%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP571-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n025.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 11:39:28 EDT 2022
% Result : Unsatisfiable 0.43s 0.60s
% Output : Refutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 7 RR)
% Number of literals : 37 ( 36 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 : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),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_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(X,double_divide(double_divide(Y,double_divide(X,Z)),inverse(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('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]) ).
cnf(10,plain,
double_divide(double_divide(X,double_divide(inverse(Y),inverse(inverse(X)))),inverse(identity)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(12,plain,
double_divide(inverse(X),inverse(identity)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(15,plain,
double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)) = inverse(X),
inference('PARAMODULATE',[status(thm)],[9,12,theory(equality)]) ).
cnf(16,plain,
inverse(X) = double_divide(Y,double_divide(inverse(X),inverse(inverse(Y)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,10,theory(equality)]),15,theory(equality)]) ).
cnf(17,plain,
inverse(X) = double_divide(Y,double_divide(double_divide(X,inverse(Y)),inverse(identity))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,9,theory(equality)]),15,theory(equality)]) ).
cnf(18,plain,
double_divide(double_divide(inverse(X),double_divide(inverse(X),inverse(inverse(inverse(Y))))),inverse(identity)) = Y,
inference('PARAMODULATE',[status(thm)],[8,16,theory(equality)]) ).
cnf(20,plain,
inverse(inverse(X)) = double_divide(identity,double_divide(X,inverse(identity))),
inference('PARAMODULATE',[status(thm)],[17,12,theory(equality)]) ).
cnf(22,plain,
inverse(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),inverse(Z)))) = inverse(inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,8,theory(equality)]),20,theory(equality)]) ).
cnf(24,plain,
inverse(inverse(identity)) = inverse(identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(30,plain,
identity = inverse(identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,24,theory(equality)]),12,theory(equality)]) ).
cnf(31,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[8,22,inverse,30,theory(equality)]) ).
cnf(33,plain,
inverse(X) = double_divide(Y,double_divide(inverse(X),Y)),
inference('REWRITE',[status(thm)],[16,31,theory(equality)]) ).
cnf(34,plain,
inverse(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),inverse(Z)))) = Y,
inference('REWRITE',[status(thm)],[22,31,theory(equality)]) ).
cnf(35,plain,
inverse(X) = double_divide(Y,inverse(double_divide(X,inverse(Y)))),
inference('REWRITE',[status(thm)],[17,inverse,30,theory(equality)]) ).
cnf(36,plain,
inverse(double_divide(inverse(X),double_divide(inverse(X),inverse(Y)))) = Y,
inference('REWRITE',[status(thm)],[18,inverse,31,30,theory(equality)]) ).
cnf(43,plain,
X = double_divide(Y,double_divide(X,Y)),
inference('PARAMODULATE',[status(thm)],[33,31,theory(equality)]) ).
cnf(44,plain,
X = double_divide(double_divide(Y,X),Y),
inference('PARAMODULATE',[status(thm)],[43,43,theory(equality)]) ).
cnf(46,plain,
inverse(double_divide(X,inverse(Y))) = double_divide(inverse(X),Y),
inference('PARAMODULATE',[status(thm)],[44,35,theory(equality)]) ).
cnf(47,plain,
double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(double_divide(c3,b3),inverse(a3)),
inference('REWRITE',[status(thm)],[7,31,46,theory(equality)]) ).
cnf(49,plain,
inverse(double_divide(X,double_divide(X,inverse(Y)))) = Y,
inference('PARAMODULATE',[status(thm)],[36,36,theory(equality)]) ).
cnf(50,plain,
inverse(X) = double_divide(Y,double_divide(Y,inverse(X))),
inference('PARAMODULATE',[status(thm)],[31,49,theory(equality)]) ).
cnf(51,plain,
X = double_divide(Y,double_divide(Y,X)),
inference('PARAMODULATE',[status(thm)],[50,31,theory(equality)]) ).
cnf(52,plain,
double_divide(X,Y) = double_divide(Y,X),
inference('PARAMODULATE',[status(thm)],[44,51,theory(equality)]) ).
cnf(55,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(double_divide(c3,b3),inverse(a3)),
inference('PARAMODULATE',[status(thm)],[47,52,theory(equality)]) ).
cnf(94,plain,
inverse(X) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),inverse(Z))),
inference('PARAMODULATE',[status(thm)],[31,34,theory(equality)]) ).
cnf(131,plain,
double_divide(double_divide(X,double_divide(Y,Z)),inverse(Z)) = double_divide(inverse(X),Y),
inference('PARAMODULATE',[status(thm)],[44,94,theory(equality)]) ).
cnf(132,plain,
double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(X),double_divide(Z,Y)),
inference('PARAMODULATE',[status(thm)],[131,44,theory(equality)]) ).
cnf(133,plain,
$false,
inference('REWRITE',[status(thm)],[55,132,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP571-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run-snark %s %d
% 0.12/0.35 % Computer : n025.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 600
% 0.12/0.35 % DateTime : Mon Jun 13 12:34:54 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.20/0.47 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 *
% 0.20/0.48 *
% 0.20/0.49 #<PACKAGE "SNARK-USER">
% 0.20/0.49 *
% 0.20/0.49 SNARK-TPTP-OPTIONS
% 0.20/0.49 *
% 0.20/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.49 (USE-FACTORING :POS)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.49 *
% 0.20/0.49 "."
