TSTP Solution File: GRA009+2 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : GRA009+2 : 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 07:16:08 EDT 2022

% Result   : Theorem 0.17s 2.36s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   96 (  17 unt;   0 def)
%            Number of atoms       :  432 ( 135 equ)
%            Maximal formula atoms :   37 (   4 avg)
%            Number of connectives :  556 ( 220   ~; 253   |;  63   &)
%                                         (   3 <=>;  15  =>;   1  <=;   1 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   2 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-4 aty)
%            Number of variables   :  197 (  23 sgn  83   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(complete_means_path_means_stuff_means_triangles,conjecture,
    ( complete
   => ! [X4,X2,X3] :
        ( shortest_path(X2,X3,X4)
       => ! [X7,X8] :
            ( ( on_path(X7,X4)
              & on_path(X8,X4)
              & sequential(X7,X8) )
           => ? [X9] : triangle(X7,X8,X9) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',complete_means_path_means_stuff_means_triangles) ).

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(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(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(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(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(triangle_defn,axiom,
    ! [X7,X8,X9] :
      ( triangle(X7,X8,X9)
    <=> ( edge(X7)
        & edge(X8)
        & edge(X9)
        & sequential(X7,X8)
        & sequential(X8,X9)
        & sequential(X9,X7) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',triangle_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(no_loops,axiom,
    ! [X1] :
      ( edge(X1)
     => head_of(X1) != tail_of(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).

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(c_0_11,negated_conjecture,
    ~ ( complete
     => ! [X4,X2,X3] :
          ( shortest_path(X2,X3,X4)
         => ! [X7,X8] :
              ( ( on_path(X7,X4)
                & on_path(X8,X4)
                & sequential(X7,X8) )
             => ? [X9] : triangle(X7,X8,X9) ) ) ),
    inference(assume_negation,[status(cth)],[complete_means_path_means_stuff_means_triangles]) ).

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,negated_conjecture,
    ! [X15] :
      ( complete
      & shortest_path(esk10_0,esk11_0,esk9_0)
      & on_path(esk12_0,esk9_0)
      & on_path(esk13_0,esk9_0)
      & sequential(esk12_0,esk13_0)
      & ~ triangle(esk12_0,esk13_0,X15) ),
    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_11])])])])])]) ).

fof(c_0_14,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])])])])])]) ).

cnf(c_0_15,plain,
    ( path(X1,X2,X3)
    | ~ shortest_path(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,negated_conjecture,
    shortest_path(esk10_0,esk11_0,esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_17,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_18,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])])])])])])]) ).

fof(c_0_19,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])])])])])])]) ).

fof(c_0_20,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_21,plain,
    ( vertex(X1)
    | ~ in_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,negated_conjecture,
    path(esk10_0,esk11_0,esk9_0),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_23,plain,
    ( in_path(tail_of(X1),X2)
    | ~ on_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24,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_18]) ).

cnf(c_0_25,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_19]) ).

cnf(c_0_26,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_20]) ).

cnf(c_0_27,negated_conjecture,
    complete,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_28,negated_conjecture,
    ( vertex(X1)
    | ~ in_path(X1,esk9_0) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    ( in_path(tail_of(X1),esk9_0)
    | ~ on_path(X1,esk9_0) ),
    inference(spm,[status(thm)],[c_0_23,c_0_22]) ).

cnf(c_0_30,plain,
    ( in_path(head_of(X1),X2)
    | ~ on_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_31,plain,
    ! [X10,X11,X12,X10,X11,X12] :
      ( ( edge(X10)
        | ~ triangle(X10,X11,X12) )
      & ( edge(X11)
        | ~ triangle(X10,X11,X12) )
      & ( edge(X12)
        | ~ triangle(X10,X11,X12) )
      & ( sequential(X10,X11)
        | ~ triangle(X10,X11,X12) )
      & ( sequential(X11,X12)
        | ~ triangle(X10,X11,X12) )
      & ( sequential(X12,X10)
        | ~ triangle(X10,X11,X12) )
      & ( ~ edge(X10)
        | ~ edge(X11)
        | ~ edge(X12)
        | ~ sequential(X10,X11)
        | ~ sequential(X11,X12)
        | ~ sequential(X12,X10)
        | triangle(X10,X11,X12) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])])])]) ).

