TSTP Solution File: SET974+1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Jul 19 05:13:46 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   16 (   8 unt;   4 nHn;  13 RR)
%            Number of literals    :   24 (   1 equ;   8 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-5 aty)
%            Number of variables   :   20 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    set_intersection2(X,X) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

cnf(8,axiom,
    ( ~ in(X,set_intersection2(cartesian_product2(Y,Z),cartesian_product2(U,V)))
    | in('SKOLEMAAAV3'(X,Y,U,Z,V),set_intersection2(Y,U)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).

cnf(9,axiom,
    ( ~ in(X,set_intersection2(cartesian_product2(Y,Z),cartesian_product2(U,V)))
    | in('SKOLEMAAAV4'(X,Y,U,Z,V),set_intersection2(Z,V)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).

cnf(10,negated_conjecture,
    ( disjoint('SKOLEMAAAV5','SKOLEMAAAV6')
    | disjoint('SKOLEMAAAV7','SKOLEMAAAV8') ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).

cnf(11,negated_conjecture,
    ~ disjoint(cartesian_product2('SKOLEMAAAV5','SKOLEMAAAV7'),cartesian_product2('SKOLEMAAAV6','SKOLEMAAAV8')),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).

cnf(12,axiom,
    ( disjoint(X,Y)
    | in('SKOLEMAAAV9'(X,Y),set_intersection2(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).

cnf(13,axiom,
    ( ~ in(X,set_intersection2(Y,Z))
    | ~ disjoint(Y,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).

cnf(14,plain,
    ( ~ in(X,Y)
    | ~ disjoint(Y,Y) ),
    inference('PARAMODULATE',[status(thm)],[13,4,theory(equality)]) ).

cnf(17,plain,
    ( disjoint(X,X)
    | in('SKOLEMAAAV9'(X,X),X) ),
    inference('PARAMODULATE',[status(thm)],[12,4,theory(equality)]) ).

cnf(18,plain,
    in('SKOLEMAAAV9'(cartesian_product2('SKOLEMAAAV5','SKOLEMAAAV7'),cartesian_product2('SKOLEMAAAV6','SKOLEMAAAV8')),set_intersection2(cartesian_product2('SKOLEMAAAV5','SKOLEMAAAV7'),cartesian_product2('SKOLEMAAAV6','SKOLEMAAAV8'))),
    inference('UR-RESOLVE',[status(thm)],[12,11]) ).

cnf(29,plain,
    ( disjoint(set_intersection2('SKOLEMAAAV7','SKOLEMAAAV8'),set_intersection2('SKOLEMAAAV7','SKOLEMAAAV8'))
    | disjoint('SKOLEMAAAV5','SKOLEMAAAV6') ),
    inference('HYPERRESOLVE',[status(thm)],[13,17,10]) ).

cnf(38,plain,
    in('SKOLEMAAAV4'('SKOLEMAAAV9'(cartesian_product2('SKOLEMAAAV5','SKOLEMAAAV7'),cartesian_product2('SKOLEMAAAV6','SKOLEMAAAV8')),'SKOLEMAAAV5','SKOLEMAAAV6','SKOLEMAAAV7','SKOLEMAAAV8'),set_intersection2('SKOLEMAAAV7','SKOLEMAAAV8')),
    inference('HYPERRESOLVE',[status(thm)],[9,18]) ).

cnf(40,plain,
    in('SKOLEMAAAV3'('SKOLEMAAAV9'(cartesian_product2('SKOLEMAAAV5','SKOLEMAAAV7'),cartesian_product2('SKOLEMAAAV6','SKOLEMAAAV8')),'SKOLEMAAAV5','SKOLEMAAAV6','SKOLEMAAAV7','SKOLEMAAAV8'),set_intersection2('SKOLEMAAAV5','SKOLEMAAAV6')),
    inference('HYPERRESOLVE',[status(thm)],[8,18]) ).

cnf(57,plain,
    disjoint('SKOLEMAAAV5','SKOLEMAAAV6'),
    inference('HYPERRESOLVE',[status(thm)],[14,38,29]) ).

cnf(61,plain,
    ~ in(X,set_intersection2('SKOLEMAAAV5','SKOLEMAAAV6')),
    inference('UR-RESOLVE',[status(thm)],[13,57]) ).

