TSTP Solution File: ANA133-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : ANA133-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n015.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 19:27:29 EDT 2022
% Result : Unsatisfiable 69.11s 69.35s
% Output : Refutation 69.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 14 RR)
% Number of literals : 39 ( 38 equ; 1 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(plus_zero,axiom,
'+'(zero,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
cnf(times_zero,axiom,
times(zero,X) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).
cnf(times_one,axiom,
times(one,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).
cnf(distributivity,axiom,
times(X,'+'(Y,Z)) = '+'(times(X,Y),times(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity) ).
cnf(minus,axiom,
'+'(X,minus(X)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus) ).
cnf(8,plain,
'+'(X,'+'(minus(X),Y)) = '+'(zero,Y),
inference('EMBED',[status(thm)],[minus]) ).
cnf(derivative_of_zero,axiom,
d(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_zero) ).
cnf(derivative_of_one,axiom,
d(one) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_one) ).
cnf(derivative_of_x,axiom,
d(x) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_x) ).
cnf(derivative_of_plus,axiom,
d('+'(X,Y)) = '+'(d(X),d(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_plus) ).
cnf(derivative_of_times,axiom,
d(times(X,Y)) = '+'(times(X,d(Y)),times(Y,d(X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_times) ).
cnf(derivative_of_sin,axiom,
d(sin(X)) = times(cos(X),d(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_sin) ).
cnf(derivative_of_cos,axiom,
d(cos(X)) = minus(times(sin(X),d(X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_cos) ).
cnf(goal,negated_conjecture,
d(X) != times(x,cos(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(20,plain,
zero = minus(zero),
inference('PARAMODULATE',[status(thm)],[plus_zero,minus,theory(equality)]) ).
cnf(21,plain,
X = minus(minus(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,8,theory(equality)]),plus_zero,theory(equality)]) ).
cnf(22,plain,
minus(X) = '+'(minus('+'(X,Y)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,8,theory(equality)]),plus_zero,theory(equality)]) ).
cnf(26,plain,
d(sin(x)) = cos(x),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[derivative_of_sin,derivative_of_x,theory(equality)]),times_one,theory(equality)]) ).
cnf(31,plain,
d('+'(one,X)) = d(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[derivative_of_plus,derivative_of_one,theory(equality)]),plus_zero,theory(equality)]) ).
cnf(34,plain,
d(cos(x)) = minus(sin(x)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[derivative_of_cos,derivative_of_x,theory(equality)]),times_one,theory(equality)]) ).
cnf(39,plain,
zero = '+'(times(X,Y),times(X,minus(Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[distributivity,minus,theory(equality)]),times_zero,theory(equality)]) ).
cnf(43,plain,
d(times(X,x)) = '+'(X,times(x,d(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[derivative_of_times,derivative_of_x,theory(equality)]),times_one,theory(equality)]) ).
cnf(44,plain,
'+'(X,'+'(times(x,d(X)),Y)) = '+'(d(times(X,x)),Y),
inference('EMBED',[status(thm)],[43]) ).
cnf(83,plain,
zero = d(minus(one)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[31,minus,theory(equality)]),derivative_of_zero,theory(equality)]) ).
cnf(88,plain,
d(times(minus(one),X)) = times(minus(one),d(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[derivative_of_times,83,theory(equality)]),plus_zero,times_zero,theory(equality)]) ).
cnf(90,plain,
sin(x) = minus(d(cos(x))),
inference('PARAMODULATE',[status(thm)],[21,34,theory(equality)]) ).
cnf(91,plain,
d(minus(d(cos(x)))) = cos(x),
inference('REWRITE',[status(thm)],[26,90,theory(equality)]) ).
cnf(148,plain,
minus('+'(X,minus(Y))) = '+'(minus(X),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22,8,theory(equality)]),plus_zero,theory(equality)]) ).
cnf(229,plain,
minus(times(X,Y)) = times(X,minus(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22,39,theory(equality)]),plus_zero,20,theory(equality)]) ).
cnf(237,plain,
d(minus(X)) = minus(d(X)),
inference('REWRITE',[status(thm)],[88,times_one,229,theory(equality)]) ).
cnf(242,plain,
d(d(minus(cos(x)))) = cos(x),
inference('REWRITE',[status(thm)],[91,237,theory(equality)]) ).
