TSTP Solution File: COL042-4 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : COL042-4 : TPTP v8.1.0. Released v1.2.0.
% 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 : Fri Jul 15 00:41:39 EDT 2022

% Result   : Unsatisfiable 21.84s 22.00s
% Output   : Refutation 21.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   24 (  23 unt;   0 nHn;   5 RR)
%            Number of literals    :   25 (  20 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   64 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
    apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).

cnf(w1_definition,axiom,
    apply(apply(w1,X),Y) = apply(apply(Y,X),X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w1_definition) ).

cnf(strong_fixed_point,axiom,
    ( apply(X,fixed_pt) != apply(fixed_pt,apply(X,fixed_pt))
    | fixed_point(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).

cnf(prove_strong_fixed_point,negated_conjecture,
    ~ fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).

cnf(5,plain,
    ~ fixed_point(apply(apply(apply(apply(b,b),apply(b,apply(w1,w1))),apply(apply(b,apply(b,w1)),b)),b)),
    inference('REWRITE',[status(thm)],[prove_strong_fixed_point,b_definition,theory(equality)]) ).

cnf(11,plain,
    apply(apply(w1,X),apply(b,Y)) = apply(Y,apply(X,X)),
    inference('PARAMODULATE',[status(thm)],[w1_definition,b_definition,theory(equality)]) ).

cnf(12,plain,
    apply(apply(w1,X),apply(apply(b,Y),Z)) = apply(apply(Y,apply(Z,X)),X),
    inference('PARAMODULATE',[status(thm)],[w1_definition,b_definition,theory(equality)]) ).

cnf(15,plain,
    apply(apply(apply(b,X),apply(apply(b,Y),Z)),U) = apply(X,apply(Y,apply(Z,U))),
    inference('PARAMODULATE',[status(thm)],[b_definition,b_definition,theory(equality)]) ).

cnf(16,plain,
    apply(apply(apply(b,X),Y),apply(Z,U)) = apply(X,apply(apply(apply(b,Y),Z),U)),
    inference('PARAMODULATE',[status(thm)],[b_definition,b_definition,theory(equality)]) ).

cnf(20,plain,
    apply(apply(apply(apply(apply(b,b),X),Y),Z),U) = apply(apply(X,Y),apply(Z,U)),
    inference('PARAMODULATE',[status(thm)],[b_definition,b_definition,theory(equality)]) ).

cnf(21,plain,
    apply(apply(apply(apply(b,apply(b,X)),Y),Z),U) = apply(X,apply(apply(Y,Z),U)),
    inference('PARAMODULATE',[status(thm)],[b_definition,b_definition,theory(equality)]) ).

cnf(34,plain,
    apply(apply(apply(b,X),Y),apply(Z,Z)) = apply(X,apply(apply(w1,Z),apply(b,Y))),
    inference('PARAMODULATE',[status(thm)],[b_definition,11,theory(equality)]) ).

cnf(123,plain,
    apply(apply(w1,X),apply(apply(b,w1),Y)) = apply(apply(X,apply(Y,X)),apply(Y,X)),
    inference('PARAMODULATE',[status(thm)],[w1_definition,12,theory(equality)]) ).

cnf(124,plain,
    apply(apply(apply(b,apply(w1,X)),apply(b,Y)),Z) = apply(apply(Y,apply(Z,X)),X),
    inference('PARAMODULATE',[status(thm)],[b_definition,12,theory(equality)]) ).

cnf(745,plain,
    apply(X,apply(Y,apply(Z,U))) = apply(X,apply(apply(apply(b,Y),Z),U)),
    inference('PARAMODULATE',[status(thm)],[b_definition,15,theory(equality)]) ).

cnf(760,plain,
    apply(apply(apply(b,apply(w1,X)),apply(apply(b,apply(b,Y)),Z)),U) = apply(apply(Y,apply(apply(Z,U),X)),X),
    inference('PARAMODULATE',[status(thm)],[12,15,theory(equality)]) ).

cnf(1839,plain,
    apply(apply(apply(apply(apply(b,b),X),apply(Y,Y)),Z),U) = apply(apply(apply(w1,Y),apply(b,X)),apply(Z,U)),
    inference('PARAMODULATE',[status(thm)],[b_definition,34,theory(equality)]) ).

