TSTP Solution File: SET025-8 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET025-8 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n008.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 : Tue Jul 19 05:06:04 EDT 2022

% Result   : Unsatisfiable 26.37s 26.57s
% Output   : Refutation 26.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   19 (  11 unt;   0 nHn;  16 RR)
%            Number of literals    :   39 (   6 equ;  22 neg)
%            Maximal clause size   :    8 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :   26 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(a2,axiom,
    ( ~ member(X,Y)
    | little_set(X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',a2) ).

cnf(non_ordered_pair4,axiom,
    little_set(non_ordered_pair(X,Y)),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair4) ).

cnf(ordered_pair,axiom,
    ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair) ).

cnf(ordered_pair_predicate1,axiom,
    ( ~ ordered_pair_predicate(X)
    | little_set(f2(X)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate1) ).

cnf(ordered_pair_predicate2,axiom,
    ( ~ ordered_pair_predicate(X)
    | little_set(f3(X)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate2) ).

cnf(ordered_pair_predicate3,axiom,
    ( ~ ordered_pair_predicate(X)
    | X = ordered_pair(f2(X),f3(X)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate3) ).

cnf(14,plain,
    ( ~ ordered_pair_predicate(X)
    | X = non_ordered_pair(singleton_set(f2(X)),non_ordered_pair(f2(X),f3(X))) ),
    inference('REWRITE',[status(thm)],[ordered_pair_predicate3,ordered_pair,theory(equality)]) ).

cnf(universal_set,axiom,
    ( member(X,universal_set)
    | ~ little_set(X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',universal_set) ).

cnf(infinity1,axiom,
    little_set(infinity),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',infinity1) ).

cnf(compose7,axiom,
    ( member(X,compose(Y,Z))
    | ~ little_set(X)
    | ~ little_set(U)
    | ~ little_set(V)
    | ~ little_set(W)
    | X != ordered_pair(U,V)
    | ~ member(ordered_pair(U,W),Y)
    | ~ member(ordered_pair(W,V),Z) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',compose7) ).

cnf(158,plain,
    ( member(X,compose(Y,Z))
    | ~ little_set(X)
    | ~ little_set(U)
    | ~ little_set(V)
    | ~ little_set(W)
    | X != non_ordered_pair(singleton_set(U),non_ordered_pair(U,V))
    | ~ member(non_ordered_pair(singleton_set(U),non_ordered_pair(U,W)),Y)
    | ~ member(non_ordered_pair(singleton_set(W),non_ordered_pair(W,V)),Z) ),
    inference('REWRITE',[status(thm)],[compose7,ordered_pair,theory(equality)]) ).

cnf(an_ordered_pair_predicate,hypothesis,
    ordered_pair_predicate(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_ordered_pair_predicate) ).

cnf(prove_predicate_is_small,negated_conjecture,
    ~ little_set(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_predicate_is_small) ).

cnf(186,plain,
    ~ member(a,X),
    inference('UR-RESOLVE',[status(thm)],[a2,prove_predicate_is_small]) ).

cnf(188,plain,
    member(non_ordered_pair(X,Y),universal_set),
    inference('HYPERRESOLVE',[status(thm)],[universal_set,non_ordered_pair4]) ).

cnf(192,plain,
    little_set(f2(a)),
    inference('HYPERRESOLVE',[status(thm)],[ordered_pair_predicate1,an_ordered_pair_predicate]) ).

cnf(193,plain,
    little_set(f3(a)),
    inference('HYPERRESOLVE',[status(thm)],[ordered_pair_predicate2,an_ordered_pair_predicate]) ).

cnf(576,plain,
    a = non_ordered_pair(singleton_set(f2(a)),non_ordered_pair(f2(a),f3(a))),
    inference('HYPERRESOLVE',[status(thm)],[14,an_ordered_pair_predicate]) ).

