TSTP Solution File: SCT007-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SCT007-1 : 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 : 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 : 300s
% DateTime : Tue Aug 22 10:55:07 EDT 2023
% Result : Unsatisfiable 38.55s 22.40s
% Output : CNFRefutation 38.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 87
% Syntax : Number of formulae : 97 ( 12 unt; 82 typ; 0 def)
% Number of atoms : 18 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 171 ( 74 >; 97 *; 0 +; 0 <<)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-9 aty)
% Number of functors : 51 ( 51 usr; 8 con; 0-5 aty)
% Number of variables : 15 (; 15 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Complete__Lattice_Ocomplete__lattice > c_Fun_Oinj__on > c_lessequals > c_fequal > c_Relation_Osingle__valued > c_Relation_Orefl__on > c_Wellfounded_Oacyclic > c_Relation_Osym > c_Relation_Oantisym > c_Finite__Set_Ofinite > hBOOL > class_Orderings_Otop > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Orderings_Obot > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Oab__group__add > class_Lattices_Oupper__semilattice > class_Lattices_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Odistrib__lattice > class_Lattices_Obounded__lattice > class_Lattices_Oboolean__algebra > class_HOL_Ouminus > class_HOL_Oord > class_HOL_Ominus > class_Finite__Set_Ofinite_Ofinite > class_Complete__Lattice_Ocomplete__lattice > c_Relation_Orel__comp > c_Set_Ovimage > c_Set_Oimage > c_Relation_Oinv__image > c_Relation_OImage > c_Product__Type_OSigma > c_Nat_Ocompow > c_Complete__Lattice_Ocomplete__lattice__class_OINFI > c_in > c_Wellfounded_Omlex__prod > c_Relation_Ototal__on > c_Relation_Oconverse > c_Relation_ORange > c_Relation_ODomain > c_Order__Relation_Owell__order__on > c_Order__Relation_Opartial__order__on > c_Order__Relation_Olinear__order__on > c_List_Osko__Recdef__Xtfl__wf__induct__1__1 > c_Lattices_Oupper__semilattice__class_Osup > c_Lattices_Olower__semilattice__class_Oinf > c_HOL_Ominus__class_Ominus > c_COMBK > c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 > tc_prod > tc_fun > hAPP > c_and > c_Wellfounded_Owf > c_Wellfounded_Omeasure > c_Transitive__Closure_Otrancl > c_Transitive__Closure_Ortrancl > c_Relation_Otrans > c_Relation_Oirrefl > c_Order__Relation_Ostrict__linear__order__on > c_List_Omeasures > c_HOL_Ouminus__class_Ouminus > c_Complete__Lattice_OSup__class_OSup > c_Collect > #nlpp > c_Relation_OId > c_Orderings_Otop__class_Otop > c_Orderings_Obot__class_Obot > v_x > v_r > v_A > tc_bool > tc_Arrow__Order__Mirabelle_Oalt > t_b > t_a > c_Arrow__Order__Mirabelle_OLin
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(c_Relation_Oantisym,type,
c_Relation_Oantisym: ( $i * $i ) > $o ).
tff(c_COMBK,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(class_HOL_Ominus,type,
class_HOL_Ominus: $i > $o ).
tff(c_Relation_Oinv__image,type,
c_Relation_Oinv__image: ( $i * $i * $i * $i ) > $i ).
tff(c_Relation_Oconverse,type,
c_Relation_Oconverse: ( $i * $i * $i ) > $i ).
tff(c_Orderings_Otop__class_Otop,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(c_Complete__Lattice_Ocomplete__lattice__class_OINFI,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: ( $i * $i * $i * $i ) > $i ).
tff(c_List_Omeasures,type,
c_List_Omeasures: ( $i * $i ) > $i ).
tff(c_Relation_Ototal__on,type,
c_Relation_Ototal__on: ( $i * $i * $i ) > $i ).
tff(c_Wellfounded_Omlex__prod,type,
c_Wellfounded_Omlex__prod: ( $i * $i * $i ) > $i ).
tff(c_Wellfounded_Omeasure,type,
c_Wellfounded_Omeasure: ( $i * $i ) > $i ).
tff(class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(c_Relation_Otrans,type,
c_Relation_Otrans: ( $i * $i ) > $i ).
tff(c_Relation_Osingle__valued,type,
c_Relation_Osingle__valued: ( $i * $i * $i ) > $o ).
tff(c_Relation_Oirrefl,type,
c_Relation_Oirrefl: ( $i * $i ) > $i ).
tff(class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
tff(c_Wellfounded_Owf,type,
c_Wellfounded_Owf: ( $i * $i ) > $i ).
tff(t_a,type,
t_a: $i ).
