TSTP Solution File: COL081-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : COL081-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n026.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 : Fri Jul 15 00:41:49 EDT 2022

% Result   : Unsatisfiable 0.77s 0.97s
% Output   : Refutation 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   10 (   8 unt;   0 nHn;   5 RR)
%            Number of literals    :   12 (  11 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   17 (   4 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
    apply(k(X),Y) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',k_definition) ).

cnf(abstraction,axiom,
    apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',abstraction) ).

cnf(extensionality2,axiom,
    ( X = Y
    | apply(X,n(X,Y)) != apply(Y,n(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',extensionality2) ).

cnf(prove_TRC2c,negated_conjecture,
    k(k(b)) != apply(abstraction,k(k(b))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC2c) ).

cnf(44,plain,
    ( k(X) = Y
    | X != apply(Y,n(k(X),Y)) ),
    inference('PARAMODULATE',[status(thm)],[extensionality2,k_definition,theory(equality)]) ).

cnf(48,plain,
    k(b) != apply(apply(abstraction,k(k(b))),n(k(k(b)),apply(abstraction,k(k(b))))),
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[extensionality2,prove_TRC2c]),k_definition,theory(equality)]) ).

cnf(52,plain,
    apply(apply(apply(abstraction,k(X)),Y),Z) = apply(X,apply(Y,Z)),
    inference('PARAMODULATE',[status(thm)],[abstraction,k_definition,theory(equality)]) ).

cnf(597,plain,
    apply(apply(apply(abstraction,k(k(X))),Y),Z) = X,
    inference('PARAMODULATE',[status(thm)],[k_definition,52,theory(equality)]) ).

cnf(671,plain,
    k(X) = apply(apply(abstraction,k(k(X))),Y),
    inference('HYPERRESOLVE',[status(thm)],[44,597]) ).

