TSTP Solution File: GRA010+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRA010+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 : n017.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 00:00:08 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 37
% Syntax : Number of formulae : 52 ( 6 unt; 35 typ; 0 def)
% Number of atoms : 65 ( 14 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 71 ( 23 ~; 25 |; 15 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 53 ( 25 >; 28 *; 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 : 44 ( 13 sgn; 21 !; 3 ?; 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 ).
tff(decl_56,type,
esk12_2: ( $i * $i ) > $i ).
fof(complete_means_sequential_pairs_and_triangles,conjecture,
( complete
=> ! [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',complete_means_sequential_pairs_and_triangles) ).
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(c_0_2,negated_conjecture,
~ ( complete
=> ! [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) ) ),
inference(assume_negation,[status(cth)],[complete_means_sequential_pairs_and_triangles]) ).
fof(c_0_3,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])])])])])]) ).
fof(c_0_4,negated_conjecture,
! [X87,X88] :
( complete
& path(esk10_0,esk11_0,esk9_0)
& ( ~ on_path(X87,esk9_0)
| ~ on_path(X88,esk9_0)
| ~ sequential(X87,X88)
| triangle(X87,X88,esk12_2(X87,X88)) )
& number_of_in(sequential_pairs,esk9_0) != number_of_in(triangles,esk9_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).
cnf(c_0_5,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_3]) ).
cnf(c_0_6,negated_conjecture,
( triangle(X1,X2,esk12_2(X1,X2))
| ~ on_path(X1,esk9_0)
| ~ on_path(X2,esk9_0)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,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_3]) ).
cnf(c_0_8,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_3]) ).
cnf(c_0_9,negated_conjecture,
path(esk10_0,esk11_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
number_of_in(sequential_pairs,esk9_0) != number_of_in(triangles,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,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_3]) ).
cnf(c_0_12,negated_conjecture,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ on_path(esk8_1(X1),esk9_0)
| ~ on_path(esk7_1(X1),esk9_0)
| ~ path(X2,X3,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
cnf(c_0_13,negated_conjecture,
on_path(esk8_1(esk9_0),esk9_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_14,negated_conjecture,
on_path(esk7_1(esk9_0),esk9_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_10]) ).
cnf(c_0_15,negated_conjecture,
~ path(X1,X2,esk9_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),c_0_10]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_9,c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 02:44:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.024000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.028000 s
%------------------------------------------------------------------------------