TSTP Solution File: GRA008+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRA008+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n022.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 : Thu Aug 31 00:00:07 EDT 2023

% Result   : Theorem 1.08s 1.17s
% Output   : CNFRefutation 1.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  137 (  18 unt;  37 typ;   0 def)
%            Number of atoms       :  453 ( 137 equ)
%            Maximal formula atoms :   37 (   4 avg)
%            Number of connectives :  575 ( 222   ~; 244   |;  81   &)
%                                         (   5 <=>;  21  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   55 (  25   >;  30   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   2 prp; 0-3 aty)
%            Number of functors    :   26 (  26 usr;  11 con; 0-4 aty)
%            Number of variables   :  233 (  15 sgn; 100   !;  10   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    edge: $i > $o ).

tff(decl_23,type,
    head_of: $i > $i ).

tff(decl_24,type,
    tail_of: $i > $i ).

tff(decl_25,type,
    vertex: $i > $o ).

tff(decl_26,type,
    complete: $o ).

tff(decl_27,type,
    path: ( $i * $i * $i ) > $o ).

tff(decl_28,type,
    empty: $i ).

tff(decl_29,type,
    path_cons: ( $i * $i ) > $i ).

tff(decl_30,type,
    on_path: ( $i * $i ) > $o ).

tff(decl_31,type,
    in_path: ( $i * $i ) > $o ).

tff(decl_32,type,
    sequential: ( $i * $i ) > $o ).

tff(decl_33,type,
    precedes: ( $i * $i * $i ) > $o ).

tff(decl_34,type,
    shortest_path: ( $i * $i * $i ) > $o ).

tff(decl_35,type,
    length_of: $i > $i ).

tff(decl_36,type,
    less_or_equal: ( $i * $i ) > $o ).

tff(decl_37,type,
    triangle: ( $i * $i * $i ) > $o ).

tff(decl_38,type,
    edges: $i ).

tff(decl_39,type,
    number_of_in: ( $i * $i ) > $i ).

tff(decl_40,type,
    sequential_pairs: $i ).

tff(decl_41,type,
    n1: $i ).

tff(decl_42,type,
    minus: ( $i * $i ) > $i ).

tff(decl_43,type,
    triangles: $i ).

tff(decl_44,type,
    graph: $i ).

tff(decl_45,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_46,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_47,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk4_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk7_1: $i > $i ).

tff(decl_52,type,
    esk8_1: $i > $i ).

tff(decl_53,type,
    esk9_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_54,type,
    esk10_0: $i ).

tff(decl_55,type,
    esk11_0: $i ).

tff(decl_56,type,
    esk12_0: $i ).

tff(decl_57,type,
    esk13_0: $i ).

tff(decl_58,type,
    esk14_0: $i ).

fof(sequential_is_triangle,conjecture,
    ( complete
   => ! [X2,X3,X7,X8,X4] :
        ( ( shortest_path(X2,X3,X4)
          & precedes(X7,X8,X4)
          & sequential(X7,X8) )
       => ? [X9] : triangle(X7,X8,X9) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_is_triangle) ).

fof(back_edge,lemma,
    ( 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/sandbox2/benchmark/theBenchmark.p',back_edge) ).

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/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).

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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GRA001+0.ax',edge_ends_are_vertices) ).

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/sandbox2/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/sandbox2/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).

fof(no_loops,axiom,
    ! [X1] :
      ( edge(X1)
     => head_of(X1) != tail_of(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',no_loops) ).

