TSTP Solution File: GRP134-2.003 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP134-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n008.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 11:37:03 EDT 2022
% Result : Unsatisfiable 0.19s 0.57s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 54 ( 23 unt; 27 nHn; 54 RR)
% Number of literals : 112 ( 0 equ; 24 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(e_1_then_e_2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_then_e_2) ).
cnf(e_3_greater_e_2,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_2) ).
cnf(no_redundancy,axiom,
( ~ product(X,e_1,Y)
| ~ next(X,Z)
| ~ greater(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_redundancy) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(product_right_cancellation,axiom,
( ~ product(X,Y,Z)
| ~ product(X,U,Z)
| equalish(Y,U) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(qg4,negated_conjecture,
( ~ product(X,Y,Z)
| ~ product(Y,X,U)
| product(Z,U,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4) ).
cnf(21,plain,
~ product(e_1,e_1,e_3),
inference('UR-RESOLVE',[status(thm)],[no_redundancy,e_1_then_e_2,e_3_greater_e_2]) ).
cnf(22,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_3,element_3]) ).
cnf(24,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_3,element_1]) ).
cnf(27,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_2,element_1]) ).
cnf(28,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_3]) ).
cnf(29,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_2]) ).
cnf(30,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_1]),21]) ).
cnf(31,plain,
~ product(e_3,e_3,e_1),
inference('UR-RESOLVE',[status(thm)],[qg4,21]) ).
cnf(32,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference('REWRITE',[status(thm)],[22,31]) ).
cnf(35,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_2,e_1) ),
inference('HYPERRESOLVE',[status(thm)],[qg4,30,30]) ).
cnf(41,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_3,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,24,32]),e_1_is_not_e_3]) ).
cnf(54,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,28,32]),e_1_is_not_e_3]) ).
cnf(57,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[qg4,28,24]),31]) ).
cnf(63,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[qg4,29,27]),31]) ).
cnf(67,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_2,e_2,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg4,41,41]) ).
cnf(69,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_2,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg4,54,54]) ).
cnf(75,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference('HYPERRESOLVE',[status(thm)],[qg4,67,35]) ).
cnf(84,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_1,e_1) ),
inference('HYPERRESOLVE',[status(thm)],[qg4,69,35]) ).
cnf(85,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,69,27]),e_2_is_not_e_1]) ).
cnf(86,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,75,30]),e_3_is_not_e_1]) ).
cnf(87,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_1,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,84,30]),e_3_is_not_e_1]) ).
cnf(88,plain,
product(e_1,e_1,e_1),
inference('HYPERRESOLVE',[status(thm)],[qg4,87,86]) ).
cnf(90,plain,
~ product(e_2,e_1,e_1),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,88,e_1_is_not_e_2]) ).
cnf(94,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[63,90]) ).
cnf(95,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[85,90]) ).
cnf(96,plain,
~ product(e_3,e_1,e_1),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,88,e_1_is_not_e_3]) ).
cnf(98,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_3,e_2) ),
inference('REWRITE',[status(thm)],[41,96]) ).
cnf(99,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference('REWRITE',[status(thm)],[57,96]) ).
cnf(105,plain,
~ product(e_1,e_2,e_1),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,88,e_1_is_not_e_2]) ).
cnf(109,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[94,105]) ).
cnf(111,plain,
~ product(e_1,e_3,e_1),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,88,e_1_is_not_e_3]) ).
cnf(117,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[95,111]) ).
cnf(118,plain,
( product(e_1,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference('REWRITE',[status(thm)],[99,111]) ).
cnf(125,plain,
product(e_3,e_1,e_2),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,118,98]),e_1_is_not_e_3]) ).
cnf(127,plain,
~ product(e_2,e_1,e_2),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,125,e_3_is_not_e_2]) ).
cnf(130,plain,
product(e_1,e_2,e_2),
inference('REWRITE',[status(thm)],[109,127]) ).
cnf(131,plain,
product(e_1,e_3,e_2),
inference('REWRITE',[status(thm)],[117,127]) ).
cnf(148,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,130,e_2_is_not_e_3]),131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP134-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 03:53:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox2/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)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T03:53:07
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n008.cluster.edu at 2022-06-14T03:53:07
% 0.19/0.57
% 0.19/0.57
% 0.19/0.57 #||
% 0.19/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.57 % SZS output start Refutation
% See solution above
% 0.19/0.57 ||#
% 0.19/0.57
% 0.19/0.57 ; Summary of computation:
% 0.19/0.57 ; 974 formulas have been input or derived (from 78 formulas).
