TSTP Solution File: GRP583-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP583-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n011.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 11:39:31 EDT 2022
% Result : Unsatisfiable 0.45s 0.61s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 6 RR)
% Number of literals : 58 ( 57 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X,double_divide(double_divide(identity,Y),double_divide(Z,double_divide(Y,X)))),double_divide(identity,identity)) = Z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X,Y) = double_divide(double_divide(Y,X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(X) = double_divide(X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(identity,axiom,
identity = double_divide(X,inverse(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(6,plain,
multiply(X,Y) = inverse(double_divide(Y,X)),
inference('REWRITE',[status(thm)],[multiply,inverse,theory(equality)]) ).
cnf(7,plain,
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_3,6,theory(equality)]) ).
cnf(8,plain,
double_divide(double_divide(X,double_divide(double_divide(identity,Y),double_divide(Z,double_divide(Y,X)))),inverse(identity)) = Z,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(9,plain,
double_divide(double_divide(inverse(X),double_divide(double_divide(identity,X),inverse(Y))),inverse(identity)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(10,plain,
double_divide(double_divide(X,double_divide(inverse(identity),double_divide(Y,double_divide(identity,X)))),inverse(identity)) = Y,
inference('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]) ).
cnf(11,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X),double_divide(Y,inverse(X)))),inverse(identity)) = Y,
inference('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]) ).
cnf(12,plain,
double_divide(double_divide(X,double_divide(identity,double_divide(Y,double_divide(inverse(identity),X)))),inverse(identity)) = Y,
inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]) ).
cnf(13,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(X,double_divide(double_divide(identity,Y),double_divide(Z,double_divide(Y,X))))),double_divide(U,Z))),inverse(identity)) = U,
inference('PARAMODULATE',[status(thm)],[8,8,theory(equality)]) ).
cnf(14,plain,
double_divide(inverse(inverse(X)),inverse(identity)) = double_divide(identity,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(15,plain,
double_divide(double_divide(inverse(identity),double_divide(inverse(identity),inverse(X))),inverse(identity)) = X,
inference('PARAMODULATE',[status(thm)],[9,inverse,theory(equality)]) ).
cnf(16,plain,
double_divide(double_divide(inverse(inverse(identity)),double_divide(identity,inverse(X))),inverse(identity)) = X,
inference('PARAMODULATE',[status(thm)],[9,identity,theory(equality)]) ).
cnf(23,plain,
double_divide(double_divide(inverse(double_divide(inverse(identity),double_divide(X,inverse(identity)))),X),inverse(identity)) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,10,theory(equality)]),inverse,theory(equality)]) ).
cnf(25,plain,
double_divide(double_divide(identity,inverse(double_divide(identity,X))),inverse(identity)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(28,plain,
double_divide(double_divide(identity,double_divide(inverse(identity),X)),inverse(identity)) = double_divide(inverse(Y),double_divide(double_divide(identity,Y),inverse(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,9,theory(equality)]),inverse,theory(equality)]) ).
cnf(29,plain,
double_divide(double_divide(identity,double_divide(inverse(identity),X)),inverse(identity)) = double_divide(inverse(identity),double_divide(inverse(identity),inverse(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,15,theory(equality)]),inverse,theory(equality)]) ).
cnf(30,plain,
double_divide(inverse(identity),double_divide(inverse(identity),inverse(X))) = double_divide(inverse(Y),double_divide(double_divide(identity,Y),inverse(X))),
inference('REWRITE',[status(thm)],[28,29,theory(equality)]) ).
cnf(33,plain,
double_divide(inverse(identity),double_divide(inverse(identity),inverse(X))) = double_divide(inverse(inverse(identity)),double_divide(identity,inverse(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,16,theory(equality)]),29,inverse,theory(equality)]) ).
cnf(37,plain,
double_divide(inverse(inverse(identity)),double_divide(identity,inverse(X))) = double_divide(inverse(Y),double_divide(double_divide(identity,Y),inverse(X))),
inference('REWRITE',[status(thm)],[30,33,theory(equality)]) ).
