TSTP Solution File: FLD029-3 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : FLD029-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : Sat Jul 16 02:27:04 EDT 2022
% Result : Unsatisfiable 6.72s 6.95s
% Output : Refutation 6.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of clauses : 24 ( 16 unt; 2 nHn; 24 RR)
% Number of literals : 40 ( 0 equ; 19 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 : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_addition_1,axiom,
( sum(X,Y,Z)
| ~ sum(X,U,V)
| ~ sum(U,W,Y)
| ~ sum(V,W,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(associativity_multiplication_1,axiom,
( product(X,Y,Z)
| ~ product(X,U,V)
| ~ product(U,W,Y)
| ~ product(V,W,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(v_is_defined,hypothesis,
defined(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_is_defined) ).
cnf(not_sum_5,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
cnf(product_6,negated_conjecture,
product(a,u,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).
cnf(product_7,negated_conjecture,
product(a,v,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_7) ).
cnf(not_product_8,negated_conjecture,
~ product(multiplicative_identity,u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_8) ).
cnf(35,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_addition,well_definedness_of_multiplicative_identity]) ).
cnf(37,plain,
product(multiplicative_identity,v,v),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,v_is_defined]) ).
cnf(49,plain,
sum(additive_inverse(v),v,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_addition,v_is_defined]) ).
cnf(228,plain,
( product(multiplicative_inverse(a),a,multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_multiplication,a_is_defined]) ).
cnf(33883,plain,
~ sum(b,v,v),
inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,49,not_sum_5,49]) ).
cnf(33890,plain,
~ sum(a,multiplicative_identity,multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[distributivity_1,33883,37,product_7,37]) ).
cnf(34003,plain,
~ sum(additive_identity,a,additive_identity),
inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,33890,35,35]) ).
cnf(34005,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference('REWRITE',[status(thm)],[228,34003]) ).
cnf(36459,plain,
product(multiplicative_inverse(a),b,v),
inference('HYPERRESOLVE',[status(thm)],[associativity_multiplication_1,34005,product_7,37]) ).
cnf(36461,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[associativity_multiplication_1,34005,not_product_8,product_6]),36459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : FLD029-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 6 18:41:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46 (USE-FACTORING :POS)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46 *
% 0.19/0.46 "."
% 0.19/0.46 *
% 0.19/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T18:41:22
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-06-06T18:41:22
% 0.19/0.48
% 0.19/0.48 ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?X ?U ?V)) (NOT (|sum| ?U ?W ?Y)) (NOT (|sum| ?V ?W ?Z))).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?U ?V ?X)) (NOT (|sum| ?V ?Y ?W)) (NOT (|sum| ?U ?W ?Z))).
% 0.19/0.48 ; Recognized commutativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?Y ?X ?Z))).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?X ?U ?V)) (NOT (|product| ?U ?W ?Y)) (NOT (|product| ?V ?W ?Z))).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?U ?V ?X)) (NOT (|product| ?V ?Y ?W)) (NOT (|product| ?U ?W ?Z))).
% 0.19/0.48 ; Recognized commutativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?Y ?X ?Z))).
% 0.19/0.48 ; Declaring sum to be commutative.
% 6.72/6.95 ; Declaring product to be commutative.
% 6.72/6.95
% 6.72/6.95 #||
% 6.72/6.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.72/6.95 % SZS output start Refutation
% See solution above
% 6.72/6.95 ||#
% 6.72/6.95
% 6.72/6.95 ; Summary of computation:
% 6.72/6.95 ; 74468 formulas have been input or derived (from 175 formulas).
% 6.72/6.95 ; 36461 (49%) were retained. Of these,
% 6.72/6.95 ; 38 ( 0%) were simplified or subsumed later,
% 6.72/6.95 ; 36423 (100%) are still being kept.
