%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV880-1 : TPTP v9.0.0. 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 : n021.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 : Wed Apr 9 09:31:50 PM UTC 2025
% Result : Unsatisfiable 26.56s 10.14s
% Output : CNFRefutation 26.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-6 aty)
% Number of functors : 38 ( 38 usr; 8 con; 0-5 aty)
% Number of variables : 45 ( 45 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Nitpick_Ofold__graph_H > c_Finite__Set_Ofold__graph > c_Fun_Oinj__on > c_lessequals > c_in > c_fequal > c_HOL_Oord__class_Oless > c_Finite__Set_Ofinite > hBOOL > class_Ring__and__Field_Oring > class_Ring__and__Field_Oordered__idom > class_Orderings_Otop > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Orderings_Obot > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oab__group__add > class_Lattices_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Obounded__lattice > class_HOL_Oord > class_Finite__Set_Ofinite_Ofinite > class_Complete__Lattice_Ocomplete__lattice > c_Fun_Ofun__upd > c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 > c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 > c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 > c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 > c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 > c_Set_Ovimage > c_Set_Oimage > c_Hilbert__Choice_Oinv__into > c_Fun_Othe__inv__into > c_Finite__Set_Osetsum > c_Set_Oinsert > c_Orderings_Oord__class_Omax > c_HOL_Ominus__class_Ominus > c_COMBK > c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 > c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 > c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 > c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 > tc_fun > hAPP > c_SetInterval_Oord__class_OlessThan > c_Inductive_Ocomplete__lattice__class_Ogfp > c_Finite__Set_Olinorder__class_OMin > c_Finite__Set_Olinorder__class_OMax > c_Finite__Set_Ocard > #nlpp > c_Orderings_Otop__class_Otop > c_Orderings_Oord__class_Omin > c_Orderings_Obot__class_Obot > c_Lattices_Olower__semilattice__class_Oinf > v_pn > v_mgt__call > v_U > v_G > tc_nat > tc_bool > tc_Com_Opname > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1,type,
c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Set_Oinsert,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1,type,
c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_SetInterval_Oord__class_OlessThan,type,
c_SetInterval_Oord__class_OlessThan: ( $i * $i ) > $i ).
tff(c_COMBK,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(c_Orderings_Oord__class_Omin,type,
c_Orderings_Oord__class_Omin: $i > $i ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Orderings_Otop__class_Otop,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1: ( $i * $i * $i ) > $i ).
tff(v_G,type,
v_G: $i ).
tff(class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
tff(c_Finite__Set_Olinorder__class_OMin,type,
c_Finite__Set_Olinorder__class_OMin: ( $i * $i ) > $i ).
tff(c_Finite__Set_Olinorder__class_OMax,type,
c_Finite__Set_Olinorder__class_OMax: ( $i * $i ) > $i ).
tff(t_a,type,
t_a: $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(c_Fun_Oinj__on,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(c_Set_Ovimage,type,
c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).
tff(v_U,type,
v_U: $i ).
tff(v_pn,type,
v_pn: $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
tff(c_Inductive_Ocomplete__lattice__class_Ogfp,type,
c_Inductive_Ocomplete__lattice__class_Ogfp: ( $i * $i ) > $i ).
tff(c_Finite__Set_Ofold__graph,type,
c_Finite__Set_Ofold__graph: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(class_Orderings_Otop,type,
class_Orderings_Otop: $i > $o ).
tff(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1,type,
c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_nat,type,
tc_nat: $i ).
tff(c_Finite__Set_Ocard,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1,type,
c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2,type,
c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Orderings_Oord__class_Omax,type,
c_Orderings_Oord__class_Omax: ( $i * $i * $i ) > $i ).
tff(c_Hilbert__Choice_Oinv__into,type,
c_Hilbert__Choice_Oinv__into: ( $i * $i * $i * $i ) > $i ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool,type,
tc_bool: $i ).
tff(c_Fun_Othe__inv__into,type,
c_Fun_Othe__inv__into: ( $i * $i * $i * $i ) > $i ).
tff(c_Fun_Ofun__upd,type,
c_Fun_Ofun__upd: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_mgt__call,type,
v_mgt__call: $i ).
tff(tc_Com_Opname,type,
tc_Com_Opname: $i ).
tff(c_fequal,type,
c_fequal: ( $i * $i * $i ) > $o ).
tff(class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
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(c_Finite__Set_Ofinite,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(c_Nitpick_Ofold__graph_H,type,
c_Nitpick_Ofold__graph_H: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Finite__Set_Osetsum,type,
c_Finite__Set_Osetsum: ( $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1,type,
c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1: ( $i * $i * $i * $i * $i ) > $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(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Set_Oimage,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(f_3195,axiom,
c_in(v_pn,v_U,tc_Com_Opname),
file(unknown,unknown) ).
tff(f_3080,axiom,
! [V_S,V_x,T_a] :
( hBOOL(hAPP(V_S,V_x))
| ~ c_in(V_x,V_S,T_a) ),
file(unknown,unknown) ).
tff(f_3075,axiom,
! [V_x,V_S,T_a] :
( c_in(V_x,V_S,T_a)
| ~ hBOOL(hAPP(V_S,V_x)) ),
file(unknown,unknown) ).
tff(f_3194,axiom,
v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
file(unknown,unknown) ).
