TSTP Solution File: SET113-7 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET113-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n021.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 05:07:32 EDT 2022

% Result   : Unsatisfiable 1.16s 1.38s
% Output   : Refutation 1.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (  11 unt;   4 nHn;   6 RR)
%            Number of literals    :   19 (  13 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :   11 (   3 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-2 aty)
%            Number of variables   :   14 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
    unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).

cnf(union,axiom,
    complement(intersection(complement(X),complement(Y))) = union(X,Y),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).

cnf(unordered_pairs_and_singletons,axiom,
    unordered_pair(X,Y) = union(singleton(X),singleton(Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_and_singletons) ).

cnf(148,plain,
    unordered_pair(X,Y) = complement(intersection(complement(singleton(X)),complement(singleton(Y)))),
    inference('REWRITE',[status(thm)],[unordered_pairs_and_singletons,union,theory(equality)]) ).

cnf(existence_of_1st_and_2nd_2,axiom,
    ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
    | first(X) = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_2) ).

cnf(existence_of_1st_and_2nd_4,axiom,
    ( ordered_pair(first(X),second(X)) = X
    | first(X) = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_4) ).

cnf(prove_unique_1st_and_2nd_in_pair_of_non_sets1_1,negated_conjecture,
    ~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets1_1) ).

cnf(prove_unique_1st_in_pair_of_non_sets,negated_conjecture,
    first(x) != x,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_in_pair_of_non_sets) ).

cnf(172,plain,
    complement(intersection(complement(singleton(singleton(X))),complement(singleton(complement(intersection(complement(singleton(X)),complement(singleton(singleton(Y))))))))) = ordered_pair(X,Y),
    inference('REWRITE',[status(thm)],[ordered_pair,148,theory(equality)]) ).

cnf(174,plain,
    ( member(complement(intersection(complement(singleton(singleton(first(X)))),complement(singleton(complement(intersection(complement(singleton(first(X))),complement(singleton(singleton(second(X)))))))))),cross_product(universal_class,universal_class))
    | first(X) = X ),
    inference('REWRITE',[status(thm)],[existence_of_1st_and_2nd_2,172,theory(equality)]) ).

cnf(176,plain,
    ( complement(intersection(complement(singleton(singleton(first(X)))),complement(singleton(complement(intersection(complement(singleton(first(X))),complement(singleton(singleton(second(X)))))))))) = X
    | first(X) = X ),
    inference('REWRITE',[status(thm)],[existence_of_1st_and_2nd_4,172,theory(equality)]) ).

cnf(178,plain,
    ~ member(complement(intersection(complement(singleton(singleton(first(x)))),complement(singleton(complement(intersection(complement(singleton(first(x))),complement(singleton(singleton(second(x)))))))))),cross_product(universal_class,universal_class)),
    inference('REWRITE',[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_non_sets1_1,172,theory(equality)]) ).

cnf(798,plain,
    ~ member(x,cross_product(universal_class,universal_class)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[178,176,theory(equality)]),prove_unique_1st_in_pair_of_non_sets]) ).

cnf(808,plain,
    complement(intersection(complement(singleton(singleton(first(x)))),complement(singleton(complement(intersection(complement(singleton(first(x))),complement(singleton(singleton(second(x)))))))))) = x,
    inference('UR-RESOLVE',[status(thm)],[176,prove_unique_1st_in_pair_of_non_sets]) ).

