TSTP Solution File: GRP101-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP101-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n015.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 11:36:09 EDT 2022
% Result : Unsatisfiable 0.53s 0.75s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 48 ( 44 unt; 0 nHn; 10 RR)
% Number of literals : 57 ( 56 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),double_divide(Z,identity))),double_divide(identity,identity)) = Y,
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))
| multiply(a4,b4) != multiply(b4,a4) ),
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))
| inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
inference('REWRITE',[status(thm)],[prove_these_axioms,inverse,identity,6,theory(equality)]) ).
cnf(8,plain,
double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),inverse(Z))),inverse(identity)) = Y,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(9,plain,
double_divide(double_divide(inverse(X),double_divide(inverse(Y),inverse(X))),inverse(identity)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(11,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(X,Y),inverse(double_divide(Z,double_divide(double_divide(Y,double_divide(U,Z)),inverse(U)))))),inverse(identity)) = X,
inference('PARAMODULATE',[status(thm)],[8,8,theory(equality)]) ).
cnf(12,plain,
double_divide(inverse(inverse(inverse(X))),inverse(identity)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(14,plain,
double_divide(double_divide(inverse(identity),X),inverse(identity)) = inverse(inverse(X)),
inference('PARAMODULATE',[status(thm)],[9,12,theory(equality)]) ).
cnf(16,plain,
inverse(inverse(double_divide(double_divide(X,Y),inverse(double_divide(Z,double_divide(double_divide(Y,double_divide(U,Z)),inverse(U))))))) = X,
inference('REWRITE',[status(thm)],[11,14,theory(equality)]) ).
cnf(20,plain,
identity = inverse(inverse(inverse(inverse(identity)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,identity,theory(equality)]),identity,theory(equality)]) ).
cnf(24,plain,
inverse(identity) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,20,theory(equality)]),identity,theory(equality)]) ).
cnf(25,plain,
( inverse(inverse(a2)) != a2
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
inference('REWRITE',[status(thm)],[7,24,theory(equality)]) ).
cnf(26,plain,
inverse(double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),inverse(Z)))) = Y,
inference('REWRITE',[status(thm)],[8,inverse,24,theory(equality)]) ).
cnf(27,plain,
inverse(inverse(double_divide(double_divide(X,Y),Y))) = X,
inference('REWRITE',[status(thm)],[16,26,theory(equality)]) ).
cnf(28,plain,
inverse(double_divide(inverse(X),double_divide(inverse(Y),inverse(X)))) = Y,
inference('REWRITE',[status(thm)],[9,inverse,24,theory(equality)]) ).
cnf(30,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference('REWRITE',[status(thm)],[12,inverse,24,theory(equality)]) ).
cnf(31,plain,
inverse(double_divide(identity,X)) = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[14,inverse,24,theory(equality)]) ).
cnf(34,plain,
inverse(double_divide(X,double_divide(double_divide(Y,double_divide(double_divide(Z,double_divide(double_divide(U,double_divide(V,Z)),inverse(V))),X)),U))) = Y,
inference('PARAMODULATE',[status(thm)],[26,26,theory(equality)]) ).
cnf(37,plain,
inverse(inverse(inverse(X))) = double_divide(Y,double_divide(double_divide(X,double_divide(Z,Y)),inverse(Z))),
inference('PARAMODULATE',[status(thm)],[30,26,theory(equality)]) ).
cnf(38,plain,
inverse(double_divide(X,double_divide(double_divide(Y,double_divide(inverse(inverse(inverse(Z))),X)),Z))) = Y,
inference('REWRITE',[status(thm)],[34,37,theory(equality)]) ).
cnf(40,plain,
inverse(X) = double_divide(identity,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[30,31,theory(equality)]),30,theory(equality)]) ).
cnf(42,plain,
inverse(inverse(X)) = double_divide(double_divide(X,Y),Y),
inference('PARAMODULATE',[status(thm)],[30,27,theory(equality)]) ).
cnf(43,plain,
identity = double_divide(inverse(X),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,40,theory(equality)]),24,theory(equality)]) ).
cnf(44,plain,
inverse(inverse(double_divide(X,Y))) = double_divide(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[42,42,theory(equality)]) ).