fof(c_0_32,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_33,negated_conjecture,
    ( head_of(X1) != head_of(X2)
    | tail_of(X3) != tail_of(X2)
    | ~ precedes(X3,X1,esk9_0) ),
    inference(spm,[status(thm)],[c_0_24,c_0_16]) ).

cnf(c_0_34,negated_conjecture,
    ( precedes(X1,X2,esk9_0)
    | ~ sequential(X1,X2)
    | ~ on_path(X2,esk9_0)
    | ~ on_path(X1,esk9_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_22]) ).

cnf(c_0_35,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_26,c_0_27])]) ).

cnf(c_0_36,negated_conjecture,
    ( vertex(tail_of(X1))
    | ~ on_path(X1,esk9_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_37,negated_conjecture,
    ( in_path(head_of(X1),esk9_0)
    | ~ on_path(X1,esk9_0) ),
    inference(spm,[status(thm)],[c_0_30,c_0_22]) ).

cnf(c_0_38,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_20]) ).

cnf(c_0_39,plain,
    ( triangle(X1,X2,X3)
    | ~ sequential(X3,X1)
    | ~ sequential(X2,X3)
    | ~ sequential(X1,X2)
    | ~ edge(X3)
    | ~ edge(X2)
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_40,plain,
    ( edge(X1)
    | ~ sequential(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_41,plain,
    ( X1 = X2
    | edge(esk1_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_42,plain,
    ( edge(X2)
    | ~ sequential(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_43,negated_conjecture,
    sequential(esk12_0,esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_44,negated_conjecture,
    ( head_of(X1) != head_of(X2)
    | tail_of(X3) != tail_of(X2)
    | ~ sequential(X3,X1)
    | ~ on_path(X1,esk9_0)
    | ~ on_path(X3,esk9_0) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_45,negated_conjecture,
    on_path(esk13_0,esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_46,negated_conjecture,
    ( tail_of(esk1_2(X1,tail_of(X2))) = tail_of(X2)
    | tail_of(esk1_2(X1,tail_of(X2))) = X1
    | X1 = tail_of(X2)
    | ~ on_path(X2,esk9_0)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_47,negated_conjecture,
    on_path(esk12_0,esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_48,negated_conjecture,
    ( vertex(head_of(X1))
    | ~ on_path(X1,esk9_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_37]) ).

cnf(c_0_49,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_38,c_0_27])]) ).

cnf(c_0_50,negated_conjecture,
    ~ triangle(esk12_0,esk13_0,X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_51,plain,
    ( triangle(X1,X2,X3)
    | ~ sequential(X3,X1)
    | ~ sequential(X2,X3)
    | ~ sequential(X1,X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_39,c_0_40]),c_0_40]),c_0_40]) ).

cnf(c_0_52,plain,
    ( sequential(X1,X2)
    | X1 = X2
    | head_of(X1) != tail_of(X2)
    | ~ edge(X2)
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_53,plain,
    ( X1 = X2
    | edge(esk1_2(X1,X2))
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_27])]) ).

cnf(c_0_54,negated_conjecture,
    edge(esk13_0),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_55,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_20]) ).

cnf(c_0_56,negated_conjecture,
    ( head_of(esk13_0) != head_of(X1)
    | tail_of(X2) != tail_of(X1)
    | ~ sequential(X2,esk13_0)
    | ~ on_path(X2,esk9_0) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_57,negated_conjecture,
    ( tail_of(esk1_2(X1,tail_of(esk12_0))) = tail_of(esk12_0)
    | tail_of(esk1_2(X1,tail_of(esk12_0))) = X1
    | X1 = tail_of(esk12_0)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_58,negated_conjecture,
    vertex(head_of(esk13_0)),
    inference(spm,[status(thm)],[c_0_48,c_0_45]) ).

cnf(c_0_59,negated_conjecture,
    ( head_of(esk1_2(X1,tail_of(X2))) = tail_of(X2)
    | head_of(esk1_2(X1,tail_of(X2))) = X1
    | X1 = tail_of(X2)
    | ~ on_path(X2,esk9_0)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_36]) ).

cnf(c_0_60,negated_conjecture,
    ( ~ sequential(X1,esk12_0)
    | ~ sequential(esk13_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_43])]) ).

