TSTP Solution File: SET122-7 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SET122-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n013.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 05:07:40 EDT 2022
% Result : Unsatisfiable 2.08s 2.29s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 25 ( 17 unt; 5 nHn; 14 RR)
% Number of literals : 34 ( 17 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 19 ( 4 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( ~ subclass(X,Y)
| ~ member(Z,X)
| member(Z,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
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(corollary_2_to_cartesian_product,axiom,
( ~ member(ordered_pair(X,Y),cross_product(Z,U))
| member(Y,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
cnf(singleton_is_null_class,axiom,
( member(X,universal_class)
| singleton(X) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
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_corollary_2_to_OP_determines_components2_1,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_OP_determines_components2_1) ).
cnf(prove_corollary_2_to_OP_determines_components2_2,negated_conjecture,
second(ordered_pair(x,y)) != ordered_pair(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_OP_determines_components2_2) ).
cnf(176,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(179,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_3,176,theory(equality)]) ).
cnf(181,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_5,176,theory(equality)]) ).
cnf(201,plain,
( ~ member(complement(intersection(complement(singleton(singleton(X))),complement(singleton(complement(intersection(complement(singleton(X)),complement(singleton(singleton(Y))))))))),cross_product(Z,U))
| member(Y,universal_class) ),
inference('REWRITE',[status(thm)],[corollary_2_to_cartesian_product,176,theory(equality)]) ).
cnf(214,plain,
second(complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y)))))))))) != complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(y))))))))),
inference('REWRITE',[status(thm)],[prove_corollary_2_to_OP_determines_components2_2,176,theory(equality)]) ).
cnf(253,plain,
singleton(y) = null_class,
inference('HYPERRESOLVE',[status(thm)],[prove_corollary_2_to_OP_determines_components2_1,singleton_is_null_class]) ).
cnf(254,plain,
second(complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class))))))))) != complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))),
inference('REWRITE',[status(thm)],[214,253,theory(equality)]) ).
cnf(280,plain,
~ member(y,X),
inference('UR-RESOLVE',[status(thm)],[subclass_members,class_elements_are_sets,prove_corollary_2_to_OP_determines_components2_1]) ).
cnf(1537,plain,
member(complement(intersection(complement(singleton(singleton(first(complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))))))),complement(singleton(complement(intersection(complement(singleton(first(complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class))))))))))),complement(singleton(singleton(second(complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))))))))))))),cross_product(universal_class,universal_class)),
inference('UR-RESOLVE',[status(thm)],[179,254]) ).
cnf(1538,plain,
complement(intersection(complement(singleton(singleton(first(complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))))))),complement(singleton(complement(intersection(complement(singleton(first(complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class))))))))))),complement(singleton(singleton(second(complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))))))))))))) = complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))),
inference('UR-RESOLVE',[status(thm)],[181,254]) ).
cnf(1539,plain,
member(complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(null_class)))))))),cross_product(universal_class,universal_class)),
inference('REWRITE',[status(thm)],[1537,1538,theory(equality)]) ).
cnf(2188,plain,
~ member(complement(intersection(complement(singleton(singleton(X))),complement(singleton(complement(intersection(complement(singleton(X)),complement(singleton(null_class)))))))),cross_product(Y,Z)),
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[201,280]),253,theory(equality)]) ).
cnf(2189,plain,
$false,
inference('REWRITE',[status(thm)],[1539,2188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET122-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.06/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n013.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 : Sat Jul 9 19:45:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 *
% 0.19/0.47 *
% 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/sandbox/benchmark/theBenchmark.p 2022-07-09T19:45:30
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n013.cluster.edu at 2022-07-09T19:45:30
% 0.19/0.52
% 0.19/0.52 ; Recognized commutativity assertion (= (|unordered_pair| ?X ?Y) (|unordered_pair| ?Y ?X)).
% 2.08/2.29 ; Declaring unordered_pair to be commutative.
% 2.08/2.29
% 2.08/2.29 #||
% 2.08/2.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.08/2.29 % SZS output start Refutation
% See solution above
% 2.13/2.31 ||#
% 2.13/2.31
% 2.13/2.31 ; Summary of computation:
% 2.13/2.31 ; 4289 formulas have been input or derived (from 161 formulas).
% 2.13/2.31 ; 2189 (51%) were retained. Of these,
% 2.13/2.31 ; 186 ( 8%) were simplified or subsumed later,
% 2.13/2.31 ; 2003 (92%) are still being kept.
