TSTP Solution File: REL013+1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : REL013+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n007.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 : Mon Jul 18 19:59:18 EDT 2022
% Result : Theorem 1.10s 1.28s
% Output : Refutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 53 ( 52 unt; 0 nHn; 12 RR)
% Number of literals : 54 ( 53 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
X = join(complement(join(complement(X),complement(Y))),complement(join(complement(X),Y))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
cnf(2,plain,
join(complement(join(complement(X),complement(Y))),join(complement(join(complement(X),Y)),Z)) = join(X,Z),
inference('EMBED',[status(thm)],[1]) ).
cnf(3,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
cnf(5,axiom,
composition(X,one) = X,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).
cnf(6,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
cnf(7,plain,
join(composition(X,Y),join(composition(Z,Y),U)) = join(composition(join(X,Z),Y),U),
inference('EMBED',[status(thm)],[6]) ).
cnf(8,axiom,
converse(converse(X)) = X,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
cnf(9,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
cnf(11,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
cnf(12,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
cnf(13,plain,
join(composition(converse(X),complement(composition(X,Y))),join(complement(Y),Z)) = join(complement(Y),Z),
inference('EMBED',[status(thm)],[12]) ).
cnf(14,axiom,
top = join(X,complement(X)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).
cnf(15,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference('EMBED',[status(thm)],[14]) ).
cnf(16,axiom,
zero = meet(X,complement(X)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).
cnf(17,plain,
zero = complement(top),
inference('REWRITE',[status(thm)],[16,3,theory(equality)]) ).
cnf(18,negated_conjecture,
( composition('SKOLEMAAAV1',zero) != zero
| composition(zero,'SKOLEMAAAV1') != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(25,plain,
join(top,X) = join(top,complement(join(Y,complement(join(X,Y))))),
inference('PARAMODULATE',[status(thm)],[15,15,theory(equality)]) ).
cnf(27,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference('PARAMODULATE',[status(thm)],[9,8,theory(equality)]) ).
cnf(34,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference('PARAMODULATE',[status(thm)],[11,8,theory(equality)]) ).
cnf(47,plain,
join(composition(join(X,Y),Z),complement(composition(X,Z))) = join(top,composition(Y,Z)),
inference('PARAMODULATE',[status(thm)],[15,7,theory(equality)]) ).
cnf(53,plain,
join(composition(converse(X),complement(composition(X,top))),zero) = zero,
inference('PARAMODULATE',[status(thm)],[12,17,theory(equality)]) ).
cnf(65,plain,
join(complement(X),complement(composition(converse(Y),complement(composition(Y,X))))) = join(top,complement(X)),
inference('PARAMODULATE',[status(thm)],[15,13,theory(equality)]) ).
cnf(77,plain,
complement(X) = join(zero,complement(join(complement(complement(X)),X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1,14,theory(equality)]),17,theory(equality)]) ).
cnf(79,plain,
X = complement(complement(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1,14,theory(equality)]),77,17,theory(equality)]) ).
cnf(84,plain,
X = join(complement(join(top,complement(X))),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1,12,theory(equality)]),79,65,theory(equality)]) ).
cnf(100,plain,
join(top,complement(X)) = join(top,complement(join(complement(Y),X))),
inference('PARAMODULATE',[status(thm)],[15,2,theory(equality)]) ).
cnf(102,plain,
join(top,X) = join(top,complement(Y)),
inference('REWRITE',[status(thm)],[25,100,theory(equality)]) ).
cnf(123,plain,
top = join(top,X),
inference('PARAMODULATE',[status(thm)],[14,102,theory(equality)]) ).
cnf(129,plain,
join(composition(join(X,Y),Z),complement(composition(X,Z))) = top,
inference('REWRITE',[status(thm)],[47,123,theory(equality)]) ).
cnf(143,plain,
X = join(zero,X),
inference('REWRITE',[status(thm)],[84,17,123,theory(equality)]) ).
cnf(147,plain,
composition(converse(X),complement(composition(X,top))) = zero,
inference('REWRITE',[status(thm)],[53,143,theory(equality)]) ).
cnf(162,plain,
converse(top) = join(X,converse(top)),
inference('PARAMODULATE',[status(thm)],[27,123,theory(equality)]) ).
cnf(164,plain,
X = join(X,converse(zero)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[27,143,theory(equality)]),8,theory(equality)]) ).
cnf(182,plain,
converse(zero) = zero,
inference('PARAMODULATE',[status(thm)],[143,164,theory(equality)]) ).
