TSTP Solution File: HEN011-2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : HEN011-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n021.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 : Sat Jul 16 13:02:34 EDT 2022

% Result   : Unsatisfiable 0.84s 1.07s
% Output   : Refutation 0.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   24 (  18 unt;   0 nHn;  22 RR)
%            Number of literals    :   40 (   5 equ;  19 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   9 con; 0-2 aty)
%            Number of variables   :   29 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(divisor_existence,axiom,
    ( ~ quotient(X,Y,Z)
    | less_equal(Z,X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).

cnf(quotient_property,axiom,
    ( ~ quotient(X,Y,Z)
    | ~ quotient(Y,U,V)
    | ~ quotient(X,U,W)
    | ~ quotient(W,V,X1)
    | ~ quotient(Z,U,Y1)
    | less_equal(X1,Y1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).

cnf(less_equal_and_equal,axiom,
    ( ~ less_equal(X,Y)
    | ~ less_equal(Y,X)
    | X = Y ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).

cnf(closure,axiom,
    quotient(X,Y,divide(X,Y)),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).

cnf(transitivity_of_less_equal,axiom,
    ( ~ less_equal(X,Y)
    | ~ less_equal(Y,Z)
    | less_equal(X,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).

cnf(xQyLEz_implies_xQzLEy,axiom,
    ( ~ quotient(X,Y,Z)
    | ~ less_equal(Z,U)
    | ~ quotient(X,U,V)
    | less_equal(V,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).

cnf(one_inversion_equals_three,axiom,
    ( ~ quotient(identity,X,Y)
    | ~ quotient(identity,Y,Z)
    | ~ quotient(identity,Z,U)
    | Y = U ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).

cnf(identity_divide_a,hypothesis,
    quotient(identity,a,idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).

cnf(identity_divide_b,hypothesis,
    quotient(identity,b,idQb),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_b) ).

cnf(identity_divide_idQb,hypothesis,
    quotient(identity,idQb,idQ_idQb),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQb) ).

cnf(idQa_divide_idQ_idQb,hypothesis,
    quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idQa_divide_idQ_idQb) ).

cnf(identity_divide_idQa,hypothesis,
    quotient(identity,idQa,idQ_idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).

cnf(idQb_divide_idQ_idQa,hypothesis,
    quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idQb_divide_idQ_idQa) ).

cnf(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa,negated_conjecture,
    idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa) ).

cnf(30,plain,
    less_equal(divide(X,Y),X),
    inference('HYPERRESOLVE',[status(thm)],[divisor_existence,closure]) ).

cnf(52,plain,
    idQa = divide(identity,idQ_idQa),
    inference('HYPERRESOLVE',[status(thm)],[one_inversion_equals_three,identity_divide_a,identity_divide_idQa,closure]) ).

cnf(54,plain,
    idQb = divide(identity,idQ_idQb),
    inference('HYPERRESOLVE',[status(thm)],[one_inversion_equals_three,identity_divide_b,identity_divide_idQb,closure]) ).

cnf(75,plain,
    less_equal(divide(idQb,idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb)),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[quotient_property,identity_divide_idQa,idQa_divide_idQ_idQb,closure,closure,closure]),54,theory(equality)]) ).

cnf(80,plain,
    less_equal(divide(idQa,idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa)),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[quotient_property,identity_divide_idQb,idQb_divide_idQ_idQa,closure,closure,closure]),52,theory(equality)]) ).

cnf(405,plain,
    less_equal(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa),
    inference('HYPERRESOLVE',[status(thm)],[transitivity_of_less_equal,75,30]) ).

cnf(411,plain,
    less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),
    inference('HYPERRESOLVE',[status(thm)],[xQyLEz_implies_xQzLEy,405,closure,idQb_divide_idQ_idQa]) ).

cnf(424,plain,
    ~ less_equal(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),
    inference('UR-RESOLVE',[status(thm)],[less_equal_and_equal,411,prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa]) ).

cnf(455,plain,
    ~ less_equal(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb),
    inference('UR-RESOLVE',[status(thm)],[xQyLEz_implies_xQzLEy,424,closure,idQa_divide_idQ_idQb]) ).