cnf(1410,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[174,prove_unique_1st_in_pair_of_non_sets]),798,808,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET113-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.11/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jul 11 07:41:38 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.45  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46  * 
% 0.19/0.46  * 
% 0.19/0.47  #<PACKAGE "SNARK-USER">
% 0.19/0.47  * 
% 0.19/0.47  SNARK-TPTP-OPTIONS
% 0.19/0.47  * 
% 0.19/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47   (USE-FACTORING :POS)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47  * 
% 0.19/0.47  "."
% 0.19/0.47  * 
% 0.19/0.47  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-11T07:41:38
% 0.19/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n021.cluster.edu at 2022-07-11T07:41:38
% 0.19/0.51  
% 0.19/0.51  ; Recognized commutativity assertion (= (|unordered_pair| ?X ?Y) (|unordered_pair| ?Y ?X)).
% 1.16/1.38  ; Declaring unordered_pair to be commutative.
% 1.16/1.38  
% 1.16/1.38  #||
% 1.16/1.38  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.16/1.38  % SZS output start Refutation
% See solution above
% 1.16/1.38  ||#
% 1.16/1.38  
% 1.16/1.38  ; Summary of computation:
% 1.16/1.38  ;      2910 formulas have been input or derived (from 129 formulas).
% 1.16/1.38  ;      1410 (48%) were retained.  Of these,
% 1.16/1.38  ;           90 ( 6%) were simplified or subsumed later,
% 1.16/1.38  ;         1320 (94%) are still being kept.
% 1.16/1.38  ; 
% 1.16/1.38  ; Run time in seconds excluding printing time:
% 1.16/1.38  ;     0.030   3%   Read assertion file          (1 call)
% 1.16/1.38  ;     0.003   0%   Assert                       (161 calls)
% 1.16/1.38  ;     0.168  18%   Process new row              (2,653 calls)
% 1.16/1.38  ;     0.062   7%   Resolution                   (256 calls)
% 1.16/1.38  ;     0.016   2%   Paramodulation               (128 calls)
% 1.16/1.38  ;     0.000   0%   Factoring                    (19 calls)
% 1.16/1.38  ;     0.022   2%   Condensing                   (1,492 calls)
% 1.16/1.38  ;     0.334  37%   Forward subsumption          (1,492 calls)
% 1.16/1.38  ;     0.070   8%   Backward subsumption         (1,152 calls)
% 1.16/1.38  ;     0.027   3%   Clause clause subsumption    (11,668 calls)
% 1.16/1.38  ;     0.124  14%   Forward simplification       (2,652 calls)
% 1.16/1.38  ;     0.011   1%   Backward simplification      (1,393 calls)
% 1.16/1.38  ;     0.014   2%   Ordering                     (5,549 calls)
% 1.16/1.38  ;     0.000   0%   Sortal reasoning             (32 calls)
% 1.16/1.38  ;     0.000   0%   Purity testing               (1 call)
% 1.16/1.38  ;     0.030   3%   Other
% 1.16/1.38  ;     0.911        Total
% 1.16/1.38  ;     0.912        Real time
% 1.16/1.38  ; 
% 1.16/1.38  ; Term-hash-array has 3,964 terms in all.
% 1.16/1.38  ; Feature-vector-row-index has 1,106 entries (1,106 at peak, 1,152 added, 46 deleted).
% 1.16/1.38  ; Feature-vector-row-index has 9,458 nodes (9,460 at peak, 9,713 added, 255 deleted).
% 1.16/1.38  ;  Retrieved 17,528 possibly forward subsuming rows in 1,492 calls.
% 1.16/1.38  ;  Retrieved 1,795 possibly backward subsumed rows in 1,152 calls.
% 1.16/1.38  ; Path-index has 3,852 entries (3,852 at peak, 4,032 added, 180 deleted).
% 1.16/1.38  ; Path-index has 9,933 nodes (9,933 at peak, 10,219 added, 286 deleted).
% 1.16/1.38  ; Trie-index has 3,852 entries (3,852 at peak, 4,032 added, 180 deleted).
% 1.16/1.38  ; Trie-index has 16,621 nodes (16,621 at peak, 17,533 added, 912 deleted).
% 1.16/1.38  ; Retrieved 12,324 generalization terms in 24,583 calls.
% 1.16/1.38  ; Retrieved 382 instance terms in 240 calls.
% 1.16/1.38  ; Retrieved 48,054 unifiable terms in 1,601 calls.
% 1.16/1.38  ; 
% 1.16/1.38  ; The agenda of rows to process has 81 entries:
% 1.16/1.38  ;     1 with value 40              2 with value 78               1 with value 98
% 1.16/1.38  ;     1 with value 42              3 with value 79               2 with value 100
% 1.16/1.38  ;     3 with value 44              1 with value 83               1 with value 101
% 1.16/1.38  ;     1 with value 46              2 with value 84               1 with value 103
% 1.16/1.38  ;     1 with value 52              1 with value 85               3 with value 104
% 1.16/1.38  ;     1 with value 54              2 with value 86               2 with value 106
% 1.16/1.38  ;     2 with value 63              2 with value 87               3 with value 108
% 1.16/1.38  ;     2 with value 64              4 with value 88               1 with value 109
% 1.16/1.38  ;     2 with value 69              2 with value 89               1 with value 111
