TSTP Solution File: ALG002-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : ALG002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n020.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 14 17:59:35 EDT 2022
% Result : Unsatisfiable 0.21s 0.56s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of clauses : 19 ( 12 unt; 2 nHn; 15 RR)
% Number of literals : 30 ( 0 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 15 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
product(X,multiplicative_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(not_abelian,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_abelian) ).
cnf(product_to_inverse,axiom,
( ~ product(X,Y,Z)
| product(X,additive_inverse(Y),additive_inverse(Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_inverse) ).
cnf(inverse_and_identity,axiom,
( product(X,multiplicative_inverse(X),multiplicative_identity)
| product(X,X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_and_identity) ).
cnf(inverse_greater_than_0,axiom,
( ~ greater_than_0(X)
| ~ greater_than_0(additive_inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_greater_than_0) ).
cnf(greater_than_0_square,axiom,
( ~ greater_than_0(X)
| ~ product(X,X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greater_than_0_square) ).
cnf(product_and_inverse,axiom,
( greater_than_0(X)
| product(X,X,additive_identity)
| greater_than_0(additive_inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_inverse) ).
cnf(square_to_0,axiom,
( ~ product(X,Y,Z)
| ~ product(X,X,additive_identity)
| product(Z,Z,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_to_0) ).
cnf(product_and_greater_than_0,axiom,
( ~ product(X,Y,Z)
| ~ greater_than_0(X)
| ~ greater_than_0(Y)
| greater_than_0(Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_greater_than_0) ).
cnf(a_greater_than_0,hypothesis,
greater_than_0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_greater_than_0) ).
cnf(prove_a_inverse_greater_than_0,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
cnf(14,plain,
~ greater_than_0(additive_inverse(a)),
inference('UR-RESOLVE',[status(thm)],[inverse_greater_than_0,a_greater_than_0]) ).
cnf(15,plain,
~ product(a,a,additive_identity),
inference('UR-RESOLVE',[status(thm)],[greater_than_0_square,a_greater_than_0]) ).
cnf(20,plain,
product(X,additive_inverse(multiplicative_identity),additive_inverse(X)),
inference('HYPERRESOLVE',[status(thm)],[product_to_inverse,right_identity]) ).
cnf(31,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[inverse_and_identity,15]) ).
cnf(45,plain,
~ greater_than_0(additive_inverse(multiplicative_identity)),
inference('UR-RESOLVE',[status(thm)],[product_and_greater_than_0,20,a_greater_than_0,14]) ).
cnf(60,plain,
product(a,additive_inverse(multiplicative_inverse(a)),additive_inverse(multiplicative_identity)),
inference('HYPERRESOLVE',[status(thm)],[product_to_inverse,31]) ).
cnf(62,plain,
greater_than_0(additive_inverse(multiplicative_inverse(a))),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[square_to_0,31,product_and_inverse]),not_abelian,prove_a_inverse_greater_than_0]) ).
cnf(88,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[product_and_greater_than_0,62,a_greater_than_0,45]),60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : run-snark %s %d
% 0.14/0.36 % Computer : n020.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 : Wed Jun 8 11:20:21 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.49 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.50 *
% 0.21/0.50 *
% 0.21/0.51 #<PACKAGE "SNARK-USER">
% 0.21/0.51 *
% 0.21/0.51 SNARK-TPTP-OPTIONS
% 0.21/0.51 *
% 0.21/0.51 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.51 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.51 (USE-FACTORING :POS)
% 0.21/0.51 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.51 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.51 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.51 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.51 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.51 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.51 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.51 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.51 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.51 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.51 *
% 0.21/0.51 "."
% 0.21/0.51 *
% 0.21/0.51 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-08T11:20:21
% 0.21/0.51 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-06-08T11:20:21
% 0.21/0.52
% 0.21/0.52 ; Recognized possible right identity assertion (|product| ?X |multiplicative_identity| ?X).
% 0.21/0.52 ; Recognized commutativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (|product| ?Y ?X ?Z)).
% 0.21/0.56 ; Declaring product to be commutative.
% 0.21/0.56
% 0.21/0.56 #||
% 0.21/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.56 % SZS output start Refutation
% See solution above
% 0.21/0.56 ||#
% 0.21/0.56
% 0.21/0.56 ; Summary of computation:
% 0.21/0.56 ; 252 formulas have been input or derived (from 36 formulas).