% 0.19/0.57 ; 148 (15%) were retained. Of these,
% 0.19/0.57 ; 93 (63%) were simplified or subsumed later,
% 0.19/0.57 ; 55 (37%) are still being kept.
% 0.19/0.57 ;
% 0.19/0.57 ; Run time in seconds excluding printing time:
% 0.19/0.57 ; 0.003 3% Read assertion file (1 call)
% 0.19/0.57 ; 0.001 1% Assert (20 calls)
% 0.19/0.57 ; 0.010 10% Process new row (785 calls)
% 0.19/0.57 ; 0.021 21% Resolution (154 calls)
% 0.19/0.57 ; 0.003 3% Paramodulation (77 calls)
% 0.19/0.57 ; 0.000 0% Factoring (39 calls)
% 0.19/0.57 ; 0.000 0% Condensing (268 calls)
% 0.19/0.57 ; 0.014 14% Forward subsumption (268 calls)
% 0.19/0.57 ; 0.006 6% Backward subsumption (99 calls)
% 0.19/0.57 ; 0.006 6% Clause clause subsumption (958 calls)
% 0.19/0.57 ; 0.013 13% Forward simplification (583 calls)
% 0.19/0.57 ; 0.001 1% Backward simplification (148 calls)
% 0.19/0.57 ; 0.002 2% Ordering (539 calls)
% 0.19/0.57 ; 0.000 0% Sortal reasoning (32 calls)
% 0.19/0.57 ; 0.000 0% Purity testing (1 call)
% 0.19/0.57 ; 0.022 22% Other
% 0.19/0.57 ; 0.102 Total
% 0.19/0.57 ; 0.108 Real time
% 0.19/0.57 ;
% 0.19/0.57 ; Term-hash-array has 66 terms in all.
% 0.19/0.57 ; Feature-vector-row-index has 6 entries (40 at peak, 99 added, 93 deleted).
% 0.19/0.57 ; Feature-vector-row-index has 14 nodes (117 at peak, 208 added, 194 deleted).
% 0.19/0.57 ; Retrieved 1,353 possibly forward subsuming rows in 268 calls.
% 0.19/0.57 ; Retrieved 289 possibly backward subsumed rows in 99 calls.
% 0.19/0.57 ; Path-index has 68 entries (68 at peak, 95 added, 27 deleted).
% 0.19/0.57 ; Path-index has 58 nodes (58 at peak, 58 added, 0 deleted).
% 0.19/0.57 ; Trie-index has 68 entries (68 at peak, 95 added, 27 deleted).
% 0.19/0.57 ; Trie-index has 93 nodes (93 at peak, 122 added, 29 deleted).
% 0.19/0.57 ; Retrieved 391 generalization terms in 1,729 calls.
% 0.19/0.57 ; Retrieved 48 instance terms in 48 calls.
% 0.19/0.57 ; Retrieved 3,891 unifiable terms in 1,002 calls.
% 0.19/0.57 ;
% 0.19/0.57 ; The agenda of rows to process has 10 entries:
% 0.19/0.57 ; 9 with value 8 1 with value 13
% 0.19/0.57 ; The agenda of rows to give has 16 entries:
% 0.19/0.57 ; 5 with value (4 7) 5 with value (4 9) 1 with value (4 12)
% 0.19/0.57 ; 4 with value (4 8) 1 with value (4 10)
% 0.19/0.57 Evaluation took:
% 0.19/0.57 0.108 seconds of real time
% 0.19/0.57 0.088141 seconds of user run time
% 0.19/0.57 0.020171 seconds of system run time
% 0.19/0.57 0 calls to %EVAL
% 0.19/0.57 0 page faults and
% 0.19/0.57 8,709,776 bytes consed.
% 0.19/0.57 :PROOF-FOUND
% 0.19/0.57 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T03:53:07
% 0.19/0.57 :PROOF-FOUND
% 0.19/0.57 *
%------------------------------------------------------------------------------