TSTP Solution File: GRP096-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP096-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n028.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 11:36:08 EDT 2022
% Result : Unsatisfiable 0.43s 0.59s
% Output : Refutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of clauses : 49 ( 43 unt; 0 nHn; 9 RR)
% Number of literals : 63 ( 62 equ; 22 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(X,inverse(divide(Y,divide(X,Z)))),Z) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X,Y) = divide(X,inverse(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),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(4,plain,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference('REWRITE',[status(thm)],[prove_these_axioms,multiply,theory(equality)]) ).
cnf(5,plain,
divide(divide(X,inverse(Y)),Z) = divide(U,inverse(divide(Y,divide(U,divide(X,Z))))),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(7,plain,
divide(divide(divide(X,inverse(Y)),Z),divide(X,Z)) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,5,theory(equality)]) ).
cnf(8,plain,
divide(X,inverse(divide(divide(Y,divide(Z,U)),divide(X,divide(Z,U))))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,5,theory(equality)]) ).
cnf(21,plain,
divide(X,divide(divide(Y,inverse(X)),divide(Y,inverse(Z)))) = Z,
inference('PARAMODULATE',[status(thm)],[7,7,theory(equality)]) ).
cnf(33,plain,
divide(divide(X,divide(Y,divide(Y,inverse(Z)))),X) = Z,
inference('PARAMODULATE',[status(thm)],[21,single_axiom,theory(equality)]) ).
cnf(35,plain,
divide(divide(divide(X,inverse(Y)),inverse(Z)),divide(X,inverse(U))) = divide(Y,inverse(divide(Z,U))),
inference('PARAMODULATE',[status(thm)],[5,21,theory(equality)]) ).
cnf(46,plain,
divide(divide(X,inverse(Y)),Z) = divide(divide(X,Z),divide(U,divide(U,inverse(Y)))),
inference('PARAMODULATE',[status(thm)],[single_axiom,33,theory(equality)]) ).
cnf(57,plain,
divide(divide(divide(X,divide(Y,divide(Y,inverse(Z)))),inverse(U)),X) = divide(V,inverse(divide(U,divide(V,Z)))),
inference('PARAMODULATE',[status(thm)],[5,33,theory(equality)]) ).
cnf(61,plain,
divide(X,inverse(divide(divide(Y,Z),divide(X,Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[8,8,theory(equality)]) ).
cnf(63,plain,
divide(X,inverse(Y)) = divide(X,divide(Z,divide(Z,inverse(Y)))),
inference('PARAMODULATE',[status(thm)],[61,33,theory(equality)]) ).
cnf(72,plain,
divide(divide(X,inverse(Y)),Z) = divide(divide(X,Z),inverse(Y)),
inference('REWRITE',[status(thm)],[46,63,theory(equality)]) ).
cnf(75,plain,
divide(divide(X,Y),inverse(divide(Z,divide(X,Y)))) = Z,
inference('REWRITE',[status(thm)],[single_axiom,72,theory(equality)]) ).
cnf(79,plain,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| divide(divide(inverse(b2),inverse(a2)),inverse(b2)) != a2
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference('REWRITE',[status(thm)],[4,72,theory(equality)]) ).
cnf(81,plain,
divide(divide(X,inverse(Y)),X) = Y,
inference('REWRITE',[status(thm)],[33,63,theory(equality)]) ).
cnf(82,plain,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference('REWRITE',[status(thm)],[79,81,theory(equality)]) ).
cnf(85,plain,
divide(divide(divide(X,inverse(Y)),inverse(Z)),X) = divide(U,inverse(divide(Z,divide(U,Y)))),
inference('REWRITE',[status(thm)],[57,63,theory(equality)]) ).
cnf(93,plain,
divide(X,Y) = divide(Z,inverse(divide(divide(divide(X,U),divide(V,U)),divide(Z,divide(V,Y))))),
inference('PARAMODULATE',[status(thm)],[5,61,theory(equality)]) ).
cnf(94,plain,
divide(X,inverse(divide(Y,Y))) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[61,21,theory(equality)]),35,5,theory(equality)]) ).
cnf(101,plain,
divide(X,inverse(divide(Y,X))) = Y,
inference('PARAMODULATE',[status(thm)],[75,75,theory(equality)]) ).
cnf(102,plain,
divide(inverse(divide(X,Y)),inverse(X)) = Y,
inference('PARAMODULATE',[status(thm)],[101,101,theory(equality)]) ).
cnf(103,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(X,Z),
inference('PARAMODULATE',[status(thm)],[7,101,theory(equality)]) ).
cnf(104,plain,
divide(X,Y) = divide(Z,inverse(divide(divide(X,U),divide(Z,divide(U,Y))))),
inference('REWRITE',[status(thm)],[93,103,theory(equality)]) ).