cnf(45,plain,
inverse(double_divide(X,double_divide(double_divide(Y,inverse(inverse(double_divide(inverse(Z),X)))),Z))) = Y,
inference('REWRITE',[status(thm)],[38,44,theory(equality)]) ).
cnf(46,plain,
inverse(inverse(inverse(X))) = inverse(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,43,theory(equality)]),40,theory(equality)]) ).
cnf(47,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[30,46,theory(equality)]) ).
cnf(48,plain,
inverse(double_divide(X,double_divide(double_divide(Y,double_divide(inverse(Z),X)),Z))) = Y,
inference('REWRITE',[status(thm)],[45,47,theory(equality)]) ).
cnf(49,plain,
X = double_divide(double_divide(X,Y),Y),
inference('REWRITE',[status(thm)],[42,47,theory(equality)]) ).
cnf(50,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
inference('REWRITE',[status(thm)],[25,47,theory(equality)]) ).
cnf(51,plain,
inverse(X) = double_divide(Y,double_divide(double_divide(X,double_divide(Z,Y)),inverse(Z))),
inference('REWRITE',[status(thm)],[37,46,theory(equality)]) ).
cnf(52,plain,
inverse(double_divide(X,double_divide(inverse(Y),X))) = Y,
inference('PARAMODULATE',[status(thm)],[28,28,theory(equality)]) ).
cnf(53,plain,
inverse(X) = double_divide(Y,double_divide(inverse(X),Y)),
inference('PARAMODULATE',[status(thm)],[47,52,theory(equality)]) ).
cnf(54,plain,
X = double_divide(Y,double_divide(X,Y)),
inference('PARAMODULATE',[status(thm)],[53,47,theory(equality)]) ).
cnf(55,plain,
double_divide(X,Y) = double_divide(Y,X),
inference('PARAMODULATE',[status(thm)],[54,49,theory(equality)]) ).
cnf(58,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[50,55,theory(equality)]),theory(equality)]) ).
cnf(59,plain,
inverse(double_divide(X,double_divide(Y,Z))) = double_divide(Y,double_divide(inverse(Z),X)),
inference('PARAMODULATE',[status(thm)],[48,49,theory(equality)]) ).
cnf(60,plain,
inverse(double_divide(X,double_divide(Y,Z))) = double_divide(Z,double_divide(X,inverse(Y))),
inference('PARAMODULATE',[status(thm)],[51,49,theory(equality)]) ).
cnf(62,plain,
inverse(double_divide(X,inverse(Y))) = double_divide(Y,inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[59,inverse,theory(equality)]),40,24,theory(equality)]) ).
cnf(63,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[58,47,62,theory(equality)]) ).
cnf(87,plain,
double_divide(inverse(X),Y) = inverse(double_divide(X,inverse(Y))),
inference('PARAMODULATE',[status(thm)],[55,62,theory(equality)]) ).
cnf(88,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(double_divide(c3,b3),inverse(a3)),
inference('REWRITE',[status(thm)],[63,47,87,theory(equality)]) ).
cnf(175,plain,
inverse(double_divide(inverse(X),double_divide(Y,Z))) = double_divide(Z,inverse(double_divide(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[60,87,theory(equality)]),47,theory(equality)]) ).
cnf(310,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[88,62,theory(equality)]),55,47,175,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP101-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n015.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 23:52:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 *
% 0.20/0.47 *
% 0.20/0.48 #<PACKAGE "SNARK-USER">
% 0.20/0.48 *
% 0.20/0.48 SNARK-TPTP-OPTIONS
% 0.20/0.48 *
% 0.20/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48 (USE-FACTORING :POS)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48 *
% 0.20/0.48 "."
% 0.20/0.48 *
% 0.20/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T23:52:23
% 0.20/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n015.cluster.edu at 2022-06-13T23:52:23
% 0.20/0.49
% 0.53/0.75 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.53/0.75
% 0.53/0.75 #||
% 0.53/0.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.75 % SZS output start Refutation
% See solution above
% 0.53/0.75 ||#
% 0.53/0.75
% 0.53/0.75 ; Summary of computation:
% 0.53/0.75 ; 950 formulas have been input or derived (from 42 formulas).
