%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP085-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n026.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 11:36:05 EDT 2022
% Result : Unsatisfiable 0.48s 0.65s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of clauses : 49 ( 45 unt; 0 nHn; 6 RR)
% Number of literals : 57 ( 56 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(multiply(X,Y),Z),inverse(multiply(X,Z))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
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(3,plain,
multiply(X,inverse(multiply(multiply(Y,X),inverse(multiply(Y,Z))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(4,plain,
multiply(multiply(X,Y),inverse(multiply(multiply(multiply(Z,X),U),Y))) = inverse(multiply(Z,U)),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(6,plain,
multiply(multiply(X,Y),inverse(multiply(Z,Y))) = inverse(multiply(multiply(U,Z),inverse(multiply(U,X)))),
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(7,plain,
multiply(X,inverse(multiply(multiply(Y,X),inverse(Z)))) = inverse(multiply(multiply(U,Y),inverse(multiply(U,Z)))),
inference('PARAMODULATE',[status(thm)],[3,3,theory(equality)]) ).
cnf(11,plain,
multiply(X,inverse(multiply(Y,inverse(multiply(multiply(Z,multiply(Y,U)),inverse(multiply(Z,X))))))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(13,plain,
multiply(multiply(X,inverse(multiply(Y,Z))),inverse(X)) = inverse(multiply(Y,Z)),
inference('PARAMODULATE',[status(thm)],[4,single_axiom,theory(equality)]) ).
cnf(14,plain,
inverse(multiply(X,multiply(Y,inverse(multiply(multiply(X,Y),Z))))) = Z,
inference('PARAMODULATE',[status(thm)],[3,4,theory(equality)]) ).
cnf(18,plain,
multiply(X,inverse(multiply(multiply(multiply(Y,Z),X),inverse(inverse(multiply(U,V)))))) = inverse(multiply(multiply(multiply(U,Y),V),Z)),
inference('PARAMODULATE',[status(thm)],[3,4,theory(equality)]) ).
cnf(21,plain,
multiply(multiply(X,Y),inverse(multiply(Z,Y))) = inverse(multiply(U,inverse(multiply(multiply(V,multiply(U,X)),inverse(multiply(V,Z)))))),
inference('PARAMODULATE',[status(thm)],[4,3,theory(equality)]) ).
cnf(23,plain,
multiply(X,inverse(multiply(multiply(multiply(Y,Z),U),inverse(multiply(multiply(V,Z),inverse(multiply(V,X))))))) = inverse(multiply(Y,U)),
inference('PARAMODULATE',[status(thm)],[4,3,theory(equality)]) ).
cnf(27,plain,
multiply(multiply(X,inverse(Y)),inverse(X)) = inverse(Y),
inference('PARAMODULATE',[status(thm)],[13,single_axiom,theory(equality)]) ).
cnf(28,plain,
multiply(inverse(X),inverse(multiply(Y,inverse(Y)))) = inverse(X),
inference('PARAMODULATE',[status(thm)],[single_axiom,27,theory(equality)]) ).
cnf(30,plain,
multiply(X,inverse(multiply(multiply(Y,X),Z))) = inverse(multiply(Y,Z)),
inference('PARAMODULATE',[status(thm)],[27,single_axiom,theory(equality)]) ).
cnf(31,plain,
inverse(multiply(multiply(X,Y),inverse(inverse(multiply(Z,U))))) = inverse(multiply(multiply(multiply(Z,X),U),Y)),
inference('REWRITE',[status(thm)],[18,30,theory(equality)]) ).
cnf(33,plain,
inverse(multiply(X,inverse(multiply(X,Y)))) = Y,
inference('REWRITE',[status(thm)],[14,30,theory(equality)]) ).
cnf(35,plain,
inverse(multiply(X,inverse(Y))) = inverse(multiply(multiply(Z,X),inverse(multiply(Z,Y)))),
inference('REWRITE',[status(thm)],[7,30,theory(equality)]) ).
cnf(37,plain,
multiply(X,inverse(multiply(multiply(multiply(Y,Z),U),inverse(multiply(Z,inverse(X)))))) = inverse(multiply(Y,U)),
inference('REWRITE',[status(thm)],[23,35,theory(equality)]) ).
cnf(38,plain,
multiply(multiply(X,Y),inverse(multiply(Z,Y))) = inverse(multiply(U,inverse(multiply(multiply(U,X),inverse(Z))))),
inference('REWRITE',[status(thm)],[21,35,theory(equality)]) ).
cnf(39,plain,
multiply(X,inverse(multiply(Y,inverse(multiply(multiply(Y,Z),inverse(X)))))) = Z,
inference('REWRITE',[status(thm)],[11,35,theory(equality)]) ).
cnf(42,plain,
multiply(multiply(X,Y),inverse(multiply(Z,Y))) = inverse(multiply(Z,inverse(X))),
inference('REWRITE',[status(thm)],[6,35,theory(equality)]) ).
