TSTP Solution File: GRP402-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP402-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n005.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 11:38:07 EDT 2022
% Result : Unsatisfiable 1.97s 2.16s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 25 ( 19 unt; 0 nHn; 9 RR)
% Number of literals : 31 ( 30 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_multiply,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-0.ax',associativity_of_multiply) ).
cnf(right_cancellation,axiom,
( multiply(X,Y) != multiply(Z,Y)
| X = Z ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-1.ax',right_cancellation) ).
cnf(left_cancellation,axiom,
( multiply(X,Y) != multiply(X,Z)
| Y = Z ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-1.ax',left_cancellation) ).
cnf(commutator,axiom,
multiply(X,Y) = multiply(Y,multiply(X,commutator(X,Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
cnf(5,plain,
multiply(X,Y) = multiply(multiply(Y,X),commutator(X,Y)),
inference('REWRITE',[status(thm)],[commutator,associativity_of_multiply,theory(equality)]) ).
cnf(nilpotency,axiom,
multiply(commutator(X,Y),Z) = multiply(Z,commutator(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nilpotency) ).
cnf(prove_commutator_is_associative,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutator_is_associative) ).
cnf(10,plain,
( multiply(X,multiply(Y,Z)) != multiply(U,Z)
| multiply(X,Y) = U ),
inference('PARAMODULATE',[status(thm)],[right_cancellation,associativity_of_multiply,theory(equality)]) ).
cnf(11,plain,
multiply(multiply(X,multiply(Y,Z)),U) = multiply(multiply(X,Y),multiply(Z,U)),
inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,associativity_of_multiply,theory(equality)]) ).
cnf(20,plain,
multiply(multiply(X,Y),multiply(Z,commutator(Z,Y))) = multiply(X,multiply(Z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,5,theory(equality)]),11,theory(equality)]) ).
cnf(24,plain,
multiply(X,Y) = multiply(commutator(X,Y),multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[5,nilpotency,theory(equality)]) ).
cnf(26,plain,
( multiply(X,commutator(Y,Z)) != multiply(commutator(Y,Z),U)
| X = U ),
inference('PARAMODULATE',[status(thm)],[left_cancellation,nilpotency,theory(equality)]) ).
cnf(28,plain,
multiply(multiply(X,commutator(Y,Z)),U) = multiply(commutator(Y,Z),multiply(X,U)),
inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,nilpotency,theory(equality)]) ).
cnf(31,plain,
( multiply(commutator(X,Y),Z) != multiply(Z,U)
| commutator(X,Y) = U ),
inference('PARAMODULATE',[status(thm)],[left_cancellation,nilpotency,theory(equality)]) ).
cnf(37,plain,
multiply(commutator(commutator(a,b),c),X) != multiply(commutator(a,commutator(b,c)),X),
inference('UR-RESOLVE',[status(thm)],[right_cancellation,prove_commutator_is_associative]) ).
cnf(92,plain,
multiply(commutator(X,X),X) = X,
inference('HYPERRESOLVE',[status(thm)],[10,24]) ).
cnf(112,plain,
multiply(commutator(X,X),multiply(Y,X)) = multiply(Y,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,92,theory(equality)]),28,theory(equality)]) ).
cnf(186,plain,
multiply(commutator(X,X),Y) = Y,
inference('HYPERRESOLVE',[status(thm)],[10,112]) ).
cnf(188,plain,
X = multiply(X,commutator(Y,Y)),
inference('HYPERRESOLVE',[status(thm)],[26,186]) ).
cnf(196,plain,
( X != multiply(X,Y)
| commutator(Z,Z) = Y ),
inference('PARAMODULATE',[status(thm)],[left_cancellation,188,theory(equality)]) ).
cnf(1516,plain,
commutator(X,Y) = multiply(commutator(X,Y),commutator(commutator(X,Y),Z)),
inference('HYPERRESOLVE',[status(thm)],[31,20]) ).
cnf(1953,plain,
multiply(commutator(commutator(a,b),c),multiply(commutator(b,c),a)) != multiply(a,commutator(b,c)),
inference('PARAMODULATE',[status(thm)],[37,24,theory(equality)]) ).
cnf(2108,plain,
commutator(X,X) = commutator(commutator(Y,Z),U),
inference('HYPERRESOLVE',[status(thm)],[196,1516]) ).
cnf(2132,plain,
multiply(commutator(commutator(X,Y),Z),U) = U,
inference('PARAMODULATE',[status(thm)],[186,2108,theory(equality)]) ).
cnf(2151,plain,
$false,
inference('REWRITE',[status(thm)],[1953,nilpotency,2132,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP402-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 11:57:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 *
% 0.20/0.47 *
% 0.20/0.48 #<PACKAGE "SNARK-USER">
% 0.20/0.48 *
% 0.20/0.48 SNARK-TPTP-OPTIONS
% 0.20/0.48 *
% 0.20/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48 (USE-FACTORING :POS)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48 *
% 0.20/0.48 "."
% 0.20/0.48 *
% 0.20/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T11:57:39
% 0.20/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n005.cluster.edu at 2022-06-13T11:57:39
% 0.20/0.49
% 1.97/2.16 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 1.97/2.16
% 1.97/2.16 #||
% 1.97/2.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.97/2.16 % SZS output start Refutation
% See solution above
% 1.97/2.16 ||#
% 1.97/2.16
% 1.97/2.16 ; Summary of computation:
% 1.97/2.16 ; 4514 formulas have been input or derived (from 62 formulas).