% 0.53/0.75 ; 310 (33%) were retained. Of these,
% 0.53/0.75 ; 67 (22%) were simplified or subsumed later,
% 0.53/0.75 ; 243 (78%) are still being kept.
% 0.53/0.75 ;
% 0.53/0.75 ; Run time in seconds excluding printing time:
% 0.53/0.76 ; 0.002 1% Read assertion file (1 call)
% 0.53/0.76 ; 0.000 0% Assert (5 calls)
% 0.53/0.76 ; 0.041 15% Process new row (918 calls)
% 0.53/0.76 ; 0.001 0% Resolution (82 calls)
% 0.53/0.76 ; 0.014 5% Paramodulation (41 calls)
% 0.53/0.76 ; 0.000 0% Condensing (4 calls)
% 0.53/0.76 ; 0.002 1% Forward subsumption (4 calls)
% 0.53/0.76 ; 0.001 0% Backward subsumption (4 calls)
% 0.53/0.76 ; 0.048 18% Forward simplification (829 calls)
% 0.53/0.76 ; 0.023 8% Backward simplification (310 calls)
% 0.53/0.76 ; 0.116 42% Ordering (17,583 calls)
% 0.53/0.76 ; 0.000 0% Sortal reasoning (32 calls)
% 0.53/0.76 ; 0.000 0% Purity testing (1 call)
% 0.53/0.76 ; 0.025 9% Other
% 0.53/0.76 ; 0.273 Total
% 0.53/0.76 ; 0.278 Real time
% 0.53/0.76 ;
% 0.53/0.76 ; Term-hash-array has 872 terms in all.
% 0.53/0.76 ; Feature-vector-row-index has 0 entries (1 at peak, 4 added, 4 deleted).
% 0.53/0.76 ; Feature-vector-row-index has 1 node (29 at peak, 104 added, 103 deleted).
% 0.53/0.76 ; Retrieved 0 possibly forward subsuming rows in 4 calls.
% 0.53/0.76 ; Retrieved 0 possibly backward subsumed rows in 4 calls.
% 0.53/0.76 ; Path-index has 652 entries (652 at peak, 999 added, 347 deleted).
% 0.53/0.76 ; Path-index has 755 nodes (755 at peak, 1,285 added, 530 deleted).
% 0.53/0.76 ; Trie-index has 652 entries (652 at peak, 999 added, 347 deleted).
% 0.53/0.76 ; Trie-index has 2,124 nodes (2,124 at peak, 3,453 added, 1,329 deleted).
% 0.53/0.76 ; Retrieved 11,276 generalization terms in 5,615 calls.
% 0.53/0.76 ; Retrieved 3,973 instance terms in 659 calls.
% 0.53/0.76 ; Retrieved 1,982 unifiable terms in 335 calls.
% 0.53/0.76 ;
% 0.53/0.76 ; The agenda of rows to process has 1 entry:
% 0.53/0.76 ; 1 with value 26
% 0.53/0.76 ; The agenda of rows to give has 219 entries:
% 0.53/0.76 ; 4 with value (4 22) 20 with value (4 26) 38 with value (4 30)
% 0.53/0.76 ; 29 with value (4 23) 34 with value (4 27) 23 with value (4 31)
% 0.53/0.76 ; 12 with value (4 24) 21 with value (4 28) 10 with value (4 32)
% 0.53/0.76 ; 15 with value (4 25) 9 with value (4 29) 4 with value (4 33)
% 0.53/0.76 Evaluation took:
% 0.53/0.76 0.278 seconds of real time
% 0.53/0.76 0.240986 seconds of user run time
% 0.53/0.76 0.036963 seconds of system run time
% 0.53/0.76 [Run times include 0.007 seconds GC run time.]
% 0.53/0.76 0 calls to %EVAL
% 0.53/0.76 0 page faults and
% 0.53/0.76 17,747,120 bytes consed.
% 0.53/0.76 :PROOF-FOUND
% 0.53/0.76 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T23:52:23
% 0.53/0.76 :PROOF-FOUND
% 0.53/0.76 *
%------------------------------------------------------------------------------