TSTP Solution File: GRA007+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : GRA007+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n032.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  : 600s
% DateTime : Sat Jul 16 07:16:07 EDT 2022

% Result   : Theorem 0.15s 1.33s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   88 (  15 unt;   0 def)
%            Number of atoms       :  386 ( 112 equ)
%            Maximal formula atoms :   37 (   4 avg)
%            Number of connectives :  487 ( 189   ~; 220   |;  59   &)
%                                         (   2 <=>;  14  =>;   1  <=;   2 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   2 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-4 aty)
%            Number of variables   :  208 (  43 sgn  83   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(back_edge,conjecture,
    ( complete
   => ! [X2,X3,X7,X8,X4] :
        ( ( shortest_path(X2,X3,X4)
          & precedes(X7,X8,X4) )
       => ? [X9] :
            ( edge(X9)
            & tail_of(X9) = head_of(X8)
            & head_of(X9) = tail_of(X7) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',back_edge) ).

fof(in_path_properties,axiom,
    ! [X2,X3,X4,X6] :
      ( ( path(X2,X3,X4)
        & in_path(X6,X4) )
     => ( vertex(X6)
        & ? [X1] :
            ( on_path(X1,X4)
            & ( X6 = head_of(X1)
              | X6 = tail_of(X1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',in_path_properties) ).

fof(shortest_path_defn,axiom,
    ! [X2,X3,X10] :
      ( shortest_path(X2,X3,X10)
    <=> ( path(X2,X3,X10)
        & X2 != X3
        & ! [X4] :
            ( path(X2,X3,X4)
           => less_or_equal(length_of(X10),length_of(X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).

fof(on_path_properties,axiom,
    ! [X2,X3,X4,X1] :
      ( ( path(X2,X3,X4)
        & on_path(X1,X4) )
     => ( edge(X1)
        & in_path(head_of(X1),X4)
        & in_path(tail_of(X1),X4) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).

fof(precedes_properties,axiom,
    ! [X4,X2,X3] :
      ( path(X2,X3,X4)
     => ! [X7,X8] :
          ( precedes(X7,X8,X4)
         => ( on_path(X7,X4)
            & on_path(X8,X4)
            & ( sequential(X7,X8)
            <~> ? [X9] :
                  ( sequential(X7,X9)
                  & precedes(X9,X8,X4) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).

fof(complete_properties,axiom,
    ( complete
   => ! [X2,X3] :
        ( ( vertex(X2)
          & vertex(X3)
          & X2 != X3 )
       => ? [X1] :
            ( edge(X1)
            & ( ( X2 = head_of(X1)
                & X3 = tail_of(X1) )
            <~> ( X3 = head_of(X1)
                & X2 = tail_of(X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',complete_properties) ).

fof(edge_ends_are_vertices,axiom,
    ! [X1] :
      ( edge(X1)
     => ( vertex(head_of(X1))
        & vertex(tail_of(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',edge_ends_are_vertices) ).

fof(shortest_path_properties,axiom,
    ! [X2,X3,X7,X8,X4] :
      ( ( shortest_path(X2,X3,X4)
        & precedes(X7,X8,X4) )
     => ( ~ ? [X9] :
              ( tail_of(X9) = tail_of(X7)
              & head_of(X9) = head_of(X8) )
        & ~ precedes(X8,X7,X4) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).

fof(precedes_defn,axiom,
    ! [X4,X2,X3] :
      ( path(X2,X3,X4)
     => ! [X7,X8] :
          ( precedes(X7,X8,X4)
         <= ( on_path(X7,X4)
            & on_path(X8,X4)
            & ( sequential(X7,X8)
              | ? [X9] :
                  ( sequential(X7,X9)
                  & precedes(X9,X8,X4) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).

fof(sequential_defn,axiom,
    ! [X7,X8] :
      ( sequential(X7,X8)
    <=> ( edge(X7)
        & edge(X8)
        & X7 != X8
        & head_of(X7) = tail_of(X8) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).