cnf(2142,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[158,188,non_ordered_pair4,192,193,infinity1,188,theory(equality)]),186,576,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET025-8 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run-snark %s %d
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 05:51:23 EDT 2022
% 0.14/0.34  % 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 2022-07-11T05:51:23
% 0.20/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n008.cluster.edu at 2022-07-11T05:51:23
% 26.37/26.57  
% 26.37/26.57  
% 26.37/26.57  #||
% 26.37/26.57  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.37/26.57  % SZS output start Refutation
% See solution above
% 26.37/26.57  ||#
% 26.37/26.57  
% 26.37/26.57  ; Summary of computation:
% 26.37/26.57  ;     33341 formulas have been input or derived (from 197 formulas).
% 26.37/26.57  ;      2142 ( 6%) were retained.  Of these,
% 26.37/26.57  ;          106 ( 5%) were simplified or subsumed later,
% 26.37/26.57  ;         2036 (95%) are still being kept.
% 26.37/26.57  ; 
% 26.37/26.57  ; Run time in seconds excluding printing time:
% 26.37/26.58  ;     0.029   0%   Read assertion file          (1 call)
% 26.37/26.58  ;     0.006   0%   Assert                       (153 calls)
% 26.37/26.58  ;     0.242   1%   Process new row              (19,460 calls)
% 26.37/26.58  ;    24.846  95%   Resolution                   (392 calls)
% 26.37/26.58  ;     0.006   0%   Paramodulation               (196 calls)
% 26.37/26.58  ;     0.000   0%   Factoring                    (13 calls)
% 26.37/26.58  ;     0.098   0%   Condensing                   (14,249 calls)
% 26.37/26.58  ;     0.428   2%   Forward subsumption          (14,249 calls)
% 26.37/26.58  ;     0.044   0%   Backward subsumption         (1,413 calls)
% 26.37/26.58  ;     0.035   0%   Clause clause subsumption    (15,329 calls)
% 26.37/26.58  ;     0.252   1%   Forward simplification       (17,783 calls)
% 26.37/26.58  ;     0.013   0%   Backward simplification      (2,112 calls)
% 26.37/26.58  ;     0.011   0%   Ordering                     (4,971 calls)
% 26.37/26.58  ;     0.000   0%   Sortal reasoning             (32 calls)
% 26.37/26.58  ;     0.000   0%   Purity testing               (1 call)
% 26.37/26.58  ;     0.085   0%   Other
% 26.37/26.58  ;    26.095        Total
% 26.37/26.58  ;    26.095        Real time
% 26.37/26.58  ; 
% 26.37/26.58  ; Term-hash-array has 4,473 terms in all.
% 26.37/26.58  ; Feature-vector-row-index has 1,401 entries (1,401 at peak, 1,413 added, 12 deleted).
% 26.37/26.58  ; Feature-vector-row-index has 8,769 nodes (8,769 at peak, 8,908 added, 139 deleted).
% 26.37/26.58  ;  Retrieved 19,833 possibly forward subsuming rows in 14,249 calls.
% 26.37/26.58  ;  Retrieved 348 possibly backward subsumed rows in 1,413 calls.
% 26.37/26.58  ; Path-index has 4,383 entries (4,383 at peak, 4,480 added, 97 deleted).
% 26.37/26.58  ; Path-index has 16,444 nodes (16,444 at peak, 16,515 added, 71 deleted).
% 26.37/26.58  ; Trie-index has 4,383 entries (4,383 at peak, 4,480 added, 97 deleted).
% 26.37/26.58  ; Trie-index has 23,946 nodes (23,946 at peak, 24,212 added, 266 deleted).
% 26.37/26.58  ; Retrieved 28,010 generalization terms in 51,520 calls.
% 26.37/26.58  ; Retrieved 707 instance terms in 698 calls.
% 26.37/26.58  ; Retrieved 51,817,395 unifiable terms in 485,112 calls.
% 26.37/26.58  ; 
% 26.37/26.58  ; The agenda of rows to process has 7955 entries:
% 26.37/26.58  ;   143 with value 19            924 with value 27             193 with value 34
% 26.37/26.58  ;   926 with value 20           1388 with value 28              72 with value 35
% 26.37/26.58  ;   212 with value 21            678 with value 29              48 with value 36
% 26.37/26.58  ;   140 with value 22            640 with value 30              24 with value 38
% 26.37/26.58  ;   298 with value 23            203 with value 31              18 with value 39
% 26.37/26.58  ;   320 with value 24            202 with value 32              16 with value 40
% 26.37/26.58  ;   526 with value 25            164 with value 33               2 with value 44
% 26.37/26.58  ;   818 with value 26
% 26.37/26.58  ; The agenda of rows to give has 1845 entries:
% 26.37/26.58  ;     1 with value (4 7)          24 with value (4 26)          38 with value (4 45)
% 26.37/26.58  ;    39 with value (4 8)          71 with value (4 27)          35 with value (4 46)
% 26.37/26.58  ;    47 with value (4 9)          34 with value (4 28)          19 with value (4 47)
% 26.37/26.58  ;    32 with value (4 10)         15 with value (4 29)           2 with value (4 48)
% 26.37/26.58  ;    50 with value (4 11)         18 with value (4 30)          12 with value (4 49)
% 26.37/26.58  ;    36 with value (4 12)         29 with value (4 31)           6 with value (4 50)
% 26.37/26.58  ;    45 with value (4 13)         35 with value (4 32)           2 with value (4 51)
% 26.37/26.58  ;    90 with value (4 14)         45 with value (4 33)           8 with value (4 53)
% 26.37/26.58  ;   111 with value (4 15)         47 with value (4 34)           9 with value (4 56)
% 26.37/26.58  ;    79 with value (4 16)         37 with value (4 35)           2 with value (4 57)
% 26.37/26.58  ;    91 with value (4 17)         36 with value (4 36)           2 with value (4 58)
% 26.37/26.58  ;   117 with value (4 18)         14 with value (4 37)           2 with value (4 59)
% 26.37/26.58  ;    91 with value (4 19)         12 with value (4 38)           9 with value (4 61)
% 26.37/26.58  ;    72 with value (4 20)         10 with value (4 39)           4 with value (4 62)
% 26.37/26.58  ;    94 with value (4 21)         20 with value (4 40)           4 with value (4 65)
% 26.37/26.58  ;    60 with value (4 22)         24 with value (4 41)           4 with value (4 74)
% 26.37/26.58  ;    39 with value (4 23)         21 with value (4 42)           2 with value (4 88)
% 26.37/26.58  ;    28 with value (4 24)         23 with value (4 43)           4 with value (4 94)
% 26.37/26.58  ;    22 with value (4 25)         18 with value (4 44)           4 with value (4 105)
% 26.37/26.58  Evaluation took:
% 26.37/26.58    26.097 seconds of real time
% 26.37/26.58    25.833485 seconds of user run time
% 26.37/26.58    0.263817 seconds of system run time
% 26.37/26.58    [Run times include 0.67 seconds GC run time.]
% 26.37/26.58    0 calls to %EVAL
% 26.37/26.58    0 page faults and
% 26.37/26.58    1,166,026,992 bytes consed.
% 26.37/26.58  :PROOF-FOUND
% 26.37/26.58  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-11T05:51:49
% 26.37/26.58  :PROOF-FOUND
% 26.37/26.58  * 
%------------------------------------------------------------------------------