TSTP Solution File: KLE143+1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : KLE143+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n013.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 02:26:49 EDT 2022
% Result : Theorem 129.11s 129.34s
% Output : Refutation 129.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of clauses : 37 ( 33 unt; 0 nHn; 8 RR)
% Number of literals : 41 ( 29 equ; 7 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/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
cnf(2,axiom,
addition(X,X) = X,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
cnf(5,axiom,
multiplication(X,one) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
cnf(6,axiom,
multiplication(one,X) = X,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
cnf(8,axiom,
multiplication(addition(X,Y),Z) = addition(multiplication(X,Z),multiplication(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
cnf(9,axiom,
multiplication(zero,X) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
cnf(10,axiom,
addition(one,multiplication(X,star(X))) = star(X),
file('/export/starexec/sandbox/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(12,axiom,
addition(one,multiplication(star(X),X)) = star(X),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
cnf(14,axiom,
( ~ leq(addition(multiplication(X,Y),Z),Y)
| leq(multiplication(star(X),Z),Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction1) ).
cnf(16,axiom,
strong_iteration(X) = addition(multiplication(X,strong_iteration(X)),one),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
cnf(19,axiom,
strong_iteration(X) = addition(star(X),multiplication(strong_iteration(X),zero)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',isolation) ).
cnf(21,axiom,
( ~ leq(X,Y)
| addition(X,Y) = Y ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
cnf(22,axiom,
( leq(X,Y)
| addition(X,Y) != Y ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
cnf(23,negated_conjecture,
multiplication(strong_iteration('SKOLEMAAAU1'),strong_iteration('SKOLEMAAAU1')) != strong_iteration('SKOLEMAAAU1'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(26,plain,
leq(X,addition(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[22,3]) ).
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(82,plain,
multiplication(X,zero) = multiplication(multiplication(X,zero),Y),
inference('PARAMODULATE',[status(thm)],[4,9,theory(equality)]) ).
cnf(108,plain,
multiplication(X,Y) = addition(multiplication(X,Y),multiplication(X,zero)),
inference('PARAMODULATE',[status(thm)],[7,1,theory(equality)]) ).
cnf(126,plain,
multiplication(star(X),Y) = addition(Y,multiplication(multiplication(star(X),X),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,12,theory(equality)]),6,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,
addition(multiplication(star('SKOLEMAAAU1'),strong_iteration('SKOLEMAAAU1')),multiplication(strong_iteration('SKOLEMAAAU1'),zero)) != strong_iteration('SKOLEMAAAU1'),
inference('REWRITE',[status(thm)],[23,132,theory(equality)]) ).
cnf(149,plain,
( ~ leq(multiplication(X,Y),Y)
| leq(multiplication(star(X),multiplication(X,Y)),Y) ),
inference('PARAMODULATE',[status(thm)],[14,2,theory(equality)]) ).
cnf(202,plain,
leq(multiplication(X,strong_iteration(X)),strong_iteration(X)),
inference('PARAMODULATE',[status(thm)],[26,16,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(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,
multiplication(star('SKOLEMAAAU1'),strong_iteration('SKOLEMAAAU1')) != strong_iteration('SKOLEMAAAU1'),
inference('REWRITE',[status(thm)],[134,1276,theory(equality)]) ).
cnf(16505,plain,
leq(multiplication(multiplication(star(X),X),strong_iteration(X)),strong_iteration(X)),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[149,202]),4,theory(equality)]) ).
cnf(16521,plain,
multiplication(star(X),strong_iteration(X)) = strong_iteration(X),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[21,16505]),126,theory(equality)]) ).
cnf(16524,plain,
$false,
inference('REWRITE',[status(thm)],[1278,16521,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE143+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 12:20:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 *
% 0.18/0.46 *
% 0.18/0.46 #<PACKAGE "SNARK-USER">
% 0.18/0.46 *
% 0.18/0.46 SNARK-TPTP-OPTIONS
% 0.18/0.46 *
% 0.18/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46 (USE-FACTORING :POS)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.46 *
% 0.18/0.46 "."
