TSTP Solution File: SYO661-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SYO661-1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n012.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 : Thu Jul 21 19:44:51 EDT 2022
% Result : Unsatisfiable 0.60s 0.83s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 53 ( 8 unt; 41 nHn; 40 RR)
% Number of literals : 168 ( 0 equ; 63 neg)
% Maximal clause size : 14 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 35 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_93,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_93) ).
cnf(clause_51,axiom,
( ~ 'LE'(f(suc(suc(X))),s('0'))
| 'E'('0',f(suc(suc(X))))
| 'LE'(f(X),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_51) ).
cnf(clause_106,axiom,
( ~ 'E'(s('0'),f(suc(X)))
| ~ 'E'(s('0'),f(Y))
| ~ 'E'(s('0'),f(Z))
| ~ 'E'(s('0'),f(suc(Y)))
| ~ 'E'(s('0'),f(suc(Z)))
| ~ 'E'(s('0'),f(X))
| ~ iLEQ(suc(Z),suc(X))
| ~ iLEQ(suc(X),suc(Y))
| 'E'(f(Z),f(suc(Z)))
| 'E'(f(X),f(suc(X)))
| 'E'(f(Y),f(suc(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_106) ).
cnf(clause_8,axiom,
( ~ 'E'(s('0'),f(suc(X)))
| ~ 'E'(s('0'),f(Y))
| ~ 'E'(s('0'),f(suc(suc(Z))))
| ~ 'E'(s('0'),f(Z))
| ~ 'E'(s('0'),f(suc(Y)))
| ~ 'E'(s('0'),f(suc(Z)))
| ~ 'E'(s('0'),f(suc(suc(Y))))
| ~ 'E'(f(Y),f(suc(Y)))
| ~ 'E'(f(Z),f(suc(Z)))
| ~ 'E'(s('0'),f(suc(suc(X))))
| ~ 'E'(s('0'),f(X))
| ~ 'E'(f(X),f(suc(X)))
| ~ iLEQ(suc(Z),suc(X))
| ~ iLEQ(suc(X),suc(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
cnf(clause_72,axiom,
'LE'(f(X),s(s('0'))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_72) ).
cnf(clause_119,axiom,
( ~ 'LE'(f(suc(X)),s(s('0')))
| 'E'(s('0'),f(suc(X)))
| 'LE'(f(X),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_119) ).
cnf(8,plain,
( 'E'(s('0'),f(suc(X)))
| 'LE'(f(X),s('0')) ),
inference('REWRITE',[status(thm)],[clause_119,clause_72]) ).
cnf(clause_57,axiom,
( ~ 'LE'(f(suc(X)),s('0'))
| 'E'('0',f(suc(X)))
| 'LE'(f(X),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_57) ).
cnf(clause_0,axiom,
( ~ 'LE'(f(X),s('0'))
| 'E'('0',f(X))
| 'LE'(f(X),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_0) ).
cnf(clause_85,axiom,
( ~ 'E'(s('0'),f(X))
| ~ 'E'(s('0'),f(suc(X)))
| 'E'(f(X),f(suc(X)))
| iLEQ(suc(X),suc(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_85) ).
cnf(clause_109,axiom,
( ~ 'E'('0',f(X))
| ~ 'E'('0',f(suc(X)))
| 'E'(f(X),f(suc(X)))
| iLEQ(suc(X),suc(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_109) ).
cnf(clause_204,axiom,
( ~ 'E'('0',f(suc(suc(X))))
| ~ 'E'('0',f(suc(Y)))
| ~ 'E'('0',f(suc(suc(Y))))
| ~ 'E'('0',f(suc(Z)))
| ~ iLEQ(suc(X),suc(Z))
| ~ 'E'('0',f(Y))
| ~ 'E'('0',f(Z))
| ~ 'E'('0',f(suc(suc(Z))))
| ~ 'E'(f(X),f(suc(X)))
| ~ 'E'('0',f(X))
| ~ 'E'('0',f(suc(X)))
| ~ 'E'(f(Z),f(suc(Z)))
| ~ iLEQ(suc(Y),suc(X))
| ~ 'E'(f(Y),f(suc(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_204) ).
cnf(clause_20,axiom,
( ~ 'E'('0',f(suc(X)))
| ~ 'E'('0',f(suc(Y)))
| ~ iLEQ(suc(Z),suc(Y))
| ~ 'E'('0',f(X))
| ~ 'E'('0',f(Y))
| ~ 'E'('0',f(Z))
| ~ 'E'('0',f(suc(Z)))
| ~ iLEQ(suc(X),suc(Z))
| 'E'(f(X),f(suc(X)))
| 'E'(f(Z),f(suc(Z)))
| 'E'(f(Y),f(suc(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20) ).