cnf(258,plain,
minus(times(X,d(Y))) = times(X,d(minus(Y))),
inference('PARAMODULATE',[status(thm)],[229,237,theory(equality)]) ).
cnf(260,plain,
d(d(cos(x))) = minus(cos(x)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[237,242,theory(equality)]),21,237,theory(equality)]) ).
cnf(262,plain,
d(d(d(d(cos(x))))) = cos(x),
inference('REWRITE',[status(thm)],[242,260,theory(equality)]) ).
cnf(364,plain,
minus('+'(d(minus(times(X,x))),X)) = times(x,d(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,44,theory(equality)]),plus_zero,237,148,theory(equality)]) ).
cnf(379,plain,
minus('+'(d(X),minus(Y))) = '+'(d(minus(X)),Y),
inference('PARAMODULATE',[status(thm)],[148,237,theory(equality)]) ).
cnf(2114,plain,
minus(times(X,d(cos(x)))) = times(d(d(d(cos(x)))),X),
inference('PARAMODULATE',[status(thm)],[258,260,theory(equality)]) ).
cnf(3259,plain,
minus('+'(minus(X),d(cos(x)))) = '+'(d(d(d(cos(x)))),X),
inference('PARAMODULATE',[status(thm)],[379,260,theory(equality)]) ).
cnf(7506,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[364,262,theory(equality)]),goal,derivative_of_plus,237,3259,21,364,2114,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ANA133-1 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.14 % Command : run-snark %s %d
% 0.15/0.35 % Computer : n015.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 : Fri Jul 8 03:15:50 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.47 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.48 *
% 0.21/0.48 *
% 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/sandbox/benchmark/theBenchmark.p 2022-07-08T03:15:50
% 0.21/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n015.cluster.edu at 2022-07-08T03:15:50
% 0.21/0.50
% 0.21/0.50 ; Recognized commutativity assertion (= (+ ?X ?Y) (+ ?Y ?X)).
% 0.21/0.50 ; Recognized associativity assertion (= (+ ?X (+ ?Y ?Z)) (+ (+ ?X ?Y) ?Z)).
% 0.21/0.50 ; Recognized commutativity assertion (= (|times| ?X ?Y) (|times| ?Y ?X)).
% 0.21/0.50 ; Recognized associativity assertion (= (|times| ?X (|times| ?Y ?Z)) (|times| (|times| ?X ?Y) ?Z)).
% 0.21/0.50 ; Recognized left identity assertion (= (+ |zero| ?X) ?X).
% 0.21/0.50 ; Recognized left identity assertion (= (|times| |one| ?X) ?X).
% 0.21/0.50 ; Recognized possible right inverse assertion (= (+ ?X (|minus| ?X)) |zero|).
% 0.21/0.50 ; Declaring + to be commutative.
% 0.21/0.50 ; Declaring + to be associative-commutative.
% 0.21/0.50 ; Declaring times to be commutative.
% 69.11/69.35 ; Declaring times to be associative-commutative.
% 69.11/69.35
% 69.11/69.35 #||
% 69.11/69.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 69.11/69.35 % SZS output start Refutation
% See solution above
% 69.11/69.35 ||#
% 69.11/69.35
% 69.11/69.35 ; Summary of computation:
% 69.11/69.35 ; 36666 formulas have been input or derived (from 697 formulas).
% 69.11/69.35 ; 7506 (20%) were retained. Of these,
% 69.11/69.35 ; 745 (10%) were simplified or subsumed later,
% 69.11/69.35 ; 6761 (90%) are still being kept.
% 69.11/69.35 ;
% 69.11/69.35 ; Run time in seconds excluding printing time:
% 69.11/69.35 ; 0.002 0% Read assertion file (1 call)
% 69.11/69.35 ; 0.001 0% Assert (17 calls)
% 69.11/69.35 ; 1.276 2% Process new row (30,695 calls)
% 69.11/69.35 ; 0.075 0% Resolution (1,392 calls)
% 69.11/69.35 ; 0.686 1% Paramodulation (696 calls)
% 69.11/69.35 ; 0.010 0% Embedding (1,045 calls)
% 69.11/69.35 ; 26.182 38% Forward simplification (29,160 calls)
% 69.11/69.35 ; 0.335 0% Backward simplification (6,628 calls)
% 69.11/69.35 ; 1.068 2% Ordering (297,350 calls)
% 69.11/69.35 ; 39.053 57% Ordering ac (332,348 calls)
% 69.11/69.35 ; 0.002 0% Sortal reasoning (32 calls)
% 69.11/69.35 ; 0.000 0% Purity testing (1 call)
% 69.11/69.35 ; 0.160 0% Other
% 69.11/69.35 ; 68.850 Total
% 69.11/69.35 ; 68.858 Real time
% 69.19/69.35 ;
% 69.19/69.35 ; Term-hash-array has 26,446 terms in all.
