TSTP Solution File: SET657+3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET657+3 : TPTP v8.1.0. Released v2.2.0.
% 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 05:11:20 EDT 2022

% Result   : Theorem 1.30s 1.48s
% Output   : Refutation 1.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   20
% Syntax   : Number of clauses     :   55 (  23 unt;   6 nHn;  51 RR)
%            Number of literals    :  126 (   8 equ;  73 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   5 con; 0-3 aty)
%            Number of variables   :   82 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( ~ ilf_type(X,binary_relation_type)
    | field_of(X) = union(domain_of(X),range_of(X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

cnf(3,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ ilf_type(Z,set_type)
    | ~ member(Z,union(X,Y))
    | member(Z,X)
    | member(Z,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

cnf(4,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ ilf_type(Z,set_type)
    | member(Z,union(X,Y))
    | ~ member(Z,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

cnf(5,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ ilf_type(Z,set_type)
    | member(Z,union(X,Y))
    | ~ member(Z,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

cnf(9,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/sandbox/benchmark/theBenchmark.p',p7) ).

cnf(13,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | subset(X,Y)
    | member('SKOLEMAAAW2'(X,Y),X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).

cnf(14,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | subset(X,Y)
    | ~ member('SKOLEMAAAW2'(X,Y),Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).

cnf(20,axiom,
    ( ~ ilf_type(X,set_type)
    | ilf_type(X,binary_relation_type)
    | ~ relation_like(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).

cnf(22,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/sandbox/benchmark/theBenchmark.p',p16) ).

cnf(26,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ member(X,power_set(Y))
    | ~ ilf_type(Z,set_type)
    | ~ member(Z,X)
    | member(Z,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).

cnf(30,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ empty(power_set(X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).

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/sandbox/benchmark/theBenchmark.p',p23) ).

cnf(45,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/sandbox/benchmark/theBenchmark.p',p27) ).

cnf(53,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ ilf_type(Z,relation_type(X,Y))
    | domain(X,Y,Z) = domain_of(Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).

cnf(54,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ ilf_type(Z,relation_type(X,Y))
    | ilf_type(domain(X,Y,Z),subset_type(X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).

cnf(55,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/sandbox/benchmark/theBenchmark.p',p35) ).

cnf(56,axiom,
    ( ~ ilf_type(X,set_type)
    | ~ ilf_type(Y,set_type)
    | ~ ilf_type(Z,relation_type(X,Y))
    | ilf_type(range(X,Y,Z),subset_type(Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p36) ).

cnf(57,axiom,
    ilf_type(X,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p37) ).

cnf(58,negated_conjecture,
    ilf_type('SKOLEMAAAW14',relation_type('SKOLEMAAAW12','SKOLEMAAAW13')),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_19) ).

cnf(59,negated_conjecture,
    ~ subset(field_of('SKOLEMAAAW14'),union('SKOLEMAAAW12','SKOLEMAAAW13')),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_19) ).

cnf(61,plain,
    ( ~ member(X,union(Y,Z))
    | member(X,Y)
    | member(X,Z) ),
    inference('REWRITE',[status(thm)],[3,57]) ).

cnf(62,plain,
    ( member(X,union(Y,Z))
    | ~ member(X,Y) ),
    inference('REWRITE',[status(thm)],[4,57]) ).

cnf(63,plain,
    ( member(X,union(Y,Z))
    | ~ member(X,Z) ),
    inference('REWRITE',[status(thm)],[5,57]) ).

cnf(65,plain,
    ( ~ ilf_type(X,relation_type(Y,Z))
    | ilf_type(X,subset_type(cross_product(Y,Z))) ),
    inference('REWRITE',[status(thm)],[9,57]) ).

cnf(68,plain,
    ( subset(X,Y)
    | member('SKOLEMAAAW2'(X,Y),X) ),
    inference('REWRITE',[status(thm)],[13,57]) ).

cnf(69,plain,
    ( subset(X,Y)
    | ~ member('SKOLEMAAAW2'(X,Y),Y) ),
    inference('REWRITE',[status(thm)],[14,57]) ).

cnf(72,plain,
    ( ilf_type(X,binary_relation_type)
    | ~ relation_like(X) ),
    inference('REWRITE',[status(thm)],[20,57]) ).