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/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_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/sandbox2/benchmark/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/sandbox2/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).

fof(c_0_12,negated_conjecture,
    ~ ( complete
     => ! [X2,X3,X7,X8,X4] :
          ( ( shortest_path(X2,X3,X4)
            & precedes(X7,X8,X4)
            & sequential(X7,X8) )
         => ? [X9] : triangle(X7,X8,X9) ) ),
    inference(assume_negation,[status(cth)],[sequential_is_triangle]) ).

fof(c_0_13,lemma,
    ! [X84,X85,X86,X87,X88] :
      ( ( edge(esk9_4(X84,X85,X86,X87))
        | ~ shortest_path(X84,X85,X88)
        | ~ precedes(X86,X87,X88)
        | ~ complete )
      & ( tail_of(esk9_4(X84,X85,X86,X87)) = head_of(X87)
        | ~ shortest_path(X84,X85,X88)
        | ~ precedes(X86,X87,X88)
        | ~ complete )
      & ( head_of(esk9_4(X84,X85,X86,X87)) = tail_of(X86)
        | ~ shortest_path(X84,X85,X88)
        | ~ precedes(X86,X87,X88)
        | ~ complete ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[back_edge])])])])])]) ).

fof(c_0_14,negated_conjecture,
    ! [X95] :
      ( complete
      & shortest_path(esk10_0,esk11_0,esk14_0)
      & precedes(esk12_0,esk13_0,esk14_0)
      & sequential(esk12_0,esk13_0)
      & ~ triangle(esk12_0,esk13_0,X95) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).

cnf(c_0_15,lemma,
    ( head_of(esk9_4(X1,X2,X3,X4)) = tail_of(X3)
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5)
    | ~ complete ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    complete,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_17,lemma,
    ( edge(esk9_4(X1,X2,X3,X4))
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5)
    | ~ complete ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_18,plain,
    ! [X53,X54,X55,X56,X57,X58,X59] :
      ( ( path(X53,X54,X55)
        | ~ shortest_path(X53,X54,X55) )
      & ( X53 != X54
        | ~ shortest_path(X53,X54,X55) )
      & ( ~ path(X53,X54,X56)
        | less_or_equal(length_of(X55),length_of(X56))
        | ~ shortest_path(X53,X54,X55) )
      & ( path(X57,X58,esk6_3(X57,X58,X59))
        | ~ path(X57,X58,X59)
        | X57 = X58
        | shortest_path(X57,X58,X59) )
      & ( ~ less_or_equal(length_of(X59),length_of(esk6_3(X57,X58,X59)))
        | ~ path(X57,X58,X59)
        | X57 = X58
        | shortest_path(X57,X58,X59) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[shortest_path_defn])])])])])]) ).

fof(c_0_19,plain,
    ! [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) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[precedes_properties]) ).

cnf(c_0_20,lemma,
    ( tail_of(esk9_4(X1,X2,X3,X4)) = head_of(X4)
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5)
    | ~ complete ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_21,plain,
    ( 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) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[complete_properties]) ).

fof(c_0_22,plain,
    ! [X14] :
      ( ( vertex(head_of(X14))
        | ~ edge(X14) )
      & ( vertex(tail_of(X14))
        | ~ edge(X14) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[edge_ends_are_vertices])])]) ).

cnf(c_0_23,lemma,
    ( head_of(esk9_4(X1,X2,X3,X4)) = tail_of(X3)
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).

cnf(c_0_24,negated_conjecture,
    shortest_path(esk10_0,esk11_0,esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_25,lemma,
    ( edge(esk9_4(X1,X2,X3,X4))
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_16])]) ).

fof(c_0_26,plain,
    ! [X33,X34,X35,X36] :
      ( ( vertex(X36)
        | ~ path(X33,X34,X35)
        | ~ in_path(X36,X35) )
      & ( on_path(esk4_4(X33,X34,X35,X36),X35)
        | ~ path(X33,X34,X35)
        | ~ in_path(X36,X35) )
      & ( X36 = head_of(esk4_4(X33,X34,X35,X36))
        | X36 = tail_of(esk4_4(X33,X34,X35,X36))
        | ~ path(X33,X34,X35)
        | ~ in_path(X36,X35) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[in_path_properties])])])]) ).

