture,
    ! [X11] :
      ( ssList(esk1_0)
      & ssList(esk2_0)
      & ssList(esk3_0)
      & ssList(esk4_0)
      & esk2_0 = esk4_0
      & esk1_0 = esk3_0
      & neq(esk2_0,nil)
      & segmentP(esk4_0,esk3_0)
      & strictorderedP(esk3_0)
      & ( ~ ssList(X11)
        | ~ neq(esk3_0,X11)
        | ~ segmentP(esk4_0,X11)
        | ~ segmentP(X11,esk3_0)
        | ~ strictorderedP(X11) )
      & ( ~ neq(esk1_0,nil)
        | ~ segmentP(esk2_0,esk1_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_15])])])])]) ).

fof(c_0_18,plain,
    ! [X70,X71] :
      ( ( nil = X71
        | nil != app(X70,X71)
        | ~ ssList(X71)
        | ~ ssList(X70) )
      & ( nil = X70
        | nil != app(X70,X71)
        | ~ ssList(X71)
        | ~ ssList(X70) )
      & ( nil != X71
        | nil != X70
        | nil = app(X70,X71)
        | ~ ssList(X71)
        | ~ ssList(X70) ) ),
    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_19,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_21,negated_conjecture,
    ssList(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    esk1_0 = esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    ( ~ neq(esk1_0,nil)
    | ~ segmentP(esk2_0,esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24,negated_conjecture,
    esk2_0 = esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,negated_conjecture,
    segmentP(esk4_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_26,plain,
    ! [X75,X76] :
      ( ~ ssList(X75)
      | ~ ssItem(X76)
      | ssList(cons(X76,X75)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).

fof(c_0_27,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[ax21]) ).

fof(c_0_28,plain,
    ! [X12,X13,X16,X17] :
      ( ( ssList(esk5_2(X12,X13))
        | ~ segmentP(X12,X13)
        | ~ ssList(X13)
        | ~ ssList(X12) )
      & ( ssList(esk6_2(X12,X13))
        | ~ segmentP(X12,X13)
        | ~ ssList(X13)
        | ~ ssList(X12) )
      & ( app(app(esk5_2(X12,X13),X13),esk6_2(X12,X13)) = X12
        | ~ segmentP(X12,X13)
        | ~ ssList(X13)
        | ~ ssList(X12) )
      & ( ~ ssList(X16)
        | ~ ssList(X17)
        | app(app(X16,X13),X17) != X12
        | segmentP(X12,X13)
        | ~ ssList(X13)
        | ~ ssList(X12) ) ),
    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)],[ax7])])])])])]) ).

fof(c_0_29,plain,
    ! [X55,X56,X57] :
      ( ~ ssList(X55)
      | ~ ssList(X56)
      | ~ ssItem(X57)
      | cons(X57,app(X56,X55)) = app(cons(X57,X56),X55) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).

fof(c_0_30,plain,
    ! [X53,X54] :
      ( ~ ssList(X53)
      | ~ ssList(X54)
      | ssList(app(X53,X54)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).

cnf(c_0_31,plain,
    ( nil = app(X2,X1)
    | nil != X1
    | nil != X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_32,plain,
    ( X1 = nil
    | neq(X1,nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_33,negated_conjecture,
    ssList(esk3_0),
    inference(rw,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_34,negated_conjecture,
    ~ neq(esk3_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_22]),c_0_24]),c_0_22]),c_0_25])]) ).

fof(c_0_35,plain,
    ! [X28] :
      ( ~ ssList(X28)
      | segmentP(X28,nil) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])])]) ).

cnf(c_0_36,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

fof(c_0_37,plain,
    ! [X37,X38] :
      ( ~ ssList(X37)
      | ~ ssItem(X38)
      | nil != cons(X38,X37) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).

cnf(c_0_38,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_28]) ).

fof(c_0_39,plain,
    ! [X58] :
      ( ~ ssList(X58)
      | app(nil,X58) = X58 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).

cnf(c_0_40,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_41,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_42,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_31])]),c_0_20])]) ).

cnf(c_0_43,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(esk3_0,X1)
    | ~ segmentP(esk4_0,X1)
    | ~ segmentP(X1,esk3_0)
    | ~ strictorderedP(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_44,negated_conjecture,
    esk3_0 = nil,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).

cnf(c_0_45,plain,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_46,plain,
    ( X1 = cons(X2,X3)
    | neq(X1,cons(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssItem(X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_36]) ).

cnf(c_0_47,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_48,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_38]) ).

cnf(c_0_49,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

fof(c_0_50,plain,
    ! [X65,X66] :
      ( ~ ssList(X65)
      | ~ ssItem(X66)
      | cons(X66,X65) = app(cons(X66,nil),X65) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).