cnf(73,plain,
    ( ~ ilf_type(X,subset_type(Y))
    | ilf_type(X,member_type(power_set(Y))) ),
    inference('REWRITE',[status(thm)],[22,57]) ).

cnf(77,plain,
    ( ~ member(X,power_set(Y))
    | ~ member(Z,X)
    | member(Z,Y) ),
    inference('REWRITE',[status(thm)],[26,57]) ).

cnf(80,plain,
    ~ empty(power_set(X)),
    inference('REWRITE',[status(thm)],[30,57]) ).

cnf(81,plain,
    ( empty(X)
    | ~ ilf_type(Y,member_type(X))
    | member(Y,X) ),
    inference('REWRITE',[status(thm)],[32,57]) ).

cnf(90,plain,
    ( ~ ilf_type(X,subset_type(cross_product(Y,Z)))
    | relation_like(X) ),
    inference('REWRITE',[status(thm)],[45,57]) ).

cnf(96,plain,
    ( ~ ilf_type(X,relation_type(Y,Z))
    | domain(Y,Z,X) = domain_of(X) ),
    inference('REWRITE',[status(thm)],[53,57]) ).

cnf(97,plain,
    ( ~ ilf_type(X,relation_type(Y,Z))
    | ilf_type(domain(Y,Z,X),subset_type(Y)) ),
    inference('REWRITE',[status(thm)],[54,57]) ).

cnf(98,plain,
    ( ~ ilf_type(X,relation_type(Y,Z))
    | range(Y,Z,X) = range_of(X) ),
    inference('REWRITE',[status(thm)],[55,57]) ).

cnf(99,plain,
    ( ~ ilf_type(X,relation_type(Y,Z))
    | ilf_type(range(Y,Z,X),subset_type(Z)) ),
    inference('REWRITE',[status(thm)],[56,57]) ).

cnf(108,plain,
    member('SKOLEMAAAW2'(field_of('SKOLEMAAAW14'),union('SKOLEMAAAW12','SKOLEMAAAW13')),field_of('SKOLEMAAAW14')),
    inference('HYPERRESOLVE',[status(thm)],[59,68]) ).

cnf(109,plain,
    ~ member('SKOLEMAAAW2'(field_of('SKOLEMAAAW14'),union('SKOLEMAAAW12','SKOLEMAAAW13')),union('SKOLEMAAAW12','SKOLEMAAAW13')),
    inference('UR-RESOLVE',[status(thm)],[69,59]) ).

cnf(140,plain,
    ilf_type('SKOLEMAAAW14',subset_type(cross_product('SKOLEMAAAW12','SKOLEMAAAW13'))),
    inference('HYPERRESOLVE',[status(thm)],[65,58]) ).

cnf(142,plain,
    domain('SKOLEMAAAW12','SKOLEMAAAW13','SKOLEMAAAW14') = domain_of('SKOLEMAAAW14'),
    inference('HYPERRESOLVE',[status(thm)],[96,58]) ).

cnf(144,plain,
    ilf_type(domain_of('SKOLEMAAAW14'),subset_type('SKOLEMAAAW12')),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[97,58]),142,theory(equality)]) ).

cnf(146,plain,
    range('SKOLEMAAAW12','SKOLEMAAAW13','SKOLEMAAAW14') = range_of('SKOLEMAAAW14'),
    inference('HYPERRESOLVE',[status(thm)],[98,58]) ).

cnf(148,plain,
    ilf_type(range_of('SKOLEMAAAW14'),subset_type('SKOLEMAAAW13')),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[99,58]),146,theory(equality)]) ).

cnf(197,plain,
    ilf_type(domain_of('SKOLEMAAAW14'),member_type(power_set('SKOLEMAAAW12'))),
    inference('HYPERRESOLVE',[status(thm)],[73,144]) ).

cnf(198,plain,
    ilf_type(range_of('SKOLEMAAAW14'),member_type(power_set('SKOLEMAAAW13'))),
    inference('HYPERRESOLVE',[status(thm)],[73,148]) ).

cnf(241,plain,
    relation_like('SKOLEMAAAW14'),
    inference('HYPERRESOLVE',[status(thm)],[90,140]) ).

cnf(243,plain,
    ilf_type('SKOLEMAAAW14',binary_relation_type),
    inference('HYPERRESOLVE',[status(thm)],[72,241]) ).

