TSTP Solution File: GRA008+2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRA008+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n028.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 07:21:53 EDT 2022

% Result   : Theorem 4.38s 4.56s
% Output   : Refutation 4.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   27 (  13 unt;   4 nHn;  27 RR)
%            Number of literals    :   58 (  15 equ;  30 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   2 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   41 (  15 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ edge(X)
    | head_of(X) != tail_of(X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).

cnf(27,axiom,
    ( ~ sequential(X,Y)
    | edge(X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).

cnf(28,axiom,
    ( ~ sequential(X,Y)
    | edge(Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).

cnf(31,axiom,
    ( sequential(X,Y)
    | ~ edge(X)
    | ~ edge(Y)
    | X = Y
    | head_of(X) != tail_of(Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).

cnf(52,axiom,
    ( triangle(X,Y,Z)
    | ~ edge(X)
    | ~ edge(Y)
    | ~ edge(Z)
    | ~ sequential(X,Y)
    | ~ sequential(Y,Z)
    | ~ sequential(Z,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).

cnf(60,axiom,
    ( ~ complete
    | ~ shortest_path(X,Y,Z)
    | ~ precedes(U,V,Z)
    | edge('SKOLEMAAAV9'(V,U)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).

cnf(61,axiom,
    ( ~ complete
    | ~ shortest_path(X,Y,Z)
    | ~ precedes(U,V,Z)
    | tail_of('SKOLEMAAAV9'(V,U)) = head_of(V) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).

cnf(62,axiom,
    ( ~ complete
    | ~ shortest_path(X,Y,Z)
    | ~ precedes(U,V,Z)
    | head_of('SKOLEMAAAV9'(V,U)) = tail_of(U) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).

cnf(63,negated_conjecture,
    complete,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).

cnf(64,negated_conjecture,
    shortest_path('SKOLEMAAAV10','SKOLEMAAAV11','SKOLEMAAAV14'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).

cnf(65,negated_conjecture,
    precedes('SKOLEMAAAV12','SKOLEMAAAV13','SKOLEMAAAV14'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).

cnf(66,negated_conjecture,
    sequential('SKOLEMAAAV12','SKOLEMAAAV13'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).

cnf(67,negated_conjecture,
    ~ triangle('SKOLEMAAAV12','SKOLEMAAAV13',X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).

cnf(74,plain,
    ( ~ shortest_path(X,Y,Z)
    | ~ precedes(U,V,Z)
    | edge('SKOLEMAAAV9'(V,U)) ),
    inference('REWRITE',[status(thm)],[60,63]) ).

cnf(75,plain,
    ( ~ shortest_path(X,Y,Z)
    | ~ precedes(U,V,Z)
    | tail_of('SKOLEMAAAV9'(V,U)) = head_of(V) ),
    inference('REWRITE',[status(thm)],[61,63]) ).

cnf(76,plain,
    ( ~ shortest_path(X,Y,Z)
    | ~ precedes(U,V,Z)
    | head_of('SKOLEMAAAV9'(V,U)) = tail_of(U) ),
    inference('REWRITE',[status(thm)],[62,63]) ).

cnf(77,plain,
    edge('SKOLEMAAAV12'),
    inference('HYPERRESOLVE',[status(thm)],[27,66]) ).

cnf(78,plain,
    edge('SKOLEMAAAV13'),
    inference('HYPERRESOLVE',[status(thm)],[28,66]) ).

cnf(87,plain,
    edge('SKOLEMAAAV9'('SKOLEMAAAV13','SKOLEMAAAV12')),
    inference('HYPERRESOLVE',[status(thm)],[74,64,65]) ).

cnf(88,plain,
    tail_of('SKOLEMAAAV9'('SKOLEMAAAV13','SKOLEMAAAV12')) = head_of('SKOLEMAAAV13'),
    inference('HYPERRESOLVE',[status(thm)],[75,64,65]) ).

cnf(89,plain,
    head_of('SKOLEMAAAV9'('SKOLEMAAAV13','SKOLEMAAAV12')) = tail_of('SKOLEMAAAV12'),
    inference('HYPERRESOLVE',[status(thm)],[76,64,65]) ).

