TSTP Solution File: SET114-7 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SET114-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 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 05:07:33 EDT 2022
% Result : Unsatisfiable 1.35s 1.54s
% Output : Refutation 1.35s
% 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/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(union,axiom,
complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
cnf(unordered_pairs_and_singletons,axiom,
unordered_pair(X,Y) = union(singleton(X),singleton(Y)),
file('/export/starexec/sandbox/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_3,axiom,
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| second(X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_3) ).
cnf(existence_of_1st_and_2nd_5,axiom,
( ordered_pair(first(X),second(X)) = X
| second(X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_5) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_non_sets2_1,negated_conjecture,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets2_1) ).
cnf(prove_unique_2nd_in_pair_of_non_sets,negated_conjecture,
second(x) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_2nd_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(175,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))
| second(X) = X ),
inference('REWRITE',[status(thm)],[existence_of_1st_and_2nd_3,172,theory(equality)]) ).
cnf(177,plain,
( complement(intersection(complement(singleton(singleton(first(X)))),complement(singleton(complement(intersection(complement(singleton(first(X))),complement(singleton(singleton(second(X)))))))))) = X
| second(X) = X ),
inference('REWRITE',[status(thm)],[existence_of_1st_and_2nd_5,172,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_sets2_1,172,theory(equality)]) ).
cnf(831,plain,
~ member(x,cross_product(universal_class,universal_class)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[178,177,theory(equality)]),prove_unique_2nd_in_pair_of_non_sets]) ).
cnf(841,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)],[177,prove_unique_2nd_in_pair_of_non_sets]) ).
cnf(1473,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[175,prove_unique_2nd_in_pair_of_non_sets]),831,841,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET114-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.08/0.14 % Command : run-snark %s %d
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jul 10 02:22:17 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.47 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.48 *
% 0.21/0.48 *
% 0.21/0.49 #<PACKAGE "SNARK-USER">
% 0.21/0.49 *
% 0.21/0.49 SNARK-TPTP-OPTIONS
% 0.21/0.49 *
% 0.21/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.49 (USE-FACTORING :POS)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.49 *
% 0.21/0.49 "."
% 0.21/0.49 *
% 0.21/0.49 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-10T02:22:17
% 0.21/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n017.cluster.edu at 2022-07-10T02:22:17
% 0.21/0.53
% 0.21/0.53 ; Recognized commutativity assertion (= (|unordered_pair| ?X ?Y) (|unordered_pair| ?Y ?X)).
% 1.35/1.54 ; Declaring unordered_pair to be commutative.
% 1.35/1.54
% 1.35/1.54 #||
% 1.35/1.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.35/1.54 % SZS output start Refutation
% See solution above
% 1.35/1.54 ||#
% 1.35/1.54
% 1.35/1.54 ; Summary of computation:
% 1.35/1.54 ; 3005 formulas have been input or derived (from 130 formulas).
% 1.35/1.54 ; 1473 (49%) were retained. Of these,
% 1.35/1.54 ; 93 ( 6%) were simplified or subsumed later,
% 1.35/1.54 ; 1380 (94%) are still being kept.
% 1.35/1.54 ;
% 1.35/1.54 ; Run time in seconds excluding printing time:
% 1.35/1.54 ; 0.030 3% Read assertion file (1 call)
% 1.35/1.54 ; 0.005 0% Assert (161 calls)
% 1.35/1.54 ; 0.202 19% Process new row (2,741 calls)
% 1.35/1.54 ; 0.059 6% Resolution (258 calls)
% 1.35/1.54 ; 0.026 2% Paramodulation (129 calls)
% 1.35/1.54 ; 0.000 0% Factoring (20 calls)
% 1.35/1.54 ; 0.034 3% Condensing (1,579 calls)
% 1.35/1.54 ; 0.395 38% Forward subsumption (1,579 calls)
% 1.35/1.54 ; 0.071 7% Backward subsumption (1,215 calls)
% 1.35/1.54 ; 0.043 4% Clause clause subsumption (12,333 calls)
% 1.35/1.54 ; 0.130 12% Forward simplification (2,740 calls)
% 1.35/1.54 ; 0.008 1% Backward simplification (1,456 calls)
% 1.35/1.54 ; 0.013 1% Ordering (5,917 calls)
% 1.35/1.54 ; 0.000 0% Sortal reasoning (32 calls)
% 1.35/1.54 ; 0.001 0% Purity testing (1 call)
% 1.35/1.54 ; 0.036 3% Other
% 1.35/1.54 ; 1.053 Total
% 1.35/1.54 ; 1.056 Real time
% 1.35/1.54 ;
% 1.35/1.55 ; Term-hash-array has 4,267 terms in all.
