TSTP Solution File: GRA012+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRA012+1 : 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 : n021.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 00:00:09 EDT 2023
% Result : Theorem 6.96s 7.01s
% Output : CNFRefutation 6.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 47
% Syntax : Number of formulae : 152 ( 21 unt; 34 typ; 0 def)
% Number of atoms : 482 ( 170 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 582 ( 218 ~; 266 |; 71 &)
% ( 4 <=>; 21 =>; 1 <=; 1 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 24 >; 27 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-4 aty)
% Number of variables : 235 ( 34 sgn; 104 !; 8 ?; 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_0: $i ).
tff(decl_54,type,
esk10_0: $i ).
tff(decl_55,type,
esk11_0: $i ).
fof(triangles_on_a_path,conjecture,
( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> number_of_in(triangles,X4) = minus(length_of(X4),n1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangles_on_a_path) ).
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(length_defn,axiom,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> length_of(X4) = number_of_in(edges,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',length_defn) ).
fof(path_length_sequential_pairs,axiom,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> number_of_in(sequential_pairs,X4) = minus(length_of(X4),n1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
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/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_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/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(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(sequential_pairs_and_triangles,axiom,
! [X4,X2,X3] :
( ( path(X2,X3,X4)
& ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) )
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
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(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(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',no_loops) ).
fof(c_0_13,negated_conjecture,
~ ( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> number_of_in(triangles,X4) = minus(length_of(X4),n1) ) ),
inference(assume_negation,[status(cth)],[triangles_on_a_path]) ).
fof(c_0_14,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_15,negated_conjecture,
( complete
& shortest_path(esk10_0,esk11_0,esk9_0)
& number_of_in(triangles,esk9_0) != minus(length_of(esk9_0),n1) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_16,plain,
! [X70,X71,X72] :
( ~ path(X70,X71,X72)
| length_of(X72) = number_of_in(edges,X72) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[length_defn])]) ).
cnf(c_0_17,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
shortest_path(esk10_0,esk11_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( length_of(X3) = number_of_in(edges,X3)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
path(esk10_0,esk11_0,esk9_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_21,plain,
! [X73,X74,X75] :
( ~ path(X73,X74,X75)
| number_of_in(sequential_pairs,X75) = minus(length_of(X75),n1) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[path_length_sequential_pairs])]) ).
fof(c_0_22,plain,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
| ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) )
=> precedes(X7,X8,X4) ) ),
inference(fof_simplification,[status(thm)],[precedes_defn]) ).
cnf(c_0_23,negated_conjecture,
number_of_in(triangles,esk9_0) != minus(length_of(esk9_0),n1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
length_of(esk9_0) = number_of_in(edges,esk9_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
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])])])]) ).
fof(c_0_27,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_28,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_29,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( ~ sequential(X43,X44)
| ~ on_path(X43,X40)
| ~ on_path(X44,X40)
| precedes(X43,X44,X40)
| ~ path(X41,X42,X40) )
& ( ~ sequential(X43,X45)
| ~ precedes(X45,X44,X40)
| ~ on_path(X43,X40)
| ~ on_path(X44,X40)
| precedes(X43,X44,X40)
| ~ path(X41,X42,X40) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
fof(c_0_30,plain,
! [X76,X77,X78,X81] :
( ( on_path(esk7_1(X76),X76)
| ~ path(X77,X78,X76)
| number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) )
& ( on_path(esk8_1(X76),X76)
| ~ path(X77,X78,X76)
| number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) )
& ( sequential(esk7_1(X76),esk8_1(X76))
| ~ path(X77,X78,X76)
| number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) )
& ( ~ triangle(esk7_1(X76),esk8_1(X76),X81)
| ~ path(X77,X78,X76)
| number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) ) ),
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)],[sequential_pairs_and_triangles])])])])])]) ).
cnf(c_0_31,negated_conjecture,
minus(number_of_in(edges,esk9_0),n1) != number_of_in(triangles,esk9_0),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
minus(number_of_in(edges,esk9_0),n1) = number_of_in(sequential_pairs,esk9_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_24]) ).
fof(c_0_33,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]) ).
cnf(c_0_34,plain,
( vertex(X1)
| ~ path(X2,X3,X4)
| ~ in_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( in_path(head_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
( in_path(tail_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_37,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_28])])])]) ).
cnf(c_0_38,plain,
( precedes(X1,X2,X3)
| ~ sequential(X1,X2)
| ~ on_path(X1,X3)
| ~ on_path(X2,X3)
| ~ path(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( on_path(esk8_1(X1),X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,negated_conjecture,
number_of_in(triangles,esk9_0) != number_of_in(sequential_pairs,esk9_0),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_41,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_33])])])])]) ).
cnf(c_0_42,negated_conjecture,
( vertex(X1)
| ~ in_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
cnf(c_0_43,negated_conjecture,
( in_path(head_of(X1),esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_20]) ).
