TSTP Solution File: HEN009-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : HEN009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n014.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 13:02:29 EDT 2022
% Result : Unsatisfiable 0.86s 1.08s
% Output : Refutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of clauses : 73 ( 67 unt; 0 nHn; 46 RR)
% Number of literals : 85 ( 18 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 : 51 ( 24 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(identity,idQ_idQa,idQ__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
cnf(prove_one_inversion_equals_three,negated_conjecture,
idQa != idQ__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_one_inversion_equals_three) ).
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(divide(X,Y),X),
inference('HYPERRESOLVE',[status(thm)],[divisor_existence,closure]) ).
cnf(22,plain,
less_equal(divide(idQa,divide(idQ_idQa,a)),divide(idQ__idQ_idQa,a)),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,identity_divide_idQ_idQa,closure,identity_divide_a,closure,closure]) ).
cnf(27,plain,
less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),divide(idQ_idQa,idQ_idQa)),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,identity_divide_idQa,closure,identity_divide_idQ_idQa,closure,closure]) ).
cnf(29,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(idQ_idQa,idQ_idQa),divide(divide(identity,identity),idQa)),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,closure,identity_divide_idQa,identity_divide_idQa,closure,closure]) ).
cnf(33,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(37,plain,
less_equal(divide(divide(X,idQ_idQa),idQ__idQ_idQa),divide(divide(X,identity),idQ_idQa)),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,closure,identity_divide_idQ_idQa,closure,closure,closure]) ).
cnf(38,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(39,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(44,plain,
zero = divide(X,identity),
inference('HYPERRESOLVE',[status(thm)],[well_defined,14,closure]) ).
cnf(45,plain,
less_equal(divide(divide(X,idQ_idQa),idQ__idQ_idQa),divide(zero,idQ_idQa)),
inference('REWRITE',[status(thm)],[37,44,theory(equality)]) ).
cnf(46,plain,
less_equal(divide(divide(X,idQa),idQ_idQa),divide(zero,idQa)),
inference('REWRITE',[status(thm)],[38,44,theory(equality)]) ).
cnf(47,plain,
less_equal(divide(divide(X,a),idQa),divide(zero,a)),
inference('REWRITE',[status(thm)],[39,44,theory(equality)]) ).
cnf(49,plain,
less_equal(divide(idQ_idQa,idQ_idQa),divide(zero,idQa)),
inference('REWRITE',[status(thm)],[32,44,theory(equality)]) ).
cnf(50,plain,
less_equal(divide(idQa,idQa),divide(zero,a)),
inference('REWRITE',[status(thm)],[33,44,theory(equality)]) ).
cnf(52,plain,
zero = divide(zero,X),
inference('HYPERRESOLVE',[status(thm)],[well_defined,15,closure]) ).
cnf(54,plain,
less_equal(divide(divide(X,a),idQa),zero),
inference('REWRITE',[status(thm)],[47,52,theory(equality)]) ).
cnf(55,plain,
less_equal(divide(idQa,idQa),zero),
inference('REWRITE',[status(thm)],[50,52,theory(equality)]) ).
cnf(56,plain,
less_equal(divide(divide(X,idQa),idQ_idQa),zero),
inference('REWRITE',[status(thm)],[46,52,theory(equality)]) ).
cnf(57,plain,
less_equal(divide(idQ_idQa,idQ_idQa),zero),
inference('REWRITE',[status(thm)],[49,52,theory(equality)]) ).
cnf(58,plain,
less_equal(divide(divide(X,idQ_idQa),idQ__idQ_idQa),zero),
inference('REWRITE',[status(thm)],[45,52,theory(equality)]) ).
cnf(64,plain,
quotient(divide(X,Y),X,zero),
inference('HYPERRESOLVE',[status(thm)],[quotient_less_equal,16]) ).
cnf(65,plain,
divide(idQa,idQa) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,55,zero_is_smallest]) ).
cnf(67,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference('REWRITE',[status(thm)],[29,65,theory(equality)]) ).
cnf(68,plain,
divide(idQ_idQa,idQ_idQa) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,57,zero_is_smallest]) ).
cnf(70,plain,
less_equal(divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)),zero),
inference('REWRITE',[status(thm)],[27,68,theory(equality)]) ).
cnf(96,plain,
divide(divide(X,a),idQa) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,54,zero_is_smallest]) ).
cnf(97,plain,
divide(divide(X,idQa),idQ_idQa) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,56,zero_is_smallest]) ).
cnf(98,plain,
divide(divide(X,idQ_idQa),idQ__idQ_idQa) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,58,zero_is_smallest]) ).
cnf(99,plain,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,67,zero_is_smallest]) ).
cnf(100,plain,
divide(idQ__idQ_idQa,divide(idQa,idQ_idQa)) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,70,zero_is_smallest]) ).