% 0.18/0.46 *
% 0.18/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T12:20:44
% 0.18/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n013.cluster.edu at 2022-06-16T12:20:44
% 0.18/0.48
% 0.18/0.48 ; Recognized commutativity assertion (= (|addition| ?X ?Y) (|addition| ?Y ?X)).
% 0.18/0.48 ; Recognized associativity assertion (= (|addition| ?X (|addition| ?Y ?Z)) (|addition| (|addition| ?X ?Y) ?Z)).
% 0.18/0.48 ; Recognized right identity assertion (= (|addition| ?X |zero|) ?X).
% 0.18/0.48 ; Recognized associativity assertion (= (|multiplication| ?X (|multiplication| ?Y ?Z)) (|multiplication| (|multiplication| ?X ?Y) ?Z)).
% 0.18/0.48 ; Recognized right identity assertion (= (|multiplication| ?X |one|) ?X).
% 0.18/0.48 ; Recognized left identity assertion (= (|multiplication| |one| ?X) ?X).
% 0.18/0.48 ; Declaring addition to be commutative.
% 129.11/129.34 ; Declaring addition to be associative-commutative.
% 129.11/129.34
% 129.11/129.34 #||
% 129.11/129.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 129.11/129.34 % SZS output start Refutation
% See solution above
% 129.11/129.35 ||#
% 129.11/129.35
% 129.11/129.35 ; Summary of computation:
% 129.11/129.35 ; 100385 formulas have been input or derived (from 616 formulas).
% 129.11/129.35 ; 16524 (16%) were retained. Of these,
% 129.11/129.35 ; 3818 (23%) were simplified or subsumed later,
% 129.11/129.35 ; 12706 (77%) are still being kept.
% 129.11/129.35 ;
% 129.11/129.35 ; Run time in seconds excluding printing time:
% 129.11/129.35 ; 0.004 0% Read assertion file (1 call)
% 129.11/129.35 ; 0.001 0% Assert (19 calls)
% 129.11/129.35 ; 2.978 2% Process new row (98,329 calls)
% 129.11/129.35 ; 0.225 0% Resolution (1,230 calls)
% 129.11/129.35 ; 1.375 1% Paramodulation (615 calls)
% 129.11/129.35 ; 0.006 0% Embedding (862 calls)
% 129.11/129.35 ; 0.134 0% Condensing (4,492 calls)
% 129.11/129.35 ; 0.508 0% Forward subsumption (4,492 calls)
% 129.11/129.35 ; 0.178 0% Backward subsumption (2,193 calls)
% 129.11/129.35 ; 0.280 0% Clause clause subsumption (37,264 calls)
% 129.11/129.35 ; 119.238 93% Forward simplification (96,066 calls)
% 129.11/129.35 ; 1.930 1% Backward simplification (15,677 calls)
% 129.11/129.35 ; 0.788 1% Ordering (184,796 calls)
% 129.11/129.35 ; 0.834 1% Ordering ac (50,813 calls)
% 129.11/129.35 ; 0.000 0% Sortal reasoning (32 calls)
% 129.11/129.35 ; 0.001 0% Purity testing (1 call)
% 129.11/129.35 ; 0.406 0% Other
% 129.11/129.35 ; 128.886 Total
% 129.11/129.35 ; 128.882 Real time
% 129.11/129.35 ;
% 129.11/129.35 ; Term-hash-array has 31,152 terms in all.
% 129.11/129.35 ; Feature-vector-row-index has 1,905 entries (1,907 at peak, 2,193 added, 288 deleted).
% 129.11/129.35 ; Feature-vector-row-index has 12,074 nodes (12,074 at peak, 14,678 added, 2,604 deleted).
% 129.11/129.35 ; Retrieved 43,534 possibly forward subsuming rows in 4,492 calls.
% 129.11/129.35 ; Retrieved 6,666 possibly backward subsumed rows in 2,193 calls.