cnf(c_0_61,plain,
    ( esk1_2(X1,X2) = X3
    | X1 = X2
    | sequential(esk1_2(X1,X2),X3)
    | tail_of(X3) != head_of(esk1_2(X1,X2))
    | ~ vertex(X2)
    | ~ vertex(X1)
    | ~ edge(X3) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_62,negated_conjecture,
    edge(esk12_0),
    inference(spm,[status(thm)],[c_0_40,c_0_43]) ).

cnf(c_0_63,negated_conjecture,
    ( esk13_0 = X1
    | sequential(esk13_0,X1)
    | tail_of(X1) != head_of(esk13_0)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[c_0_52,c_0_54]) ).

cnf(c_0_64,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_55,c_0_27])]) ).

cnf(c_0_65,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_20]) ).

cnf(c_0_66,negated_conjecture,
    ( head_of(esk13_0) != head_of(X1)
    | tail_of(esk12_0) != tail_of(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_47]),c_0_43])]) ).

cnf(c_0_67,negated_conjecture,
    ( tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
    | tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
    | tail_of(esk12_0) = head_of(esk13_0) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_68,negated_conjecture,
    ( head_of(esk1_2(X1,tail_of(esk12_0))) = tail_of(esk12_0)
    | head_of(esk1_2(X1,tail_of(esk12_0))) = X1
    | X1 = tail_of(esk12_0)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[c_0_59,c_0_47]) ).

cnf(c_0_69,negated_conjecture,
    ( esk1_2(X1,X2) = esk12_0
    | X1 = X2
    | head_of(esk1_2(X1,X2)) != tail_of(esk12_0)
    | ~ sequential(esk13_0,esk1_2(X1,X2))
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).

cnf(c_0_70,negated_conjecture,
    ( head_of(esk1_2(X1,X2)) = X1
    | esk1_2(X1,X2) = esk13_0
    | X1 = X2
    | sequential(esk13_0,esk1_2(X1,X2))
    | X1 != head_of(esk13_0)
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_53]) ).

cnf(c_0_71,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_65,c_0_27])]) ).

cnf(c_0_72,negated_conjecture,
    ( tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
    | tail_of(esk12_0) = head_of(esk13_0)
    | head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) != head_of(esk13_0) ),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_73,negated_conjecture,
    ( head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
    | head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
    | tail_of(esk12_0) = head_of(esk13_0) ),
    inference(spm,[status(thm)],[c_0_68,c_0_58]) ).

cnf(c_0_74,plain,
    ( head_of(X1) = tail_of(X2)
    | ~ sequential(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_75,plain,
    ( ~ precedes(X1,X2,X3)
    | ~ shortest_path(X4,X5,X3)
    | ~ precedes(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_76,negated_conjecture,
    ( head_of(esk1_2(X1,X2)) = X1
    | esk1_2(X1,X2) = esk13_0
    | esk1_2(X1,X2) = esk12_0
    | X1 = X2
    | head_of(esk1_2(X1,X2)) != tail_of(esk12_0)
    | X1 != head_of(esk13_0)
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_77,negated_conjecture,
    ( head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
    | tail_of(esk12_0) = head_of(esk13_0)
    | ~ vertex(tail_of(esk12_0)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_58])]),c_0_73]) ).

cnf(c_0_78,negated_conjecture,
    tail_of(esk13_0) = head_of(esk12_0),
    inference(spm,[status(thm)],[c_0_74,c_0_43]) ).

fof(c_0_79,plain,
    ! [X2] :
      ( ~ edge(X2)
      | head_of(X2) != tail_of(X2) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[no_loops])]) ).

cnf(c_0_80,negated_conjecture,
    ( ~ precedes(X1,X2,esk9_0)
    | ~ precedes(X2,X1,esk9_0) ),
    inference(spm,[status(thm)],[c_0_75,c_0_16]) ).

cnf(c_0_81,negated_conjecture,
    ( esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk12_0
    | esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk13_0
    | tail_of(esk12_0) = head_of(esk13_0)
    | ~ vertex(tail_of(esk12_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_58])]) ).

cnf(c_0_82,negated_conjecture,
    tail_of(esk12_0) != head_of(esk12_0),
    inference(spm,[status(thm)],[c_0_66,c_0_78]) ).