cnf(111,plain,
quotient(divide(X,a),idQa,zero),
inference('PARAMODULATE',[status(thm)],[closure,96,theory(equality)]) ).
cnf(112,plain,
less_equal(divide(X,a),idQa),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,111]) ).
cnf(118,plain,
quotient(divide(X,idQa),idQ_idQa,zero),
inference('PARAMODULATE',[status(thm)],[closure,97,theory(equality)]) ).
cnf(119,plain,
less_equal(divide(X,idQa),idQ_idQa),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,118]) ).
cnf(125,plain,
quotient(divide(X,idQ_idQa),idQ__idQ_idQa,zero),
inference('PARAMODULATE',[status(thm)],[closure,98,theory(equality)]) ).
cnf(126,plain,
less_equal(divide(X,idQ_idQa),idQ__idQ_idQa),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,125]) ).
cnf(131,plain,
quotient(idQ_idQa,divide(a,idQa),zero),
inference('PARAMODULATE',[status(thm)],[closure,99,theory(equality)]) ).
cnf(132,plain,
less_equal(idQ_idQa,divide(a,idQa)),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,131]) ).
cnf(140,plain,
idQ_idQa = divide(a,idQa),
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,132,119]) ).
cnf(141,plain,
quotient(idQ__idQ_idQa,divide(idQa,idQ_idQa),zero),
inference('PARAMODULATE',[status(thm)],[closure,100,theory(equality)]) ).
cnf(142,plain,
less_equal(idQ__idQ_idQa,divide(idQa,idQ_idQa)),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,141]) ).
cnf(149,plain,
idQ__idQ_idQa = divide(idQa,idQ_idQa),
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,142,126]) ).
cnf(151,plain,
quotient(idQ_idQa,a,zero),
inference('PARAMODULATE',[status(thm)],[64,140,theory(equality)]) ).
cnf(153,plain,
zero = divide(idQ_idQa,a),
inference('HYPERRESOLVE',[status(thm)],[well_defined,151,closure]) ).
cnf(154,plain,
less_equal(divide(idQa,zero),divide(idQ__idQ_idQa,a)),
inference('REWRITE',[status(thm)],[22,153,theory(equality)]) ).
cnf(160,plain,
quotient(divide(idQa,zero),divide(idQ__idQ_idQa,a),zero),
inference('HYPERRESOLVE',[status(thm)],[quotient_less_equal,154]) ).
cnf(167,plain,
less_equal(idQ__idQ_idQa,idQa),
inference('PARAMODULATE',[status(thm)],[16,149,theory(equality)]) ).
cnf(170,plain,
~ less_equal(idQa,idQ__idQ_idQa),
inference('UR-RESOLVE',[status(thm)],[less_equal_and_equal,167,prove_one_inversion_equals_three]) ).
cnf(192,plain,
less_equal(divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero),zero),
inference('HYPERRESOLVE',[status(thm)],[quotient_property,160,closure,15,closure,closure]) ).
cnf(263,plain,
divide(divide(idQa,divide(idQ__idQ_idQa,a)),zero) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,192,zero_is_smallest]) ).
cnf(354,plain,
quotient(divide(idQa,divide(idQ__idQ_idQa,a)),zero,zero),
inference('PARAMODULATE',[status(thm)],[closure,263,theory(equality)]) ).
cnf(358,plain,
less_equal(divide(idQa,divide(idQ__idQ_idQa,a)),zero),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,354]) ).
cnf(361,plain,
divide(idQa,divide(idQ__idQ_idQa,a)) = zero,
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,358,zero_is_smallest]) ).
cnf(385,plain,
quotient(idQa,divide(idQ__idQ_idQa,a),zero),
inference('PARAMODULATE',[status(thm)],[closure,361,theory(equality)]) ).
cnf(392,plain,
less_equal(idQa,divide(idQ__idQ_idQa,a)),
inference('HYPERRESOLVE',[status(thm)],[less_equal_quotient,385]) ).
cnf(399,plain,
idQa = divide(idQ__idQ_idQa,a),
inference('HYPERRESOLVE',[status(thm)],[less_equal_and_equal,392,112]) ).
cnf(409,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,399,theory(equality)]),170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 1 14:07:10 EDT 2022
% 0.12/0.34 % 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 2022-07-01T14:07:11
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n014.cluster.edu at 2022-07-01T14:07:11
% 0.19/0.48
% 0.19/0.48 ; Recognized relation function assertion (|quotient| ?X ?Y (|divide| ?X ?Y)).
% 0.86/1.08 ; Recognized relation functionality assertion (OR (NOT (|quotient| ?X ?Y ?Z)) (NOT (|quotient| ?X ?Y ?U)) (= ?Z ?U)).