% 1.35/1.55 ; Feature-vector-row-index has 1,166 entries (1,166 at peak, 1,215 added, 49 deleted).
% 1.35/1.55 ; Feature-vector-row-index has 10,438 nodes (10,440 at peak, 10,711 added, 273 deleted).
% 1.35/1.55 ; Retrieved 19,583 possibly forward subsuming rows in 1,579 calls.
% 1.35/1.55 ; Retrieved 1,823 possibly backward subsumed rows in 1,215 calls.
% 1.35/1.55 ; Path-index has 4,154 entries (4,154 at peak, 4,335 added, 181 deleted).
% 1.35/1.55 ; Path-index has 10,450 nodes (10,450 at peak, 10,737 added, 287 deleted).
% 1.35/1.55 ; Trie-index has 4,154 entries (4,154 at peak, 4,335 added, 181 deleted).
% 1.35/1.55 ; Trie-index has 19,940 nodes (19,940 at peak, 20,854 added, 914 deleted).
% 1.35/1.55 ; Retrieved 13,305 generalization terms in 26,521 calls.
% 1.35/1.55 ; Retrieved 382 instance terms in 240 calls.
% 1.35/1.55 ; Retrieved 50,231 unifiable terms in 1,630 calls.
% 1.35/1.55 ;
% 1.35/1.55 ; The agenda of rows to process has 86 entries:
% 1.35/1.55 ; 1 with value 40 4 with value 78 1 with value 98
% 1.35/1.55 ; 1 with value 42 3 with value 79 2 with value 100
% 1.35/1.55 ; 3 with value 44 1 with value 83 1 with value 101
% 1.35/1.55 ; 1 with value 46 2 with value 84 1 with value 103
% 1.35/1.55 ; 2 with value 52 1 with value 85 3 with value 104
% 1.35/1.55 ; 1 with value 54 2 with value 86 2 with value 106
% 1.35/1.55 ; 2 with value 63 2 with value 87 3 with value 108
% 1.35/1.55 ; 2 with value 64 4 with value 88 1 with value 109
% 1.35/1.55 ; 2 with value 69 2 with value 89 1 with value 111
% 1.35/1.55 ; 1 with value 70 1 with value 91 3 with value 114
% 1.35/1.55 ; 1 with value 71 5 with value 92 4 with value 115
% 1.35/1.55 ; 4 with value 74 2 with value 93 2 with value 122
% 1.35/1.55 ; 2 with value 75 3 with value 94 3 with value 126
% 1.35/1.55 ; 3 with value 77 1 with value 96
% 1.35/1.55 ; The agenda of input rows to give has 22 entries:
% 1.35/1.55 ; 1 with value 43 1 with value 57 2 with value 94
% 1.35/1.55 ; 4 with value 46 2 with value 62 1 with value 123
% 1.35/1.55 ; 1 with value 48 1 with value 64 2 with value 139
% 1.35/1.55 ; 2 with value 53 1 with value 66 2 with value 212
% 1.35/1.55 ; 1 with value 56 1 with value 74
% 1.35/1.55 ; The agenda of rows to give has 1230 entries:
% 1.35/1.55 ; 2 with value (4 4) 23 with value (4 42) 3 with value (4 79)
% 1.35/1.55 ; 4 with value (4 5) 26 with value (4 43) 5 with value (4 80)
% 1.35/1.55 ; 15 with value (4 7) 18 with value (4 44) 6 with value (4 81)
% 1.35/1.55 ; 14 with value (4 8) 9 with value (4 45) 4 with value (4 82)
% 1.35/1.55 ; 11 with value (4 9) 23 with value (4 46) 8 with value (4 83)
% 1.35/1.55 ; 9 with value (4 10) 14 with value (4 47) 7 with value (4 84)
% 1.35/1.55 ; 12 with value (4 11) 22 with value (4 48) 1 with value (4 85)
