TSTP Solution File: KLE084-10 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : KLE084-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n010.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 02:26:33 EDT 2022

% Result   : Unsatisfiable 15.60s 15.77s
% Output   : Refutation 15.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   39 (  39 unt;   0 nHn;   5 RR)
%            Number of literals    :   39 (  38 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-4 aty)
%            Number of variables   :   63 (  12 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
    ifeq2(X,X,Y,Z) = Y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).

cnf(ifeq_axiom_001,axiom,
    ifeq(X,X,Y,Z) = Y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).

cnf(additive_identity,axiom,
    addition(X,zero) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).

cnf(additive_idempotence,axiom,
    addition(X,X) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).

cnf(5,plain,
    addition(X,addition(X,Y)) = addition(X,Y),
    inference('EMBED',[status(thm)],[additive_idempotence]) ).

cnf(multiplicative_associativity,axiom,
    multiplication(X,multiplication(Y,Z)) = multiplication(multiplication(X,Y),Z),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).

cnf(multiplicative_right_identity,axiom,
    multiplication(X,one) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).

cnf(multiplicative_left_identity,axiom,
    multiplication(one,X) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).

cnf(right_distributivity,axiom,
    multiplication(X,addition(Y,Z)) = addition(multiplication(X,Y),multiplication(X,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).

cnf(left_distributivity,axiom,
    multiplication(addition(X,Y),Z) = addition(multiplication(X,Z),multiplication(Y,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).

cnf(left_annihilation,axiom,
    multiplication(zero,X) = zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).

cnf(order_1,axiom,
    ifeq(leq(X,Y),true,addition(X,Y),Y) = Y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order_1) ).

cnf(order,axiom,
    ifeq2(addition(X,Y),Y,leq(X,Y),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

cnf(domain1,axiom,
    multiplication(antidomain(X),X) = zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).

cnf(domain2,axiom,
    addition(antidomain(multiplication(X,Y)),antidomain(multiplication(X,antidomain(antidomain(Y))))) = antidomain(multiplication(X,antidomain(antidomain(Y)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).

cnf(domain3,axiom,
    addition(antidomain(antidomain(X)),antidomain(X)) = one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).

cnf(19,plain,
    addition(antidomain(antidomain(X)),addition(antidomain(X),Y)) = addition(one,Y),
    inference('EMBED',[status(thm)],[domain3]) ).

cnf(domain4,axiom,
    domain(X) = antidomain(antidomain(X)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).

cnf(goals,negated_conjecture,
    domain(multiplication(sK2_goals_X0,sK1_goals_X1)) != domain(multiplication(sK2_goals_X0,domain(sK1_goals_X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(28,plain,
    antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))) != antidomain(antidomain(multiplication(sK2_goals_X0,antidomain(antidomain(sK1_goals_X1))))),
    inference('REWRITE',[status(thm)],[goals,domain4,theory(equality)]) ).

cnf(29,plain,
    zero = antidomain(one),
    inference('PARAMODULATE',[status(thm)],[multiplicative_right_identity,domain1,theory(equality)]) ).

cnf(31,plain,
    addition(one,antidomain(X)) = one,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,19,theory(equality)]),domain3,theory(equality)]) ).

cnf(36,plain,
    multiplication(antidomain(X),multiplication(X,Y)) = zero,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[multiplicative_associativity,domain1,theory(equality)]),left_annihilation,theory(equality)]) ).

cnf(72,plain,
    leq(X,addition(X,Y)) = true,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[order,5,theory(equality)]),ifeq_axiom,theory(equality)]) ).

cnf(88,plain,
    X = addition(multiplication(X,antidomain(antidomain(Y))),multiplication(X,antidomain(Y))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[right_distributivity,domain3,theory(equality)]),multiplicative_right_identity,theory(equality)]) ).

cnf(98,plain,
    X = addition(multiplication(antidomain(antidomain(Y)),X),multiplication(antidomain(Y),X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[left_distributivity,domain3,theory(equality)]),multiplicative_left_identity,theory(equality)]) ).

cnf(134,plain,
    ifeq(leq(antidomain(multiplication(X,antidomain(antidomain(Y)))),antidomain(multiplication(X,Y))),true,antidomain(multiplication(X,antidomain(antidomain(Y)))),antidomain(multiplication(X,Y))) = antidomain(multiplication(X,Y)),
    inference('PARAMODULATE',[status(thm)],[order_1,domain2,theory(equality)]) ).

cnf(194,plain,
    antidomain(zero) = one,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[domain3,29,theory(equality)]),additive_identity,theory(equality)]) ).

