TSTP Solution File: SET681+3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n014.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 05:11:30 EDT 2022

% Result   : Theorem 0.39s 0.57s
% Output   : Refutation 0.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   33 (  12 unt;   4 nHn;  32 RR)
%            Number of literals    :   80 (   3 equ;  48 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   7 con; 0-3 aty)
%            Number of variables   :   48 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,binary_relation_type)
    | ~ member(X,range_of(Y))
    | member(ordered_pair('SKOLEMAAAR1'(X,Y),X),Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

cnf(3,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,binary_relation_type)
    | member(X,range_of(Y))
    | ~ ilf_type(Z,set_type)
    | ~ member(ordered_pair(Z,X),Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

cnf(5,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ ilf_type(Z,set_type)
    | ~ ilf_type(U,set_type)
    | ~ ilf_type(V,relation_type(X,Y))
    | ~ member(ordered_pair(Z,U),V)
    | member(Z,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).

cnf(13,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ ilf_type(Z,relation_type(X,Y))
    | ilf_type(Z,subset_type(cross_product(X,Y))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).

cnf(16,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',p8) ).

cnf(28,axiom,
    ( ~ ilf_type(X,set_type)
    | ilf_type(X,binary_relation_type)
    | ~ relation_like(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).

cnf(50,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ ilf_type(Z,subset_type(cross_product(X,Y)))
    | relation_like(Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).

cnf(53,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ ilf_type(Z,relation_type(X,Y))
    | range(X,Y,Z) = range_of(Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).

cnf(55,axiom,
    ilf_type(X,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).

cnf(57,negated_conjecture,
    ~ empty('SKOLEMAAAR13'),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_48) ).

cnf(58,negated_conjecture,
    ilf_type('SKOLEMAAAR14',relation_type('SKOLEMAAAR13','SKOLEMAAAR12')),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_48) ).

cnf(60,negated_conjecture,
    ( ~ member('SKOLEMAAAR15',range('SKOLEMAAAR13','SKOLEMAAAR12','SKOLEMAAAR14'))
    | ~ ilf_type(X,member_type('SKOLEMAAAR13'))
    | ~ member(ordered_pair(X,'SKOLEMAAAR15'),'SKOLEMAAAR14') ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_48) ).

cnf(62,negated_conjecture,
    ( member('SKOLEMAAAR15',range('SKOLEMAAAR13','SKOLEMAAAR12','SKOLEMAAAR14'))
    | member(ordered_pair('SKOLEMAAAR16','SKOLEMAAAR15'),'SKOLEMAAAR14') ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_48) ).

cnf(63,plain,
    ( ~ ilf_type(X,binary_relation_type)
    | ~ member(Y,range_of(X))
    | member(ordered_pair('SKOLEMAAAR1'(Y,X),Y),X) ),
    inference('REWRITE',[status(thm)],[2,55]) ).

cnf(64,plain,
    ( ~ ilf_type(X,binary_relation_type)
    | member(Y,range_of(X))
    | ~ member(ordered_pair(Z,Y),X) ),
    inference('REWRITE',[status(thm)],[3,55]) ).

cnf(66,plain,
    ( ~ ilf_type(X,relation_type(Y,Z))
    | ~ member(ordered_pair(U,V),X)
    | member(U,Y) ),
    inference('REWRITE',[status(thm)],[5,55]) ).

cnf(71,plain,
    ( ~ ilf_type(X,relation_type(Y,Z))
    | ilf_type(X,subset_type(cross_product(Y,Z))) ),
    inference('REWRITE',[status(thm)],[13,55]) ).

cnf(74,plain,
    ( empty(X)
    | ilf_type(Y,member_type(X))
    | ~ member(Y,X) ),
    inference('REWRITE',[status(thm)],[16,55]) ).

cnf(80,plain,
    ( ilf_type(X,binary_relation_type)
    | ~ relation_like(X) ),
    inference('REWRITE',[status(thm)],[28,55]) ).

cnf(95,plain,
    ( ~ ilf_type(X,subset_type(cross_product(Y,Z)))
    | relation_like(X) ),
    inference('REWRITE',[status(thm)],[50,55]) ).

cnf(98,plain,
    ( ~ ilf_type(X,relation_type(Y,Z))
    | range(Y,Z,X) = range_of(X) ),
    inference('REWRITE',[status(thm)],[53,55]) ).

cnf(131,plain,
    ilf_type('SKOLEMAAAR14',subset_type(cross_product('SKOLEMAAAR13','SKOLEMAAAR12'))),
    inference('HYPERRESOLVE',[status(thm)],[71,58]) ).

cnf(137,plain,
    range('SKOLEMAAAR13','SKOLEMAAAR12','SKOLEMAAAR14') = range_of('SKOLEMAAAR14'),
    inference('HYPERRESOLVE',[status(thm)],[98,58]) ).

