%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP099-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n008.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 11:36:08 EDT 2022
% Result : Unsatisfiable 1.17s 1.34s
% Output : Refutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of clauses : 46 ( 41 unt; 0 nHn; 9 RR)
% Number of literals : 56 ( 55 equ; 17 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 74 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),double_divide(identity,Z))),double_divide(identity,identity)) = Y,
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))
| multiply(a4,b4) != multiply(b4,a4) ),
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))
| 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(X,Z)),double_divide(identity,Z))),inverse(identity)) = Y,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(9,plain,
double_divide(double_divide(X,double_divide(double_divide(Y,inverse(X)),inverse(identity))),inverse(identity)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]),inverse,theory(equality)]) ).
cnf(10,plain,
double_divide(double_divide(X,double_divide(inverse(Y),double_divide(identity,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(X,inverse(double_divide(Y,double_divide(X,inverse(identity))))),inverse(identity)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(13,plain,
double_divide(inverse(X),inverse(identity)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,identity,theory(equality)]),inverse,identity,theory(equality)]) ).
cnf(14,plain,
double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)) = double_divide(Y,double_divide(double_divide(X,inverse(Y)),inverse(identity))),
inference('PARAMODULATE',[status(thm)],[9,9,theory(equality)]) ).
cnf(15,plain,
double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),double_divide(identity,Z))),
inference('PARAMODULATE',[status(thm)],[9,8,theory(equality)]) ).
cnf(16,plain,
double_divide(double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)),inverse(identity)) = X,
inference('REWRITE',[status(thm)],[8,15,theory(equality)]) ).
cnf(18,plain,
double_divide(double_divide(identity,X),inverse(identity)) = double_divide(identity,double_divide(X,inverse(identity))),
inference('PARAMODULATE',[status(thm)],[9,16,theory(equality)]) ).
cnf(19,plain,
double_divide(double_divide(double_divide(identity,X),inverse(identity)),inverse(identity)) = double_divide(Y,double_divide(double_divide(X,inverse(Y)),inverse(identity))),
inference('REWRITE',[status(thm)],[14,18,theory(equality)]) ).
cnf(21,plain,
double_divide(double_divide(double_divide(identity,X),inverse(identity)),inverse(identity)) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),double_divide(identity,Z))),
inference('REWRITE',[status(thm)],[15,18,theory(equality)]) ).
cnf(23,plain,
inverse(identity) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,identity,theory(equality)]),13,inverse,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))
| inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
inference('REWRITE',[status(thm)],[7,23,theory(equality)]) ).
cnf(25,plain,
inverse(double_divide(X,double_divide(inverse(Y),double_divide(identity,inverse(X))))) = Y,
inference('REWRITE',[status(thm)],[10,inverse,23,theory(equality)]) ).
cnf(26,plain,
inverse(double_divide(X,inverse(double_divide(Y,inverse(X))))) = Y,
inference('REWRITE',[status(thm)],[11,inverse,23,theory(equality)]) ).
cnf(27,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[13,inverse,23,theory(equality)]) ).
cnf(28,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)],[24,27,theory(equality)]) ).
cnf(29,plain,
inverse(double_divide(identity,X)) = double_divide(identity,inverse(X)),
inference('REWRITE',[status(thm)],[18,inverse,23,theory(equality)]) ).
cnf(30,plain,
inverse(double_divide(X,double_divide(inverse(Y),inverse(double_divide(identity,X))))) = Y,
inference('REWRITE',[status(thm)],[25,29,theory(equality)]) ).
cnf(31,plain,
double_divide(identity,X) = double_divide(Y,inverse(double_divide(X,inverse(Y)))),
inference('REWRITE',[status(thm)],[19,27,inverse,23,theory(equality)]) ).
cnf(32,plain,
inverse(double_divide(identity,X)) = X,
inference('REWRITE',[status(thm)],[26,31,theory(equality)]) ).