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(c_Relation_ORange,type,
c_Relation_ORange: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1: ( $i * $i * $i ) > $i ).
tff(c_Fun_Oinj__on,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(c_List_Osko__Recdef__Xtfl__wf__induct__1__1,type,
c_List_Osko__Recdef__Xtfl__wf__induct__1__1: ( $i * $i * $i ) > $i ).
tff(c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(c_Set_Ovimage,type,
c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).
tff(tc_prod,type,
tc_prod: ( $i * $i ) > $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $i ).
tff(c_Collect,type,
c_Collect: ( $i * $i ) > $i ).
tff(class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Otop,type,
class_Orderings_Otop: $i > $o ).
tff(c_and,type,
c_and: ( $i * $i ) > $i ).
tff(c_Relation_Osym,type,
c_Relation_Osym: ( $i * $i ) > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Order__Relation_Opartial__order__on,type,
c_Order__Relation_Opartial__order__on: ( $i * $i * $i ) > $i ).
tff(c_Order__Relation_Ostrict__linear__order__on,type,
c_Order__Relation_Ostrict__linear__order__on: ( $i * $i ) > $i ).
tff(c_Wellfounded_Oacyclic,type,
c_Wellfounded_Oacyclic: ( $i * $i ) > $o ).
tff(c_Relation_Orefl__on,type,
c_Relation_Orefl__on: ( $i * $i * $i ) > $o ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool,type,
tc_bool: $i ).
tff(c_Relation_Orel__comp,type,
c_Relation_Orel__comp: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_r,type,
v_r: $i ).
tff(c_Product__Type_OSigma,type,
c_Product__Type_OSigma: ( $i * $i * $i * $i ) > $i ).
tff(class_Lattices_Oupper__semilattice,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(c_fequal,type,
c_fequal: ( $i * $i * $i ) > $o ).
tff(class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
tff(c_Relation_OImage,type,
c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).
tff(c_Complete__Lattice_Ocomplete__lattice,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(c_Arrow__Order__Mirabelle_OLin,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(c_Complete__Lattice_OSup__class_OSup,type,
c_Complete__Lattice_OSup__class_OSup: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(class_Finite__Set_Ofinite_Ofinite,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(c_Finite__Set_Ofinite,type,
c_Finite__Set_Ofinite: ( $i * $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(c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: ( $i * $i * $i ) > $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(c_Relation_OId,type,
c_Relation_OId: $i > $i ).
tff(c_Nat_Ocompow,type,
c_Nat_Ocompow: ( $i * $i * $i * $i ) > $i ).
tff(class_HOL_Ouminus,type,
class_HOL_Ouminus: $i > $o ).
tff(c_Order__Relation_Owell__order__on,type,
c_Order__Relation_Owell__order__on: ( $i * $i * $i ) > $i ).
tff(class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(tc_Arrow__Order__Mirabelle_Oalt,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(v_A,type,
v_A: $i ).
tff(class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(t_b,type,
t_b: $i ).
tff(c_Transitive__Closure_Otrancl,type,
c_Transitive__Closure_Otrancl: ( $i * $i ) > $i ).
tff(c_Set_Oimage,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(c_Relation_ODomain,type,
c_Relation_ODomain: ( $i * $i * $i ) > $i ).
tff(c_Order__Relation_Olinear__order__on,type,
c_Order__Relation_Olinear__order__on: ( $i * $i * $i ) > $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(f_2800,axiom,
c_Arrow__Order__Mirabelle_OLin = c_Collect(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
file(unknown,unknown) ).
tff(f_140,axiom,
! [V_P,T_a] : ( c_Collect(V_P,T_a) = V_P ),
file(unknown,unknown) ).
tff(f_2843,axiom,
! [V_x] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x)),
file(unknown,unknown) ).
