%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP489-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n003.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 11:39:07 EDT 2022
% Result : Unsatisfiable 0.39s 0.57s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 5 RR)
% Number of literals : 38 ( 37 equ; 3 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 : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(X,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X,identity),double_divide(Y,Z))),Y),identity)) = Z,
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_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/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(X,inverse(double_divide(double_divide(identity,double_divide(inverse(X),double_divide(Y,Z))),Y))) = Z,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(10,plain,
double_divide(X,inverse(double_divide(double_divide(identity,inverse(inverse(X))),Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(13,plain,
double_divide(X,inverse(identity)) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
inference('PARAMODULATE',[status(thm)],[10,identity,theory(equality)]) ).
cnf(14,plain,
double_divide(X,double_divide(X,inverse(identity))) = inverse(identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,inverse,theory(equality)]),13,theory(equality)]) ).
cnf(19,plain,
double_divide(X,inverse(Y)) = inverse(inverse(double_divide(double_divide(identity,double_divide(inverse(double_divide(identity,inverse(inverse(X)))),double_divide(Z,Y))),Z))),
inference('PARAMODULATE',[status(thm)],[10,8,theory(equality)]) ).
cnf(20,plain,
double_divide(X,inverse(double_divide(identity,inverse(X)))) = inverse(identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,14,theory(equality)]),identity,theory(equality)]) ).
cnf(26,plain,
identity = inverse(identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20,identity,theory(equality)]),identity,theory(equality)]) ).
cnf(27,plain,
inverse(X) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
inference('REWRITE',[status(thm)],[13,inverse,26,theory(equality)]) ).
cnf(30,plain,
double_divide(X,inverse(double_divide(identity,inverse(X)))) = identity,
inference('REWRITE',[status(thm)],[20,26,theory(equality)]) ).
cnf(31,plain,
double_divide(identity,inverse(double_divide(identity,X))) = inverse(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,26,theory(equality)]),inverse,26,theory(equality)]) ).
cnf(32,plain,
double_divide(identity,inverse(double_divide(double_divide(identity,double_divide(identity,double_divide(X,Y))),X))) = Y,
inference('PARAMODULATE',[status(thm)],[8,26,theory(equality)]) ).
cnf(36,plain,
inverse(X) = inverse(double_divide(identity,inverse(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,30,theory(equality)]),10,inverse,theory(equality)]) ).
cnf(37,plain,
double_divide(X,inverse(Y)) = inverse(inverse(double_divide(double_divide(identity,double_divide(inverse(inverse(X)),double_divide(Z,Y))),Z))),
inference('REWRITE',[status(thm)],[19,36,theory(equality)]) ).
cnf(38,plain,
inverse(X) = inverse(inverse(inverse(X))),
inference('REWRITE',[status(thm)],[27,36,theory(equality)]) ).
cnf(41,plain,
double_divide(inverse(X),inverse(double_divide(double_divide(identity,inverse(X)),Y))) = inverse(Y),
inference('PARAMODULATE',[status(thm)],[10,38,theory(equality)]) ).
cnf(44,plain,
inverse(double_divide(identity,X)) = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[36,10,theory(equality)]),inverse,26,theory(equality)]) ).
cnf(45,plain,
double_divide(identity,inverse(inverse(X))) = inverse(X),
inference('REWRITE',[status(thm)],[31,44,theory(equality)]) ).
cnf(47,plain,
double_divide(X,inverse(double_divide(inverse(X),Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[10,45,theory(equality)]) ).
cnf(52,plain,
inverse(X) = inverse(double_divide(double_divide(identity,double_divide(identity,double_divide(Y,X))),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[44,8,theory(equality)]),38,26,theory(equality)]) ).
cnf(54,plain,
double_divide(identity,inverse(X)) = X,
inference('REWRITE',[status(thm)],[32,52,theory(equality)]) ).
cnf(58,plain,
double_divide(inverse(X),inverse(double_divide(X,Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[41,54,theory(equality)]) ).
cnf(60,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[54,38,theory(equality)]),54,theory(equality)]) ).
cnf(63,plain,
double_divide(X,inverse(Y)) = double_divide(double_divide(identity,double_divide(X,double_divide(Z,Y))),Z),
inference('REWRITE',[status(thm)],[37,60,theory(equality)]) ).
cnf(69,plain,
double_divide(identity,X) = inverse(X),
inference('PARAMODULATE',[status(thm)],[54,60,theory(equality)]) ).
cnf(71,plain,
double_divide(X,inverse(Y)) = double_divide(inverse(double_divide(X,double_divide(Z,Y))),Z),
inference('REWRITE',[status(thm)],[63,69,theory(equality)]) ).
cnf(72,plain,
inverse(X) = double_divide(inverse(double_divide(X,inverse(Y))),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[71,inverse,theory(equality)]),inverse,26,theory(equality)]) ).