% 0.21/0.56 ; 88 (35%) were retained. Of these,
% 0.21/0.56 ; 3 ( 3%) were simplified or subsumed later,
% 0.21/0.56 ; 85 (97%) are still being kept.
% 0.21/0.56 ;
% 0.21/0.56 ; Run time in seconds excluding printing time:
% 0.21/0.56 ; 0.002 4% Read assertion file (1 call)
% 0.21/0.56 ; 0.001 2% Assert (14 calls)
% 0.21/0.56 ; 0.006 13% Process new row (184 calls)
% 0.21/0.56 ; 0.005 11% Resolution (70 calls)
% 0.21/0.56 ; 0.000 0% Paramodulation (35 calls)
% 0.21/0.56 ; 0.000 0% Factoring (2 calls)
% 0.21/0.56 ; 0.004 9% Condensing (28 calls)
% 0.21/0.56 ; 0.001 2% Forward subsumption (28 calls)
% 0.21/0.56 ; 0.001 2% Backward subsumption (21 calls)
% 0.21/0.56 ; 0.000 0% Clause clause subsumption (18 calls)
% 0.21/0.56 ; 0.001 2% Forward simplification (184 calls)
% 0.21/0.56 ; 0.000 0% Backward simplification (88 calls)
% 0.21/0.56 ; 0.000 0% Ordering (38 calls)
% 0.21/0.56 ; 0.002 4% Sortal reasoning (32 calls)
% 0.21/0.56 ; 0.000 0% Purity testing (1 call)
% 0.21/0.56 ; 0.023 50% Other
% 0.21/0.56 ; 0.046 Total
% 0.21/0.56 ; 0.049 Real time
% 0.21/0.56 ;
% 0.21/0.56 ; Term-hash-array has 107 terms in all.
% 0.21/0.56 ; Feature-vector-row-index has 18 entries (20 at peak, 21 added, 3 deleted).
% 0.21/0.56 ; Feature-vector-row-index has 67 nodes (78 at peak, 81 added, 14 deleted).
% 0.21/0.56 ; Retrieved 20 possibly forward subsuming rows in 28 calls.
% 0.21/0.56 ; Retrieved 2 possibly backward subsumed rows in 21 calls.
% 0.21/0.56 ; Path-index has 110 entries (110 at peak, 113 added, 3 deleted).
% 0.21/0.56 ; Path-index has 94 nodes (94 at peak, 97 added, 3 deleted).
% 0.21/0.56 ; Trie-index has 110 entries (110 at peak, 113 added, 3 deleted).
% 0.21/0.56 ; Trie-index has 255 nodes (255 at peak, 258 added, 3 deleted).
% 0.21/0.56 ; Retrieved 141 generalization terms in 239 calls.
% 0.21/0.56 ; Retrieved 82 instance terms in 66 calls.
% 0.21/0.56 ; Retrieved 2,192 unifiable terms in 513 calls.
% 0.21/0.56 ;
% 0.21/0.56 ; The agenda of rows to process has 24 entries:
% 0.21/0.56 ; 9 with value 14 12 with value 16 1 with value 23
% 0.21/0.56 ; 1 with value 15 1 with value 20
% 0.21/0.56 ; The agenda of rows to give has 49 entries:
% 0.21/0.56 ; 1 with value (4 10) 18 with value (4 13) 2 with value (4 16)
% 0.21/0.56 ; 4 with value (4 11) 6 with value (4 14) 2 with value (4 17)
% 0.21/0.56 ; 10 with value (4 12) 4 with value (4 15) 2 with value (4 18)
% 0.21/0.56 Evaluation took:
% 0.21/0.56 0.049 seconds of real time
% 0.21/0.56 0.042244 seconds of user run time
% 0.21/0.56 0.007192 seconds of system run time
% 0.21/0.56 0 calls to %EVAL
% 0.21/0.56 0 page faults and
% 0.21/0.56 3,164,960 bytes consed.
% 0.21/0.56 :PROOF-FOUND
% 0.21/0.56 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-08T11:20:21
% 0.21/0.56 :PROOF-FOUND
% 0.21/0.56 *
%------------------------------------------------------------------------------