cnf(clause_148,axiom,
( ~ 'E'('0',f(suc(suc(X))))
| ~ 'E'('0',f(suc(X)))
| ~ 'E'(f(X),f(suc(X)))
| ~ 'E'('0',f(X))
| iLEQ(suc(X),suc(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_148) ).
cnf(clause_33,axiom,
( ~ 'LE'(f(suc(suc(X))),s(s('0')))
| 'E'(s('0'),f(suc(suc(X))))
| 'LE'(f(X),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_33) ).
cnf(25,plain,
( 'E'(s('0'),f(suc(suc(X))))
| 'LE'(f(X),s('0')) ),
inference('REWRITE',[status(thm)],[clause_33,clause_72]) ).
cnf(clause_118,axiom,
( ~ 'LE'(f(X),s(s('0')))
| 'E'(s('0'),f(X))
| 'LE'(f(X),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_118) ).
cnf(28,plain,
( 'E'(s('0'),f(X))
| 'LE'(f(X),s('0')) ),
inference('REWRITE',[status(thm)],[clause_118,clause_72]) ).
cnf(clause_25,axiom,
( ~ 'E'(s('0'),f(suc(suc(X))))
| ~ 'E'(s('0'),f(suc(X)))
| ~ 'E'(f(X),f(suc(X)))
| ~ 'E'(s('0'),f(X))
| iLEQ(suc(X),suc(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_25) ).
cnf(32,plain,
( 'E'(s('0'),f(X))
| 'E'('0',f(X))
| 'LE'(f(X),'0') ),
inference('HYPERRESOLVE',[status(thm)],[clause_0,28]) ).
cnf(33,plain,
( 'E'(s('0'),f(suc(X)))
| 'E'('0',f(X))
| 'LE'(f(X),'0') ),
inference('HYPERRESOLVE',[status(thm)],[clause_0,8]) ).
cnf(34,plain,
( 'E'(s('0'),f(suc(suc(X))))
| 'E'('0',f(X))
| 'LE'(f(X),'0') ),
inference('HYPERRESOLVE',[status(thm)],[clause_0,25]) ).
cnf(35,plain,
( 'E'(s('0'),f(suc(X)))
| 'E'('0',f(suc(X)))
| 'LE'(f(X),'0') ),
inference('HYPERRESOLVE',[status(thm)],[clause_57,28]) ).
cnf(36,plain,
( 'E'(s('0'),f(suc(suc(X))))
| 'E'('0',f(suc(X)))
| 'LE'(f(X),'0') ),
inference('HYPERRESOLVE',[status(thm)],[clause_57,8]) ).
cnf(37,plain,
( 'E'(s('0'),f(suc(suc(suc(X)))))
| 'E'('0',f(suc(X)))
| 'LE'(f(X),'0') ),
inference('HYPERRESOLVE',[status(thm)],[clause_57,25]) ).
cnf(38,plain,
( 'E'(s('0'),f(suc(suc(X))))
| 'E'('0',f(suc(suc(X))))
| 'LE'(f(X),'0') ),
inference('HYPERRESOLVE',[status(thm)],[clause_51,28]) ).
cnf(39,plain,
( 'E'(s('0'),f(suc(suc(suc(X)))))
| 'E'('0',f(suc(suc(X))))
| 'LE'(f(X),'0') ),
inference('HYPERRESOLVE',[status(thm)],[clause_51,8]) ).
cnf(40,plain,
( 'E'(s('0'),f(suc(suc(suc(suc(X))))))
| 'E'('0',f(suc(suc(X))))
| 'LE'(f(X),'0') ),
inference('HYPERRESOLVE',[status(thm)],[clause_51,25]) ).
cnf(41,plain,
( 'E'(s('0'),f(z))
| 'E'('0',f(z)) ),
inference('HYPERRESOLVE',[status(thm)],[clause_93,32]) ).
cnf(42,plain,
( 'E'(s('0'),f(suc(z)))
| 'E'('0',f(z)) ),
inference('HYPERRESOLVE',[status(thm)],[clause_93,33]) ).
cnf(43,plain,
( 'E'('0',f(z))
| 'E'(f(z),f(suc(z)))
| iLEQ(suc(z),suc(z)) ),
inference('HYPERRESOLVE',[status(thm)],[clause_85,42,41]) ).
