TSTP Solution File: GRP039-4 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP039-4 : 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 7.71s 7.91s
% Output : Refutation 7.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of clauses : 24 ( 15 unt; 5 nHn; 19 RR)
% Number of literals : 41 ( 0 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X,identity,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',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/Axioms/GRP003-0.ax',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/Axioms/GRP003-0.ax',associativity2) ).
cnf(closure_of_inverse,axiom,
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-1.ax',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/Axioms/GRP003-1.ax',closure_of_product) ).
cnf(identity_is_in_subgroup,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_in_subgroup) ).
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,
product(inverse(a),d,c),
inference('HYPERRESOLVE',[status(thm)],[associativity1,left_inverse,a_times_c_is_d,left_identity]) ).
cnf(101,plain,
product(c,a,b),
inference('HYPERRESOLVE',[status(thm)],[associativity2,b_times_a_inverse_is_c,left_inverse,right_identity]) ).
cnf(188,plain,
product(inverse(c),b,a),
inference('HYPERRESOLVE',[status(thm)],[associativity1,101,left_inverse,left_identity]) ).
cnf(286,plain,
( subgroup_member(a)
| product(identity,element_in_O2(a,d),c) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[associativity2,48,left_inverse,property_of_O2]),prove_d_is_in_subgroup]) ).
cnf(19351,plain,
( subgroup_member(a)
| subgroup_member(c) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[closure_of_product,286,identity_is_in_subgroup,an_element_in_O2]),prove_d_is_in_subgroup]) ).
cnf(19386,plain,
( subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference('HYPERRESOLVE',[status(thm)],[closure_of_inverse,19351]) ).
cnf(19428,plain,
subgroup_member(a),
inference('HYPERRESOLVE',[status(thm)],[closure_of_product,19386,b_is_in_subgroup,188]) ).
cnf(19429,plain,
~ subgroup_member(c),
inference('UR-RESOLVE',[status(thm)],[closure_of_product,19428,a_times_c_is_d,prove_d_is_in_subgroup]) ).
cnf(19490,plain,
subgroup_member(inverse(a)),
inference('HYPERRESOLVE',[status(thm)],[closure_of_inverse,19428]) ).
cnf(19845,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[closure_of_product,19429,b_is_in_subgroup,b_times_a_inverse_is_c]),19490]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP039-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % 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 : Mon Jun 13 19:19:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.46 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 *
% 0.19/0.47 *
% 0.19/0.48 #<PACKAGE "SNARK-USER">
% 0.19/0.48 *
% 0.19/0.48 SNARK-TPTP-OPTIONS
% 0.19/0.48 *
% 0.19/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.48 (USE-FACTORING :POS)
% 0.19/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.48 *
% 0.19/0.48 "."
% 0.19/0.48 *
% 0.19/0.48 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T19:19:10
% 0.19/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n012.cluster.edu at 2022-06-13T19:19:10
% 0.19/0.50
% 0.19/0.50 ; Recognized possible left identity assertion (|product| |identity| ?X ?X).
% 0.19/0.50 ; Recognized possible right identity assertion (|product| ?X |identity| ?X).
% 0.19/0.50 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |identity|).
% 0.19/0.50 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |identity|).
% 0.19/0.50 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.19/0.50 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.50 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 7.71/7.91 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 7.71/7.91
% 7.71/7.91 #||
% 7.71/7.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.71/7.91 % SZS output start Refutation
% See solution above
% 7.73/7.91 ||#
% 7.73/7.91
% 7.73/7.91 ; Summary of computation:
% 7.73/7.91 ; 76411 formulas have been input or derived (from 467 formulas).
% 7.73/7.91 ; 19845 (26%) were retained. Of these,
% 7.73/7.91 ; 1427 ( 7%) were simplified or subsumed later,
% 7.73/7.91 ; 18418 (93%) are still being kept.