cnf(249,plain,
    field_of('SKOLEMAAAW14') = union(domain_of('SKOLEMAAAW14'),range_of('SKOLEMAAAW14')),
    inference('HYPERRESOLVE',[status(thm)],[2,243]) ).

cnf(298,plain,
    member(domain_of('SKOLEMAAAW14'),power_set('SKOLEMAAAW12')),
    inference('UR-RESOLVE',[status(thm)],[81,197,80]) ).

cnf(308,plain,
    member(range_of('SKOLEMAAAW14'),power_set('SKOLEMAAAW13')),
    inference('UR-RESOLVE',[status(thm)],[81,198,80]) ).

cnf(625,plain,
    ~ member('SKOLEMAAAW2'(field_of('SKOLEMAAAW14'),union('SKOLEMAAAW12','SKOLEMAAAW13')),'SKOLEMAAAW13'),
    inference('UR-RESOLVE',[status(thm)],[63,109]) ).

cnf(626,plain,
    ~ member('SKOLEMAAAW2'(field_of('SKOLEMAAAW14'),union('SKOLEMAAAW12','SKOLEMAAAW13')),'SKOLEMAAAW12'),
    inference('UR-RESOLVE',[status(thm)],[62,109]) ).

cnf(670,plain,
    ~ member('SKOLEMAAAW2'(field_of('SKOLEMAAAW14'),union('SKOLEMAAAW12','SKOLEMAAAW13')),range_of('SKOLEMAAAW14')),
    inference('UR-RESOLVE',[status(thm)],[77,625,308]) ).

cnf(714,plain,
    ~ member('SKOLEMAAAW2'(field_of('SKOLEMAAAW14'),union('SKOLEMAAAW12','SKOLEMAAAW13')),domain_of('SKOLEMAAAW14')),
    inference('UR-RESOLVE',[status(thm)],[77,626,298]) ).