cnf(116,plain,
divide(inverse(X),inverse(Y)) = inverse(divide(X,Y)),
inference('PARAMODULATE',[status(thm)],[101,102,theory(equality)]) ).
cnf(118,plain,
inverse(divide(divide(X,Y),X)) = Y,
inference('REWRITE',[status(thm)],[102,116,theory(equality)]) ).
cnf(119,plain,
( inverse(divide(a1,a1)) != inverse(divide(b1,b1))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference('REWRITE',[status(thm)],[82,116,theory(equality)]) ).
cnf(123,plain,
divide(divide(X,Y),Z) = divide(U,inverse(divide(divide(divide(V,Y),V),divide(U,divide(X,Z))))),
inference('PARAMODULATE',[status(thm)],[5,118,theory(equality)]) ).
cnf(129,plain,
inverse(divide(X,X)) = inverse(divide(Y,Y)),
inference('PARAMODULATE',[status(thm)],[118,94,theory(equality)]) ).
cnf(130,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference('REWRITE',[status(thm)],[119,129,theory(equality)]) ).
cnf(135,plain,
divide(X,inverse(Y)) = divide(Z,inverse(divide(Y,divide(Z,X)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,94,theory(equality)]),94,theory(equality)]) ).
cnf(140,plain,
divide(divide(X,Y),Z) = divide(divide(X,Z),Y),
inference('REWRITE',[status(thm)],[123,118,135,theory(equality)]) ).
cnf(144,plain,
divide(X,Y) = divide(divide(Z,Y),inverse(divide(X,Z))),
inference('REWRITE',[status(thm)],[104,135,theory(equality)]) ).
cnf(153,plain,
divide(divide(divide(X,inverse(Y)),inverse(Z)),X) = divide(Y,inverse(Z)),
inference('REWRITE',[status(thm)],[85,135,theory(equality)]) ).
cnf(162,plain,
inverse(divide(divide(X,Y),divide(X,Z))) = divide(Y,Z),
inference('PARAMODULATE',[status(thm)],[118,103,theory(equality)]) ).
cnf(164,plain,
divide(X,divide(Y,Z)) = divide(divide(Z,inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[103,81,theory(equality)]) ).
cnf(165,plain,
divide(X,divide(Y,inverse(divide(X,Z)))) = divide(Z,Y),
inference('PARAMODULATE',[status(thm)],[103,101,theory(equality)]) ).
cnf(166,plain,
divide(divide(X,Y),Z) = divide(X,divide(Y,inverse(Z))),
inference('PARAMODULATE',[status(thm)],[103,81,theory(equality)]) ).
cnf(167,plain,
divide(X,inverse(Y)) = divide(Y,inverse(X)),
inference('REWRITE',[status(thm)],[153,144,116,166,theory(equality)]) ).
cnf(180,plain,
divide(divide(b3,inverse(a3)),inverse(c3)) != divide(b3,divide(inverse(a3),c3)),
inference('REWRITE',[status(thm)],[130,164,167,theory(equality)]) ).
cnf(182,plain,
divide(divide(X,Y),divide(X,Z)) = divide(Z,Y),
inference('REWRITE',[status(thm)],[165,166,theory(equality)]) ).
cnf(185,plain,
inverse(divide(X,Y)) = divide(Y,X),
inference('REWRITE',[status(thm)],[162,182,theory(equality)]) ).
cnf(199,plain,
divide(inverse(X),inverse(Y)) = divide(Y,X),
inference('REWRITE',[status(thm)],[116,185,theory(equality)]) ).
cnf(211,plain,
divide(divide(X,Y),inverse(Z)) = divide(Z,divide(Y,X)),
inference('PARAMODULATE',[status(thm)],[199,185,theory(equality)]) ).
cnf(219,plain,
divide(c3,divide(inverse(a3),b3)) != divide(b3,divide(inverse(a3),c3)),
inference('REWRITE',[status(thm)],[180,211,theory(equality)]) ).
cnf(223,plain,
divide(X,divide(Y,Z)) = divide(Z,divide(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[185,140,theory(equality)]),185,theory(equality)]) ).
cnf(224,plain,
$false,
inference('REWRITE',[status(thm)],[219,223,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP096-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.10/0.12 % Command : run-snark %s %d
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jun 13 22:24:53 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 *
% 0.18/0.46 *
% 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 *
% 0.18/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T22:24:53
% 0.18/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n028.cluster.edu at 2022-06-13T22:24:53
% 0.43/0.59
% 0.43/0.59
% 0.43/0.59 #||
% 0.43/0.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/0.59 % SZS output start Refutation
% See solution above
% 0.43/0.60 ||#
% 0.43/0.60
% 0.43/0.60 ; Summary of computation:
% 0.43/0.60 ; 614 formulas have been input or derived (from 33 formulas).