% 2.13/2.31 ;
% 2.13/2.31 ; Run time in seconds excluding printing time:
% 2.13/2.31 ; 0.031 2% Read assertion file (1 call)
% 2.13/2.31 ; 0.003 0% Assert (169 calls)
% 2.13/2.31 ; 0.386 21% Process new row (4,015 calls)
% 2.13/2.31 ; 0.114 6% Resolution (320 calls)
% 2.13/2.31 ; 0.036 2% Paramodulation (160 calls)
% 2.13/2.31 ; 0.000 0% Factoring (23 calls)
% 2.13/2.31 ; 0.042 2% Condensing (2,437 calls)
% 2.13/2.31 ; 0.608 34% Forward subsumption (2,437 calls)
% 2.13/2.31 ; 0.144 8% Backward subsumption (1,891 calls)
% 2.13/2.31 ; 0.055 3% Clause clause subsumption (18,724 calls)
% 2.13/2.31 ; 0.326 18% Forward simplification (4,012 calls)
% 2.13/2.31 ; 0.013 1% Backward simplification (2,172 calls)
% 2.13/2.31 ; 0.014 1% Ordering (8,971 calls)
% 2.13/2.31 ; 0.000 0% Sortal reasoning (32 calls)
% 2.13/2.31 ; 0.000 0% Purity testing (1 call)
% 2.13/2.31 ; 0.041 2% Other
% 2.13/2.31 ; 1.813 Total
% 2.13/2.31 ; 1.833 Real time
% 2.13/2.31 ;
% 2.13/2.31 ; Term-hash-array has 5,450 terms in all.
% 2.13/2.31 ; Feature-vector-row-index has 1,748 entries (1,763 at peak, 1,891 added, 143 deleted).
% 2.13/2.31 ; Feature-vector-row-index has 17,065 nodes (17,203 at peak, 18,378 added, 1,313 deleted).
% 2.13/2.31 ; Retrieved 30,248 possibly forward subsuming rows in 2,437 calls.
% 2.13/2.31 ; Retrieved 3,049 possibly backward subsumed rows in 1,891 calls.
% 2.13/2.31 ; Path-index has 5,269 entries (5,270 at peak, 5,702 added, 433 deleted).
% 2.13/2.31 ; Path-index has 14,114 nodes (14,114 at peak, 14,730 added, 616 deleted).
% 2.13/2.31 ; Trie-index has 5,269 entries (5,270 at peak, 5,702 added, 433 deleted).
% 2.13/2.31 ; Trie-index has 29,337 nodes (29,340 at peak, 32,138 added, 2,801 deleted).
% 2.13/2.31 ; Retrieved 31,240 generalization terms in 84,884 calls.
% 2.13/2.31 ; Retrieved 430 instance terms in 280 calls.
% 2.13/2.31 ; Retrieved 83,684 unifiable terms in 2,467 calls.
% 2.13/2.31 ;
% 2.13/2.31 ; The agenda of rows to process has 17 entries:
% 2.13/2.31 ; 4 with value 33 2 with value 40 4 with value 49
% 2.13/2.31 ; 1 with value 35 1 with value 43 1 with value 58
% 2.13/2.31 ; 2 with value 37 2 with value 46
% 2.13/2.31 ; The agenda of rows to give has 1844 entries:
% 2.13/2.31 ; 2 with value (4 6) 19 with value (4 55) 8 with value (4 104)
% 2.13/2.31 ; 17 with value (4 7) 19 with value (4 56) 4 with value (4 105)
% 2.13/2.31 ; 13 with value (4 8) 17 with value (4 57) 8 with value (4 106)
% 2.13/2.31 ; 15 with value (4 9) 17 with value (4 58) 5 with value (4 108)
% 2.13/2.31 ; 13 with value (4 10) 37 with value (4 59) 8 with value (4 109)
% 2.13/2.31 ; 13 with value (4 11) 16 with value (4 60) 1 with value (4 110)
% 2.13/2.31 ; 11 with value (4 12) 13 with value (4 61) 13 with value (4 111)
% 2.13/2.31 ; 16 with value (4 13) 22 with value (4 62) 5 with value (4 112)
% 2.13/2.31 ; 17 with value (4 14) 18 with value (4 63) 5 with value (4 113)
% 2.13/2.31 ; 19 with value (4 15) 15 with value (4 64) 14 with value (4 114)
% 2.13/2.31 ; 14 with value (4 16) 21 with value (4 65) 9 with value (4 115)
% 2.13/2.31 ; 24 with value (4 17) 18 with value (4 66) 9 with value (4 116)
% 2.13/2.31 ; 23 with value (4 18) 19 with value (4 67) 2 with value (4 118)
