TSTP Solution File: GRP079-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP079-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n013.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 11:36:03 EDT 2022
% Result : Unsatisfiable 0.19s 0.54s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of clauses : 38 ( 35 unt; 0 nHn; 8 RR)
% Number of literals : 43 ( 42 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(identity,X),double_divide(double_divide(double_divide(Y,Z),double_divide(identity,identity)),double_divide(X,Z))) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X,Y) = double_divide(double_divide(Y,X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(X) = double_divide(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(identity,axiom,
identity = double_divide(X,inverse(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(6,plain,
multiply(X,Y) = inverse(double_divide(Y,X)),
inference('REWRITE',[status(thm)],[multiply,inverse,theory(equality)]) ).
cnf(7,plain,
( inverse(identity) != identity
| inverse(inverse(a2)) != a2
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)) ),
inference('REWRITE',[status(thm)],[prove_these_axioms,inverse,identity,6,theory(equality)]) ).
cnf(8,plain,
double_divide(double_divide(identity,X),double_divide(double_divide(double_divide(Y,Z),inverse(identity)),double_divide(X,Z))) = Y,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(12,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(X,inverse(Y)))) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),identity,theory(equality)]) ).
cnf(16,plain,
double_divide(double_divide(identity,X),inverse(identity)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(18,plain,
double_divide(identity,double_divide(identity,double_divide(inverse(identity),inverse(X)))) = X,
inference('PARAMODULATE',[status(thm)],[12,identity,theory(equality)]) ).
cnf(19,plain,
double_divide(double_divide(identity,X),double_divide(double_divide(Y,inverse(identity)),double_divide(X,double_divide(identity,double_divide(Z,inverse(Y)))))) = double_divide(identity,Z),
inference('PARAMODULATE',[status(thm)],[8,12,theory(equality)]) ).
cnf(22,plain,
inverse(identity) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,identity,theory(equality)]),identity,theory(equality)]) ).
cnf(23,plain,
( inverse(inverse(a2)) != a2
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)) ),
inference('REWRITE',[status(thm)],[7,22,theory(equality)]) ).
cnf(24,plain,
double_divide(double_divide(identity,X),double_divide(inverse(double_divide(Y,Z)),double_divide(X,Z))) = Y,
inference('REWRITE',[status(thm)],[8,inverse,22,theory(equality)]) ).
cnf(30,plain,
inverse(double_divide(identity,X)) = X,
inference('REWRITE',[status(thm)],[16,inverse,22,theory(equality)]) ).
cnf(31,plain,
double_divide(identity,double_divide(identity,double_divide(identity,inverse(X)))) = X,
inference('REWRITE',[status(thm)],[18,22,theory(equality)]) ).
cnf(32,plain,
double_divide(double_divide(identity,X),double_divide(inverse(Y),double_divide(X,double_divide(identity,double_divide(Z,inverse(Y)))))) = double_divide(identity,Z),
inference('REWRITE',[status(thm)],[19,inverse,22,theory(equality)]) ).
cnf(35,plain,
identity = double_divide(double_divide(identity,X),X),
inference('PARAMODULATE',[status(thm)],[identity,30,theory(equality)]) ).
cnf(37,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(X,Y))) = double_divide(identity,Y),
inference('PARAMODULATE',[status(thm)],[12,30,theory(equality)]) ).
cnf(38,plain,
double_divide(identity,inverse(X)) = X,
inference('REWRITE',[status(thm)],[12,37,theory(equality)]) ).
cnf(39,plain,
double_divide(identity,double_divide(identity,X)) = X,
inference('REWRITE',[status(thm)],[31,38,theory(equality)]) ).
cnf(44,plain,
inverse(X) = double_divide(identity,X),
inference('PARAMODULATE',[status(thm)],[30,39,theory(equality)]) ).
cnf(47,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[38,44,theory(equality)]) ).
cnf(48,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[23,47,theory(equality)]) ).
cnf(50,plain,
double_divide(inverse(X),double_divide(inverse(double_divide(Y,Z)),double_divide(X,Z))) = Y,
inference('REWRITE',[status(thm)],[24,44,theory(equality)]) ).
cnf(53,plain,
double_divide(inverse(X),double_divide(inverse(Y),double_divide(X,inverse(double_divide(Z,inverse(Y)))))) = inverse(Z),
inference('REWRITE',[status(thm)],[32,44,theory(equality)]) ).
cnf(54,plain,
identity = double_divide(inverse(X),X),
inference('REWRITE',[status(thm)],[35,44,theory(equality)]) ).
cnf(57,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[50,54,theory(equality)]),inverse,47,theory(equality)]) ).
cnf(58,plain,
double_divide(double_divide(X,Y),X) = Y,
inference('PARAMODULATE',[status(thm)],[57,57,theory(equality)]) ).
cnf(62,plain,
double_divide(inverse(X),double_divide(inverse(Y),double_divide(X,Z))) = double_divide(Z,Y),
inference('PARAMODULATE',[status(thm)],[50,58,theory(equality)]) ).
cnf(63,plain,
double_divide(inverse(double_divide(X,inverse(Y))),Y) = inverse(X),
inference('REWRITE',[status(thm)],[53,62,theory(equality)]) ).