% 0.43/0.60 ; 224 (36%) were retained. Of these,
% 0.43/0.60 ; 178 (79%) were simplified or subsumed later,
% 0.43/0.60 ; 46 (21%) are still being kept.
% 0.43/0.60 ;
% 0.43/0.60 ; Run time in seconds excluding printing time:
% 0.43/0.60 ; 0.001 1% Read assertion file (1 call)
% 0.43/0.60 ; 0.000 0% Assert (3 calls)
% 0.43/0.60 ; 0.014 11% Process new row (575 calls)
% 0.43/0.60 ; 0.003 2% Resolution (64 calls)
% 0.43/0.60 ; 0.009 7% Paramodulation (32 calls)
% 0.43/0.60 ; 0.000 0% Condensing (9 calls)
% 0.43/0.60 ; 0.000 0% Forward subsumption (9 calls)
% 0.43/0.60 ; 0.000 0% Backward subsumption (5 calls)
% 0.43/0.60 ; 0.000 0% Clause clause subsumption (4 calls)
% 0.43/0.60 ; 0.030 24% Forward simplification (502 calls)
% 0.43/0.60 ; 0.017 13% Backward simplification (223 calls)
% 0.43/0.60 ; 0.026 21% Ordering (2,853 calls)
% 0.43/0.60 ; 0.002 2% Sortal reasoning (32 calls)
% 0.43/0.60 ; 0.000 0% Purity testing (1 call)
% 0.43/0.60 ; 0.024 19% Other
% 0.43/0.60 ; 0.126 Total
% 0.43/0.60 ; 0.137 Real time
% 0.43/0.60 ;
% 0.43/0.60 ; Term-hash-array has 896 terms in all.
% 0.43/0.60 ; Feature-vector-row-index has 0 entries (1 at peak, 5 added, 5 deleted).
% 0.43/0.60 ; Feature-vector-row-index has 1 node (36 at peak, 152 added, 151 deleted).
% 0.43/0.60 ; Retrieved 4 possibly forward subsuming rows in 9 calls.
% 0.43/0.60 ; Retrieved 0 possibly backward subsumed rows in 5 calls.
% 0.43/0.60 ; Path-index has 166 entries (445 at peak, 1,077 added, 911 deleted).
% 0.43/0.60 ; Path-index has 1,019 nodes (1,299 at peak, 1,842 added, 823 deleted).
% 0.43/0.60 ; Trie-index has 166 entries (445 at peak, 1,077 added, 911 deleted).
% 0.43/0.60 ; Trie-index has 535 nodes (1,860 at peak, 4,024 added, 3,489 deleted).
% 0.43/0.60 ; Retrieved 2,527 generalization terms in 3,161 calls.
% 0.43/0.60 ; Retrieved 2,253 instance terms in 276 calls.
% 0.43/0.60 ; Retrieved 3,390 unifiable terms in 295 calls.
% 0.43/0.60 ;
% 0.43/0.60 ; The agenda of backward simplifiable rows to process has 1 entry:
% 0.43/0.60 ; 1 with value 0
% 0.43/0.60 ; The agenda of rows to process has 29 entries:
% 0.43/0.60 ; 11 with value 21 6 with value 22 12 with value 23
% 0.43/0.60 ; The agenda of rows to give has 35 entries:
% 0.43/0.60 ; 3 with value (4 17) 2 with value (4 22) 1 with value (4 27)
% 0.43/0.60 ; 1 with value (4 18) 5 with value (4 23) 2 with value (4 28)
% 0.43/0.60 ; 2 with value (4 19) 2 with value (4 24) 1 with value (4 30)
% 0.43/0.60 ; 4 with value (4 20) 5 with value (4 25) 3 with value (4 31)
% 0.43/0.60 ; 3 with value (4 21) 1 with value (4 26)
% 0.43/0.60 Evaluation took:
% 0.43/0.60 0.138 seconds of real time
% 0.43/0.60 0.120252 seconds of user run time
% 0.43/0.60 0.017002 seconds of system run time
% 0.43/0.60 [Run times include 0.006 seconds GC run time.]
% 0.43/0.60 0 calls to %EVAL
% 0.43/0.60 0 page faults and
% 0.43/0.60 13,191,952 bytes consed.
% 0.43/0.60 :PROOF-FOUND
% 0.43/0.60 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T22:24:53
% 0.43/0.60 :PROOF-FOUND
% 0.43/0.60 *
%------------------------------------------------------------------------------