%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP512-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n016.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 11:39:13 EDT 2022
% Result : Unsatisfiable 0.21s 0.55s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 2 RR)
% Number of literals : 25 ( 24 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(multiply(X,Y),Z),inverse(multiply(X,Z))) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_4,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
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(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(27,plain,
multiply(multiply(X,inverse(Y)),inverse(X)) = inverse(Y),
inference('PARAMODULATE',[status(thm)],[13,single_axiom,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(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(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(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(55,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[44,47,52,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,
$false,
inference('REWRITE',[status(thm)],[prove_these_axioms_4,69,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP512-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.14 % Command : run-snark %s %d
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 13 06:35:59 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.47 /export/starexec/sandbox2/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 *
% 0.21/0.49 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T06:35:59
% 0.21/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n016.cluster.edu at 2022-06-13T06:35:59
% 0.21/0.55
% 0.21/0.55
% 0.21/0.55 #||
% 0.21/0.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.55 % SZS output start Refutation
% See solution above
% 0.21/0.55 ||#
% 0.21/0.55
% 0.21/0.55 ; Summary of computation:
% 0.21/0.55 ; 138 formulas have been input or derived (from 12 formulas).
% 0.21/0.55 ; 70 (51%) were retained. Of these,
% 0.21/0.55 ; 45 (64%) were simplified or subsumed later,
% 0.21/0.55 ; 25 (36%) are still being kept.
% 0.21/0.55 ;
% 0.21/0.55 ; Run time in seconds excluding printing time:
% 0.21/0.55 ; 0.001 2% Read assertion file (1 call)
% 0.21/0.55 ; 0.000 0% Assert (2 calls)
% 0.21/0.55 ; 0.010 18% Process new row (138 calls)
% 0.21/0.55 ; 0.000 0% Resolution (22 calls)
% 0.21/0.55 ; 0.007 12% Paramodulation (11 calls)
% 0.21/0.55 ; 0.005 9% Forward simplification (109 calls)
% 0.21/0.55 ; 0.008 14% Backward simplification (70 calls)
% 0.21/0.55 ; 0.004 7% Ordering (374 calls)
% 0.21/0.55 ; 0.000 0% Sortal reasoning (32 calls)
% 0.21/0.55 ; 0.000 0% Purity testing (1 call)
% 0.21/0.55 ; 0.022 39% Other
% 0.21/0.55 ; 0.057 Total
% 0.21/0.55 ; 0.061 Real time
% 0.21/0.55 ;
% 0.21/0.55 ; Term-hash-array has 350 terms in all.
% 0.21/0.55 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.21/0.55 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.21/0.55 ; Path-index has 131 entries (204 at peak, 406 added, 275 deleted).
% 0.21/0.55 ; Path-index has 725 nodes (735 at peak, 980 added, 255 deleted).
% 0.21/0.55 ; Trie-index has 131 entries (204 at peak, 406 added, 275 deleted).
% 0.21/0.55 ; Trie-index has 547 nodes (865 at peak, 1,661 added, 1,114 deleted).
% 0.21/0.55 ; Retrieved 192 generalization terms in 760 calls.
% 0.21/0.55 ; Retrieved 335 instance terms in 77 calls.
% 0.21/0.55 ; Retrieved 499 unifiable terms in 79 calls.
% 0.21/0.55 ;
% 0.21/0.55 ; The agenda of rows to give has 21 entries:
% 0.21/0.55 ; 1 with value (4 15) 2 with value (4 22) 2 with value (4 29)
% 0.21/0.55 ; 1 with value (4 17) 1 with value (4 23) 1 with value (4 30)
% 0.21/0.55 ; 2 with value (4 18) 2 with value (4 24) 1 with value (4 31)
% 0.21/0.55 ; 1 with value (4 19) 1 with value (4 26) 1 with value (4 32)
% 0.21/0.55 ; 1 with value (4 20) 1 with value (4 28) 1 with value (4 36)
% 0.21/0.55 ; 2 with value (4 21)
% 0.21/0.55 Evaluation took:
% 0.21/0.55 0.061 seconds of real time
% 0.21/0.55 0.05363 seconds of user run time
% 0.21/0.55 0.007567 seconds of system run time
% 0.21/0.55 0 calls to %EVAL
% 0.21/0.55 0 page faults and
% 0.21/0.55 4,941,816 bytes consed.
% 0.21/0.55 :PROOF-FOUND
% 0.21/0.55 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T06:35:59
% 0.21/0.56 :PROOF-FOUND
% 0.21/0.56 *
%------------------------------------------------------------------------------