TSTP Solution File: SET020-7 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SET020-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n003.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 05:05:57 EDT 2022
% Result : Unsatisfiable 2.14s 2.35s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 13 unt; 0 nHn; 14 RR)
% Number of literals : 27 ( 15 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 20 ( 4 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 14 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(cartesian_product1,axiom,
( ~ member(ordered_pair(X,Y),cross_product(Z,U))
| member(X,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
cnf(cartesian_product4,axiom,
( ~ member(X,cross_product(Y,Z))
| ordered_pair(first(X),second(X)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
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(ordered_pair_determines_components1,axiom,
( ordered_pair(X,Y) != ordered_pair(Z,U)
| ~ member(X,universal_class)
| X = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_determines_components1) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_sets1_1,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_1) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_sets1_2,negated_conjecture,
first(ordered_pair(u,v)) != u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_2) ).
cnf(170,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(171,plain,
( ~ member(X,cross_product(Y,Z))
| complement(intersection(complement(singleton(singleton(first(X)))),complement(singleton(complement(intersection(complement(singleton(first(X))),complement(singleton(singleton(second(X)))))))))) = X ),
inference('REWRITE',[status(thm)],[cartesian_product4,170,theory(equality)]) ).
cnf(182,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,Z) ),
inference('REWRITE',[status(thm)],[cartesian_product1,170,theory(equality)]) ).
cnf(200,plain,
( complement(intersection(complement(singleton(singleton(X))),complement(singleton(complement(intersection(complement(singleton(X)),complement(singleton(singleton(Y))))))))) != complement(intersection(complement(singleton(singleton(Z))),complement(singleton(complement(intersection(complement(singleton(Z)),complement(singleton(singleton(U)))))))))
| ~ member(X,universal_class)
| X = Z ),
inference('REWRITE',[status(thm)],[ordered_pair_determines_components1,170,theory(equality)]) ).
cnf(203,plain,
member(complement(intersection(complement(singleton(singleton(u))),complement(singleton(complement(intersection(complement(singleton(u)),complement(singleton(singleton(v))))))))),cross_product(universal_class,universal_class)),
inference('REWRITE',[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_sets1_1,170,theory(equality)]) ).
cnf(204,plain,
first(complement(intersection(complement(singleton(singleton(u))),complement(singleton(complement(intersection(complement(singleton(u)),complement(singleton(singleton(v)))))))))) != u,
inference('REWRITE',[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_sets1_2,170,theory(equality)]) ).
cnf(739,plain,
member(u,universal_class),
inference('HYPERRESOLVE',[status(thm)],[182,203]) ).
cnf(1443,plain,
complement(intersection(complement(singleton(singleton(first(complement(intersection(complement(singleton(singleton(u))),complement(singleton(complement(intersection(complement(singleton(u)),complement(singleton(singleton(v))))))))))))),complement(singleton(complement(intersection(complement(singleton(first(complement(intersection(complement(singleton(singleton(u))),complement(singleton(complement(intersection(complement(singleton(u)),complement(singleton(singleton(v)))))))))))),complement(singleton(singleton(second(complement(intersection(complement(singleton(singleton(u))),complement(singleton(complement(intersection(complement(singleton(u)),complement(singleton(singleton(v))))))))))))))))))) = complement(intersection(complement(singleton(singleton(u))),complement(singleton(complement(intersection(complement(singleton(u)),complement(singleton(singleton(v))))))))),
inference('HYPERRESOLVE',[status(thm)],[171,203]) ).
cnf(2140,plain,
complement(intersection(complement(singleton(singleton(u))),complement(singleton(complement(intersection(complement(singleton(u)),complement(singleton(singleton(X))))))))) != complement(intersection(complement(singleton(singleton(first(complement(intersection(complement(singleton(singleton(u))),complement(singleton(complement(intersection(complement(singleton(u)),complement(singleton(singleton(v))))))))))))),complement(singleton(complement(intersection(complement(singleton(first(complement(intersection(complement(singleton(singleton(u))),complement(singleton(complement(intersection(complement(singleton(u)),complement(singleton(singleton(v)))))))))))),complement(singleton(singleton(Y))))))))),
inference('UR-RESOLVE',[status(thm)],[200,739,204]) ).
cnf(2141,plain,
$false,
inference('REWRITE',[status(thm)],[1443,2140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET020-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n003.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 : Sun Jul 10 00:14:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 *
% 0.20/0.47 *
% 0.20/0.47 #<PACKAGE "SNARK-USER">
% 0.20/0.47 *
% 0.20/0.47 SNARK-TPTP-OPTIONS
% 0.20/0.47 *
% 0.20/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47 (USE-FACTORING :POS)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47 *
% 0.20/0.47 "."