cnf(81,plain,
X = double_divide(Y,double_divide(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[72,58,theory(equality)]),60,theory(equality)]) ).
cnf(89,plain,
double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
inference('PARAMODULATE',[status(thm)],[47,81,theory(equality)]) ).
cnf(91,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[7,89,theory(equality)]) ).
cnf(92,plain,
double_divide(X,inverse(double_divide(Y,Z))) = double_divide(inverse(double_divide(X,Y)),Z),
inference('PARAMODULATE',[status(thm)],[71,81,theory(equality)]) ).
cnf(93,plain,
$false,
inference('REWRITE',[status(thm)],[91,60,89,92,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP489-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.14 % Command : run-snark %s %d
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 10:29:55 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.49 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.50 *
% 0.21/0.50 *
% 0.21/0.50 #<PACKAGE "SNARK-USER">
% 0.21/0.50 *
% 0.21/0.50 SNARK-TPTP-OPTIONS
% 0.21/0.50 *
% 0.21/0.50 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.50 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.50 (USE-FACTORING :POS)
% 0.21/0.50 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.50 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.50 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.50 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.50 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.50 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.50 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.50 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.50 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.50 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.50 *
% 0.21/0.50 "."
% 0.21/0.50 *
% 0.21/0.50 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T10:29:55
% 0.21/0.50 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n003.cluster.edu at 2022-06-14T10:29:55
% 0.21/0.52
% 0.39/0.57 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.39/0.57
% 0.39/0.57 #||
% 0.39/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.57 % SZS output start Refutation
% See solution above
% 0.39/0.57 ||#
% 0.39/0.57
% 0.39/0.57 ; Summary of computation:
% 0.39/0.57 ; 257 formulas have been input or derived (from 26 formulas).
% 0.39/0.57 ; 93 (36%) were retained. Of these,
% 0.39/0.57 ; 71 (76%) were simplified or subsumed later,
% 0.39/0.57 ; 22 (24%) are still being kept.
% 0.39/0.57 ;
% 0.39/0.57 ; Run time in seconds excluding printing time:
% 0.39/0.57 ; 0.001 2% Read assertion file (1 call)
% 0.39/0.57 ; 0.000 0% Assert (5 calls)
% 0.39/0.57 ; 0.016 26% Process new row (254 calls)
% 0.39/0.57 ; 0.001 2% Resolution (50 calls)
% 0.39/0.57 ; 0.005 8% Paramodulation (25 calls)
% 0.39/0.57 ; 0.003 5% Forward simplification (239 calls)
% 0.39/0.57 ; 0.009 15% Backward simplification (93 calls)
% 0.39/0.57 ; 0.003 5% Ordering (549 calls)
% 0.39/0.57 ; 0.001 2% Sortal reasoning (32 calls)
% 0.39/0.57 ; 0.001 2% Purity testing (1 call)
% 0.39/0.57 ; 0.021 34% Other
% 0.39/0.57 ; 0.061 Total
% 0.39/0.57 ; 0.067 Real time
% 0.39/0.57 ;
% 0.39/0.57 ; Term-hash-array has 329 terms in all.
% 0.39/0.57 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.39/0.57 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.39/0.57 ; Path-index has 87 entries (126 at peak, 412 added, 325 deleted).
% 0.39/0.57 ; Path-index has 546 nodes (567 at peak, 959 added, 413 deleted).
% 0.39/0.57 ; Trie-index has 87 entries (126 at peak, 412 added, 325 deleted).
% 0.39/0.57 ; Trie-index has 293 nodes (526 at peak, 1,579 added, 1,286 deleted).
% 0.39/0.57 ; Retrieved 563 generalization terms in 1,385 calls.
% 0.39/0.57 ; Retrieved 209 instance terms in 107 calls.
% 0.39/0.57 ; Retrieved 412 unifiable terms in 171 calls.
% 0.39/0.57 ;
% 0.39/0.57 ; The agenda of rows to process has 1 entry:
% 0.39/0.57 ; 1 with value 22
% 0.39/0.57 ; The agenda of rows to give has 11 entries:
% 0.39/0.57 ; 2 with value (4 18) 4 with value (4 22) 1 with value (4 24)
% 0.39/0.57 ; 1 with value (4 19) 1 with value (4 23) 2 with value (4 27)
% 0.39/0.57 Evaluation took:
% 0.39/0.57 0.067 seconds of real time
% 0.39/0.57 0.055027 seconds of user run time
% 0.39/0.57 0.012092 seconds of system run time
% 0.39/0.57 0 calls to %EVAL
% 0.39/0.57 0 page faults and
% 0.39/0.57 6,198,744 bytes consed.
% 0.39/0.57 :PROOF-FOUND
% 0.39/0.57 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T10:29:55
% 0.39/0.57 :PROOF-FOUND
% 0.39/0.57 *
%------------------------------------------------------------------------------