fof(c_0_10,negated_conjecture,
    ~ ( complete
     => ! [X2,X3,X7,X8,X4] :
          ( ( shortest_path(X2,X3,X4)
            & precedes(X7,X8,X4) )
         => ? [X9] :
              ( edge(X9)
              & tail_of(X9) = head_of(X8)
              & head_of(X9) = tail_of(X7) ) ) ),
    inference(assume_negation,[status(cth)],[back_edge]) ).

fof(c_0_11,plain,
    ! [X7,X8,X9,X10] :
      ( ( vertex(X10)
        | ~ path(X7,X8,X9)
        | ~ in_path(X10,X9) )
      & ( on_path(esk4_4(X7,X8,X9,X10),X9)
        | ~ path(X7,X8,X9)
        | ~ in_path(X10,X9) )
      & ( X10 = head_of(esk4_4(X7,X8,X9,X10))
        | X10 = tail_of(esk4_4(X7,X8,X9,X10))
        | ~ path(X7,X8,X9)
        | ~ in_path(X10,X9) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[in_path_properties])])])])])]) ).

fof(c_0_12,plain,
    ! [X11,X12,X13,X14,X11,X12,X13] :
      ( ( path(X11,X12,X13)
        | ~ shortest_path(X11,X12,X13) )
      & ( X11 != X12
        | ~ shortest_path(X11,X12,X13) )
      & ( ~ path(X11,X12,X14)
        | less_or_equal(length_of(X13),length_of(X14))
        | ~ shortest_path(X11,X12,X13) )
      & ( path(X11,X12,esk6_3(X11,X12,X13))
        | ~ path(X11,X12,X13)
        | X11 = X12
        | shortest_path(X11,X12,X13) )
      & ( ~ less_or_equal(length_of(X13),length_of(esk6_3(X11,X12,X13)))
        | ~ path(X11,X12,X13)
        | X11 = X12
        | shortest_path(X11,X12,X13) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[shortest_path_defn])])])])])])]) ).

fof(c_0_13,plain,
    ! [X5,X6,X7,X8] :
      ( ( edge(X8)
        | ~ path(X5,X6,X7)
        | ~ on_path(X8,X7) )
      & ( in_path(head_of(X8),X7)
        | ~ path(X5,X6,X7)
        | ~ on_path(X8,X7) )
      & ( in_path(tail_of(X8),X7)
        | ~ path(X5,X6,X7)
        | ~ on_path(X8,X7) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])]) ).

fof(c_0_14,plain,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ( on_path(X13,X10)
        | ~ precedes(X13,X14,X10)
        | ~ path(X11,X12,X10) )
      & ( on_path(X14,X10)
        | ~ precedes(X13,X14,X10)
        | ~ path(X11,X12,X10) )
      & ( ~ sequential(X13,X14)
        | ~ sequential(X13,X15)
        | ~ precedes(X15,X14,X10)
        | ~ precedes(X13,X14,X10)
        | ~ path(X11,X12,X10) )
      & ( sequential(X13,esk5_3(X10,X13,X14))
        | sequential(X13,X14)
        | ~ precedes(X13,X14,X10)
        | ~ path(X11,X12,X10) )
      & ( precedes(esk5_3(X10,X13,X14),X14,X10)
        | sequential(X13,X14)
        | ~ precedes(X13,X14,X10)
        | ~ path(X11,X12,X10) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[precedes_properties])])])])])])])]) ).

fof(c_0_15,negated_conjecture,
    ! [X15] :
      ( complete
      & shortest_path(esk9_0,esk10_0,esk13_0)
      & precedes(esk11_0,esk12_0,esk13_0)
      & ( ~ edge(X15)
        | tail_of(X15) != head_of(esk12_0)
        | head_of(X15) != tail_of(esk11_0) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])]) ).