cnf(203,plain,
    X = addition(X,multiplication(antidomain(Y),X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[left_distributivity,31,theory(equality)]),multiplicative_left_identity,theory(equality)]) ).

cnf(255,plain,
    one = antidomain(multiplication(antidomain(X),antidomain(antidomain(multiplication(X,Y))))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[domain2,36,theory(equality)]),31,194,theory(equality)]) ).

cnf(264,plain,
    leq(multiplication(antidomain(X),Y),Y) = true,
    inference('PARAMODULATE',[status(thm)],[72,203,theory(equality)]) ).

cnf(1023,plain,
    X = multiplication(antidomain(antidomain(X)),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[98,domain1,theory(equality)]),additive_identity,theory(equality)]) ).

cnf(1060,plain,
    multiplication(X,Y) = multiplication(multiplication(X,antidomain(antidomain(Y))),Y),
    inference('PARAMODULATE',[status(thm)],[multiplicative_associativity,1023,theory(equality)]) ).

cnf(1437,plain,
    multiplication(antidomain(X),antidomain(antidomain(multiplication(X,Y)))) = zero,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[domain1,255,theory(equality)]),multiplicative_left_identity,theory(equality)]) ).

cnf(1438,plain,
    antidomain(X) = multiplication(antidomain(X),antidomain(multiplication(X,Y))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[88,1437,theory(equality)]),additive_identity,theory(equality)]) ).

cnf(1450,plain,
    leq(antidomain(X),antidomain(multiplication(X,Y))) = true,
    inference('PARAMODULATE',[status(thm)],[264,1438,theory(equality)]) ).

cnf(3357,plain,
    leq(antidomain(multiplication(X,antidomain(antidomain(Y)))),antidomain(multiplication(X,Y))) = true,
    inference('PARAMODULATE',[status(thm)],[1450,1060,theory(equality)]) ).

cnf(3359,plain,
    antidomain(multiplication(X,antidomain(antidomain(Y)))) = antidomain(multiplication(X,Y)),
    inference('REWRITE',[status(thm)],[134,ifeq_axiom_001,3357,theory(equality)]) ).