cnf(66,plain,
double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
inference('PARAMODULATE',[status(thm)],[57,63,theory(equality)]) ).
cnf(67,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[48,66,theory(equality)]) ).
cnf(68,plain,
double_divide(inverse(X),Y) = inverse(double_divide(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[63,58,theory(equality)]) ).
cnf(72,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
inference('REWRITE',[status(thm)],[67,68,theory(equality)]) ).
cnf(93,plain,
double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(Y),double_divide(Z,X)),
inference('PARAMODULATE',[status(thm)],[58,62,theory(equality)]) ).
cnf(94,plain,
$false,
inference('REWRITE',[status(thm)],[72,93,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP079-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.03/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n013.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 12:30:44 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 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 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 2022-06-13T12:30:44
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n013.cluster.edu at 2022-06-13T12:30:44
% 0.19/0.48
% 0.19/0.54 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.19/0.54
% 0.19/0.54 #||
% 0.19/0.54 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.54 % SZS output start Refutation
% See solution above
% 0.19/0.54 ||#
% 0.19/0.54
% 0.19/0.54 ; Summary of computation:
% 0.19/0.54 ; 423 formulas have been input or derived (from 33 formulas).
% 0.19/0.54 ; 94 (22%) were retained. Of these,
% 0.19/0.54 ; 59 (63%) were simplified or subsumed later,
% 0.19/0.54 ; 35 (37%) are still being kept.
% 0.19/0.54 ;
% 0.19/0.54 ; Run time in seconds excluding printing time:
% 0.19/0.54 ; 0.002 3% Read assertion file (1 call)
% 0.19/0.54 ; 0.000 0% Assert (5 calls)
% 0.19/0.54 ; 0.024 33% Process new row (390 calls)
% 0.19/0.54 ; 0.002 3% Resolution (64 calls)
% 0.19/0.54 ; 0.008 11% Paramodulation (32 calls)
% 0.19/0.54 ; 0.000 0% Condensing (3 calls)
% 0.19/0.54 ; 0.000 0% Forward subsumption (3 calls)
% 0.19/0.54 ; 0.000 0% Backward subsumption (3 calls)
% 0.19/0.54 ; 0.005 7% Forward simplification (317 calls)
% 0.19/0.54 ; 0.005 7% Backward simplification (94 calls)
% 0.19/0.54 ; 0.006 8% Ordering (1,037 calls)
% 0.19/0.54 ; 0.000 0% Sortal reasoning (32 calls)
% 0.19/0.54 ; 0.000 0% Purity testing (1 call)
% 0.19/0.54 ; 0.020 28% Other
% 0.19/0.54 ; 0.072 Total
% 0.19/0.54 ; 0.078 Real time
% 0.19/0.54 ;
% 0.19/0.54 ; Term-hash-array has 328 terms in all.
% 0.19/0.54 ; Feature-vector-row-index has 0 entries (1 at peak, 3 added, 3 deleted).
% 0.19/0.54 ; Feature-vector-row-index has 1 node (26 at peak, 69 added, 68 deleted).
% 0.19/0.54 ; Retrieved 0 possibly forward subsuming rows in 3 calls.
% 0.19/0.54 ; Retrieved 0 possibly backward subsumed rows in 3 calls.
% 0.19/0.54 ; Path-index has 111 entries (138 at peak, 446 added, 335 deleted).
% 0.19/0.54 ; Path-index has 530 nodes (583 at peak, 1,005 added, 475 deleted).
% 0.19/0.54 ; Trie-index has 111 entries (138 at peak, 446 added, 335 deleted).
% 0.19/0.54 ; Trie-index has 472 nodes (588 at peak, 1,730 added, 1,258 deleted).
% 0.19/0.54 ; Retrieved 1,060 generalization terms in 1,804 calls.
% 0.19/0.54 ; Retrieved 261 instance terms in 112 calls.
% 0.19/0.54 ; Retrieved 898 unifiable terms in 255 calls.
% 0.19/0.54 ;
% 0.19/0.54 ; The agenda of backward simplifiable rows to process has 1 entry:
% 0.19/0.54 ; 1 with value 0
% 0.19/0.54 ; The agenda of rows to process has 27 entries:
% 0.19/0.54 ; 6 with value 23 1 with value 26 5 with value 29
% 0.19/0.54 ; 5 with value 24 2 with value 27 4 with value 30
% 0.19/0.54 ; 1 with value 25 1 with value 28 2 with value 31
% 0.19/0.54 ; The agenda of rows to give has 19 entries:
% 0.19/0.54 ; 2 with value (4 23) 3 with value (4 26) 4 with value (4 28)
% 0.19/0.54 ; 1 with value (4 24) 5 with value (4 27) 4 with value (4 29)
% 0.19/0.54 Evaluation took:
% 0.19/0.54 0.078 seconds of real time
% 0.19/0.54 0.069189 seconds of user run time
% 0.19/0.54 0.009185 seconds of system run time
% 0.19/0.54 0 calls to %EVAL
% 0.19/0.54 0 page faults and
% 0.19/0.54 6,674,632 bytes consed.
% 0.19/0.54 :PROOF-FOUND
% 0.19/0.54 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T12:30:44
% 0.19/0.55 :PROOF-FOUND
% 0.19/0.55 *
%------------------------------------------------------------------------------