cnf(43,plain,
inverse(multiply(X,inverse(Y))) = inverse(multiply(Z,inverse(multiply(multiply(Z,Y),inverse(X))))),
inference('REWRITE',[status(thm)],[38,42,theory(equality)]) ).
cnf(44,plain,
multiply(X,inverse(multiply(X,inverse(Y)))) = Y,
inference('REWRITE',[status(thm)],[39,43,theory(equality)]) ).
cnf(47,plain,
multiply(multiply(X,Y),inverse(X)) = Y,
inference('PARAMODULATE',[status(thm)],[27,33,theory(equality)]) ).
cnf(50,plain,
multiply(multiply(multiply(X,inverse(multiply(X,Y))),Z),Y) = Z,
inference('PARAMODULATE',[status(thm)],[47,33,theory(equality)]) ).
cnf(51,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('PARAMODULATE',[status(thm)],[44,47,theory(equality)]) ).
cnf(52,plain,
multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
inference('PARAMODULATE',[status(thm)],[47,44,theory(equality)]) ).
cnf(53,plain,
inverse(multiply(multiply(X,inverse(Y)),inverse(inverse(multiply(multiply(Z,U),inverse(multiply(U,inverse(Y)))))))) = inverse(multiply(Z,X)),
inference('REWRITE',[status(thm)],[37,31,52,theory(equality)]) ).
cnf(55,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[44,47,52,theory(equality)]) ).
cnf(56,plain,
inverse(multiply(multiply(X,inverse(Y)),multiply(multiply(Z,U),inverse(multiply(U,inverse(Y)))))) = inverse(multiply(Z,X)),
inference('REWRITE',[status(thm)],[53,55,theory(equality)]) ).
cnf(63,plain,
multiply(multiply(inverse(X),Y),X) = Y,
inference('REWRITE',[status(thm)],[50,47,52,theory(equality)]) ).
cnf(67,plain,
multiply(inverse(X),multiply(Y,inverse(Y))) = inverse(X),
inference('REWRITE',[status(thm)],[28,52,theory(equality)]) ).
cnf(68,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('PARAMODULATE',[status(thm)],[51,55,theory(equality)]) ).
cnf(69,plain,
multiply(X,Y) = multiply(Y,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[51,47,theory(equality)]),55,theory(equality)]) ).
cnf(70,plain,
( 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)) ),
inference('REWRITE',[status(thm)],[prove_these_axioms,69,theory(equality)]) ).
cnf(73,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) ),
inference('PARAMODULATE',[status(thm)],[70,69,theory(equality)]) ).
cnf(82,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference('PARAMODULATE',[status(thm)],[67,55,theory(equality)]) ).
cnf(84,plain,
multiply(inverse(X),X) = multiply(Y,inverse(Y)),
inference('PARAMODULATE',[status(thm)],[63,82,theory(equality)]) ).
cnf(92,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('PARAMODULATE',[status(thm)],[68,84,theory(equality)]) ).
cnf(93,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) ),
inference('REWRITE',[status(thm)],[73,92,theory(equality)]) ).
cnf(98,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[84,84,theory(equality)]) ).
cnf(99,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference('REWRITE',[status(thm)],[93,98,theory(equality)]) ).
cnf(106,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[52,55,theory(equality)]) ).
cnf(156,plain,
multiply(multiply(X,Y),inverse(multiply(Y,Z))) = inverse(multiply(Z,inverse(X))),
inference('PARAMODULATE',[status(thm)],[42,69,theory(equality)]) ).
cnf(157,plain,
inverse(multiply(multiply(X,inverse(Y)),multiply(Z,Y))) = inverse(multiply(Z,X)),
inference('REWRITE',[status(thm)],[56,55,106,156,theory(equality)]) ).
cnf(242,plain,
multiply(X,Y) = multiply(multiply(Y,inverse(Z)),multiply(X,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[55,157,theory(equality)]),55,theory(equality)]) ).
cnf(243,plain,
multiply(X,multiply(Y,Z)) = multiply(Z,multiply(X,Y)),
inference('PARAMODULATE',[status(thm)],[242,47,theory(equality)]) ).
cnf(244,plain,
$false,
inference('REWRITE',[status(thm)],[99,243,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP085-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.04/0.14 % Command : run-snark %s %d
% 0.14/0.35 % Computer : n026.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 10:01:51 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.48 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.49 *
% 0.21/0.49 *
% 0.21/0.49 #<PACKAGE "SNARK-USER">
% 0.21/0.49 *
% 0.21/0.49 SNARK-TPTP-OPTIONS
% 0.21/0.49 *
% 0.21/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.49 (USE-FACTORING :POS)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.49 *
% 0.21/0.49 "."
