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