cnf(62,plain,
    $false,
    inference('REWRITE',[status(thm)],[40,61]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : run-snark %s %d
% 0.13/0.33  % Computer : n028.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 : Sun Jul 10 15:11:42 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.45  /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p 2022-07-10T15:11:42
% 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 2022-07-10T15:11:42
% 0.19/0.48  
% 0.19/0.48  ; Recognized commutativity assertion (= (|unordered_pair| ?X ?Y) (|unordered_pair| ?Y ?X)).
% 0.19/0.48  ; Recognized commutativity assertion (= (|set_intersection2| ?X ?Y) (|set_intersection2| ?Y ?X)).
% 0.19/0.48  ; Recognized commutativity assertion (OR (NOT (|disjoint| ?X ?Y)) (|disjoint| ?Y ?X)).
% 0.19/0.48  ; Declaring unordered_pair to be commutative.
% 0.19/0.48  ; Declaring set_intersection2 to be commutative.
% 0.19/0.51  ; Declaring disjoint to be commutative.
% 0.19/0.51  
% 0.19/0.51  #||
% 0.19/0.51  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.51  % SZS output start Refutation
% See solution above
% 0.19/0.51  ||#
% 0.19/0.51  
% 0.19/0.51  ; Summary of computation:
% 0.19/0.51  ;       117 formulas have been input or derived (from 28 formulas).
% 0.19/0.51  ;        62 (53%) were retained.  Of these,
% 0.19/0.51  ;            6 (10%) were simplified or subsumed later,
% 0.19/0.51  ;           56 (90%) are still being kept.
% 0.19/0.51  ; 
% 0.19/0.51  ; Run time in seconds excluding printing time:
% 0.19/0.51  ;     0.003   7%   Read assertion file          (1 call)
% 0.19/0.51  ;     0.001   2%   Assert                       (12 calls)
% 0.19/0.51  ;     0.007  15%   Process new row              (93 calls)
% 0.19/0.51  ;     0.003   7%   Resolution                   (54 calls)
% 0.19/0.51  ;     0.003   7%   Paramodulation               (27 calls)
% 0.19/0.51  ;     0.000   0%   Factoring                    (4 calls)
% 0.19/0.51  ;     0.002   4%   Condensing                   (28 calls)
% 0.19/0.51  ;     0.001   2%   Forward subsumption          (28 calls)
% 0.19/0.51  ;     0.000   0%   Backward subsumption         (24 calls)
% 0.19/0.51  ;     0.000   0%   Clause clause subsumption    (16 calls)
% 0.19/0.51  ;     0.002   4%   Forward simplification       (93 calls)
% 0.19/0.51  ;     0.000   0%   Backward simplification      (62 calls)
% 0.19/0.51  ;     0.002   4%   Ordering                     (79 calls)
% 0.19/0.51  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.19/0.51  ;     0.000   0%   Purity testing               (1 call)
% 0.19/0.51  ;     0.022  48%   Other
% 0.19/0.51  ;     0.046        Total
% 0.19/0.51  ;     0.049        Real time
% 0.19/0.51  ; 
% 0.19/0.51  ; Term-hash-array has 151 terms in all.
% 0.19/0.51  ; Feature-vector-row-index has 22 entries (24 at peak, 24 added, 2 deleted).
% 0.19/0.51  ; Feature-vector-row-index has 79 nodes (95 at peak, 95 added, 16 deleted).
% 0.19/0.51  ;  Retrieved 7 possibly forward subsuming rows in 28 calls.
% 0.19/0.51  ;  Retrieved 9 possibly backward subsumed rows in 24 calls.
% 0.19/0.51  ; Path-index has 153 entries (157 at peak, 159 added, 6 deleted).
% 0.19/0.51  ; Path-index has 873 nodes (889 at peak, 893 added, 20 deleted).
% 0.19/0.51  ; Trie-index has 153 entries (157 at peak, 159 added, 6 deleted).
% 0.19/0.51  ; Trie-index has 1,150 nodes (1,188 at peak, 1,195 added, 45 deleted).
% 0.19/0.51  ; Retrieved 64 generalization terms in 178 calls.
% 0.19/0.51  ; Retrieved 41 instance terms in 37 calls.
% 0.19/0.51  ; Retrieved 468 unifiable terms in 233 calls.
% 0.19/0.51  ; 
% 0.19/0.51  ; The agenda of rows to process has 1 entry:
% 0.19/0.51  ;     1 with value 13
% 0.19/0.51  ; The agenda of rows to give has 30 entries:
% 0.19/0.51  ;     1 with value (4 7)           2 with value (4 26)           1 with value (4 36)
% 0.19/0.51  ;     1 with value (4 11)          2 with value (4 29)           4 with value (4 40)
% 0.19/0.51  ;     1 with value (4 12)          5 with value (4 30)           2 with value (4 48)
% 0.19/0.51  ;     3 with value (4 22)          2 with value (4 34)           2 with value (4 49)
% 0.19/0.51  ;     1 with value (4 23)          1 with value (4 35)           1 with value (4 83)
% 0.19/0.51  ;     1 with value (4 25)
% 0.19/0.51  Evaluation took:
% 0.19/0.51    0.049 seconds of real time
% 0.19/0.51    0.039239 seconds of user run time
% 0.19/0.51    0.010064 seconds of system run time
% 0.19/0.51    0 calls to %EVAL
% 0.19/0.51    0 page faults and
% 0.19/0.51    3,566,296 bytes consed.
% 0.19/0.51  :PROOF-FOUND
% 0.19/0.51  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-10T15:11:42
% 0.19/0.51  :PROOF-FOUND
% 0.19/0.51  * 
%------------------------------------------------------------------------------