tff(f_2838,axiom,
! [V_A,T_a,V_r] :
( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A,T_a),c_HOL_Ominus__class_Ominus(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))))
| ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A,V_r,T_a)) ),
file(unknown,unknown) ).
tff(f_2839,axiom,
hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)),
file(unknown,unknown) ).
tff(c_1124,plain,
c_Collect(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Arrow__Order__Mirabelle_OLin,
inference(cnfTransformation,[status(thm)],[f_2800]) ).
tff(c_58,plain,
! [V_P_79,T_a_80] : ( c_Collect(V_P_79,T_a_80) = V_P_79 ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_38908,plain,
c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) = c_Arrow__Order__Mirabelle_OLin,
inference(superposition,[status(thm),theory(equality)],[c_1124,c_58]) ).
tff(c_1144,plain,
! [V_x_1889] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),V_x_1889)),
inference(cnfTransformation,[status(thm)],[f_2843]) ).
tff(c_38916,plain,
! [V_x_1889] : ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,V_x_1889)),
inference(demodulation,[status(thm),theory(equality)],[c_38908,c_1144]) ).
tff(c_135905,plain,
! [V_A_3791,V_r_3792,T_a_3793] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(V_A_3791,V_r_3792,T_a_3793))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(V_A_3791,T_a_3793),c_HOL_Ominus__class_Ominus(V_r_3792,c_Relation_OId(T_a_3793),tc_fun(tc_prod(T_a_3793,T_a_3793),tc_bool)))) ),
inference(cnfTransformation,[status(thm)],[f_2838]) ).
tff(c_135939,plain,
! [V_r_3792] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),V_r_3792,tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_HOL_Ominus__class_Ominus(V_r_3792,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ),
inference(superposition,[status(thm),theory(equality)],[c_38908,c_135905]) ).
tff(c_135951,plain,
! [V_r_3792] : ~ hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),V_r_3792,tc_Arrow__Order__Mirabelle_Oalt)),
inference(negUnitSimplification,[status(thm)],[c_38916,c_135939]) ).
tff(c_1140,plain,
hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)),
inference(cnfTransformation,[status(thm)],[f_2839]) ).
tff(c_135953,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_135951,c_1140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT007-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 13:17:03 EDT 2023
% 0.13/0.35 % CPUTime :
% 38.55/22.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.55/22.41
% 38.55/22.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 38.55/22.43
% 38.55/22.43 Inference rules
% 38.55/22.43 ----------------------
% 38.55/22.43 #Ref : 10
% 38.55/22.43 #Sup : 29317
% 38.55/22.43 #Fact : 2
% 38.55/22.43 #Define : 0
% 38.55/22.43 #Split : 1
% 38.55/22.43 #Chain : 0
% 38.55/22.43 #Close : 0
% 38.55/22.43
% 38.55/22.43 Ordering : KBO
% 38.55/22.43
% 38.55/22.43 Simplification rules
% 38.55/22.44 ----------------------
% 38.55/22.44 #Subsume : 4701
% 38.55/22.44 #Demod : 27102
% 38.55/22.44 #Tautology : 14438
% 38.55/22.44 #SimpNegUnit : 120
% 38.55/22.44 #BackRed : 14
% 38.55/22.44
% 38.55/22.44 #Partial instantiations: 0
% 38.55/22.44 #Strategies tried : 1
% 38.55/22.44
% 38.55/22.44 Timing (in seconds)
% 38.55/22.44 ----------------------
% 38.55/22.44 Preprocessing : 1.56
% 38.55/22.44 Parsing : 0.84
% 38.55/22.44 CNF conversion : 0.14
% 38.55/22.44 Main loop : 19.80
% 38.55/22.44 Inferencing : 2.75
% 38.55/22.44 Reduction : 10.76
% 38.55/22.44 Demodulation : 9.27
% 38.55/22.44 BG Simplification : 0.31
% 38.55/22.44 Subsumption : 5.17
% 38.55/22.44 Abstraction : 0.35
% 38.55/22.44 MUC search : 0.00
% 38.55/22.44 Cooper : 0.00
% 38.55/22.44 Total : 21.41
% 38.55/22.44 Index Insertion : 0.00
% 38.55/22.44 Index Deletion : 0.00
% 38.55/22.44 Index Matching : 0.00
% 38.55/22.44 BG Taut test : 0.00
%------------------------------------------------------------------------------