TSTP Solution File: GRP040-4 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n026.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 11:35:26 EDT 2022
% Result : Unsatisfiable 0.42s 0.62s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 16
% Syntax : Number of clauses : 24 ( 17 unt; 2 nHn; 18 RR)
% Number of literals : 40 ( 3 equ; 14 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X,identity,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(closure_of_product_and_inverse,axiom,
( ~ subgroup_member(X)
| ~ subgroup_member(Y)
| ~ product(X,inverse(Y),Z)
| subgroup_member(Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
cnf(closure_of_inverse,axiom,
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).
cnf(product_right_cancellation,axiom,
( ~ product(X,Y,Z)
| ~ product(X,U,Z)
| U = Y ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
cnf(a_in_subgroup,hypothesis,
~ subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_in_subgroup) ).
cnf(b_is_in_subgroup,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(d_in_subgroup,hypothesis,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_in_subgroup) ).
cnf(b_times_a_inverse_is_c,hypothesis,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(a_times_c_is_d,hypothesis,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(prove_inverse_is_self_cancelling,negated_conjecture,
inverse(inverse(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
cnf(22,plain,
subgroup_member(inverse(b)),
inference('HYPERRESOLVE',[status(thm)],[closure_of_inverse,b_is_in_subgroup]) ).
cnf(25,plain,
subgroup_member(element_in_O2(a,d)),
inference('UR-RESOLVE',[status(thm)],[an_element_in_O2,d_in_subgroup,a_in_subgroup]) ).
cnf(44,plain,
c = element_in_O2(a,d),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,property_of_O2,a_times_c_is_d]),a_in_subgroup,d_in_subgroup]) ).
cnf(45,plain,
subgroup_member(c),
inference('REWRITE',[status(thm)],[25,44,theory(equality)]) ).
cnf(112,plain,
product(c,a,b),
inference('HYPERRESOLVE',[status(thm)],[associativity2,b_times_a_inverse_is_c,left_inverse,right_identity]) ).
cnf(147,plain,
subgroup_member(inverse(c)),
inference('HYPERRESOLVE',[status(thm)],[closure_of_inverse,45]) ).
cnf(216,plain,
product(inverse(c),b,a),
inference('HYPERRESOLVE',[status(thm)],[associativity1,112,left_inverse,left_identity]) ).
cnf(350,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[closure_of_product_and_inverse,147,22,a_in_subgroup]),216,prove_inverse_is_self_cancelling,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.13 % Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.14 % Command : run-snark %s %d
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 23:15:51 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.48 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.49 *
% 0.21/0.49 *
% 0.21/0.49 #<PACKAGE "SNARK-USER">
% 0.21/0.49 *
% 0.21/0.49 SNARK-TPTP-OPTIONS
% 0.21/0.49 *
% 0.21/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.49 (USE-FACTORING :POS)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.49 *
% 0.21/0.49 "."
% 0.21/0.49 *
% 0.21/0.49 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T23:15:51
% 0.21/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-06-13T23:15:51
% 0.21/0.51
% 0.21/0.51 ; Recognized possible left identity assertion (|product| |identity| ?X ?X).
% 0.21/0.51 ; Recognized possible right identity assertion (|product| ?X |identity| ?X).
% 0.21/0.51 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |identity|).
% 0.21/0.51 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |identity|).
% 0.21/0.51 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.21/0.51 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.21/0.51 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 0.42/0.62 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 0.42/0.62
% 0.42/0.62 #||
% 0.42/0.62 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.62 % SZS output start Refutation
% See solution above
% 0.42/0.63 ||#
% 0.42/0.63
% 0.42/0.63 ; Summary of computation:
% 0.42/0.63 ; 1547 formulas have been input or derived (from 36 formulas).
% 0.42/0.63 ; 350 (23%) were retained. Of these,
% 0.42/0.63 ; 10 ( 3%) were simplified or subsumed later,
% 0.42/0.63 ; 340 (97%) are still being kept.