cnf(c_0_27,plain,
    ( path(X1,X2,X3)
    | ~ shortest_path(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_28,plain,
    ! [X29,X30,X31,X32] :
      ( ( edge(X32)
        | ~ path(X29,X30,X31)
        | ~ on_path(X32,X31) )
      & ( in_path(head_of(X32),X31)
        | ~ path(X29,X30,X31)
        | ~ on_path(X32,X31) )
      & ( in_path(tail_of(X32),X31)
        | ~ path(X29,X30,X31)
        | ~ on_path(X32,X31) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])]) ).

fof(c_0_29,plain,
    ! [X46,X47,X48,X49,X50,X51] :
      ( ( on_path(X49,X46)
        | ~ precedes(X49,X50,X46)
        | ~ path(X47,X48,X46) )
      & ( on_path(X50,X46)
        | ~ precedes(X49,X50,X46)
        | ~ path(X47,X48,X46) )
      & ( ~ sequential(X49,X50)
        | ~ sequential(X49,X51)
        | ~ precedes(X51,X50,X46)
        | ~ precedes(X49,X50,X46)
        | ~ path(X47,X48,X46) )
      & ( sequential(X49,esk5_3(X46,X49,X50))
        | sequential(X49,X50)
        | ~ precedes(X49,X50,X46)
        | ~ path(X47,X48,X46) )
      & ( precedes(esk5_3(X46,X49,X50),X50,X46)
        | sequential(X49,X50)
        | ~ precedes(X49,X50,X46)
        | ~ path(X47,X48,X46) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])]) ).

fof(c_0_30,plain,
    ! [X13] :
      ( ~ edge(X13)
      | head_of(X13) != tail_of(X13) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[no_loops])]) ).

cnf(c_0_31,lemma,
    ( tail_of(esk9_4(X1,X2,X3,X4)) = head_of(X4)
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_16])]) ).

fof(c_0_32,plain,
    ! [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) ) ),
    inference(fof_simplification,[status(thm)],[shortest_path_properties]) ).

fof(c_0_33,plain,
    ! [X15,X16] :
      ( ( edge(esk1_2(X15,X16))
        | ~ vertex(X15)
        | ~ vertex(X16)
        | X15 = X16
        | ~ complete )
      & ( X15 != head_of(esk1_2(X15,X16))
        | X16 != tail_of(esk1_2(X15,X16))
        | X16 != head_of(esk1_2(X15,X16))
        | X15 != tail_of(esk1_2(X15,X16))
        | ~ vertex(X15)
        | ~ vertex(X16)
        | X15 = X16
        | ~ complete )
      & ( X16 = head_of(esk1_2(X15,X16))
        | X15 = head_of(esk1_2(X15,X16))
        | ~ vertex(X15)
        | ~ vertex(X16)
        | X15 = X16
        | ~ complete )
      & ( X15 = tail_of(esk1_2(X15,X16))
        | X15 = head_of(esk1_2(X15,X16))
        | ~ vertex(X15)
        | ~ vertex(X16)
        | X15 = X16
        | ~ complete )
      & ( X16 = head_of(esk1_2(X15,X16))
        | X16 = tail_of(esk1_2(X15,X16))
        | ~ vertex(X15)
        | ~ vertex(X16)
        | X15 = X16
        | ~ complete )
      & ( X15 = tail_of(esk1_2(X15,X16))
        | X16 = tail_of(esk1_2(X15,X16))
        | ~ vertex(X15)
        | ~ vertex(X16)
        | X15 = X16
        | ~ complete ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).

cnf(c_0_34,plain,
    ( vertex(head_of(X1))
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_35,negated_conjecture,
    ( head_of(esk9_4(esk10_0,esk11_0,X1,X2)) = tail_of(X1)
    | ~ precedes(X1,X2,esk14_0) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_36,negated_conjecture,
    ( edge(esk9_4(esk10_0,esk11_0,X1,X2))
    | ~ precedes(X1,X2,esk14_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_24]) ).

