%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : FLD012-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n032.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 02:26:58 EDT 2022
% Result : Unsatisfiable 11.85s 12.02s
% Output : Refutation 11.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of clauses : 30 ( 22 unt; 2 nHn; 30 RR)
% Number of literals : 46 ( 0 equ; 20 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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_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,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
cnf(not_sum_6,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_6) ).
cnf(product_7,negated_conjecture,
product(a,b,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_7) ).
cnf(product_8,negated_conjecture,
product(multiplicative_inverse(a),multiplicative_inverse(b),v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_8) ).
cnf(not_product_9,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(u),v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_9) ).
cnf(33,plain,
sum(additive_identity,u,u),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_addition,u_is_defined]) ).
cnf(38,plain,
product(multiplicative_identity,v,v),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,v_is_defined]) ).
cnf(40,plain,
product(multiplicative_identity,b,b),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,b_is_defined]) ).
cnf(52,plain,
sum(additive_inverse(b),b,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_addition,b_is_defined]) ).
cnf(226,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[existence_of_inverse_multiplication,not_sum_5,a_is_defined]) ).
cnf(227,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[existence_of_inverse_multiplication,not_sum_6,b_is_defined]) ).
cnf(229,plain,
( product(multiplicative_inverse(u),u,multiplicative_identity)
| sum(additive_identity,u,additive_identity) ),
inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_multiplication,u_is_defined]) ).
cnf(34699,plain,
~ sum(b,b,b),
inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,52,not_sum_6,52]) ).
cnf(34782,plain,
product(multiplicative_inverse(a),u,b),
inference('HYPERRESOLVE',[status(thm)],[associativity_multiplication_1,226,product_7,40]) ).
cnf(47821,plain,
product(u,v,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[associativity_multiplication_1,34782,product_8,227]) ).
cnf(47822,plain,
~ sum(u,u,u),
inference('UR-RESOLVE',[status(thm)],[distributivity_1,34782,34699,34782,34782]) ).
cnf(47890,plain,
~ product(multiplicative_inverse(u),u,multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[associativity_multiplication_1,47821,not_product_9,38]) ).
cnf(47891,plain,
sum(additive_identity,u,additive_identity),
inference('REWRITE',[status(thm)],[229,47890]) ).
cnf(48025,plain,
$false,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[associativity_addition_1,47891,33,33]),47822]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : FLD012-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.10 % Command : run-snark %s %d
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Mon Jun 6 20:41:05 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.38 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.39 *
% 0.15/0.39 *
% 0.15/0.39 #<PACKAGE "SNARK-USER">
% 0.15/0.39 *
% 0.15/0.39 SNARK-TPTP-OPTIONS
% 0.15/0.39 *
% 0.15/0.39 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.15/0.39 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.15/0.39 (USE-FACTORING :POS)
% 0.15/0.39 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.15/0.39 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.15/0.39 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.15/0.39 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.15/0.39 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.15/0.39 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.15/0.39 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.15/0.39 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.15/0.39 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.15/0.39 (DECLARE-TPTP-SYMBOLS2))
% 0.15/0.39 *
% 0.15/0.39 "."
% 0.15/0.39 *
% 0.15/0.39 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T20:41:05
% 0.15/0.39 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n032.cluster.edu at 2022-06-06T20:41:05
% 0.15/0.40
% 0.15/0.40 ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?X ?U ?V)) (NOT (|sum| ?U ?W ?Y)) (NOT (|sum| ?V ?W ?Z))).
% 0.15/0.40 ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?U ?V ?X)) (NOT (|sum| ?V ?Y ?W)) (NOT (|sum| ?U ?W ?Z))).
% 0.15/0.40 ; Recognized commutativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?Y ?X ?Z))).
% 0.15/0.40 ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?X ?U ?V)) (NOT (|product| ?U ?W ?Y)) (NOT (|product| ?V ?W ?Z))).
% 0.15/0.40 ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?U ?V ?X)) (NOT (|product| ?V ?Y ?W)) (NOT (|product| ?U ?W ?Z))).
% 0.15/0.40 ; Recognized commutativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?Y ?X ?Z))).
% 0.15/0.40 ; Declaring sum to be commutative.
% 11.85/12.02 ; Declaring product to be commutative.
% 11.85/12.02
% 11.85/12.02 #||
% 11.85/12.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.85/12.02 % SZS output start Refutation
% See solution above
% 11.85/12.02 ||#
% 11.85/12.02
% 11.85/12.02 ; Summary of computation:
% 11.85/12.02 ; 103699 formulas have been input or derived (from 319 formulas).
% 11.85/12.02 ; 48025 (46%) were retained. Of these,
% 11.85/12.02 ; 177 ( 0%) were simplified or subsumed later,
% 11.85/12.02 ; 47848 (100%) are still being kept.
