TSTP Solution File: ALG377-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG377-1 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n032.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 10:32:38 EDT 2023
% Result : Unsatisfiable 47.13s 31.45s
% Output : CNFRefutation 47.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 63
% Syntax : Number of formulae : 70 ( 9 unt; 58 typ; 0 def)
% Number of atoms : 20 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 70 ( 53 >; 17 *; 0 +; 0 <<)
% Number of predicates : 40 ( 39 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 12 (; 12 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odivision__by__zero > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Oabs__if > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__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_Oordered__ab__group__add > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Nat_Osemiring__char__0 > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > class_Divides_Osemiring__div > class_Divides_Oring__div > c_HOL_Oplus__class_Oplus > c_HOL_Oinverse__class_Odivide > c_Divides_Odiv__class_Omod > c_Divides_Odiv__class_Odiv > c_RealVector_Onorm__class_Onorm > c_RealDef_Oreal > c_Nat_Osemiring__1__class_Oof__nat > c_HOL_Ouminus__class_Ouminus > c_HOL_Oabs__class_Oabs > #nlpp > v_f____ > c_Suc > c_RComplete_Onatfloor > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > v_s____ > v_N2____ > v_N1____ > tc_nat > tc_RealDef_Oreal
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_OrderedGroup_Oordered__ab__group__add,type,
class_OrderedGroup_Oordered__ab__group__add: $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_RealDef_Oreal,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $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(c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $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(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_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(c_RComplete_Onatfloor,type,
c_RComplete_Onatfloor: $i > $i ).
tff(class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(v_N1____,type,
v_N1____: $i ).
tff(v_N2____,type,
v_N2____: $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(c_Suc,type,
c_Suc: $i > $i ).
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_Divides_Oring__div,type,
class_Divides_Oring__div: $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(tc_nat,type,
tc_nat: $i ).
tff(c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $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_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: ( $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_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(c_HOL_Ouminus__class_Ouminus,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(v_f____,type,
v_f____: $i > $i ).
tff(class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
tff(c_HOL_Oabs__class_Oabs,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $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_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(v_s____,type,
v_s____: $i ).
tff(f_3611,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3588,axiom,
c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3149,axiom,
! [V_w] : c_lessequals(V_w,V_w,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_3220,axiom,
! [V_a,T_a,V_d,V_c,V_b] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a) ),
file(unknown,unknown) ).
tff(f_3590,axiom,
~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(c_1056,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_3611]) ).
tff(c_1012,plain,
c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_3588]) ).
tff(c_860,plain,
! [V_w_1003] : c_lessequals(V_w_1003,V_w_1003,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_3149]) ).
tff(c_890,plain,
! [V_a_1036,V_c_1039,V_d_1038,T_a_1037,V_b_1040] :
( ~ c_lessequals(V_a_1036,V_b_1040,T_a_1037)
| ~ c_lessequals(V_c_1039,V_d_1038,T_a_1037)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a_1036,V_c_1039,T_a_1037),c_HOL_Oplus__class_Oplus(V_b_1040,V_d_1038,T_a_1037),T_a_1037)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a_1037) ),
inference(cnfTransformation,[status(thm)],[f_3220]) ).
tff(c_1014,plain,
~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_3590]) ).
tff(c_165525,plain,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_890,c_1014]) ).
tff(c_165602,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1056,c_1012,c_860,c_165525]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG377-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.09 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Thu Aug 3 20:18:06 EDT 2023
% 0.08/0.29 % CPUTime :
% 47.13/31.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.13/31.45
% 47.13/31.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 47.20/31.48
% 47.20/31.48 Inference rules
% 47.20/31.48 ----------------------
% 47.20/31.48 #Ref : 45
% 47.20/31.48 #Sup : 35086
% 47.20/31.48 #Fact : 16
% 47.20/31.48 #Define : 0
% 47.20/31.48 #Split : 6
% 47.20/31.48 #Chain : 0
% 47.20/31.48 #Close : 0
% 47.20/31.48
% 47.20/31.48 Ordering : KBO
% 47.20/31.48
% 47.20/31.48 Simplification rules
% 47.20/31.48 ----------------------
% 47.20/31.48 #Subsume : 9319
% 47.20/31.48 #Demod : 27908
% 47.20/31.48 #Tautology : 7280
% 47.20/31.48 #SimpNegUnit : 1428
% 47.20/31.48 #BackRed : 46
% 47.20/31.48
% 47.20/31.48 #Partial instantiations: 0
% 47.20/31.48 #Strategies tried : 1
% 47.20/31.48
% 47.20/31.48 Timing (in seconds)
% 47.20/31.48 ----------------------
% 47.20/31.49 Preprocessing : 1.40
% 47.20/31.49 Parsing : 0.72
% 47.20/31.49 CNF conversion : 0.16
% 47.20/31.49 Main loop : 29.10
% 47.20/31.49 Inferencing : 3.68
% 47.20/31.49 Reduction : 15.24
% 47.20/31.49 Demodulation : 12.02
% 47.20/31.49 BG Simplification : 0.40
% 47.20/31.49 Subsumption : 8.35
% 47.20/31.49 Abstraction : 0.42
% 47.20/31.49 MUC search : 0.00
% 47.20/31.49 Cooper : 0.00
% 47.20/31.49 Total : 30.56
% 47.20/31.49 Index Insertion : 0.00
% 47.20/31.49 Index Deletion : 0.00
% 47.20/31.49 Index Matching : 0.00
% 47.20/31.49 BG Taut test : 0.00
%------------------------------------------------------------------------------