cnf(34,plain,
inverse(double_divide(X,double_divide(inverse(Y),X))) = Y,
inference('REWRITE',[status(thm)],[30,32,theory(equality)]) ).
cnf(35,plain,
inverse(X) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),double_divide(identity,Z))),
inference('REWRITE',[status(thm)],[21,32,inverse,23,theory(equality)]) ).
cnf(38,plain,
inverse(X) = double_divide(identity,X),
inference('PARAMODULATE',[status(thm)],[27,32,theory(equality)]) ).
cnf(39,plain,
inverse(X) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),inverse(Z))),
inference('REWRITE',[status(thm)],[35,38,theory(equality)]) ).
cnf(40,plain,
inverse(X) = double_divide(Y,inverse(double_divide(X,inverse(Y)))),
inference('REWRITE',[status(thm)],[31,38,theory(equality)]) ).
cnf(41,plain,
inverse(X) = double_divide(Y,double_divide(inverse(X),Y)),
inference('PARAMODULATE',[status(thm)],[27,34,theory(equality)]) ).
cnf(43,plain,
X = double_divide(Y,double_divide(X,Y)),
inference('PARAMODULATE',[status(thm)],[41,27,theory(equality)]) ).
cnf(44,plain,
X = double_divide(double_divide(Y,X),Y),
inference('PARAMODULATE',[status(thm)],[43,43,theory(equality)]) ).
cnf(45,plain,
inverse(double_divide(X,inverse(Y))) = double_divide(inverse(X),Y),
inference('PARAMODULATE',[status(thm)],[44,40,theory(equality)]) ).
cnf(46,plain,
( double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(double_divide(c3,b3),inverse(a3))
| inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
inference('REWRITE',[status(thm)],[28,27,45,theory(equality)]) ).
cnf(49,plain,
X = double_divide(Y,double_divide(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[39,44,theory(equality)]),27,theory(equality)]) ).
cnf(53,plain,
inverse(X) = double_divide(double_divide(Y,double_divide(X,Z)),double_divide(inverse(Y),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[39,39,theory(equality)]),27,theory(equality)]) ).
cnf(55,plain,
double_divide(X,Y) = double_divide(Y,X),
inference('PARAMODULATE',[status(thm)],[44,49,theory(equality)]) ).
cnf(57,plain,
double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(double_divide(c3,b3),inverse(a3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[46,55,theory(equality)]),theory(equality)]) ).
cnf(71,plain,
inverse(X) = double_divide(double_divide(inverse(Y),double_divide(X,Z)),double_divide(Y,Z)),
inference('PARAMODULATE',[status(thm)],[53,27,theory(equality)]) ).
cnf(85,plain,
double_divide(inverse(X),double_divide(Y,Z)) = double_divide(double_divide(X,Z),inverse(Y)),
inference('PARAMODULATE',[status(thm)],[43,71,theory(equality)]) ).
cnf(86,plain,
double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(inverse(c3),double_divide(a3,b3)),
inference('REWRITE',[status(thm)],[57,85,theory(equality)]) ).
cnf(632,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[86,55,theory(equality)]),theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP099-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 12:58:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 *
% 0.20/0.46 *
% 0.20/0.47 #<PACKAGE "SNARK-USER">
% 0.20/0.47 *
% 0.20/0.47 SNARK-TPTP-OPTIONS
% 0.20/0.47 *
% 0.20/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47 (USE-FACTORING :POS)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47 *
% 0.20/0.47 "."
% 0.20/0.47 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T12:58:22
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n008.cluster.edu at 2022-06-13T12:58:22
% 0.20/0.48
% 1.17/1.34 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 1.17/1.34
% 1.17/1.34 #||
% 1.17/1.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.17/1.34 % SZS output start Refutation
% See solution above
% 1.17/1.34 ||#
% 1.17/1.34
% 1.17/1.34 ; Summary of computation:
% 1.17/1.34 ; 2149 formulas have been input or derived (from 50 formulas).