cnf(39,plain,
identity = inverse(identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[25,identity,theory(equality)]),identity,theory(equality)]) ).
cnf(40,plain,
inverse(double_divide(X,double_divide(double_divide(identity,Y),double_divide(Z,double_divide(Y,X))))) = Z,
inference('REWRITE',[status(thm)],[8,inverse,39,theory(equality)]) ).
cnf(41,plain,
inverse(double_divide(X,double_divide(identity,double_divide(Y,double_divide(identity,X))))) = Y,
inference('REWRITE',[status(thm)],[12,inverse,39,theory(equality)]) ).
cnf(42,plain,
inverse(double_divide(identity,double_divide(double_divide(identity,double_divide(X,double_divide(double_divide(identity,Y),double_divide(Z,double_divide(Y,X))))),double_divide(U,Z)))) = U,
inference('REWRITE',[status(thm)],[13,inverse,39,theory(equality)]) ).
cnf(43,plain,
inverse(inverse(inverse(X))) = double_divide(identity,X),
inference('REWRITE',[status(thm)],[14,inverse,39,theory(equality)]) ).
cnf(44,plain,
inverse(double_divide(X,inverse(inverse(inverse(double_divide(Y,inverse(inverse(inverse(X))))))))) = Y,
inference('REWRITE',[status(thm)],[41,43,theory(equality)]) ).
cnf(45,plain,
inverse(double_divide(X,double_divide(inverse(inverse(inverse(Y))),double_divide(Z,double_divide(Y,X))))) = Z,
inference('REWRITE',[status(thm)],[40,43,theory(equality)]) ).
cnf(46,plain,
inverse(inverse(inverse(inverse(double_divide(inverse(inverse(X)),double_divide(Y,X)))))) = Y,
inference('REWRITE',[status(thm)],[42,45,43,theory(equality)]) ).
cnf(47,plain,
inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X)))))))) = X,
inference('REWRITE',[status(thm)],[16,inverse,43,39,theory(equality)]) ).
cnf(49,plain,
inverse(double_divide(inverse(inverse(inverse(inverse(inverse(X))))),X)) = identity,
inference('REWRITE',[status(thm)],[23,43,inverse,39,theory(equality)]) ).
cnf(50,plain,
inverse(inverse(inverse(inverse(inverse(inverse(inverse(X))))))) = double_divide(inverse(Y),double_divide(inverse(inverse(inverse(Y))),inverse(X))),
inference('REWRITE',[status(thm)],[37,43,39,theory(equality)]) ).
cnf(69,plain,
inverse(double_divide(X,inverse(inverse(inverse(X))))) = identity,
inference('PARAMODULATE',[status(thm)],[49,47,theory(equality)]) ).
cnf(70,plain,
inverse(inverse(inverse(inverse(X)))) = double_divide(inverse(inverse(Y)),double_divide(X,Y)),
inference('PARAMODULATE',[status(thm)],[47,46,theory(equality)]) ).
cnf(75,plain,
inverse(inverse(inverse(inverse(inverse(inverse(inverse(X))))))) = double_divide(Y,double_divide(inverse(inverse(inverse(Z))),double_divide(X,double_divide(Z,Y)))),
inference('PARAMODULATE',[status(thm)],[47,45,theory(equality)]) ).
cnf(76,plain,
identity = double_divide(X,inverse(inverse(inverse(X)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[47,69,theory(equality)]),39,theory(equality)]) ).
cnf(77,plain,
inverse(inverse(inverse(inverse(X)))) = inverse(inverse(inverse(inverse(inverse(inverse(X)))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[70,76,theory(equality)]),inverse,theory(equality)]) ).
cnf(78,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference('REWRITE',[status(thm)],[47,77,theory(equality)]) ).
cnf(80,plain,
X = double_divide(inverse(inverse(Y)),double_divide(X,Y)),
inference('REWRITE',[status(thm)],[70,78,theory(equality)]) ).
