%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP126-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n003.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 11:36:50 EDT 2022
% Result : Unsatisfiable 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of clauses : 48 ( 33 unt; 10 nHn; 47 RR)
% Number of literals : 80 ( 0 equ; 41 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(row_surjectivity,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(e_1,X,Y)
| product(e_2,X,Y)
| product(e_3,X,Y)
| product(e_4,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
cnf(column_surjectivity,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(X,e_1,Y)
| product(X,e_2,Y)
| product(X,e_3,Y)
| product(X,e_4,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',column_surjectivity) ).
cnf(qg4_1,negated_conjecture,
( product(X,Y,Z)
| ~ product(Z,U,Y)
| ~ product(Y,X,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4_1) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(product_total_function1,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(product_total_function2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,U)
| equalish(Z,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
cnf(product_right_cancellation,axiom,
( ~ product(X,Y,Z)
| ~ product(X,U,Z)
| equalish(Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(product_left_cancellation,axiom,
( ~ product(X,Y,Z)
| ~ product(U,Y,Z)
| equalish(X,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(product_idempotence,axiom,
product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
cnf(qg4,negated_conjecture,
( ~ product(X,Y,Z)
| ~ product(Y,X,U)
| product(Z,U,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4) ).
cnf(30,plain,
~ product(e_4,e_4,e_3),
inference('UR-RESOLVE',[status(thm)],[product_total_function2,product_idempotence,e_3_is_not_e_4]) ).
cnf(32,plain,
~ product(e_3,e_3,e_2),
inference('UR-RESOLVE',[status(thm)],[product_total_function2,product_idempotence,e_2_is_not_e_3]) ).
cnf(35,plain,
~ product(e_2,e_2,e_3),
inference('UR-RESOLVE',[status(thm)],[product_total_function2,product_idempotence,e_3_is_not_e_2]) ).
cnf(37,plain,
~ product(e_1,e_1,e_2),
inference('UR-RESOLVE',[status(thm)],[product_total_function2,product_idempotence,e_2_is_not_e_1]) ).
cnf(41,plain,
~ product(e_4,e_2,e_4),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,product_idempotence,e_2_is_not_e_4]) ).
cnf(43,plain,
~ product(e_3,e_1,e_3),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,product_idempotence,e_1_is_not_e_3]) ).
cnf(45,plain,
~ product(e_3,e_4,e_3),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,product_idempotence,e_4_is_not_e_3]) ).
cnf(47,plain,
~ product(e_2,e_3,e_2),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,product_idempotence,e_3_is_not_e_2]) ).
cnf(50,plain,
~ product(e_1,e_3,e_1),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,product_idempotence,e_3_is_not_e_1]) ).
cnf(51,plain,
~ product(e_1,e_4,e_1),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,product_idempotence,e_4_is_not_e_1]) ).
cnf(52,plain,
~ product(e_1,e_4,e_4),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,product_idempotence,e_1_is_not_e_4]) ).
cnf(58,plain,
~ product(e_1,e_2,e_2),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,product_idempotence,e_1_is_not_e_2]) ).
cnf(62,plain,
~ product(e_3,e_1,e_1),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,product_idempotence,e_3_is_not_e_1]) ).
cnf(64,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[row_surjectivity,element_4,element_3]),30,45]) ).
cnf(68,plain,
( product(e_1,e_3,e_2)
| product(e_4,e_3,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[row_surjectivity,element_3,element_2]),32,47]) ).
cnf(87,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_4,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[column_surjectivity,element_1,element_2]),58,37]) ).
cnf(93,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_4) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_3,element_1]),43,62]) ).
cnf(97,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_4]),52,51]) ).
cnf(103,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_4,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[qg4_1,68,64]),41]) ).
cnf(221,plain,
( product(e_1,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[qg4_1,97,93]),50]) ).
cnf(227,plain,
product(e_1,e_3,e_2),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function2,103,87]),e_3_is_not_e_2]) ).
cnf(228,plain,
~ product(e_3,e_1,e_2),
inference('UR-RESOLVE',[status(thm)],[qg4,227,35]) ).
cnf(243,plain,
product(e_1,e_4,e_2),
inference('REWRITE',[status(thm)],[221,228]) ).
cnf(245,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,227,e_3_is_not_e_4]),243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GRP126-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.08 % Command : run-snark %s %d
% 0.07/0.27 % Computer : n003.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Tue Jun 14 12:03:10 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.11/0.34 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.34 *
% 0.11/0.34 *
% 0.11/0.35 #<PACKAGE "SNARK-USER">
% 0.11/0.35 *
% 0.11/0.35 SNARK-TPTP-OPTIONS
% 0.11/0.35 *
% 0.11/0.35 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.11/0.35 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.11/0.35 (USE-FACTORING :POS)
% 0.11/0.35 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.11/0.35 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.11/0.35 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.11/0.35 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.11/0.35 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.11/0.35 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.11/0.35 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.11/0.35 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.11/0.35 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.11/0.35 (DECLARE-TPTP-SYMBOLS2))
% 0.11/0.35 *
% 0.11/0.35 "."
