TSTP Solution File: KLE143+2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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  * 
%------------------------------------------------------------------------------