% 1.17/1.34 ; 632 (29%) were retained. Of these,
% 1.17/1.34 ; 80 (13%) were simplified or subsumed later,
% 1.17/1.34 ; 552 (87%) are still being kept.
% 1.17/1.34 ;
% 1.17/1.34 ; Run time in seconds excluding printing time:
% 1.17/1.34 ; 0.002 0% Read assertion file (1 call)
% 1.17/1.34 ; 0.000 0% Assert (5 calls)
% 1.17/1.34 ; 0.071 8% Process new row (2,061 calls)
% 1.17/1.34 ; 0.002 0% Resolution (98 calls)
% 1.17/1.34 ; 0.030 3% Paramodulation (49 calls)
% 1.17/1.34 ; 0.000 0% Condensing (5 calls)
% 1.17/1.34 ; 0.000 0% Forward subsumption (5 calls)
% 1.17/1.34 ; 0.000 0% Backward subsumption (5 calls)
% 1.17/1.34 ; 0.198 23% Forward simplification (1,972 calls)
% 1.17/1.34 ; 0.059 7% Backward simplification (632 calls)
% 1.17/1.34 ; 0.475 55% Ordering (80,191 calls)
% 1.17/1.34 ; 0.001 0% Sortal reasoning (32 calls)
% 1.17/1.34 ; 0.000 0% Purity testing (1 call)
% 1.17/1.34 ; 0.028 3% Other
% 1.17/1.34 ; 0.866 Total
% 1.17/1.34 ; 0.870 Real time
% 1.17/1.34 ;
% 1.17/1.34 ; Term-hash-array has 1,568 terms in all.
% 1.17/1.34 ; Feature-vector-row-index has 0 entries (1 at peak, 5 added, 5 deleted).
% 1.17/1.34 ; Feature-vector-row-index has 1 node (29 at peak, 127 added, 126 deleted).
% 1.17/1.34 ; Retrieved 0 possibly forward subsuming rows in 5 calls.
% 1.17/1.34 ; Retrieved 0 possibly backward subsumed rows in 5 calls.
% 1.17/1.34 ; Path-index has 1,369 entries (1,369 at peak, 1,703 added, 334 deleted).
% 1.17/1.34 ; Path-index has 604 nodes (604 at peak, 1,074 added, 470 deleted).
% 1.17/1.34 ; Trie-index has 1,369 entries (1,369 at peak, 1,703 added, 334 deleted).
% 1.17/1.34 ; Trie-index has 4,183 nodes (4,183 at peak, 5,502 added, 1,319 deleted).
% 1.17/1.34 ; Retrieved 47,530 generalization terms in 16,720 calls.
% 1.17/1.34 ; Retrieved 15,321 instance terms in 1,329 calls.
% 1.17/1.34 ; Retrieved 5,672 unifiable terms in 392 calls.
% 1.17/1.34 ;
% 1.17/1.34 ; The agenda of rows to process has 17 entries:
% 1.17/1.34 ; 11 with value 25 4 with value 28 2 with value 29
% 1.17/1.34 ; The agenda of rows to give has 518 entries:
% 1.17/1.34 ; 18 with value (4 24) 28 with value (4 27) 67 with value (4 30)
% 1.17/1.34 ; 37 with value (4 25) 39 with value (4 28) 118 with value (4 31)
% 1.17/1.34 ; 16 with value (4 26) 108 with value (4 29) 87 with value (4 32)
% 1.17/1.34 Evaluation took:
% 1.17/1.34 0.871 seconds of real time
% 1.17/1.34 0.754048 seconds of user run time
% 1.17/1.34 0.115996 seconds of system run time
% 1.17/1.34 [Run times include 0.017 seconds GC run time.]
% 1.17/1.34 0 calls to %EVAL
% 1.17/1.34 0 page faults and
% 1.17/1.34 56,745,160 bytes consed.
% 1.17/1.34 :PROOF-FOUND
% 1.17/1.34 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T12:58:23
% 1.17/1.34 :PROOF-FOUND
% 1.17/1.34 *
%------------------------------------------------------------------------------