TSTP Solution File: GRP100-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP100-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n011.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 0.46s 0.70s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 45 ( 40 unt; 0 nHn; 10 RR)
% Number of literals : 55 ( 54 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 : 76 ( 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,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(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,
inverse(identity) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,24,theory(equality)]),12,theory(equality)]) ).
cnf(31,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)],[7,30,theory(equality)]) ).
cnf(32,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[8,22,inverse,30,theory(equality)]) ).
cnf(34,plain,
inverse(X) = double_divide(Y,double_divide(inverse(X),Y)),
inference('REWRITE',[status(thm)],[16,32,theory(equality)]) ).
cnf(35,plain,
inverse(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),inverse(Z)))) = Y,
inference('REWRITE',[status(thm)],[22,32,theory(equality)]) ).
cnf(36,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)],[31,32,theory(equality)]) ).
cnf(37,plain,
inverse(X) = double_divide(Y,inverse(double_divide(X,inverse(Y)))),
inference('REWRITE',[status(thm)],[17,inverse,30,theory(equality)]) ).
cnf(38,plain,
inverse(double_divide(inverse(X),double_divide(inverse(X),inverse(Y)))) = Y,
inference('REWRITE',[status(thm)],[18,inverse,32,30,theory(equality)]) ).
cnf(45,plain,
X = double_divide(Y,double_divide(X,Y)),
inference('PARAMODULATE',[status(thm)],[34,32,theory(equality)]) ).
cnf(46,plain,
X = double_divide(double_divide(Y,X),Y),
inference('PARAMODULATE',[status(thm)],[45,45,theory(equality)]) ).
cnf(48,plain,
inverse(double_divide(X,inverse(Y))) = double_divide(inverse(X),Y),
inference('PARAMODULATE',[status(thm)],[46,37,theory(equality)]) ).
cnf(49,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)],[36,32,48,theory(equality)]) ).
cnf(51,plain,
inverse(double_divide(X,double_divide(X,inverse(Y)))) = Y,
inference('PARAMODULATE',[status(thm)],[38,38,theory(equality)]) ).
cnf(52,plain,
inverse(X) = double_divide(Y,double_divide(Y,inverse(X))),
inference('PARAMODULATE',[status(thm)],[32,51,theory(equality)]) ).
cnf(53,plain,
X = double_divide(Y,double_divide(Y,X)),
inference('PARAMODULATE',[status(thm)],[52,32,theory(equality)]) ).
cnf(54,plain,
double_divide(X,Y) = double_divide(Y,X),
inference('PARAMODULATE',[status(thm)],[46,53,theory(equality)]) ).
cnf(56,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)],[49,54,theory(equality)]),theory(equality)]) ).
cnf(93,plain,
inverse(X) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),inverse(Z))),
inference('PARAMODULATE',[status(thm)],[32,35,theory(equality)]) ).
cnf(130,plain,
double_divide(double_divide(X,double_divide(Y,Z)),inverse(Z)) = double_divide(inverse(X),Y),
inference('PARAMODULATE',[status(thm)],[46,93,theory(equality)]) ).
cnf(131,plain,
double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(X),double_divide(Z,Y)),
inference('PARAMODULATE',[status(thm)],[130,46,theory(equality)]) ).
cnf(132,plain,
double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(inverse(c3),double_divide(a3,b3)),
inference('REWRITE',[status(thm)],[56,131,theory(equality)]) ).
cnf(134,plain,
double_divide(X,double_divide(Y,Z)) = double_divide(inverse(Z),double_divide(inverse(X),Y)),
inference('PARAMODULATE',[status(thm)],[45,130,theory(equality)]) ).
cnf(167,plain,
double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(Y),double_divide(Z,X)),
inference('PARAMODULATE',[status(thm)],[131,54,theory(equality)]) ).
cnf(171,plain,
double_divide(inverse(double_divide(X,Y)),double_divide(Y,Z)) = double_divide(inverse(Z),X),
inference('REWRITE',[status(thm)],[130,167,theory(equality)]) ).
cnf(213,plain,
double_divide(inverse(X),double_divide(Y,Z)) = double_divide(inverse(Z),double_divide(Y,X)),
inference('PARAMODULATE',[status(thm)],[171,46,theory(equality)]) ).
cnf(265,plain,
double_divide(inverse(X),double_divide(Y,Z)) = double_divide(inverse(X),double_divide(Z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[213,134,theory(equality)]),32,theory(equality)]) ).
cnf(266,plain,
$false,
inference('REWRITE',[status(thm)],[132,265,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP100-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.12/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n011.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 : Tue Jun 14 11:30:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 *
% 0.18/0.45 *
% 0.18/0.46 #<PACKAGE "SNARK-USER">
% 0.18/0.46 *
% 0.18/0.46 SNARK-TPTP-OPTIONS
% 0.18/0.46 *
% 0.18/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46 (USE-FACTORING :POS)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.46 *
% 0.18/0.46 "."