cnf(138,plain,
    ( ~ member('SKOLEMAAAR15',range_of('SKOLEMAAAR14'))
    | ~ ilf_type(X,member_type('SKOLEMAAAR13'))
    | ~ member(ordered_pair(X,'SKOLEMAAAR15'),'SKOLEMAAAR14') ),
    inference('REWRITE',[status(thm)],[60,137,theory(equality)]) ).

cnf(140,plain,
    ( member('SKOLEMAAAR15',range_of('SKOLEMAAAR14'))
    | member(ordered_pair('SKOLEMAAAR16','SKOLEMAAAR15'),'SKOLEMAAAR14') ),
    inference('REWRITE',[status(thm)],[62,137,theory(equality)]) ).

cnf(216,plain,
    relation_like('SKOLEMAAAR14'),
    inference('HYPERRESOLVE',[status(thm)],[95,131]) ).

cnf(218,plain,
    ilf_type('SKOLEMAAAR14',binary_relation_type),
    inference('HYPERRESOLVE',[status(thm)],[80,216]) ).

cnf(225,plain,
    member('SKOLEMAAAR15',range_of('SKOLEMAAAR14')),
    inference('HYPERRESOLVE',[status(thm)],[64,218,140]) ).

cnf(226,plain,
    ( ~ ilf_type(X,member_type('SKOLEMAAAR13'))
    | ~ member(ordered_pair(X,'SKOLEMAAAR15'),'SKOLEMAAAR14') ),
    inference('REWRITE',[status(thm)],[138,225]) ).

cnf(243,plain,
    member(ordered_pair('SKOLEMAAAR1'('SKOLEMAAAR15','SKOLEMAAAR14'),'SKOLEMAAAR15'),'SKOLEMAAAR14'),
    inference('HYPERRESOLVE',[status(thm)],[63,225,218]) ).

cnf(491,plain,
    member('SKOLEMAAAR1'('SKOLEMAAAR15','SKOLEMAAAR14'),'SKOLEMAAAR13'),
    inference('HYPERRESOLVE',[status(thm)],[66,243,58]) ).

cnf(493,plain,
    ~ ilf_type('SKOLEMAAAR1'('SKOLEMAAAR15','SKOLEMAAAR14'),member_type('SKOLEMAAAR13')),
    inference('UR-RESOLVE',[status(thm)],[226,243]) ).

