TSTP Solution File: FLD026-3 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : FLD026-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n028.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 02:27:03 EDT 2022
% Result : Unsatisfiable 2.87s 3.05s
% Output : Refutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of clauses : 25 ( 18 unt; 4 nHn; 25 RR)
% Number of literals : 39 ( 0 equ; 13 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_multiplication_1,axiom,
( product(X,Y,Z)
| ~ product(X,U,V)
| ~ product(U,W,Y)
| ~ product(V,W,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(distributivity_1,axiom,
( sum(X,Y,Z)
| ~ sum(U,V,W)
| ~ product(W,X1,Z)
| ~ product(U,X1,X)
| ~ product(V,X1,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
cnf(product_4,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_4) ).
cnf(not_product_5,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_5) ).
cnf(33,plain,
product(multiplicative_identity,a,a),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,a_is_defined]) ).
cnf(34,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,well_definedness_of_multiplicative_identity]) ).
cnf(35,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,well_definedness_of_additive_identity]) ).
cnf(77,plain,
( defined(multiplicative_inverse(b))
| sum(additive_identity,b,additive_identity) ),
inference('HYPERRESOLVE',[status(thm)],[well_definedness_of_multiplicative_inverse,b_is_defined]) ).
cnf(121,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[existence_of_inverse_multiplication,not_sum_3,a_is_defined]) ).
cnf(122,plain,
( product(multiplicative_inverse(b),b,multiplicative_identity)
| sum(additive_identity,b,additive_identity) ),
inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_multiplication,b_is_defined]) ).
cnf(128,plain,
product(multiplicative_identity,b,a),
inference('HYPERRESOLVE',[status(thm)],[associativity_multiplication_1,33,product_4,33]) ).
cnf(8250,plain,
~ sum(additive_identity,b,additive_identity),
inference('UR-RESOLVE',[status(thm)],[distributivity_1,128,not_sum_3,35,35]) ).
cnf(8251,plain,
defined(multiplicative_inverse(b)),
inference('REWRITE',[status(thm)],[77,8250]) ).
cnf(8252,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference('REWRITE',[status(thm)],[122,8250]) ).
cnf(8263,plain,
product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b)),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,8251]) ).
cnf(8730,plain,
product(multiplicative_inverse(a),b,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[associativity_multiplication_1,121,product_4,34]) ).
cnf(14623,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[associativity_multiplication_1,8730,not_product_5,8252]),8263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : FLD026-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.14/0.15 % Command : run-snark %s %d
% 0.14/0.36 % Computer : n028.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 : Tue Jun 7 03:25:59 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.49 /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p 2022-06-07T03:25:59
% 0.21/0.51 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n028.cluster.edu at 2022-06-07T03:25:59
% 0.21/0.53
% 0.21/0.53 ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?X ?U ?V)) (NOT (|sum| ?U ?W ?Y)) (NOT (|sum| ?V ?W ?Z))).
% 0.21/0.53 ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?U ?V ?X)) (NOT (|sum| ?V ?Y ?W)) (NOT (|sum| ?U ?W ?Z))).
% 0.21/0.53 ; Recognized commutativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?Y ?X ?Z))).
% 0.21/0.53 ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?X ?U ?V)) (NOT (|product| ?U ?W ?Y)) (NOT (|product| ?V ?W ?Z))).
% 0.21/0.53 ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?U ?V ?X)) (NOT (|product| ?V ?Y ?W)) (NOT (|product| ?U ?W ?Z))).
% 0.21/0.53 ; Recognized commutativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?Y ?X ?Z))).
% 0.21/0.53 ; Declaring sum to be commutative.
% 2.87/3.05 ; Declaring product to be commutative.
% 2.87/3.05
% 2.87/3.05 #||
% 2.87/3.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.87/3.05 % SZS output start Refutation
% See solution above
% 2.87/3.05 ||#
% 2.87/3.05
% 2.87/3.05 ; Summary of computation:
% 2.87/3.05 ; 34086 formulas have been input or derived (from 189 formulas).
% 2.87/3.05 ; 14623 (43%) were retained. Of these,
% 2.87/3.05 ; 95 ( 1%) were simplified or subsumed later,
% 2.87/3.05 ; 14528 (99%) are still being kept.