% 0.21/0.49 *
% 0.21/0.50 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T10:01:51
% 0.21/0.50 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-06-14T10:01:51
% 0.48/0.65
% 0.48/0.65
% 0.48/0.65 #||
% 0.48/0.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.65 % SZS output start Refutation
% See solution above
% 0.48/0.66 ||#
% 0.48/0.66
% 0.48/0.66 ; Summary of computation:
% 0.48/0.66 ; 1276 formulas have been input or derived (from 42 formulas).
% 0.48/0.66 ; 244 (19%) were retained. Of these,
% 0.48/0.66 ; 114 (47%) were simplified or subsumed later,
% 0.48/0.66 ; 130 (53%) are still being kept.
% 0.48/0.66 ;
% 0.48/0.66 ; Run time in seconds excluding printing time:
% 0.48/0.66 ; 0.001 1% Read assertion file (1 call)
% 0.48/0.66 ; 0.001 1% Assert (2 calls)
% 0.48/0.66 ; 0.020 13% Process new row (1,145 calls)
% 0.48/0.66 ; 0.003 2% Resolution (82 calls)
% 0.48/0.66 ; 0.017 11% Paramodulation (41 calls)
% 0.48/0.66 ; 0.000 0% Condensing (24 calls)
% 0.48/0.66 ; 0.005 3% Forward subsumption (24 calls)
% 0.48/0.66 ; 0.000 0% Backward subsumption (16 calls)
% 0.48/0.66 ; 0.001 1% Clause clause subsumption (140 calls)
% 0.48/0.66 ; 0.030 19% Forward simplification (1,021 calls)
% 0.48/0.66 ; 0.019 12% Backward simplification (244 calls)
% 0.48/0.66 ; 0.032 21% Ordering (6,090 calls)
% 0.48/0.66 ; 0.000 0% Sortal reasoning (32 calls)
% 0.48/0.66 ; 0.000 0% Purity testing (1 call)
% 0.48/0.66 ; 0.026 17% Other
% 0.48/0.66 ; 0.155 Total
% 0.48/0.66 ; 0.166 Real time
% 0.48/0.66 ;
% 0.48/0.66 ; Term-hash-array has 742 terms in all.
% 0.48/0.66 ; Feature-vector-row-index has 0 entries (9 at peak, 16 added, 16 deleted).
% 0.48/0.66 ; Feature-vector-row-index has 1 node (73 at peak, 108 added, 107 deleted).
% 0.48/0.66 ; Retrieved 118 possibly forward subsuming rows in 24 calls.
% 0.48/0.66 ; Retrieved 58 possibly backward subsumed rows in 16 calls.
% 0.48/0.66 ; Path-index has 395 entries (418 at peak, 871 added, 476 deleted).
% 0.48/0.66 ; Path-index has 867 nodes (889 at peak, 1,327 added, 460 deleted).
% 0.48/0.66 ; Trie-index has 395 entries (418 at peak, 871 added, 476 deleted).
% 0.48/0.66 ; Trie-index has 1,272 nodes (1,369 at peak, 3,174 added, 1,902 deleted).
% 0.48/0.66 ; Retrieved 4,519 generalization terms in 6,781 calls.
% 0.48/0.66 ; Retrieved 1,612 instance terms in 340 calls.
% 0.48/0.66 ; Retrieved 3,409 unifiable terms in 328 calls.
% 0.48/0.66 ;
% 0.48/0.66 ; The agenda of backward simplifiable rows to process has 9 entries:
% 0.48/0.66 ; 9 with value 0
% 0.48/0.66 ; The agenda of rows to process has 63 entries:
% 0.48/0.66 ; 2 with value 20 5 with value 24 5 with value 28
% 0.48/0.66 ; 1 with value 21 9 with value 25 6 with value 29
% 0.48/0.66 ; 1 with value 22 15 with value 26 3 with value 30
% 0.48/0.66 ; 12 with value 23 4 with value 27
% 0.48/0.66 ; The agenda of rows to give has 104 entries:
% 0.48/0.66 ; 1 with value (4 19) 15 with value (4 25) 2 with value (4 29)
% 0.48/0.66 ; 5 with value (4 22) 23 with value (4 26) 1 with value (4 30)
% 0.48/0.66 ; 2 with value (4 23) 8 with value (4 27) 1 with value (4 32)
% 0.48/0.66 ; 13 with value (4 24) 32 with value (4 28) 1 with value (4 36)
% 0.48/0.66 Evaluation took:
% 0.48/0.66 0.166 seconds of real time
% 0.48/0.66 0.145566 seconds of user run time
% 0.48/0.66 0.021141 seconds of system run time
% 0.48/0.66 [Run times include 0.005 seconds GC run time.]
% 0.48/0.66 0 calls to %EVAL
% 0.48/0.66 0 page faults and
% 0.48/0.66 13,564,296 bytes consed.
% 0.48/0.66 :PROOF-FOUND
% 0.48/0.66 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T10:01:52
% 0.48/0.66 :PROOF-FOUND
% 0.48/0.66 *
%------------------------------------------------------------------------------