% 2.13/2.31 ; 27 with value (4 19) 20 with value (4 68) 1 with value (4 120)
% 2.13/2.31 ; 26 with value (4 20) 25 with value (4 69) 11 with value (4 122)
% 2.13/2.31 ; 20 with value (4 21) 17 with value (4 70) 8 with value (4 123)
% 2.13/2.31 ; 14 with value (4 22) 18 with value (4 71) 1 with value (4 124)
% 2.13/2.31 ; 25 with value (4 23) 10 with value (4 72) 5 with value (4 125)
% 2.13/2.31 ; 23 with value (4 24) 15 with value (4 73) 10 with value (4 126)
% 2.13/2.31 ; 20 with value (4 25) 11 with value (4 74) 2 with value (4 129)
% 2.13/2.31 ; 15 with value (4 26) 19 with value (4 75) 2 with value (4 130)
% 2.13/2.31 ; 21 with value (4 27) 15 with value (4 76) 2 with value (4 131)
% 2.13/2.31 ; 13 with value (4 28) 20 with value (4 77) 4 with value (4 134)
% 2.13/2.31 ; 15 with value (4 29) 23 with value (4 78) 3 with value (4 139)
% 2.13/2.31 ; 17 with value (4 30) 19 with value (4 79) 3 with value (4 141)
% 2.13/2.31 ; 26 with value (4 31) 13 with value (4 80) 1 with value (4 142)
% 2.13/2.31 ; 12 with value (4 32) 10 with value (4 81) 5 with value (4 144)
% 2.13/2.31 ; 13 with value (4 33) 8 with value (4 82) 2 with value (4 145)
% 2.13/2.31 ; 15 with value (4 34) 10 with value (4 83) 2 with value (4 146)
% 2.13/2.31 ; 15 with value (4 35) 13 with value (4 84) 1 with value (4 149)
% 2.13/2.31 ; 14 with value (4 36) 16 with value (4 85) 3 with value (4 150)
% 2.13/2.31 ; 7 with value (4 37) 18 with value (4 86) 1 with value (4 152)
% 2.13/2.31 ; 15 with value (4 38) 28 with value (4 87) 2 with value (4 157)
% 2.13/2.31 ; 20 with value (4 39) 12 with value (4 88) 1 with value (4 168)
% 2.13/2.31 ; 36 with value (4 40) 10 with value (4 89) 1 with value (4 173)
% 2.13/2.31 ; 24 with value (4 41) 16 with value (4 90) 1 with value (4 183)
% 2.13/2.31 ; 25 with value (4 42) 7 with value (4 91) 4 with value (4 187)
% 2.13/2.31 ; 36 with value (4 43) 4 with value (4 92) 2 with value (4 193)
% 2.13/2.31 ; 22 with value (4 44) 15 with value (4 93) 1 with value (4 198)
% 2.13/2.31 ; 12 with value (4 45) 11 with value (4 94) 4 with value (4 203)
% 2.13/2.31 ; 34 with value (4 46) 10 with value (4 95) 1 with value (4 208)
% 2.13/2.31 ; 17 with value (4 47) 10 with value (4 96) 2 with value (4 209)
% 2.13/2.31 ; 33 with value (4 48) 16 with value (4 98) 1 with value (4 210)
% 2.13/2.31 ; 18 with value (4 49) 5 with value (4 99) 2 with value (4 214)
% 2.13/2.31 ; 19 with value (4 50) 8 with value (4 100) 1 with value (4 216)
% 2.13/2.31 ; 22 with value (4 51) 8 with value (4 101) 1 with value (4 238)
% 2.13/2.31 ; 24 with value (4 52) 8 with value (4 102) 1 with value (4 239)
% 2.13/2.31 ; 17 with value (4 53) 5 with value (4 103) 1 with value (4 349)
% 2.13/2.31 ; 27 with value (4 54)
% 2.13/2.31 Evaluation took:
% 2.13/2.31 1.836 seconds of real time
% 2.13/2.31 1.719457 seconds of user run time
% 2.13/2.31 0.115995 seconds of system run time
% 2.13/2.31 [Run times include 0.193 seconds GC run time.]
% 2.13/2.31 0 calls to %EVAL
% 2.13/2.31 0 page faults and
% 2.13/2.31 191,398,080 bytes consed.
% 2.13/2.31 :PROOF-FOUND
% 2.13/2.31 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-09T19:45:31
% 2.13/2.31 :PROOF-FOUND
% 2.13/2.31 *
%------------------------------------------------------------------------------