TSTP Solution File: ALG369-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG369-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n011.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 : 300s
% DateTime : Tue Aug 22 10:32:37 EDT 2023
% Result : Unsatisfiable 25.59s 10.84s
% Output : CNFRefutation 25.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 82
% Syntax : Number of formulae : 90 ( 9 unt; 77 typ; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 73 >; 17 *; 0 +; 0 <<)
% Number of predicates : 62 ( 61 usr; 2 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 3 con; 0-3 aty)
% Number of variables : 3 (; 3 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > class_SEQ_Obanach > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osgn__if > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring__abs > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Olordered__ring > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odivision__ring > class_Ring__and__Field_Odivision__by__zero > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Oabs__if > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__field > class_RealVector_Oreal__div__algebra > class_RealVector_Oreal__algebra__1 > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Int_Onumber__ring > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Oinverse__class_Odivide > v_sko__CHAINED__1 > c_Transcendental_Oexp > c_RealVector_Oof__real > c_RealVector_Onorm__class_Onorm > c_HOL_Osgn__class_Osgn > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > #nlpp > c_Transcendental_Oln > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > v_thesis____ > v_m____ > v_e > tc_RealDef_Oreal
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(c_Transcendental_Oln,type,
c_Transcendental_Oln: $i > $i ).
tff(class_Ring__and__Field_Opordered__ring__abs,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_HOL_Oinverse__class_Oinverse,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(class_RealVector_Oreal__normed__field,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add__abs,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(v_e,type,
v_e: $i ).
tff(v_thesis____,type,
v_thesis____: $o ).
tff(class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(c_HOL_Oinverse__class_Odivide,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Odivision__by__zero,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(class_SEQ_Obanach,type,
class_SEQ_Obanach: $i > $o ).
tff(class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(v_sko__CHAINED__1,type,
v_sko__CHAINED__1: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(class_RealVector_Oreal__normed__div__algebra,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__mult,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(v_m____,type,
v_m____: $i ).
tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_Ring__and__Field_Oabs__if,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(class_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(class_RealVector_Oreal__algebra__1,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(c_Transcendental_Oexp,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Omult__mono1,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(c_HOL_Osgn__class_Osgn,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(c_RealVector_Onorm__class_Onorm,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Olordered__ab__group__add__abs,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(class_Ring__and__Field_Olordered__ring,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(class_Ring__and__Field_Osgn__if,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
tff(class_Ring__and__Field_Omult__mono,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(c_HOL_Oabs__class_Oabs,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_RealVector_Oof__real,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(class_Ring__and__Field_Odivision__ring,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(class_RealVector_Oreal__field,type,
class_RealVector_Oreal__field: $i > $o ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(class_RealVector_Oreal__div__algebra,type,
class_RealVector_Oreal__div__algebra: $i > $o ).
tff(f_5184,axiom,
c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_5185,axiom,
c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_5186,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_5188,axiom,
~ v_thesis____,
file(unknown,unknown) ).
tff(f_4735,axiom,
! [V_d] :
( v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(c_1132,plain,
c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_5184]) ).
tff(c_1134,plain,
c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_5185]) ).
tff(c_1136,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_5186]) ).
tff(c_1138,plain,
~ v_thesis____,
inference(cnfTransformation,[status(thm)],[f_5188]) ).
tff(c_1030,plain,
! [V_d_1491] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d_1491,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d_1491,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d_1491,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_thesis____ ),
inference(cnfTransformation,[status(thm)],[f_4735]) ).
tff(c_53161,plain,
! [V_d_2376] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d_2376,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d_2376,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d_2376,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(negUnitSimplification,[status(thm)],[c_1138,c_1030]) ).
tff(c_53282,plain,
( ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1136,c_53161]) ).
tff(c_53373,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1132,c_1134,c_53282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : ALG369-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.37 % Computer : n011.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu Aug 3 20:23:06 EDT 2023
% 0.14/0.37 % CPUTime :
% 25.59/10.84 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.59/10.85
% 25.59/10.85 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.59/10.88
% 25.59/10.88 Inference rules
% 25.59/10.88 ----------------------
% 25.59/10.88 #Ref : 10
% 25.59/10.88 #Sup : 11281
% 25.59/10.88 #Fact : 6
% 25.59/10.88 #Define : 0
% 25.59/10.88 #Split : 4
% 25.59/10.88 #Chain : 0
% 25.59/10.88 #Close : 0
% 25.59/10.88
% 25.59/10.88 Ordering : KBO
% 25.59/10.88
% 25.59/10.88 Simplification rules
% 25.59/10.88 ----------------------
% 25.59/10.88 #Subsume : 2481
% 25.59/10.88 #Demod : 7411
% 25.59/10.88 #Tautology : 3392
% 25.59/10.88 #SimpNegUnit : 505
% 25.59/10.88 #BackRed : 5
% 25.59/10.88
% 25.59/10.88 #Partial instantiations: 0
% 25.59/10.88 #Strategies tried : 1
% 25.59/10.88
% 25.59/10.88 Timing (in seconds)
% 25.59/10.88 ----------------------
% 25.59/10.88 Preprocessing : 1.54
% 25.59/10.88 Parsing : 0.90
% 25.59/10.88 CNF conversion : 0.12
% 25.59/10.88 Main loop : 8.12
% 25.59/10.88 Inferencing : 1.47
% 25.59/10.88 Reduction : 3.84
% 25.59/10.88 Demodulation : 2.89
% 25.59/10.88 BG Simplification : 0.23
% 25.59/10.88 Subsumption : 2.17
% 25.59/10.88 Abstraction : 0.15
% 25.59/10.88 MUC search : 0.00
% 25.59/10.88 Cooper : 0.00
% 25.59/10.88 Total : 9.71
% 25.59/10.88 Index Insertion : 0.00
% 25.59/10.88 Index Deletion : 0.00
% 25.59/10.88 Index Matching : 0.00
% 25.59/10.88 BG Taut test : 0.00
%------------------------------------------------------------------------------