TSTP Solution File: HEN010-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : HEN010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n012.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 : Sat Jul 16 13:02:32 EDT 2022
% Result : Unsatisfiable 1.88s 2.10s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of clauses : 72 ( 66 unt; 0 nHn; 31 RR)
% Number of literals : 84 ( 19 equ; 14 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 77 ( 35 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal,axiom,
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(less_equal_quotient,axiom,
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(divisor_existence,axiom,
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(quotient_property,axiom,
( ~ quotient(X,Y,Z)
| ~ quotient(Y,U,V)
| ~ quotient(X,U,W)
| ~ quotient(W,V,X1)
| ~ quotient(Z,U,Y1)
| less_equal(X1,Y1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| X = Y ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(identity_is_largest,axiom,
less_equal(X,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',identity_is_largest) ).
cnf(closure,axiom,
quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(well_defined,axiom,
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,U)
| Z = U ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',well_defined) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
cnf(prove_idQa_equals_idQa_Q__idQ_idQa,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
cnf(14,plain,
quotient(X,identity,zero),
inference('HYPERRESOLVE',[status(thm)],[quotient_less_equal,identity_is_largest]) ).
cnf(15,plain,
quotient(zero,X,zero),
inference('HYPERRESOLVE',[status(thm)],[quotient_less_equal,zero_is_smallest]) ).
cnf(16,plain,
less_equal(idQa_Q__idQ_idQa,idQa),
inference('HYPERRESOLVE',[status(thm)],[divisor_existence,identity_divide_idQ_idQa]) ).
cnf(17,plain,
less_equal(divide(X,Y),X),
inference('HYPERRESOLVE',[status(thm)],[divisor_existence,closure]) ).
cnf(28,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,identity_divide_a,closure,identity_divide_idQa,closure,closure]) ).
cnf(32,plain,
less_equal(divide(idQa,idQa),divide(divide(identity,identity),a)),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,closure,identity_divide_a,identity_divide_a,closure,closure]) ).
cnf(36,plain,
less_equal(divide(divide(X,idQ_idQa),idQa_Q__idQ_idQa),divide(divide(X,idQa),idQ_idQa)),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,closure,identity_divide_idQ_idQa,closure,closure,closure]) ).
cnf(37,plain,
less_equal(divide(divide(X,idQa),idQ_idQa),divide(divide(X,identity),idQa)),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,closure,identity_divide_idQa,closure,closure,closure]) ).
cnf(38,plain,
less_equal(divide(divide(X,a),idQa),divide(divide(X,identity),a)),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,closure,identity_divide_a,closure,closure,closure]) ).
cnf(41,plain,
less_equal(divide(idQa,divide(X,a)),divide(divide(identity,X),a)),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,closure,closure,identity_divide_a,closure,closure]) ).
cnf(43,plain,
~ less_equal(idQa,idQa_Q__idQ_idQa),
inference('UR-RESOLVE',[status(thm)],[less_equal_and_equal,16,prove_idQa_equals_idQa_Q__idQ_idQa]) ).
cnf(45,plain,
zero = divide(X,identity),
inference('HYPERRESOLVE',[status(thm)],[well_defined,14,closure]) ).
cnf(46,plain,
less_equal(divide(divide(X,idQa),idQ_idQa),divide(zero,idQa)),
inference('REWRITE',[status(thm)],[37,45,theory(equality)]) ).
cnf(47,plain,
less_equal(divide(divide(X,a),idQa),divide(zero,a)),
inference('REWRITE',[status(thm)],[38,45,theory(equality)]) ).
cnf(49,plain,
less_equal(divide(idQa,idQa),divide(zero,a)),
inference('REWRITE',[status(thm)],[32,45,theory(equality)]) ).
cnf(51,plain,
less_equal(divide(divide(X,Y),divide(identity,Y)),divide(zero,Y)),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,14,closure,closure,closure,closure]) ).
cnf(52,plain,
zero = divide(zero,X),
inference('HYPERRESOLVE',[status(thm)],[well_defined,15,closure]) ).
