TSTP Solution File: COL077-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : COL077-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n025.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 00:41:48 EDT 2022

% Result   : Unsatisfiable 1.47s 1.67s
% Output   : Refutation 1.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   15 (  13 unt;   0 nHn;   6 RR)
%            Number of literals    :   17 (  16 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    7 (   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   :   24 (   7 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
    apply(k(X),Y) = X,
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/COL001-0.ax',abstraction) ).

cnf(extensionality2,axiom,
    ( X = Y
    | apply(X,n(X,Y)) != apply(Y,n(X,Y)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/COL001-0.ax',extensionality2) ).

cnf(identity_definition,axiom,
    apply(identity,X) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_definition) ).

cnf(prove_TRC1a,negated_conjecture,
    apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_TRC1a) ).

cnf(13,plain,
    apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction) != identity,
    inference('REWRITE',[status(thm)],[prove_TRC1a,k_definition,abstraction,theory(equality)]) ).

cnf(43,plain,
    ( k(X) = Y
    | X != apply(Y,n(k(X),Y)) ),
    inference('PARAMODULATE',[status(thm)],[extensionality2,k_definition,theory(equality)]) ).

cnf(48,plain,
    n(identity,apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction)) != apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),n(identity,apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction))),
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[extensionality2,13]),identity_definition,theory(equality)]) ).

cnf(51,plain,
    apply(apply(apply(abstraction,k(X)),Y),Z) = apply(X,apply(Y,Z)),
    inference('PARAMODULATE',[status(thm)],[abstraction,k_definition,theory(equality)]) ).

cnf(583,plain,
    apply(apply(apply(abstraction,k(k(X))),Y),Z) = X,
    inference('PARAMODULATE',[status(thm)],[k_definition,51,theory(equality)]) ).

cnf(655,plain,
    k(X) = apply(apply(abstraction,k(k(X))),Y),
    inference('HYPERRESOLVE',[status(thm)],[43,583]) ).

cnf(656,plain,
    k(k(X)) = apply(abstraction,k(k(X))),
    inference('HYPERRESOLVE',[status(thm)],[43,655]) ).

cnf(659,plain,
    apply(apply(apply(abstraction,abstraction),X),k(Y)) = k(Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[abstraction,656,theory(equality)]),k_definition,theory(equality)]) ).

cnf(1290,plain,
    apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X)),Y),Z) = Z,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[abstraction,659,theory(equality)]),k_definition,theory(equality)]) ).