% 0.20/0.49 *
% 0.20/0.49 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T12:34:54
% 0.20/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n025.cluster.edu at 2022-06-13T12:34:54
% 0.20/0.50
% 0.43/0.60 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.43/0.60
% 0.43/0.60 #||
% 0.43/0.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/0.61 % SZS output start Refutation
% See solution above
% 0.43/0.61 ||#
% 0.43/0.61
% 0.43/0.61 ; Summary of computation:
% 0.43/0.61 ; 780 formulas have been input or derived (from 39 formulas).
% 0.43/0.61 ; 133 (17%) were retained. Of these,
% 0.43/0.61 ; 42 (32%) were simplified or subsumed later,
% 0.43/0.61 ; 91 (68%) are still being kept.
% 0.43/0.61 ;
% 0.43/0.61 ; Run time in seconds excluding printing time:
% 0.43/0.61 ; 0.001 1% Read assertion file (1 call)
% 0.43/0.61 ; 0.001 1% Assert (5 calls)
% 0.43/0.61 ; 0.018 16% Process new row (707 calls)
% 0.43/0.61 ; 0.003 3% Resolution (76 calls)
% 0.43/0.61 ; 0.012 11% Paramodulation (38 calls)
% 0.43/0.61 ; 0.014 12% Forward simplification (570 calls)
% 0.43/0.61 ; 0.011 10% Backward simplification (133 calls)
% 0.43/0.61 ; 0.027 24% Ordering (3,505 calls)
% 0.43/0.61 ; 0.001 1% Sortal reasoning (32 calls)
% 0.43/0.61 ; 0.000 0% Purity testing (1 call)
% 0.43/0.61 ; 0.026 23% Other
% 0.43/0.61 ; 0.114 Total
% 0.43/0.61 ; 0.117 Real time
% 0.43/0.61 ;
% 0.43/0.61 ; Term-hash-array has 380 terms in all.
% 0.43/0.61 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.43/0.61 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.43/0.61 ; Path-index has 235 entries (256 at peak, 418 added, 183 deleted).
% 0.43/0.61 ; Path-index has 474 nodes (532 at peak, 766 added, 292 deleted).
% 0.43/0.61 ; Trie-index has 235 entries (256 at peak, 418 added, 183 deleted).
% 0.43/0.61 ; Trie-index has 881 nodes (959 at peak, 1,713 added, 832 deleted).
% 0.43/0.61 ; Retrieved 3,297 generalization terms in 3,214 calls.
% 0.43/0.61 ; Retrieved 671 instance terms in 222 calls.
% 0.43/0.61 ; Retrieved 1,160 unifiable terms in 273 calls.
% 0.43/0.61 ;
% 0.43/0.61 ; The agenda of backward simplifiable rows to process has 4 entries:
% 0.43/0.61 ; 4 with value 0
% 0.43/0.61 ; The agenda of rows to process has 43 entries:
% 0.43/0.61 ; 3 with value 22 2 with value 26 3 with value 30
% 0.43/0.61 ; 4 with value 23 7 with value 28 5 with value 31
% 0.43/0.61 ; 5 with value 24 4 with value 29 2 with value 33
% 0.43/0.61 ; 8 with value 25
% 0.43/0.61 ; The agenda of rows to give has 69 entries:
% 0.43/0.61 ; 1 with value (4 22) 10 with value (4 26) 28 with value (4 29)
% 0.43/0.61 ; 5 with value (4 23) 4 with value (4 27) 8 with value (4 30)
% 0.43/0.61 ; 1 with value (4 25) 12 with value (4 28)
% 0.43/0.61 Evaluation took:
% 0.43/0.61 0.118 seconds of real time
% 0.43/0.61 0.092297 seconds of user run time
% 0.43/0.61 0.025895 seconds of system run time
% 0.43/0.61 0 calls to %EVAL
% 0.43/0.61 0 page faults and
% 0.43/0.61 7,845,648 bytes consed.
% 0.43/0.61 :PROOF-FOUND
% 0.43/0.61 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T12:34:54
% 0.43/0.61 :PROOF-FOUND
% 0.43/0.61 *
%------------------------------------------------------------------------------