TSTP Solution File: GRP078-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP078-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n019.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 0.22s 0.56s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 43 ( 40 unt; 0 nHn; 10 RR)
% Number of literals : 48 ( 47 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 : 63 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(double_divide(double_divide(X,Y),identity),double_divide(Z,Y)))) = 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,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox/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(identity,double_divide(inverse(double_divide(X,Y)),double_divide(Z,Y)))) = Z,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(9,plain,
double_divide(inverse(identity),double_divide(identity,double_divide(inverse(double_divide(identity,X)),double_divide(Y,X)))) = Y,
inference('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]) ).
cnf(10,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(inverse(inverse(X)),inverse(Y)))) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]),inverse,theory(equality)]) ).
cnf(16,plain,
double_divide(double_divide(identity,X),inverse(identity)) = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(18,plain,
double_divide(identity,double_divide(identity,double_divide(inverse(inverse(inverse(identity))),inverse(X)))) = X,
inference('PARAMODULATE',[status(thm)],[10,identity,theory(equality)]) ).
cnf(22,plain,
identity = inverse(inverse(inverse(identity))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,identity,theory(equality)]),identity,theory(equality)]) ).
cnf(23,plain,
double_divide(identity,double_divide(identity,double_divide(identity,inverse(X)))) = X,
inference('REWRITE',[status(thm)],[18,22,theory(equality)]) ).
cnf(25,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(inverse(double_divide(X,inverse(identity))),inverse(inverse(Y))))) = double_divide(identity,Y),
inference('PARAMODULATE',[status(thm)],[8,16,theory(equality)]) ).
cnf(27,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(inverse(inverse(X))))) = inverse(inverse(identity)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,22,theory(equality)]),inverse,theory(equality)]) ).
cnf(29,plain,
inverse(identity) = inverse(inverse(identity)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[23,22,theory(equality)]),identity,inverse,theory(equality)]) ).
cnf(32,plain,
inverse(identity) = identity,
inference('REWRITE',[status(thm)],[22,29,theory(equality)]) ).
cnf(33,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)],[7,32,theory(equality)]) ).
cnf(34,plain,
double_divide(identity,double_divide(identity,double_divide(inverse(double_divide(identity,X)),double_divide(Y,X)))) = Y,
inference('REWRITE',[status(thm)],[9,32,theory(equality)]) ).
cnf(36,plain,
inverse(double_divide(identity,X)) = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[16,inverse,32,theory(equality)]) ).
cnf(37,plain,
double_divide(identity,double_divide(identity,double_divide(inverse(inverse(X)),double_divide(Y,X)))) = Y,
inference('REWRITE',[status(thm)],[34,36,theory(equality)]) ).
cnf(39,plain,
inverse(X) = double_divide(identity,X),
inference('REWRITE',[status(thm)],[25,10,inverse,32,theory(equality)]) ).
cnf(40,plain,
inverse(inverse(double_divide(inverse(inverse(X)),double_divide(Y,X)))) = Y,
inference('REWRITE',[status(thm)],[37,39,theory(equality)]) ).
cnf(41,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference('REWRITE',[status(thm)],[23,39,theory(equality)]) ).
cnf(42,plain,
double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,Y)),double_divide(Z,Y)))) = Z,
inference('REWRITE',[status(thm)],[8,39,theory(equality)]) ).
cnf(50,plain,
double_divide(inverse(X),X) = identity,
inference('REWRITE',[status(thm)],[27,32,41,39,29,theory(equality)]) ).
cnf(52,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,50,theory(equality)]),inverse,32,theory(equality)]) ).
cnf(56,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference('REWRITE',[status(thm)],[40,52,theory(equality)]) ).
cnf(59,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[33,52,theory(equality)]) ).
cnf(60,plain,
double_divide(inverse(X),inverse(double_divide(X,Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,50,theory(equality)]),52,inverse,theory(equality)]) ).
cnf(61,plain,
double_divide(double_divide(X,Y),X) = Y,
inference('PARAMODULATE',[status(thm)],[56,56,theory(equality)]) ).
cnf(64,plain,
double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,double_divide(Y,Z))),Y))) = Z,
inference('PARAMODULATE',[status(thm)],[42,56,theory(equality)]) ).
cnf(68,plain,
double_divide(inverse(X),inverse(Y)) = inverse(double_divide(Y,X)),
inference('PARAMODULATE',[status(thm)],[61,60,theory(equality)]) ).
cnf(70,plain,
inverse(double_divide(double_divide(inverse(double_divide(X,double_divide(Y,Z))),Y),X)) = Z,
inference('REWRITE',[status(thm)],[64,68,theory(equality)]) ).
cnf(73,plain,
double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
inference('PARAMODULATE',[status(thm)],[68,52,theory(equality)]) ).
cnf(75,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[59,73,theory(equality)]) ).
cnf(76,plain,
double_divide(inverse(X),Y) = inverse(double_divide(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[68,52,theory(equality)]) ).
cnf(77,plain,
double_divide(inverse(X),double_divide(inverse(Y),double_divide(X,double_divide(Y,Z)))) = Z,
inference('REWRITE',[status(thm)],[70,52,76,theory(equality)]) ).
cnf(79,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
inference('REWRITE',[status(thm)],[75,76,theory(equality)]) ).
cnf(80,plain,
double_divide(X,inverse(Y)) = double_divide(inverse(Z),double_divide(Y,double_divide(Z,X))),
inference('PARAMODULATE',[status(thm)],[61,77,theory(equality)]) ).
