%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP498-1 : TPTP v8.1.0. Released v2.6.0.
% 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 11:39:09 EDT 2022
% Result : Unsatisfiable 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 6 RR)
% Number of literals : 41 ( 40 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 67 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),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(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) = Z,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(9,plain,
identity = inverse(identity),
inference('PARAMODULATE',[status(thm)],[identity,8,theory(equality)]) ).
cnf(10,plain,
double_divide(identity,inverse(double_divide(X,double_divide(Y,X)))) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),9,inverse,theory(equality)]) ).
cnf(11,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X))),inverse(double_divide(X,inverse(Y)))) = Y,
inference('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]) ).
cnf(15,plain,
double_divide(double_divide(identity,inverse(X)),inverse(double_divide(identity,double_divide(Y,X)))) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,9,theory(equality)]),inverse,theory(equality)]) ).
cnf(16,plain,
double_divide(identity,inverse(double_divide(identity,inverse(X)))) = X,
inference('PARAMODULATE',[status(thm)],[10,inverse,theory(equality)]) ).
cnf(17,plain,
double_divide(identity,inverse(inverse(inverse(X)))) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(24,plain,
double_divide(identity,inverse(X)) = inverse(inverse(X)),
inference('PARAMODULATE',[status(thm)],[16,17,theory(equality)]) ).
cnf(27,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference('REWRITE',[status(thm)],[17,24,theory(equality)]) ).
cnf(28,plain,
double_divide(inverse(inverse(inverse(X))),inverse(double_divide(X,inverse(Y)))) = Y,
inference('REWRITE',[status(thm)],[11,24,theory(equality)]) ).
cnf(29,plain,
double_divide(inverse(inverse(X)),inverse(double_divide(identity,double_divide(Y,X)))) = Y,
inference('REWRITE',[status(thm)],[15,24,theory(equality)]) ).
cnf(30,plain,
inverse(inverse(double_divide(X,double_divide(Y,X)))) = Y,
inference('REWRITE',[status(thm)],[10,24,theory(equality)]) ).
cnf(32,plain,
double_divide(identity,X) = inverse(X),
inference('PARAMODULATE',[status(thm)],[24,27,theory(equality)]) ).
cnf(33,plain,
double_divide(inverse(inverse(X)),inverse(inverse(double_divide(Y,X)))) = Y,
inference('REWRITE',[status(thm)],[29,32,theory(equality)]) ).
cnf(42,plain,
double_divide(inverse(double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) = Z,
inference('REWRITE',[status(thm)],[8,32,theory(equality)]) ).
cnf(44,plain,
double_divide(inverse(double_divide(X,Y)),inverse(double_divide(inverse(inverse(inverse(Y))),double_divide(Z,X)))) = Z,
inference('PARAMODULATE',[status(thm)],[42,27,theory(equality)]) ).
cnf(46,plain,
inverse(inverse(X)) = double_divide(Y,double_divide(X,Y)),
inference('PARAMODULATE',[status(thm)],[27,30,theory(equality)]) ).
cnf(52,plain,
double_divide(inverse(inverse(inverse(X))),inverse(inverse(X))) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[28,9,theory(equality)]),inverse,theory(equality)]) ).
cnf(53,plain,
double_divide(inverse(inverse(inverse(X))),inverse(double_divide(X,Y))) = inverse(inverse(inverse(Y))),
inference('PARAMODULATE',[status(thm)],[28,27,theory(equality)]) ).
cnf(54,plain,
double_divide(inverse(X),X) = identity,
inference('PARAMODULATE',[status(thm)],[52,27,theory(equality)]) ).
cnf(55,plain,
inverse(inverse(inverse(X))) = inverse(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[46,54,theory(equality)]),inverse,theory(equality)]) ).
cnf(57,plain,
double_divide(inverse(double_divide(X,Y)),inverse(double_divide(inverse(Y),double_divide(Z,X)))) = Z,
inference('REWRITE',[status(thm)],[44,55,theory(equality)]) ).
cnf(58,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[27,55,theory(equality)]) ).
cnf(59,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference('REWRITE',[status(thm)],[33,58,theory(equality)]) ).
cnf(64,plain,
double_divide(inverse(X),inverse(double_divide(X,Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[53,58,55,theory(equality)]) ).
cnf(66,plain,
double_divide(inverse(X),inverse(Y)) = inverse(double_divide(Y,X)),
inference('PARAMODULATE',[status(thm)],[64,59,theory(equality)]) ).
cnf(68,plain,
inverse(double_divide(double_divide(inverse(X),double_divide(Y,Z)),double_divide(Z,X))) = Y,
inference('REWRITE',[status(thm)],[57,66,theory(equality)]) ).
cnf(70,plain,
double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
inference('PARAMODULATE',[status(thm)],[66,58,theory(equality)]) ).
