%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV836-1 : 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/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 : n020.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 09:31:45 PM UTC 2025
% Result : Unsatisfiable 34.24s 16.86s
% Output : CNFRefutation 34.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 31 ( 29 usr; 1 prp; 0-9 aty)
% Number of functors : 41 ( 41 usr; 8 con; 0-4 aty)
% Number of variables : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Complete__Lattice_Ocomplete__lattice > c_Nitpick_Ofold__graph_H > c_Finite__Set_Ofold__graph > c_lessequals > c_Hoare__Mirabelle_Ohoare__derivs > c_HOL_Oord__class_Oless > c_Finite__Set_Ofinite > hBOOL > class_Ring__and__Field_Oring > class_Ring__and__Field_Oordered__idom > 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_Finite__Set_Osetsum > c_Complete__Lattice_Ocomplete__lattice__class_OSUPR > c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 > c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 > c_in > c_Set_Oinsert > c_SetInterval_Oord__class_OgreaterThanLessThan > c_SetInterval_Oord__class_OgreaterThanAtMost > c_SetInterval_Oord__class_OatLeastLessThan > c_SetInterval_Oord__class_OatLeastAtMost > c_Lattices_Oupper__semilattice__class_Osup > c_HOL_Ominus__class_Ominus > c_Finite__Set_Ofold1Set > c_Finite__Set_Ofold1 > tc_fun > hAPP > c_fequal > c_The > c_Set_Ocontents > c_SetInterval_Oord__class_OlessThan > c_SetInterval_Oord__class_OgreaterThan > c_SetInterval_Oord__class_OatMost > c_SetInterval_Oord__class_OatLeast > c_Nitpick_Osko__Nitpick__XEx1__def__1__3 > c_HOL_Ouminus__class_Ouminus > c_Finite__Set_Olinorder__class_OMin > c_Finite__Set_Olinorder__class_OMax > c_Complete__Lattice_OSup__class_OSup > c_Complete__Lattice_OInf__class_OInf > c_Collect > #nlpp > tc_Hoare__Mirabelle_Otriple > c_Orderings_Obot__class_Obot > c_Lattices_Olower__semilattice__class_Oinf > v_x > v_tsa > v_t > v_Ga > v_G > tc_nat > tc_bool > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $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_SetInterval_Oord__class_OlessThan,type,
c_SetInterval_Oord__class_OlessThan: ( $i * $i ) > $i ).
tff(class_HOL_Ominus,type,
class_HOL_Ominus: $i > $o ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Finite__Set_Ofold1Set,type,
c_Finite__Set_Ofold1Set: ( $i * $i * $i ) > $i ).
tff(v_G,type,
v_G: $i ).
tff(c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1,type,
c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_SetInterval_Oord__class_OatLeast,type,
c_SetInterval_Oord__class_OatLeast: ( $i * $i ) > $i ).
tff(class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(c_Finite__Set_Ofold1,type,
c_Finite__Set_Ofold1: ( $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(v_tsa,type,
v_tsa: $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_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(c_SetInterval_Oord__class_OgreaterThan,type,
c_SetInterval_Oord__class_OgreaterThan: ( $i * $i ) > $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(c_Complete__Lattice_OInf__class_OInf,type,
c_Complete__Lattice_OInf__class_OInf: ( $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_ATP__Linkup_Osko__Orderings__Xle__funI__1__1,type,
c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: $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_Finite__Set_Ofold__graph,type,
c_Finite__Set_Ofold__graph: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(c_fequal,type,
c_fequal: ( $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_Complete__Lattice_Ocomplete__lattice__class_OSUPR,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: ( $i * $i * $i * $i ) > $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(c_Hoare__Mirabelle_Ohoare__derivs,type,
c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).
tff(tc_bool,type,
tc_bool: $i ).
tff(c_SetInterval_Oord__class_OgreaterThanLessThan,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: ( $i * $i * $i ) > $i ).
tff(class_Lattices_Oupper__semilattice,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(v_Ga,type,
v_Ga: $i ).