% 69.19/69.35 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 69.19/69.35 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 69.19/69.35 ; Path-index has 24,020 entries (24,020 at peak, 26,762 added, 2,742 deleted).
% 69.19/69.35 ; Path-index has 14,541 nodes (14,541 at peak, 15,286 added, 745 deleted).
% 69.19/69.35 ; Trie-index has 24,020 entries (24,020 at peak, 26,762 added, 2,742 deleted).
% 69.19/69.35 ; Trie-index has 2,787 nodes (2,787 at peak, 3,073 added, 286 deleted).
% 69.19/69.35 ; Retrieved 59,263,113 generalization terms in 387,250 calls.
% 69.19/69.35 ; Retrieved 30,930 instance terms in 7,469 calls.
% 69.19/69.35 ; Retrieved 155,388 unifiable terms in 6,110 calls.
% 69.19/69.35 ;
% 69.19/69.35 ; The agenda of rows to process has 374 entries:
% 69.19/69.35 ; 34 with value 34 88 with value 36 92 with value 38
% 69.19/69.35 ; 34 with value 35 57 with value 37 69 with value 39
% 69.19/69.35 ; The agenda of rows to give has 6078 entries:
% 69.19/69.35 ; 349 with value (4 21) 11 with value (4 40) 9 with value (4 63)
% 69.19/69.35 ; 488 with value (4 22) 31 with value (4 41) 2 with value (4 64)
% 69.19/69.35 ; 780 with value (4 23) 33 with value (4 42) 8 with value (4 65)
% 69.19/69.35 ; 994 with value (4 24) 22 with value (4 43) 10 with value (4 66)
% 69.19/69.35 ; 1276 with value (4 25) 8 with value (4 44) 2 with value (4 67)
% 69.19/69.35 ; 507 with value (4 26) 4 with value (4 45) 3 with value (4 68)
% 69.19/69.35 ; 149 with value (4 27) 5 with value (4 46) 1 with value (4 71)
% 69.19/69.35 ; 94 with value (4 28) 15 with value (4 47) 1 with value (4 72)
% 69.19/69.35 ; 129 with value (4 29) 12 with value (4 48) 1 with value (4 76)
% 69.19/69.35 ; 150 with value (4 30) 4 with value (4 49) 1 with value (4 78)
% 69.19/69.35 ; 174 with value (4 31) 17 with value (4 50) 24 with value (4 83)
% 69.19/69.35 ; 100 with value (4 32) 4 with value (4 51) 1 with value (4 92)
% 69.19/69.35 ; 133 with value (4 33) 2 with value (4 52) 8 with value (4 93)
% 69.19/69.35 ; 173 with value (4 34) 8 with value (4 53) 16 with value (4 95)
% 69.19/69.35 ; 54 with value (4 35) 19 with value (4 54) 8 with value (4 101)
% 69.19/69.35 ; 35 with value (4 36) 8 with value (4 56) 16 with value (4 103)
% 69.19/69.35 ; 52 with value (4 37) 10 with value (4 57) 8 with value (4 111)
% 69.19/69.35 ; 41 with value (4 38) 9 with value (4 59) 2 with value (4 119)
% 69.19/69.35 ; 41 with value (4 39) 15 with value (4 62) 1 with value (4 150)
% 69.19/69.35 Evaluation took:
% 69.19/69.35 68.86 seconds of real time
% 69.19/69.35 67.82767 seconds of user run time
% 69.19/69.35 1.026936 seconds of system run time
% 69.19/69.35 [Run times include 2.36 seconds GC run time.]
% 69.19/69.35 0 calls to %EVAL
% 69.19/69.35 0 page faults and
% 69.19/69.35 2,955,020,200 bytes consed.
% 69.19/69.35 :PROOF-FOUND
% 69.19/69.35 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-08T03:16:59
% 69.19/69.35 :PROOF-FOUND
% 69.19/69.35 *
%------------------------------------------------------------------------------