cnf(2868,plain,
    apply(apply(apply(apply(apply(b,b),w1),X),apply(b,w1)),Y) = apply(apply(X,apply(Y,X)),apply(Y,X)),
    inference('PARAMODULATE',[status(thm)],[123,20,theory(equality)]) ).

cnf(3205,plain,
    apply(apply(w1,apply(X,Y)),apply(apply(b,apply(b,Z)),Y)) = apply(Z,apply(apply(w1,Y),apply(apply(b,w1),X))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[21,123,theory(equality)]),w1_definition,theory(equality)]) ).

cnf(4575,plain,
    apply(apply(apply(apply(b,apply(w1,X)),apply(b,b)),Y),Z) = apply(apply(Y,X),apply(X,Z)),
    inference('PARAMODULATE',[status(thm)],[b_definition,124,theory(equality)]) ).

cnf(4598,plain,
    apply(apply(apply(b,apply(w1,X)),apply(b,Y)),apply(apply(b,Z),U)) = apply(apply(apply(apply(b,Y),Z),apply(U,X)),X),
    inference('PARAMODULATE',[status(thm)],[124,16,theory(equality)]) ).

cnf(4602,plain,
    ~ fixed_point(apply(apply(apply(b,apply(w1,b)),apply(b,b)),apply(apply(apply(apply(b,b),b),apply(w1,w1)),apply(b,apply(b,w1))))),
    inference('REWRITE',[status(thm)],[5,b_definition,4598,theory(equality)]) ).

cnf(4654,plain,
    apply(apply(X,apply(apply(Y,apply(Z,U)),V)),V) = apply(apply(apply(b,apply(w1,V)),apply(b,X)),apply(apply(apply(b,Y),Z),U)),
    inference('PARAMODULATE',[status(thm)],[745,124,theory(equality)]) ).

