TSTP Solution File: GRP039-6 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP039-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n012.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 11:35:25 EDT 2022
% Result : Unsatisfiable 1.52s 1.74s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of clauses : 24 ( 13 unt; 5 nHn; 19 RR)
% Number of literals : 45 ( 0 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subgroup_member_substitution,axiom,
( ~ equalish(X,Y)
| ~ subgroup_member(X)
| subgroup_member(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgroup_member_substitution) ).
cnf(closure_of_inverse,axiom,
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).
cnf(closure_of_product,axiom,
( ~ subgroup_member(X)
| ~ subgroup_member(Y)
| ~ product(X,Y,Z)
| subgroup_member(Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product) ).
cnf(left_identity,axiom,
product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
cnf(right_identity,axiom,
product(X,identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(associativity1,axiom,
( ~ product(X,Y,Z)
| ~ product(Y,U,V)
| ~ product(Z,U,W)
| product(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
cnf(associativity2,axiom,
( ~ product(X,Y,Z)
| ~ product(Y,U,V)
| ~ product(X,V,W)
| product(Z,U,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
cnf(product_right_cancellation,axiom,
( ~ product(X,Y,Z)
| ~ product(X,U,Z)
| equalish(U,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(element_in_O2(X,Y))
| subgroup_member(Y)
| subgroup_member(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(property_of_O2,axiom,
( product(X,element_in_O2(X,Y),Y)
| subgroup_member(Y)
| subgroup_member(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
cnf(b_is_in_subgroup,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(a_times_c_is_d,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(prove_d_is_in_subgroup,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
cnf(48,plain,
( subgroup_member(a)
| equalish(element_in_O2(a,d),c) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,property_of_O2,a_times_c_is_d]),prove_d_is_in_subgroup]) ).
cnf(61,plain,
product(c,a,b),
inference('HYPERRESOLVE',[status(thm)],[associativity2,b_times_a_inverse_is_c,left_inverse,right_identity]) ).
cnf(123,plain,
product(inverse(c),b,a),
inference('HYPERRESOLVE',[status(thm)],[associativity1,61,left_inverse,left_identity]) ).
cnf(1582,plain,
( subgroup_member(a)
| subgroup_member(c) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[subgroup_member_substitution,48,an_element_in_O2]),prove_d_is_in_subgroup]) ).
cnf(1591,plain,
( subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference('HYPERRESOLVE',[status(thm)],[closure_of_inverse,1582]) ).
cnf(2590,plain,
subgroup_member(a),
inference('HYPERRESOLVE',[status(thm)],[closure_of_product,1591,b_is_in_subgroup,123]) ).
cnf(2591,plain,
~ subgroup_member(c),
inference('UR-RESOLVE',[status(thm)],[closure_of_product,2590,a_times_c_is_d,prove_d_is_in_subgroup]) ).
cnf(2619,plain,
subgroup_member(inverse(a)),
inference('HYPERRESOLVE',[status(thm)],[closure_of_inverse,2590]) ).
cnf(2694,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[closure_of_product,2591,b_is_in_subgroup,b_times_a_inverse_is_c]),2619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP039-6 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 07:51:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.47 #<PACKAGE "SNARK-USER">
% 0.19/0.47 *
% 0.19/0.47 SNARK-TPTP-OPTIONS
% 0.19/0.47 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (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 2022-06-14T07:51:55
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n012.cluster.edu at 2022-06-14T07:51:55
% 0.19/0.48
% 0.19/0.48 ; Recognized possible left identity assertion (|product| |identity| ?X ?X).
% 0.19/0.48 ; Recognized possible right identity assertion (|product| ?X |identity| ?X).
% 0.19/0.48 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |identity|).
% 0.19/0.48 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |identity|).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 1.52/1.74 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 1.52/1.74
% 1.52/1.74 #||
% 1.52/1.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.52/1.74 % SZS output start Refutation
% See solution above
% 1.52/1.74 ||#
% 1.52/1.74
% 1.52/1.74 ; Summary of computation:
% 1.52/1.74 ; 42139 formulas have been input or derived (from 272 formulas).
% 1.52/1.74 ; 2694 ( 6%) were retained. Of these,
% 1.52/1.74 ; 275 (10%) were simplified or subsumed later,
% 1.52/1.74 ; 2419 (90%) are still being kept.
