TSTP Solution File: SET071-7 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET071-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n017.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 05:06:52 EDT 2022

% Result   : Unsatisfiable 2.13s 2.35s
% Output   : Refutation 2.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   26 (  18 unt;   3 nHn;  16 RR)
%            Number of literals    :   37 (  13 equ;  17 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   30 (   8 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
    ( ~ subclass(X,Y)
    | ~ member(Z,X)
    | member(Z,Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).

cnf(class_elements_are_sets,axiom,
    subclass(X,universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).

cnf(equal_implies_subclass1,axiom,
    ( X != Y
    | subclass(X,Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',equal_implies_subclass1) ).

cnf(unordered_pair_member,axiom,
    ( ~ member(X,unordered_pair(Y,Z))
    | X = Y
    | X = Z ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).

cnf(singleton_set,axiom,
    unordered_pair(X,X) = singleton(X),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).

cnf(regularity1,axiom,
    ( X = null_class
    | member(regular(X),X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).

cnf(transitivity_of_subclass,axiom,
    ( ~ subclass(X,Y)
    | ~ subclass(Y,Z)
    | subclass(X,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subclass) ).

cnf(corollary_of_null_class_is_subclass,axiom,
    ( ~ subclass(X,null_class)
    | X = null_class ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).

cnf(singleton_in_unordered_pair1,axiom,
    subclass(singleton(X),unordered_pair(X,Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair1) ).

cnf(unordered_pair_equals_singleton1,axiom,
    ( member(X,universal_class)
    | unordered_pair(X,Y) = singleton(Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).

cnf(prove_null_unordered_pair_1,negated_conjecture,
    unordered_pair(x,y) != null_class,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_unordered_pair_1) ).

cnf(prove_null_unordered_pair_2,negated_conjecture,
    ~ member(x,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_unordered_pair_2) ).

cnf(prove_null_unordered_pair_3,negated_conjecture,
    ~ member(y,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_unordered_pair_3) ).

cnf(125,plain,
    ~ subclass(unordered_pair(x,y),null_class),
    inference('UR-RESOLVE',[status(thm)],[corollary_of_null_class_is_subclass,prove_null_unordered_pair_1]) ).

cnf(166,plain,
    ~ member(x,X),
    inference('UR-RESOLVE',[status(thm)],[subclass_members,class_elements_are_sets,prove_null_unordered_pair_2]) ).

cnf(167,plain,
    ~ member(y,X),
    inference('UR-RESOLVE',[status(thm)],[subclass_members,class_elements_are_sets,prove_null_unordered_pair_3]) ).

cnf(248,plain,
    ( ~ member(X,singleton(Y))
    | X = Y ),
    inference('PARAMODULATE',[status(thm)],[unordered_pair_member,singleton_set,theory(equality)]) ).

cnf(435,plain,
    unordered_pair(x,X) = singleton(X),
    inference('HYPERRESOLVE',[status(thm)],[166,unordered_pair_equals_singleton1]) ).

cnf(437,plain,
    ~ subclass(singleton(y),null_class),
    inference('REWRITE',[status(thm)],[125,435,theory(equality)]) ).

cnf(448,plain,
    unordered_pair(y,X) = singleton(X),
    inference('HYPERRESOLVE',[status(thm)],[167,unordered_pair_equals_singleton1]) ).

cnf(706,plain,
    ~ subclass(singleton(X),null_class),
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[transitivity_of_subclass,437,singleton_in_unordered_pair1]),448,theory(equality)]) ).

cnf(1160,plain,
    singleton(X) != null_class,
    inference('UR-RESOLVE',[status(thm)],[equal_implies_subclass1,706]) ).

cnf(3824,plain,
    subclass(singleton(x),singleton(X)),
    inference('PARAMODULATE',[status(thm)],[singleton_in_unordered_pair1,435,theory(equality)]) ).

cnf(7898,plain,
    member(regular(singleton(x)),singleton(X)),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[subclass_members,3824,regularity1]),1160]) ).

cnf(8683,plain,
    regular(singleton(X)) = X,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[248,regularity1]),1160]) ).