cnf(82,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[77,78,theory(equality)]) ).
cnf(84,plain,
X = double_divide(Y,double_divide(X,Y)),
inference('REWRITE',[status(thm)],[80,82,theory(equality)]) ).
cnf(86,plain,
inverse(double_divide(X,inverse(double_divide(Y,inverse(X))))) = Y,
inference('REWRITE',[status(thm)],[44,82,theory(equality)]) ).
cnf(87,plain,
inverse(X) = double_divide(inverse(Y),double_divide(inverse(Y),inverse(X))),
inference('REWRITE',[status(thm)],[50,82,77,theory(equality)]) ).
cnf(88,plain,
inverse(X) = double_divide(Y,double_divide(inverse(Z),double_divide(X,double_divide(Z,Y)))),
inference('REWRITE',[status(thm)],[75,82,77,theory(equality)]) ).
cnf(89,plain,
X = double_divide(double_divide(Y,X),Y),
inference('PARAMODULATE',[status(thm)],[84,84,theory(equality)]) ).
cnf(91,plain,
inverse(double_divide(X,inverse(Y))) = double_divide(inverse(X),Y),
inference('PARAMODULATE',[status(thm)],[86,89,theory(equality)]) ).
cnf(92,plain,
double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(double_divide(c3,b3),inverse(a3)),
inference('REWRITE',[status(thm)],[7,82,91,theory(equality)]) ).
cnf(94,plain,
inverse(X) = double_divide(double_divide(inverse(X),inverse(Y)),inverse(Y)),
inference('PARAMODULATE',[status(thm)],[84,87,theory(equality)]) ).
cnf(97,plain,
inverse(double_divide(X,Y)) = double_divide(inverse(X),inverse(Y)),
inference('PARAMODULATE',[status(thm)],[91,82,theory(equality)]) ).
cnf(98,plain,
inverse(X) = inverse(double_divide(double_divide(X,Y),Y)),
inference('REWRITE',[status(thm)],[94,97,theory(equality)]) ).
cnf(106,plain,
double_divide(double_divide(X,Y),Y) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[82,98,theory(equality)]),82,theory(equality)]) ).
cnf(107,plain,
double_divide(X,Y) = double_divide(Y,X),
inference('PARAMODULATE',[status(thm)],[84,106,theory(equality)]) ).
cnf(113,plain,
double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(inverse(a3),double_divide(c3,b3)),
inference('PARAMODULATE',[status(thm)],[92,107,theory(equality)]) ).
cnf(131,plain,
inverse(X) = double_divide(double_divide(Y,Z),double_divide(inverse(Z),double_divide(X,Y))),
inference('PARAMODULATE',[status(thm)],[88,84,theory(equality)]) ).
cnf(145,plain,
double_divide(inverse(X),double_divide(Y,Z)) = double_divide(inverse(Y),double_divide(Z,X)),
inference('PARAMODULATE',[status(thm)],[89,131,theory(equality)]) ).
cnf(146,plain,
$false,
inference('REWRITE',[status(thm)],[113,145,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP583-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : run-snark %s %d
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 21:14:34 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.22/0.48 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.49 *
% 0.22/0.49 *
% 0.22/0.49 #<PACKAGE "SNARK-USER">
% 0.22/0.49 *
% 0.22/0.49 SNARK-TPTP-OPTIONS
% 0.22/0.49 *
% 0.22/0.50 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.22/0.50 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.22/0.50 (USE-FACTORING :POS)
% 0.22/0.50 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.22/0.50 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.22/0.50 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.22/0.50 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.22/0.50 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.22/0.50 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.22/0.50 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.22/0.50 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.22/0.50 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.22/0.50 (DECLARE-TPTP-SYMBOLS2))
% 0.22/0.50 *
% 0.22/0.50 "."