cnf(c_0_44,negated_conjecture,
( in_path(tail_of(X1),esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_20]) ).
cnf(c_0_45,plain,
( on_path(esk7_1(X1),X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_46,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_37]) ).
cnf(c_0_47,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_38,c_0_20]) ).
cnf(c_0_48,negated_conjecture,
on_path(esk8_1(esk9_0),esk9_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_20]),c_0_40]) ).
cnf(c_0_49,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_41]) ).
cnf(c_0_50,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_51,negated_conjecture,
( vertex(head_of(X1))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,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_41]) ).
cnf(c_0_53,negated_conjecture,
( vertex(tail_of(X1))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_54,negated_conjecture,
on_path(esk7_1(esk9_0),esk9_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_20]),c_0_40]) ).
cnf(c_0_55,plain,
( edge(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_56,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_41]) ).
cnf(c_0_57,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_41]) ).
cnf(c_0_58,plain,
( edge(X1)
| ~ path(X2,X3,X4)
| ~ on_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_59,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ precedes(X3,X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_18]) ).
cnf(c_0_60,negated_conjecture,
( precedes(X1,esk8_1(esk9_0),esk9_0)
| ~ sequential(X1,esk8_1(esk9_0))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_61,plain,
( sequential(esk7_1(X1),esk8_1(X1))
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_62,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_49,c_0_50])]) ).
cnf(c_0_63,negated_conjecture,
vertex(head_of(esk8_1(esk9_0))),
inference(spm,[status(thm)],[c_0_51,c_0_48]) ).
cnf(c_0_64,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_52,c_0_50])]) ).
cnf(c_0_65,negated_conjecture,
vertex(tail_of(esk7_1(esk9_0))),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_66,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_50])]) ).
cnf(c_0_67,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_56,c_0_50])]) ).
cnf(c_0_68,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_57,c_0_50])]) ).
fof(c_0_69,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_70,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_71,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_20]) ).
cnf(c_0_72,negated_conjecture,
( head_of(X1) != head_of(esk8_1(esk9_0))
| tail_of(X1) != tail_of(X2)
| ~ sequential(X2,esk8_1(esk9_0))
| ~ on_path(X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_73,negated_conjecture,
sequential(esk7_1(esk9_0),esk8_1(esk9_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_20]),c_0_40]) ).
cnf(c_0_74,negated_conjecture,
( tail_of(esk1_2(X1,head_of(esk8_1(esk9_0)))) = X1
| head_of(esk1_2(X1,head_of(esk8_1(esk9_0)))) = X1
| X1 = head_of(esk8_1(esk9_0))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_75,negated_conjecture,
( head_of(esk1_2(tail_of(esk7_1(esk9_0)),X1)) = tail_of(esk7_1(esk9_0))
| head_of(esk1_2(tail_of(esk7_1(esk9_0)),X1)) = X1
| X1 = tail_of(esk7_1(esk9_0))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_76,negated_conjecture,
( X1 = head_of(esk8_1(esk9_0))
| edge(esk1_2(X1,head_of(esk8_1(esk9_0))))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_63]) ).
cnf(c_0_77,negated_conjecture,
( tail_of(esk1_2(X1,head_of(esk8_1(esk9_0)))) = head_of(esk8_1(esk9_0))
| tail_of(esk1_2(X1,head_of(esk8_1(esk9_0)))) = X1
| X1 = head_of(esk8_1(esk9_0))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_63]) ).
cnf(c_0_78,negated_conjecture,
( tail_of(esk1_2(tail_of(esk7_1(esk9_0)),X1)) = X1
| head_of(esk1_2(tail_of(esk7_1(esk9_0)),X1)) = X1
| X1 = tail_of(esk7_1(esk9_0))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_65]) ).
cnf(c_0_79,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_69]) ).
cnf(c_0_80,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_81,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_82,negated_conjecture,
edge(esk7_1(esk9_0)),
inference(spm,[status(thm)],[c_0_71,c_0_54]) ).
cnf(c_0_83,negated_conjecture,
( head_of(X1) != head_of(esk8_1(esk9_0))
| tail_of(X1) != tail_of(esk7_1(esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_54])]) ).
cnf(c_0_84,negated_conjecture,
( head_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = tail_of(esk7_1(esk9_0))
| tail_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = tail_of(esk7_1(esk9_0))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(spm,[status(thm)],[c_0_74,c_0_65]) ).
cnf(c_0_85,negated_conjecture,
( head_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = head_of(esk8_1(esk9_0))
| head_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = tail_of(esk7_1(esk9_0))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(spm,[status(thm)],[c_0_75,c_0_63]) ).
cnf(c_0_86,negated_conjecture,
( tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0))
| edge(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) ),
inference(spm,[status(thm)],[c_0_76,c_0_65]) ).