% 7.73/7.91 ;
% 7.73/7.91 ; Run time in seconds excluding printing time:
% 7.73/7.91 ; 0.004 0% Read assertion file (1 call)
% 7.73/7.91 ; 0.001 0% Assert (17 calls)
% 7.73/7.91 ; 1.200 16% Process new row (73,439 calls)
% 7.73/7.91 ; 4.393 59% Resolution (932 calls)
% 7.73/7.91 ; 0.019 0% Paramodulation (466 calls)
% 7.73/7.91 ; 0.000 0% Factoring (13 calls)
% 7.73/7.91 ; 0.015 0% Condensing (1,509 calls)
% 7.73/7.91 ; 0.093 1% Forward subsumption (1,509 calls)
% 7.73/7.91 ; 0.024 0% Backward subsumption (935 calls)
% 7.73/7.91 ; 0.022 0% Clause clause subsumption (8,255 calls)
% 7.73/7.91 ; 1.070 14% Forward simplification (70,907 calls)
% 7.73/7.91 ; 0.327 4% Backward simplification (19,845 calls)
% 7.73/7.91 ; 0.005 0% Ordering (3,754 calls)
% 7.73/7.91 ; 0.000 0% Sortal reasoning (32 calls)
% 7.73/7.91 ; 0.000 0% Purity testing (1 call)
% 7.73/7.91 ; 0.251 3% Other
% 7.73/7.91 ; 7.424 Total
% 7.73/7.91 ; 7.425 Real time
% 7.73/7.91 ;
% 7.73/7.91 ; Term-hash-array has 24,863 terms in all.
% 7.73/7.91 ; Feature-vector-row-index has 505 entries (817 at peak, 935 added, 430 deleted).
% 7.73/7.91 ; Feature-vector-row-index has 2,138 nodes (4,281 at peak, 4,928 added, 2,790 deleted).
% 7.73/7.91 ; Retrieved 10,185 possibly forward subsuming rows in 1,509 calls.
% 7.73/7.91 ; Retrieved 1,777 possibly backward subsumed rows in 935 calls.
% 7.73/7.91 ; Path-index has 23,123 entries (23,283 at peak, 24,980 added, 1,857 deleted).
% 7.73/7.91 ; Path-index has 3,394 nodes (3,574 at peak, 3,856 added, 462 deleted).
% 7.73/7.91 ; Trie-index has 23,123 entries (23,283 at peak, 24,980 added, 1,857 deleted).
% 7.73/7.91 ; Trie-index has 66,101 nodes (66,970 at peak, 71,506 added, 5,405 deleted).
% 7.73/7.91 ; Retrieved 211,059 generalization terms in 315,165 calls.
% 7.73/7.91 ; Retrieved 25,546 instance terms in 18,909 calls.
% 7.73/7.91 ; Retrieved 3,358,681 unifiable terms in 50,482 calls.
% 7.73/7.91 ;
% 7.73/7.91 ; The agenda of rows to process has 278 entries:
% 7.73/7.91 ; 6 with value 12 9 with value 17 51 with value 22
% 7.73/7.91 ; 7 with value 13 50 with value 18 8 with value 23
% 7.73/7.91 ; 7 with value 14 28 with value 19 14 with value 24
% 7.73/7.91 ; 18 with value 15 27 with value 20 12 with value 25
% 7.73/7.91 ; 10 with value 16 30 with value 21 1 with value 26
% 7.73/7.91 ; The agenda of rows to give has 17983 entries:
% 7.73/7.91 ; 6 with value (4 11) 2696 with value (4 21) 40 with value (4 30)
% 7.73/7.91 ; 6 with value (4 12) 1920 with value (4 22) 15 with value (4 31)
% 7.73/7.91 ; 390 with value (4 13) 729 with value (4 23) 15 with value (4 32)
% 7.73/7.91 ; 618 with value (4 14) 187 with value (4 24) 2 with value (4 33)
% 7.73/7.91 ; 1008 with value (4 15) 118 with value (4 25) 6 with value (4 34)
% 7.73/7.91 ; 1426 with value (4 16) 46 with value (4 26) 4 with value (4 35)
% 7.73/7.91 ; 1879 with value (4 17) 23 with value (4 27) 4 with value (4 36)
% 7.73/7.91 ; 2357 with value (4 18) 49 with value (4 28) 2 with value (4 37)
% 7.73/7.91 ; 2319 with value (4 19) 16 with value (4 29) 1 with value (4 38)
% 7.73/7.91 ; 2101 with value (4 20)
% 7.73/7.91 Evaluation took:
% 7.73/7.91 7.427 seconds of real time
% 7.73/7.91 7.081362 seconds of user run time
% 7.73/7.91 0.345907 seconds of system run time
% 7.73/7.91 [Run times include 0.641 seconds GC run time.]
% 7.73/7.91 0 calls to %EVAL
% 7.73/7.91 0 page faults and
% 7.73/7.91 322,484,432 bytes consed.
% 7.73/7.91 :PROOF-FOUND
% 7.73/7.91 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T19:19:18
% 7.73/7.91 :PROOF-FOUND
% 7.73/7.91 *
%------------------------------------------------------------------------------