% 0.20/0.47 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-10T00:14:14
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n003.cluster.edu at 2022-07-10T00:14:14
% 0.20/0.52
% 0.20/0.52 ; Recognized commutativity assertion (= (|unordered_pair| ?X ?Y) (|unordered_pair| ?Y ?X)).
% 2.14/2.35 ; Declaring unordered_pair to be commutative.
% 2.14/2.35
% 2.14/2.35 #||
% 2.14/2.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.14/2.35 % SZS output start Refutation
% See solution above
% 2.14/2.36 ||#
% 2.14/2.36
% 2.14/2.36 ; Summary of computation:
% 2.14/2.36 ; 4069 formulas have been input or derived (from 155 formulas).
% 2.14/2.36 ; 2141 (53%) were retained. Of these,
% 2.14/2.36 ; 141 ( 7%) were simplified or subsumed later,
% 2.14/2.36 ; 2000 (93%) are still being kept.
% 2.14/2.36 ;
% 2.14/2.36 ; Run time in seconds excluding printing time:
% 2.14/2.36 ; 0.029 2% Read assertion file (1 call)
% 2.14/2.36 ; 0.003 0% Assert (159 calls)
% 2.14/2.36 ; 0.415 22% Process new row (3,802 calls)
% 2.14/2.36 ; 0.159 8% Resolution (308 calls)
% 2.14/2.36 ; 0.040 2% Paramodulation (154 calls)
% 2.14/2.36 ; 0.001 0% Factoring (21 calls)
% 2.14/2.36 ; 0.044 2% Condensing (2,247 calls)
% 2.14/2.36 ; 0.633 34% Forward subsumption (2,247 calls)
% 2.14/2.36 ; 0.157 8% Backward subsumption (1,799 calls)
% 2.14/2.36 ; 0.062 3% Clause clause subsumption (16,360 calls)
% 2.14/2.36 ; 0.258 14% Forward simplification (3,801 calls)
% 2.14/2.36 ; 0.017 1% Backward simplification (2,124 calls)
% 2.14/2.36 ; 0.020 1% Ordering (8,479 calls)
% 2.14/2.36 ; 0.000 0% Sortal reasoning (32 calls)
% 2.14/2.36 ; 0.000 0% Purity testing (1 call)
% 2.14/2.36 ; 0.042 2% Other
% 2.14/2.36 ; 1.880 Total
% 2.14/2.36 ; 1.882 Real time
% 2.14/2.36 ;
% 2.14/2.36 ; Term-hash-array has 5,917 terms in all.
% 2.14/2.36 ; Feature-vector-row-index has 1,698 entries (1,698 at peak, 1,799 added, 101 deleted).
% 2.14/2.36 ; Feature-vector-row-index has 17,072 nodes (17,072 at peak, 18,039 added, 967 deleted).
% 2.14/2.36 ; Retrieved 26,184 possibly forward subsuming rows in 2,247 calls.
% 2.14/2.36 ; Retrieved 2,496 possibly backward subsumed rows in 1,799 calls.
% 2.14/2.36 ; Path-index has 5,818 entries (5,829 at peak, 6,185 added, 367 deleted).
% 2.14/2.36 ; Path-index has 14,319 nodes (14,350 at peak, 14,881 added, 562 deleted).
% 2.14/2.36 ; Trie-index has 5,818 entries (5,829 at peak, 6,185 added, 367 deleted).
% 2.14/2.36 ; Trie-index has 32,567 nodes (32,786 at peak, 34,867 added, 2,300 deleted).
% 2.14/2.36 ; Retrieved 25,704 generalization terms in 46,160 calls.
% 2.14/2.36 ; Retrieved 469 instance terms in 324 calls.
% 2.14/2.36 ; Retrieved 82,670 unifiable terms in 2,490 calls.