% 129.11/129.35 ; Path-index has 24,355 entries (24,367 at peak, 32,140 added, 7,785 deleted).
% 129.11/129.35 ; Path-index has 6,329 nodes (6,336 at peak, 7,081 added, 752 deleted).
% 129.11/129.35 ; Trie-index has 24,355 entries (24,367 at peak, 32,140 added, 7,785 deleted).
% 129.11/129.35 ; Trie-index has 7,012 nodes (7,041 at peak, 8,914 added, 1,902 deleted).
% 129.11/129.35 ; Retrieved 152,417,188 generalization terms in 893,523 calls.
% 129.11/129.35 ; Retrieved 134,415 instance terms in 13,660 calls.
% 129.11/129.35 ; Retrieved 325,945 unifiable terms in 5,293 calls.
% 129.11/129.35 ;
% 129.11/129.35 ; The agenda of rows to process has 7 entries:
% 129.11/129.35 ; 1 with value 23 1 with value 25 1 with value 28
% 129.11/129.35 ; 2 with value 24 1 with value 27 1 with value 33
% 129.11/129.35 ; The agenda of rows to give has 12175 entries:
% 129.11/129.35 ; 1 with value (4 15) 273 with value (4 37) 37 with value (4 57)
% 129.11/129.35 ; 1 with value (4 17) 193 with value (4 38) 19 with value (4 58)
% 129.11/129.35 ; 233 with value (4 19) 159 with value (4 39) 6 with value (4 59)
% 129.11/129.35 ; 350 with value (4 20) 178 with value (4 40) 15 with value (4 60)
% 129.11/129.35 ; 501 with value (4 21) 167 with value (4 41) 18 with value (4 61)
% 129.11/129.35 ; 516 with value (4 22) 220 with value (4 42) 19 with value (4 62)
% 129.11/129.35 ; 716 with value (4 23) 168 with value (4 43) 12 with value (4 63)
% 129.11/129.35 ; 750 with value (4 24) 135 with value (4 44) 14 with value (4 64)
% 129.11/129.35 ; 658 with value (4 25) 130 with value (4 45) 5 with value (4 65)
% 129.11/129.35 ; 833 with value (4 26) 125 with value (4 46) 1 with value (4 66)
% 129.11/129.35 ; 644 with value (4 27) 119 with value (4 47) 1 with value (4 67)
% 129.11/129.35 ; 739 with value (4 28) 83 with value (4 48) 2 with value (4 68)
% 129.11/129.35 ; 633 with value (4 29) 71 with value (4 49) 4 with value (4 69)
% 129.11/129.35 ; 560 with value (4 30) 58 with value (4 50) 2 with value (4 70)
% 129.11/129.35 ; 569 with value (4 31) 47 with value (4 51) 1 with value (4 72)
% 129.11/129.35 ; 522 with value (4 32) 68 with value (4 52) 1 with value (4 76)
% 129.11/129.35 ; 481 with value (4 33) 30 with value (4 53) 1 with value (4 77)
% 129.11/129.35 ; 309 with value (4 34) 40 with value (4 54) 1 with value (4 78)
% 129.11/129.35 ; 312 with value (4 35) 42 with value (4 55) 1 with value (4 83)
% 129.11/129.35 ; 354 with value (4 36) 26 with value (4 56) 1 with value (4 86)
% 129.11/129.35 Evaluation took:
% 129.11/129.35 128.884 seconds of real time
% 129.11/129.35 127.62367 seconds of user run time
% 129.11/129.35 1.265963 seconds of system run time
% 129.11/129.35 [Run times include 6.381 seconds GC run time.]
% 129.11/129.35 0 calls to %EVAL
% 129.11/129.35 0 page faults and
% 129.11/129.35 7,374,304,592 bytes consed.
% 129.11/129.35 :PROOF-FOUND
% 129.11/129.35 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T12:22:53
% 129.11/129.35 :PROOF-FOUND
% 129.11/129.35 *
%------------------------------------------------------------------------------