% 0.11/0.35 *
% 0.11/0.35 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T12:03:10
% 0.11/0.35 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n003.cluster.edu at 2022-06-14T12:03:10
% 0.11/0.45
% 0.11/0.45
% 0.11/0.45 #||
% 0.11/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 % SZS output start Refutation
% See solution above
% 0.11/0.46 ||#
% 0.11/0.46
% 0.11/0.46 ; Summary of computation:
% 0.11/0.46 ; 1381 formulas have been input or derived (from 104 formulas).
% 0.11/0.46 ; 245 (18%) were retained. Of these,
% 0.11/0.46 ; 162 (66%) were simplified or subsumed later,
% 0.11/0.46 ; 83 (34%) are still being kept.
% 0.11/0.46 ;
% 0.11/0.46 ; Run time in seconds excluding printing time:
% 0.11/0.46 ; 0.002 2% Read assertion file (1 call)
% 0.11/0.46 ; 0.001 1% Assert (26 calls)
% 0.11/0.46 ; 0.009 8% Process new row (1,281 calls)
% 0.11/0.46 ; 0.026 25% Resolution (206 calls)
% 0.11/0.46 ; 0.000 0% Paramodulation (103 calls)
% 0.11/0.46 ; 0.000 0% Factoring (39 calls)
% 0.11/0.46 ; 0.002 2% Condensing (643 calls)
% 0.11/0.46 ; 0.023 22% Forward subsumption (643 calls)
% 0.11/0.46 ; 0.001 1% Backward subsumption (172 calls)
% 0.11/0.46 ; 0.009 8% Clause clause subsumption (9,823 calls)
% 0.11/0.46 ; 0.014 13% Forward simplification (1,237 calls)
% 0.11/0.46 ; 0.003 3% Backward simplification (245 calls)
% 0.11/0.46 ; 0.000 0% Ordering (384 calls)
% 0.11/0.46 ; 0.000 0% Sortal reasoning (32 calls)
% 0.11/0.46 ; 0.000 0% Purity testing (1 call)
% 0.11/0.46 ; 0.016 15% Other
% 0.11/0.46 ; 0.106 Total
% 0.11/0.46 ; 0.114 Real time
% 0.11/0.46 ;
% 0.11/0.46 ; Term-hash-array has 102 terms in all.
% 0.11/0.46 ; Feature-vector-row-index has 10 entries (147 at peak, 172 added, 162 deleted).
% 0.11/0.46 ; Feature-vector-row-index has 19 nodes (85 at peak, 139 added, 120 deleted).
% 0.11/0.46 ; Retrieved 17,331 possibly forward subsuming rows in 643 calls.
% 0.11/0.46 ; Retrieved 1,705 possibly backward subsumed rows in 172 calls.
% 0.11/0.46 ; Path-index has 102 entries (106 at peak, 107 added, 5 deleted).
% 0.11/0.46 ; Path-index has 43 nodes (43 at peak, 43 added, 0 deleted).
% 0.11/0.46 ; Trie-index has 102 entries (106 at peak, 107 added, 5 deleted).
% 0.11/0.46 ; Trie-index has 130 nodes (134 at peak, 135 added, 5 deleted).
% 0.11/0.46 ; Retrieved 3,076 generalization terms in 3,096 calls.
% 0.11/0.46 ; Retrieved 106 instance terms in 72 calls.
% 0.11/0.46 ; Retrieved 16,919 unifiable terms in 2,465 calls.
% 0.11/0.46 ;
% 0.11/0.46 ; The agenda of rows to process has 44 entries:
% 0.11/0.46 ; 22 with value 9 10 with value 13 12 with value 14
% 0.11/0.46 ; The agenda of rows to give has 17 entries:
% 0.11/0.46 ; 3 with value (4 6) 12 with value (4 7) 2 with value (4 9)
% 0.11/0.46 Evaluation took:
% 0.11/0.46 0.115 seconds of real time
% 0.11/0.46 0.092094 seconds of user run time
% 0.11/0.46 0.022586 seconds of system run time
% 0.11/0.46 [Run times include 0.005 seconds GC run time.]
% 0.11/0.46 0 calls to %EVAL
% 0.11/0.46 0 page faults and
% 0.11/0.46 13,201,288 bytes consed.
% 0.11/0.46 :PROOF-FOUND
% 0.11/0.46 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T12:03:10
% 0.11/0.46 :PROOF-FOUND
% 0.11/0.46 *
%------------------------------------------------------------------------------