% 0.22/0.50 *
% 0.22/0.50 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T21:14:34
% 0.22/0.50 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n011.cluster.edu at 2022-06-13T21:14:34
% 0.22/0.51
% 0.45/0.61 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.45/0.61
% 0.45/0.61 #||
% 0.45/0.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.61 % SZS output start Refutation
% See solution above
% 0.45/0.62 ||#
% 0.45/0.62
% 0.45/0.62 ; Summary of computation:
% 0.45/0.62 ; 822 formulas have been input or derived (from 46 formulas).
% 0.45/0.62 ; 146 (18%) were retained. Of these,
% 0.45/0.62 ; 87 (60%) were simplified or subsumed later,
% 0.45/0.62 ; 59 (40%) are still being kept.
% 0.45/0.62 ;
% 0.45/0.62 ; Run time in seconds excluding printing time:
% 0.45/0.62 ; 0.002 2% Read assertion file (1 call)
% 0.45/0.62 ; 0.000 0% Assert (5 calls)
% 0.45/0.62 ; 0.026 22% Process new row (730 calls)
% 0.45/0.62 ; 0.001 1% Resolution (90 calls)
% 0.45/0.62 ; 0.018 15% Paramodulation (45 calls)
% 0.45/0.62 ; 0.026 22% Forward simplification (660 calls)
% 0.45/0.62 ; 0.007 6% Backward simplification (146 calls)
% 0.45/0.62 ; 0.010 9% Ordering (2,341 calls)
% 0.45/0.62 ; 0.000 0% Sortal reasoning (32 calls)
% 0.45/0.62 ; 0.000 0% Purity testing (1 call)
% 0.45/0.62 ; 0.027 23% Other
% 0.45/0.62 ; 0.117 Total
% 0.45/0.62 ; 0.122 Real time
% 0.45/0.62 ;
% 0.45/0.62 ; Term-hash-array has 528 terms in all.
% 0.45/0.62 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.45/0.62 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.45/0.62 ; Path-index has 169 entries (206 at peak, 581 added, 412 deleted).
% 0.45/0.62 ; Path-index has 1,278 nodes (1,414 at peak, 2,025 added, 747 deleted).
% 0.45/0.62 ; Trie-index has 169 entries (206 at peak, 581 added, 412 deleted).
% 0.45/0.62 ; Trie-index has 728 nodes (1,191 at peak, 3,204 added, 2,476 deleted).
% 0.45/0.62 ; Retrieved 2,889 generalization terms in 4,296 calls.
% 0.45/0.62 ; Retrieved 355 instance terms in 179 calls.
% 0.45/0.62 ; Retrieved 1,184 unifiable terms in 347 calls.
% 0.45/0.62 ;
% 0.45/0.62 ; The agenda of rows to process has 52 entries:
% 0.45/0.62 ; 8 with value 21 6 with value 25 9 with value 28
% 0.45/0.62 ; 5 with value 22 3 with value 26 9 with value 29
% 0.45/0.62 ; 3 with value 23 2 with value 27 4 with value 30
% 0.45/0.62 ; 3 with value 24
% 0.45/0.62 ; The agenda of rows to give has 36 entries:
% 0.45/0.62 ; 1 with value (4 21) 2 with value (4 25) 10 with value (4 27)
% 0.45/0.62 ; 6 with value (4 22) 3 with value (4 26) 8 with value (4 28)
% 0.45/0.62 ; 6 with value (4 24)
% 0.45/0.62 Evaluation took:
% 0.45/0.62 0.122 seconds of real time
% 0.45/0.62 0.106103 seconds of user run time
% 0.45/0.62 0.015558 seconds of system run time
% 0.45/0.62 0 calls to %EVAL
% 0.45/0.62 0 page faults and
% 0.45/0.62 11,010,320 bytes consed.
% 0.45/0.62 :PROOF-FOUND
% 0.45/0.62 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T21:14:34
% 0.45/0.62 :PROOF-FOUND
% 0.45/0.62 *
%------------------------------------------------------------------------------