cnf(c_0_51,plain,
    ( ssList(app(cons(X1,X2),X3))
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_40]),c_0_41]) ).

cnf(c_0_52,plain,
    ( app(cons(X1,nil),nil) = cons(X1,nil)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_20])]) ).

fof(c_0_53,plain,
    ! [X34] :
      ( ( ssList(esk7_1(X34))
        | nil = X34
        | ~ ssList(X34) )
      & ( ssItem(esk8_1(X34))
        | nil = X34
        | ~ ssList(X34) )
      & ( cons(esk8_1(X34),esk7_1(X34)) = X34
        | nil = X34
        | ~ ssList(X34) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).

cnf(c_0_54,negated_conjecture,
    ssList(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_55,negated_conjecture,
    ( ~ strictorderedP(X1)
    | ~ segmentP(esk4_0,X1)
    | ~ ssList(X1)
    | ~ neq(nil,X1) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_44]),c_0_45]) ).

cnf(c_0_56,plain,
    ( neq(nil,cons(X1,X2))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_20]),c_0_47]) ).

fof(c_0_57,plain,
    ! [X50] :
      ( ~ ssItem(X50)
      | strictorderedP(cons(X50,nil)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax68])])]) ).

cnf(c_0_58,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_48,c_0_49]),c_0_20])]),c_0_41]) ).

cnf(c_0_59,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_60,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_20])]) ).

cnf(c_0_61,plain,
    ( cons(esk8_1(X1),esk7_1(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_62,negated_conjecture,
    ssList(esk4_0),
    inference(rw,[status(thm)],[c_0_54,c_0_24]) ).

cnf(c_0_63,plain,
    ( ssItem(esk8_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_64,plain,
    ( ssList(esk7_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_65,negated_conjecture,
    ( ~ strictorderedP(cons(X1,X2))
    | ~ segmentP(esk4_0,cons(X1,X2))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_36]) ).

cnf(c_0_66,plain,
    ( strictorderedP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_67,plain,
    ( segmentP(cons(X1,X2),cons(X1,nil))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).

cnf(c_0_68,negated_conjecture,
    ( cons(esk8_1(esk4_0),esk7_1(esk4_0)) = esk4_0
    | esk4_0 = nil ),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

cnf(c_0_69,negated_conjecture,
    ( esk4_0 = nil
    | ssItem(esk8_1(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_63,c_0_62]) ).

cnf(c_0_70,negated_conjecture,
    ( esk4_0 = nil
    | ssList(esk7_1(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_64,c_0_62]) ).

cnf(c_0_71,negated_conjecture,
    neq(esk2_0,nil),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_72,negated_conjecture,
    ( ~ segmentP(esk4_0,cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_20])]) ).

cnf(c_0_73,negated_conjecture,
    ( esk4_0 = nil
    | segmentP(esk4_0,cons(esk8_1(esk4_0),nil)) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_70]) ).

cnf(c_0_74,negated_conjecture,
    neq(esk4_0,nil),
    inference(rw,[status(thm)],[c_0_71,c_0_24]) ).

cnf(c_0_75,negated_conjecture,
    esk4_0 = nil,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_69]) ).