cnf(128,plain,
    tail_of('SKOLEMAAAV12') != head_of('SKOLEMAAAV13'),
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[1,87]),88,89,theory(equality)]) ).

cnf(244,plain,
    ( sequential('SKOLEMAAAV13','SKOLEMAAAV9'('SKOLEMAAAV13','SKOLEMAAAV12'))
    | 'SKOLEMAAAV13' = 'SKOLEMAAAV9'('SKOLEMAAAV13','SKOLEMAAAV12') ),
    inference('HYPERRESOLVE',[status(thm)],[31,88,78,87]) ).

cnf(251,plain,
    ( sequential('SKOLEMAAAV9'('SKOLEMAAAV13','SKOLEMAAAV12'),'SKOLEMAAAV12')
    | 'SKOLEMAAAV9'('SKOLEMAAAV13','SKOLEMAAAV12') = 'SKOLEMAAAV12' ),
    inference('HYPERRESOLVE',[status(thm)],[31,89,87,77]) ).

cnf(2555,plain,
    ( 'SKOLEMAAAV9'('SKOLEMAAAV13','SKOLEMAAAV12') = 'SKOLEMAAAV12'
    | 'SKOLEMAAAV13' = 'SKOLEMAAAV9'('SKOLEMAAAV13','SKOLEMAAAV12') ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[52,251,77,78,87,66,244]),67]) ).

cnf(4089,plain,
    'SKOLEMAAAV9'('SKOLEMAAAV13','SKOLEMAAAV12') = 'SKOLEMAAAV12',
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[89,2555,theory(equality)]),128]) ).