cnf(44,plain,
( 'E'(s('0'),f(suc(suc(z))))
| 'E'('0',f(z)) ),
inference('HYPERRESOLVE',[status(thm)],[clause_93,34]) ).
cnf(46,plain,
( 'E'(s('0'),f(suc(z)))
| 'E'('0',f(suc(z))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_93,35]) ).
cnf(47,plain,
( 'E'('0',f(z))
| 'E'(f(z),f(suc(z))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_106,43,42,41,41,42,42,41,43]) ).
cnf(48,plain,
( 'E'('0',f(z))
| iLEQ(suc(z),suc(z)) ),
inference('HYPERRESOLVE',[status(thm)],[clause_25,47,44,42,41]) ).
cnf(49,plain,
'E'('0',f(z)),
inference('HYPERRESOLVE',[status(thm)],[clause_8,48,42,41,44,41,42,42,44,47,47,44,41,47,48]) ).
cnf(50,plain,
( 'E'(s('0'),f(suc(suc(z))))
| 'E'('0',f(suc(z))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_93,36]) ).
cnf(51,plain,
( 'E'('0',f(suc(z)))
| 'E'(f(suc(z)),f(suc(suc(z))))
| iLEQ(suc(suc(z)),suc(suc(z))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_85,50,46]) ).
cnf(52,plain,
( 'E'(s('0'),f(suc(suc(suc(z)))))
| 'E'('0',f(suc(z))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_93,37]) ).
cnf(54,plain,
( 'E'(s('0'),f(suc(suc(z))))
| 'E'('0',f(suc(suc(z)))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_93,38]) ).
cnf(55,plain,
( 'E'(s('0'),f(suc(suc(suc(z)))))
| 'E'('0',f(suc(suc(z)))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_93,39]) ).
cnf(56,plain,
( 'E'('0',f(suc(suc(z))))
| 'E'(f(suc(suc(z))),f(suc(suc(suc(z)))))
| iLEQ(suc(suc(suc(z))),suc(suc(suc(z)))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_85,55,54]) ).
cnf(57,plain,
( 'E'(s('0'),f(suc(suc(suc(suc(z))))))
| 'E'('0',f(suc(suc(z)))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_93,40]) ).
cnf(59,plain,
( 'E'('0',f(suc(z)))
| 'E'(f(suc(z)),f(suc(suc(z)))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_106,51,50,46,46,50,50,46,51]) ).
cnf(60,plain,
( 'E'('0',f(suc(z)))
| iLEQ(suc(suc(z)),suc(suc(z))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_25,59,52,50,46]) ).
cnf(61,plain,
'E'('0',f(suc(z))),
inference('HYPERRESOLVE',[status(thm)],[clause_8,60,50,46,52,46,50,50,52,59,59,52,46,59,60]) ).
cnf(62,plain,
( 'E'(f(z),f(suc(z)))
| iLEQ(suc(z),suc(z)) ),
inference('HYPERRESOLVE',[status(thm)],[clause_109,61,49]) ).
cnf(63,plain,
'E'(f(z),f(suc(z))),
inference('HYPERRESOLVE',[status(thm)],[clause_20,62,61,61,49,49,49,61,62]) ).
cnf(64,plain,
( 'E'('0',f(suc(suc(z))))
| 'E'(f(suc(suc(z))),f(suc(suc(suc(z))))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_106,56,55,54,54,55,55,54,56]) ).
cnf(65,plain,
( 'E'('0',f(suc(suc(z))))
| iLEQ(suc(suc(suc(z))),suc(suc(suc(z)))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_25,64,57,55,54]) ).
cnf(66,plain,
'E'('0',f(suc(suc(z)))),
inference('HYPERRESOLVE',[status(thm)],[clause_8,65,55,54,57,54,55,55,57,64,64,57,54,64,65]) ).
cnf(67,plain,
iLEQ(suc(z),suc(z)),
inference('HYPERRESOLVE',[status(thm)],[clause_148,66,61,63,49]) ).
cnf(68,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[clause_204,66,61,66,61,49,49,66,63,49,61,63,63]),67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO661-1 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n012.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 : 600
% 0.13/0.34 % DateTime : Sat Jul 9 12:15:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 *
% 0.20/0.46 *
% 0.20/0.47 #<PACKAGE "SNARK-USER">
% 0.20/0.47 *
% 0.20/0.47 SNARK-TPTP-OPTIONS
% 0.20/0.47 *
% 0.20/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47 (USE-FACTORING :POS)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47 *
% 0.20/0.47 "."
