TSTP Solution File: BOO022-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO022-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n032.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 : Thu Jul 14 23:48:58 EDT 2022
% Result : Unsatisfiable 2.64s 2.80s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 4 RR)
% Number of literals : 58 ( 57 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 112 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply_add,axiom,
multiply(add(X,Y),Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add) ).
cnf(multiply_add_property,axiom,
multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
cnf(additive_inverse,axiom,
add(X,inverse(X)) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
cnf(add_multiply,axiom,
add(multiply(X,Y),Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply) ).
cnf(add_multiply_property,axiom,
add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply_property) ).
cnf(6,plain,
add(X,multiply(Y,Z)) = add(add(multiply(Y,Z),multiply(X,Z)),add(multiply(Y,X),multiply(X,X))),
inference('REWRITE',[status(thm)],[add_multiply_property,multiply_add_property,theory(equality)]) ).
cnf(multiplicative_inverse,axiom,
multiply(X,inverse(X)) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse) ).
cnf(prove_associativity_of_multiply,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
cnf(10,plain,
multiply(X,X) = X,
inference('PARAMODULATE',[status(thm)],[multiply_add,add_multiply,theory(equality)]) ).
cnf(11,plain,
add(X,multiply(Y,Z)) = add(add(multiply(Y,Z),multiply(X,Z)),X),
inference('REWRITE',[status(thm)],[6,add_multiply,10,theory(equality)]) ).
cnf(12,plain,
add(X,X) = X,
inference('PARAMODULATE',[status(thm)],[add_multiply,multiply_add,theory(equality)]) ).
cnf(14,plain,
multiply(X,n1) = add(multiply(Y,X),multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,additive_inverse,theory(equality)]) ).
cnf(15,plain,
multiply(X,Y) = add(multiply(multiply(Z,Y),X),multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,add_multiply,theory(equality)]) ).
cnf(19,plain,
add(X,Y) = add(add(Y,multiply(X,Y)),X),
inference('PARAMODULATE',[status(thm)],[11,multiply_add,theory(equality)]) ).
cnf(25,plain,
add(X,multiply(Y,X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,10,theory(equality)]),12,add_multiply,theory(equality)]) ).
cnf(26,plain,
add(X,Y) = add(Y,X),
inference('REWRITE',[status(thm)],[19,25,theory(equality)]) ).
cnf(27,plain,
multiply(X,Y) = multiply(Y,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[multiply_add_property,12,theory(equality)]),12,theory(equality)]) ).
cnf(28,plain,
add(inverse(X),X) = n1,
inference('PARAMODULATE',[status(thm)],[additive_inverse,26,theory(equality)]) ).
cnf(46,plain,
multiply(inverse(X),X) = n0,
inference('PARAMODULATE',[status(thm)],[multiplicative_inverse,27,theory(equality)]) ).
cnf(51,plain,
multiply(multiply(b,a),c) != multiply(a,multiply(b,c)),
inference('PARAMODULATE',[status(thm)],[prove_associativity_of_multiply,27,theory(equality)]) ).
cnf(53,plain,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,27,theory(equality)]) ).
cnf(57,plain,
multiply(X,n1) = add(multiply(inverse(Y),X),multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,28,theory(equality)]) ).
cnf(59,plain,
add(X,multiply(X,Y)) = X,
inference('PARAMODULATE',[status(thm)],[25,27,theory(equality)]) ).
cnf(63,plain,
add(X,n0) = X,
inference('PARAMODULATE',[status(thm)],[25,46,theory(equality)]) ).
cnf(66,plain,
add(n0,X) = X,
inference('PARAMODULATE',[status(thm)],[add_multiply,46,theory(equality)]) ).
cnf(93,plain,
multiply(X,n1) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,10,theory(equality)]),63,46,theory(equality)]) ).
cnf(95,plain,
X = add(multiply(Y,X),multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[14,93,theory(equality)]) ).
cnf(96,plain,
X = add(multiply(inverse(Y),X),multiply(Y,X)),
inference('REWRITE',[status(thm)],[57,93,theory(equality)]) ).
cnf(108,plain,
add(inverse(X),multiply(X,Y)) = add(Y,inverse(X)),
inference('PARAMODULATE',[status(thm)],[11,95,theory(equality)]) ).
cnf(110,plain,
X = add(multiply(Y,X),multiply(X,inverse(Y))),
inference('PARAMODULATE',[status(thm)],[95,27,theory(equality)]) ).
cnf(111,plain,
X = multiply(inverse(inverse(X)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[95,46,theory(equality)]),66,theory(equality)]) ).
cnf(112,plain,
inverse(inverse(X)) = multiply(X,inverse(inverse(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[95,multiplicative_inverse,theory(equality)]),63,theory(equality)]) ).
cnf(113,plain,
multiply(X,Y) = add(multiply(multiply(Z,Y),X),multiply(multiply(inverse(Z),Y),X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,95,theory(equality)]) ).
cnf(118,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[27,111,theory(equality)]),112,theory(equality)]) ).
cnf(128,plain,
add(inverse(X),multiply(Y,X)) = add(Y,inverse(X)),
inference('PARAMODULATE',[status(thm)],[108,27,theory(equality)]) ).
