TSTP Solution File: GEO570+1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GEO570+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n014.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 06:16:46 EDT 2022
% Result : Theorem 10.92s 11.13s
% Output : Refutation 10.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of clauses : 67 ( 34 unt; 0 nHn; 36 RR)
% Number of literals : 122 ( 0 equ; 60 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 251 ( 59 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ coll(X,Y,Z)
| ~ coll(X,Y,U)
| coll(Z,U,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD3) ).
cnf(7,axiom,
( ~ perp(X,Y,Z,U)
| perp(Z,U,X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD8) ).
cnf(8,axiom,
( ~ perp(X,Y,Z,U)
| ~ perp(Z,U,V,W)
| para(X,Y,V,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD9) ).
cnf(11,axiom,
( ~ cong(X,Y,X,Z)
| ~ cong(X,Y,X,U)
| circle(X,Y,Z,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD12) ).
cnf(16,axiom,
( ~ cyclic(X,Y,Z,U)
| ~ cyclic(X,Y,Z,V)
| cyclic(Y,Z,U,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD17) ).
cnf(17,axiom,
( ~ eqangle(X,Y,Z,U,V,W,X1,Y1)
| eqangle(Y,X,Z,U,V,W,X1,Y1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD18) ).
cnf(18,axiom,
( ~ eqangle(X,Y,Z,U,V,W,X1,Y1)
| eqangle(Z,U,X,Y,X1,Y1,V,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD19) ).
cnf(19,axiom,
( ~ eqangle(X,Y,Z,U,V,W,X1,Y1)
| eqangle(V,W,X1,Y1,X,Y,Z,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD20) ).
cnf(20,axiom,
( ~ eqangle(X,Y,Z,U,V,W,X1,Y1)
| eqangle(X,Y,V,W,Z,U,X1,Y1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD21) ).
cnf(21,axiom,
( ~ eqangle(X,Y,Z,U,V,W,X1,Y1)
| ~ eqangle(V,W,X1,Y1,Z1,U1,V1,W1)
| eqangle(X,Y,Z,U,Z1,U1,V1,W1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD22) ).
cnf(38,axiom,
( ~ eqangle(X,Y,Z,U,V,W,Z,U)
| para(X,Y,V,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD39) ).
cnf(39,axiom,
( ~ para(X,Y,Z,U)
| eqangle(X,Y,V,W,Z,U,V,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD40) ).
cnf(40,axiom,
( ~ cyclic(X,Y,Z,U)
| eqangle(Z,X,Z,Y,U,X,U,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD41) ).
cnf(42,axiom,
( ~ eqangle(X,Y,X,Z,U,Y,U,Z)
| ~ coll(X,U,Z)
| cyclic(Y,Z,X,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD42b) ).
cnf(43,axiom,
( ~ cyclic(X,Y,Z,U)
| ~ cyclic(X,Y,Z,V)
| ~ cyclic(X,Y,Z,W)
| ~ eqangle(Z,X,Z,Y,W,U,W,V)
| cong(X,Y,U,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD43) ).
cnf(50,axiom,
( ~ circle(X,Y,Z,U)
| ~ midp(V,Z,U)
| eqangle(Y,Z,Y,U,X,Z,X,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD50) ).
cnf(51,axiom,
( ~ circle(X,Y,Z,U)
| ~ coll(V,Z,U)
| ~ eqangle(Y,Z,Y,U,X,Z,X,V)
| midp(V,Z,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD51) ).
cnf(52,axiom,
( ~ perp(X,Y,Y,Z)
| ~ midp(U,X,Z)
| cong(X,U,Y,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD52) ).
cnf(55,axiom,
( ~ midp(X,Y,Z)
| ~ perp(U,X,Y,Z)
| cong(U,Y,U,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD55) ).
cnf(56,axiom,
( ~ cong(X,Y,Z,Y)
| ~ cong(X,U,Z,U)
| perp(X,Z,Y,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD56) ).
cnf(57,axiom,
( ~ cong(X,Y,Z,Y)
| ~ cong(X,U,Z,U)
| ~ cyclic(X,Z,Y,U)
| perp(Y,X,X,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD57) ).
cnf(64,axiom,
( ~ midp(X,Y,Z)
| ~ para(Y,U,Z,V)
| ~ para(Y,V,Z,U)
| midp(X,U,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD64) ).
cnf(66,axiom,
( ~ para(X,Y,X,Z)
| coll(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD66) ).
cnf(104,axiom,
( ~ perp(X,Y,Y,Z)
| ~ cyclic(X,Z,Y,U)
| circle('SKOLEMAAAV16'(X,Y,Z,U),X,Z,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleX14) ).
cnf(116,negated_conjecture,
perp('SKOLEMAAAV27','SKOLEMAAAV26','SKOLEMAAAV23','SKOLEMAAAV25'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL214032) ).