cnf(717,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[transitivity_of_less_equal,80,30]),455]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : HEN011-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jul  1 14:53:59 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47  * 
% 0.19/0.47  * 
% 0.19/0.48  #<PACKAGE "SNARK-USER">
% 0.19/0.48  * 
% 0.19/0.48  SNARK-TPTP-OPTIONS
% 0.19/0.48  * 
% 0.19/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.48   (USE-FACTORING :POS)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.48  * 
% 0.19/0.48  "."
% 0.19/0.48  * 
% 0.19/0.48  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-01T14:53:59
% 0.19/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n021.cluster.edu at 2022-07-01T14:53:59
% 0.19/0.49  
% 0.19/0.49  ; Recognized relation function assertion (|quotient| ?X ?Y (|divide| ?X ?Y)).
% 0.19/0.49  ; Recognized relation functionality assertion (OR (NOT (|quotient| ?X ?Y ?Z)) (NOT (|quotient| ?X ?Y ?U)) (= ?Z ?U)).
% 0.84/1.07  ; Recognized possible right identity assertion (|quotient| ?X |zero| ?X).
% 0.84/1.07  
% 0.84/1.07  #||
% 0.84/1.07  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.84/1.07  % SZS output start Refutation
% See solution above
% 0.84/1.07  ||#
% 0.84/1.07  
% 0.84/1.07  ; Summary of computation:
% 0.84/1.07  ;     16011 formulas have been input or derived (from 108 formulas).
% 0.84/1.07  ;       717 ( 4%) were retained.  Of these,
% 0.84/1.07  ;           40 ( 6%) were simplified or subsumed later,
% 0.84/1.07  ;          677 (94%) are still being kept.
% 0.84/1.07  ; 
% 0.84/1.07  ; Run time in seconds excluding printing time:
% 0.84/1.07  ;     0.005   1%   Read assertion file          (1 call)
% 0.84/1.07  ;     0.001   0%   Assert                       (26 calls)
% 0.84/1.07  ;     0.055   9%   Process new row              (11,405 calls)
% 0.84/1.07  ;     0.388  66%   Resolution                   (214 calls)
% 0.84/1.07  ;     0.004   1%   Paramodulation               (107 calls)
% 0.84/1.07  ;     0.000   0%   Condensing                   (12 calls)
% 0.84/1.07  ;     0.000   0%   Forward subsumption          (12 calls)
% 0.84/1.07  ;     0.000   0%   Backward subsumption         (12 calls)
% 0.84/1.07  ;     0.000   0%   Clause clause subsumption    (14 calls)
% 0.84/1.07  ;     0.066  11%   Forward simplification       (11,211 calls)
% 0.84/1.07  ;     0.011   2%   Backward simplification      (717 calls)
% 0.84/1.07  ;     0.000   0%   Ordering                     (210 calls)
% 0.84/1.07  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.84/1.07  ;     0.000   0%   Purity testing               (1 call)
% 0.84/1.07  ;     0.060  10%   Other
% 0.84/1.07  ;     0.590        Total
% 0.84/1.07  ;     0.591        Real time
% 0.84/1.07  ; 
% 0.84/1.07  ; Term-hash-array has 1,048 terms in all.
% 0.84/1.07  ; Feature-vector-row-index has 12 entries (12 at peak, 12 added, 0 deleted).
% 0.84/1.07  ; Feature-vector-row-index has 20 nodes (20 at peak, 20 added, 0 deleted).
% 0.84/1.07  ;  Retrieved 9 possibly forward subsuming rows in 12 calls.
% 0.84/1.07  ;  Retrieved 5 possibly backward subsumed rows in 12 calls.
% 0.84/1.07  ; Path-index has 1,009 entries (1,009 at peak, 1,058 added, 49 deleted).
% 0.84/1.07  ; Path-index has 388 nodes (388 at peak, 390 added, 2 deleted).
% 0.84/1.07  ; Trie-index has 1,009 entries (1,009 at peak, 1,058 added, 49 deleted).
% 0.84/1.07  ; Trie-index has 2,044 nodes (2,044 at peak, 2,145 added, 101 deleted).
% 0.84/1.07  ; Retrieved 28,945 generalization terms in 23,392 calls.
% 0.84/1.07  ; Retrieved 894 instance terms in 704 calls.
% 0.84/1.07  ; Retrieved 238,189 unifiable terms in 66,450 calls.
% 0.84/1.07  ; 
% 0.84/1.07  ; The agenda of rows to process has 52 entries:
% 0.84/1.07  ;     5 with value 9              12 with value 12              21 with value 14
% 0.84/1.07  ;     1 with value 10              1 with value 13               7 with value 16
% 0.84/1.07  ;     5 with value 11
% 0.84/1.07  ; The agenda of rows to give has 576 entries:
% 0.84/1.07  ;    56 with value (4 10)        124 with value (4 14)          16 with value (4 17)
% 0.84/1.07  ;   112 with value (4 11)         58 with value (4 15)          10 with value (4 18)
% 0.84/1.07  ;    45 with value (4 12)         27 with value (4 16)           1 with value (4 21)
% 0.84/1.07  ;   127 with value (4 13)
% 0.84/1.07  Evaluation took:
% 0.84/1.07    0.591 seconds of real time
% 0.84/1.07    0.54228 seconds of user run time
% 0.84/1.07    0.049118 seconds of system run time
% 0.84/1.07    [Run times include 0.016 seconds GC run time.]
% 0.84/1.07    0 calls to %EVAL
% 0.84/1.07    0 page faults and
% 0.84/1.07    42,493,728 bytes consed.
% 0.84/1.07  :PROOF-FOUND
% 0.84/1.07  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-01T14:53:59
% 0.84/1.07  :PROOF-FOUND
% 0.84/1.07  * 
%------------------------------------------------------------------------------