TSTP Solution File: KLE143+2 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : KLE143+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n014.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 : Sun Jul 17 02:26:50 EDT 2022
% Result : Theorem 1.65s 1.82s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of clauses : 36 ( 31 unt; 0 nHn; 7 RR)
% Number of literals : 41 ( 27 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
addition(X,zero) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
cnf(2,axiom,
addition(X,X) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
cnf(3,plain,
addition(X,addition(X,Y)) = addition(X,Y),
inference('EMBED',[status(thm)],[2]) ).
cnf(4,axiom,
multiplication(X,multiplication(Y,Z)) = multiplication(multiplication(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
cnf(5,axiom,
multiplication(X,one) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
cnf(6,axiom,
multiplication(one,X) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
cnf(7,axiom,
multiplication(X,addition(Y,Z)) = addition(multiplication(X,Y),multiplication(X,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
cnf(8,axiom,
multiplication(addition(X,Y),Z) = addition(multiplication(X,Z),multiplication(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
cnf(9,axiom,
multiplication(zero,X) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
cnf(10,axiom,
addition(one,multiplication(X,star(X))) = star(X),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
cnf(11,plain,
addition(one,addition(multiplication(X,star(X)),Y)) = addition(star(X),Y),
inference('EMBED',[status(thm)],[10]) ).
cnf(14,axiom,
( ~ leq(addition(multiplication(X,Y),Z),Y)
| leq(multiplication(star(X),Z),Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction1) ).
cnf(16,axiom,
strong_iteration(X) = addition(multiplication(X,strong_iteration(X)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
cnf(17,plain,
addition(multiplication(X,strong_iteration(X)),addition(one,Y)) = addition(strong_iteration(X),Y),
inference('EMBED',[status(thm)],[16]) ).
cnf(19,axiom,
strong_iteration(X) = addition(star(X),multiplication(strong_iteration(X),zero)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',isolation) ).
cnf(20,plain,
addition(star(X),addition(multiplication(strong_iteration(X),zero),Y)) = addition(strong_iteration(X),Y),
inference('EMBED',[status(thm)],[19]) ).
cnf(21,axiom,
( ~ leq(X,Y)
| addition(X,Y) = Y ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
cnf(22,axiom,
( leq(X,Y)
| addition(X,Y) != Y ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
cnf(23,negated_conjecture,
( ~ leq(multiplication(strong_iteration('SKOLEMAAAV1'),strong_iteration('SKOLEMAAAV1')),strong_iteration('SKOLEMAAAV1'))
| ~ leq(strong_iteration('SKOLEMAAAV1'),multiplication(strong_iteration('SKOLEMAAAV1'),strong_iteration('SKOLEMAAAV1'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(25,plain,
leq(X,X),
inference('HYPERRESOLVE',[status(thm)],[22,2]) ).
cnf(35,plain,
addition(star(X),one) = star(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,11,theory(equality)]),10,theory(equality)]) ).
cnf(66,plain,
addition(strong_iteration(X),one) = strong_iteration(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,17,theory(equality)]),16,theory(equality)]) ).
cnf(82,plain,
multiplication(X,zero) = multiplication(multiplication(X,zero),Y),
inference('PARAMODULATE',[status(thm)],[4,9,theory(equality)]) ).
cnf(103,plain,
addition(strong_iteration(Y),multiplication(X,strong_iteration(X))) = addition(strong_iteration(X),strong_iteration(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,20,theory(equality)]),19,66,theory(equality)]) ).
cnf(108,plain,
multiplication(X,Y) = addition(multiplication(X,Y),multiplication(X,zero)),
inference('PARAMODULATE',[status(thm)],[7,1,theory(equality)]) ).
cnf(132,plain,
multiplication(strong_iteration(X),Y) = addition(multiplication(star(X),Y),multiplication(strong_iteration(X),zero)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,19,theory(equality)]),82,theory(equality)]) ).
cnf(134,plain,
( ~ leq(addition(multiplication(star('SKOLEMAAAV1'),strong_iteration('SKOLEMAAAV1')),multiplication(strong_iteration('SKOLEMAAAV1'),zero)),strong_iteration('SKOLEMAAAV1'))
| ~ leq(strong_iteration('SKOLEMAAAV1'),addition(multiplication(star('SKOLEMAAAV1'),strong_iteration('SKOLEMAAAV1')),multiplication(strong_iteration('SKOLEMAAAV1'),zero))) ),
inference('REWRITE',[status(thm)],[23,132,theory(equality)]) ).