% 0.18/0.46 *
% 0.18/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T11:30:49
% 0.18/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n011.cluster.edu at 2022-06-14T11:30:49
% 0.18/0.47
% 0.46/0.70 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.46/0.70
% 0.46/0.70 #||
% 0.46/0.70 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.70 % SZS output start Refutation
% See solution above
% 0.53/0.71 ||#
% 0.53/0.71
% 0.53/0.71 ; Summary of computation:
% 0.53/0.71 ; 1190 formulas have been input or derived (from 44 formulas).
% 0.53/0.71 ; 266 (22%) were retained. Of these,
% 0.53/0.71 ; 80 (30%) were simplified or subsumed later,
% 0.53/0.71 ; 186 (70%) are still being kept.
% 0.53/0.71 ;
% 0.53/0.71 ; Run time in seconds excluding printing time:
% 0.53/0.71 ; 0.001 0% Read assertion file (1 call)
% 0.53/0.71 ; 0.000 0% Assert (5 calls)
% 0.53/0.71 ; 0.021 9% Process new row (1,088 calls)
% 0.53/0.71 ; 0.002 1% Resolution (86 calls)
% 0.53/0.71 ; 0.022 9% Paramodulation (43 calls)
% 0.53/0.71 ; 0.000 0% Condensing (5 calls)
% 0.53/0.71 ; 0.000 0% Forward subsumption (5 calls)
% 0.53/0.71 ; 0.000 0% Backward subsumption (5 calls)
% 0.53/0.71 ; 0.043 18% Forward simplification (929 calls)
% 0.53/0.71 ; 0.018 8% Backward simplification (266 calls)
% 0.53/0.71 ; 0.104 44% Ordering (13,323 calls)
% 0.53/0.71 ; 0.001 0% Sortal reasoning (32 calls)
% 0.53/0.71 ; 0.000 0% Purity testing (1 call)
% 0.53/0.71 ; 0.027 11% Other
% 0.53/0.71 ; 0.239 Total
% 0.53/0.71 ; 0.249 Real time
% 0.53/0.71 ;
% 0.53/0.71 ; Term-hash-array has 709 terms in all.
% 0.53/0.71 ; Feature-vector-row-index has 0 entries (1 at peak, 5 added, 5 deleted).
% 0.53/0.71 ; Feature-vector-row-index has 1 node (29 at peak, 127 added, 126 deleted).
% 0.53/0.71 ; Retrieved 0 possibly forward subsuming rows in 5 calls.
% 0.53/0.71 ; Retrieved 0 possibly backward subsumed rows in 5 calls.
% 0.53/0.71 ; Path-index has 467 entries (476 at peak, 825 added, 358 deleted).
% 0.53/0.71 ; Path-index has 535 nodes (553 at peak, 1,014 added, 479 deleted).
% 0.53/0.71 ; Trie-index has 467 entries (476 at peak, 825 added, 358 deleted).
% 0.53/0.71 ; Trie-index has 1,629 nodes (1,653 at peak, 3,066 added, 1,437 deleted).
% 0.53/0.71 ; Retrieved 10,159 generalization terms in 6,339 calls.
% 0.53/0.71 ; Retrieved 3,653 instance terms in 489 calls.
% 0.53/0.71 ; Retrieved 2,053 unifiable terms in 344 calls.
% 0.53/0.71 ;
% 0.53/0.71 ; The agenda of rows to process has 61 entries:
% 0.53/0.71 ; 7 with value 27 7 with value 29 18 with value 31
% 0.53/0.71 ; 10 with value 28 13 with value 30 6 with value 32
% 0.53/0.71 ; The agenda of rows to give has 163 entries:
% 0.53/0.71 ; 1 with value (4 21) 17 with value (4 26) 21 with value (4 30)
% 0.53/0.71 ; 5 with value (4 23) 14 with value (4 27) 6 with value (4 31)
% 0.53/0.71 ; 22 with value (4 24) 24 with value (4 28) 8 with value (4 32)
% 0.53/0.71 ; 12 with value (4 25) 31 with value (4 29) 2 with value (4 35)
% 0.53/0.71 Evaluation took:
% 0.53/0.71 0.249 seconds of real time
% 0.53/0.71 0.2158 seconds of user run time
% 0.53/0.71 0.032919 seconds of system run time
% 0.53/0.71 [Run times include 0.005 seconds GC run time.]
% 0.53/0.71 0 calls to %EVAL
% 0.53/0.71 0 page faults and
% 0.53/0.71 16,392,696 bytes consed.
% 0.53/0.71 :PROOF-FOUND
% 0.53/0.71 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T11:30:50
% 0.53/0.71 :PROOF-FOUND
% 0.53/0.71 *
%------------------------------------------------------------------------------