% 0.86/1.08
% 0.86/1.08 #||
% 0.86/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.86/1.08 % SZS output start Refutation
% See solution above
% 0.91/1.08 ||#
% 0.91/1.08
% 0.91/1.08 ; Summary of computation:
% 0.91/1.08 ; 18747 formulas have been input or derived (from 155 formulas).
% 0.91/1.08 ; 409 ( 2%) were retained. Of these,
% 0.91/1.08 ; 177 (43%) were simplified or subsumed later,
% 0.91/1.08 ; 232 (57%) are still being kept.
% 0.91/1.08 ;
% 0.91/1.08 ; Run time in seconds excluding printing time:
% 0.91/1.08 ; 0.003 0% Read assertion file (1 call)
% 0.91/1.08 ; 0.001 0% Assert (13 calls)
% 0.91/1.08 ; 0.049 8% Process new row (11,522 calls)
% 0.91/1.08 ; 0.382 63% Resolution (308 calls)
% 0.91/1.08 ; 0.009 1% Paramodulation (154 calls)
% 0.91/1.08 ; 0.000 0% Condensing (6 calls)
% 0.91/1.08 ; 0.000 0% Forward subsumption (6 calls)
% 0.91/1.08 ; 0.000 0% Backward subsumption (6 calls)
% 0.91/1.08 ; 0.000 0% Clause clause subsumption (2 calls)
% 0.91/1.08 ; 0.090 15% Forward simplification (11,492 calls)
% 0.91/1.08 ; 0.012 2% Backward simplification (409 calls)
% 0.91/1.08 ; 0.000 0% Ordering (879 calls)
% 0.91/1.08 ; 0.000 0% Sortal reasoning (32 calls)
% 0.91/1.08 ; 0.000 0% Purity testing (1 call)
% 0.91/1.08 ; 0.062 10% Other
% 0.91/1.08 ; 0.608 Total
% 0.91/1.08 ; 0.612 Real time
% 0.91/1.08 ;
% 0.91/1.08 ; Term-hash-array has 959 terms in all.
% 0.91/1.08 ; Feature-vector-row-index has 6 entries (6 at peak, 6 added, 0 deleted).
% 0.91/1.08 ; Feature-vector-row-index has 12 nodes (12 at peak, 12 added, 0 deleted).
% 0.91/1.08 ; Retrieved 1 possibly forward subsuming row in 6 calls.
% 0.91/1.08 ; Retrieved 1 possibly backward subsumed row in 6 calls.
% 0.91/1.08 ; Path-index has 595 entries (629 at peak, 987 added, 392 deleted).
% 0.91/1.08 ; Path-index has 610 nodes (623 at peak, 740 added, 130 deleted).
% 0.91/1.08 ; Trie-index has 595 entries (629 at peak, 987 added, 392 deleted).
% 0.91/1.08 ; Trie-index has 2,366 nodes (2,537 at peak, 3,754 added, 1,388 deleted).
% 0.91/1.08 ; Retrieved 35,506 generalization terms in 32,283 calls.
% 0.91/1.08 ; Retrieved 798 instance terms in 402 calls.
% 0.91/1.08 ; Retrieved 218,372 unifiable terms in 80,296 calls.
% 0.91/1.08 ;
% 0.91/1.08 ; The agenda of rows to process has 17 entries:
% 0.91/1.08 ; 1 with value 15 1 with value 19 2 with value 24
% 0.91/1.08 ; 3 with value 16 1 with value 21 3 with value 25
% 0.91/1.08 ; 3 with value 18 3 with value 23
% 0.91/1.08 ; The agenda of rows to give has 140 entries:
% 0.91/1.08 ; 1 with value (4 17) 10 with value (4 22) 10 with value (4 27)
% 0.91/1.08 ; 7 with value (4 18) 8 with value (4 23) 3 with value (4 29)
% 0.91/1.08 ; 20 with value (4 19) 10 with value (4 24) 6 with value (4 30)
% 0.91/1.08 ; 21 with value (4 20) 12 with value (4 25) 3 with value (4 31)
% 0.91/1.08 ; 18 with value (4 21) 11 with value (4 26)
% 0.91/1.08 Evaluation took:
% 0.91/1.08 0.612 seconds of real time
% 0.91/1.08 0.566237 seconds of user run time
% 0.91/1.08 0.04599 seconds of system run time
% 0.91/1.08 [Run times include 0.017 seconds GC run time.]
% 0.91/1.08 0 calls to %EVAL
% 0.91/1.08 0 page faults and
% 0.91/1.08 57,132,360 bytes consed.
% 0.91/1.08 :PROOF-FOUND
% 0.91/1.08 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-01T14:07:11
% 0.91/1.08 :PROOF-FOUND
% 0.91/1.08 *
%------------------------------------------------------------------------------