cnf(672,plain,
    $false,
    inference('REWRITE',[status(thm)],[48,671,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : COL081-1 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.12  % Command  : run-snark %s %d
% 0.13/0.33  % Computer : n026.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 : Tue May 31 09:19:56 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.43  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44  * 
% 0.19/0.44  * 
% 0.19/0.45  #<PACKAGE "SNARK-USER">
% 0.19/0.45  * 
% 0.19/0.45  SNARK-TPTP-OPTIONS
% 0.19/0.45  * 
% 0.19/0.45  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.45   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.45   (USE-FACTORING :POS)
% 0.19/0.45   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.45   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.45   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.45   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.45   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.45   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.45   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.45   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.45   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.45   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.45  * 
% 0.19/0.45  "."
% 0.19/0.45  * 
% 0.19/0.45  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-31T09:19:56
% 0.19/0.45  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-05-31T09:19:56
% 0.19/0.47  
% 0.77/0.97  ; Recognized left identity assertion (= (|apply| |identity| ?X) ?X).
% 0.77/0.97  
% 0.77/0.97  #||
% 0.77/0.97  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/0.97  % SZS output start Refutation
% See solution above
% 0.77/0.97  ||#
% 0.77/0.97  
% 0.77/0.97  ; Summary of computation:
% 0.77/0.97  ;      1737 formulas have been input or derived (from 88 formulas).
% 0.77/0.97  ;       672 (39%) were retained.  Of these,
% 0.77/0.97  ;          147 (22%) were simplified or subsumed later,
% 0.77/0.97  ;          525 (78%) are still being kept.
% 0.77/0.97  ; 
% 0.77/0.97  ; Run time in seconds excluding printing time:
% 0.77/0.97  ;     0.003   1%   Read assertion file          (1 call)
% 0.77/0.97  ;     0.000   0%   Assert                       (12 calls)
% 0.77/0.97  ;     0.091  18%   Process new row              (1,534 calls)
% 0.77/0.97  ;     0.021   4%   Resolution                   (174 calls)
% 0.77/0.97  ;     0.029   6%   Paramodulation               (87 calls)
% 0.77/0.97  ;     0.000   0%   Factoring                    (1 call)
% 0.77/0.97  ;     0.000   0%   Condensing                   (105 calls)
% 0.77/0.97  ;     0.006   1%   Forward subsumption          (105 calls)
% 0.77/0.97  ;     0.001   0%   Backward subsumption         (65 calls)
% 0.77/0.97  ;     0.000   0%   Clause clause subsumption    (177 calls)
% 0.77/0.97  ;     0.120  23%   Forward simplification       (1,263 calls)
% 0.77/0.97  ;     0.049  10%   Backward simplification      (672 calls)
% 0.77/0.97  ;     0.163  32%   Ordering                     (30,400 calls)
% 0.77/0.97  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.77/0.97  ;     0.000   0%   Purity testing               (1 call)
% 0.77/0.97  ;     0.030   6%   Other
% 0.77/0.97  ;     0.513        Total
% 0.77/0.97  ;     0.514        Real time
% 0.77/0.97  ; 
% 0.77/0.97  ; Term-hash-array has 2,760 terms in all.
% 0.77/0.97  ; Feature-vector-row-index has 51 entries (51 at peak, 65 added, 14 deleted).
% 0.77/0.97  ; Feature-vector-row-index has 403 nodes (403 at peak, 501 added, 98 deleted).
% 0.77/0.97  ;  Retrieved 164 possibly forward subsuming rows in 105 calls.
% 0.77/0.97  ;  Retrieved 30 possibly backward subsumed rows in 65 calls.
% 0.77/0.97  ; Path-index has 2,315 entries (2,323 at peak, 2,899 added, 584 deleted).
% 0.77/0.97  ; Path-index has 3,734 nodes (3,755 at peak, 4,176 added, 442 deleted).
% 0.77/0.97  ; Trie-index has 2,315 entries (2,323 at peak, 2,899 added, 584 deleted).
% 0.77/0.97  ; Trie-index has 12,376 nodes (12,446 at peak, 15,255 added, 2,879 deleted).
% 0.77/0.97  ; Retrieved 19,200 generalization terms in 10,275 calls.
% 0.77/0.97  ; Retrieved 6,074 instance terms in 1,234 calls.
% 0.77/0.97  ; Retrieved 8,955 unifiable terms in 744 calls.
% 0.77/0.97  ; 
% 0.77/0.97  ; The agenda of rows to process has 22 entries:
% 0.77/0.97  ;     1 with value 18              3 with value 23               3 with value 30
% 0.77/0.97  ;     3 with value 20              4 with value 28               3 with value 34
% 0.77/0.97  ;     2 with value 22              1 with value 29               2 with value 37
% 0.77/0.97  ; The agenda of rows to give has 455 entries:
% 0.77/0.97  ;     1 with value (4 18)          8 with value (4 35)          11 with value (4 50)
% 0.77/0.97  ;    17 with value (4 20)          8 with value (4 36)           6 with value (4 51)
% 0.77/0.97  ;    33 with value (4 21)         15 with value (4 37)           7 with value (4 52)
% 0.77/0.97  ;    21 with value (4 22)         12 with value (4 38)           3 with value (4 53)
% 0.77/0.97  ;    22 with value (4 23)         10 with value (4 39)           4 with value (4 54)
% 0.77/0.97  ;    10 with value (4 24)         18 with value (4 40)           9 with value (4 55)
% 0.77/0.97  ;    16 with value (4 25)         13 with value (4 41)           3 with value (4 56)
% 0.77/0.97  ;    12 with value (4 26)         11 with value (4 42)           2 with value (4 57)
% 0.77/0.97  ;    12 with value (4 27)          7 with value (4 43)           1 with value (4 58)
% 0.77/0.97  ;    11 with value (4 28)          5 with value (4 44)           1 with value (4 61)
% 0.77/0.97  ;    10 with value (4 29)          5 with value (4 45)           3 with value (4 64)
% 0.77/0.97  ;    24 with value (4 30)          6 with value (4 46)           1 with value (4 66)
% 0.77/0.97  ;    18 with value (4 31)         12 with value (4 47)           2 with value (4 67)
% 0.77/0.97  ;    18 with value (4 32)          8 with value (4 48)           3 with value (4 69)
% 0.77/0.97  ;    17 with value (4 33)          9 with value (4 49)           1 with value (4 72)
% 0.77/0.97  ;     9 with value (4 34)
% 0.77/0.97  Evaluation took:
% 0.77/0.97    0.515 seconds of real time
% 0.77/0.97    0.454935 seconds of user run time
% 0.77/0.97    0.060169 seconds of system run time
% 0.77/0.97    [Run times include 0.018 seconds GC run time.]
% 0.77/0.97    0 calls to %EVAL
% 0.77/0.97    0 page faults and
% 0.77/0.97    26,464,824 bytes consed.
% 0.77/0.97  :PROOF-FOUND
% 0.77/0.97  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-31T09:19:56
% 0.77/0.97  :PROOF-FOUND
% 0.77/0.97  * 
%------------------------------------------------------------------------------