TSTP Solution File: SET120-7 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SET120-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n023.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 05:07:38 EDT 2022
% Result : Unsatisfiable 1.83s 2.04s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 29 ( 19 unt; 7 nHn; 15 RR)
% Number of literals : 40 ( 20 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 20 ( 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 : 36 ( 11 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_1_to_cartesian_product,axiom,
( ~ member(ordered_pair(X,Y),cross_product(Z,U))
| member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
cnf(unordered_pair_equals_singleton1,axiom,
( member(X,universal_class)
| unordered_pair(X,Y) = singleton(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
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_components1_1,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_OP_determines_components1_1) ).
cnf(prove_corollary_2_to_OP_determines_components1_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_components1_2) ).
cnf(174,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(177,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_3,174,theory(equality)]) ).
cnf(179,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_5,174,theory(equality)]) ).
cnf(198,plain,
( ~ member(complement(intersection(complement(singleton(singleton(X))),complement(singleton(complement(intersection(complement(singleton(X)),complement(singleton(singleton(Y))))))))),cross_product(Z,U))
| member(X,universal_class) ),
inference('REWRITE',[status(thm)],[corollary_1_to_cartesian_product,174,theory(equality)]) ).
cnf(210,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_components1_2,174,theory(equality)]) ).
cnf(217,plain,
( member(X,universal_class)
| complement(intersection(complement(singleton(X)),complement(singleton(Y)))) = singleton(Y) ),
inference('REWRITE',[status(thm)],[unordered_pair_equals_singleton1,148,theory(equality)]) ).
cnf(249,plain,
singleton(x) = null_class,
inference('HYPERRESOLVE',[status(thm)],[prove_corollary_2_to_OP_determines_components1_1,singleton_is_null_class]) ).
cnf(250,plain,
second(complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y)))))))))) != complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y))))))))),
inference('REWRITE',[status(thm)],[210,249,theory(equality)]) ).
cnf(276,plain,
~ member(x,X),
inference('UR-RESOLVE',[status(thm)],[subclass_members,class_elements_are_sets,prove_corollary_2_to_OP_determines_components1_1]) ).
cnf(1533,plain,
member(complement(intersection(complement(singleton(singleton(first(complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y))))))))))))),complement(singleton(complement(intersection(complement(singleton(first(complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y)))))))))))),complement(singleton(singleton(second(complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y))))))))))))))))))),cross_product(universal_class,universal_class)),
inference('UR-RESOLVE',[status(thm)],[177,250]) ).
cnf(1534,plain,
complement(intersection(complement(singleton(singleton(first(complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y))))))))))))),complement(singleton(complement(intersection(complement(singleton(first(complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y)))))))))))),complement(singleton(singleton(second(complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y))))))))))))))))))) = complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y))))))))),
inference('UR-RESOLVE',[status(thm)],[179,250]) ).
cnf(1535,plain,
member(complement(intersection(complement(singleton(null_class)),complement(singleton(complement(intersection(complement(null_class),complement(singleton(singleton(y))))))))),cross_product(universal_class,universal_class)),
inference('REWRITE',[status(thm)],[1533,1534,theory(equality)]) ).
cnf(2020,plain,
complement(intersection(complement(null_class),complement(singleton(X)))) = singleton(X),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[276,217]),249,theory(equality)]) ).
cnf(2026,plain,
member(complement(intersection(complement(singleton(null_class)),complement(singleton(singleton(singleton(y)))))),cross_product(universal_class,universal_class)),
inference('REWRITE',[status(thm)],[1535,2020,theory(equality)]) ).
cnf(2032,plain,
~ member(complement(intersection(complement(singleton(null_class)),complement(singleton(singleton(singleton(X)))))),cross_product(Y,Z)),
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[198,276]),2020,249,theory(equality)]) ).
cnf(2033,plain,
$false,
inference('REWRITE',[status(thm)],[2026,2032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET120-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.03/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 08:26:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 *
% 0.19/0.45 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46 (USE-FACTORING :POS)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46 *
% 0.19/0.46 "."
% 0.19/0.46 *
% 0.19/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-11T08:26:40
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n023.cluster.edu at 2022-07-11T08:26:40
% 0.19/0.50
% 0.19/0.50 ; Recognized commutativity assertion (= (|unordered_pair| ?X ?Y) (|unordered_pair| ?Y ?X)).
% 1.83/2.04 ; Declaring unordered_pair to be commutative.
% 1.83/2.04
% 1.83/2.04 #||
% 1.83/2.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.83/2.04 % SZS output start Refutation
% See solution above
% 1.83/2.06 ||#
% 1.83/2.06
% 1.83/2.06 ; Summary of computation:
% 1.83/2.06 ; 3847 formulas have been input or derived (from 159 formulas).