cnf(163,plain,
multiply(multiply(b,a),c) != multiply(multiply(b,c),a),
inference('PARAMODULATE',[status(thm)],[51,27,theory(equality)]) ).
cnf(170,plain,
X = add(multiply(X,inverse(Y)),multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[96,27,theory(equality)]) ).
cnf(229,plain,
n0 = multiply(multiply(X,Y),inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,multiplicative_inverse,theory(equality)]),63,46,theory(equality)]) ).
cnf(245,plain,
multiply(inverse(X),multiply(Y,X)) = n0,
inference('PARAMODULATE',[status(thm)],[27,229,theory(equality)]) ).
cnf(246,plain,
n0 = multiply(multiply(X,Y),inverse(X)),
inference('PARAMODULATE',[status(thm)],[229,27,theory(equality)]) ).
cnf(248,plain,
inverse(X) = multiply(inverse(multiply(Y,X)),inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[95,229,theory(equality)]),66,theory(equality)]) ).
cnf(252,plain,
n0 = multiply(multiply(X,multiply(Y,Z)),inverse(Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,229,theory(equality)]),63,245,theory(equality)]) ).
cnf(257,plain,
multiply(X,multiply(Y,inverse(X))) = n0,
inference('PARAMODULATE',[status(thm)],[245,118,theory(equality)]) ).
cnf(258,plain,
n0 = multiply(multiply(X,inverse(Y)),multiply(Z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,245,theory(equality)]),63,229,theory(equality)]) ).
cnf(259,plain,
n0 = multiply(multiply(inverse(X),Y),X),
inference('PARAMODULATE',[status(thm)],[246,118,theory(equality)]) ).
cnf(261,plain,
inverse(X) = multiply(inverse(X),inverse(multiply(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[110,246,theory(equality)]),66,theory(equality)]) ).
cnf(283,plain,
add(inverse(multiply(X,Y)),inverse(Y)) = inverse(multiply(X,Y)),
inference('PARAMODULATE',[status(thm)],[59,248,theory(equality)]) ).
cnf(293,plain,
n0 = multiply(multiply(multiply(X,Y),Z),inverse(Y)),
inference('PARAMODULATE',[status(thm)],[252,27,theory(equality)]) ).
cnf(306,plain,
X = add(multiply(X,inverse(Y)),multiply(X,Y)),
inference('PARAMODULATE',[status(thm)],[170,27,theory(equality)]) ).
cnf(322,plain,
n0 = multiply(multiply(inverse(X),Y),multiply(Z,X)),
inference('PARAMODULATE',[status(thm)],[258,27,theory(equality)]) ).
cnf(361,plain,
n0 = multiply(multiply(inverse(X),Y),multiply(X,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[293,261,theory(equality)]),118,theory(equality)]) ).
cnf(478,plain,
multiply(inverse(X),Y) = multiply(multiply(inverse(X),Y),inverse(multiply(X,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[306,361,theory(equality)]),63,theory(equality)]) ).
cnf(2222,plain,
multiply(multiply(X,Y),Z) = multiply(multiply(X,Z),multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,361,theory(equality)]),63,theory(equality)]) ).
cnf(2225,plain,
multiply(inverse(multiply(X,Y)),Y) = multiply(inverse(X),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,multiplicative_inverse,theory(equality)]),66,478,theory(equality)]) ).
cnf(2248,plain,
multiply(multiply(X,inverse(multiply(inverse(Y),Z))),Z) = multiply(multiply(Y,Z),multiply(X,inverse(multiply(inverse(Y),Z)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,257,theory(equality)]),63,theory(equality)]) ).
cnf(2262,plain,
add(inverse(X),inverse(Y)) = inverse(multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[128,2225,theory(equality)]),283,128,theory(equality)]) ).
cnf(2504,plain,
multiply(multiply(X,Y),Z) = multiply(multiply(X,Z),Y),
inference('REWRITE',[status(thm)],[2248,322,2222,63,259,53,multiply_add_property,118,2262,theory(equality)]) ).
cnf(2505,plain,
$false,
inference('REWRITE',[status(thm)],[163,2504,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO022-1 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.12 % Command : run-snark %s %d
% 0.13/0.32 % Computer : n032.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Wed Jun 1 22:52:45 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.18/0.41 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 *
% 0.18/0.42 *
% 0.18/0.42 #<PACKAGE "SNARK-USER">
% 0.18/0.42 *
% 0.18/0.42 SNARK-TPTP-OPTIONS
% 0.18/0.42 *
% 0.18/0.42 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.42 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.43 (USE-FACTORING :POS)
% 0.18/0.43 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.43 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.43 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.43 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.43 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.43 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.43 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.43 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.43 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.43 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.43 *
% 0.18/0.43 "."
% 0.18/0.43 *
% 0.18/0.43 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T22:52:45
% 0.18/0.43 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n032.cluster.edu at 2022-06-01T22:52:45
% 0.18/0.43
% 0.18/0.43 ; Recognized possible right inverse assertion (= (|add| ?X (|inverse| ?X)) |n1|).