cnf(188,plain,
top = converse(top),
inference('PARAMODULATE',[status(thm)],[14,162,theory(equality)]) ).
cnf(195,plain,
composition(top,complement(composition(top,top))) = zero,
inference('PARAMODULATE',[status(thm)],[147,188,theory(equality)]) ).
cnf(218,plain,
X = composition(converse(one),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[34,5,theory(equality)]),8,theory(equality)]) ).
cnf(242,plain,
one = converse(one),
inference('PARAMODULATE',[status(thm)],[5,218,theory(equality)]) ).
cnf(243,plain,
X = composition(one,X),
inference('REWRITE',[status(thm)],[218,242,theory(equality)]) ).
cnf(246,plain,
composition(join(one,X),Y) = join(composition(X,Y),Y),
inference('PARAMODULATE',[status(thm)],[6,243,theory(equality)]) ).
cnf(501,plain,
join(composition(X,Y),complement(composition(zero,Y))) = top,
inference('PARAMODULATE',[status(thm)],[129,143,theory(equality)]) ).
cnf(503,plain,
join(composition(top,X),complement(composition(Y,X))) = top,
inference('PARAMODULATE',[status(thm)],[129,14,theory(equality)]) ).
cnf(598,plain,
join(X,complement(composition(zero,X))) = top,
inference('PARAMODULATE',[status(thm)],[501,243,theory(equality)]) ).
cnf(614,plain,
complement(composition(zero,zero)) = top,
inference('PARAMODULATE',[status(thm)],[143,598,theory(equality)]) ).
cnf(625,plain,
composition(zero,zero) = zero,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[79,614,theory(equality)]),17,theory(equality)]) ).
cnf(631,plain,
composition(X,zero) = composition(join(one,X),zero),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[6,625,theory(equality)]),246,143,theory(equality)]) ).
cnf(669,plain,
join(composition(top,X),complement(X)) = top,
inference('PARAMODULATE',[status(thm)],[503,243,theory(equality)]) ).
cnf(686,plain,
composition(top,top) = top,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[669,17,theory(equality)]),143,theory(equality)]) ).
cnf(687,plain,
composition(top,zero) = zero,
inference('REWRITE',[status(thm)],[195,17,686,theory(equality)]) ).
cnf(704,plain,
zero = composition(X,zero),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[6,687,theory(equality)]),631,246,687,123,theory(equality)]) ).
cnf(713,plain,
composition(zero,'SKOLEMAAAV1') != zero,
inference('REWRITE',[status(thm)],[18,704,theory(equality)]) ).
cnf(714,plain,
zero = composition(zero,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[34,704,theory(equality)]),182,theory(equality)]) ).
cnf(715,plain,
$false,
inference('REWRITE',[status(thm)],[713,714,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL013+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Fri Jul 8 12:02:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p 2022-07-08T12:02:00
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n007.cluster.edu at 2022-07-08T12:02:00
% 0.19/0.48
% 0.19/0.48 ; Recognized commutativity assertion (= (|join| ?X ?Y) (|join| ?Y ?X)).
% 0.19/0.48 ; Recognized associativity assertion (= (|join| ?X (|join| ?Y ?Z)) (|join| (|join| ?X ?Y) ?Z)).
% 0.19/0.48 ; Recognized associativity assertion (= (|composition| ?X (|composition| ?Y ?Z)) (|composition| (|composition| ?X ?Y) ?Z)).
% 0.19/0.48 ; Recognized right identity assertion (= (|composition| ?X |one|) ?X).
% 0.19/0.48 ; Recognized possible right inverse assertion (= |top| (|join| ?X (|complement| ?X))).
% 0.19/0.48 ; Recognized possible right inverse assertion (= |zero| (|meet| ?X (|complement| ?X))).
% 0.19/0.48 ; Declaring join to be commutative.
% 1.10/1.28 ; Declaring join to be associative-commutative.
% 1.10/1.28
% 1.10/1.28 #||
% 1.10/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.10/1.28 % SZS output start Refutation
% See solution above
% 1.10/1.28 ||#
% 1.10/1.28
% 1.10/1.28 ; Summary of computation:
% 1.10/1.28 ; 3185 formulas have been input or derived (from 78 formulas).
% 1.10/1.28 ; 715 (22%) were retained. Of these,
% 1.10/1.28 ; 334 (47%) were simplified or subsumed later,
% 1.10/1.28 ; 381 (53%) are still being kept.