cnf(4856,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[strong_fixed_point,4602]),2868,3205,b_definition,4654,760,11,1839,4575,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : COL042-4 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.13  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n028.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 : Tue May 31 13:10:21 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.45  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46  * 
% 0.19/0.46  * 
% 0.19/0.46  #<PACKAGE "SNARK-USER">
% 0.19/0.46  * 
% 0.19/0.46  SNARK-TPTP-OPTIONS
% 0.19/0.46  * 
% 0.19/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46   (USE-FACTORING :POS)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46  * 
% 0.19/0.46  "."
% 0.19/0.46  * 
% 0.19/0.46  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T13:10:21
% 0.19/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n028.cluster.edu at 2022-05-31T13:10:21
% 21.84/22.00  
% 21.84/22.00  
% 21.84/22.00  #||
% 21.84/22.00  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.84/22.00  % SZS output start Refutation
% See solution above
% 21.84/22.01  ||#
% 21.84/22.01  
% 21.84/22.01  ; Summary of computation:
% 21.84/22.01  ;     10590 formulas have been input or derived (from 58 formulas).
% 21.84/22.01  ;      4856 (46%) were retained.  Of these,
% 21.84/22.01  ;          429 ( 9%) were simplified or subsumed later,
% 21.84/22.01  ;         4427 (91%) are still being kept.
% 21.84/22.01  ; 
% 21.84/22.01  ; Run time in seconds excluding printing time:
% 21.84/22.01  ;     0.002   0%   Read assertion file          (1 call)
% 21.84/22.01  ;     0.000   0%   Assert                       (4 calls)
% 21.84/22.01  ;     0.776   4%   Process new row              (10,562 calls)
% 21.84/22.01  ;     0.025   0%   Resolution                   (114 calls)
% 21.84/22.01  ;     0.283   1%   Paramodulation               (57 calls)
% 21.84/22.01  ;     0.002   0%   Condensing                   (172 calls)
% 21.84/22.01  ;     0.021   0%   Forward subsumption          (172 calls)
% 21.84/22.01  ;     0.005   0%   Backward subsumption         (115 calls)
% 21.84/22.01  ;     0.000   0%   Clause clause subsumption    (250 calls)
% 21.84/22.01  ;     5.502  26%   Forward simplification       (10,551 calls)
% 21.84/22.01  ;     2.029   9%   Backward simplification      (4,855 calls)
% 21.84/22.01  ;    12.829  60%   Ordering                     (1,272,999 calls)
% 21.84/22.01  ;     0.000   0%   Sortal reasoning             (32 calls)
% 21.84/22.01  ;     0.000   0%   Purity testing               (1 call)
% 21.84/22.01  ;     0.065   0%   Other
% 21.84/22.01  ;    21.539        Total
% 21.84/22.01  ;    21.541        Real time
% 21.84/22.01  ; 
% 21.84/22.01  ; Term-hash-array has 17,598 terms in all.
% 21.84/22.01  ; Feature-vector-row-index has 102 entries (102 at peak, 115 added, 13 deleted).
% 21.84/22.01  ; Feature-vector-row-index has 1,419 nodes (1,419 at peak, 1,592 added, 173 deleted).
% 21.84/22.01  ;  Retrieved 202 possibly forward subsuming rows in 172 calls.
% 21.84/22.01  ;  Retrieved 84 possibly backward subsumed rows in 115 calls.
% 21.84/22.01  ; Path-index has 16,319 entries (16,319 at peak, 17,805 added, 1,486 deleted).
% 21.84/22.01  ; Path-index has 2,076 nodes (2,076 at peak, 2,197 added, 121 deleted).
% 21.84/22.01  ; Trie-index has 16,319 entries (16,319 at peak, 17,805 added, 1,486 deleted).
% 21.84/22.01  ; Trie-index has 93,239 nodes (93,239 at peak, 102,323 added, 9,084 deleted).
% 21.84/22.01  ; Retrieved 2,350,909 generalization terms in 165,289 calls.
% 21.84/22.01  ; Retrieved 736,274 instance terms in 13,443 calls.
% 21.84/22.01  ; Retrieved 172,188 unifiable terms in 617 calls.
% 21.84/22.01  ; 
% 21.84/22.01  ; The agenda of rows to give has 4372 entries:
% 21.84/22.01  ;     1 with value (4 24)        519 with value (4 40)          15 with value (4 55)
% 21.84/22.01  ;    11 with value (4 26)        353 with value (4 41)          17 with value (4 56)
% 21.84/22.01  ;    19 with value (4 27)        291 with value (4 42)          12 with value (4 57)
% 21.84/22.01  ;    25 with value (4 28)        198 with value (4 43)           7 with value (4 58)
% 21.84/22.01  ;    47 with value (4 29)        149 with value (4 44)           5 with value (4 59)
% 21.84/22.01  ;    44 with value (4 30)        164 with value (4 45)           5 with value (4 60)
% 21.84/22.01  ;    82 with value (4 31)        138 with value (4 46)           2 with value (4 61)
% 21.84/22.01  ;   100 with value (4 32)         53 with value (4 47)           3 with value (4 62)
% 21.84/22.01  ;   165 with value (4 33)         57 with value (4 48)           3 with value (4 63)
% 21.84/22.01  ;   154 with value (4 34)         37 with value (4 49)           2 with value (4 64)
% 21.84/22.01  ;   241 with value (4 35)         34 with value (4 50)           2 with value (4 65)
% 21.84/22.01  ;   292 with value (4 36)         37 with value (4 51)           2 with value (4 66)
% 21.84/22.01  ;   270 with value (4 37)         27 with value (4 52)           1 with value (4 69)
% 21.84/22.01  ;   340 with value (4 38)         19 with value (4 53)           1 with value (4 70)
% 21.84/22.01  ;   405 with value (4 39)         21 with value (4 54)           2 with value (4 72)
% 21.84/22.01  Evaluation took:
% 21.84/22.01    21.542 seconds of real time
% 21.84/22.01    19.919756 seconds of user run time
% 21.84/22.01    1.62325 seconds of system run time
% 21.84/22.01    [Run times include 1.756 seconds GC run time.]
% 21.84/22.01    0 calls to %EVAL
% 21.84/22.01    0 page faults and
% 21.84/22.01    1,455,420,544 bytes consed.
% 21.84/22.01  :PROOF-FOUND
% 21.84/22.01  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T13:10:42
% 21.84/22.01  :PROOF-FOUND
% 21.84/22.01  * 
%------------------------------------------------------------------------------