TSTP Solution File: GRP579-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP579-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n013.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 11:39:30 EDT 2022
% Result : Unsatisfiable 0.54s 0.75s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of clauses : 63 ( 63 unt; 0 nHn; 9 RR)
% Number of literals : 63 ( 62 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 110 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X,double_divide(double_divide(double_divide(Y,X),Z),double_divide(Y,identity))),double_divide(identity,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(X,double_divide(double_divide(double_divide(Y,X),Z),inverse(Y))),inverse(identity)) = Z,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(9,plain,
double_divide(double_divide(inverse(X),double_divide(double_divide(identity,Y),inverse(X))),inverse(identity)) = Y,
inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]) ).
cnf(10,plain,
double_divide(double_divide(X,double_divide(identity,inverse(Y))),inverse(identity)) = inverse(double_divide(Y,X)),
inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]) ).
cnf(13,plain,
double_divide(double_divide(X,Y),inverse(identity)) = double_divide(double_divide(double_divide(Z,double_divide(identity,X)),Y),inverse(Z)),
inference('PARAMODULATE',[status(thm)],[8,8,theory(equality)]) ).
cnf(15,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(X,Y),inverse(double_divide(Z,double_divide(double_divide(double_divide(U,Z),X),inverse(U)))))),inverse(identity)) = Y,
inference('PARAMODULATE',[status(thm)],[8,8,theory(equality)]) ).
cnf(16,plain,
double_divide(inverse(inverse(double_divide(identity,X))),inverse(identity)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(17,plain,
double_divide(double_divide(inverse(X),double_divide(inverse(identity),inverse(X))),inverse(identity)) = identity,
inference('PARAMODULATE',[status(thm)],[9,inverse,theory(equality)]) ).
cnf(18,plain,
double_divide(double_divide(inverse(identity),X),inverse(identity)) = double_divide(double_divide(inverse(Y),X),inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,8,theory(equality)]),inverse,theory(equality)]) ).
cnf(22,plain,
double_divide(inverse(inverse(inverse(identity))),inverse(identity)) = identity,
inference('PARAMODULATE',[status(thm)],[16,inverse,theory(equality)]) ).
cnf(26,plain,
double_divide(inverse(X),inverse(identity)) = inverse(double_divide(identity,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(27,plain,
inverse(double_divide(identity,inverse(double_divide(identity,X)))) = X,
inference('REWRITE',[status(thm)],[16,26,theory(equality)]) ).
cnf(28,plain,
inverse(double_divide(identity,inverse(inverse(identity)))) = identity,
inference('REWRITE',[status(thm)],[22,26,theory(equality)]) ).
cnf(29,plain,
double_divide(double_divide(inverse(identity),inverse(inverse(X))),inverse(identity)) = double_divide(identity,inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,10,theory(equality)]),inverse,theory(equality)]) ).
cnf(30,plain,
double_divide(double_divide(X,inverse(double_divide(Y,double_divide(identity,X)))),inverse(identity)) = double_divide(identity,inverse(Y)),
inference('PARAMODULATE',[status(thm)],[8,10,theory(equality)]) ).
cnf(32,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(inverse(double_divide(X,Y)),Z),inverse(double_divide(Y,double_divide(identity,inverse(X)))))),inverse(identity)) = Z,
inference('PARAMODULATE',[status(thm)],[8,10,theory(equality)]) ).
cnf(33,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(inverse(double_divide(identity,X)),Y),inverse(inverse(X)))),inverse(identity)) = Y,
inference('PARAMODULATE',[status(thm)],[8,26,theory(equality)]) ).
cnf(36,plain,
double_divide(X,inverse(identity)) = inverse(double_divide(identity,double_divide(identity,inverse(double_divide(identity,X))))),
inference('PARAMODULATE',[status(thm)],[26,27,theory(equality)]) ).
cnf(43,plain,
double_divide(double_divide(X,double_divide(inverse(identity),X)),inverse(identity)) = identity,
inference('PARAMODULATE',[status(thm)],[17,27,theory(equality)]) ).
cnf(45,plain,
inverse(double_divide(identity,X)) = double_divide(inverse(identity),double_divide(identity,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,43,theory(equality)]),26,inverse,theory(equality)]) ).
cnf(47,plain,
inverse(identity) = inverse(inverse(identity)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[45,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(49,plain,
inverse(identity) = identity,
inference('REWRITE',[status(thm)],[28,identity,47,theory(equality)]) ).
cnf(50,plain,
inverse(double_divide(X,double_divide(double_divide(double_divide(Y,X),Z),inverse(Y)))) = Z,
inference('REWRITE',[status(thm)],[8,inverse,49,theory(equality)]) ).
cnf(51,plain,
inverse(double_divide(X,double_divide(identity,inverse(Y)))) = inverse(double_divide(Y,X)),
inference('REWRITE',[status(thm)],[10,inverse,49,theory(equality)]) ).
cnf(55,plain,
inverse(double_divide(X,Y)) = double_divide(double_divide(double_divide(Z,double_divide(identity,X)),Y),inverse(Z)),
inference('REWRITE',[status(thm)],[13,inverse,49,theory(equality)]) ).