cnf(3363,plain,
    $false,
    inference('REWRITE',[status(thm)],[28,3359,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : KLE084-10 : TPTP v8.1.0. Released v7.5.0.
% 0.02/0.12  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n010.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 10:00:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45  * 
% 0.18/0.45  * 
% 0.18/0.45  #<PACKAGE "SNARK-USER">
% 0.18/0.45  * 
% 0.18/0.45  SNARK-TPTP-OPTIONS
% 0.18/0.45  * 
% 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 2022-06-16T10:00:39
% 0.18/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n010.cluster.edu at 2022-06-16T10:00:39
% 0.18/0.47  
% 0.18/0.47  ; Recognized commutativity assertion (= (|addition| ?X ?Y) (|addition| ?Y ?X)).
% 0.18/0.47  ; Recognized associativity assertion (= (|addition| ?X (|addition| ?Y ?Z)) (|addition| (|addition| ?X ?Y) ?Z)).
% 0.18/0.47  ; Recognized right identity assertion (= (|addition| ?X |zero|) ?X).
% 0.18/0.47  ; Recognized associativity assertion (= (|multiplication| ?X (|multiplication| ?Y ?Z)) (|multiplication| (|multiplication| ?X ?Y) ?Z)).
% 0.18/0.47  ; Recognized right identity assertion (= (|multiplication| ?X |one|) ?X).
% 0.18/0.47  ; Recognized left identity assertion (= (|multiplication| |one| ?X) ?X).
% 0.18/0.47  ; Recognized possible left inverse assertion (= (|multiplication| (|antidomain| ?X) ?X) |zero|).
% 0.18/0.47  ; Recognized possible right inverse assertion (= (|multiplication| ?X (|coantidomain| ?X)) |zero|).
% 0.18/0.47  ; Declaring addition to be commutative.
% 15.60/15.77  ; Declaring addition to be associative-commutative.
% 15.60/15.77  
% 15.60/15.77  #||
% 15.60/15.77  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.60/15.77  % SZS output start Refutation
% See solution above
% 15.60/15.78  ||#
% 15.60/15.78  
% 15.60/15.78  ; Summary of computation:
% 15.60/15.78  ;     25175 formulas have been input or derived (from 192 formulas).
% 15.60/15.78  ;      3363 (13%) were retained.  Of these,
% 15.60/15.78  ;          468 (14%) were simplified or subsumed later,
% 15.60/15.78  ;         2895 (86%) are still being kept.
% 15.60/15.78  ; 
% 15.60/15.78  ; Run time in seconds excluding printing time:
% 15.60/15.78  ;     0.004   0%   Read assertion file          (1 call)
% 15.60/15.78  ;     0.001   0%   Assert                       (24 calls)
% 15.60/15.78  ;     0.434   3%   Process new row              (24,594 calls)
% 15.60/15.78  ;     0.011   0%   Resolution                   (382 calls)
% 15.60/15.78  ;     0.374   2%   Paramodulation               (191 calls)
% 15.60/15.78  ;     0.011   0%   Embedding                    (879 calls)
% 15.60/15.78  ;    13.967  91%   Forward simplification       (23,647 calls)
% 15.60/15.78  ;     0.094   1%   Backward simplification      (2,665 calls)
% 15.60/15.78  ;     0.289   2%   Ordering                     (53,744 calls)
% 15.60/15.78  ;     0.014   0%   Ordering ac                  (3,363 calls)
% 15.60/15.78  ;     0.000   0%   Sortal reasoning             (32 calls)
% 15.60/15.78  ;     0.000   0%   Purity testing               (1 call)
% 15.60/15.78  ;     0.116   1%   Other
% 15.60/15.78  ;    15.315        Total
% 15.60/15.78  ;    15.320        Real time
% 15.60/15.78  ; 
% 15.60/15.78  ; Term-hash-array has 9,513 terms in all.
% 15.60/15.78  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 15.60/15.78  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 15.60/15.78  ; Path-index has 8,203 entries (8,488 at peak, 9,578 added, 1,375 deleted).
% 15.60/15.78  ; Path-index has 5,076 nodes (5,267 at peak, 6,006 added, 930 deleted).
% 15.60/15.78  ; Trie-index has 8,203 entries (8,488 at peak, 9,578 added, 1,375 deleted).
% 15.60/15.78  ; Trie-index has 9,202 nodes (9,757 at peak, 12,209 added, 3,007 deleted).
% 15.60/15.78  ; Retrieved 27,231,232 generalization terms in 305,396 calls.
% 15.60/15.78  ; Retrieved 6,994 instance terms in 2,684 calls.
% 15.60/15.78  ; Retrieved 63,159 unifiable terms in 1,211 calls.
% 15.60/15.78  ; 
% 15.60/15.78  ; The agenda of rows to process has 31 entries:
% 15.60/15.78  ;     1 with value 25              2 with value 29               3 with value 36
% 15.60/15.78  ;     4 with value 26              1 with value 30               2 with value 37
% 15.60/15.78  ;     3 with value 27              8 with value 31               1 with value 39
% 15.60/15.78  ;     4 with value 28              2 with value 33
% 15.60/15.78  ; The agenda of rows to give has 2734 entries:
% 15.60/15.78  ;     1 with value (4 17)         26 with value (4 29)          93 with value (4 41)
% 15.60/15.78  ;     1 with value (4 18)        120 with value (4 30)          20 with value (4 42)
% 15.60/15.78  ;     3 with value (4 19)         48 with value (4 31)           9 with value (4 43)
% 15.60/15.78  ;    58 with value (4 20)        158 with value (4 32)          19 with value (4 44)
% 15.60/15.78  ;    85 with value (4 21)         25 with value (4 33)           8 with value (4 45)
% 15.60/15.78  ;    60 with value (4 22)        142 with value (4 34)          17 with value (4 46)
% 15.60/15.78  ;    89 with value (4 23)         54 with value (4 35)           1 with value (4 47)
% 15.60/15.78  ;   243 with value (4 24)         67 with value (4 36)          17 with value (4 48)
% 15.60/15.78  ;   197 with value (4 25)         44 with value (4 37)           1 with value (4 49)
% 15.60/15.78  ;   165 with value (4 26)         75 with value (4 38)          16 with value (4 50)
% 15.60/15.78  ;   162 with value (4 27)         82 with value (4 39)          17 with value (4 52)
% 15.60/15.78  ;   586 with value (4 28)         24 with value (4 40)           1 with value (4 53)
% 15.60/15.78  Evaluation took:
% 15.60/15.78    15.321 seconds of real time
% 15.60/15.78    15.06873 seconds of user run time
% 15.60/15.78    0.248924 seconds of system run time
% 15.60/15.78    [Run times include 0.465 seconds GC run time.]
% 15.60/15.78    0 calls to %EVAL
% 15.60/15.78    0 page faults and
% 15.60/15.78    764,087,296 bytes consed.
% 15.60/15.78  :PROOF-FOUND
% 15.60/15.78  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T10:00:54
% 15.60/15.78  :PROOF-FOUND
% 15.60/15.78  * 
%------------------------------------------------------------------------------