% 2.64/2.80 ; Recognized possible right inverse assertion (= (|multiply| ?X (|inverse| ?X)) |n0|).
% 2.64/2.80
% 2.64/2.80 #||
% 2.64/2.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.64/2.80 % SZS output start Refutation
% See solution above
% 2.64/2.81 ||#
% 2.64/2.81
% 2.64/2.81 ; Summary of computation:
% 2.64/2.81 ; 48203 formulas have been input or derived (from 283 formulas).
% 2.64/2.81 ; 2505 ( 5%) were retained. Of these,
% 2.64/2.81 ; 1060 (42%) were simplified or subsumed later,
% 2.64/2.81 ; 1445 (58%) are still being kept.
% 2.64/2.81 ;
% 2.64/2.81 ; Run time in seconds excluding printing time:
% 2.64/2.81 ; 0.001 0% Read assertion file (1 call)
% 2.64/2.81 ; 0.000 0% Assert (7 calls)
% 2.64/2.81 ; 0.273 11% Process new row (40,604 calls)
% 2.64/2.81 ; 0.030 1% Resolution (564 calls)
% 2.64/2.81 ; 0.484 20% Paramodulation (282 calls)
% 2.64/2.81 ; 1.261 53% Forward simplification (40,569 calls)
% 2.64/2.81 ; 0.104 4% Backward simplification (2,504 calls)
% 2.64/2.81 ; 0.107 4% Ordering (58,514 calls)
% 2.64/2.81 ; 0.001 0% Sortal reasoning (32 calls)
% 2.64/2.81 ; 0.000 0% Purity testing (1 call)
% 2.64/2.81 ; 0.117 5% Other
% 2.64/2.81 ; 2.378 Total
% 2.64/2.81 ; 2.382 Real time
% 2.64/2.81 ;
% 2.64/2.81 ; Term-hash-array has 6,472 terms in all.
% 2.64/2.81 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 2.64/2.81 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 2.64/2.81 ; Path-index has 3,853 entries (5,375 at peak, 6,536 added, 2,683 deleted).
% 2.64/2.81 ; Path-index has 4,321 nodes (4,558 at peak, 5,381 added, 1,060 deleted).
% 2.64/2.81 ; Trie-index has 3,853 entries (5,375 at peak, 6,536 added, 2,683 deleted).
% 2.64/2.81 ; Trie-index has 11,216 nodes (15,696 at peak, 20,533 added, 9,317 deleted).
% 2.64/2.81 ; Retrieved 625,238 generalization terms in 286,420 calls.
% 2.64/2.81 ; Retrieved 18,541 instance terms in 2,505 calls.
% 2.64/2.81 ; Retrieved 92,782 unifiable terms in 1,940 calls.
% 2.64/2.81 ;
% 2.64/2.81 ; The agenda of backward simplifiable rows to process has 298 entries:
% 2.64/2.81 ; 298 with value 0
% 2.64/2.81 ; The agenda of rows to process has 391 entries:
% 2.64/2.81 ; 54 with value 23 27 with value 28 8 with value 33
% 2.64/2.81 ; 67 with value 24 32 with value 29 6 with value 34
% 2.64/2.81 ; 37 with value 25 32 with value 30 3 with value 35
% 2.64/2.81 ; 35 with value 26 41 with value 31 4 with value 36
% 2.64/2.81 ; 29 with value 27 15 with value 32 1 with value 38
% 2.64/2.81 ; The agenda of rows to give has 1236 entries:
% 2.64/2.81 ; 1 with value (4 17) 76 with value (4 30) 14 with value (4 40)
% 2.64/2.81 ; 1 with value (4 21) 54 with value (4 31) 3 with value (4 42)
% 2.64/2.81 ; 3 with value (4 22) 64 with value (4 32) 9 with value (4 43)
% 2.64/2.81 ; 44 with value (4 23) 55 with value (4 33) 1 with value (4 44)
% 2.64/2.81 ; 92 with value (4 24) 32 with value (4 34) 4 with value (4 45)
% 2.64/2.81 ; 111 with value (4 25) 33 with value (4 35) 8 with value (4 46)
% 2.64/2.81 ; 129 with value (4 26) 48 with value (4 36) 4 with value (4 47)
% 2.64/2.81 ; 75 with value (4 27) 48 with value (4 37) 8 with value (4 48)
% 2.64/2.81 ; 216 with value (4 28) 18 with value (4 38) 1 with value (4 50)
% 2.64/2.81 ; 75 with value (4 29) 9 with value (4 39)
% 2.64/2.81 Evaluation took:
% 2.64/2.81 2.383 seconds of real time
% 2.64/2.81 2.142694 seconds of user run time
% 2.64/2.81 0.239675 seconds of system run time
% 2.64/2.81 [Run times include 0.142 seconds GC run time.]
% 2.64/2.81 0 calls to %EVAL
% 2.64/2.81 0 page faults and
% 2.64/2.81 183,095,632 bytes consed.
% 2.64/2.81 :PROOF-FOUND
% 2.64/2.81 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T22:52:47
% 2.64/2.81 :PROOF-FOUND
% 2.64/2.81 *
%------------------------------------------------------------------------------