cnf(510,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[74,491,57]),493]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% 0.02/0.10  % Command  : run-snark %s %d
% 0.10/0.30  % Computer : n014.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 600
% 0.10/0.30  % DateTime : Sun Jul 10 18:19:50 EDT 2022
% 0.10/0.30  % CPUTime  : 
% 0.15/0.39  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.40  * 
% 0.15/0.40  * 
% 0.15/0.41  #<PACKAGE "SNARK-USER">
% 0.15/0.41  * 
% 0.15/0.41  SNARK-TPTP-OPTIONS
% 0.15/0.41  * 
% 0.15/0.41  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.15/0.41   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.15/0.41   (USE-FACTORING :POS)
% 0.15/0.41   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.15/0.41   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.15/0.41   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.15/0.41   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.15/0.41   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.15/0.41   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.15/0.41   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.15/0.41   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.15/0.41   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.15/0.41   (DECLARE-TPTP-SYMBOLS2))
% 0.15/0.41  * 
% 0.15/0.41  "."
% 0.15/0.41  * 
% 0.15/0.41  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-10T18:19:50
% 0.15/0.41  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n014.cluster.edu at 2022-07-10T18:19:50
% 0.39/0.57  
% 0.39/0.57  
% 0.39/0.57  #||
% 0.39/0.57  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.57  % SZS output start Refutation
% See solution above
% 0.39/0.59  ||#
% 0.39/0.59  
% 0.39/0.59  ; Summary of computation:
% 0.39/0.59  ;       964 formulas have been input or derived (from 132 formulas).
% 0.39/0.59  ;       510 (53%) were retained.  Of these,
% 0.39/0.59  ;           82 (16%) were simplified or subsumed later,
% 0.39/0.59  ;          428 (84%) are still being kept.
% 0.39/0.59  ; 
% 0.39/0.59  ; Run time in seconds excluding printing time:
% 0.39/0.59  ;     0.009   6%   Read assertion file          (1 call)
% 0.39/0.59  ;     0.001   1%   Assert                       (32 calls)
% 0.39/0.59  ;     0.048  30%   Process new row              (832 calls)
% 0.39/0.59  ;     0.025  15%   Resolution                   (262 calls)
% 0.39/0.59  ;     0.000   0%   Paramodulation               (131 calls)
% 0.39/0.59  ;     0.000   0%   Factoring                    (12 calls)
% 0.39/0.59  ;     0.008   5%   Condensing                   (371 calls)
% 0.39/0.59  ;     0.014   9%   Forward subsumption          (371 calls)
% 0.39/0.59  ;     0.005   3%   Backward subsumption         (263 calls)
% 0.39/0.59  ;     0.001   1%   Clause clause subsumption    (385 calls)
% 0.39/0.59  ;     0.014   9%   Forward simplification       (830 calls)
% 0.39/0.59  ;     0.005   3%   Backward simplification      (508 calls)
% 0.39/0.59  ;     0.002   1%   Ordering                     (629 calls)
% 0.39/0.59  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.39/0.59  ;     0.000   0%   Purity testing               (1 call)
% 0.39/0.59  ;     0.030  19%   Other
% 0.39/0.59  ;     0.162        Total
% 0.39/0.59  ;     0.184        Real time
% 0.39/0.59  ; 
% 0.39/0.59  ; Term-hash-array has 1,253 terms in all.
% 0.39/0.59  ; Feature-vector-row-index has 189 entries (193 at peak, 263 added, 74 deleted).
% 0.39/0.59  ; Feature-vector-row-index has 1,119 nodes (1,147 at peak, 1,598 added, 479 deleted).
% 0.39/0.59  ;  Retrieved 449 possibly forward subsuming rows in 371 calls.
% 0.39/0.59  ;  Retrieved 92 possibly backward subsumed rows in 263 calls.
% 0.39/0.59  ; Path-index has 1,186 entries (1,186 at peak, 1,348 added, 162 deleted).
% 0.39/0.59  ; Path-index has 5,522 nodes (5,522 at peak, 5,730 added, 208 deleted).
% 0.39/0.59  ; Trie-index has 1,186 entries (1,186 at peak, 1,348 added, 162 deleted).
% 0.39/0.59  ; Trie-index has 5,648 nodes (5,648 at peak, 6,083 added, 435 deleted).
% 0.39/0.59  ; Retrieved 520 generalization terms in 1,543 calls.
% 0.39/0.59  ; Retrieved 286 instance terms in 244 calls.
% 0.39/0.59  ; Retrieved 14,216 unifiable terms in 1,677 calls.
% 0.39/0.59  ; 
% 0.39/0.59  ; The agenda of rows to process has 1 entry:
% 0.39/0.59  ;     1 with value 18
% 0.39/0.59  ; The agenda of rows to give has 302 entries:
% 0.39/0.59  ;     2 with value (4 13)          5 with value (4 28)           6 with value (4 43)
% 0.39/0.59  ;     4 with value (4 14)          1 with value (4 29)           2 with value (4 44)
% 0.39/0.59  ;    16 with value (4 15)          8 with value (4 30)           6 with value (4 46)
% 0.39/0.59  ;    21 with value (4 16)          4 with value (4 31)           2 with value (4 47)
% 0.39/0.59  ;    23 with value (4 17)          4 with value (4 32)           1 with value (4 48)
% 0.39/0.59  ;    19 with value (4 18)          2 with value (4 34)           4 with value (4 49)
% 0.39/0.59  ;    33 with value (4 19)          7 with value (4 35)           7 with value (4 51)
% 0.39/0.59  ;    24 with value (4 20)          4 with value (4 36)           2 with value (4 52)
% 0.39/0.59  ;    11 with value (4 21)         10 with value (4 37)           2 with value (4 54)
% 0.39/0.59  ;    15 with value (4 22)          2 with value (4 38)           1 with value (4 55)
% 0.39/0.59  ;    15 with value (4 23)          3 with value (4 39)           4 with value (4 60)
% 0.39/0.59  ;     7 with value (4 24)          1 with value (4 40)           2 with value (4 61)
% 0.39/0.59  ;     2 with value (4 25)          3 with value (4 41)           4 with value (4 65)
% 0.39/0.59  ;     5 with value (4 26)          2 with value (4 42)           2 with value (4 70)
% 0.39/0.59  ;     4 with value (4 27)
% 0.39/0.59  Evaluation took:
% 0.39/0.59    0.184 seconds of real time
% 0.39/0.59    0.171226 seconds of user run time
% 0.39/0.59    0.012885 seconds of system run time
% 0.39/0.59    [Run times include 0.018 seconds GC run time.]
% 0.39/0.59    0 calls to %EVAL
% 0.39/0.59    0 page faults and
% 0.39/0.59    12,765,824 bytes consed.
% 0.39/0.59  :PROOF-FOUND
% 0.39/0.59  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-10T18:19:50
% 0.39/0.59  :PROOF-FOUND
% 0.39/0.59  * 
%------------------------------------------------------------------------------