TSTP Solution File: KLE144+1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : KLE144+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n027.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 23.27s 23.48s
% Output   : Refutation 23.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   49 (  44 unt;   0 nHn;   7 RR)
%            Number of literals    :   54 (  38 equ;   6 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   :   75 (  15 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(13,plain,
    addition(one,addition(multiplication(star(X),X),Y)) = addition(star(X),Y),
    inference('EMBED',[status(thm)],[12]) ).

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(18,axiom,
    ( ~ leq(X,addition(multiplication(Y,X),Z))
    | leq(X,multiplication(strong_iteration(Y),Z)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).

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,
    strong_iteration(star('SKOLEMAAAV1')) != strong_iteration(one),
    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(179,plain,
    leq(X,multiplication(strong_iteration(one),Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,6,theory(equality)]),26]) ).

cnf(180,plain,
    ( ~ leq(X,multiplication(Y,X))
    | leq(X,multiplication(strong_iteration(Y),zero)) ),
    inference('PARAMODULATE',[status(thm)],[18,1,theory(equality)]) ).

cnf(181,plain,
    ( ~ leq(X,star(X))
    | leq(X,strong_iteration(star(X))) ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,12,theory(equality)]),5,theory(equality)]) ).

cnf(223,plain,
    leq(X,strong_iteration(one)),
    inference('PARAMODULATE',[status(thm)],[179,5,theory(equality)]) ).

cnf(227,plain,
    addition(strong_iteration(one),X) = strong_iteration(one),
    inference('HYPERRESOLVE',[status(thm)],[21,223]) ).

cnf(230,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(231,plain,
    addition(X,addition(multiplication(star(Y),X),Z)) = addition(multiplication(star(Y),X),Z),
    inference('EMBED',[status(thm)],[230]) ).

cnf(276,plain,
    addition(one,multiplication(X,zero)) = star(multiplication(X,zero)),
    inference('PARAMODULATE',[status(thm)],[10,82,theory(equality)]) ).

cnf(278,plain,
    strong_iteration(multiplication(X,zero)) = star(multiplication(X,zero)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,82,theory(equality)]),276,theory(equality)]) ).

cnf(362,plain,
    X = addition(X,multiplication(X,zero)),
    inference('PARAMODULATE',[status(thm)],[108,5,theory(equality)]) ).

cnf(363,plain,
    addition(X,addition(multiplication(X,zero),Y)) = addition(X,Y),
    inference('EMBED',[status(thm)],[362]) ).

cnf(1162,plain,
    leq(X,multiplication(star(Y),X)),
    inference('HYPERRESOLVE',[status(thm)],[22,230]) ).

cnf(1168,plain,
    multiplication(star(X),strong_iteration(one)) = strong_iteration(one),
    inference('PARAMODULATE',[status(thm)],[227,230,theory(equality)]) ).

cnf(1260,plain,
    leq(X,multiplication(strong_iteration(star(Y)),zero)),
    inference('HYPERRESOLVE',[status(thm)],[180,1162]) ).

cnf(1282,plain,
    addition(X,multiplication(strong_iteration(star(Y)),zero)) = multiplication(strong_iteration(star(Y)),zero),
    inference('HYPERRESOLVE',[status(thm)],[21,1260]) ).

cnf(1314,plain,
    star(X) = addition(star(X),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[13,231,theory(equality)]),12,theory(equality)]) ).

cnf(1455,plain,
    leq(X,star(X)),
    inference('HYPERRESOLVE',[status(thm)],[22,1314]) ).

cnf(1456,plain,
    leq(X,strong_iteration(star(X))),
    inference('REWRITE',[status(thm)],[181,1455]) ).

cnf(1534,plain,
    addition(X,strong_iteration(star(X))) = strong_iteration(star(X)),
    inference('HYPERRESOLVE',[status(thm)],[21,1456]) ).

cnf(1535,plain,
    addition(X,addition(strong_iteration(star(X)),Y)) = addition(strong_iteration(star(X)),Y),
    inference('EMBED',[status(thm)],[1534]) ).

cnf(2392,plain,
    multiplication(strong_iteration(star(X)),zero) = strong_iteration(star(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[363,1535,theory(equality)]),1534,1282,theory(equality)]) ).