cnf(5961,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[61,714,670]),108,249,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET657+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 08:56:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48  * 
% 0.20/0.48  * 
% 0.20/0.48  #<PACKAGE "SNARK-USER">
% 0.20/0.48  * 
% 0.20/0.48  SNARK-TPTP-OPTIONS
% 0.20/0.48  * 
% 0.20/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48   (USE-FACTORING :POS)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48  * 
% 0.20/0.48  "."
% 0.20/0.48  * 
% 0.20/0.48  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-10T08:56:08
% 0.20/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n019.cluster.edu at 2022-07-10T08:56:08
% 1.30/1.48  
% 1.30/1.48  
% 1.30/1.48  #||
% 1.30/1.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.30/1.48  % SZS output start Refutation
% See solution above
% 1.30/1.48  ||#
% 1.30/1.48  
% 1.30/1.48  ; Summary of computation:
% 1.30/1.48  ;     10470 formulas have been input or derived (from 413 formulas).
% 1.30/1.48  ;      5961 (57%) were retained.  Of these,
% 1.30/1.48  ;          456 ( 8%) were simplified or subsumed later,
% 1.30/1.48  ;         5505 (92%) are still being kept.
% 1.30/1.48  ; 
% 1.30/1.48  ; Run time in seconds excluding printing time:
% 1.30/1.48  ;     0.012   1%   Read assertion file          (1 call)
% 1.30/1.48  ;     0.003   0%   Assert                       (38 calls)
% 1.30/1.48  ;     0.417  42%   Process new row              (9,446 calls)
% 1.30/1.48  ;     0.188  19%   Resolution                   (824 calls)
% 1.30/1.48  ;     0.013   1%   Paramodulation               (412 calls)
% 1.30/1.48  ;     0.000   0%   Factoring                    (35 calls)
% 1.30/1.48  ;     0.011   1%   Condensing                   (1,127 calls)
% 1.30/1.48  ;     0.031   3%   Forward subsumption          (1,127 calls)
% 1.30/1.48  ;     0.020   2%   Backward subsumption         (614 calls)
% 1.30/1.48  ;     0.020   2%   Clause clause subsumption    (2,482 calls)
% 1.30/1.48  ;     0.150  15%   Forward simplification       (9,446 calls)
% 1.30/1.48  ;     0.055   6%   Backward simplification      (5,961 calls)
% 1.30/1.48  ;     0.009   1%   Ordering                     (2,502 calls)
% 1.30/1.48  ;     0.000   0%   Sortal reasoning             (32 calls)
% 1.30/1.48  ;     0.000   0%   Purity testing               (1 call)
% 1.30/1.48  ;     0.064   6%   Other
% 1.30/1.48  ;     0.993        Total
% 1.30/1.48  ;     0.997        Real time
% 1.30/1.48  ; 
% 1.30/1.48  ; Term-hash-array has 9,532 terms in all.
% 1.30/1.48  ; Feature-vector-row-index has 560 entries (560 at peak, 614 added, 54 deleted).
% 1.30/1.48  ; Feature-vector-row-index has 3,016 nodes (3,016 at peak, 3,252 added, 236 deleted).
% 1.30/1.48  ;  Retrieved 3,452 possibly forward subsuming rows in 1,127 calls.
% 1.30/1.48  ;  Retrieved 352 possibly backward subsumed rows in 614 calls.
% 1.30/1.48  ; Path-index has 9,075 entries (9,075 at peak, 9,592 added, 517 deleted).
% 1.30/1.48  ; Path-index has 14,341 nodes (14,341 at peak, 15,310 added, 969 deleted).
% 1.30/1.48  ; Trie-index has 9,075 entries (9,075 at peak, 9,592 added, 517 deleted).
% 1.30/1.48  ; Trie-index has 34,665 nodes (34,665 at peak, 38,701 added, 4,036 deleted).
% 1.30/1.48  ; Retrieved 7,501 generalization terms in 25,261 calls.
% 1.30/1.48  ; Retrieved 5,674 instance terms in 5,346 calls.
% 1.30/1.48  ; Retrieved 165,957 unifiable terms in 8,867 calls.
% 1.30/1.48  ; 
% 1.30/1.48  ; The agenda of rows to process has 61 entries:
% 1.30/1.48  ;     9 with value 20              5 with value 23              12 with value 26
% 1.30/1.48  ;    10 with value 21             12 with value 25               1 with value 28
% 1.30/1.48  ;    12 with value 22
% 1.30/1.48  ; The agenda of rows to give has 5092 entries:
% 1.30/1.48  ;     4 with value (4 15)         46 with value (4 29)           5 with value (4 43)
% 1.30/1.48  ;   110 with value (4 16)         28 with value (4 30)           2 with value (4 44)
% 1.30/1.48  ;   199 with value (4 17)         45 with value (4 31)           2 with value (4 45)
% 1.30/1.48  ;   316 with value (4 18)         39 with value (4 32)           7 with value (4 46)
% 1.30/1.48  ;   457 with value (4 19)         31 with value (4 33)          11 with value (4 47)
% 1.30/1.48  ;   508 with value (4 20)         33 with value (4 34)           4 with value (4 48)
% 1.30/1.48  ;   632 with value (4 21)         54 with value (4 35)          10 with value (4 49)
% 1.30/1.48  ;   685 with value (4 22)         50 with value (4 36)           4 with value (4 51)
% 1.30/1.48  ;   567 with value (4 23)         35 with value (4 37)           6 with value (4 53)
% 1.30/1.48  ;   519 with value (4 24)         16 with value (4 38)           2 with value (4 58)
% 1.30/1.48  ;   328 with value (4 25)         33 with value (4 39)           2 with value (4 59)
% 1.30/1.48  ;   162 with value (4 26)         18 with value (4 40)           2 with value (4 60)
% 1.30/1.48  ;    51 with value (4 27)          4 with value (4 41)           2 with value (4 61)
% 1.30/1.48  ;    49 with value (4 28)         10 with value (4 42)           4 with value (4 65)
% 1.30/1.48  Evaluation took:
% 1.30/1.48    0.998 seconds of real time
% 1.30/1.48    0.910042 seconds of user run time
% 1.30/1.48    0.087792 seconds of system run time
% 1.30/1.48    [Run times include 0.128 seconds GC run time.]
% 1.30/1.48    0 calls to %EVAL
% 1.30/1.48    0 page faults and
% 1.30/1.48    74,625,464 bytes consed.
% 1.30/1.48  :PROOF-FOUND
% 1.30/1.48  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-10T08:56:09
% 1.30/1.48  :PROOF-FOUND
% 1.30/1.48  * 
%------------------------------------------------------------------------------