TSTP Solution File: SET012-4 by SNARK---20120808r022

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%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n019.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 05:05:40 EDT 2022

% Result   : Unsatisfiable 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   18 (   8 unt;   6 nHn;  14 RR)
%            Number of literals    :   31 (   6 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   13 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(extensionality1,axiom,
    ( little_set(f1(X,Y))
    | X = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).

cnf(extensionality2,axiom,
    ( member(f1(X,Y),X)
    | member(f1(X,Y),Y)
    | X = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).

cnf(extensionality3,axiom,
    ( ~ member(f1(X,Y),X)
    | ~ member(f1(X,Y),Y)
    | X = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality3) ).

cnf(complement1,axiom,
    ( ~ member(X,complement(Y))
    | ~ member(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).

cnf(complement2,axiom,
    ( member(X,complement(Y))
    | ~ little_set(X)
    | member(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).

cnf(complement_of_a_is_b,hypothesis,
    complement(as) = bs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_is_b) ).

cnf(complement_of_b_is_c,hypothesis,
    complement(bs) = cs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_b_is_c) ).

cnf(prove_a_equals_c,negated_conjecture,
    as != cs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_c) ).

cnf(12,plain,
    little_set(f1(as,cs)),
    inference('UR-RESOLVE',[status(thm)],[extensionality1,prove_a_equals_c]) ).

cnf(15,plain,
    ( ~ member(X,cs)
    | ~ member(X,bs) ),
    inference('PARAMODULATE',[status(thm)],[complement1,complement_of_b_is_c,theory(equality)]) ).

cnf(16,plain,
    ( ~ member(X,bs)
    | ~ member(X,as) ),
    inference('PARAMODULATE',[status(thm)],[complement1,complement_of_a_is_b,theory(equality)]) ).

cnf(22,plain,
    ( member(f1(as,cs),complement(X))
    | member(f1(as,cs),X) ),
    inference('HYPERRESOLVE',[status(thm)],[complement2,12]) ).

cnf(39,plain,
    ( member(f1(as,cs),cs)
    | member(f1(as,cs),bs) ),
    inference('PARAMODULATE',[status(thm)],[22,complement_of_b_is_c,theory(equality)]) ).

cnf(40,plain,
    ( member(f1(as,cs),bs)
    | member(f1(as,cs),as) ),
    inference('PARAMODULATE',[status(thm)],[22,complement_of_a_is_b,theory(equality)]) ).

cnf(45,plain,
    member(f1(as,cs),as),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[15,40,extensionality2]),prove_a_equals_c]) ).

cnf(46,plain,
    ~ member(f1(as,cs),bs),
    inference('UR-RESOLVE',[status(thm)],[16,45]) ).

cnf(47,plain,
    member(f1(as,cs),cs),
    inference('REWRITE',[status(thm)],[39,46]) ).

cnf(48,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[extensionality3,45,prove_a_equals_c]),47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n019.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 : Sun Jul 10 19:44:53 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.44  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45  * 
% 0.19/0.45  * 
% 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 2022-07-10T19:44:53
% 0.19/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n019.cluster.edu at 2022-07-10T19:44:53
% 0.19/0.50  
% 0.19/0.50  
% 0.19/0.50  #||
% 0.19/0.50  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.50  % SZS output start Refutation
% See solution above
% 0.19/0.50  ||#
% 0.19/0.50  
% 0.19/0.50  ; Summary of computation:
% 0.19/0.50  ;       155 formulas have been input or derived (from 35 formulas).
% 0.19/0.50  ;        48 (31%) were retained.  Of these,
% 0.19/0.50  ;            9 (19%) were simplified or subsumed later,
% 0.19/0.50  ;           39 (81%) are still being kept.
% 0.19/0.50  ; 
% 0.19/0.50  ; Run time in seconds excluding printing time:
% 0.19/0.50  ;     0.002   5%   Read assertion file          (1 call)
% 0.19/0.50  ;     0.000   0%   Assert                       (11 calls)
% 0.19/0.50  ;     0.007  18%   Process new row              (120 calls)
% 0.19/0.50  ;     0.002   5%   Resolution                   (68 calls)
% 0.19/0.50  ;     0.000   0%   Paramodulation               (34 calls)
% 0.19/0.50  ;     0.001   2%   Factoring                    (9 calls)
% 0.19/0.50  ;     0.001   2%   Condensing                   (40 calls)
% 0.19/0.50  ;     0.001   2%   Forward subsumption          (40 calls)
% 0.19/0.50  ;     0.000   0%   Backward subsumption         (23 calls)
% 0.19/0.50  ;     0.001   2%   Clause clause subsumption    (35 calls)
% 0.19/0.50  ;     0.002   5%   Forward simplification       (118 calls)
% 0.19/0.50  ;     0.000   0%   Backward simplification      (48 calls)
% 0.19/0.50  ;     0.000   0%   Ordering                     (104 calls)
% 0.19/0.50  ;     0.001   2%   Sortal reasoning             (32 calls)
% 0.19/0.50  ;     0.000   0%   Purity testing               (1 call)
% 0.19/0.50  ;     0.022  55%   Other
% 0.19/0.50  ;     0.040        Total
% 0.19/0.50  ;     0.042        Real time
% 0.19/0.50  ; 
% 0.19/0.50  ; Term-hash-array has 69 terms in all.
% 0.19/0.50  ; Feature-vector-row-index has 18 entries (21 at peak, 23 added, 5 deleted).
% 0.19/0.50  ; Feature-vector-row-index has 68 nodes (68 at peak, 75 added, 7 deleted).
% 0.19/0.50  ;  Retrieved 33 possibly forward subsuming rows in 40 calls.
% 0.19/0.50  ;  Retrieved 6 possibly backward subsumed rows in 23 calls.
% 0.19/0.50  ; Path-index has 64 entries (64 at peak, 75 added, 11 deleted).
% 0.19/0.50  ; Path-index has 84 nodes (84 at peak, 91 added, 7 deleted).
% 0.19/0.50  ; Trie-index has 64 entries (64 at peak, 75 added, 11 deleted).
% 0.19/0.50  ; Trie-index has 105 nodes (106 at peak, 125 added, 20 deleted).
% 0.19/0.50  ; Retrieved 51 generalization terms in 190 calls.
% 0.19/0.50  ; Retrieved 24 instance terms in 24 calls.
% 0.19/0.50  ; Retrieved 1,081 unifiable terms in 315 calls.
% 0.19/0.50  ; 
% 0.19/0.50  ; The agenda of rows to process has 3 entries:
% 0.19/0.50  ;     1 with value 13              2 with value 16
% 0.19/0.50  ; The agenda of rows to give has 8 entries:
% 0.19/0.50  ;     1 with value (4 10)          3 with value (4 17)           1 with value (4 20)
% 0.19/0.50  ;     1 with value (4 12)          2 with value (4 19)
% 0.19/0.50  Evaluation took:
% 0.19/0.50    0.043 seconds of real time
% 0.19/0.50    0.036219 seconds of user run time
% 0.19/0.50    0.006153 seconds of system run time
% 0.19/0.50    0 calls to %EVAL
% 0.19/0.50    0 page faults and
% 0.19/0.50    2,935,328 bytes consed.
% 0.19/0.50  :PROOF-FOUND
% 0.19/0.50  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-10T19:44:53
% 0.19/0.50  :PROOF-FOUND
% 0.19/0.50  * 
%------------------------------------------------------------------------------