cnf(1291,plain,
    $false,
    inference('REWRITE',[status(thm)],[48,1290,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : COL077-1 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n025.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 15:06:43 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47  * 
% 0.20/0.47  * 
% 0.20/0.48  #<PACKAGE "SNARK-USER">
% 0.20/0.48  * 
% 0.20/0.48  SNARK-TPTP-OPTIONS
% 0.20/0.48  * 
% 0.20/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48   (USE-FACTORING :POS)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48  * 
% 0.20/0.48  "."
% 0.20/0.48  * 
% 0.20/0.48  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T15:06:43
% 0.20/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n025.cluster.edu at 2022-05-31T15:06:43
% 0.20/0.49  
% 1.47/1.67  ; Recognized left identity assertion (= (|apply| |identity| ?X) ?X).
% 1.47/1.67  
% 1.47/1.67  #||
% 1.47/1.67  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.47/1.67  % SZS output start Refutation
% See solution above
% 1.47/1.67  ||#
% 1.47/1.67  
% 1.47/1.67  ; Summary of computation:
% 1.47/1.67  ;      3006 formulas have been input or derived (from 109 formulas).
% 1.47/1.67  ;      1291 (43%) were retained.  Of these,
% 1.47/1.67  ;          534 (41%) were simplified or subsumed later,
% 1.47/1.67  ;          757 (59%) are still being kept.
% 1.47/1.67  ; 
% 1.47/1.67  ; Run time in seconds excluding printing time:
% 1.47/1.67  ;     0.003   0%   Read assertion file          (1 call)
% 1.47/1.67  ;     0.001   0%   Assert                       (12 calls)
% 1.47/1.67  ;     0.180  15%   Process new row              (2,740 calls)
% 1.47/1.67  ;     0.012   1%   Resolution                   (216 calls)
% 1.47/1.67  ;     0.046   4%   Paramodulation               (108 calls)
% 1.47/1.67  ;     0.000   0%   Factoring                    (2 calls)
% 1.47/1.67  ;     0.002   0%   Condensing                   (234 calls)
% 1.47/1.67  ;     0.013   1%   Forward subsumption          (234 calls)
% 1.47/1.67  ;     0.003   0%   Backward subsumption         (150 calls)
% 1.47/1.67  ;     0.003   0%   Clause clause subsumption    (543 calls)
% 1.47/1.67  ;     0.235  20%   Forward simplification       (2,277 calls)
% 1.47/1.67  ;     0.123  10%   Backward simplification      (1,290 calls)
% 1.47/1.67  ;     0.529  44%   Ordering                     (88,779 calls)
% 1.47/1.67  ;     0.000   0%   Sortal reasoning             (32 calls)
% 1.47/1.67  ;     0.000   0%   Purity testing               (1 call)
% 1.47/1.67  ;     0.043   4%   Other
% 1.47/1.67  ;     1.193        Total
% 1.47/1.67  ;     1.195        Real time
% 1.47/1.67  ; 
% 1.47/1.68  ; Term-hash-array has 4,714 terms in all.
% 1.47/1.68  ; Feature-vector-row-index has 101 entries (101 at peak, 150 added, 49 deleted).
% 1.47/1.68  ; Feature-vector-row-index has 854 nodes (854 at peak, 1,270 added, 416 deleted).
% 1.47/1.68  ;  Retrieved 474 possibly forward subsuming rows in 234 calls.
% 1.47/1.68  ;  Retrieved 123 possibly backward subsumed rows in 150 calls.
% 1.47/1.68  ; Path-index has 2,850 entries (2,862 at peak, 5,292 added, 2,442 deleted).
% 1.47/1.68  ; Path-index has 4,339 nodes (4,558 at peak, 6,080 added, 1,741 deleted).
% 1.47/1.68  ; Trie-index has 2,850 entries (2,862 at peak, 5,292 added, 2,442 deleted).
% 1.47/1.68  ; Trie-index has 15,110 nodes (15,212 at peak, 29,643 added, 14,533 deleted).
% 1.47/1.68  ; Retrieved 61,926 generalization terms in 26,213 calls.
% 1.47/1.68  ; Retrieved 13,708 instance terms in 2,459 calls.
% 1.47/1.68  ; Retrieved 14,987 unifiable terms in 988 calls.
% 1.47/1.68  ; 
% 1.47/1.68  ; The agenda of backward simplifiable rows to process has 1 entry:
% 1.47/1.68  ;     1 with value 0
% 1.47/1.68  ; The agenda of rows to process has 3 entries:
% 1.47/1.68  ;     1 with value 32              2 with value 33
% 1.47/1.68  ; The agenda of rows to give has 673 entries:
% 1.47/1.68  ;    29 with value (4 21)         30 with value (4 32)          27 with value (4 42)
% 1.47/1.68  ;    21 with value (4 22)         26 with value (4 33)           8 with value (4 43)
% 1.47/1.68  ;    27 with value (4 23)         30 with value (4 34)          14 with value (4 44)
% 1.47/1.68  ;    25 with value (4 24)         14 with value (4 35)           9 with value (4 45)
% 1.47/1.68  ;    33 with value (4 25)         23 with value (4 36)           5 with value (4 46)
% 1.47/1.68  ;    32 with value (4 26)         29 with value (4 37)           6 with value (4 47)
% 1.47/1.68  ;    32 with value (4 27)         24 with value (4 38)           3 with value (4 48)
% 1.47/1.68  ;    15 with value (4 28)         18 with value (4 39)           1 with value (4 49)
% 1.47/1.68  ;    35 with value (4 29)         27 with value (4 40)           1 with value (4 53)
% 1.47/1.68  ;    46 with value (4 30)         33 with value (4 41)           1 with value (4 54)
% 1.47/1.68  ;    49 with value (4 31)
% 1.47/1.68  Evaluation took:
% 1.47/1.68    1.195 seconds of real time
% 1.47/1.68    1.074353 seconds of user run time
% 1.47/1.68    0.120376 seconds of system run time
% 1.47/1.68    [Run times include 0.073 seconds GC run time.]
% 1.47/1.68    0 calls to %EVAL
% 1.47/1.68    0 page faults and
% 1.47/1.68    67,564,728 bytes consed.
% 1.47/1.68  :PROOF-FOUND
% 1.47/1.68  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T15:06:44
% 1.47/1.68  :PROOF-FOUND
% 1.47/1.68  * 
%------------------------------------------------------------------------------