% 1.16/1.38  ;     1 with value 70              1 with value 91               3 with value 114
% 1.16/1.38  ;     1 with value 71              5 with value 92               2 with value 115
% 1.16/1.38  ;     4 with value 74              2 with value 93               2 with value 122
% 1.16/1.38  ;     2 with value 75              3 with value 94               3 with value 126
% 1.16/1.38  ;     3 with value 77              1 with value 96
% 1.16/1.38  ; The agenda of input rows to give has 23 entries:
% 1.16/1.38  ;     1 with value 41              1 with value 56               1 with value 74
% 1.16/1.38  ;     1 with value 43              1 with value 57               2 with value 94
% 1.16/1.38  ;     4 with value 46              2 with value 62               1 with value 123
% 1.16/1.38  ;     1 with value 48              1 with value 64               2 with value 139
% 1.16/1.38  ;     2 with value 53              1 with value 66               2 with value 212
% 1.16/1.38  ; The agenda of rows to give has 1170 entries:
% 1.16/1.38  ;     2 with value (4 4)          15 with value (4 38)          12 with value (4 71)
% 1.16/1.38  ;     4 with value (4 5)          13 with value (4 39)           9 with value (4 72)
% 1.16/1.38  ;    15 with value (4 7)          35 with value (4 40)          14 with value (4 73)
% 1.16/1.38  ;    14 with value (4 8)          18 with value (4 41)           7 with value (4 74)
% 1.16/1.38  ;    11 with value (4 9)          23 with value (4 42)          14 with value (4 75)
% 1.16/1.38  ;     9 with value (4 10)         26 with value (4 43)           5 with value (4 76)
% 1.16/1.38  ;    12 with value (4 11)         15 with value (4 44)          10 with value (4 77)
% 1.16/1.38  ;     9 with value (4 12)          9 with value (4 45)          13 with value (4 78)
% 1.16/1.38  ;    15 with value (4 13)         22 with value (4 46)           2 with value (4 79)
% 1.16/1.38  ;    16 with value (4 14)         14 with value (4 47)           5 with value (4 80)
% 1.16/1.38  ;    21 with value (4 15)         22 with value (4 48)           6 with value (4 81)
% 1.16/1.38  ;    16 with value (4 16)         13 with value (4 49)           4 with value (4 82)
% 1.16/1.38  ;    22 with value (4 17)         15 with value (4 50)           7 with value (4 83)
% 1.16/1.38  ;    25 with value (4 18)         15 with value (4 51)           6 with value (4 84)
% 1.16/1.38  ;    27 with value (4 19)         12 with value (4 52)           9 with value (4 86)
% 1.16/1.38  ;    27 with value (4 20)         12 with value (4 53)          10 with value (4 87)
% 1.16/1.38  ;    19 with value (4 21)         19 with value (4 54)           2 with value (4 88)
% 1.16/1.38  ;    13 with value (4 22)         10 with value (4 55)           4 with value (4 89)
% 1.16/1.38  ;    23 with value (4 23)         11 with value (4 56)           5 with value (4 90)
% 1.16/1.38  ;    18 with value (4 24)         16 with value (4 57)           6 with value (4 93)
% 1.16/1.38  ;    16 with value (4 25)         13 with value (4 58)           2 with value (4 94)
% 1.16/1.38  ;    11 with value (4 26)         25 with value (4 59)           4 with value (4 96)
% 1.16/1.38  ;    18 with value (4 27)          8 with value (4 60)           3 with value (4 99)
% 1.16/1.38  ;    14 with value (4 28)          8 with value (4 61)           2 with value (4 100)
% 1.16/1.38  ;     8 with value (4 29)         16 with value (4 62)           4 with value (4 102)
% 1.16/1.38  ;    15 with value (4 30)          3 with value (4 63)           2 with value (4 103)
% 1.16/1.38  ;    21 with value (4 31)          9 with value (4 64)           2 with value (4 104)
% 1.16/1.38  ;    10 with value (4 32)         13 with value (4 65)           4 with value (4 106)
% 1.16/1.38  ;    14 with value (4 33)         11 with value (4 66)           1 with value (4 109)
% 1.16/1.38  ;    19 with value (4 34)         17 with value (4 67)           1 with value (4 113)
% 1.16/1.38  ;    13 with value (4 35)         14 with value (4 68)           2 with value (4 127)
% 1.16/1.38  ;    12 with value (4 36)         11 with value (4 69)           2 with value (4 129)
% 1.16/1.38  ;     6 with value (4 37)         11 with value (4 70)           2 with value (4 144)
% 1.16/1.38  Evaluation took:
% 1.16/1.38    0.913 seconds of real time
% 1.16/1.38    0.857547 seconds of user run time
% 1.16/1.38    0.056118 seconds of system run time
% 1.16/1.38    [Run times include 0.081 seconds GC run time.]
% 1.16/1.38    0 calls to %EVAL
% 1.16/1.38    0 page faults and
% 1.16/1.38    92,745,728 bytes consed.
% 1.16/1.38  :PROOF-FOUND
% 1.16/1.38  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-11T07:41:39
% 1.16/1.38  :PROOF-FOUND
% 1.16/1.38  * 
%------------------------------------------------------------------------------