cnf(120,negated_conjecture,
~ eqangle('SKOLEMAAAV21','SKOLEMAAAV26','SKOLEMAAAV26','SKOLEMAAAV27','SKOLEMAAAV28','SKOLEMAAAV26','SKOLEMAAAV26','SKOLEMAAAV22'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL214032) ).
cnf(131,plain,
perp('SKOLEMAAAV23','SKOLEMAAAV25','SKOLEMAAAV27','SKOLEMAAAV26'),
inference('HYPERRESOLVE',[status(thm)],[7,116]) ).
cnf(144,plain,
~ eqangle('SKOLEMAAAV26','SKOLEMAAAV21','SKOLEMAAAV26','SKOLEMAAAV27','SKOLEMAAAV28','SKOLEMAAAV26','SKOLEMAAAV26','SKOLEMAAAV22'),
inference('UR-RESOLVE',[status(thm)],[17,120]) ).
cnf(178,plain,
para('SKOLEMAAAV23','SKOLEMAAAV25','SKOLEMAAAV23','SKOLEMAAAV25'),
inference('HYPERRESOLVE',[status(thm)],[8,131,116]) ).
cnf(234,plain,
eqangle('SKOLEMAAAV23','SKOLEMAAAV25',X,Y,'SKOLEMAAAV23','SKOLEMAAAV25',X,Y),
inference('HYPERRESOLVE',[status(thm)],[39,178]) ).
cnf(1882,plain,
~ eqangle('SKOLEMAAAV28','SKOLEMAAAV26','SKOLEMAAAV26','SKOLEMAAAV22','SKOLEMAAAV26','SKOLEMAAAV21','SKOLEMAAAV26','SKOLEMAAAV27'),
inference('UR-RESOLVE',[status(thm)],[19,144]) ).
cnf(2011,plain,
~ eqangle('SKOLEMAAAV26','SKOLEMAAAV28','SKOLEMAAAV26','SKOLEMAAAV22','SKOLEMAAAV26','SKOLEMAAAV21','SKOLEMAAAV26','SKOLEMAAAV27'),
inference('UR-RESOLVE',[status(thm)],[17,1882]) ).
cnf(2092,plain,
eqangle('SKOLEMAAAV23','SKOLEMAAAV25','SKOLEMAAAV23','SKOLEMAAAV25',X,Y,X,Y),
inference('HYPERRESOLVE',[status(thm)],[20,234]) ).
cnf(2093,plain,
eqangle(X,Y,'SKOLEMAAAV23','SKOLEMAAAV25',X,Y,'SKOLEMAAAV23','SKOLEMAAAV25'),
inference('HYPERRESOLVE',[status(thm)],[18,234]) ).
cnf(2648,plain,
~ eqangle('SKOLEMAAAV26','SKOLEMAAAV28','SKOLEMAAAV26','SKOLEMAAAV21','SKOLEMAAAV26','SKOLEMAAAV22','SKOLEMAAAV26','SKOLEMAAAV27'),
inference('UR-RESOLVE',[status(thm)],[20,2011]) ).
cnf(4040,plain,
para(X,Y,X,Y),
inference('HYPERRESOLVE',[status(thm)],[38,2093]) ).
cnf(4046,plain,
coll(X,Y,Y),
inference('HYPERRESOLVE',[status(thm)],[66,4040]) ).
cnf(4053,plain,
coll(X,X,Y),
inference('HYPERRESOLVE',[status(thm)],[2,4046,4046]) ).
cnf(6898,plain,
coll(X,Y,Z),
inference('HYPERRESOLVE',[status(thm)],[2,4053,4053]) ).
cnf(6902,plain,
( ~ circle(X,Y,Z,U)
| ~ eqangle(Y,Z,Y,U,X,Z,X,V)
| midp(V,Z,U) ),
inference('REWRITE',[status(thm)],[51,6898]) ).
cnf(6904,plain,
( ~ eqangle(X,Y,X,Z,U,Y,U,Z)
| cyclic(Y,Z,X,U) ),
inference('REWRITE',[status(thm)],[42,6898]) ).
cnf(6909,plain,
cyclic('SKOLEMAAAV25','SKOLEMAAAV25','SKOLEMAAAV23',X),
inference('HYPERRESOLVE',[status(thm)],[6904,2092]) ).
cnf(6924,plain,
cyclic('SKOLEMAAAV25','SKOLEMAAAV23',X,Y),
inference('HYPERRESOLVE',[status(thm)],[16,6909,6909]) ).
cnf(6928,plain,
cyclic('SKOLEMAAAV23',X,Y,Z),
inference('HYPERRESOLVE',[status(thm)],[16,6924,6924]) ).