cnf(c_0_83,plain,
    ( head_of(X1) != tail_of(X1)
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_79]) ).

cnf(c_0_84,negated_conjecture,
    ( ~ precedes(X1,X2,esk9_0)
    | ~ sequential(X2,X1)
    | ~ on_path(X1,esk9_0)
    | ~ on_path(X2,esk9_0) ),
    inference(spm,[status(thm)],[c_0_80,c_0_34]) ).

cnf(c_0_85,negated_conjecture,
    ( esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk12_0
    | tail_of(esk12_0) = head_of(esk13_0)
    | ~ vertex(tail_of(esk12_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_81]),c_0_78]),c_0_58])]),c_0_82]) ).

cnf(c_0_86,negated_conjecture,
    head_of(esk13_0) != head_of(esk12_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_78]),c_0_54])]) ).

fof(c_0_87,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_88,negated_conjecture,
    ( ~ sequential(X1,X2)
    | ~ sequential(X2,X1)
    | ~ on_path(X2,esk9_0)
    | ~ on_path(X1,esk9_0) ),
    inference(spm,[status(thm)],[c_0_84,c_0_34]) ).

cnf(c_0_89,negated_conjecture,
    ( tail_of(esk12_0) = head_of(esk13_0)
    | ~ vertex(tail_of(esk12_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_85]),c_0_58])]),c_0_86]) ).

cnf(c_0_90,plain,
    ( vertex(tail_of(X1))
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_87]) ).

cnf(c_0_91,negated_conjecture,
    ( ~ sequential(X1,esk13_0)
    | ~ sequential(esk13_0,X1)
    | ~ on_path(X1,esk9_0) ),
    inference(spm,[status(thm)],[c_0_88,c_0_45]) ).

cnf(c_0_92,negated_conjecture,
    tail_of(esk12_0) = head_of(esk13_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_62])]) ).

cnf(c_0_93,negated_conjecture,
    ~ sequential(esk13_0,esk12_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_47]),c_0_43])]) ).

cnf(c_0_94,negated_conjecture,
    esk13_0 = esk12_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_92]),c_0_62])]),c_0_93]) ).