cnf(71,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[7,70,theory(equality)]) ).
cnf(72,plain,
double_divide(inverse(X),Y) = inverse(double_divide(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[66,58,theory(equality)]) ).
cnf(74,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
inference('REWRITE',[status(thm)],[71,72,theory(equality)]) ).
cnf(85,plain,
inverse(X) = double_divide(double_divide(inverse(Y),double_divide(X,Z)),double_divide(Z,Y)),
inference('PARAMODULATE',[status(thm)],[58,68,theory(equality)]) ).
cnf(94,plain,
double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(Y),double_divide(Z,X)),
inference('PARAMODULATE',[status(thm)],[59,85,theory(equality)]) ).
cnf(95,plain,
$false,
inference('REWRITE',[status(thm)],[74,94,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP498-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 15:07:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 *
% 0.19/0.45 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46 (USE-FACTORING :POS)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46 *
% 0.19/0.46 "."
% 0.19/0.46 *
% 0.19/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T15:07:12
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n006.cluster.edu at 2022-06-13T15:07:12
% 0.19/0.47
% 0.19/0.53 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.19/0.53
% 0.19/0.53 #||
% 0.19/0.53 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.53 % SZS output start Refutation
% See solution above
% 0.19/0.54 ||#
% 0.19/0.54
% 0.19/0.54 ; Summary of computation:
% 0.19/0.54 ; 417 formulas have been input or derived (from 32 formulas).
% 0.19/0.54 ; 95 (23%) were retained. Of these,
% 0.19/0.54 ; 59 (62%) were simplified or subsumed later,
% 0.19/0.54 ; 36 (38%) are still being kept.
% 0.19/0.54 ;
% 0.19/0.54 ; Run time in seconds excluding printing time:
% 0.19/0.54 ; 0.001 1% Read assertion file (1 call)
% 0.19/0.54 ; 0.000 0% Assert (5 calls)
% 0.19/0.54 ; 0.012 17% Process new row (385 calls)
% 0.19/0.54 ; 0.001 1% Resolution (62 calls)
% 0.19/0.54 ; 0.009 13% Paramodulation (31 calls)
% 0.19/0.54 ; 0.006 9% Forward simplification (315 calls)
% 0.19/0.54 ; 0.006 9% Backward simplification (95 calls)
% 0.19/0.54 ; 0.004 6% Ordering (967 calls)
% 0.19/0.54 ; 0.001 1% Sortal reasoning (32 calls)
% 0.19/0.54 ; 0.000 0% Purity testing (1 call)
% 0.19/0.54 ; 0.030 43% Other
% 0.19/0.54 ; 0.070 Total
% 0.19/0.54 ; 0.076 Real time
% 0.19/0.54 ;
% 0.19/0.54 ; Term-hash-array has 304 terms in all.
% 0.19/0.54 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.19/0.54 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.19/0.54 ; Path-index has 117 entries (127 at peak, 391 added, 274 deleted).
% 0.19/0.54 ; Path-index has 521 nodes (542 at peak, 872 added, 351 deleted).
% 0.19/0.54 ; Trie-index has 117 entries (127 at peak, 391 added, 274 deleted).
% 0.19/0.54 ; Trie-index has 531 nodes (558 at peak, 1,614 added, 1,083 deleted).
% 0.19/0.54 ; Retrieved 1,015 generalization terms in 1,877 calls.
% 0.19/0.54 ; Retrieved 246 instance terms in 117 calls.
% 0.19/0.54 ; Retrieved 695 unifiable terms in 226 calls.
% 0.19/0.54 ;
% 0.19/0.54 ; The agenda of rows to process has 30 entries:
% 0.19/0.54 ; 7 with value 21 3 with value 26 4 with value 29
% 0.19/0.54 ; 6 with value 22 2 with value 27 3 with value 30
% 0.19/0.54 ; 2 with value 23 3 with value 28
% 0.19/0.54 ; The agenda of rows to give has 20 entries:
% 0.19/0.54 ; 1 with value (4 21) 1 with value (4 24) 1 with value (4 27)
% 0.19/0.54 ; 1 with value (4 23) 8 with value (4 26) 8 with value (4 28)
% 0.19/0.54 Evaluation took:
% 0.19/0.54 0.076 seconds of real time
% 0.19/0.54 0.061443 seconds of user run time
% 0.19/0.54 0.014234 seconds of system run time
% 0.19/0.54 0 calls to %EVAL
% 0.19/0.54 0 page faults and
% 0.19/0.54 6,588,584 bytes consed.
% 0.19/0.54 :PROOF-FOUND
% 0.19/0.54 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T15:07:12
% 0.19/0.54 :PROOF-FOUND
% 0.19/0.54 *
%------------------------------------------------------------------------------