cnf(231,plain,
multiplication(star(X),Y) = addition(Y,multiplication(star(X),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,35,theory(equality)]),6,theory(equality)]) ).
cnf(363,plain,
X = addition(X,multiplication(X,zero)),
inference('PARAMODULATE',[status(thm)],[108,5,theory(equality)]) ).
cnf(364,plain,
addition(X,addition(multiplication(X,zero),Y)) = addition(X,Y),
inference('EMBED',[status(thm)],[363]) ).
cnf(402,plain,
leq(multiplication(X,zero),addition(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[22,364]) ).
cnf(1163,plain,
leq(X,multiplication(star(Y),X)),
inference('HYPERRESOLVE',[status(thm)],[22,231]) ).
cnf(1168,plain,
leq(multiplication(X,zero),multiplication(star(Y),X)),
inference('PARAMODULATE',[status(thm)],[402,231,theory(equality)]) ).
cnf(1276,plain,
addition(multiplication(X,zero),multiplication(star(Y),X)) = multiplication(star(Y),X),
inference('HYPERRESOLVE',[status(thm)],[21,1168]) ).
cnf(1278,plain,
~ leq(multiplication(star('SKOLEMAAAV1'),strong_iteration('SKOLEMAAAV1')),strong_iteration('SKOLEMAAAV1')),
inference('REWRITE',[status(thm)],[134,1163,1276,theory(equality)]) ).
cnf(1280,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[14,1278]),25,2,103,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE143+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n014.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 : Thu Jun 16 07:12:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.47 #<PACKAGE "SNARK-USER">
% 0.19/0.47 *
% 0.19/0.47 SNARK-TPTP-OPTIONS
% 0.19/0.47 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-16T07:12:50
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n014.cluster.edu at 2022-06-16T07:12:50
% 0.19/0.48
% 0.19/0.48 ; Recognized commutativity assertion (= (|addition| ?X ?Y) (|addition| ?Y ?X)).
% 0.19/0.48 ; Recognized associativity assertion (= (|addition| ?X (|addition| ?Y ?Z)) (|addition| (|addition| ?X ?Y) ?Z)).
% 0.19/0.48 ; Recognized right identity assertion (= (|addition| ?X |zero|) ?X).
% 0.19/0.48 ; Recognized associativity assertion (= (|multiplication| ?X (|multiplication| ?Y ?Z)) (|multiplication| (|multiplication| ?X ?Y) ?Z)).
% 0.19/0.48 ; Recognized right identity assertion (= (|multiplication| ?X |one|) ?X).
% 0.19/0.48 ; Recognized left identity assertion (= (|multiplication| |one| ?X) ?X).
% 0.19/0.48 ; Declaring addition to be commutative.
% 1.65/1.82 ; Declaring addition to be associative-commutative.
% 1.65/1.82
% 1.65/1.82 #||
% 1.65/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.65/1.82 % SZS output start Refutation
% See solution above
% 1.65/1.83 ||#
% 1.65/1.83
% 1.65/1.83 ; Summary of computation:
% 1.65/1.83 ; 8256 formulas have been input or derived (from 165 formulas).
% 1.65/1.83 ; 1280 (16%) were retained. Of these,
% 1.65/1.83 ; 152 (12%) were simplified or subsumed later,
% 1.65/1.83 ; 1128 (88%) are still being kept.