cnf(c_0_87,negated_conjecture,
( tail_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = tail_of(esk7_1(esk9_0))
| tail_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = head_of(esk8_1(esk9_0))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(spm,[status(thm)],[c_0_77,c_0_65]) ).
cnf(c_0_88,negated_conjecture,
( head_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = head_of(esk8_1(esk9_0))
| tail_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = head_of(esk8_1(esk9_0))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(spm,[status(thm)],[c_0_78,c_0_63]) ).
cnf(c_0_89,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ triangle(esk7_1(X1),esk8_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_90,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_79,c_0_80]),c_0_80]),c_0_80]) ).
cnf(c_0_91,negated_conjecture,
( X1 = esk7_1(esk9_0)
| sequential(X1,esk7_1(esk9_0))
| tail_of(esk7_1(esk9_0)) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_92,negated_conjecture,
( head_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = tail_of(esk7_1(esk9_0))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_93,negated_conjecture,
( X1 = esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0))
| sequential(X1,esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))))
| tail_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_86]) ).
cnf(c_0_94,negated_conjecture,
( tail_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = head_of(esk8_1(esk9_0))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_87]),c_0_88]) ).
cnf(c_0_95,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ sequential(X2,esk7_1(X1))
| ~ sequential(esk8_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_61]) ).
cnf(c_0_96,negated_conjecture,
( esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))) = esk7_1(esk9_0)
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0))
| sequential(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))),esk7_1(esk9_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_86]) ).
cnf(c_0_97,negated_conjecture,
( X1 = esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0))
| sequential(X1,esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))))
| head_of(esk8_1(esk9_0)) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_98,negated_conjecture,
edge(esk8_1(esk9_0)),
inference(spm,[status(thm)],[c_0_71,c_0_48]) ).
cnf(c_0_99,negated_conjecture,
( esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))) = esk7_1(esk9_0)
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0))
| ~ sequential(esk8_1(esk9_0),esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))))
| ~ path(X1,X2,esk9_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_40]) ).
cnf(c_0_100,negated_conjecture,
( esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))) = esk8_1(esk9_0)
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0))
| sequential(esk8_1(esk9_0),esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_97]),c_0_98])]) ).
fof(c_0_101,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_102,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_103,negated_conjecture,
( esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))) = esk8_1(esk9_0)
| esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))) = esk7_1(esk9_0)
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0))
| ~ path(X1,X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_104,plain,
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_105,negated_conjecture,
tail_of(esk8_1(esk9_0)) = head_of(esk7_1(esk9_0)),
inference(spm,[status(thm)],[c_0_102,c_0_73]) ).
cnf(c_0_106,negated_conjecture,
( esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))) = esk7_1(esk9_0)
| esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))) = esk8_1(esk9_0)
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(spm,[status(thm)],[c_0_103,c_0_20]) ).
cnf(c_0_107,negated_conjecture,
head_of(esk8_1(esk9_0)) != head_of(esk7_1(esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_98])]) ).
cnf(c_0_108,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_109,negated_conjecture,
( esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))) = esk7_1(esk9_0)
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_106]),c_0_105]),c_0_107]) ).
cnf(c_0_110,negated_conjecture,
( ~ precedes(X1,X2,esk9_0)
| ~ precedes(X2,X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_108,c_0_18]) ).
cnf(c_0_111,negated_conjecture,
tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)),
inference(spm,[status(thm)],[c_0_94,c_0_109]) ).
cnf(c_0_112,negated_conjecture,
( ~ precedes(esk8_1(esk9_0),X1,esk9_0)
| ~ sequential(X1,esk8_1(esk9_0))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_110,c_0_60]) ).
cnf(c_0_113,negated_conjecture,
( precedes(X1,esk7_1(esk9_0),esk9_0)
| ~ sequential(X1,esk7_1(esk9_0))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_54]) ).
cnf(c_0_114,negated_conjecture,
( X1 = esk7_1(esk9_0)
| sequential(X1,esk7_1(esk9_0))
| head_of(esk8_1(esk9_0)) != head_of(X1)
| ~ edge(X1) ),
inference(rw,[status(thm)],[c_0_91,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
~ sequential(esk8_1(esk9_0),esk7_1(esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_73]),c_0_54]),c_0_48])]) ).
cnf(c_0_116,negated_conjecture,
esk8_1(esk9_0) = esk7_1(esk9_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_114]),c_0_98])]),c_0_115]) ).
cnf(c_0_117,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_116])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRA012+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 03:46:27 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 6.96/7.01 % Version : CSE_E---1.5
% 6.96/7.01 % Problem : theBenchmark.p
% 6.96/7.01 % Proof found
% 6.96/7.01 % SZS status Theorem for theBenchmark.p
% 6.96/7.01 % SZS output start Proof
% See solution above
% 6.99/7.03 % Total time : 6.466000 s
% 6.99/7.03 % SZS output end Proof
% 6.99/7.03 % Total time : 6.469000 s
%------------------------------------------------------------------------------