TSTP Solution File: GRP077-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP077-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n006.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 0.19s 0.54s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 40 ( 37 unt; 0 nHn; 7 RR)
% Number of literals : 45 ( 44 equ; 10 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 : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(X,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X,identity),double_divide(Y,Z))),Y),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(X,inverse(double_divide(double_divide(identity,double_divide(inverse(X),double_divide(Y,Z))),Y))) = Z,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(10,plain,
double_divide(X,inverse(double_divide(double_divide(identity,inverse(inverse(X))),Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(13,plain,
double_divide(X,inverse(identity)) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
inference('PARAMODULATE',[status(thm)],[10,identity,theory(equality)]) ).
cnf(14,plain,
double_divide(X,double_divide(X,inverse(identity))) = inverse(identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,inverse,theory(equality)]),13,theory(equality)]) ).
cnf(19,plain,
double_divide(X,inverse(Y)) = inverse(inverse(double_divide(double_divide(identity,double_divide(inverse(double_divide(identity,inverse(inverse(X)))),double_divide(Z,Y))),Z))),
inference('PARAMODULATE',[status(thm)],[10,8,theory(equality)]) ).
cnf(20,plain,
double_divide(X,inverse(double_divide(identity,inverse(X)))) = inverse(identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,14,theory(equality)]),identity,theory(equality)]) ).
cnf(26,plain,
inverse(identity) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20,identity,theory(equality)]),identity,theory(equality)]) ).
cnf(27,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)],[7,26,theory(equality)]) ).
cnf(28,plain,
inverse(X) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
inference('REWRITE',[status(thm)],[13,inverse,26,theory(equality)]) ).
cnf(31,plain,
double_divide(X,inverse(double_divide(identity,inverse(X)))) = identity,
inference('REWRITE',[status(thm)],[20,26,theory(equality)]) ).
cnf(32,plain,
double_divide(identity,inverse(double_divide(identity,X))) = inverse(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,26,theory(equality)]),inverse,26,theory(equality)]) ).
cnf(33,plain,
double_divide(identity,inverse(double_divide(double_divide(identity,double_divide(identity,double_divide(X,Y))),X))) = Y,
inference('PARAMODULATE',[status(thm)],[8,26,theory(equality)]) ).
cnf(37,plain,
inverse(X) = inverse(double_divide(identity,inverse(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,31,theory(equality)]),10,inverse,theory(equality)]) ).
cnf(38,plain,
double_divide(X,inverse(Y)) = inverse(inverse(double_divide(double_divide(identity,double_divide(inverse(inverse(X)),double_divide(Z,Y))),Z))),
inference('REWRITE',[status(thm)],[19,37,theory(equality)]) ).
cnf(39,plain,
inverse(X) = inverse(inverse(inverse(X))),
inference('REWRITE',[status(thm)],[28,37,theory(equality)]) ).
cnf(42,plain,
double_divide(inverse(X),inverse(double_divide(double_divide(identity,inverse(X)),Y))) = inverse(Y),
inference('PARAMODULATE',[status(thm)],[10,39,theory(equality)]) ).
cnf(45,plain,
inverse(double_divide(identity,X)) = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[37,10,theory(equality)]),inverse,26,theory(equality)]) ).
cnf(46,plain,
double_divide(identity,inverse(inverse(X))) = inverse(X),
inference('REWRITE',[status(thm)],[32,45,theory(equality)]) ).
cnf(48,plain,
double_divide(X,inverse(double_divide(inverse(X),Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[10,46,theory(equality)]) ).
cnf(53,plain,
inverse(X) = inverse(double_divide(double_divide(identity,double_divide(identity,double_divide(Y,X))),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[45,8,theory(equality)]),39,26,theory(equality)]) ).
cnf(55,plain,
double_divide(identity,inverse(X)) = X,
inference('REWRITE',[status(thm)],[33,53,theory(equality)]) ).
cnf(59,plain,
double_divide(inverse(X),inverse(double_divide(X,Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[42,55,theory(equality)]) ).
cnf(61,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[55,39,theory(equality)]),55,theory(equality)]) ).
cnf(64,plain,
double_divide(X,inverse(Y)) = double_divide(double_divide(identity,double_divide(X,double_divide(Z,Y))),Z),
inference('REWRITE',[status(thm)],[38,61,theory(equality)]) ).
cnf(69,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[27,61,theory(equality)]) ).
cnf(71,plain,
double_divide(identity,X) = inverse(X),
inference('PARAMODULATE',[status(thm)],[55,61,theory(equality)]) ).
cnf(73,plain,
double_divide(X,inverse(Y)) = double_divide(inverse(double_divide(X,double_divide(Z,Y))),Z),
inference('REWRITE',[status(thm)],[64,71,theory(equality)]) ).
cnf(74,plain,
inverse(X) = double_divide(inverse(double_divide(X,inverse(Y))),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[73,inverse,theory(equality)]),inverse,26,theory(equality)]) ).