cnf(8691,plain,
    $false,
    inference('REWRITE',[status(thm)],[7898,166,8683,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET071-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.14  % Command  : run-snark %s %d
% 0.14/0.36  % Computer : n017.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sat Jul  9 22:56:47 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.21/0.49  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.50  * 
% 0.21/0.50  * 
% 0.21/0.51  #<PACKAGE "SNARK-USER">
% 0.21/0.51  * 
% 0.21/0.51  SNARK-TPTP-OPTIONS
% 0.21/0.51  * 
% 0.21/0.51  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.51   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.51   (USE-FACTORING :POS)
% 0.21/0.51   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.51   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.51   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.51   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.51   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.51   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.51   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.51   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.51   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.51   (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.51  * 
% 0.21/0.51  "."
% 0.21/0.51  * 
% 0.21/0.51  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-09T22:56:47
% 0.21/0.51  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n017.cluster.edu at 2022-07-09T22:56:47
% 0.38/0.55  
% 0.38/0.55  ; Recognized commutativity assertion (= (|unordered_pair| ?X ?Y) (|unordered_pair| ?Y ?X)).
% 2.13/2.35  ; Declaring unordered_pair to be commutative.
% 2.13/2.35  
% 2.13/2.35  #||
% 2.13/2.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.13/2.35  % SZS output start Refutation
% See solution above
% 2.13/2.35  ||#
% 2.13/2.35  
% 2.13/2.35  ; Summary of computation:
% 2.13/2.35  ;     18234 formulas have been input or derived (from 316 formulas).
% 2.13/2.35  ;      8691 (48%) were retained.  Of these,
% 2.13/2.35  ;         1002 (12%) were simplified or subsumed later,
% 2.13/2.35  ;         7689 (88%) are still being kept.
% 2.13/2.35  ; 
% 2.13/2.35  ; Run time in seconds excluding printing time:
% 2.13/2.35  ;     0.021   1%   Read assertion file          (1 call)
% 2.13/2.35  ;     0.004   0%   Assert                       (115 calls)
% 2.13/2.35  ;     0.646  35%   Process new row              (17,433 calls)
% 2.13/2.35  ;     0.535  29%   Resolution                   (630 calls)
% 2.13/2.35  ;     0.008   0%   Paramodulation               (315 calls)
% 2.13/2.35  ;     0.000   0%   Factoring                    (9 calls)
% 2.13/2.35  ;     0.025   1%   Condensing                   (1,892 calls)
% 2.13/2.35  ;     0.100   5%   Forward subsumption          (1,892 calls)
% 2.13/2.35  ;     0.061   3%   Backward subsumption         (1,600 calls)
% 2.13/2.35  ;     0.010   1%   Clause clause subsumption    (3,847 calls)
% 2.13/2.35  ;     0.206  11%   Forward simplification       (17,361 calls)
% 2.13/2.35  ;     0.123   7%   Backward simplification      (8,679 calls)
% 2.13/2.35  ;     0.012   1%   Ordering                     (4,973 calls)
% 2.13/2.35  ;     0.000   0%   Sortal reasoning             (32 calls)
% 2.13/2.35  ;     0.001   0%   Purity testing               (1 call)
% 2.13/2.35  ;     0.088   5%   Other
% 2.13/2.35  ;     1.840        Total
% 2.13/2.35  ;     1.842        Real time
% 2.13/2.35  ; 
% 2.13/2.35  ; Term-hash-array has 12,600 terms in all.
% 2.13/2.35  ; Feature-vector-row-index has 1,368 entries (1,541 at peak, 1,600 added, 232 deleted).
% 2.13/2.35  ; Feature-vector-row-index has 6,110 nodes (7,139 at peak, 7,529 added, 1,419 deleted).
% 2.13/2.35  ;  Retrieved 4,035 possibly forward subsuming rows in 1,892 calls.
% 2.13/2.35  ;  Retrieved 1,046 possibly backward subsumed rows in 1,600 calls.
% 2.13/2.35  ; Path-index has 11,168 entries (11,842 at peak, 12,678 added, 1,510 deleted).
% 2.13/2.35  ; Path-index has 4,484 nodes (5,085 at peak, 5,288 added, 804 deleted).
% 2.13/2.35  ; Trie-index has 11,168 entries (11,842 at peak, 12,678 added, 1,510 deleted).
% 2.13/2.35  ; Trie-index has 32,529 nodes (34,187 at peak, 36,013 added, 3,484 deleted).
% 2.13/2.35  ; Retrieved 11,390 generalization terms in 47,266 calls.
% 2.13/2.36  ; Retrieved 7,472 instance terms in 7,078 calls.
% 2.13/2.36  ; Retrieved 1,015,674 unifiable terms in 12,332 calls.
% 2.13/2.36  ; 
% 2.13/2.36  ; The agenda of rows to process has 3 entries:
% 2.13/2.36  ;     1 with value 17              2 with value 26
% 2.13/2.36  ; The agenda of input rows to give has 3 entries:
% 2.13/2.36  ;     1 with value 10              1 with value 11               1 with value 18
% 2.13/2.36  ; The agenda of rows to give has 7466 entries:
% 2.13/2.36  ;     2 with value (4 8)         123 with value (4 22)           1 with value (4 35)
% 2.13/2.36  ;     2 with value (4 10)         50 with value (4 23)           3 with value (4 37)
% 2.13/2.36  ;    87 with value (4 11)         83 with value (4 24)           1 with value (4 38)
% 2.13/2.36  ;   115 with value (4 12)         15 with value (4 25)           1 with value (4 42)
% 2.13/2.36  ;   208 with value (4 13)         21 with value (4 26)           1 with value (4 43)
% 2.13/2.36  ;   277 with value (4 14)         26 with value (4 27)           1 with value (4 44)
% 2.13/2.36  ;   379 with value (4 15)         40 with value (4 28)           1 with value (4 45)
% 2.13/2.36  ;   745 with value (4 16)         78 with value (4 29)           3 with value (4 46)
% 2.13/2.36  ;  1182 with value (4 17)         15 with value (4 30)           1 with value (4 49)
% 2.13/2.36  ;  1662 with value (4 18)          2 with value (4 31)           1 with value (4 51)
% 2.13/2.36  ;  1208 with value (4 19)          5 with value (4 32)           1 with value (4 53)
% 2.13/2.36  ;   741 with value (4 20)          2 with value (4 33)           1 with value (4 59)
% 2.13/2.36  ;   379 with value (4 21)          2 with value (4 34)           1 with value (4 63)
% 2.13/2.36  Evaluation took:
% 2.13/2.36    1.843 seconds of real time
% 2.13/2.36    1.699011 seconds of user run time
% 2.13/2.36    0.14436 seconds of system run time
% 2.13/2.36    [Run times include 0.246 seconds GC run time.]
% 2.13/2.36    0 calls to %EVAL
% 2.13/2.36    0 page faults and
% 2.13/2.36    120,085,576 bytes consed.
% 2.13/2.36  :PROOF-FOUND
% 2.13/2.36  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-09T22:56:49
% 2.13/2.36  :PROOF-FOUND
% 2.13/2.36  * 
%------------------------------------------------------------------------------