cnf(c_0_95,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_94])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : GRA009+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.05/0.10  % Command  : run_ET %s %d
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 600
% 0.10/0.29  % DateTime : Mon May 30 22:30:58 EDT 2022
% 0.10/0.29  % CPUTime  : 
% 0.17/2.36  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.17/2.36  # Preprocessing time       : 0.013 s
% 0.17/2.36  
% 0.17/2.36  # Proof found!
% 0.17/2.36  # SZS status Theorem
% 0.17/2.36  # SZS output start CNFRefutation
% See solution above
% 0.17/2.36  # Proof object total steps             : 96
% 0.17/2.36  # Proof object clause steps            : 73
% 0.17/2.36  # Proof object formula steps           : 23
% 0.17/2.36  # Proof object conjectures             : 50
% 0.17/2.36  # Proof object clause conjectures      : 47
% 0.17/2.36  # Proof object formula conjectures     : 3
% 0.17/2.36  # Proof object initial clauses used    : 25
% 0.17/2.36  # Proof object initial formulas used   : 11
% 0.17/2.36  # Proof object generating inferences   : 41
% 0.17/2.36  # Proof object simplifying inferences  : 43
% 0.17/2.36  # Training examples: 0 positive, 0 negative
% 0.17/2.36  # Parsed axioms                        : 18
% 0.17/2.36  # Removed by relevancy pruning/SinE    : 0
% 0.17/2.36  # Initial clauses                      : 65
% 0.17/2.36  # Removed in clause preprocessing      : 1
% 0.17/2.36  # Initial clauses in saturation        : 64
% 0.17/2.36  # Processed clauses                    : 6095
% 0.17/2.36  # ...of these trivial                  : 414
% 0.17/2.36  # ...subsumed                          : 3020
% 0.17/2.36  # ...remaining for further processing  : 2661
% 0.17/2.36  # Other redundant clauses eliminated   : 102
% 0.17/2.36  # Clauses deleted for lack of memory   : 0
% 0.17/2.36  # Backward-subsumed                    : 249
% 0.17/2.36  # Backward-rewritten                   : 1448
% 0.17/2.36  # Generated clauses                    : 38546
% 0.17/2.36  # ...of the previous two non-trivial   : 35768
% 0.17/2.36  # Contextual simplify-reflections      : 6455
% 0.17/2.36  # Paramodulations                      : 38133
% 0.17/2.36  # Factorizations                       : 145
% 0.17/2.36  # Equation resolutions                 : 268
% 0.17/2.36  # Current number of processed clauses  : 962
% 0.17/2.36  #    Positive orientable unit clauses  : 14
% 0.17/2.36  #    Positive unorientable unit clauses: 0
% 0.17/2.36  #    Negative unit clauses             : 2
% 0.17/2.36  #    Non-unit-clauses                  : 946
% 0.17/2.36  # Current number of unprocessed clauses: 9212
% 0.17/2.36  # ...number of literals in the above   : 76440
% 0.17/2.36  # Current number of archived formulas  : 0
% 0.17/2.36  # Current number of archived clauses   : 1697
% 0.17/2.36  # Clause-clause subsumption calls (NU) : 1290944
% 0.17/2.36  # Rec. Clause-clause subsumption calls : 90175
% 0.17/2.36  # Non-unit clause-clause subsumptions  : 9087
% 0.17/2.36  # Unit Clause-clause subsumption calls : 989
% 0.17/2.36  # Rewrite failures with RHS unbound    : 0
% 0.17/2.36  # BW rewrite match attempts            : 5
% 0.17/2.36  # BW rewrite match successes           : 4
% 0.17/2.36  # Condensation attempts                : 0
% 0.17/2.36  # Condensation successes               : 0
% 0.17/2.36  # Termbank termtop insertions          : 1185705
% 0.17/2.36  
% 0.17/2.36  # -------------------------------------------------
% 0.17/2.36  # User time                : 1.217 s
% 0.17/2.36  # System time              : 0.026 s
% 0.17/2.36  # Total time               : 1.243 s
% 0.17/2.36  # Maximum resident set size: 32580 pages
% 0.17/23.34  eprover: CPU time limit exceeded, terminating
% 0.17/23.35  eprover: CPU time limit exceeded, terminating
% 0.17/23.35  eprover: CPU time limit exceeded, terminating
% 0.17/23.36  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.36  eprover: No such file or directory
% 0.17/23.36  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.36  eprover: No such file or directory
% 0.17/23.36  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.36  eprover: No such file or directory
% 0.17/23.37  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.37  eprover: No such file or directory
% 0.17/23.37  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.37  eprover: No such file or directory
% 0.17/23.37  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.37  eprover: No such file or directory
% 0.17/23.37  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.37  eprover: No such file or directory
% 0.17/23.37  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.37  eprover: No such file or directory
% 0.17/23.37  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.37  eprover: No such file or directory
% 0.17/23.37  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.37  eprover: No such file or directory
% 0.17/23.38  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.38  eprover: No such file or directory
% 0.17/23.38  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.38  eprover: No such file or directory
% 0.17/23.38  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.38  eprover: No such file or directory
% 0.17/23.38  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.38  eprover: No such file or directory
% 0.17/23.38  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.38  eprover: No such file or directory
% 0.17/23.38  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.38  eprover: No such file or directory
% 0.17/23.38  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.38  eprover: No such file or directory
% 0.17/23.39  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.39  eprover: No such file or directory
% 0.17/23.39  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.39  eprover: No such file or directory
% 0.17/23.39  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.39  eprover: No such file or directory
% 0.17/23.39  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.39  eprover: No such file or directory
% 0.17/23.39  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.peprover: 
% 0.17/23.39  Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.39  eprover: No such file or directory
% 0.17/23.39  eprover: No such file or directory
% 0.17/23.39  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.39  eprover: No such file or directory
% 0.17/23.40  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.40  eprover: No such file or directory
% 0.17/23.40  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.40  eprover: No such file or directory
% 0.17/23.40  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.40  eprover: No such file or directory
% 0.17/23.40  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.40  eprover: No such file or directory
% 0.17/23.40  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.40  eprover: No such file or directory
% 0.17/23.40  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.40  eprover: No such file or directory
% 0.17/23.40  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.40  eprover: No such file or directory
% 0.17/23.41  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.41  eprover: No such file or directory
% 0.17/23.41  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.41  eprover: No such file or directory
%------------------------------------------------------------------------------