TSTP Solution File: NUM017-2 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : NUM017-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n004.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 : Mon Jul 18 14:06:08 EDT 2022
% Result : Unsatisfiable 0.48s 0.65s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 12 unt; 0 nHn; 11 RR)
% Number of literals : 28 ( 6 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_product,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product) ).
cnf(product_left_cancellation,axiom,
( ~ product(X,Y,Z)
| ~ product(X,U,Z)
| Y = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(well_defined_product,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,U)
| U = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined_product) ).
cnf(divides_implies_product,axiom,
( ~ divides(X,Y)
| product(X,second_divided_by_1st(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divides_implies_product) ).
cnf(product_divisible_by_operand,axiom,
( ~ product(X,Y,Z)
| divides(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_divisible_by_operand) ).
cnf(primes_lemma1,axiom,
( ~ divides(X,Y)
| ~ product(Z,Z,Y)
| ~ prime(X)
| divides(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',primes_lemma1) ).
cnf(a_is_prime,hypothesis,
prime(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_prime) ).
cnf(prove_there_is_no_common_divisor,negated_conjecture,
( ~ divides(X,c)
| ~ divides(X,b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_no_common_divisor) ).
cnf(16,plain,
divides(X,multiply(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[product_divisible_by_operand,closure_of_product]) ).
cnf(26,plain,
divides(a,a),
inference('HYPERRESOLVE',[status(thm)],[primes_lemma1,16,closure_of_product,a_is_prime]) ).
cnf(29,plain,
product(X,second_divided_by_1st(X,multiply(X,Y)),multiply(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[divides_implies_product,16]) ).
cnf(30,plain,
product(a,second_divided_by_1st(a,a),a),
inference('HYPERRESOLVE',[status(thm)],[divides_implies_product,26]) ).
cnf(46,plain,
multiply(a,second_divided_by_1st(a,a)) = a,
inference('HYPERRESOLVE',[status(thm)],[well_defined_product,30,closure_of_product]) ).
cnf(47,plain,
multiply(a,multiply(second_divided_by_1st(a,a),X)) = multiply(a,X),
inference('EMBED',[status(thm)],[46]) ).
cnf(79,plain,
second_divided_by_1st(X,multiply(X,Y)) = Y,
inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,29,closure_of_product]) ).
cnf(86,plain,
X = multiply(X,second_divided_by_1st(a,a)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[79,47,theory(equality)]),79,theory(equality)]) ).
cnf(91,plain,
divides(second_divided_by_1st(a,a),X),
inference('PARAMODULATE',[status(thm)],[16,86,theory(equality)]) ).
cnf(108,plain,
$false,
inference('HYPERRESOLVE',[status(thm)],[prove_there_is_no_common_divisor,91,91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM017-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n004.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jul 5 09:22:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.47 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 *
% 0.21/0.48 *
% 0.21/0.49 #<PACKAGE "SNARK-USER">
% 0.21/0.49 *
% 0.21/0.49 SNARK-TPTP-OPTIONS
% 0.21/0.49 *
% 0.21/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.49 (USE-FACTORING :POS)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.49 *
% 0.21/0.49 "."
% 0.21/0.49 *
% 0.21/0.49 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-05T09:22:08
% 0.21/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n004.cluster.edu at 2022-07-05T09:22:08
% 0.21/0.50
% 0.21/0.50 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.21/0.50 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?U ?V ?Y)) (NOT (|product| ?X ?U ?W)) (|product| ?W ?V ?Z)).
% 0.21/0.50 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?U ?Y ?V)) (NOT (|product| ?W ?U ?X)) (|product| ?W ?V ?Z)).
% 0.21/0.50 ; Recognized commutativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (|product| ?Y ?X ?Z)).
% 0.21/0.50 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?U ?Z)).
% 0.21/0.50 ; Declaring product to be commutative.
% 0.21/0.50 ; Declaring multiply to be commutative.
% 0.48/0.65 ; Declaring multiply to be associative-commutative.
% 0.48/0.65
% 0.48/0.65 #||
% 0.48/0.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.65 % SZS output start Refutation
% See solution above
% 0.48/0.65 ||#
% 0.48/0.65
% 0.48/0.65 ; Summary of computation:
% 0.48/0.65 ; 2405 formulas have been input or derived (from 55 formulas).