cnf(c_0_37,plain,
    ( vertex(X1)
    | ~ path(X2,X3,X4)
    | ~ in_path(X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_38,negated_conjecture,
    path(esk10_0,esk11_0,esk14_0),
    inference(spm,[status(thm)],[c_0_27,c_0_24]) ).

cnf(c_0_39,plain,
    ( in_path(head_of(X1),X2)
    | ~ path(X3,X4,X2)
    | ~ on_path(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_40,plain,
    ( on_path(X1,X2)
    | ~ precedes(X3,X1,X2)
    | ~ path(X4,X5,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_41,negated_conjecture,
    precedes(esk12_0,esk13_0,esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_42,plain,
    ( ~ edge(X1)
    | head_of(X1) != tail_of(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_43,negated_conjecture,
    ( tail_of(esk9_4(esk10_0,esk11_0,X1,X2)) = head_of(X2)
    | ~ precedes(X1,X2,esk14_0) ),
    inference(spm,[status(thm)],[c_0_31,c_0_24]) ).

fof(c_0_44,plain,
    ! [X61,X62,X63,X64,X65,X66] :
      ( ( tail_of(X66) != tail_of(X63)
        | head_of(X66) != head_of(X64)
        | ~ shortest_path(X61,X62,X65)
        | ~ precedes(X63,X64,X65) )
      & ( ~ precedes(X64,X63,X65)
        | ~ shortest_path(X61,X62,X65)
        | ~ precedes(X63,X64,X65) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])]) ).

cnf(c_0_45,plain,
    ( X1 = tail_of(esk1_2(X1,X2))
    | X2 = tail_of(esk1_2(X1,X2))
    | X1 = X2
    | ~ vertex(X1)
    | ~ vertex(X2)
    | ~ complete ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_46,negated_conjecture,
    ( vertex(tail_of(X1))
    | ~ precedes(X1,X2,esk14_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_47,negated_conjecture,
    ( vertex(X1)
    | ~ in_path(X1,esk14_0) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_48,negated_conjecture,
    ( in_path(head_of(X1),esk14_0)
    | ~ on_path(X1,esk14_0) ),
    inference(spm,[status(thm)],[c_0_39,c_0_38]) ).

cnf(c_0_49,negated_conjecture,
    ( on_path(esk13_0,esk14_0)
    | ~ path(X1,X2,esk14_0) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_50,negated_conjecture,
    ( head_of(esk9_4(esk10_0,esk11_0,X1,X2)) != head_of(X2)
    | ~ precedes(X1,X2,esk14_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_36]) ).

cnf(c_0_51,plain,
    ( tail_of(X1) != tail_of(X2)
    | head_of(X1) != head_of(X3)
    | ~ shortest_path(X4,X5,X6)
    | ~ precedes(X2,X3,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_52,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_45,c_0_16])]) ).

cnf(c_0_53,negated_conjecture,
    vertex(tail_of(esk12_0)),
    inference(spm,[status(thm)],[c_0_46,c_0_41]) ).

cnf(c_0_54,negated_conjecture,
    ( vertex(head_of(X1))
    | ~ on_path(X1,esk14_0) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_55,negated_conjecture,
    on_path(esk13_0,esk14_0),
    inference(spm,[status(thm)],[c_0_49,c_0_38]) ).

cnf(c_0_56,negated_conjecture,
    ( tail_of(X1) != head_of(X2)
    | ~ precedes(X1,X2,esk14_0) ),
    inference(spm,[status(thm)],[c_0_50,c_0_35]) ).

