TSTP Solution File: SET666+3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET666+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n004.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 05:11:23 EDT 2022

% Result   : Theorem 0.39s 0.63s
% Output   : Refutation 0.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   27 (  11 unt;   4 nHn;  24 RR)
%            Number of literals    :   62 (   0 equ;  39 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   2 con; 0-2 aty)
%            Number of variables   :   37 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ ilf_type(Z,subset_type(cross_product(X,Y)))
    | ilf_type(Z,relation_type(X,Y)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

cnf(4,axiom,
    ( ~ ilf_type(X,set_type)
    | subset(identity_relation_of(X),cross_product(X,X)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).

cnf(10,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ilf_type(Y,identity_relation_of_type(X))
    | ~ ilf_type(Y,relation_type(X,X)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).

cnf(18,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ilf_type(Y,subset_type(X))
    | ~ ilf_type(Y,member_type(power_set(X))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).

cnf(20,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ subset(X,Y)
    | ~ ilf_type(Z,set_type)
    | ~ member(Z,X)
    | member(Z,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).

cnf(27,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | member(X,power_set(Y))
    | member('SKOLEMAAAV6'(X,Y),X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).

cnf(28,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | member(X,power_set(Y))
    | ~ member('SKOLEMAAAV6'(X,Y),Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).

cnf(29,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ empty(power_set(X)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).

cnf(32,axiom,
    ( ~ ilf_type(X,set_type)
    | empty(Y)
    | ~ ilf_type(Y,set_type)
    | ilf_type(X,member_type(Y))
    | ~ member(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).

cnf(45,axiom,
    ilf_type(X,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).

cnf(46,negated_conjecture,
    ~ ilf_type(identity_relation_of('SKOLEMAAAV12'),identity_relation_of_type('SKOLEMAAAV12')),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_29) ).

cnf(47,plain,
    ( ~ ilf_type(X,subset_type(cross_product(Y,Z)))
    | ilf_type(X,relation_type(Y,Z)) ),
    inference('REWRITE',[status(thm)],[1,45]) ).

cnf(50,plain,
    subset(identity_relation_of(X),cross_product(X,X)),
    inference('REWRITE',[status(thm)],[4,45]) ).

cnf(56,plain,
    ( ilf_type(X,identity_relation_of_type(Y))
    | ~ ilf_type(X,relation_type(Y,Y)) ),
    inference('REWRITE',[status(thm)],[10,45]) ).

cnf(61,plain,
    ( ilf_type(X,subset_type(Y))
    | ~ ilf_type(X,member_type(power_set(Y))) ),
    inference('REWRITE',[status(thm)],[18,45]) ).

cnf(63,plain,
    ( ~ subset(X,Y)
    | ~ member(Z,X)
    | member(Z,Y) ),
    inference('REWRITE',[status(thm)],[20,45]) ).

cnf(68,plain,
    ( member(X,power_set(Y))
    | member('SKOLEMAAAV6'(X,Y),X) ),
    inference('REWRITE',[status(thm)],[27,45]) ).

cnf(69,plain,
    ( member(X,power_set(Y))
    | ~ member('SKOLEMAAAV6'(X,Y),Y) ),
    inference('REWRITE',[status(thm)],[28,45]) ).

cnf(70,plain,
    ~ empty(power_set(X)),
    inference('REWRITE',[status(thm)],[29,45]) ).

cnf(72,plain,
    ( empty(X)
    | ilf_type(Y,member_type(X))
    | ~ member(Y,X) ),
    inference('REWRITE',[status(thm)],[32,45]) ).

cnf(91,plain,
    ~ ilf_type(identity_relation_of('SKOLEMAAAV12'),relation_type('SKOLEMAAAV12','SKOLEMAAAV12')),
    inference('UR-RESOLVE',[status(thm)],[56,46]) ).

cnf(126,plain,
    ~ ilf_type(identity_relation_of('SKOLEMAAAV12'),subset_type(cross_product('SKOLEMAAAV12','SKOLEMAAAV12'))),
    inference('UR-RESOLVE',[status(thm)],[47,91]) ).

cnf(188,plain,
    ~ ilf_type(identity_relation_of('SKOLEMAAAV12'),member_type(power_set(cross_product('SKOLEMAAAV12','SKOLEMAAAV12')))),
    inference('UR-RESOLVE',[status(thm)],[61,126]) ).

cnf(234,plain,
    ~ member(identity_relation_of('SKOLEMAAAV12'),power_set(cross_product('SKOLEMAAAV12','SKOLEMAAAV12'))),
    inference('UR-RESOLVE',[status(thm)],[72,188,70]) ).

cnf(237,plain,
    member('SKOLEMAAAV6'(identity_relation_of('SKOLEMAAAV12'),cross_product('SKOLEMAAAV12','SKOLEMAAAV12')),identity_relation_of('SKOLEMAAAV12')),
    inference('UR-RESOLVE',[status(thm)],[68,234]) ).

cnf(239,plain,
    ~ member('SKOLEMAAAV6'(identity_relation_of('SKOLEMAAAV12'),cross_product('SKOLEMAAAV12','SKOLEMAAAV12')),cross_product('SKOLEMAAAV12','SKOLEMAAAV12')),
    inference('UR-RESOLVE',[status(thm)],[69,234]) ).