% 1.52/1.74 ;
% 1.52/1.74 ; Run time in seconds excluding printing time:
% 1.52/1.74 ; 0.004 0% Read assertion file (1 call)
% 1.52/1.74 ; 0.001 0% Assert (22 calls)
% 1.52/1.74 ; 0.194 15% Process new row (33,574 calls)
% 1.52/1.74 ; 0.721 57% Resolution (542 calls)
% 1.52/1.74 ; 0.003 0% Paramodulation (271 calls)
% 1.52/1.74 ; 0.000 0% Factoring (10 calls)
% 1.52/1.74 ; 0.004 0% Condensing (476 calls)
% 1.52/1.74 ; 0.011 1% Forward subsumption (476 calls)
% 1.52/1.74 ; 0.005 0% Backward subsumption (262 calls)
% 1.52/1.74 ; 0.007 1% Clause clause subsumption (2,431 calls)
% 1.52/1.74 ; 0.179 14% Forward simplification (33,039 calls)
% 1.52/1.74 ; 0.020 2% Backward simplification (2,694 calls)
% 1.52/1.74 ; 0.001 0% Ordering (665 calls)
% 1.52/1.74 ; 0.000 0% Sortal reasoning (32 calls)
% 1.52/1.74 ; 0.000 0% Purity testing (1 call)
% 1.52/1.74 ; 0.123 10% Other
% 1.52/1.74 ; 1.273 Total
% 1.52/1.74 ; 1.274 Real time
% 1.52/1.74 ;
% 1.52/1.74 ; Term-hash-array has 2,811 terms in all.
% 1.52/1.74 ; Feature-vector-row-index has 104 entries (226 at peak, 262 added, 158 deleted).
% 1.52/1.74 ; Feature-vector-row-index has 238 nodes (778 at peak, 947 added, 709 deleted).
% 1.52/1.74 ; Retrieved 3,303 possibly forward subsuming rows in 476 calls.
% 1.52/1.74 ; Retrieved 470 possibly backward subsumed rows in 262 calls.
% 1.52/1.74 ; Path-index has 2,534 entries (2,614 at peak, 2,862 added, 328 deleted).
% 1.52/1.74 ; Path-index has 617 nodes (671 at peak, 713 added, 96 deleted).
% 1.52/1.74 ; Trie-index has 2,534 entries (2,614 at peak, 2,862 added, 328 deleted).
% 1.52/1.74 ; Trie-index has 5,349 nodes (5,699 at peak, 6,152 added, 803 deleted).
% 1.52/1.74 ; Retrieved 47,061 generalization terms in 36,201 calls.
% 1.52/1.74 ; Retrieved 3,652 instance terms in 2,431 calls.
% 1.52/1.74 ; Retrieved 798,029 unifiable terms in 32,531 calls.
% 1.52/1.74 ;
% 1.52/1.74 ; The agenda of rows to process has 148 entries:
% 1.52/1.74 ; 6 with value 11 17 with value 15 14 with value 18
% 1.52/1.74 ; 7 with value 12 19 with value 16 13 with value 19
% 1.52/1.74 ; 17 with value 13 26 with value 17 10 with value 20
% 1.52/1.74 ; 19 with value 14
% 1.52/1.74 ; The agenda of rows to give has 2156 entries:
% 1.52/1.74 ; 2 with value (4 9) 325 with value (4 17) 3 with value (4 24)
% 1.52/1.74 ; 10 with value (4 10) 382 with value (4 18) 2 with value (4 25)
% 1.52/1.74 ; 18 with value (4 11) 78 with value (4 19) 9 with value (4 26)
% 1.52/1.74 ; 147 with value (4 12) 28 with value (4 20) 5 with value (4 27)
% 1.52/1.74 ; 192 with value (4 13) 3 with value (4 21) 4 with value (4 28)
% 1.52/1.74 ; 267 with value (4 14) 2 with value (4 22) 2 with value (4 29)
% 1.52/1.74 ; 320 with value (4 15) 8 with value (4 23) 1 with value (4 30)
% 1.52/1.74 ; 348 with value (4 16)
% 1.52/1.74 Evaluation took:
% 1.52/1.74 1.275 seconds of real time
% 1.52/1.74 1.159675 seconds of user run time
% 1.52/1.74 0.115111 seconds of system run time
% 1.52/1.74 [Run times include 0.065 seconds GC run time.]
% 1.52/1.74 0 calls to %EVAL
% 1.52/1.74 0 page faults and
% 1.52/1.74 77,180,504 bytes consed.
% 1.52/1.74 :PROOF-FOUND
% 1.52/1.74 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T07:51:56
% 1.52/1.74 :PROOF-FOUND
% 1.52/1.74 *
%------------------------------------------------------------------------------