cnf(c_0_16,plain,
    ( vertex(X1)
    | ~ in_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    ( path(X1,X2,X3)
    | ~ shortest_path(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( in_path(head_of(X1),X2)
    | ~ on_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    ( on_path(X5,X3)
    | ~ path(X1,X2,X3)
    | ~ precedes(X4,X5,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    precedes(esk11_0,esk12_0,esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_21,plain,
    ! [X4,X5] :
      ( ( edge(esk1_2(X4,X5))
        | ~ vertex(X4)
        | ~ vertex(X5)
        | X4 = X5
        | ~ complete )
      & ( X4 != head_of(esk1_2(X4,X5))
        | X5 != tail_of(esk1_2(X4,X5))
        | X5 != head_of(esk1_2(X4,X5))
        | X4 != tail_of(esk1_2(X4,X5))
        | ~ vertex(X4)
        | ~ vertex(X5)
        | X4 = X5
        | ~ complete )
      & ( X5 = head_of(esk1_2(X4,X5))
        | X4 = head_of(esk1_2(X4,X5))
        | ~ vertex(X4)
        | ~ vertex(X5)
        | X4 = X5
        | ~ complete )
      & ( X4 = tail_of(esk1_2(X4,X5))
        | X4 = head_of(esk1_2(X4,X5))
        | ~ vertex(X4)
        | ~ vertex(X5)
        | X4 = X5
        | ~ complete )
      & ( X5 = head_of(esk1_2(X4,X5))
        | X5 = tail_of(esk1_2(X4,X5))
        | ~ vertex(X4)
        | ~ vertex(X5)
        | X4 = X5
        | ~ complete )
      & ( X4 = tail_of(esk1_2(X4,X5))
        | X5 = tail_of(esk1_2(X4,X5))
        | ~ vertex(X4)
        | ~ vertex(X5)
        | X4 = X5
        | ~ complete ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[complete_properties])])])])])])])]) ).

cnf(c_0_22,plain,
    ( vertex(X1)
    | ~ shortest_path(X2,X3,X4)
    | ~ in_path(X1,X4) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    shortest_path(esk9_0,esk10_0,esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,plain,
    ( in_path(head_of(X1),X2)
    | ~ shortest_path(X3,X4,X2)
    | ~ on_path(X1,X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_17]) ).

cnf(c_0_25,negated_conjecture,
    ( on_path(esk12_0,esk13_0)
    | ~ path(X1,X2,esk13_0) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,plain,
    ( on_path(X4,X3)
    | ~ path(X1,X2,X3)
    | ~ precedes(X4,X5,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_27,plain,
    ( X1 = X2
    | X1 = head_of(esk1_2(X1,X2))
    | X2 = head_of(esk1_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    complete,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_29,plain,
    ! [X2] :
      ( ( vertex(head_of(X2))
        | ~ edge(X2) )
      & ( vertex(tail_of(X2))
        | ~ edge(X2) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[edge_ends_are_vertices])])]) ).

cnf(c_0_30,negated_conjecture,
    ( vertex(X1)
    | ~ in_path(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_31,negated_conjecture,
    ( in_path(head_of(X1),esk13_0)
    | ~ on_path(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_24,c_0_23]) ).

cnf(c_0_32,negated_conjecture,
    ( on_path(esk12_0,esk13_0)
    | ~ shortest_path(X1,X2,esk13_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_17]) ).

cnf(c_0_33,plain,
    ( edge(X1)
    | ~ on_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_34,negated_conjecture,
    ( on_path(esk11_0,esk13_0)
    | ~ path(X1,X2,esk13_0) ),
    inference(spm,[status(thm)],[c_0_26,c_0_20]) ).

cnf(c_0_35,plain,
    ( in_path(tail_of(X1),X2)
    | ~ on_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_36,plain,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ( tail_of(X15) != tail_of(X12)
        | head_of(X15) != head_of(X13)
        | ~ shortest_path(X10,X11,X14)
        | ~ precedes(X12,X13,X14) )
      & ( ~ precedes(X13,X12,X14)
        | ~ shortest_path(X10,X11,X14)
        | ~ precedes(X12,X13,X14) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[shortest_path_properties])])])])])])]) ).