cnf(53,plain,
less_equal(divide(divide(X,Y),divide(identity,Y)),zero),
inference('REWRITE',[status(thm)],[51,52,theory(equality)]) ).
cnf(55,plain,
less_equal(divide(divide(X,a),idQa),zero),
inference('REWRITE',[status(thm)],[47,52,theory(equality)]) ).
cnf(56,plain,
less_equal(divide(idQa,idQa),zero),
inference('REWRITE',[status(thm)],[49,52,theory(equality)]) ).
cnf(57,plain,
less_equal(divide(divide(X,idQa),idQ_idQa),zero),
inference('REWRITE',[status(thm)],[46,52,theory(equality)]) ).
cnf(73,plain,
quotient(divide(X,Y),X,zero),
inference('HYPERRESOLVE',[status(thm)],[quotient_less_equal,17]) ).
cnf(74,plain,
divide(idQa,idQa) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,56,zero_is_smallest]) ).
cnf(76,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference('REWRITE',[status(thm)],[28,74,theory(equality)]) ).
cnf(95,plain,
zero = divide(divide(X,Y),X),
inference('HYPERRESOLVE',[status(thm)],[well_defined,73,closure]) ).
cnf(100,plain,
less_equal(divide(divide(divide(X,Y),Z),divide(X,Z)),zero),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,73,closure,closure,closure,15]) ).
cnf(108,plain,
divide(divide(X,a),idQa) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,55,zero_is_smallest]) ).
cnf(109,plain,
divide(divide(X,idQa),idQ_idQa) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,57,zero_is_smallest]) ).
cnf(110,plain,
less_equal(divide(divide(X,idQ_idQa),idQa_Q__idQ_idQa),zero),
inference('REWRITE',[status(thm)],[36,109,theory(equality)]) ).
cnf(111,plain,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,76,zero_is_smallest]) ).
cnf(112,plain,
divide(divide(X,idQ_idQa),idQa_Q__idQ_idQa) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,110,zero_is_smallest]) ).
cnf(124,plain,
quotient(divide(X,a),idQa,zero),
inference('PARAMODULATE',[status(thm)],[closure,108,theory(equality)]) ).
cnf(125,plain,
less_equal(divide(X,a),idQa),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,124]) ).
cnf(131,plain,
quotient(divide(X,idQa),idQ_idQa,zero),
inference('PARAMODULATE',[status(thm)],[closure,109,theory(equality)]) ).
cnf(132,plain,
less_equal(divide(X,idQa),idQ_idQa),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,131]) ).
cnf(137,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference('PARAMODULATE',[status(thm)],[closure,111,theory(equality)]) ).
cnf(138,plain,
less_equal(idQ_idQa,divide(a,idQa)),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,137]) ).
cnf(146,plain,
idQ_idQa = divide(a,idQa),
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,138,132]) ).
cnf(147,plain,
quotient(divide(X,idQ_idQa),idQa_Q__idQ_idQa,zero),
inference('PARAMODULATE',[status(thm)],[closure,112,theory(equality)]) ).
cnf(149,plain,
less_equal(divide(divide(X,idQa_Q__idQ_idQa),divide(idQ_idQa,idQa_Q__idQ_idQa)),zero),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,147,closure,closure,closure,closure]) ).
cnf(208,plain,
divide(divide(X,Y),divide(identity,Y)) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,53,zero_is_smallest]) ).
cnf(231,plain,
quotient(divide(X,Y),divide(identity,Y),zero),
inference('PARAMODULATE',[status(thm)],[closure,208,theory(equality)]) ).
cnf(232,plain,
less_equal(divide(X,Y),divide(identity,Y)),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,231]) ).
cnf(242,plain,
divide(divide(X,idQa_Q__idQ_idQa),divide(idQ_idQa,idQa_Q__idQ_idQa)) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,149,zero_is_smallest]) ).