cnf(2393,plain,
    addition(X,strong_iteration(star(Y))) = strong_iteration(star(Y)),
    inference('REWRITE',[status(thm)],[1282,2392,theory(equality)]) ).

cnf(2809,plain,
    strong_iteration(strong_iteration(star(X))) = star(strong_iteration(star(X))),
    inference('PARAMODULATE',[status(thm)],[278,2392,theory(equality)]) ).

cnf(2810,plain,
    strong_iteration(star(X)) = multiplication(strong_iteration(star(X)),Y),
    inference('PARAMODULATE',[status(thm)],[82,2392,theory(equality)]) ).

cnf(5540,plain,
    star(strong_iteration(star(X))) = strong_iteration(star(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,2809,theory(equality)]),2393,2810,theory(equality)]) ).

cnf(5872,plain,
    strong_iteration(star(X)) = strong_iteration(one),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1168,5540,theory(equality)]),2810,theory(equality)]) ).

cnf(5873,plain,
    $false,
    inference('REWRITE',[status(thm)],[23,5872,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : KLE144+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : run-snark %s %d
% 0.13/0.33  % Computer : n027.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Thu Jun 16 16:50:05 EDT 2022
% 0.13/0.34  % 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  * 
% 0.18/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.47   (USE-FACTORING :POS)
% 0.18/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.47  * 
% 0.18/0.47  "."
% 0.18/0.47  * 
% 0.18/0.47  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T16:50:06
% 0.18/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n027.cluster.edu at 2022-06-16T16:50:06
% 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.
% 23.27/23.48  ; Declaring addition to be associative-commutative.
% 23.27/23.48  
% 23.27/23.48  #||
% 23.27/23.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.27/23.48  % SZS output start Refutation
% See solution above
% 23.27/23.49  ||#
% 23.27/23.49  
% 23.27/23.49  ; Summary of computation:
% 23.27/23.49  ;     41482 formulas have been input or derived (from 379 formulas).
% 23.27/23.49  ;      5873 (14%) were retained.  Of these,
% 23.27/23.49  ;         1297 (22%) were simplified or subsumed later,
% 23.27/23.49  ;         4576 (78%) are still being kept.
% 23.27/23.49  ; 
% 23.27/23.49  ; Run time in seconds excluding printing time:
% 23.27/23.49  ;     0.004   0%   Read assertion file          (1 call)
% 23.27/23.49  ;     0.001   0%   Assert                       (19 calls)
% 23.27/23.49  ;     0.699   3%   Process new row              (40,114 calls)
% 23.27/23.49  ;     0.116   1%   Resolution                   (756 calls)
% 23.27/23.49  ;     0.497   2%   Paramodulation               (378 calls)
% 23.27/23.49  ;     0.004   0%   Embedding                    (362 calls)
% 23.27/23.49  ;     0.090   0%   Condensing                   (2,727 calls)
% 23.27/23.49  ;     0.208   1%   Forward subsumption          (2,727 calls)
% 23.27/23.49  ;     0.064   0%   Backward subsumption         (1,245 calls)
% 23.27/23.49  ;     0.132   1%   Clause clause subsumption    (13,897 calls)
% 23.27/23.49  ;    20.580  89%   Forward simplification       (38,899 calls)
% 23.27/23.49  ;     0.274   1%   Backward simplification      (5,516 calls)
% 23.27/23.49  ;     0.131   1%   Ordering                     (36,223 calls)
% 23.27/23.49  ;     0.062   0%   Ordering ac                  (5,073 calls)
% 23.27/23.49  ;     0.000   0%   Sortal reasoning             (32 calls)
% 23.27/23.49  ;     0.000   0%   Purity testing               (1 call)
% 23.27/23.49  ;     0.154   1%   Other
% 23.27/23.49  ;    23.016        Total
% 23.27/23.49  ;    23.025        Real time
% 23.27/23.49  ; 
% 23.27/23.49  ; Term-hash-array has 11,400 terms in all.