cnf(c_0_37,plain,
    ( head_of(esk1_2(X1,X2)) = X1
    | head_of(esk1_2(X1,X2)) = X2
    | X1 = X2
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).

cnf(c_0_38,plain,
    ( vertex(tail_of(X1))
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_39,negated_conjecture,
    ( vertex(head_of(X1))
    | ~ on_path(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_40,negated_conjecture,
    on_path(esk12_0,esk13_0),
    inference(spm,[status(thm)],[c_0_32,c_0_23]) ).

cnf(c_0_41,plain,
    ( edge(X1)
    | ~ shortest_path(X2,X3,X4)
    | ~ on_path(X1,X4) ),
    inference(spm,[status(thm)],[c_0_33,c_0_17]) ).

cnf(c_0_42,negated_conjecture,
    ( on_path(esk11_0,esk13_0)
    | ~ shortest_path(X1,X2,esk13_0) ),
    inference(spm,[status(thm)],[c_0_34,c_0_17]) ).

cnf(c_0_43,plain,
    ( X1 = X2
    | X2 = tail_of(esk1_2(X1,X2))
    | X1 = tail_of(esk1_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_44,plain,
    ( in_path(tail_of(X1),X2)
    | ~ shortest_path(X3,X4,X2)
    | ~ on_path(X1,X2) ),
    inference(spm,[status(thm)],[c_0_35,c_0_17]) ).

cnf(c_0_45,plain,
    ( ~ precedes(X1,X2,X3)
    | ~ shortest_path(X4,X5,X3)
    | head_of(X6) != head_of(X2)
    | tail_of(X6) != tail_of(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_46,plain,
    ( head_of(esk1_2(X1,tail_of(X2))) = tail_of(X2)
    | head_of(esk1_2(X1,tail_of(X2))) = X1
    | X1 = tail_of(X2)
    | ~ vertex(X1)
    | ~ edge(X2) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_47,negated_conjecture,
    vertex(head_of(esk12_0)),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_48,negated_conjecture,
    ( edge(X1)
    | ~ on_path(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_41,c_0_23]) ).

cnf(c_0_49,negated_conjecture,
    on_path(esk11_0,esk13_0),
    inference(spm,[status(thm)],[c_0_42,c_0_23]) ).

cnf(c_0_50,plain,
    ( tail_of(esk1_2(X1,X2)) = X1
    | tail_of(esk1_2(X1,X2)) = X2
    | X1 = X2
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_28])]) ).

cnf(c_0_51,negated_conjecture,
    ( in_path(tail_of(X1),esk13_0)
    | ~ on_path(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_44,c_0_23]) ).

cnf(c_0_52,negated_conjecture,
    ( head_of(X1) != head_of(X2)
    | tail_of(X3) != tail_of(X2)
    | ~ precedes(X3,X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_45,c_0_23]) ).

cnf(c_0_53,negated_conjecture,
    ( head_of(esk1_2(head_of(esk12_0),tail_of(X1))) = head_of(esk12_0)
    | head_of(esk1_2(head_of(esk12_0),tail_of(X1))) = tail_of(X1)
    | head_of(esk12_0) = tail_of(X1)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_54,negated_conjecture,
    edge(esk11_0),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_55,plain,
    ( tail_of(esk1_2(X1,tail_of(X2))) = tail_of(X2)
    | tail_of(esk1_2(X1,tail_of(X2))) = X1
    | X1 = tail_of(X2)
    | ~ vertex(X1)
    | ~ edge(X2) ),
    inference(spm,[status(thm)],[c_0_50,c_0_38]) ).

fof(c_0_56,plain,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ( ~ sequential(X13,X14)
        | ~ on_path(X13,X10)
        | ~ on_path(X14,X10)
        | precedes(X13,X14,X10)
        | ~ path(X11,X12,X10) )
      & ( ~ sequential(X13,X15)
        | ~ precedes(X15,X14,X10)
        | ~ on_path(X13,X10)
        | ~ on_path(X14,X10)
        | precedes(X13,X14,X10)
        | ~ path(X11,X12,X10) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[precedes_defn])])])])])])]) ).

