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  * 
%------------------------------------------------------------------------------