TSTP Solution File: GRA002+3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRA002+3 : 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 : n023.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 00:00:04 EDT 2023
% Result : Theorem 0.53s 0.60s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 43
% Syntax : Number of formulae : 82 ( 12 unt; 35 typ; 0 def)
% Number of atoms : 158 ( 29 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 173 ( 62 ~; 72 |; 23 &)
% ( 1 <=>; 14 =>; 1 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 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 : 24 ( 24 usr; 9 con; 0-4 aty)
% Number of variables : 121 ( 20 sgn; 68 !; 4 ?; 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 ).
fof(maximal_path_length,conjecture,
( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> less_or_equal(minus(length_of(X4),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maximal_path_length) ).
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(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(sequential_is_triangle,lemma,
( 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(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(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(graph_has_them_all,axiom,
! [X11,X12] : less_or_equal(number_of_in(X11,X12),number_of_in(X11,graph)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(c_0_8,negated_conjecture,
~ ( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> less_or_equal(minus(length_of(X4),n1),number_of_in(triangles,graph)) ) ),
inference(assume_negation,[status(cth)],[maximal_path_length]) ).
fof(c_0_9,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]) ).
fof(c_0_10,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_11,negated_conjecture,
( complete
& shortest_path(esk11_0,esk12_0,esk10_0)
& ~ less_or_equal(minus(length_of(esk10_0),n1),number_of_in(triangles,graph)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,lemma,
! [X84,X85,X86,X87,X88] :
( ~ complete
| ~ shortest_path(X84,X85,X88)
| ~ precedes(X86,X87,X88)
| ~ sequential(X86,X87)
| triangle(X86,X87,esk9_4(X84,X85,X86,X87)) ),
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_is_triangle])])])])]) ).
fof(c_0_13,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_9])])])]) ).
cnf(c_0_14,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
shortest_path(esk11_0,esk12_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,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_17,lemma,
( triangle(X4,X5,esk9_4(X1,X2,X4,X5))
| ~ complete
| ~ shortest_path(X1,X2,X3)
| ~ precedes(X4,X5,X3)
| ~ sequential(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,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_13]) ).
cnf(c_0_20,negated_conjecture,
path(esk11_0,esk12_0,esk10_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,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_16]) ).
cnf(c_0_22,lemma,
( triangle(X1,X2,esk9_4(X3,X4,X1,X2))
| ~ shortest_path(X3,X4,X5)
| ~ precedes(X1,X2,X5)
| ~ sequential(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_23,negated_conjecture,
( precedes(X1,X2,esk10_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk10_0)
| ~ on_path(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| on_path(esk8_1(esk10_0),esk10_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_25,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_16]) ).
cnf(c_0_26,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_16]) ).
fof(c_0_27,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_28,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_16]) ).
cnf(c_0_29,negated_conjecture,
( triangle(X1,X2,esk9_4(esk11_0,esk12_0,X1,X2))
| ~ precedes(X1,X2,esk10_0)
| ~ sequential(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_30,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| precedes(X1,esk8_1(esk10_0),esk10_0)
| ~ sequential(X1,esk8_1(esk10_0))
| ~ on_path(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| sequential(esk7_1(esk10_0),esk8_1(esk10_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_32,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| on_path(esk7_1(esk10_0),esk10_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
fof(c_0_33,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])]) ).
cnf(c_0_34,plain,
( length_of(X3) = number_of_in(edges,X3)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ precedes(esk7_1(X1),esk8_1(X1),esk10_0)
| ~ path(X2,X3,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]) ).
cnf(c_0_36,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| precedes(esk7_1(esk10_0),esk8_1(esk10_0),esk10_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_37,plain,
( number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
length_of(esk10_0) = number_of_in(edges,esk10_0),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
fof(c_0_39,plain,
! [X82,X83] : less_or_equal(number_of_in(X82,X83),number_of_in(X82,graph)),
inference(variable_rename,[status(thm)],[graph_has_them_all]) ).
cnf(c_0_40,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| ~ path(X1,X2,esk10_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
~ less_or_equal(minus(length_of(esk10_0),n1),number_of_in(triangles,graph)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_42,negated_conjecture,
minus(number_of_in(edges,esk10_0),n1) = number_of_in(sequential_pairs,esk10_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_20]),c_0_38]) ).
cnf(c_0_43,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,negated_conjecture,
number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_45,negated_conjecture,
~ less_or_equal(number_of_in(sequential_pairs,esk10_0),number_of_in(triangles,graph)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRA002+3 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33 % Computer : n023.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 04:04:41 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.53/0.60 % Version : CSE_E---1.5
% 0.53/0.60 % Problem : theBenchmark.p
% 0.53/0.60 % Proof found
% 0.53/0.60 % SZS status Theorem for theBenchmark.p
% 0.53/0.60 % SZS output start Proof
% See solution above
% 0.57/0.61 % Total time : 0.040000 s
% 0.57/0.61 % SZS output end Proof
% 0.57/0.61 % Total time : 0.043000 s
%------------------------------------------------------------------------------