TSTP Solution File: GRP076-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP076-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n018.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 11:36:02 EDT 2022
% Result : Unsatisfiable 0.13s 0.48s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of clauses : 44 ( 41 unt; 0 nHn; 8 RR)
% Number of literals : 49 ( 48 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 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 : 72 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),double_divide(Y,identity))),double_divide(identity,identity)) = Z,
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(X,double_divide(double_divide(double_divide(X,Y),Z),inverse(Y))),inverse(identity)) = Z,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(9,plain,
double_divide(double_divide(X,double_divide(identity,inverse(Y))),inverse(identity)) = inverse(double_divide(X,Y)),
inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]) ).
cnf(10,plain,
double_divide(double_divide(X,double_divide(double_divide(inverse(X),Y),inverse(identity))),inverse(identity)) = Y,
inference('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]) ).
cnf(16,plain,
double_divide(inverse(X),inverse(identity)) = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(17,plain,
double_divide(double_divide(X,inverse(double_divide(inverse(X),Y))),inverse(identity)) = double_divide(identity,inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,9,theory(equality)]),inverse,theory(equality)]) ).
cnf(21,plain,
double_divide(double_divide(X,inverse(inverse(inverse(X)))),inverse(identity)) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,inverse,theory(equality)]),16,theory(equality)]) ).
cnf(23,plain,
inverse(identity) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,16,theory(equality)]),21,16,theory(equality)]) ).
cnf(24,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)],[7,23,theory(equality)]) ).
cnf(25,plain,
inverse(double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),inverse(Y)))) = Z,
inference('REWRITE',[status(thm)],[8,inverse,23,theory(equality)]) ).
cnf(27,plain,
inverse(double_divide(X,inverse(double_divide(inverse(X),Y)))) = Y,
inference('REWRITE',[status(thm)],[10,inverse,23,theory(equality)]) ).
cnf(33,plain,
X = double_divide(identity,inverse(X)),
inference('REWRITE',[status(thm)],[17,27,inverse,23,theory(equality)]) ).
cnf(34,plain,
inverse(double_divide(X,inverse(inverse(inverse(X))))) = identity,
inference('REWRITE',[status(thm)],[21,inverse,23,theory(equality)]) ).
cnf(37,plain,
inverse(double_divide(X,double_divide(double_divide(double_divide(X,double_divide(Y,double_divide(double_divide(double_divide(Y,Z),U),inverse(Z)))),V),U))) = V,
inference('PARAMODULATE',[status(thm)],[25,25,theory(equality)]) ).
cnf(38,plain,
inverse(double_divide(identity,double_divide(double_divide(X,Y),inverse(inverse(X))))) = Y,
inference('PARAMODULATE',[status(thm)],[25,33,theory(equality)]) ).
cnf(39,plain,
double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),inverse(Y))) = double_divide(identity,Z),
inference('PARAMODULATE',[status(thm)],[33,25,theory(equality)]) ).
cnf(40,plain,
inverse(double_divide(X,double_divide(double_divide(double_divide(X,double_divide(identity,Y)),Z),Y))) = Z,
inference('REWRITE',[status(thm)],[37,39,theory(equality)]) ).
cnf(41,plain,
inverse(double_divide(identity,X)) = X,
inference('REWRITE',[status(thm)],[25,39,theory(equality)]) ).
cnf(42,plain,
double_divide(double_divide(X,Y),inverse(inverse(X))) = Y,
inference('REWRITE',[status(thm)],[38,41,theory(equality)]) ).
cnf(46,plain,
double_divide(X,inverse(inverse(double_divide(Y,X)))) = inverse(inverse(Y)),
inference('PARAMODULATE',[status(thm)],[42,42,theory(equality)]) ).
cnf(47,plain,
double_divide(X,inverse(double_divide(inverse(X),Y))) = double_divide(identity,Y),
inference('PARAMODULATE',[status(thm)],[33,27,theory(equality)]) ).