% 2.14/2.36 ;
% 2.14/2.36 ; The agenda of rows to give has 1846 entries:
% 2.14/2.36 ; 1 with value (4 5) 19 with value (4 53) 7 with value (4 102)
% 2.14/2.36 ; 2 with value (4 6) 23 with value (4 54) 8 with value (4 103)
% 2.14/2.36 ; 16 with value (4 7) 17 with value (4 55) 10 with value (4 104)
% 2.14/2.36 ; 20 with value (4 8) 15 with value (4 56) 4 with value (4 105)
% 2.14/2.36 ; 17 with value (4 9) 17 with value (4 57) 8 with value (4 106)
% 2.14/2.36 ; 13 with value (4 10) 15 with value (4 58) 3 with value (4 108)
% 2.14/2.36 ; 13 with value (4 11) 34 with value (4 59) 10 with value (4 109)
% 2.14/2.36 ; 12 with value (4 12) 17 with value (4 60) 1 with value (4 110)
% 2.14/2.36 ; 18 with value (4 13) 14 with value (4 61) 9 with value (4 111)
% 2.14/2.36 ; 17 with value (4 14) 23 with value (4 62) 5 with value (4 112)
% 2.14/2.36 ; 19 with value (4 15) 14 with value (4 63) 5 with value (4 113)
% 2.14/2.36 ; 16 with value (4 16) 13 with value (4 64) 10 with value (4 114)
% 2.14/2.36 ; 25 with value (4 17) 22 with value (4 65) 7 with value (4 115)
% 2.14/2.36 ; 23 with value (4 18) 13 with value (4 66) 1 with value (4 118)
% 2.14/2.36 ; 27 with value (4 19) 20 with value (4 67) 1 with value (4 120)
% 2.14/2.36 ; 26 with value (4 20) 25 with value (4 68) 9 with value (4 122)
% 2.14/2.36 ; 18 with value (4 21) 27 with value (4 69) 6 with value (4 123)
% 2.14/2.36 ; 14 with value (4 22) 19 with value (4 70) 1 with value (4 124)
% 2.14/2.36 ; 24 with value (4 23) 18 with value (4 71) 9 with value (4 125)
% 2.14/2.36 ; 24 with value (4 24) 11 with value (4 72) 2 with value (4 126)
% 2.14/2.36 ; 19 with value (4 25) 16 with value (4 73) 2 with value (4 129)
% 2.14/2.36 ; 14 with value (4 26) 15 with value (4 74) 2 with value (4 130)
% 2.14/2.36 ; 21 with value (4 27) 24 with value (4 75) 2 with value (4 131)
% 2.14/2.36 ; 13 with value (4 28) 11 with value (4 76) 2 with value (4 134)
% 2.14/2.36 ; 15 with value (4 29) 22 with value (4 77) 3 with value (4 139)
% 2.14/2.36 ; 17 with value (4 30) 25 with value (4 78) 5 with value (4 141)
% 2.14/2.36 ; 25 with value (4 31) 14 with value (4 79) 1 with value (4 142)
% 2.14/2.36 ; 12 with value (4 32) 11 with value (4 80) 5 with value (4 144)
% 2.14/2.36 ; 21 with value (4 33) 10 with value (4 81) 4 with value (4 145)
% 2.14/2.36 ; 21 with value (4 34) 8 with value (4 82) 2 with value (4 146)
% 2.14/2.36 ; 17 with value (4 35) 11 with value (4 83) 1 with value (4 149)
% 2.14/2.36 ; 16 with value (4 36) 13 with value (4 84) 5 with value (4 150)
% 2.14/2.36 ; 7 with value (4 37) 10 with value (4 85) 3 with value (4 152)
% 2.14/2.36 ; 15 with value (4 38) 19 with value (4 86) 4 with value (4 157)
% 2.14/2.36 ; 24 with value (4 39) 19 with value (4 87) 1 with value (4 168)
% 2.14/2.36 ; 37 with value (4 40) 15 with value (4 88) 1 with value (4 173)
% 2.14/2.36 ; 29 with value (4 41) 6 with value (4 89) 1 with value (4 183)
% 2.14/2.36 ; 26 with value (4 42) 10 with value (4 90) 4 with value (4 187)
% 2.14/2.36 ; 34 with value (4 43) 8 with value (4 91) 2 with value (4 193)
% 2.14/2.36 ; 27 with value (4 44) 8 with value (4 92) 1 with value (4 198)
% 2.14/2.36 ; 10 with value (4 45) 17 with value (4 93) 1 with value (4 208)
% 2.14/2.36 ; 33 with value (4 46) 12 with value (4 94) 2 with value (4 209)
% 2.14/2.36 ; 17 with value (4 47) 9 with value (4 95) 1 with value (4 210)
% 2.14/2.36 ; 33 with value (4 48) 9 with value (4 96) 2 with value (4 214)
% 2.14/2.36 ; 20 with value (4 49) 13 with value (4 98) 1 with value (4 216)
% 2.14/2.36 ; 20 with value (4 50) 5 with value (4 99) 1 with value (4 238)
% 2.14/2.36 ; 22 with value (4 51) 8 with value (4 100) 1 with value (4 239)
% 2.14/2.36 ; 28 with value (4 52) 7 with value (4 101) 1 with value (4 349)
% 2.14/2.36 Evaluation took:
% 2.14/2.36 1.885 seconds of real time
% 2.14/2.36 1.765637 seconds of user run time
% 2.14/2.36 0.120039 seconds of system run time
% 2.14/2.36 [Run times include 0.2 seconds GC run time.]
% 2.14/2.36 0 calls to %EVAL
% 2.14/2.36 0 page faults and
% 2.14/2.36 169,762,296 bytes consed.
% 2.14/2.36 :PROOF-FOUND
% 2.14/2.36 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-10T00:14:16
% 2.14/2.36 :PROOF-FOUND
% 2.14/2.36 *
%------------------------------------------------------------------------------