cnf(c_0_57,plain,
    ( X1 = X2
    | X2 = tail_of(esk1_2(X1,X2))
    | X2 = head_of(esk1_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_58,negated_conjecture,
    ( vertex(tail_of(X1))
    | ~ on_path(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_30,c_0_51]) ).

cnf(c_0_59,negated_conjecture,
    ( head_of(esk12_0) != head_of(X1)
    | tail_of(esk11_0) != tail_of(X1) ),
    inference(spm,[status(thm)],[c_0_52,c_0_20]) ).

cnf(c_0_60,negated_conjecture,
    ( head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = tail_of(esk11_0)
    | head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
    | head_of(esk12_0) = tail_of(esk11_0) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_61,plain,
    ( X1 = X2
    | X1 = head_of(esk1_2(X1,X2))
    | X1 = tail_of(esk1_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_62,negated_conjecture,
    ( tail_of(esk1_2(head_of(esk12_0),tail_of(X1))) = head_of(esk12_0)
    | tail_of(esk1_2(head_of(esk12_0),tail_of(X1))) = tail_of(X1)
    | head_of(esk12_0) = tail_of(X1)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[c_0_55,c_0_47]) ).

cnf(c_0_63,plain,
    ( ~ precedes(X1,X2,X3)
    | ~ shortest_path(X4,X5,X3)
    | ~ precedes(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_64,plain,
    ( precedes(X4,X5,X3)
    | ~ path(X1,X2,X3)
    | ~ on_path(X5,X3)
    | ~ on_path(X4,X3)
    | ~ sequential(X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_65,plain,
    ( tail_of(esk1_2(X1,X2)) = X2
    | head_of(esk1_2(X1,X2)) = X2
    | X1 = X2
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_28])]) ).

cnf(c_0_66,negated_conjecture,
    vertex(tail_of(esk11_0)),
    inference(spm,[status(thm)],[c_0_58,c_0_49]) ).

cnf(c_0_67,negated_conjecture,
    ( head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = tail_of(esk11_0)
    | head_of(esk12_0) = tail_of(esk11_0)
    | tail_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) != tail_of(esk11_0) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_68,plain,
    ( tail_of(esk1_2(X1,X2)) = X1
    | head_of(esk1_2(X1,X2)) = X1
    | X1 = X2
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_28])]) ).

cnf(c_0_69,negated_conjecture,
    ( tail_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = tail_of(esk11_0)
    | tail_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
    | head_of(esk12_0) = tail_of(esk11_0) ),
    inference(spm,[status(thm)],[c_0_62,c_0_54]) ).

cnf(c_0_70,negated_conjecture,
    ( ~ precedes(X1,X2,esk13_0)
    | ~ precedes(X2,X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_63,c_0_23]) ).

cnf(c_0_71,plain,
    ( precedes(X1,X2,X3)
    | ~ shortest_path(X4,X5,X3)
    | ~ sequential(X1,X2)
    | ~ on_path(X2,X3)
    | ~ on_path(X1,X3) ),
    inference(spm,[status(thm)],[c_0_64,c_0_17]) ).

cnf(c_0_72,negated_conjecture,
    ( head_of(X1) != tail_of(esk11_0)
    | tail_of(X1) != head_of(esk12_0)
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_73,negated_conjecture,
    ( head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = tail_of(esk11_0)
    | head_of(esk12_0) = tail_of(esk11_0) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_60]),c_0_66]),c_0_47])]),c_0_67]) ).

cnf(c_0_74,negated_conjecture,
    ( tail_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
    | head_of(esk12_0) = tail_of(esk11_0) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_67]),c_0_66]),c_0_47])]),c_0_69]) ).

cnf(c_0_75,plain,
    ( X1 = X2
    | edge(esk1_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_76,negated_conjecture,
    ~ precedes(esk12_0,esk11_0,esk13_0),
    inference(spm,[status(thm)],[c_0_70,c_0_20]) ).