% 1.10/1.28 ;
% 1.10/1.28 ; Run time in seconds excluding printing time:
% 1.10/1.28 ; 0.004 0% Read assertion file (1 call)
% 1.10/1.28 ; 0.001 0% Assert (14 calls)
% 1.10/1.28 ; 0.063 8% Process new row (3,093 calls)
% 1.10/1.28 ; 0.003 0% Resolution (154 calls)
% 1.10/1.28 ; 0.059 7% Paramodulation (77 calls)
% 1.10/1.28 ; 0.003 0% Embedding (285 calls)
% 1.10/1.28 ; 0.000 0% Condensing (1 call)
% 1.10/1.28 ; 0.001 0% Forward subsumption (1 call)
% 1.10/1.28 ; 0.000 0% Backward subsumption (1 call)
% 1.10/1.28 ; 0.294 36% Forward simplification (2,474 calls)
% 1.10/1.28 ; 0.029 4% Backward simplification (436 calls)
% 1.10/1.28 ; 0.029 4% Ordering (7,264 calls)
% 1.10/1.28 ; 0.291 36% Ordering ac (4,547 calls)
% 1.10/1.28 ; 0.000 0% Sortal reasoning (32 calls)
% 1.10/1.28 ; 0.000 0% Purity testing (1 call)
% 1.10/1.28 ; 0.033 4% Other
% 1.10/1.28 ; 0.810 Total
% 1.10/1.28 ; 0.815 Real time
% 1.10/1.28 ;
% 1.10/1.28 ; Term-hash-array has 2,156 terms in all.
% 1.10/1.28 ; Feature-vector-row-index has 0 entries (1 at peak, 1 added, 1 deleted).
% 1.10/1.28 ; Feature-vector-row-index has 1 node (11 at peak, 11 added, 10 deleted).
% 1.10/1.28 ; Retrieved 0 possibly forward subsuming rows in 1 call.
% 1.10/1.28 ; Retrieved 0 possibly backward subsumed rows in 1 call.
% 1.10/1.28 ; Path-index has 1,297 entries (1,787 at peak, 2,242 added, 945 deleted).
% 1.10/1.28 ; Path-index has 1,631 nodes (1,909 at peak, 2,042 added, 411 deleted).
% 1.10/1.28 ; Trie-index has 1,297 entries (1,787 at peak, 2,242 added, 945 deleted).
% 1.10/1.28 ; Trie-index has 877 nodes (1,314 at peak, 1,626 added, 749 deleted).
% 1.10/1.28 ; Retrieved 645,134 generalization terms in 20,908 calls.
% 1.10/1.28 ; Retrieved 1,556 instance terms in 529 calls.
% 1.10/1.28 ; Retrieved 11,105 unifiable terms in 455 calls.
% 1.10/1.28 ;
% 1.10/1.28 ; The agenda of backward simplifiable rows to process has 29 entries:
% 1.10/1.28 ; 29 with value 0
% 1.10/1.28 ; The agenda of rows to process has 13 entries:
% 1.10/1.28 ; 4 with value 18 3 with value 21 1 with value 22
% 1.10/1.28 ; 5 with value 19
% 1.10/1.28 ; The agenda of rows to give has 336 entries:
% 1.10/1.28 ; 2 with value (4 14) 51 with value (4 22) 19 with value (4 30)
% 1.10/1.28 ; 1 with value (4 15) 41 with value (4 23) 8 with value (4 31)
% 1.10/1.28 ; 3 with value (4 16) 34 with value (4 24) 9 with value (4 32)
% 1.10/1.28 ; 14 with value (4 17) 13 with value (4 25) 4 with value (4 33)
% 1.10/1.28 ; 6 with value (4 18) 16 with value (4 26) 2 with value (4 34)
% 1.10/1.28 ; 5 with value (4 19) 11 with value (4 27) 2 with value (4 36)
% 1.10/1.28 ; 26 with value (4 20) 31 with value (4 28) 4 with value (4 37)
% 1.10/1.28 ; 29 with value (4 21) 3 with value (4 29) 2 with value (4 39)
% 1.10/1.28 Evaluation took:
% 1.10/1.28 0.815 seconds of real time
% 1.10/1.28 0.79293 seconds of user run time
% 1.10/1.28 0.021665 seconds of system run time
% 1.10/1.28 [Run times include 0.017 seconds GC run time.]
% 1.10/1.28 0 calls to %EVAL
% 1.10/1.28 0 page faults and
% 1.10/1.28 44,131,456 bytes consed.
% 1.10/1.28 :PROOF-FOUND
% 1.10/1.28 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-08T12:02:01
% 1.10/1.28 :PROOF-FOUND
% 1.10/1.28 *
%------------------------------------------------------------------------------