% 0.42/0.63 ;
% 0.42/0.63 ; Run time in seconds excluding printing time:
% 0.42/0.63 ; 0.004 3% Read assertion file (1 call)
% 0.42/0.63 ; 0.001 1% Assert (21 calls)
% 0.42/0.63 ; 0.026 20% Process new row (1,319 calls)
% 0.42/0.63 ; 0.030 23% Resolution (70 calls)
% 0.42/0.63 ; 0.000 0% Paramodulation (35 calls)
% 0.42/0.63 ; 0.000 0% Factoring (4 calls)
% 0.42/0.63 ; 0.003 2% Condensing (169 calls)
% 0.42/0.63 ; 0.005 4% Forward subsumption (169 calls)
% 0.42/0.63 ; 0.002 2% Backward subsumption (96 calls)
% 0.42/0.63 ; 0.002 2% Clause clause subsumption (305 calls)
% 0.42/0.63 ; 0.023 18% Forward simplification (1,319 calls)
% 0.42/0.63 ; 0.001 1% Backward simplification (350 calls)
% 0.42/0.63 ; 0.001 1% Ordering (396 calls)
% 0.42/0.63 ; 0.000 0% Sortal reasoning (32 calls)
% 0.42/0.63 ; 0.000 0% Purity testing (1 call)
% 0.42/0.63 ; 0.032 25% Other
% 0.42/0.63 ; 0.130 Total
% 0.42/0.63 ; 0.132 Real time
% 0.42/0.63 ;
% 0.42/0.63 ; Term-hash-array has 544 terms in all.
% 0.42/0.63 ; Feature-vector-row-index has 96 entries (96 at peak, 96 added, 0 deleted).
% 0.42/0.63 ; Feature-vector-row-index has 424 nodes (424 at peak, 424 added, 0 deleted).
% 0.42/0.63 ; Retrieved 469 possibly forward subsuming rows in 169 calls.
% 0.42/0.63 ; Retrieved 53 possibly backward subsumed rows in 96 calls.
% 0.42/0.63 ; Path-index has 539 entries (539 at peak, 549 added, 10 deleted).
% 0.42/0.63 ; Path-index has 484 nodes (484 at peak, 486 added, 2 deleted).
% 0.42/0.63 ; Trie-index has 539 entries (539 at peak, 549 added, 10 deleted).
% 0.42/0.63 ; Trie-index has 1,121 nodes (1,121 at peak, 1,137 added, 16 deleted).
% 0.42/0.63 ; Retrieved 2,142 generalization terms in 4,057 calls.
% 0.42/0.63 ; Retrieved 283 instance terms in 253 calls.
% 0.42/0.63 ; Retrieved 18,716 unifiable terms in 1,854 calls.
% 0.42/0.63 ;
% 0.42/0.63 ; The agenda of rows to process has 43 entries:
% 0.42/0.63 ; 7 with value 13 12 with value 15 2 with value 21
% 0.42/0.63 ; 20 with value 14 2 with value 18
% 0.42/0.63 ; The agenda of rows to give has 304 entries:
% 0.42/0.63 ; 20 with value (4 7) 26 with value (4 14) 13 with value (4 21)
% 0.42/0.63 ; 16 with value (4 8) 17 with value (4 15) 2 with value (4 22)
% 0.42/0.63 ; 29 with value (4 9) 5 with value (4 16) 3 with value (4 23)
% 0.42/0.63 ; 35 with value (4 10) 11 with value (4 17) 1 with value (4 24)
% 0.42/0.63 ; 32 with value (4 11) 14 with value (4 18) 1 with value (4 25)
% 0.42/0.63 ; 43 with value (4 12) 6 with value (4 19) 1 with value (4 26)
% 0.42/0.63 ; 21 with value (4 13) 8 with value (4 20)
% 0.42/0.63 Evaluation took:
% 0.42/0.63 0.132 seconds of real time
% 0.42/0.63 0.11927 seconds of user run time
% 0.42/0.63 0.013138 seconds of system run time
% 0.42/0.63 0 calls to %EVAL
% 0.42/0.63 0 page faults and
% 0.42/0.63 7,608,552 bytes consed.
% 0.42/0.63 :PROOF-FOUND
% 0.42/0.63 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T23:15:51
% 0.42/0.63 :PROOF-FOUND
% 0.42/0.63 *
%------------------------------------------------------------------------------