% 1.97/2.16 ; 2151 (48%) were retained. Of these,
% 1.97/2.16 ; 396 (18%) were simplified or subsumed later,
% 1.97/2.16 ; 1755 (82%) are still being kept.
% 1.97/2.16 ;
% 1.97/2.16 ; Run time in seconds excluding printing time:
% 1.97/2.16 ; 0.003 0% Read assertion file (1 call)
% 1.97/2.16 ; 0.000 0% Assert (6 calls)
% 1.97/2.16 ; 0.161 10% Process new row (4,252 calls)
% 1.97/2.16 ; 0.050 3% Resolution (122 calls)
% 1.97/2.16 ; 0.060 4% Paramodulation (61 calls)
% 1.97/2.16 ; 0.017 1% Condensing (1,453 calls)
% 1.97/2.16 ; 0.118 7% Forward subsumption (1,453 calls)
% 1.97/2.16 ; 0.043 3% Backward subsumption (866 calls)
% 1.97/2.16 ; 0.142 8% Clause clause subsumption (39,892 calls)
% 1.97/2.16 ; 0.291 17% Forward simplification (4,197 calls)
% 1.97/2.16 ; 0.094 6% Backward simplification (2,150 calls)
% 1.97/2.16 ; 0.664 40% Ordering (89,424 calls)
% 1.97/2.16 ; 0.000 0% Sortal reasoning (32 calls)
% 1.97/2.16 ; 0.000 0% Purity testing (1 call)
% 1.97/2.16 ; 0.034 2% Other
% 1.97/2.16 ; 1.677 Total
% 1.97/2.16 ; 1.680 Real time
% 1.97/2.16 ;
% 1.97/2.16 ; Term-hash-array has 4,566 terms in all.
% 1.97/2.16 ; Feature-vector-row-index has 750 entries (763 at peak, 866 added, 116 deleted).
% 1.97/2.16 ; Feature-vector-row-index has 652 nodes (671 at peak, 856 added, 204 deleted).
% 1.97/2.16 ; Retrieved 37,653 possibly forward subsuming rows in 1,453 calls.
% 1.97/2.16 ; Retrieved 9,950 possibly backward subsumed rows in 866 calls.
% 1.97/2.16 ; Path-index has 3,725 entries (3,967 at peak, 4,642 added, 917 deleted).
% 1.97/2.16 ; Path-index has 2,108 nodes (2,286 at peak, 2,585 added, 477 deleted).
% 1.97/2.16 ; Trie-index has 3,725 entries (3,967 at peak, 4,642 added, 917 deleted).
% 1.97/2.16 ; Trie-index has 13,750 nodes (15,484 at peak, 18,043 added, 4,293 deleted).
% 1.97/2.16 ; Retrieved 51,547 generalization terms in 31,494 calls.
% 1.97/2.16 ; Retrieved 12,527 instance terms in 2,769 calls.
% 1.97/2.16 ; Retrieved 124,642 unifiable terms in 632 calls.
% 1.97/2.16 ;
% 1.97/2.16 ; The agenda of backward simplifiable rows to process has 24 entries:
% 1.97/2.16 ; 24 with value 0
% 1.97/2.16 ; The agenda of rows to process has 44 entries:
% 1.97/2.16 ; 1 with value 21 5 with value 26 3 with value 31
% 1.97/2.16 ; 3 with value 22 11 with value 27 8 with value 32
% 1.97/2.16 ; 1 with value 23 3 with value 30 2 with value 33
% 1.97/2.16 ; 7 with value 25
% 1.97/2.16 ; The agenda of rows to give has 1713 entries:
% 1.97/2.16 ; 1 with value (4 19) 199 with value (4 26) 26 with value (4 33)
% 1.97/2.16 ; 9 with value (4 20) 43 with value (4 27) 7 with value (4 34)
% 1.97/2.16 ; 33 with value (4 21) 31 with value (4 28) 41 with value (4 35)
% 1.97/2.16 ; 11 with value (4 22) 53 with value (4 29) 21 with value (4 36)
% 1.97/2.16 ; 12 with value (4 23) 498 with value (4 30) 44 with value (4 37)
% 1.97/2.16 ; 22 with value (4 24) 431 with value (4 31) 3 with value (4 38)
% 1.97/2.16 ; 117 with value (4 25) 102 with value (4 32) 9 with value (4 39)
% 1.97/2.16 Evaluation took:
% 1.97/2.16 1.68 seconds of real time
% 1.97/2.16 1.479902 seconds of user run time
% 1.97/2.16 0.2002 seconds of system run time
% 1.97/2.16 [Run times include 0.084 seconds GC run time.]
% 1.97/2.16 0 calls to %EVAL
% 1.97/2.16 0 page faults and
% 1.97/2.16 121,376,448 bytes consed.
% 1.97/2.16 :PROOF-FOUND
% 1.97/2.16 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T11:57:41
% 1.97/2.16 :PROOF-FOUND
% 1.97/2.16 *
%------------------------------------------------------------------------------