cnf(48,plain,
double_divide(X,inverse(inverse(inverse(X)))) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[33,34,theory(equality)]),23,inverse,theory(equality)]) ).
cnf(50,plain,
inverse(X) = inverse(inverse(inverse(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,48,theory(equality)]),33,theory(equality)]) ).
cnf(51,plain,
X = inverse(inverse(X)),
inference('PARAMODULATE',[status(thm)],[50,41,theory(equality)]) ).
cnf(52,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference('REWRITE',[status(thm)],[46,51,theory(equality)]) ).
cnf(53,plain,
double_divide(double_divide(X,Y),X) = Y,
inference('REWRITE',[status(thm)],[42,51,theory(equality)]) ).
cnf(54,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[24,51,theory(equality)]) ).
cnf(55,plain,
inverse(X) = double_divide(identity,X),
inference('PARAMODULATE',[status(thm)],[33,51,theory(equality)]) ).
cnf(59,plain,
inverse(double_divide(X,double_divide(double_divide(double_divide(X,inverse(Y)),Z),Y))) = Z,
inference('REWRITE',[status(thm)],[40,55,theory(equality)]) ).
cnf(60,plain,
double_divide(X,inverse(double_divide(inverse(X),Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[47,55,theory(equality)]) ).
cnf(65,plain,
double_divide(inverse(X),Y) = inverse(double_divide(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[53,60,theory(equality)]) ).
cnf(66,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(a3),double_divide(c3,b3)),
inference('REWRITE',[status(thm)],[54,65,theory(equality)]) ).
cnf(67,plain,
double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
inference('PARAMODULATE',[status(thm)],[60,52,theory(equality)]) ).
cnf(69,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
inference('REWRITE',[status(thm)],[66,67,theory(equality)]) ).
cnf(70,plain,
double_divide(inverse(X),inverse(Y)) = inverse(double_divide(Y,X)),
inference('PARAMODULATE',[status(thm)],[65,51,theory(equality)]) ).
cnf(89,plain,
inverse(double_divide(X,double_divide(Y,Z))) = double_divide(Y,double_divide(X,inverse(Z))),
inference('PARAMODULATE',[status(thm)],[59,52,theory(equality)]) ).
cnf(136,plain,
inverse(double_divide(X,inverse(double_divide(Y,Z)))) = double_divide(inverse(Z),double_divide(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[89,70,theory(equality)]),51,theory(equality)]) ).
cnf(137,plain,
$false,
inference('REWRITE',[status(thm)],[69,51,67,136,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP076-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.00/0.09 % Command : run-snark %s %d
% 0.09/0.29 % Computer : n018.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Tue Jun 14 02:19:13 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.13/0.38 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 *
% 0.13/0.38 *
% 0.13/0.39 #<PACKAGE "SNARK-USER">
% 0.13/0.39 *
% 0.13/0.39 SNARK-TPTP-OPTIONS
% 0.13/0.39 *
% 0.13/0.39 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.13/0.39 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.13/0.39 (USE-FACTORING :POS)
% 0.13/0.39 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.13/0.39 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.13/0.39 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.13/0.39 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.13/0.39 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.13/0.39 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.13/0.39 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.13/0.39 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.13/0.39 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.13/0.39 (DECLARE-TPTP-SYMBOLS2))
% 0.13/0.39 *
% 0.13/0.39 "."
% 0.13/0.39 *
% 0.13/0.39 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T02:19:13
% 0.13/0.39 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n018.cluster.edu at 2022-06-14T02:19:13
% 0.13/0.40
% 0.13/0.48 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.13/0.48
% 0.13/0.48 #||
% 0.13/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.48 % SZS output start Refutation
% See solution above
% 0.13/0.48 ||#
% 0.13/0.48
% 0.13/0.48 ; Summary of computation:
% 0.13/0.48 ; 531 formulas have been input or derived (from 38 formulas).
% 0.13/0.48 ; 137 (26%) were retained. Of these,
% 0.13/0.48 ; 69 (50%) were simplified or subsumed later,
% 0.13/0.48 ; 68 (50%) are still being kept.