cnf(346,plain,
quotient(divide(X,idQa_Q__idQ_idQa),divide(idQ_idQa,idQa_Q__idQ_idQa),zero),
inference('PARAMODULATE',[status(thm)],[closure,242,theory(equality)]) ).
cnf(350,plain,
less_equal(divide(X,idQa_Q__idQ_idQa),divide(idQ_idQa,idQa_Q__idQ_idQa)),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,346]) ).
cnf(353,plain,
divide(identity,idQa_Q__idQ_idQa) = divide(idQ_idQa,idQa_Q__idQ_idQa),
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,350,232]) ).
cnf(383,plain,
less_equal(divide(idQa,divide(idQa_Q__idQ_idQa,a)),divide(divide(idQ_idQa,idQa_Q__idQ_idQa),a)),
inference('PARAMODULATE',[status(thm)],[41,353,theory(equality)]) ).
cnf(397,plain,
divide(divide(divide(X,Y),Z),divide(X,Z)) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,100,zero_is_smallest]) ).
cnf(522,plain,
quotient(divide(divide(X,Y),Z),divide(X,Z),zero),
inference('PARAMODULATE',[status(thm)],[closure,397,theory(equality)]) ).
cnf(545,plain,
quotient(divide(idQ_idQa,X),divide(a,X),zero),
inference('PARAMODULATE',[status(thm)],[522,146,theory(equality)]) ).
cnf(581,plain,
less_equal(divide(idQ_idQa,X),divide(a,X)),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,545]) ).
cnf(591,plain,
divide(idQ_idQa,idQa_Q__idQ_idQa) = divide(a,idQa_Q__idQ_idQa),
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,581,350]) ).
cnf(608,plain,
less_equal(divide(idQa,divide(idQa_Q__idQ_idQa,a)),zero),
inference('REWRITE',[status(thm)],[383,95,591,theory(equality)]) ).
cnf(710,plain,
divide(idQa,divide(idQa_Q__idQ_idQa,a)) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,608,zero_is_smallest]) ).
cnf(1002,plain,
quotient(idQa,divide(idQa_Q__idQ_idQa,a),zero),
inference('PARAMODULATE',[status(thm)],[closure,710,theory(equality)]) ).
cnf(1026,plain,
less_equal(idQa,divide(idQa_Q__idQ_idQa,a)),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,1002]) ).
cnf(1031,plain,
idQa = divide(idQa_Q__idQ_idQa,a),
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,1026,125]) ).
cnf(1033,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,1031,theory(equality)]),43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : HEN010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n012.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 1 14:36:02 EDT 2022
% 0.13/0.33 % 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 2022-07-01T14:36:02
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n012.cluster.edu at 2022-07-01T14:36:02
% 0.19/0.47
% 0.19/0.47 ; Recognized relation function assertion (|quotient| ?X ?Y (|divide| ?X ?Y)).
% 1.88/2.10 ; Recognized relation functionality assertion (OR (NOT (|quotient| ?X ?Y ?Z)) (NOT (|quotient| ?X ?Y ?U)) (= ?Z ?U)).
% 1.88/2.10
% 1.88/2.10 #||
% 1.88/2.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.88/2.10 % SZS output start Refutation
% See solution above
% 1.88/2.11 ||#
% 1.88/2.11
% 1.88/2.11 ; Summary of computation:
% 1.88/2.11 ; 55396 formulas have been input or derived (from 274 formulas).
% 1.88/2.11 ; 1033 ( 2%) were retained. Of these,
% 1.88/2.11 ; 430 (42%) were simplified or subsumed later,
% 1.88/2.11 ; 603 (58%) are still being kept.