tff(f_3184,axiom,
! [T_a,V_A,V_f,T_b,V_x] :
( c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b)
| ~ c_in(V_x,V_A,T_a) ),
file(unknown,unknown) ).
tff(f_3026,axiom,
! [T_a,V_A] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
file(unknown,unknown) ).
tff(f_2873,axiom,
! [V_x,V_A,T_a,V_B] :
( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) ),
file(unknown,unknown) ).
tff(f_3197,axiom,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file(unknown,unknown) ).
tff(c_954,plain,
c_in(v_pn,v_U,tc_Com_Opname),
inference(cnfTransformation,[status(thm)],[f_3195]) ).
tff(c_1088,plain,
! [V_x_1878,V_S_1879,T_a_1880] :
( ~ c_in(V_x_1878,V_S_1879,T_a_1880)
| hBOOL(hAPP(V_S_1879,V_x_1878)) ),
inference(cnfTransformation,[status(thm)],[f_3080]) ).
tff(c_1099,plain,
hBOOL(hAPP(v_U,v_pn)),
inference(resolution,[status(thm)],[c_954,c_1088]) ).
tff(c_1101,plain,
! [V_S_1884,V_x_1885,T_a_1886] :
( ~ hBOOL(hAPP(V_S_1884,V_x_1885))
| c_in(V_x_1885,V_S_1884,T_a_1886) ),
inference(cnfTransformation,[status(thm)],[f_3075]) ).
tff(c_1110,plain,
! [T_a_1886] : c_in(v_pn,v_U,T_a_1886),
inference(resolution,[status(thm)],[c_1099,c_1101]) ).
tff(c_952,plain,
c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) = v_G,
inference(cnfTransformation,[status(thm)],[f_3194]) ).
tff(c_22217,plain,
! [T_b_2572,T_a_2574,V_f_2571,V_x_2570,V_A_2573] :
( ~ c_in(V_x_2570,V_A_2573,T_a_2574)
| c_in(hAPP(V_f_2571,V_x_2570),c_Set_Oimage(V_f_2571,V_A_2573,T_a_2574,T_b_2572),T_b_2572) ),
inference(cnfTransformation,[status(thm)],[f_3184]) ).
tff(c_22304,plain,
! [V_x_2575] :
( ~ c_in(V_x_2575,v_U,tc_Com_Opname)
| c_in(hAPP(v_mgt__call,V_x_2575),v_G,t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_952,c_22217]) ).
tff(c_906,plain,
! [V_x_1705,V_S_1704,T_a_1706] :
( ~ c_in(V_x_1705,V_S_1704,T_a_1706)
| hBOOL(hAPP(V_S_1704,V_x_1705)) ),
inference(cnfTransformation,[status(thm)],[f_3080]) ).
tff(c_22312,plain,
! [V_x_2576] :
( hBOOL(hAPP(v_G,hAPP(v_mgt__call,V_x_2576)))
| ~ c_in(V_x_2576,v_U,tc_Com_Opname) ),
inference(resolution,[status(thm)],[c_22304,c_906]) ).
tff(c_904,plain,
! [V_S_1702,V_x_1701,T_a_1703] :
( ~ hBOOL(hAPP(V_S_1702,V_x_1701))
| c_in(V_x_1701,V_S_1702,T_a_1703) ),
inference(cnfTransformation,[status(thm)],[f_3075]) ).
tff(c_22315,plain,
! [V_x_2576,T_a_1703] :
( c_in(hAPP(v_mgt__call,V_x_2576),v_G,T_a_1703)
| ~ c_in(V_x_2576,v_U,tc_Com_Opname) ),
inference(resolution,[status(thm)],[c_22312,c_904]) ).
tff(c_882,plain,
! [T_a_1660,V_A_1661] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a_1660,tc_bool)),V_A_1661,tc_fun(T_a_1660,tc_bool)),
inference(cnfTransformation,[status(thm)],[f_3026]) ).
tff(c_61331,plain,
! [V_x_3285,V_B_3286,T_a_3287,V_A_3288] :
( ~ c_in(V_x_3285,V_B_3286,T_a_3287)
| ~ c_lessequals(V_A_3288,V_B_3286,tc_fun(T_a_3287,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x_3285,V_A_3288,T_a_3287),V_B_3286,tc_fun(T_a_3287,tc_bool)) ),
inference(cnfTransformation,[status(thm)],[f_2873]) ).
tff(c_956,plain,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(cnfTransformation,[status(thm)],[f_3197]) ).
tff(c_1015,plain,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),v_G,tc_fun(t_a,tc_bool)),
inference(demodulation,[status(thm),theory(equality)],[c_952,c_956]) ).
tff(c_61381,plain,
( ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a)
| ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool)) ),
inference(resolution,[status(thm)],[c_61331,c_1015]) ).
tff(c_61482,plain,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(demodulation,[status(thm),theory(equality)],[c_882,c_61381]) ).
tff(c_61509,plain,
~ c_in(v_pn,v_U,tc_Com_Opname),
inference(resolution,[status(thm)],[c_22315,c_61482]) ).
tff(c_61513,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1110,c_61509]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV880-1 : TPTP v9.0.0. Released v4.1.0.
% 0.09/0.10 % 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
% 0.10/0.30 % Computer : n021.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Wed Apr 9 04:53:29 EDT 2025
% 0.10/0.30 % CPUTime :
% 26.56/10.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.56/10.14
% 26.56/10.14 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------