% 23.27/23.49  ; Feature-vector-row-index has 1,088 entries (1,096 at peak, 1,245 added, 157 deleted).
% 23.27/23.49  ; Feature-vector-row-index has 7,165 nodes (7,212 at peak, 8,540 added, 1,375 deleted).
% 23.27/23.49  ;  Retrieved 17,616 possibly forward subsuming rows in 2,727 calls.
% 23.27/23.49  ;  Retrieved 1,878 possibly backward subsumed rows in 1,245 calls.
% 23.27/23.49  ; Path-index has 9,129 entries (9,204 at peak, 11,740 added, 2,611 deleted).
% 23.27/23.49  ; Path-index has 3,744 nodes (3,799 at peak, 4,253 added, 509 deleted).
% 23.27/23.49  ; Trie-index has 9,129 entries (9,204 at peak, 11,740 added, 2,611 deleted).
% 23.27/23.49  ; Trie-index has 3,207 nodes (3,345 at peak, 4,199 added, 992 deleted).
% 23.27/23.49  ; Retrieved 23,583,036 generalization terms in 296,709 calls.
% 23.27/23.49  ; Retrieved 28,173 instance terms in 4,303 calls.
% 23.27/23.49  ; Retrieved 113,543 unifiable terms in 3,150 calls.
% 23.27/23.49  ; 
% 23.27/23.49  ; The agenda of rows to process has 157 entries:
% 23.27/23.49  ;     8 with value 19             14 with value 23               7 with value 27
% 23.27/23.49  ;    29 with value 20             22 with value 24               1 with value 28
% 23.27/23.49  ;    38 with value 21              7 with value 25               1 with value 30
% 23.27/23.49  ;    26 with value 22              4 with value 26
% 23.27/23.49  ; The agenda of rows to give has 4247 entries:
% 23.27/23.49  ;     1 with value (4 15)         53 with value (4 34)          13 with value (4 52)
% 23.27/23.49  ;     2 with value (4 17)         55 with value (4 35)           3 with value (4 53)
% 23.27/23.49  ;   155 with value (4 18)         70 with value (4 36)          13 with value (4 54)
% 23.27/23.49  ;   220 with value (4 19)         50 with value (4 37)          13 with value (4 55)
% 23.27/23.49  ;   217 with value (4 20)         47 with value (4 38)          12 with value (4 56)
% 23.27/23.49  ;   304 with value (4 21)         41 with value (4 39)           2 with value (4 57)
% 23.27/23.49  ;   347 with value (4 22)         36 with value (4 40)           4 with value (4 58)
% 23.27/23.49  ;   342 with value (4 23)         30 with value (4 41)           1 with value (4 59)
% 23.27/23.49  ;   287 with value (4 24)         25 with value (4 42)           1 with value (4 60)
% 23.27/23.49  ;   336 with value (4 25)         21 with value (4 43)           1 with value (4 61)
% 23.27/23.49  ;   301 with value (4 26)         21 with value (4 44)           7 with value (4 62)
% 23.27/23.49  ;   207 with value (4 27)         19 with value (4 45)           4 with value (4 63)
% 23.27/23.49  ;   226 with value (4 28)         25 with value (4 46)           5 with value (4 64)
% 23.27/23.49  ;   177 with value (4 29)         21 with value (4 47)           2 with value (4 65)
% 23.27/23.49  ;   139 with value (4 30)          9 with value (4 48)           1 with value (4 69)
% 23.27/23.49  ;   141 with value (4 31)          3 with value (4 49)           1 with value (4 70)
% 23.27/23.49  ;   129 with value (4 32)         13 with value (4 50)           1 with value (4 77)
% 23.27/23.49  ;    80 with value (4 33)         13 with value (4 51)
% 23.27/23.49  Evaluation took:
% 23.27/23.49    23.026 seconds of real time
% 23.27/23.49    22.682892 seconds of user run time
% 23.27/23.49    0.344783 seconds of system run time
% 23.27/23.49    [Run times include 0.999 seconds GC run time.]
% 23.27/23.49    0 calls to %EVAL
% 23.27/23.49    0 page faults and
% 23.27/23.49    1,714,084,912 bytes consed.
% 23.27/23.49  :PROOF-FOUND
% 23.27/23.49  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T16:50:29
% 23.27/23.49  :PROOF-FOUND
% 23.27/23.49  * 
%------------------------------------------------------------------------------