cnf(6941,plain,
cyclic(X,Y,Z,U),
inference('HYPERRESOLVE',[status(thm)],[16,6928,6928]) ).
cnf(6942,plain,
( ~ cong(X,Y,Z,Y)
| ~ cong(X,U,Z,U)
| perp(Y,X,X,U) ),
inference('REWRITE',[status(thm)],[57,6941]) ).
cnf(6943,plain,
( ~ perp(X,Y,Y,Z)
| circle('SKOLEMAAAV16'(X,Y,Z,U),X,Z,Y) ),
inference('REWRITE',[status(thm)],[104,6941]) ).
cnf(6944,plain,
eqangle(X,Y,X,Z,U,Y,U,Z),
inference('REWRITE',[status(thm)],[40,6941]) ).
cnf(6945,plain,
( ~ eqangle(X,Y,X,Z,U,V,U,W)
| cong(Y,Z,V,W) ),
inference('REWRITE',[status(thm)],[43,6941]) ).
cnf(6973,plain,
cong(X,Y,X,Y),
inference('HYPERRESOLVE',[status(thm)],[6945,6944]) ).
cnf(6996,plain,
perp(X,Y,Y,Z),
inference('HYPERRESOLVE',[status(thm)],[6942,6973,6973]) ).
cnf(7001,plain,
( ~ midp(X,Y,Z)
| cong(Y,X,U,X) ),
inference('REWRITE',[status(thm)],[52,6996]) ).
cnf(7003,plain,
circle('SKOLEMAAAV16'(X,Y,Z,U),X,Z,Y),
inference('REWRITE',[status(thm)],[6943,6996]) ).
cnf(7010,plain,
midp(X,Y,X),
inference('HYPERRESOLVE',[status(thm)],[6902,7003,6944]) ).
cnf(7057,plain,
cong(X,Y,Z,Y),
inference('HYPERRESOLVE',[status(thm)],[7001,7010]) ).
cnf(7058,plain,
perp(X,Y,Z,U),
inference('REWRITE',[status(thm)],[56,7057]) ).
cnf(7060,plain,
( ~ midp(X,Y,Z)
| cong(U,Y,U,Z) ),
inference('REWRITE',[status(thm)],[55,7058]) ).
cnf(7061,plain,
para(X,Y,Z,U),
inference('REWRITE',[status(thm)],[8,7058]) ).
cnf(7062,plain,
( ~ midp(X,Y,Z)
| midp(X,U,V) ),
inference('REWRITE',[status(thm)],[64,7061]) ).
cnf(7064,plain,
eqangle(X,Y,Z,U,V,W,Z,U),
inference('REWRITE',[status(thm)],[39,7061]) ).
cnf(7071,plain,
midp(X,Y,Z),
inference('HYPERRESOLVE',[status(thm)],[7062,7010]) ).
cnf(7072,plain,
( ~ circle(X,Y,Z,U)
| eqangle(Y,Z,Y,U,X,Z,X,V) ),
inference('REWRITE',[status(thm)],[50,7071]) ).
cnf(7074,plain,
cong(X,Y,X,Z),
inference('REWRITE',[status(thm)],[7060,7071]) ).
cnf(7077,plain,
circle(X,Y,Z,U),
inference('REWRITE',[status(thm)],[11,7074]) ).
cnf(7078,plain,
eqangle(X,Y,X,Z,U,Y,U,V),
inference('REWRITE',[status(thm)],[7072,7077]) ).
cnf(7098,plain,
eqangle(X,Y,X,Z,U,V,W,X1),
inference('HYPERRESOLVE',[status(thm)],[21,7078,7064]) ).
cnf(7099,plain,
$false,
inference('REWRITE',[status(thm)],[2648,7098]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO570+1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.14 % Command : run-snark %s %d
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jun 18 09:34:34 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.48 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.49 *
% 0.21/0.49 *
% 0.21/0.50 #<PACKAGE "SNARK-USER">
% 0.21/0.50 *
% 0.21/0.50 SNARK-TPTP-OPTIONS
% 0.21/0.50 *
% 0.21/0.50 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.50 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.50 (USE-FACTORING :POS)
% 0.21/0.50 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.50 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.50 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.50 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.50 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.50 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.50 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.50 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.50 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.50 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.50 *
% 0.21/0.50 "."
% 0.21/0.50 *
% 0.21/0.50 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-18T09:34:34
% 0.21/0.50 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n014.cluster.edu at 2022-06-18T09:34:34
% 0.21/0.54
% 0.21/0.54 WARNING: In quantification, variable ?M is being rebound.
% 0.21/0.54 ; Recognized commutativity assertion (OR (NOT (|coll| ?X ?Y ?Z)) (|coll| ?Y ?X ?Z)).