fof(c_0_57,plain,
    ! [X67,X68,X69] :
      ( ( edge(X67)
        | ~ triangle(X67,X68,X69) )
      & ( edge(X68)
        | ~ triangle(X67,X68,X69) )
      & ( edge(X69)
        | ~ triangle(X67,X68,X69) )
      & ( sequential(X67,X68)
        | ~ triangle(X67,X68,X69) )
      & ( sequential(X68,X69)
        | ~ triangle(X67,X68,X69) )
      & ( sequential(X69,X67)
        | ~ triangle(X67,X68,X69) )
      & ( ~ edge(X67)
        | ~ edge(X68)
        | ~ edge(X69)
        | ~ sequential(X67,X68)
        | ~ sequential(X68,X69)
        | ~ sequential(X69,X67)
        | triangle(X67,X68,X69) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])]) ).

fof(c_0_58,plain,
    ! [X38,X39] :
      ( ( edge(X38)
        | ~ sequential(X38,X39) )
      & ( edge(X39)
        | ~ sequential(X38,X39) )
      & ( X38 != X39
        | ~ sequential(X38,X39) )
      & ( head_of(X38) = tail_of(X39)
        | ~ sequential(X38,X39) )
      & ( ~ edge(X38)
        | ~ edge(X39)
        | X38 = X39
        | head_of(X38) != tail_of(X39)
        | sequential(X38,X39) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_defn])])]) ).

cnf(c_0_59,negated_conjecture,
    ( head_of(X1) != head_of(X2)
    | tail_of(X1) != tail_of(X3)
    | ~ precedes(X3,X2,esk14_0) ),
    inference(spm,[status(thm)],[c_0_51,c_0_24]) ).

cnf(c_0_60,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_52,c_0_53]) ).

cnf(c_0_61,negated_conjecture,
    vertex(head_of(esk13_0)),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_62,negated_conjecture,
    tail_of(esk12_0) != head_of(esk13_0),
    inference(spm,[status(thm)],[c_0_56,c_0_41]) ).

cnf(c_0_63,plain,
    ( triangle(X1,X2,X3)
    | ~ edge(X1)
    | ~ edge(X2)
    | ~ edge(X3)
    | ~ sequential(X1,X2)
    | ~ sequential(X2,X3)
    | ~ sequential(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_64,plain,
    ( edge(X1)
    | ~ sequential(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_65,plain,
    ( edge(esk1_2(X1,X2))
    | X1 = X2
    | ~ vertex(X1)
    | ~ vertex(X2)
    | ~ complete ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_66,plain,
    ( edge(X1)
    | ~ sequential(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_67,negated_conjecture,
    sequential(esk12_0,esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_68,plain,
    ( X1 = head_of(esk1_2(X2,X1))
    | X2 = head_of(esk1_2(X2,X1))
    | X2 = X1
    | ~ vertex(X2)
    | ~ vertex(X1)
    | ~ complete ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_69,negated_conjecture,
    ( head_of(X1) != head_of(esk13_0)
    | tail_of(X1) != tail_of(esk12_0) ),
    inference(spm,[status(thm)],[c_0_59,c_0_41]) ).

cnf(c_0_70,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) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).

cnf(c_0_71,negated_conjecture,
    ~ triangle(esk12_0,esk13_0,X1),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_72,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_63,c_0_64]),c_0_64]),c_0_64]) ).

cnf(c_0_73,plain,
    ( X1 = X2
    | sequential(X1,X2)
    | ~ edge(X1)
    | ~ edge(X2)
    | head_of(X1) != tail_of(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_74,plain,
    ( X1 = X2
    | edge(esk1_2(X1,X2))
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_16])]) ).

cnf(c_0_75,negated_conjecture,
    edge(esk13_0),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_76,plain,
    ( X1 = tail_of(esk1_2(X1,X2))
    | X1 = head_of(esk1_2(X1,X2))
    | X1 = X2
    | ~ vertex(X1)
    | ~ vertex(X2)
    | ~ complete ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_77,plain,
    ( head_of(esk1_2(X1,X2)) = X2
    | head_of(esk1_2(X1,X2)) = X1
    | X2 = X1
    | ~ vertex(X1)
    | ~ vertex(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_16])]) ).