cnf(4090,plain,
    $false,
    inference('REWRITE',[status(thm)],[88,128,4089,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRA008+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.06/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n028.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 : Tue May 31 01:04:05 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p 2022-05-31T01:04:05
% 0.19/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n028.cluster.edu at 2022-05-31T01:04:05
% 4.38/4.56  
% 4.38/4.56  
% 4.38/4.56  #||
% 4.38/4.56  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.38/4.56  % SZS output start Refutation
% See solution above
% 4.38/4.57  ||#
% 4.38/4.57  
% 4.38/4.57  ; Summary of computation:
% 4.38/4.57  ;      4810 formulas have been input or derived (from 181 formulas).
% 4.38/4.57  ;      4090 (85%) were retained.  Of these,
% 4.38/4.57  ;           37 ( 1%) were simplified or subsumed later,
% 4.38/4.57  ;         4053 (99%) are still being kept.
% 4.38/4.57  ; 
% 4.38/4.57  ; Run time in seconds excluding printing time:
% 4.38/4.57  ;     0.008   0%   Read assertion file          (1 call)
% 4.38/4.57  ;     0.003   0%   Assert                       (19 calls)
% 4.38/4.57  ;     0.524  13%   Process new row              (4,568 calls)
% 4.38/4.57  ;     2.405  59%   Resolution                   (360 calls)
% 4.38/4.57  ;     0.005   0%   Paramodulation               (180 calls)
% 4.38/4.57  ;     0.000   0%   Factoring                    (15 calls)
% 4.38/4.57  ;     0.011   0%   Condensing                   (3,916 calls)
% 4.38/4.57  ;     0.563  14%   Forward subsumption          (3,916 calls)
% 4.38/4.57  ;     0.195   5%   Backward subsumption         (3,912 calls)
% 4.38/4.57  ;     0.104   3%   Clause clause subsumption    (36,218 calls)
% 4.38/4.57  ;     0.177   4%   Forward simplification       (4,568 calls)
% 4.38/4.57  ;     0.007   0%   Backward simplification      (4,090 calls)
% 4.38/4.57  ;     0.034   1%   Ordering                     (8,663 calls)
% 4.38/4.57  ;     0.000   0%   Sortal reasoning             (32 calls)
% 4.38/4.57  ;     0.000   0%   Purity testing               (1 call)
% 4.38/4.57  ;     0.049   1%   Other
% 4.38/4.57  ;     4.085        Total
% 4.38/4.57  ;     4.095        Real time
% 4.38/4.57  ; 
% 4.38/4.57  ; Term-hash-array has 6,882 terms in all.
% 4.38/4.57  ; Feature-vector-row-index has 3,884 entries (3,901 at peak, 3,912 added, 28 deleted).
% 4.38/4.57  ; Feature-vector-row-index has 9,945 nodes (10,190 at peak, 10,242 added, 297 deleted).
% 4.38/4.57  ;  Retrieved 20,810 possibly forward subsuming rows in 3,916 calls.
% 4.38/4.57  ;  Retrieved 15,410 possibly backward subsumed rows in 3,912 calls.
% 4.38/4.57  ; Path-index has 6,837 entries (6,892 at peak, 6,908 added, 71 deleted).
% 4.38/4.57  ; Path-index has 2,311 nodes (2,430 at peak, 2,458 added, 147 deleted).
% 4.38/4.57  ; Trie-index has 6,837 entries (6,892 at peak, 6,908 added, 71 deleted).
% 4.38/4.57  ; Trie-index has 24,439 nodes (24,760 at peak, 24,809 added, 370 deleted).
% 4.38/4.57  ; Retrieved 512 generalization terms in 32,554 calls.
% 4.38/4.57  ; Retrieved 200 instance terms in 177 calls.
% 4.38/4.57  ; Retrieved 4,181,942 unifiable terms in 152,775 calls.
% 4.38/4.57  ; 
% 4.38/4.57  ; The agenda of backward simplifiable rows to process has 24 entries:
% 4.38/4.57  ;    24 with value 0
% 4.38/4.57  ; The agenda of rows to process has 5 entries:
% 4.38/4.57  ;     1 with value 18              3 with value 19               1 with value 21
% 4.38/4.57  ; The agenda of rows to give has 3879 entries:
% 4.38/4.57  ;     1 with value (4 11)         61 with value (4 39)          33 with value (4 57)
% 4.38/4.57  ;    12 with value (4 19)          1 with value (4 40)          96 with value (4 58)
% 4.38/4.57  ;    38 with value (4 20)        264 with value (4 41)          48 with value (4 59)
% 4.38/4.57  ;    19 with value (4 21)         20 with value (4 42)         153 with value (4 60)
% 4.38/4.57  ;     2 with value (4 22)          1 with value (4 43)         100 with value (4 61)
% 4.38/4.57  ;     1 with value (4 23)          4 with value (4 44)           8 with value (4 62)
% 4.38/4.57  ;    19 with value (4 24)         50 with value (4 45)          72 with value (4 64)
% 4.38/4.57  ;    16 with value (4 25)          8 with value (4 46)          48 with value (4 65)
% 4.38/4.57  ;     8 with value (4 26)         26 with value (4 47)         192 with value (4 66)
% 4.38/4.57  ;    28 with value (4 27)         20 with value (4 48)          48 with value (4 67)
% 4.38/4.57  ;    13 with value (4 28)         54 with value (4 49)         192 with value (4 68)
% 4.38/4.57  ;    30 with value (4 29)         24 with value (4 50)         240 with value (4 70)
% 4.38/4.57  ;     4 with value (4 30)         72 with value (4 51)          24 with value (4 71)
% 4.38/4.57  ;    96 with value (4 31)         14 with value (4 52)          48 with value (4 72)
% 4.38/4.57  ;    27 with value (4 32)          1 with value (4 53)         168 with value (4 73)
% 4.38/4.57  ;   129 with value (4 33)         48 with value (4 54)         288 with value (4 74)
% 4.38/4.57  ;     2 with value (4 34)         66 with value (4 55)         144 with value (4 75)
% 4.38/4.57  ;   145 with value (4 37)        169 with value (4 56)         480 with value (4 76)
% 4.38/4.57  ;     4 with value (4 38)
% 4.38/4.57  Evaluation took:
% 4.38/4.57    4.097 seconds of real time
% 4.38/4.57    3.960676 seconds of user run time
% 4.38/4.57    0.135974 seconds of system run time
% 4.38/4.57    [Run times include 0.254 seconds GC run time.]
% 4.38/4.57    0 calls to %EVAL
% 4.38/4.57    0 page faults and
% 4.38/4.57    302,973,312 bytes consed.
% 4.38/4.57  :PROOF-FOUND
% 4.38/4.57  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-31T01:04:09
% 4.38/4.57  :PROOF-FOUND
% 4.38/4.57  * 
%------------------------------------------------------------------------------