% 2.87/3.05 ;
% 2.87/3.05 ; Run time in seconds excluding printing time:
% 2.87/3.05 ; 0.006 0% Read assertion file (1 call)
% 2.87/3.05 ; 0.000 0% Assert (31 calls)
% 2.87/3.05 ; 0.902 36% Process new row (32,735 calls)
% 2.87/3.05 ; 1.071 42% Resolution (376 calls)
% 2.87/3.05 ; 0.002 0% Paramodulation (188 calls)
% 2.87/3.05 ; 0.000 0% Factoring (5 calls)
% 2.87/3.05 ; 0.004 0% Condensing (3,192 calls)
% 2.87/3.05 ; 0.100 4% Forward subsumption (3,192 calls)
% 2.87/3.05 ; 0.036 1% Backward subsumption (1,736 calls)
% 2.87/3.05 ; 0.011 0% Clause clause subsumption (10,157 calls)
% 2.87/3.05 ; 0.184 7% Forward simplification (32,735 calls)
% 2.87/3.05 ; 0.100 4% Backward simplification (14,623 calls)
% 2.87/3.05 ; 0.002 0% Ordering (2,076 calls)
% 2.87/3.05 ; 0.000 0% Sortal reasoning (32 calls)
% 2.87/3.05 ; 0.000 0% Purity testing (1 call)
% 2.87/3.05 ; 0.121 5% Other
% 2.87/3.05 ; 2.539 Total
% 2.87/3.05 ; 2.540 Real time
% 2.87/3.05 ;
% 2.87/3.05 ; Term-hash-array has 21,443 terms in all.
% 2.87/3.05 ; Feature-vector-row-index has 1,663 entries (1,663 at peak, 1,736 added, 73 deleted).
% 2.87/3.05 ; Feature-vector-row-index has 1,946 nodes (1,946 at peak, 2,016 added, 70 deleted).
% 2.87/3.05 ; Retrieved 22,993 possibly forward subsuming rows in 3,192 calls.
% 2.87/3.05 ; Retrieved 8,396 possibly backward subsumed rows in 1,736 calls.
% 2.87/3.05 ; Path-index has 21,412 entries (21,412 at peak, 21,527 added, 115 deleted).
% 2.87/3.05 ; Path-index has 1,170 nodes (1,170 at peak, 1,187 added, 17 deleted).
% 2.87/3.05 ; Trie-index has 21,412 entries (21,412 at peak, 21,527 added, 115 deleted).
% 2.87/3.05 ; Trie-index has 60,342 nodes (60,342 at peak, 60,518 added, 176 deleted).
% 2.87/3.05 ; Retrieved 16,669 generalization terms in 35,999 calls.
% 2.87/3.05 ; Retrieved 13,065 instance terms in 12,886 calls.
% 2.87/3.05 ; Retrieved 2,685,822 unifiable terms in 36,836 calls.
% 2.87/3.05 ;
% 2.87/3.05 ; The agenda of rows to process has 133 entries:
% 2.87/3.05 ; 34 with value 11 18 with value 13 36 with value 14
% 2.87/3.05 ; 45 with value 12
% 2.87/3.05 ; The agenda of rows to give has 14345 entries:
% 2.87/3.05 ; 27 with value (4 9) 2250 with value (4 15) 478 with value (4 20)
% 2.87/3.05 ; 335 with value (4 10) 149 with value (4 16) 1560 with value (4 21)
% 2.87/3.05 ; 924 with value (4 11) 1062 with value (4 17) 17 with value (4 22)
% 2.87/3.05 ; 1352 with value (4 12) 241 with value (4 18) 365 with value (4 23)
% 2.87/3.05 ; 2694 with value (4 13) 2370 with value (4 19) 10 with value (4 25)
% 2.87/3.05 ; 511 with value (4 14)
% 2.87/3.05 Evaluation took:
% 2.87/3.05 2.541 seconds of real time
% 2.87/3.05 2.364499 seconds of user run time
% 2.87/3.05 0.177548 seconds of system run time
% 2.87/3.05 [Run times include 0.296 seconds GC run time.]
% 2.87/3.05 0 calls to %EVAL
% 2.87/3.05 0 page faults and
% 2.87/3.05 172,060,800 bytes consed.
% 2.87/3.05 :PROOF-FOUND
% 2.87/3.05 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-07T03:26:02
% 2.87/3.05 :PROOF-FOUND
% 2.87/3.05 *
%------------------------------------------------------------------------------