cnf(425,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[63,237,50]),239]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET666+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.14/0.34  % Computer : n004.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 : Sun Jul 10 17:08:22 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.47  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48  * 
% 0.21/0.48  * 
% 0.21/0.48  #<PACKAGE "SNARK-USER">
% 0.21/0.48  * 
% 0.21/0.48  SNARK-TPTP-OPTIONS
% 0.21/0.48  * 
% 0.21/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.48   (USE-FACTORING :POS)
% 0.21/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.48  * 
% 0.21/0.48  "."
% 0.21/0.48  * 
% 0.21/0.48  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-10T17:08:22
% 0.21/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n004.cluster.edu at 2022-07-10T17:08:22
% 0.39/0.63  
% 0.39/0.63  
% 0.39/0.63  #||
% 0.39/0.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.63  % SZS output start Refutation
% See solution above
% 0.48/0.63  ||#
% 0.48/0.63  
% 0.48/0.63  ; Summary of computation:
% 0.48/0.63  ;       783 formulas have been input or derived (from 114 formulas).
% 0.48/0.63  ;       425 (54%) were retained.  Of these,
% 0.48/0.63  ;           43 (10%) were simplified or subsumed later,
% 0.48/0.63  ;          382 (90%) are still being kept.
% 0.48/0.63  ; 
% 0.48/0.63  ; Run time in seconds excluding printing time:
% 0.48/0.63  ;     0.007   5%   Read assertion file          (1 call)
% 0.48/0.63  ;     0.001   1%   Assert                       (25 calls)
% 0.48/0.63  ;     0.037  25%   Process new row              (645 calls)
% 0.48/0.63  ;     0.023  16%   Resolution                   (226 calls)
% 0.48/0.63  ;     0.002   1%   Paramodulation               (113 calls)
% 0.48/0.63  ;     0.000   0%   Factoring                    (22 calls)
% 0.48/0.63  ;     0.005   3%   Condensing                   (366 calls)
% 0.48/0.63  ;     0.015  10%   Forward subsumption          (366 calls)
% 0.48/0.63  ;     0.011   8%   Backward subsumption         (313 calls)
% 0.48/0.63  ;     0.001   1%   Clause clause subsumption    (576 calls)
% 0.48/0.63  ;     0.009   6%   Forward simplification       (645 calls)
% 0.48/0.63  ;     0.003   2%   Backward simplification      (425 calls)
% 0.48/0.63  ;     0.003   2%   Ordering                     (573 calls)
% 0.48/0.63  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.48/0.63  ;     0.001   1%   Purity testing               (1 call)
% 0.48/0.63  ;     0.028  19%   Other
% 0.48/0.63  ;     0.146        Total
% 0.48/0.63  ;     0.148        Real time
% 0.48/0.63  ; 
% 0.48/0.63  ; Term-hash-array has 927 terms in all.
% 0.48/0.63  ; Feature-vector-row-index has 270 entries (270 at peak, 313 added, 43 deleted).
% 0.48/0.63  ; Feature-vector-row-index has 1,772 nodes (1,772 at peak, 1,966 added, 194 deleted).
% 0.48/0.63  ;  Retrieved 690 possibly forward subsuming rows in 366 calls.
% 0.48/0.63  ;  Retrieved 16 possibly backward subsumed rows in 313 calls.
% 0.48/0.63  ; Path-index has 905 entries (905 at peak, 979 added, 74 deleted).
% 0.48/0.63  ; Path-index has 3,968 nodes (3,968 at peak, 4,050 added, 82 deleted).
% 0.48/0.63  ; Trie-index has 905 entries (905 at peak, 979 added, 74 deleted).
% 0.48/0.63  ; Trie-index has 4,226 nodes (4,226 at peak, 4,395 added, 169 deleted).
% 0.48/0.63  ; Retrieved 339 generalization terms in 1,345 calls.
% 0.48/0.63  ; Retrieved 138 instance terms in 111 calls.
% 0.48/0.63  ; Retrieved 5,331 unifiable terms in 1,158 calls.
% 0.48/0.63  ; 
% 0.48/0.63  ; The agenda of rows to process has 5 entries:
% 0.48/0.63  ;     1 with value 24              3 with value 27               1 with value 33
% 0.48/0.63  ; The agenda of rows to give has 268 entries:
% 0.48/0.63  ;     1 with value (4 11)          6 with value (4 29)           2 with value (4 41)
% 0.48/0.63  ;    14 with value (4 18)         11 with value (4 30)           3 with value (4 42)
% 0.48/0.63  ;    16 with value (4 19)          6 with value (4 31)           5 with value (4 43)
% 0.48/0.63  ;     9 with value (4 20)         13 with value (4 32)           1 with value (4 44)
% 0.48/0.63  ;    17 with value (4 21)          6 with value (4 33)           6 with value (4 45)
% 0.48/0.63  ;    10 with value (4 22)          6 with value (4 34)           2 with value (4 46)
% 0.48/0.63  ;    15 with value (4 23)         12 with value (4 35)           1 with value (4 47)
% 0.48/0.63  ;    18 with value (4 24)         10 with value (4 36)           1 with value (4 48)
% 0.48/0.63  ;    22 with value (4 25)          5 with value (4 37)           7 with value (4 49)
% 0.48/0.63  ;    12 with value (4 26)          3 with value (4 38)           1 with value (4 58)
% 0.48/0.63  ;    11 with value (4 27)          6 with value (4 40)           1 with value (4 59)
% 0.48/0.63  ;     9 with value (4 28)
% 0.48/0.63  Evaluation took:
% 0.48/0.63    0.148 seconds of real time
% 0.48/0.63    0.130478 seconds of user run time
% 0.48/0.63    0.017996 seconds of system run time
% 0.48/0.63    0 calls to %EVAL
% 0.48/0.63    0 page faults and
% 0.48/0.63    10,797,072 bytes consed.
% 0.48/0.63  :PROOF-FOUND
% 0.48/0.63  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-10T17:08:22
% 0.48/0.63  :PROOF-FOUND
% 0.48/0.63  * 
%------------------------------------------------------------------------------