% 0.13/0.48 ;
% 0.13/0.48 ; Run time in seconds excluding printing time:
% 0.13/0.48 ; 0.002 2% Read assertion file (1 call)
% 0.13/0.48 ; 0.000 0% Assert (5 calls)
% 0.13/0.48 ; 0.026 29% Process new row (503 calls)
% 0.13/0.48 ; 0.000 0% Resolution (74 calls)
% 0.13/0.48 ; 0.008 9% Paramodulation (37 calls)
% 0.13/0.49 ; 0.000 0% Condensing (3 calls)
% 0.13/0.49 ; 0.000 0% Forward subsumption (3 calls)
% 0.13/0.49 ; 0.000 0% Backward subsumption (3 calls)
% 0.13/0.49 ; 0.008 9% Forward simplification (434 calls)
% 0.13/0.49 ; 0.011 12% Backward simplification (137 calls)
% 0.13/0.49 ; 0.016 18% Ordering (2,279 calls)
% 0.13/0.49 ; 0.000 0% Sortal reasoning (32 calls)
% 0.13/0.49 ; 0.000 0% Purity testing (1 call)
% 0.13/0.49 ; 0.020 22% Other
% 0.13/0.49 ; 0.091 Total
% 0.13/0.49 ; 0.096 Real time
% 0.13/0.49 ;
% 0.13/0.49 ; Term-hash-array has 454 terms in all.
% 0.13/0.49 ; Feature-vector-row-index has 0 entries (1 at peak, 3 added, 3 deleted).
% 0.13/0.49 ; Feature-vector-row-index has 1 node (26 at peak, 69 added, 68 deleted).
% 0.13/0.49 ; Retrieved 0 possibly forward subsuming rows in 3 calls.
% 0.13/0.49 ; Retrieved 0 possibly backward subsumed rows in 3 calls.
% 0.13/0.49 ; Path-index has 252 entries (262 at peak, 565 added, 313 deleted).
% 0.13/0.49 ; Path-index has 705 nodes (723 at peak, 1,258 added, 553 deleted).
% 0.13/0.49 ; Trie-index has 252 entries (262 at peak, 565 added, 313 deleted).
% 0.13/0.49 ; Trie-index has 997 nodes (1,031 at peak, 2,488 added, 1,491 deleted).
% 0.13/0.49 ; Retrieved 2,251 generalization terms in 2,622 calls.
% 0.13/0.49 ; Retrieved 572 instance terms in 213 calls.
% 0.13/0.49 ; Retrieved 980 unifiable terms in 294 calls.
% 0.13/0.49 ;
% 0.13/0.49 ; The agenda of rows to process has 24 entries:
% 0.13/0.49 ; 2 with value 28 7 with value 30 2 with value 32
% 0.13/0.49 ; 2 with value 29 8 with value 31 3 with value 33
% 0.13/0.49 ; The agenda of rows to give has 53 entries:
% 0.13/0.49 ; 4 with value (4 23) 4 with value (4 27) 1 with value (4 31)
% 0.13/0.49 ; 3 with value (4 24) 4 with value (4 28) 1 with value (4 32)
% 0.13/0.49 ; 13 with value (4 25) 2 with value (4 29) 1 with value (4 33)
% 0.13/0.49 ; 12 with value (4 26) 8 with value (4 30)
% 0.13/0.49 Evaluation took:
% 0.13/0.49 0.096 seconds of real time
% 0.13/0.49 0.079659 seconds of user run time
% 0.13/0.49 0.01583 seconds of system run time
% 0.13/0.49 0 calls to %EVAL
% 0.13/0.49 0 page faults and
% 0.13/0.49 8,402,192 bytes consed.
% 0.13/0.49 :PROOF-FOUND
% 0.13/0.49 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T02:19:13
% 0.13/0.49 :PROOF-FOUND
% 0.13/0.49 *
%------------------------------------------------------------------------------