cnf(c_0_76,negated_conjecture,
    ~ neq(nil,nil),
    inference(rw,[status(thm)],[c_0_34,c_0_44]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SWC125+1 : TPTP v8.2.0. Released v2.4.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun May 19 02:53:22 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.27/4.10  # Version: 3.1.0
% 28.27/4.10  # Preprocessing class: FSLSSMSSSSSNFFN.
% 28.27/4.10  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.27/4.10  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 28.27/4.10  # Starting new_bool_3 with 300s (1) cores
% 28.27/4.10  # Starting new_bool_1 with 300s (1) cores
% 28.27/4.10  # Starting sh5l with 300s (1) cores
% 28.27/4.10  # new_bool_3 with pid 10191 completed with status 0
% 28.27/4.10  # Result found by new_bool_3
% 28.27/4.10  # Preprocessing class: FSLSSMSSSSSNFFN.
% 28.27/4.10  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.27/4.10  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 28.27/4.10  # Starting new_bool_3 with 300s (1) cores
% 28.27/4.10  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 28.27/4.10  # Search class: FGHSF-FFMM21-MFFFFFNN
% 28.27/4.10  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 28.27/4.10  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 28.27/4.10  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 10194 completed with status 0
% 28.27/4.10  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 28.27/4.10  # Preprocessing class: FSLSSMSSSSSNFFN.
% 28.27/4.10  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.27/4.10  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 28.27/4.10  # Starting new_bool_3 with 300s (1) cores
% 28.27/4.10  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 28.27/4.10  # Search class: FGHSF-FFMM21-MFFFFFNN
% 28.27/4.10  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 28.27/4.10  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 28.27/4.10  # Preprocessing time       : 0.002 s
% 28.27/4.10  # Presaturation interreduction done
% 28.27/4.10  
% 28.27/4.10  # Proof found!
% 28.27/4.10  # SZS status Theorem
% 28.27/4.10  # SZS output start CNFRefutation
% See solution above
% 28.27/4.10  # Parsed axioms                        : 96
% 28.27/4.10  # Removed by relevancy pruning/SinE    : 47
% 28.27/4.10  # Initial clauses                      : 87
% 28.27/4.10  # Removed in clause preprocessing      : 1
% 28.27/4.10  # Initial clauses in saturation        : 86
% 28.27/4.10  # Processed clauses                    : 12566
% 28.27/4.10  # ...of these trivial                  : 40
% 28.27/4.10  # ...subsumed                          : 9064
% 28.27/4.10  # ...remaining for further processing  : 3462
% 28.27/4.10  # Other redundant clauses eliminated   : 269
% 28.27/4.10  # Clauses deleted for lack of memory   : 0
% 28.27/4.10  # Backward-subsumed                    : 127
% 28.27/4.10  # Backward-rewritten                   : 2592
% 28.27/4.10  # Generated clauses                    : 291328
% 28.27/4.10  # ...of the previous two non-redundant : 288322
% 28.27/4.10  # ...aggressively subsumed             : 0
% 28.27/4.10  # Contextual simplify-reflections      : 579
% 28.27/4.10  # Paramodulations                      : 290962
% 28.27/4.10  # Factorizations                       : 0
% 28.27/4.10  # NegExts                              : 0
% 28.27/4.10  # Equation resolutions                 : 367
% 28.27/4.10  # Disequality decompositions           : 0
% 28.27/4.10  # Total rewrite steps                  : 54504
% 28.27/4.10  # ...of those cached                   : 54482
% 28.27/4.10  # Propositional unsat checks           : 0
% 28.27/4.10  #    Propositional check models        : 0
% 28.27/4.10  #    Propositional check unsatisfiable : 0
% 28.27/4.10  #    Propositional clauses             : 0
% 28.27/4.10  #    Propositional clauses after purity: 0
% 28.27/4.10  #    Propositional unsat core size     : 0
% 28.27/4.10  #    Propositional preprocessing time  : 0.000
% 28.27/4.10  #    Propositional encoding time       : 0.000
% 28.27/4.10  #    Propositional solver time         : 0.000
% 28.27/4.10  #    Success case prop preproc time    : 0.000
% 28.27/4.10  #    Success case prop encoding time   : 0.000
% 28.27/4.10  #    Success case prop solver time     : 0.000
% 28.27/4.10  # Current number of processed clauses  : 654
% 28.27/4.10  #    Positive orientable unit clauses  : 13
% 28.27/4.10  #    Positive unorientable unit clauses: 0
% 28.27/4.10  #    Negative unit clauses             : 2
% 28.27/4.10  #    Non-unit-clauses                  : 639
% 28.27/4.10  # Current number of unprocessed clauses: 275106
% 28.27/4.10  # ...number of literals in the above   : 1295790
% 28.27/4.10  # Current number of archived formulas  : 0
% 28.27/4.10  # Current number of archived clauses   : 2800
% 28.27/4.10  # Clause-clause subsumption calls (NU) : 702800
% 28.27/4.10  # Rec. Clause-clause subsumption calls : 173241
% 28.27/4.10  # Non-unit clause-clause subsumptions  : 9763
% 28.27/4.10  # Unit Clause-clause subsumption calls : 1955
% 28.27/4.10  # Rewrite failures with RHS unbound    : 0
% 28.27/4.10  # BW rewrite match attempts            : 9
% 28.27/4.10  # BW rewrite match successes           : 9
% 28.27/4.10  # Condensation attempts                : 0
% 28.27/4.10  # Condensation successes               : 0
% 28.27/4.10  # Termbank termtop insertions          : 6714200
% 28.27/4.10  # Search garbage collected termcells   : 2180
% 28.27/4.10  
% 28.27/4.10  # -------------------------------------------------
% 28.27/4.10  # User time                : 3.279 s
% 28.27/4.10  # System time              : 0.182 s
% 28.27/4.10  # Total time               : 3.461 s
% 28.27/4.10  # Maximum resident set size: 2072 pages
% 28.27/4.10  
% 28.27/4.10  # -------------------------------------------------
% 28.27/4.10  # User time                : 3.283 s
% 28.27/4.10  # System time              : 0.184 s
% 28.27/4.10  # Total time               : 3.467 s
% 28.27/4.10  # Maximum resident set size: 1824 pages
% 28.27/4.10  % E---3.1 exiting
% 28.27/4.10  % E exiting
%------------------------------------------------------------------------------