cnf(c_0_77,negated_conjecture,
    ( precedes(X1,X2,esk13_0)
    | ~ sequential(X1,X2)
    | ~ on_path(X2,esk13_0)
    | ~ on_path(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_71,c_0_23]) ).

fof(c_0_78,plain,
    ! [X9,X10,X9,X10] :
      ( ( edge(X9)
        | ~ sequential(X9,X10) )
      & ( edge(X10)
        | ~ sequential(X9,X10) )
      & ( X9 != X10
        | ~ sequential(X9,X10) )
      & ( head_of(X9) = tail_of(X10)
        | ~ sequential(X9,X10) )
      & ( ~ edge(X9)
        | ~ edge(X10)
        | X9 = X10
        | head_of(X9) != tail_of(X10)
        | sequential(X9,X10) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_defn])])])])]) ).

cnf(c_0_79,negated_conjecture,
    ( head_of(esk12_0) = tail_of(esk11_0)
    | ~ edge(esk1_2(head_of(esk12_0),tail_of(esk11_0))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).

cnf(c_0_80,plain,
    ( X1 = X2
    | edge(esk1_2(X1,X2))
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_28])]) ).

cnf(c_0_81,negated_conjecture,
    ~ sequential(esk12_0,esk11_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_49]),c_0_40])]) ).

cnf(c_0_82,plain,
    ( sequential(X1,X2)
    | X1 = X2
    | head_of(X1) != tail_of(X2)
    | ~ edge(X2)
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_78]) ).

cnf(c_0_83,negated_conjecture,
    head_of(esk12_0) = tail_of(esk11_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_66]),c_0_47])]) ).

cnf(c_0_84,negated_conjecture,
    edge(esk12_0),
    inference(spm,[status(thm)],[c_0_48,c_0_40]) ).

cnf(c_0_85,negated_conjecture,
    tail_of(esk12_0) != tail_of(esk11_0),
    inference(er,[status(thm)],[c_0_59]) ).

cnf(c_0_86,negated_conjecture,
    esk12_0 = esk11_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_54]),c_0_84])]) ).