% 0.20/0.47 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-09T12:15:44
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n012.cluster.edu at 2022-07-09T12:15:44
% 0.60/0.83
% 0.60/0.83
% 0.60/0.83 #||
% 0.60/0.83 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.83 % SZS output start Refutation
% See solution above
% 0.60/0.83 ||#
% 0.60/0.83
% 0.60/0.83 ; Summary of computation:
% 0.60/0.83 ; 687 formulas have been input or derived (from 61 formulas).
% 0.60/0.83 ; 68 (10%) were retained. Of these,
% 0.60/0.83 ; 25 (37%) were simplified or subsumed later,
% 0.60/0.83 ; 43 (63%) are still being kept.
% 0.60/0.83 ;
% 0.60/0.83 ; Run time in seconds excluding printing time:
% 0.60/0.83 ; 0.019 5% Read assertion file (1 call)
% 0.60/0.83 ; 0.005 1% Assert (28 calls)
% 0.60/0.83 ; 0.007 2% Process new row (82 calls)
% 0.60/0.83 ; 0.276 78% Resolution (120 calls)
% 0.60/0.83 ; 0.000 0% Paramodulation (60 calls)
% 0.60/0.83 ; 0.002 1% Factoring (31 calls)
% 0.60/0.83 ; 0.005 1% Condensing (65 calls)
% 0.60/0.83 ; 0.008 2% Forward subsumption (65 calls)
% 0.60/0.83 ; 0.006 2% Backward subsumption (57 calls)
% 0.60/0.83 ; 0.001 0% Clause clause subsumption (97 calls)
% 0.60/0.83 ; 0.001 0% Forward simplification (73 calls)
% 0.60/0.83 ; 0.002 1% Backward simplification (65 calls)
% 0.60/0.83 ; 0.000 0% Ordering (80 calls)
% 0.60/0.83 ; 0.000 0% Sortal reasoning (32 calls)
% 0.60/0.83 ; 0.000 0% Purity testing (1 call)
% 0.60/0.83 ; 0.023 6% Other
% 0.60/0.83 ; 0.355 Total
% 0.60/0.83 ; 0.362 Real time
% 0.60/0.83 ;
% 0.60/0.83 ; Term-hash-array has 81 terms in all.
% 0.60/0.83 ; Feature-vector-row-index has 35 entries (46 at peak, 57 added, 22 deleted).
% 0.60/0.83 ; Feature-vector-row-index has 237 nodes (350 at peak, 452 added, 215 deleted).
% 0.60/0.83 ; Retrieved 74 possibly forward subsuming rows in 65 calls.
% 0.60/0.83 ; Retrieved 30 possibly backward subsumed rows in 57 calls.
% 0.60/0.83 ; Path-index has 68 entries (80 at peak, 97 added, 29 deleted).
% 0.60/0.83 ; Path-index has 85 nodes (97 at peak, 120 added, 35 deleted).
% 0.60/0.83 ; Trie-index has 68 entries (80 at peak, 97 added, 29 deleted).
% 0.60/0.83 ; Trie-index has 88 nodes (128 at peak, 187 added, 99 deleted).
% 0.60/0.83 ; Retrieved 4 generalization terms in 65 calls.
% 0.60/0.83 ; Retrieved 7 instance terms in 7 calls.
% 0.60/0.83 ; Retrieved 193,402 unifiable terms in 48,609 calls.
% 0.60/0.83 ;
% 0.60/0.83 ; The agenda of rows to process has 1 entry:
% 0.60/0.83 ; 1 with value 29
% 0.60/0.83 ; The agenda of rows to give has 1 entry:
% 0.60/0.83 ; 1 with value (4 16)
% 0.60/0.83 Evaluation took:
% 0.60/0.83 0.363 seconds of real time
% 0.60/0.83 0.345422 seconds of user run time
% 0.60/0.83 0.01687 seconds of system run time
% 0.60/0.83 [Run times include 0.006 seconds GC run time.]
% 0.60/0.83 0 calls to %EVAL
% 0.60/0.83 0 page faults and
% 0.60/0.83 33,204,336 bytes consed.
% 0.60/0.83 :PROOF-FOUND
% 0.60/0.83 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-09T12:15:44
% 0.60/0.83 :PROOF-FOUND
% 0.60/0.83 *
%------------------------------------------------------------------------------