% 1.83/2.06 ; 2033 (53%) were retained. Of these,
% 1.83/2.06 ; 157 ( 8%) were simplified or subsumed later,
% 1.83/2.06 ; 1876 (92%) are still being kept.
% 1.83/2.06 ;
% 1.83/2.06 ; Run time in seconds excluding printing time:
% 1.83/2.06 ; 0.030 2% Read assertion file (1 call)
% 1.83/2.06 ; 0.005 0% Assert (167 calls)
% 1.83/2.06 ; 0.294 19% Process new row (3,590 calls)
% 1.83/2.06 ; 0.100 6% Resolution (316 calls)
% 1.83/2.06 ; 0.029 2% Paramodulation (158 calls)
% 1.83/2.06 ; 0.000 0% Factoring (21 calls)
% 1.83/2.06 ; 0.040 3% Condensing (2,182 calls)
% 1.83/2.06 ; 0.582 37% Forward subsumption (2,182 calls)
% 1.83/2.06 ; 0.111 7% Backward subsumption (1,728 calls)
% 1.83/2.06 ; 0.041 3% Clause clause subsumption (15,848 calls)
% 1.83/2.06 ; 0.273 17% Forward simplification (3,587 calls)
% 1.83/2.06 ; 0.013 1% Backward simplification (2,016 calls)
% 1.83/2.06 ; 0.024 2% Ordering (8,284 calls)
% 1.83/2.06 ; 0.000 0% Sortal reasoning (32 calls)
% 1.83/2.06 ; 0.000 0% Purity testing (1 call)
% 1.83/2.06 ; 0.040 3% Other
% 1.83/2.06 ; 1.582 Total
% 1.83/2.06 ; 1.602 Real time
% 1.83/2.06 ;
% 1.83/2.06 ; Term-hash-array has 5,486 terms in all.
% 1.83/2.06 ; Feature-vector-row-index has 1,622 entries (1,637 at peak, 1,728 added, 106 deleted).
% 1.83/2.06 ; Feature-vector-row-index has 15,999 nodes (16,138 at peak, 17,000 added, 1,001 deleted).
% 1.83/2.06 ; Retrieved 25,366 possibly forward subsuming rows in 2,182 calls.
% 1.83/2.06 ; Retrieved 2,519 possibly backward subsumed rows in 1,728 calls.
% 1.83/2.06 ; Path-index has 5,321 entries (5,322 at peak, 5,765 added, 444 deleted).
% 1.83/2.06 ; Path-index has 14,367 nodes (14,367 at peak, 15,159 added, 792 deleted).
% 1.83/2.06 ; Trie-index has 5,321 entries (5,322 at peak, 5,765 added, 444 deleted).
% 1.83/2.06 ; Trie-index has 29,526 nodes (29,909 at peak, 32,908 added, 3,382 deleted).
% 1.83/2.06 ; Retrieved 23,822 generalization terms in 65,759 calls.
% 1.83/2.06 ; Retrieved 436 instance terms in 287 calls.
% 1.83/2.06 ; Retrieved 75,607 unifiable terms in 2,419 calls.
% 1.83/2.06 ;
% 1.83/2.06 ; The agenda of rows to process has 16 entries:
% 1.83/2.06 ; 7 with value 33 2 with value 40 2 with value 46
% 1.83/2.06 ; 1 with value 35 1 with value 43 1 with value 58
% 1.83/2.06 ; 2 with value 37
% 1.83/2.06 ; The agenda of input rows to give has 1 entry:
% 1.83/2.06 ; 1 with value 30
% 1.83/2.06 ; The agenda of rows to give has 1719 entries:
% 1.83/2.06 ; 2 with value (4 6) 21 with value (4 54) 7 with value (4 102)
% 1.83/2.06 ; 17 with value (4 7) 15 with value (4 55) 5 with value (4 103)
% 1.83/2.06 ; 13 with value (4 8) 15 with value (4 56) 10 with value (4 104)
% 1.83/2.06 ; 15 with value (4 9) 17 with value (4 57) 2 with value (4 105)
% 1.83/2.06 ; 13 with value (4 10) 15 with value (4 58) 8 with value (4 106)
% 1.83/2.06 ; 13 with value (4 11) 31 with value (4 59) 3 with value (4 108)
% 1.83/2.06 ; 11 with value (4 12) 14 with value (4 60) 8 with value (4 109)
% 1.83/2.06 ; 16 with value (4 13) 13 with value (4 61) 1 with value (4 110)
% 1.83/2.06 ; 17 with value (4 14) 22 with value (4 62) 9 with value (4 111)
% 1.83/2.06 ; 19 with value (4 15) 14 with value (4 63) 5 with value (4 112)
% 1.83/2.06 ; 14 with value (4 16) 11 with value (4 64) 5 with value (4 113)