cnf(57,plain,
inverse(double_divide(identity,double_divide(double_divide(X,Y),X))) = Y,
inference('REWRITE',[status(thm)],[15,inverse,50,49,theory(equality)]) ).
cnf(58,plain,
inverse(double_divide(identity,X)) = double_divide(double_divide(inverse(Y),X),inverse(Y)),
inference('REWRITE',[status(thm)],[18,inverse,49,theory(equality)]) ).
cnf(62,plain,
inverse(inverse(X)) = inverse(double_divide(identity,X)),
inference('REWRITE',[status(thm)],[26,inverse,49,theory(equality)]) ).
cnf(64,plain,
inverse(inverse(double_divide(double_divide(X,Y),X))) = Y,
inference('REWRITE',[status(thm)],[57,62,theory(equality)]) ).
cnf(65,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference('REWRITE',[status(thm)],[27,62,theory(equality)]) ).
cnf(67,plain,
inverse(inverse(X)) = double_divide(double_divide(inverse(Y),X),inverse(Y)),
inference('REWRITE',[status(thm)],[58,62,theory(equality)]) ).
cnf(68,plain,
X = double_divide(identity,inverse(X)),
inference('REWRITE',[status(thm)],[29,65,62,inverse,49,theory(equality)]) ).
cnf(70,plain,
inverse(double_divide(X,Y)) = inverse(double_divide(Y,X)),
inference('REWRITE',[status(thm)],[51,68,theory(equality)]) ).
cnf(71,plain,
inverse(double_divide(X,inverse(double_divide(Y,double_divide(identity,X))))) = Y,
inference('REWRITE',[status(thm)],[30,68,inverse,49,theory(equality)]) ).
cnf(73,plain,
inverse(inverse(double_divide(double_divide(inverse(double_divide(X,Y)),Z),inverse(double_divide(Y,X))))) = Z,
inference('REWRITE',[status(thm)],[32,62,inverse,68,49,theory(equality)]) ).
cnf(74,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[33,inverse,68,67,62,49,theory(equality)]) ).
cnf(76,plain,
double_divide(double_divide(inverse(double_divide(X,Y)),Z),inverse(double_divide(Y,X))) = Z,
inference('REWRITE',[status(thm)],[73,74,theory(equality)]) ).
cnf(77,plain,
double_divide(double_divide(X,Y),X) = Y,
inference('REWRITE',[status(thm)],[64,74,theory(equality)]) ).
cnf(78,plain,
X = inverse(double_divide(identity,X)),
inference('REWRITE',[status(thm)],[62,74,theory(equality)]) ).
cnf(81,plain,
inverse(X) = double_divide(identity,X),
inference('REWRITE',[status(thm)],[36,78,inverse,49,theory(equality)]) ).
cnf(83,plain,
inverse(double_divide(X,Y)) = double_divide(double_divide(double_divide(Z,inverse(X)),Y),inverse(Z)),
inference('REWRITE',[status(thm)],[55,81,theory(equality)]) ).
cnf(84,plain,
inverse(double_divide(X,inverse(double_divide(Y,inverse(X))))) = Y,
inference('REWRITE',[status(thm)],[71,81,theory(equality)]) ).
cnf(91,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference('PARAMODULATE',[status(thm)],[77,77,theory(equality)]) ).
cnf(97,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(b3,c3)),a3)),
inference('PARAMODULATE',[status(thm)],[7,70,theory(equality)]) ).
cnf(103,plain,
inverse(double_divide(X,inverse(Y))) = double_divide(inverse(X),Y),
inference('PARAMODULATE',[status(thm)],[84,77,theory(equality)]) ).
cnf(108,plain,
double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(double_divide(b3,c3),inverse(a3)),
inference('REWRITE',[status(thm)],[97,74,103,theory(equality)]) ).
cnf(109,plain,
inverse(double_divide(X,Y)) = double_divide(inverse(X),inverse(Y)),
inference('PARAMODULATE',[status(thm)],[103,74,theory(equality)]) ).
cnf(110,plain,
inverse(double_divide(inverse(X),Y)) = double_divide(inverse(Y),X),
inference('PARAMODULATE',[status(thm)],[70,103,theory(equality)]) ).
cnf(111,plain,
inverse(double_divide(inverse(X),Y)) = double_divide(X,inverse(Y)),
inference('PARAMODULATE',[status(thm)],[74,103,theory(equality)]) ).
cnf(132,plain,
inverse(double_divide(inverse(X),double_divide(Y,Z))) = double_divide(inverse(double_divide(Z,Y)),X),
inference('PARAMODULATE',[status(thm)],[110,70,theory(equality)]) ).
cnf(141,plain,
inverse(double_divide(inverse(X),double_divide(Y,Z))) = double_divide(X,inverse(double_divide(Z,Y))),
inference('PARAMODULATE',[status(thm)],[111,70,theory(equality)]) ).
cnf(209,plain,
double_divide(X,inverse(double_divide(Y,Z))) = double_divide(X,inverse(double_divide(Z,Y))),
inference('PARAMODULATE',[status(thm)],[76,91,theory(equality)]) ).