cnf(83,plain,
X = double_divide(Y,double_divide(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[74,59,theory(equality)]),61,theory(equality)]) ).
cnf(91,plain,
double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
inference('PARAMODULATE',[status(thm)],[48,83,theory(equality)]) ).
cnf(93,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[69,91,theory(equality)]) ).
cnf(94,plain,
double_divide(X,inverse(double_divide(Y,Z))) = double_divide(inverse(double_divide(X,Y)),Z),
inference('PARAMODULATE',[status(thm)],[73,83,theory(equality)]) ).
cnf(95,plain,
$false,
inference('REWRITE',[status(thm)],[93,61,91,94,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP077-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.03/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 02:37:26 EDT 2022
% 0.12/0.34 % 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 2022-06-14T02:37:27
% 0.19/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n006.cluster.edu at 2022-06-14T02:37:27
% 0.19/0.49
% 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
% 0.39/0.55 ||#
% 0.39/0.55
% 0.39/0.55 ; Summary of computation:
% 0.39/0.55 ; 259 formulas have been input or derived (from 28 formulas).
% 0.39/0.55 ; 95 (37%) were retained. Of these,
% 0.39/0.55 ; 73 (77%) were simplified or subsumed later,
% 0.39/0.55 ; 22 (23%) are still being kept.
% 0.39/0.55 ;
% 0.39/0.55 ; Run time in seconds excluding printing time:
% 0.39/0.55 ; 0.001 2% Read assertion file (1 call)
% 0.39/0.55 ; 0.001 2% Assert (5 calls)
% 0.39/0.55 ; 0.014 22% Process new row (256 calls)
% 0.39/0.55 ; 0.001 2% Resolution (54 calls)
% 0.39/0.55 ; 0.004 6% Paramodulation (27 calls)
% 0.39/0.55 ; 0.000 0% Condensing (3 calls)
% 0.39/0.55 ; 0.000 0% Forward subsumption (3 calls)
% 0.39/0.55 ; 0.000 0% Backward subsumption (3 calls)
% 0.39/0.55 ; 0.005 8% Forward simplification (241 calls)
% 0.39/0.55 ; 0.012 19% Backward simplification (95 calls)
% 0.39/0.55 ; 0.001 2% Ordering (551 calls)
% 0.39/0.55 ; 0.000 0% Sortal reasoning (32 calls)
% 0.39/0.55 ; 0.000 0% Purity testing (1 call)
% 0.39/0.55 ; 0.024 38% Other
% 0.39/0.55 ; 0.063 Total
% 0.39/0.55 ; 0.070 Real time
% 0.39/0.55 ;
% 0.39/0.55 ; Term-hash-array has 337 terms in all.
% 0.39/0.55 ; Feature-vector-row-index has 0 entries (1 at peak, 3 added, 3 deleted).
% 0.39/0.55 ; Feature-vector-row-index has 1 node (26 at peak, 69 added, 68 deleted).
% 0.39/0.55 ; Retrieved 0 possibly forward subsuming rows in 3 calls.
% 0.39/0.55 ; Retrieved 0 possibly backward subsumed rows in 3 calls.
% 0.39/0.55 ; Path-index has 89 entries (131 at peak, 453 added, 364 deleted).
% 0.39/0.55 ; Path-index has 550 nodes (571 at peak, 1,035 added, 485 deleted).
% 0.39/0.55 ; Trie-index has 89 entries (131 at peak, 453 added, 364 deleted).
% 0.39/0.55 ; Trie-index has 295 nodes (532 at peak, 1,683 added, 1,388 deleted).
% 0.39/0.55 ; Retrieved 570 generalization terms in 1,403 calls.
% 0.39/0.55 ; Retrieved 209 instance terms in 106 calls.
% 0.39/0.55 ; Retrieved 455 unifiable terms in 207 calls.
% 0.39/0.55 ;
% 0.39/0.55 ; The agenda of rows to process has 1 entry:
% 0.39/0.55 ; 1 with value 22
% 0.39/0.55 ; The agenda of rows to give has 11 entries:
% 0.39/0.55 ; 2 with value (4 18) 4 with value (4 22) 1 with value (4 24)
% 0.39/0.55 ; 1 with value (4 19) 1 with value (4 23) 2 with value (4 27)
% 0.39/0.55 Evaluation took:
% 0.39/0.55 0.071 seconds of real time
% 0.39/0.55 0.05713 seconds of user run time
% 0.39/0.55 0.013149 seconds of system run time
% 0.39/0.55 0 calls to %EVAL
% 0.39/0.55 0 page faults and
% 0.39/0.55 6,681,840 bytes consed.
% 0.39/0.55 :PROOF-FOUND
% 0.39/0.55 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T02:37:27
% 0.39/0.55 :PROOF-FOUND
% 0.39/0.55 *
%------------------------------------------------------------------------------