TSTP Solution File: GRP129-4.004 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP129-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n017.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 11:36:57 EDT 2022
% Result : Unsatisfiable 1.37s 1.59s
% Output : Refutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of clauses : 63 ( 23 unt; 36 nHn; 63 RR)
% Number of literals : 159 ( 0 equ; 29 neg)
% Maximal clause size : 6 ( 2 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 : 22 ( 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(qg3_1,negated_conjecture,
( product(X,Y,Z)
| ~ product(Z,X,U)
| ~ product(Y,Z,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_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_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_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
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_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
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(29,plain,
( product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_4,e_4,e_1) ),
inference('HYPERRESOLVE',[status(thm)],[row_surjectivity,element_4,element_1]) ).
cnf(37,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_4,e_2,e_1) ),
inference('HYPERRESOLVE',[status(thm)],[row_surjectivity,element_2,element_1]) ).
cnf(45,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_3,e_1)
| product(e_4,e_4,e_1) ),
inference('HYPERRESOLVE',[status(thm)],[column_surjectivity,element_4,element_1]) ).
cnf(49,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_4,e_1) ),
inference('HYPERRESOLVE',[status(thm)],[column_surjectivity,element_3,element_1]) ).
cnf(53,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_4,e_1) ),
inference('HYPERRESOLVE',[status(thm)],[column_surjectivity,element_2,element_1]) ).
cnf(68,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_2,element_2]) ).
cnf(73,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_1]) ).
cnf(86,plain,
( product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_4,e_4,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,29,29]) ).
cnf(210,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_3,e_1)
| product(e_4,e_4,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,45,45]) ).
cnf(353,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_2,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,53,37]) ).
cnf(645,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,68,68]) ).
cnf(646,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,645,645]) ).
cnf(754,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,73,73]) ).
cnf(755,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,754,754]) ).
cnf(756,plain,
product(e_1,e_1,e_1),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,755,755]) ).
cnf(758,plain,
~ product(e_2,e_1,e_1),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,756,e_1_is_not_e_2]) ).
cnf(764,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_2,e_4) ),
inference('REWRITE',[status(thm)],[353,758]) ).
cnf(807,plain,
~ product(e_3,e_1,e_1),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,756,e_1_is_not_e_3]) ).
cnf(808,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_4,e_1) ),
inference('REWRITE',[status(thm)],[49,807]) ).
cnf(858,plain,
~ product(e_4,e_1,e_1),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,756,e_1_is_not_e_4]) ).
cnf(859,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_3,e_1)
| product(e_4,e_4,e_1) ),
inference('REWRITE',[status(thm)],[45,858]) ).
cnf(862,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_3,e_1)
| product(e_4,e_4,e_4) ),
inference('REWRITE',[status(thm)],[210,858]) ).
cnf(923,plain,
~ product(e_1,e_2,e_1),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,756,e_1_is_not_e_2]) ).
cnf(924,plain,
( product(e_2,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_4,e_2,e_1) ),
inference('REWRITE',[status(thm)],[37,923]) ).
cnf(957,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_2,e_4) ),
inference('REWRITE',[status(thm)],[764,923]) ).
cnf(1017,plain,
~ product(e_1,e_4,e_1),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,756,e_1_is_not_e_4]) ).
cnf(1018,plain,
( product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_4,e_4,e_1) ),
inference('REWRITE',[status(thm)],[29,1017]) ).
cnf(1021,plain,
( product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_4,e_4,e_4) ),
inference('REWRITE',[status(thm)],[86,1017]) ).
cnf(1242,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_3,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function2,862,859]),e_4_is_not_e_1]) ).
cnf(1263,plain,
( product(e_2,e_4,e_1)
| product(e_3,e_4,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function2,1021,1018]),e_4_is_not_e_1]) ).
cnf(1264,plain,
( product(e_2,e_4,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_4,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,1263,1242]) ).
cnf(1315,plain,
( product(e_2,e_4,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_4,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,1264,1264]) ).
cnf(1370,plain,
( product(e_2,e_4,e_1)
| product(e_4,e_2,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function2,1315,1264]),e_4_is_not_e_3]) ).
cnf(1371,plain,
( product(e_4,e_2,e_1)
| product(e_3,e_2,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,1370,1242]) ).
cnf(1637,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function2,957,646]),e_4_is_not_e_2]) ).
cnf(1638,plain,
( product(e_2,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_4,e_2) ),
inference('HYPERRESOLVE',[status(thm)],[qg3_1,1637,924]) ).
cnf(1655,plain,
( product(e_2,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_3,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function2,1638,808]),e_2_is_not_e_1]) ).
cnf(1682,plain,
( product(e_2,e_2,e_1)
| product(e_3,e_2,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,1655,1637]),e_3_is_not_e_2]) ).
cnf(1684,plain,
( product(e_2,e_2,e_1)
| product(e_4,e_2,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function2,1682,1371]),e_1_is_not_e_4]) ).
cnf(1702,plain,
product(e_2,e_2,e_1),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,1684,1682]),e_4_is_not_e_3]) ).
cnf(1761,plain,
~ product(e_4,e_2,e_1),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,1702,e_2_is_not_e_4]) ).
cnf(1772,plain,
product(e_2,e_4,e_1),
inference('REWRITE',[status(thm)],[1370,1761]) ).
cnf(1832,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,1702,e_2_is_not_e_4]),1772]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP129-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : run-snark %s %d
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 06:40:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 *
% 0.20/0.47 *
% 0.20/0.48 #<PACKAGE "SNARK-USER">
% 0.20/0.48 *
% 0.20/0.48 SNARK-TPTP-OPTIONS
% 0.20/0.48 *
% 0.20/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48 (USE-FACTORING :POS)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48 *
% 0.20/0.48 "."