cnf(81,plain,
double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(Y),double_divide(Z,X)),
inference('PARAMODULATE',[status(thm)],[80,56,theory(equality)]) ).
cnf(82,plain,
$false,
inference('REWRITE',[status(thm)],[79,81,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP078-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.08/0.15 % Command : run-snark %s %d
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 16:45:54 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.49 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.50 *
% 0.22/0.50 *
% 0.22/0.51 #<PACKAGE "SNARK-USER">
% 0.22/0.51 *
% 0.22/0.51 SNARK-TPTP-OPTIONS
% 0.22/0.51 *
% 0.22/0.51 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.22/0.51 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.22/0.51 (USE-FACTORING :POS)
% 0.22/0.51 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.22/0.51 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.22/0.51 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.22/0.51 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.22/0.51 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.22/0.51 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.22/0.51 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.22/0.51 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.22/0.51 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.22/0.51 (DECLARE-TPTP-SYMBOLS2))
% 0.22/0.51 *
% 0.22/0.51 "."
% 0.22/0.51 *
% 0.22/0.51 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T16:45:55
% 0.22/0.51 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n019.cluster.edu at 2022-06-13T16:45:55
% 0.22/0.52
% 0.22/0.56 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.22/0.56
% 0.22/0.56 #||
% 0.22/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.56 % SZS output start Refutation
% See solution above
% 0.22/0.57 ||#
% 0.22/0.57
% 0.22/0.57 ; Summary of computation:
% 0.22/0.57 ; 217 formulas have been input or derived (from 25 formulas).
% 0.22/0.57 ; 82 (38%) were retained. Of these,
% 0.22/0.57 ; 65 (79%) were simplified or subsumed later,
% 0.22/0.57 ; 17 (21%) are still being kept.
% 0.22/0.57 ;
% 0.22/0.57 ; Run time in seconds excluding printing time:
% 0.22/0.57 ; 0.002 3% Read assertion file (1 call)
% 0.22/0.57 ; 0.000 0% Assert (5 calls)
% 0.22/0.57 ; 0.012 21% Process new row (205 calls)
% 0.22/0.57 ; 0.001 2% Resolution (48 calls)
% 0.22/0.57 ; 0.003 5% Paramodulation (24 calls)
% 0.22/0.57 ; 0.000 0% Condensing (3 calls)
% 0.22/0.57 ; 0.000 0% Forward subsumption (3 calls)
% 0.22/0.57 ; 0.000 0% Backward subsumption (3 calls)
% 0.22/0.57 ; 0.007 12% Forward simplification (174 calls)
% 0.22/0.57 ; 0.008 14% Backward simplification (82 calls)
% 0.22/0.57 ; 0.003 5% Ordering (426 calls)
% 0.22/0.57 ; 0.000 0% Sortal reasoning (32 calls)
% 0.22/0.57 ; 0.000 0% Purity testing (1 call)
% 0.22/0.57 ; 0.022 38% Other
% 0.22/0.57 ; 0.058 Total
% 0.22/0.57 ; 0.064 Real time
% 0.22/0.57 ;
% 0.22/0.57 ; Term-hash-array has 328 terms in all.
% 0.22/0.57 ; Feature-vector-row-index has 0 entries (1 at peak, 3 added, 3 deleted).
% 0.22/0.57 ; Feature-vector-row-index has 1 node (26 at peak, 69 added, 68 deleted).
% 0.22/0.57 ; Retrieved 0 possibly forward subsuming rows in 3 calls.
% 0.22/0.57 ; Retrieved 0 possibly backward subsumed rows in 3 calls.
% 0.22/0.57 ; Path-index has 54 entries (143 at peak, 446 added, 392 deleted).
% 0.22/0.57 ; Path-index has 642 nodes (694 at peak, 1,228 added, 586 deleted).
% 0.22/0.57 ; Trie-index has 54 entries (143 at peak, 446 added, 392 deleted).
% 0.22/0.57 ; Trie-index has 169 nodes (600 at peak, 1,675 added, 1,506 deleted).
% 0.22/0.57 ; Retrieved 445 generalization terms in 967 calls.
% 0.22/0.57 ; Retrieved 181 instance terms in 84 calls.
% 0.22/0.57 ; Retrieved 459 unifiable terms in 195 calls.
% 0.22/0.57 ;
% 0.22/0.57 ; The agenda of backward simplifiable rows to process has 1 entry:
% 0.22/0.57 ; 1 with value 0
% 0.22/0.57 ; The agenda of rows to process has 11 entries:
% 0.22/0.57 ; 1 with value 20 2 with value 22 1 with value 24
% 0.22/0.57 ; 4 with value 21 1 with value 23 2 with value 28
% 0.22/0.57 ; The agenda of rows to give has 5 entries:
% 0.22/0.57 ; 1 with value (4 20) 3 with value (4 21) 1 with value (4 22)
% 0.22/0.57 Evaluation took:
% 0.22/0.57 0.064 seconds of real time
% 0.22/0.57 0.057871 seconds of user run time
% 0.22/0.57 0.005962 seconds of system run time
% 0.22/0.57 0 calls to %EVAL
% 0.22/0.57 0 page faults and
% 0.22/0.57 6,764,488 bytes consed.
% 0.22/0.57 :PROOF-FOUND
% 0.22/0.57 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T16:45:55
% 0.22/0.57 :PROOF-FOUND
% 0.22/0.57 *
%------------------------------------------------------------------------------