cnf(c_0_87,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : GRA007+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.00/0.08  % Command  : run_ET %s %d
% 0.08/0.27  % Computer : n032.cluster.edu
% 0.08/0.27  % Model    : x86_64 x86_64
% 0.08/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27  % Memory   : 8042.1875MB
% 0.08/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27  % CPULimit : 300
% 0.08/0.27  % WCLimit  : 600
% 0.08/0.27  % DateTime : Mon May 30 22:57:43 EDT 2022
% 0.08/0.27  % CPUTime  : 
% 0.15/1.33  # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.15/1.33  # Preprocessing time       : 0.017 s
% 0.15/1.33  
% 0.15/1.33  # Proof found!
% 0.15/1.33  # SZS status Theorem
% 0.15/1.33  # SZS output start CNFRefutation
% See solution above
% 0.15/1.33  # Proof object total steps             : 88
% 0.15/1.33  # Proof object clause steps            : 67
% 0.15/1.33  # Proof object formula steps           : 21
% 0.15/1.33  # Proof object conjectures             : 41
% 0.15/1.33  # Proof object clause conjectures      : 38
% 0.15/1.33  # Proof object formula conjectures     : 3
% 0.15/1.33  # Proof object initial clauses used    : 21
% 0.15/1.33  # Proof object initial formulas used   : 10
% 0.15/1.33  # Proof object generating inferences   : 40
% 0.15/1.33  # Proof object simplifying inferences  : 31
% 0.15/1.33  # Training examples: 0 positive, 0 negative
% 0.15/1.33  # Parsed axioms                        : 18
% 0.15/1.33  # Removed by relevancy pruning/SinE    : 0
% 0.15/1.33  # Initial clauses                      : 63
% 0.15/1.33  # Removed in clause preprocessing      : 1
% 0.15/1.33  # Initial clauses in saturation        : 62
% 0.15/1.33  # Processed clauses                    : 802
% 0.15/1.33  # ...of these trivial                  : 72
% 0.15/1.33  # ...subsumed                          : 243
% 0.15/1.33  # ...remaining for further processing  : 487
% 0.15/1.33  # Other redundant clauses eliminated   : 37
% 0.15/1.33  # Clauses deleted for lack of memory   : 0
% 0.15/1.33  # Backward-subsumed                    : 13
% 0.15/1.33  # Backward-rewritten                   : 127
% 0.15/1.33  # Generated clauses                    : 5590
% 0.15/1.33  # ...of the previous two non-trivial   : 5233
% 0.15/1.33  # Contextual simplify-reflections      : 199
% 0.15/1.33  # Paramodulations                      : 5444
% 0.15/1.33  # Factorizations                       : 78
% 0.15/1.33  # Equation resolutions                 : 62
% 0.15/1.33  # Current number of processed clauses  : 341
% 0.15/1.33  #    Positive orientable unit clauses  : 16
% 0.15/1.33  #    Positive unorientable unit clauses: 0
% 0.15/1.33  #    Negative unit clauses             : 3
% 0.15/1.33  #    Non-unit-clauses                  : 322
% 0.15/1.33  # Current number of unprocessed clauses: 2885
% 0.15/1.33  # ...number of literals in the above   : 22655
% 0.15/1.33  # Current number of archived formulas  : 0
% 0.15/1.33  # Current number of archived clauses   : 143
% 0.15/1.33  # Clause-clause subsumption calls (NU) : 36161
% 0.15/1.33  # Rec. Clause-clause subsumption calls : 11188
% 0.15/1.33  # Non-unit clause-clause subsumptions  : 409
% 0.15/1.33  # Unit Clause-clause subsumption calls : 542
% 0.15/1.33  # Rewrite failures with RHS unbound    : 0
% 0.15/1.33  # BW rewrite match attempts            : 5
% 0.15/1.33  # BW rewrite match successes           : 5
% 0.15/1.33  # Condensation attempts                : 0
% 0.15/1.33  # Condensation successes               : 0
% 0.15/1.33  # Termbank termtop insertions          : 151679
% 0.15/1.33  
% 0.15/1.33  # -------------------------------------------------
% 0.15/1.33  # User time                : 0.157 s
% 0.15/1.33  # System time              : 0.006 s
% 0.15/1.33  # Total time               : 0.162 s
% 0.15/1.33  # Maximum resident set size: 7760 pages
% 0.15/23.32  eprover: CPU time limit exceeded, terminating
% 0.15/23.33  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.15/23.33  eprover: No such file or directory
% 0.15/23.34  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.15/23.34  eprover: No such file or directory
% 0.15/23.34  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.15/23.34  eprover: No such file or directory
% 0.15/23.35  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.15/23.35  eprover: No such file or directory
% 0.15/23.35  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.15/23.35  eprover: No such file or directory
% 0.15/23.35  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.15/23.35  eprover: No such file or directory
% 0.15/23.36  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.15/23.36  eprover: No such file or directory
% 0.15/23.36  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.15/23.36  eprover: No such file or directory
% 0.15/23.37  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.15/23.37  eprover: No such file or directory
% 0.15/23.37  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.15/23.37  eprover: No such file or directory
% 0.15/23.38  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.15/23.38  eprover: No such file or directory
% 0.15/23.41  eprover: CPU time limit exceeded, terminating
% 0.15/23.41  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.15/23.41  eprover: No such file or directory
% 0.15/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.15/23.42  eprover: No such file or directory
% 0.15/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.15/23.42  eprover: No such file or directory
% 0.15/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.15/23.43  eprover: No such file or directory
% 0.15/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.15/23.43  eprover: No such file or directory
% 0.15/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.15/23.44  eprover: No such file or directory
% 0.15/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.15/23.44  eprover: No such file or directory
% 0.15/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.15/23.44  eprover: No such file or directory
% 0.15/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.15/23.45  eprover: No such file or directory
%------------------------------------------------------------------------------