cnf(c_0_78,negated_conjecture,
    ( tail_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))) != head_of(esk13_0) ),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_79,negated_conjecture,
    ( ~ sequential(X1,esk12_0)
    | ~ sequential(esk13_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_67])]) ).

cnf(c_0_80,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_73,c_0_74]) ).

cnf(c_0_81,negated_conjecture,
    edge(esk12_0),
    inference(spm,[status(thm)],[c_0_64,c_0_67]) ).

cnf(c_0_82,negated_conjecture,
    ( esk13_0 = X1
    | sequential(esk13_0,X1)
    | tail_of(X1) != head_of(esk13_0)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[c_0_73,c_0_75]) ).

cnf(c_0_83,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_76,c_0_16])]) ).

cnf(c_0_84,negated_conjecture,
    ( head_of(esk1_2(head_of(esk13_0),X1)) = head_of(esk13_0)
    | head_of(esk1_2(head_of(esk13_0),X1)) = X1
    | X1 = head_of(esk13_0)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[c_0_77,c_0_61]) ).

cnf(c_0_85,negated_conjecture,
    ( head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) != head_of(esk13_0)
    | ~ edge(esk1_2(head_of(esk13_0),tail_of(esk12_0))) ),
    inference(spm,[status(thm)],[c_0_42,c_0_78]) ).

cnf(c_0_86,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_79,c_0_80]),c_0_81])]) ).

cnf(c_0_87,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_82,c_0_83]),c_0_74]) ).

cnf(c_0_88,negated_conjecture,
    ( head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
    | head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_53]),c_0_62]) ).

cnf(c_0_89,negated_conjecture,
    head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) != head_of(esk13_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_74]),c_0_53]),c_0_61])]),c_0_62]) ).

cnf(c_0_90,plain,
    ( head_of(X1) = tail_of(X2)
    | ~ sequential(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_91,plain,
    ( X1 = head_of(esk1_2(X2,X1))
    | X1 = tail_of(esk1_2(X2,X1))
    | X2 = X1
    | ~ vertex(X2)
    | ~ vertex(X1)
    | ~ complete ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_92,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_86,c_0_87]) ).

cnf(c_0_93,negated_conjecture,
    head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0),
    inference(sr,[status(thm)],[c_0_88,c_0_89]) ).

cnf(c_0_94,negated_conjecture,
    tail_of(esk13_0) = head_of(esk12_0),
    inference(spm,[status(thm)],[c_0_90,c_0_67]) ).

cnf(c_0_95,plain,
    ( tail_of(esk1_2(X1,X2)) = X2
    | head_of(esk1_2(X1,X2)) = X2
    | X2 = X1
    | ~ vertex(X1)
    | ~ vertex(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_16])]) ).

cnf(c_0_96,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 ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_53]),c_0_61])]),c_0_62]) ).

cnf(c_0_97,negated_conjecture,
    tail_of(esk12_0) != head_of(esk12_0),
    inference(spm,[status(thm)],[c_0_69,c_0_94]) ).

cnf(c_0_98,negated_conjecture,
    esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk12_0,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_94]),c_0_61]),c_0_53])]),c_0_97]),c_0_62]) ).

cnf(c_0_99,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_98]),c_0_97]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRA008+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun Aug 27 03:29:10 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.59  start to proof: theBenchmark
% 1.08/1.17  % Version  : CSE_E---1.5
% 1.08/1.17  % Problem  : theBenchmark.p
% 1.08/1.17  % Proof found
% 1.08/1.17  % SZS status Theorem for theBenchmark.p
% 1.08/1.17  % SZS output start Proof
% See solution above
% 1.08/1.18  % Total time : 0.571000 s
% 1.08/1.18  % SZS output end Proof
% 1.08/1.18  % Total time : 0.575000 s
%------------------------------------------------------------------------------