% 6.72/6.95 ;
% 6.72/6.95 ; Run time in seconds excluding printing time:
% 6.72/6.95 ; 0.007 0% Read assertion file (1 call)
% 6.72/6.95 ; 0.001 0% Assert (34 calls)
% 6.72/6.95 ; 2.421 37% Process new row (73,901 calls)
% 6.72/6.95 ; 2.544 39% Resolution (348 calls)
% 6.72/6.95 ; 0.003 0% Paramodulation (174 calls)
% 6.72/6.95 ; 0.016 0% Condensing (8,024 calls)
% 6.72/6.95 ; 0.340 5% Forward subsumption (8,024 calls)
% 6.72/6.95 ; 0.117 2% Backward subsumption (4,107 calls)
% 6.72/6.95 ; 0.033 1% Clause clause subsumption (32,941 calls)
% 6.72/6.95 ; 0.399 6% Forward simplification (73,901 calls)
% 6.72/6.95 ; 0.356 5% Backward simplification (36,461 calls)
% 6.72/6.95 ; 0.003 0% Ordering (2,252 calls)
% 6.72/6.95 ; 0.000 0% Sortal reasoning (32 calls)
% 6.72/6.95 ; 0.000 0% Purity testing (1 call)
% 6.72/6.95 ; 0.248 4% Other
% 6.72/6.95 ; 6.488 Total
% 6.72/6.95 ; 6.488 Real time
% 6.72/6.95 ;
% 6.72/6.96 ; Term-hash-array has 56,485 terms in all.
% 6.72/6.96 ; Feature-vector-row-index has 4,093 entries (4,093 at peak, 4,107 added, 14 deleted).
% 6.72/6.96 ; Feature-vector-row-index has 2,510 nodes (2,510 at peak, 2,566 added, 56 deleted).
% 6.72/6.96 ; Retrieved 69,826 possibly forward subsuming rows in 8,024 calls.
% 6.72/6.96 ; Retrieved 31,746 possibly backward subsumed rows in 4,107 calls.
% 6.72/6.96 ; Path-index has 56,467 entries (56,467 at peak, 56,512 added, 45 deleted).
% 6.72/6.96 ; Path-index has 1,199 nodes (1,199 at peak, 1,220 added, 21 deleted).
% 6.72/6.96 ; Trie-index has 56,467 entries (56,467 at peak, 56,512 added, 45 deleted).
% 6.72/6.96 ; Trie-index has 155,408 nodes (155,408 at peak, 155,465 added, 57 deleted).
% 6.72/6.96 ; Retrieved 33,524 generalization terms in 81,896 calls.
% 6.72/6.96 ; Retrieved 32,430 instance terms in 32,353 calls.
% 6.72/6.96 ; Retrieved 9,167,316 unifiable terms in 13,331 calls.
% 6.72/6.96 ;
% 6.72/6.96 ; The agenda of rows to process has 41 entries:
% 6.72/6.96 ; 1 with value 9 35 with value 11 1 with value 13
% 6.72/6.96 ; 3 with value 10 1 with value 12
% 6.72/6.96 ; The agenda of rows to give has 36252 entries:
% 6.72/6.96 ; 2 with value (4 8) 10634 with value (4 13) 864 with value (4 18)
% 6.72/6.96 ; 162 with value (4 9) 138 with value (4 14) 10375 with value (4 19)
% 6.72/6.96 ; 390 with value (4 10) 1970 with value (4 15) 2556 with value (4 20)
% 6.80/6.96 ; 2096 with value (4 11) 494 with value (4 16) 72 with value (4 22)
% 6.80/6.96 ; 3331 with value (4 12) 3168 with value (4 17)
% 6.80/6.96 Evaluation took:
% 6.80/6.96 6.491 seconds of real time
% 6.80/6.96 5.984202 seconds of user run time
% 6.80/6.96 0.506883 seconds of system run time
% 6.80/6.96 [Run times include 1.068 seconds GC run time.]
% 6.80/6.96 0 calls to %EVAL
% 6.80/6.96 0 page faults and
% 6.80/6.96 438,780,344 bytes consed.
% 6.80/6.96 :PROOF-FOUND
% 6.80/6.96 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T18:41:28
% 6.80/6.96 :PROOF-FOUND
% 6.80/6.96 *
%------------------------------------------------------------------------------