% 0.20/0.48 *
% 0.20/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T06:40:23
% 0.20/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n017.cluster.edu at 2022-06-13T06:40:23
% 1.37/1.59
% 1.37/1.59
% 1.37/1.59 #||
% 1.37/1.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.37/1.59 % SZS output start Refutation
% See solution above
% 1.37/1.60 ||#
% 1.37/1.60
% 1.37/1.60 ; Summary of computation:
% 1.37/1.60 ; 6105 formulas have been input or derived (from 165 formulas).
% 1.37/1.60 ; 1832 (30%) were retained. Of these,
% 1.37/1.60 ; 1685 (92%) were simplified or subsumed later,
% 1.37/1.60 ; 147 ( 8%) are still being kept.
% 1.37/1.60 ;
% 1.37/1.60 ; Run time in seconds excluding printing time:
% 1.37/1.60 ; 0.004 0% Read assertion file (1 call)
% 1.37/1.60 ; 0.001 0% Assert (25 calls)
% 1.37/1.60 ; 0.121 11% Process new row (5,661 calls)
% 1.37/1.60 ; 0.110 10% Resolution (328 calls)
% 1.37/1.60 ; 0.001 0% Paramodulation (164 calls)
% 1.37/1.60 ; 0.000 0% Factoring (124 calls)
% 1.37/1.60 ; 0.006 1% Condensing (3,971 calls)
% 1.37/1.60 ; 0.342 31% Forward subsumption (3,971 calls)
% 1.37/1.60 ; 0.172 15% Backward subsumption (1,791 calls)
% 1.37/1.60 ; 0.161 14% Clause clause subsumption (105,078 calls)
% 1.37/1.60 ; 0.090 8% Forward simplification (4,575 calls)
% 1.37/1.60 ; 0.043 4% Backward simplification (1,832 calls)
% 1.37/1.60 ; 0.017 2% Ordering (12,158 calls)
% 1.37/1.60 ; 0.001 0% Sortal reasoning (32 calls)
% 1.37/1.60 ; 0.000 0% Purity testing (1 call)
% 1.37/1.60 ; 0.044 4% Other
% 1.37/1.60 ; 1.113 Total
% 1.37/1.60 ; 1.121 Real time
% 1.37/1.60 ;
% 1.37/1.60 ; Term-hash-array has 109 terms in all.
% 1.37/1.60 ; Feature-vector-row-index has 106 entries (691 at peak, 1,791 added, 1,685 deleted).
% 1.37/1.60 ; Feature-vector-row-index has 370 nodes (1,051 at peak, 2,489 added, 2,119 deleted).
% 1.37/1.60 ; Retrieved 92,844 possibly forward subsuming rows in 3,971 calls.
% 1.37/1.60 ; Retrieved 45,530 possibly backward subsumed rows in 1,791 calls.
% 1.37/1.60 ; Path-index has 111 entries (113 at peak, 114 added, 3 deleted).
% 1.37/1.60 ; Path-index has 43 nodes (43 at peak, 43 added, 0 deleted).
% 1.37/1.60 ; Trie-index has 111 entries (113 at peak, 114 added, 3 deleted).
% 1.37/1.60 ; Trie-index has 140 nodes (142 at peak, 143 added, 3 deleted).
% 1.37/1.60 ; Retrieved 1,901 generalization terms in 15,943 calls.
% 1.37/1.60 ; Retrieved 40 instance terms in 40 calls.
% 1.37/1.60 ; Retrieved 25,528 unifiable terms in 2,872 calls.
% 1.37/1.60 ;
% 1.37/1.60 ; The agenda of rows to process has 41 entries:
% 1.37/1.60 ; 17 with value 15 2 with value 20 8 with value 25
% 1.37/1.60 ; 4 with value 19 8 with value 24 2 with value 30
% 1.37/1.60 ; The agenda of rows to give has 93 entries:
% 1.37/1.60 ; 1 with value (4 8) 1 with value (4 18) 7 with value (4 26)
% 1.37/1.60 ; 1 with value (4 11) 6 with value (4 19) 14 with value (4 27)
% 1.37/1.60 ; 2 with value (4 12) 1 with value (4 21) 9 with value (4 29)
% 1.37/1.60 ; 3 with value (4 14) 10 with value (4 22) 6 with value (4 30)
% 1.37/1.60 ; 6 with value (4 15) 5 with value (4 23) 3 with value (4 31)
% 1.37/1.60 ; 1 with value (4 16) 1 with value (4 24) 2 with value (4 32)
% 1.37/1.60 ; 2 with value (4 17) 12 with value (4 25)
% 1.37/1.60 Evaluation took:
% 1.37/1.60 1.122 seconds of real time
% 1.37/1.60 0.930566 seconds of user run time
% 1.37/1.60 0.191076 seconds of system run time
% 1.37/1.60 [Run times include 0.046 seconds GC run time.]
% 1.37/1.60 0 calls to %EVAL
% 1.37/1.60 0 page faults and
% 1.37/1.60 129,697,168 bytes consed.
% 1.37/1.60 :PROOF-FOUND
% 1.37/1.60 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T06:40:24
% 1.37/1.60 :PROOF-FOUND
% 1.37/1.60 *
%------------------------------------------------------------------------------