% 1.88/2.11 ;
% 1.88/2.11 ; Run time in seconds excluding printing time:
% 1.88/2.11 ; 0.002 0% Read assertion file (1 call)
% 1.88/2.11 ; 0.000 0% Assert (13 calls)
% 1.88/2.11 ; 0.117 7% Process new row (30,301 calls)
% 1.88/2.11 ; 1.094 67% Resolution (546 calls)
% 1.88/2.11 ; 0.033 2% Paramodulation (273 calls)
% 1.88/2.11 ; 0.000 0% Condensing (6 calls)
% 1.88/2.11 ; 0.000 0% Forward subsumption (6 calls)
% 1.88/2.11 ; 0.000 0% Backward subsumption (6 calls)
% 1.88/2.11 ; 0.000 0% Clause clause subsumption (2 calls)
% 1.88/2.11 ; 0.253 15% Forward simplification (30,112 calls)
% 1.88/2.11 ; 0.028 2% Backward simplification (1,033 calls)
% 1.88/2.11 ; 0.004 0% Ordering (3,286 calls)
% 1.88/2.11 ; 0.001 0% Sortal reasoning (32 calls)
% 1.88/2.11 ; 0.000 0% Purity testing (1 call)
% 1.88/2.11 ; 0.105 6% Other
% 1.88/2.11 ; 1.637 Total
% 1.88/2.11 ; 1.646 Real time
% 1.88/2.11 ;
% 1.88/2.11 ; Term-hash-array has 2,220 terms in all.
% 1.88/2.11 ; Feature-vector-row-index has 6 entries (6 at peak, 6 added, 0 deleted).
% 1.88/2.11 ; Feature-vector-row-index has 12 nodes (12 at peak, 12 added, 0 deleted).
% 1.88/2.11 ; Retrieved 1 possibly forward subsuming row in 6 calls.
% 1.88/2.11 ; Retrieved 1 possibly backward subsumed row in 6 calls.
% 1.88/2.11 ; Path-index has 1,392 entries (1,504 at peak, 2,260 added, 868 deleted).
% 1.88/2.11 ; Path-index has 1,055 nodes (1,086 at peak, 1,316 added, 261 deleted).
% 1.88/2.11 ; Trie-index has 1,392 entries (1,504 at peak, 2,260 added, 868 deleted).
% 1.88/2.11 ; Trie-index has 6,347 nodes (6,763 at peak, 9,825 added, 3,478 deleted).
% 1.88/2.11 ; Retrieved 118,068 generalization terms in 93,128 calls.
% 1.88/2.11 ; Retrieved 2,153 instance terms in 1,026 calls.
% 1.88/2.11 ; Retrieved 730,325 unifiable terms in 225,911 calls.
% 1.88/2.11 ;
% 1.88/2.11 ; The agenda of rows to process has 44 entries:
% 1.88/2.11 ; 1 with value 18 2 with value 23 6 with value 27
% 1.88/2.11 ; 4 with value 19 6 with value 24 4 with value 28
% 1.88/2.11 ; 5 with value 21 2 with value 25 6 with value 29
% 1.88/2.11 ; 2 with value 22 6 with value 26
% 1.88/2.11 ; The agenda of rows to give has 449 entries:
% 1.88/2.11 ; 38 with value (4 21) 47 with value (4 26) 13 with value (4 31)
% 1.88/2.11 ; 40 with value (4 22) 75 with value (4 27) 2 with value (4 32)
% 1.88/2.11 ; 34 with value (4 23) 44 with value (4 28) 7 with value (4 33)
% 1.88/2.11 ; 34 with value (4 24) 35 with value (4 29) 2 with value (4 35)
% 1.88/2.11 ; 56 with value (4 25) 19 with value (4 30) 3 with value (4 36)
% 1.88/2.11 Evaluation took:
% 1.88/2.11 1.647 seconds of real time
% 1.88/2.11 1.529824 seconds of user run time
% 1.88/2.11 0.115901 seconds of system run time
% 1.88/2.11 [Run times include 0.071 seconds GC run time.]
% 1.88/2.11 0 calls to %EVAL
% 1.88/2.11 0 page faults and
% 1.88/2.11 167,962,384 bytes consed.
% 1.88/2.11 :PROOF-FOUND
% 1.88/2.11 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-01T14:36:04
% 1.88/2.11 :PROOF-FOUND
% 1.88/2.11 *
%------------------------------------------------------------------------------