% 1.65/1.83 ;
% 1.65/1.83 ; Run time in seconds excluding printing time:
% 1.65/1.83 ; 0.004 0% Read assertion file (1 call)
% 1.65/1.83 ; 0.001 0% Assert (19 calls)
% 1.65/1.83 ; 0.124 9% Process new row (7,808 calls)
% 1.65/1.83 ; 0.021 2% Resolution (328 calls)
% 1.65/1.83 ; 0.106 8% Paramodulation (164 calls)
% 1.65/1.83 ; 0.002 0% Embedding (107 calls)
% 1.65/1.83 ; 0.035 3% Condensing (1,176 calls)
% 1.65/1.83 ; 0.053 4% Forward subsumption (1,176 calls)
% 1.65/1.83 ; 0.016 1% Backward subsumption (532 calls)
% 1.65/1.83 ; 0.030 2% Clause clause subsumption (3,574 calls)
% 1.65/1.83 ; 0.858 63% Forward simplification (7,513 calls)
% 1.65/1.83 ; 0.022 2% Backward simplification (1,178 calls)
% 1.65/1.83 ; 0.024 2% Ordering (7,098 calls)
% 1.65/1.83 ; 0.009 1% Ordering ac (1,104 calls)
% 1.65/1.83 ; 0.001 0% Sortal reasoning (32 calls)
% 1.65/1.83 ; 0.000 0% Purity testing (1 call)
% 1.65/1.83 ; 0.051 4% Other
% 1.65/1.83 ; 1.357 Total
% 1.65/1.83 ; 1.365 Real time
% 1.65/1.83 ;
% 1.65/1.83 ; Term-hash-array has 2,709 terms in all.
% 1.65/1.83 ; Feature-vector-row-index has 495 entries (496 at peak, 532 added, 37 deleted).
% 1.65/1.83 ; Feature-vector-row-index has 3,531 nodes (3,550 at peak, 3,828 added, 297 deleted).
% 1.65/1.83 ; Retrieved 4,238 possibly forward subsuming rows in 1,176 calls.
% 1.65/1.83 ; Retrieved 624 possibly backward subsumed rows in 532 calls.
% 1.65/1.83 ; Path-index has 2,432 entries (2,435 at peak, 2,740 added, 308 deleted).
% 1.65/1.83 ; Path-index has 1,523 nodes (1,532 at peak, 1,649 added, 126 deleted).
% 1.65/1.83 ; Trie-index has 2,432 entries (2,435 at peak, 2,740 added, 308 deleted).
% 1.65/1.83 ; Trie-index has 1,384 nodes (1,384 at peak, 1,640 added, 256 deleted).
% 1.65/1.83 ; Retrieved 1,142,341 generalization terms in 52,797 calls.
% 1.65/1.83 ; Retrieved 2,381 instance terms in 678 calls.
% 1.65/1.83 ; Retrieved 24,002 unifiable terms in 1,229 calls.
% 1.65/1.83 ;
% 1.65/1.83 ; The agenda of rows to process has 2 entries:
% 1.65/1.83 ; 1 with value 16 1 with value 17
% 1.65/1.83 ; The agenda of rows to give has 974 entries:
% 1.65/1.83 ; 2 with value (4 15) 42 with value (4 27) 17 with value (4 39)
% 1.65/1.83 ; 6 with value (4 16) 60 with value (4 28) 11 with value (4 40)
% 1.65/1.83 ; 43 with value (4 17) 42 with value (4 29) 5 with value (4 41)
% 1.65/1.83 ; 34 with value (4 18) 19 with value (4 30) 3 with value (4 42)
% 1.65/1.83 ; 66 with value (4 19) 24 with value (4 31) 2 with value (4 43)
% 1.65/1.83 ; 71 with value (4 20) 30 with value (4 32) 2 with value (4 44)
% 1.65/1.83 ; 72 with value (4 21) 24 with value (4 33) 3 with value (4 45)
% 1.65/1.83 ; 85 with value (4 22) 22 with value (4 34) 1 with value (4 46)
% 1.65/1.83 ; 56 with value (4 23) 8 with value (4 35) 1 with value (4 47)
% 1.65/1.83 ; 56 with value (4 24) 18 with value (4 36) 1 with value (4 49)
% 1.65/1.83 ; 55 with value (4 25) 9 with value (4 37) 3 with value (4 50)
% 1.65/1.83 ; 75 with value (4 26) 6 with value (4 38)
% 1.65/1.83 Evaluation took:
% 1.65/1.83 1.366 seconds of real time
% 1.65/1.83 1.299877 seconds of user run time
% 1.65/1.83 0.066064 seconds of system run time
% 1.65/1.83 [Run times include 0.047 seconds GC run time.]
% 1.65/1.83 0 calls to %EVAL
% 1.65/1.83 0 page faults and
% 1.65/1.83 103,133,112 bytes consed.
% 1.65/1.83 :PROOF-FOUND
% 1.65/1.83 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-16T07:12:52
% 1.65/1.83 :PROOF-FOUND
% 1.65/1.83 *
%------------------------------------------------------------------------------