cnf(227,plain,
inverse(double_divide(X,double_divide(Y,Z))) = double_divide(double_divide(X,inverse(Y)),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[91,83,theory(equality)]),109,theory(equality)]) ).
cnf(265,plain,
double_divide(X,double_divide(Y,Z)) = double_divide(X,double_divide(Z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[111,209,theory(equality)]),74,109,theory(equality)]) ).
cnf(296,plain,
inverse(double_divide(inverse(X),double_divide(Y,Z))) = double_divide(inverse(double_divide(X,Y)),Z),
inference('PARAMODULATE',[status(thm)],[227,109,theory(equality)]) ).
cnf(310,plain,
inverse(double_divide(X,inverse(double_divide(Y,Z)))) = double_divide(double_divide(X,Y),inverse(Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[227,109,theory(equality)]),74,theory(equality)]) ).
cnf(315,plain,
$false,
inference('REWRITE',[status(thm)],[108,265,74,132,296,141,310,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP579-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n013.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 12:18:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 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 2022-06-14T12:18:59
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n013.cluster.edu at 2022-06-14T12:18:59
% 0.19/0.47
% 0.54/0.75 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.54/0.75
% 0.54/0.75 #||
% 0.54/0.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.75 % SZS output start Refutation
% See solution above
% 0.54/0.75 ||#
% 0.54/0.75
% 0.54/0.75 ; Summary of computation:
% 0.54/0.75 ; 2048 formulas have been input or derived (from 54 formulas).
% 0.54/0.75 ; 315 (15%) were retained. Of these,
% 0.54/0.75 ; 117 (37%) were simplified or subsumed later,
% 0.54/0.75 ; 198 (63%) are still being kept.
% 0.54/0.75 ;
% 0.54/0.75 ; Run time in seconds excluding printing time:
% 0.54/0.75 ; 0.001 0% Read assertion file (1 call)
% 0.54/0.75 ; 0.001 0% Assert (5 calls)
% 0.54/0.75 ; 0.038 13% Process new row (1,861 calls)
% 0.54/0.75 ; 0.006 2% Resolution (106 calls)
% 0.54/0.75 ; 0.030 11% Paramodulation (53 calls)
% 0.54/0.75 ; 0.075 27% Forward simplification (1,772 calls)
% 0.54/0.75 ; 0.024 9% Backward simplification (315 calls)
% 0.54/0.75 ; 0.081 29% Ordering (12,657 calls)
% 0.54/0.75 ; 0.000 0% Sortal reasoning (32 calls)
% 0.54/0.75 ; 0.000 0% Purity testing (1 call)
% 0.54/0.75 ; 0.026 9% Other
% 0.54/0.75 ; 0.282 Total
% 0.54/0.75 ; 0.290 Real time
% 0.54/0.75 ;
% 0.54/0.75 ; Term-hash-array has 848 terms in all.
% 0.54/0.75 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.54/0.75 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.54/0.75 ; Path-index has 494 entries (503 at peak, 934 added, 440 deleted).
% 0.54/0.75 ; Path-index has 966 nodes (966 at peak, 1,571 added, 605 deleted).
% 0.54/0.75 ; Trie-index has 494 entries (503 at peak, 934 added, 440 deleted).
% 0.54/0.75 ; Trie-index has 1,960 nodes (2,057 at peak, 4,179 added, 2,219 deleted).
% 0.54/0.75 ; Retrieved 13,905 generalization terms in 11,684 calls.
% 0.54/0.75 ; Retrieved 2,549 instance terms in 458 calls.
% 0.54/0.75 ; Retrieved 3,255 unifiable terms in 415 calls.
% 0.54/0.75 ;
% 0.54/0.75 ; The agenda of backward simplifiable rows to process has 6 entries:
% 0.54/0.75 ; 6 with value 0
% 0.54/0.75 ; The agenda of rows to process has 88 entries:
% 0.54/0.75 ; 10 with value 26 27 with value 28 13 with value 30
% 0.54/0.75 ; 16 with value 27 21 with value 29 1 with value 31
% 0.54/0.75 ; The agenda of rows to give has 168 entries:
% 0.54/0.75 ; 3 with value (4 20) 29 with value (4 24) 14 with value (4 27)
% 0.54/0.75 ; 11 with value (4 21) 34 with value (4 25) 1 with value (4 28)
% 0.54/0.75 ; 13 with value (4 22) 41 with value (4 26) 4 with value (4 29)
% 0.54/0.75 ; 18 with value (4 23)
% 0.54/0.75 Evaluation took:
% 0.54/0.75 0.29 seconds of real time
% 0.54/0.75 0.256908 seconds of user run time
% 0.54/0.75 0.03056 seconds of system run time
% 0.54/0.75 [Run times include 0.006 seconds GC run time.]
% 0.54/0.75 0 calls to %EVAL
% 0.54/0.75 0 page faults and
% 0.54/0.75 18,873,480 bytes consed.
% 0.54/0.75 :PROOF-FOUND
% 0.54/0.75 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T12:18:59
% 0.54/0.75 :PROOF-FOUND
% 0.54/0.75 *
%------------------------------------------------------------------------------