% 10.92/11.13 ; Declaring coll to be commutative.
% 10.92/11.13
% 10.92/11.13 #||
% 10.92/11.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.92/11.13 % SZS output start Refutation
% See solution above
% 10.92/11.14 ||#
% 10.92/11.14
% 10.92/11.14 ; Summary of computation:
% 10.92/11.14 ; 52441 formulas have been input or derived (from 845 formulas).
% 10.92/11.14 ; 7099 (14%) were retained. Of these,
% 10.92/11.14 ; 7002 (99%) were simplified or subsumed later,
% 10.92/11.14 ; 97 ( 1%) are still being kept.
% 10.92/11.14 ;
% 10.92/11.14 ; Run time in seconds excluding printing time:
% 10.92/11.14 ; 0.031 0% Read assertion file (1 call)
% 10.92/11.14 ; 0.006 0% Assert (95 calls)
% 10.92/11.14 ; 0.438 4% Process new row (51,095 calls)
% 10.92/11.14 ; 9.435 89% Resolution (1,688 calls)
% 10.92/11.14 ; 0.009 0% Paramodulation (844 calls)
% 10.92/11.14 ; 0.002 0% Condensing (162 calls)
% 10.92/11.14 ; 0.001 0% Forward subsumption (162 calls)
% 10.92/11.14 ; 0.001 0% Backward subsumption (160 calls)
% 10.92/11.14 ; 0.001 0% Clause clause subsumption (199 calls)
% 10.92/11.14 ; 0.165 2% Forward simplification (33,313 calls)
% 10.92/11.14 ; 0.370 3% Backward simplification (7,099 calls)
% 10.92/11.14 ; 0.001 0% Ordering (48 calls)
% 10.92/11.14 ; 0.000 0% Sortal reasoning (32 calls)
% 10.92/11.14 ; 0.000 0% Purity testing (1 call)
% 10.92/11.14 ; 0.167 2% Other
% 10.92/11.14 ; 10.627 Total
% 10.92/11.14 ; 10.643 Real time
% 10.92/11.14 ;
% 10.92/11.14 ; Term-hash-array has 9,734 terms in all.
% 10.92/11.14 ; Feature-vector-row-index has 26 entries (127 at peak, 160 added, 134 deleted).
% 10.92/11.14 ; Feature-vector-row-index has 26 nodes (261 at peak, 311 added, 285 deleted).
% 10.92/11.14 ; Retrieved 166 possibly forward subsuming rows in 162 calls.
% 10.92/11.14 ; Retrieved 71 possibly backward subsumed rows in 160 calls.
% 10.92/11.14 ; Path-index has 112 entries (7,895 at peak, 9,777 added, 9,665 deleted).
% 10.92/11.14 ; Path-index has 681 nodes (1,659 at peak, 2,138 added, 1,457 deleted).
% 10.92/11.14 ; Trie-index has 112 entries (7,895 at peak, 9,777 added, 9,665 deleted).
% 10.92/11.14 ; Trie-index has 341 nodes (20,273 at peak, 24,949 added, 24,608 deleted).
% 10.92/11.14 ; Retrieved 37,784 generalization terms in 33,297 calls.
% 10.92/11.14 ; Retrieved 24,177 instance terms in 6,938 calls.
% 10.92/11.14 ; Retrieved 13,189,710 unifiable terms in 663,212 calls.
% 10.92/11.14 ;
% 10.92/11.14 ; The agenda of backward simplifiable rows to process has 1 entry:
% 10.92/11.14 ; 1 with value 0
% 10.92/11.14 ; The agenda of rows to process has 15 entries:
% 10.92/11.14 ; 15 with value 11
% 10.92/11.14 ; The agenda of input rows to give has 1 entry:
% 10.92/11.14 ; 1 with value 10
% 10.92/11.14 ; The agenda of rows to give has 50 entries:
% 10.92/11.14 ; 3 with value (4 7) 3 with value (4 12) 25 with value (4 14)
% 10.92/11.14 ; 1 with value (4 8) 4 with value (4 13) 5 with value (4 15)
% 10.92/11.14 ; 9 with value (4 11)
% 10.92/11.14 Evaluation took:
% 10.92/11.14 10.644 seconds of real time
% 10.92/11.14 10.401246 seconds of user run time
% 10.92/11.14 0.242163 seconds of system run time
% 10.92/11.14 [Run times include 0.501 seconds GC run time.]
% 10.92/11.14 0 calls to %EVAL
% 10.92/11.14 0 page faults and
% 10.92/11.14 720,663,432 bytes consed.
% 10.92/11.14 :PROOF-FOUND
% 10.92/11.14 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-18T09:34:45
% 10.92/11.14 :PROOF-FOUND
% 10.92/11.14 *
%------------------------------------------------------------------------------