% 1.35/1.55 ; 9 with value (4 12) 13 with value (4 49) 11 with value (4 86)
% 1.35/1.55 ; 17 with value (4 13) 15 with value (4 50) 12 with value (4 87)
% 1.35/1.55 ; 17 with value (4 14) 15 with value (4 51) 6 with value (4 88)
% 1.35/1.55 ; 21 with value (4 15) 13 with value (4 52) 4 with value (4 89)
% 1.35/1.55 ; 16 with value (4 16) 12 with value (4 53) 5 with value (4 90)
% 1.35/1.55 ; 22 with value (4 17) 20 with value (4 54) 1 with value (4 91)
% 1.35/1.55 ; 25 with value (4 18) 10 with value (4 55) 1 with value (4 92)
% 1.35/1.55 ; 27 with value (4 19) 11 with value (4 56) 8 with value (4 93)
% 1.35/1.55 ; 25 with value (4 20) 16 with value (4 57) 5 with value (4 94)
% 1.35/1.55 ; 19 with value (4 21) 13 with value (4 58) 5 with value (4 96)
% 1.35/1.55 ; 13 with value (4 22) 25 with value (4 59) 1 with value (4 98)
% 1.35/1.55 ; 23 with value (4 23) 8 with value (4 60) 3 with value (4 99)
% 1.35/1.55 ; 18 with value (4 24) 8 with value (4 61) 3 with value (4 100)
% 1.35/1.55 ; 16 with value (4 25) 16 with value (4 62) 1 with value (4 101)
% 1.35/1.55 ; 11 with value (4 26) 5 with value (4 63) 4 with value (4 102)
% 1.35/1.55 ; 18 with value (4 27) 11 with value (4 64) 3 with value (4 103)
% 1.35/1.55 ; 14 with value (4 28) 13 with value (4 65) 5 with value (4 104)
% 1.35/1.55 ; 8 with value (4 29) 11 with value (4 66) 6 with value (4 106)
% 1.35/1.55 ; 15 with value (4 30) 17 with value (4 67) 1 with value (4 108)
% 1.35/1.55 ; 21 with value (4 31) 14 with value (4 68) 2 with value (4 109)
% 1.35/1.55 ; 10 with value (4 32) 13 with value (4 69) 1 with value (4 111)
% 1.35/1.55 ; 14 with value (4 33) 12 with value (4 70) 1 with value (4 113)
% 1.35/1.55 ; 19 with value (4 34) 13 with value (4 71) 1 with value (4 114)
% 1.35/1.55 ; 13 with value (4 35) 9 with value (4 72) 1 with value (4 115)
% 1.35/1.55 ; 12 with value (4 36) 14 with value (4 73) 2 with value (4 122)
% 1.35/1.55 ; 6 with value (4 37) 9 with value (4 74) 1 with value (4 126)
% 1.35/1.55 ; 15 with value (4 38) 16 with value (4 75) 2 with value (4 127)
% 1.35/1.55 ; 13 with value (4 39) 5 with value (4 76) 2 with value (4 129)
% 1.35/1.55 ; 35 with value (4 40) 13 with value (4 77) 2 with value (4 144)
% 1.35/1.55 ; 18 with value (4 41) 14 with value (4 78)
% 1.35/1.55 Evaluation took:
% 1.35/1.55 1.057 seconds of real time
% 1.35/1.55 0.986914 seconds of user run time
% 1.35/1.55 0.06961 seconds of system run time
% 1.35/1.55 [Run times include 0.101 seconds GC run time.]
% 1.35/1.55 0 calls to %EVAL
% 1.35/1.55 0 page faults and
% 1.35/1.55 103,397,768 bytes consed.
% 1.35/1.55 :PROOF-FOUND
% 1.35/1.55 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-10T02:22:18
% 1.35/1.55 :PROOF-FOUND
% 1.35/1.55 *
%------------------------------------------------------------------------------