% 0.48/0.65 ; 108 ( 4%) were retained. Of these,
% 0.48/0.65 ; 39 (36%) were simplified or subsumed later,
% 0.48/0.65 ; 69 (64%) are still being kept.
% 0.48/0.65 ;
% 0.48/0.65 ; Run time in seconds excluding printing time:
% 0.48/0.65 ; 0.003 2% Read assertion file (1 call)
% 0.48/0.65 ; 0.001 1% Assert (15 calls)
% 0.48/0.65 ; 0.012 7% Process new row (1,901 calls)
% 0.48/0.65 ; 0.063 39% Resolution (108 calls)
% 0.48/0.65 ; 0.005 3% Paramodulation (54 calls)
% 0.48/0.65 ; 0.000 0% Embedding (8 calls)
% 0.48/0.65 ; 0.001 1% Condensing (9 calls)
% 0.48/0.65 ; 0.000 0% Forward subsumption (9 calls)
% 0.48/0.65 ; 0.000 0% Backward subsumption (8 calls)
% 0.48/0.65 ; 0.001 1% Clause clause subsumption (4 calls)
% 0.48/0.65 ; 0.037 23% Forward simplification (1,358 calls)
% 0.48/0.65 ; 0.003 2% Backward simplification (105 calls)
% 0.48/0.65 ; 0.000 0% Ordering (246 calls)
% 0.48/0.65 ; 0.001 1% Ordering ac (31 calls)
% 0.48/0.65 ; 0.000 0% Sortal reasoning (32 calls)
% 0.48/0.65 ; 0.000 0% Purity testing (1 call)
% 0.48/0.65 ; 0.035 22% Other
% 0.48/0.65 ; 0.162 Total
% 0.48/0.65 ; 0.165 Real time
% 0.48/0.65 ;
% 0.48/0.65 ; Term-hash-array has 171 terms in all.
% 0.48/0.65 ; Feature-vector-row-index has 8 entries (8 at peak, 8 added, 0 deleted).
% 0.48/0.65 ; Feature-vector-row-index has 18 nodes (18 at peak, 18 added, 0 deleted).
% 0.48/0.65 ; Retrieved 3 possibly forward subsuming rows in 9 calls.
% 0.48/0.65 ; Retrieved 1 possibly backward subsumed row in 8 calls.
% 0.48/0.65 ; Path-index has 118 entries (141 at peak, 176 added, 58 deleted).
% 0.48/0.65 ; Path-index has 161 nodes (174 at peak, 190 added, 29 deleted).
% 0.48/0.65 ; Trie-index has 118 entries (141 at peak, 176 added, 58 deleted).
% 0.48/0.65 ; Trie-index has 133 nodes (141 at peak, 199 added, 66 deleted).
% 0.48/0.65 ; Retrieved 7,450 generalization terms in 2,825 calls.
% 0.48/0.65 ; Retrieved 206 instance terms in 97 calls.
% 0.48/0.65 ; Retrieved 14,357 unifiable terms in 2,937 calls.
% 0.48/0.65 ;
% 0.48/0.65 ; The agenda of rows to process has 29 entries:
% 0.48/0.65 ; 10 with value 14 10 with value 16 1 with value 20
% 0.48/0.65 ; 2 with value 15 6 with value 18
% 0.48/0.65 ; The agenda of rows to give has 25 entries:
% 0.48/0.65 ; 2 with value (4 13) 8 with value (4 16) 1 with value (4 21)
% 0.48/0.65 ; 3 with value (4 14) 2 with value (4 18) 1 with value (4 26)
% 0.48/0.65 ; 6 with value (4 15) 2 with value (4 20)
% 0.48/0.65 Evaluation took:
% 0.48/0.65 0.165 seconds of real time
% 0.48/0.65 0.147763 seconds of user run time
% 0.48/0.65 0.017158 seconds of system run time
% 0.48/0.65 0 calls to %EVAL
% 0.48/0.65 0 page faults and
% 0.48/0.65 8,156,704 bytes consed.
% 0.48/0.65 :PROOF-FOUND
% 0.48/0.65 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-05T09:22:08
% 0.48/0.65 :PROOF-FOUND
% 0.48/0.65 *
%------------------------------------------------------------------------------