% 11.85/12.02 ;
% 11.85/12.02 ; Run time in seconds excluding printing time:
% 11.85/12.02 ; 0.004 0% Read assertion file (1 call)
% 11.85/12.02 ; 0.001 0% Assert (35 calls)
% 11.85/12.02 ; 3.580 31% Process new row (100,607 calls)
% 11.85/12.02 ; 5.751 49% Resolution (636 calls)
% 11.85/12.02 ; 0.004 0% Paramodulation (318 calls)
% 11.85/12.02 ; 0.000 0% Factoring (15 calls)
% 11.85/12.02 ; 0.018 0% Condensing (11,018 calls)
% 11.85/12.02 ; 0.473 4% Forward subsumption (11,018 calls)
% 11.85/12.02 ; 0.233 2% Backward subsumption (5,937 calls)
% 11.85/12.02 ; 0.051 0% Clause clause subsumption (47,611 calls)
% 11.85/12.02 ; 0.605 5% Forward simplification (100,607 calls)
% 11.85/12.02 ; 0.495 4% Backward simplification (48,025 calls)
% 11.85/12.02 ; 0.029 0% Ordering (6,399 calls)
% 11.85/12.02 ; 0.000 0% Sortal reasoning (32 calls)
% 11.85/12.02 ; 0.000 0% Purity testing (1 call)
% 11.85/12.02 ; 0.386 3% Other
% 11.85/12.02 ; 11.630 Total
% 11.85/12.02 ; 11.632 Real time
% 11.85/12.03 ;
% 11.85/12.03 ; Term-hash-array has 71,808 terms in all.
% 11.85/12.03 ; Feature-vector-row-index has 5,782 entries (5,869 at peak, 5,937 added, 155 deleted).
% 11.85/12.03 ; Feature-vector-row-index has 5,385 nodes (5,427 at peak, 5,492 added, 107 deleted).
% 11.85/12.03 ; Retrieved 93,059 possibly forward subsuming rows in 11,018 calls.
% 11.85/12.03 ; Retrieved 38,942 possibly backward subsumed rows in 5,937 calls.
% 11.85/12.03 ; Path-index has 71,778 entries (71,778 at peak, 71,888 added, 110 deleted).
% 11.85/12.03 ; Path-index has 1,499 nodes (1,500 at peak, 1,515 added, 16 deleted).
% 11.85/12.03 ; Trie-index has 71,778 entries (71,778 at peak, 71,888 added, 110 deleted).
% 11.85/12.03 ; Trie-index has 199,930 nodes (199,930 at peak, 200,095 added, 165 deleted).
% 11.85/12.03 ; Retrieved 47,516 generalization terms in 111,948 calls.
% 11.85/12.03 ; Retrieved 42,618 instance terms in 42,087 calls.
% 11.85/12.03 ; Retrieved 15,815,943 unifiable terms in 98,384 calls.
% 11.85/12.03 ;
% 11.85/12.03 ; The agenda of rows to process has 1145 entries:
% 11.85/12.03 ; 98 with value 7 284 with value 10 36 with value 13
% 11.85/12.03 ; 58 with value 8 62 with value 11 328 with value 14
% 11.85/12.03 ; 71 with value 9 208 with value 12
% 11.85/12.03 ; The agenda of rows to give has 47536 entries:
% 11.85/12.03 ; 2 with value (4 6) 11374 with value (4 13) 10876 with value (4 19)
% 11.85/12.03 ; 1 with value (4 7) 1122 with value (4 14) 2541 with value (4 20)
% 11.85/12.03 ; 2 with value (4 8) 6194 with value (4 15) 3864 with value (4 21)
% 11.85/12.03 ; 46 with value (4 9) 472 with value (4 16) 57 with value (4 22)
% 11.85/12.03 ; 504 with value (4 10) 2892 with value (4 17) 930 with value (4 23)
% 11.85/12.03 ; 2368 with value (4 11) 705 with value (4 18) 12 with value (4 25)
% 11.85/12.03 ; 3574 with value (4 12)
% 11.85/12.03 Evaluation took:
% 11.85/12.03 11.635 seconds of real time
% 11.85/12.03 10.95762 seconds of user run time
% 11.85/12.03 0.676857 seconds of system run time
% 11.85/12.03 [Run times include 1.877 seconds GC run time.]
% 11.85/12.03 0 calls to %EVAL
% 11.85/12.03 0 page faults and
% 11.85/12.03 645,389,920 bytes consed.
% 11.85/12.03 :PROOF-FOUND
% 11.85/12.03 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T20:41:16
% 11.85/12.03 :PROOF-FOUND
% 11.85/12.03 *
%------------------------------------------------------------------------------