% 1.83/2.06 ; 24 with value (4 17) 21 with value (4 65) 10 with value (4 114)
% 1.83/2.06 ; 23 with value (4 18) 16 with value (4 66) 7 with value (4 115)
% 1.83/2.06 ; 27 with value (4 19) 17 with value (4 67) 1 with value (4 120)
% 1.83/2.06 ; 26 with value (4 20) 20 with value (4 68) 9 with value (4 122)
% 1.83/2.06 ; 20 with value (4 21) 21 with value (4 69) 6 with value (4 123)
% 1.83/2.06 ; 14 with value (4 22) 17 with value (4 70) 1 with value (4 124)
% 1.83/2.06 ; 25 with value (4 23) 18 with value (4 71) 9 with value (4 125)
% 1.83/2.06 ; 23 with value (4 24) 11 with value (4 72) 2 with value (4 126)
% 1.83/2.06 ; 20 with value (4 25) 15 with value (4 73) 2 with value (4 129)
% 1.83/2.06 ; 15 with value (4 26) 11 with value (4 74) 2 with value (4 130)
% 1.83/2.06 ; 21 with value (4 27) 19 with value (4 75) 2 with value (4 131)
% 1.83/2.06 ; 13 with value (4 28) 10 with value (4 76) 2 with value (4 134)
% 1.83/2.06 ; 15 with value (4 29) 20 with value (4 77) 3 with value (4 139)
% 1.83/2.06 ; 17 with value (4 30) 23 with value (4 78) 5 with value (4 141)
% 1.83/2.06 ; 25 with value (4 31) 13 with value (4 79) 1 with value (4 142)
% 1.83/2.06 ; 13 with value (4 32) 5 with value (4 80) 5 with value (4 144)
% 1.83/2.06 ; 14 with value (4 33) 6 with value (4 81) 4 with value (4 145)
% 1.83/2.06 ; 16 with value (4 34) 8 with value (4 82) 2 with value (4 146)
% 1.83/2.06 ; 15 with value (4 35) 10 with value (4 83) 1 with value (4 149)
% 1.83/2.06 ; 14 with value (4 36) 13 with value (4 84) 5 with value (4 150)
% 1.83/2.06 ; 7 with value (4 37) 10 with value (4 85) 3 with value (4 152)
% 1.83/2.06 ; 15 with value (4 38) 19 with value (4 86) 4 with value (4 157)
% 1.83/2.06 ; 20 with value (4 39) 18 with value (4 87) 1 with value (4 168)
% 1.83/2.06 ; 36 with value (4 40) 12 with value (4 88) 1 with value (4 173)
% 1.83/2.06 ; 24 with value (4 41) 6 with value (4 89) 1 with value (4 183)
% 1.83/2.06 ; 25 with value (4 42) 9 with value (4 90) 4 with value (4 187)
% 1.83/2.06 ; 36 with value (4 43) 7 with value (4 91) 2 with value (4 193)
% 1.83/2.06 ; 22 with value (4 44) 8 with value (4 92) 1 with value (4 198)
% 1.83/2.06 ; 12 with value (4 45) 15 with value (4 93) 1 with value (4 208)
% 1.83/2.06 ; 33 with value (4 46) 9 with value (4 94) 2 with value (4 209)
% 1.83/2.06 ; 16 with value (4 47) 8 with value (4 95) 1 with value (4 210)
% 1.83/2.06 ; 32 with value (4 48) 8 with value (4 96) 2 with value (4 214)
% 1.83/2.06 ; 18 with value (4 49) 12 with value (4 98) 1 with value (4 216)
% 1.83/2.06 ; 19 with value (4 50) 5 with value (4 99) 1 with value (4 238)
% 1.83/2.06 ; 22 with value (4 51) 8 with value (4 100) 1 with value (4 239)
% 1.83/2.06 ; 24 with value (4 52) 6 with value (4 101) 1 with value (4 349)
% 1.83/2.06 ; 17 with value (4 53)
% 1.83/2.06 Evaluation took:
% 1.83/2.06 1.604 seconds of real time
% 1.83/2.06 1.510648 seconds of user run time
% 1.83/2.06 0.092842 seconds of system run time
% 1.83/2.06 [Run times include 0.186 seconds GC run time.]
% 1.83/2.06 0 calls to %EVAL
% 1.83/2.06 0 page faults and
% 1.83/2.06 165,408,856 bytes consed.
% 1.83/2.06 :PROOF-FOUND
% 1.83/2.06 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-11T08:26:41
% 1.83/2.06 :PROOF-FOUND
% 1.83/2.06 *
%------------------------------------------------------------------------------