tff(c_SetInterval_Oord__class_OatLeastLessThan,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
tff(c_Complete__Lattice_Ocomplete__lattice,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
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_SetInterval_Oord__class_OatMost,type,
c_SetInterval_Oord__class_OatMost: ( $i * $i ) > $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(c_Nitpick_Osko__Nitpick__XEx1__def__1__3,type,
c_Nitpick_Osko__Nitpick__XEx1__def__1__3: ( $i * $i ) > $i ).
tff(class_HOL_Ouminus,type,
class_HOL_Ouminus: $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(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_SetInterval_Oord__class_OgreaterThanAtMost,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: ( $i * $i * $i ) > $i ).
tff(tc_Hoare__Mirabelle_Otriple,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(c_The,type,
c_The: ( $i * $i ) > $i ).
tff(class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(c_SetInterval_Oord__class_OatLeastAtMost,type,
c_SetInterval_Oord__class_OatLeastAtMost: ( $i * $i * $i ) > $i ).
tff(c_Set_Ocontents,type,
c_Set_Ocontents: ( $i * $i ) > $i ).
tff(v_t,type,
v_t: $i ).
tff(f_3497,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,v_tsa,t_a),
file(unknown,unknown) ).
tff(f_2647,axiom,
! [V_P,T_a] : ( c_Collect(V_P,T_a) = V_P ),
file(unknown,unknown) ).
tff(f_3094,axiom,
! [V_a,T_a] : ( c_Collect(c_fequal(V_a,T_a),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file(unknown,unknown) ).
tff(f_3496,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(v_t,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file(unknown,unknown) ).
tff(f_3257,axiom,
! [V_G,V_t,V_ts,T_a] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,V_ts,tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ),
file(unknown,unknown) ).
tff(f_3499,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(v_t,v_tsa,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file(unknown,unknown) ).
tff(c_1114,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,v_tsa,t_a),
inference(cnfTransformation,[status(thm)],[f_3497]) ).
tff(c_818,plain,
! [V_P_1440,T_a_1441] : ( c_Collect(V_P_1440,T_a_1441) = V_P_1440 ),
inference(cnfTransformation,[status(thm)],[f_2647]) ).
tff(c_950,plain,
! [V_a_1664,T_a_1665] : ( c_Set_Oinsert(V_a_1664,c_Orderings_Obot__class_Obot(tc_fun(T_a_1665,tc_bool)),T_a_1665) = c_Collect(c_fequal(V_a_1664,T_a_1665),T_a_1665) ),
inference(cnfTransformation,[status(thm)],[f_3094]) ).
tff(c_1112,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(v_t,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(cnfTransformation,[status(thm)],[f_3496]) ).
tff(c_1200,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Collect(c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(demodulation,[status(thm),theory(equality)],[c_950,c_1112]) ).
tff(c_1236,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(demodulation,[status(thm),theory(equality)],[c_818,c_1200]) ).
tff(c_1022,plain,
! [V_G_1801,V_t_1802,T_a_1804,V_ts_1803] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_1801,c_Set_Oinsert(V_t_1802,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a_1804),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a_1804)),T_a_1804)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_1801,V_ts_1803,T_a_1804)
| c_Hoare__Mirabelle_Ohoare__derivs(V_G_1801,c_Set_Oinsert(V_t_1802,V_ts_1803,tc_Hoare__Mirabelle_Otriple(T_a_1804)),T_a_1804) ),
inference(cnfTransformation,[status(thm)],[f_3257]) ).
tff(c_1210,plain,
! [V_G_1801,V_t_1802,T_a_1804,V_ts_1803] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_1801,c_Collect(c_fequal(V_t_1802,tc_Hoare__Mirabelle_Otriple(T_a_1804)),tc_Hoare__Mirabelle_Otriple(T_a_1804)),T_a_1804)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_1801,V_ts_1803,T_a_1804)
| c_Hoare__Mirabelle_Ohoare__derivs(V_G_1801,c_Set_Oinsert(V_t_1802,V_ts_1803,tc_Hoare__Mirabelle_Otriple(T_a_1804)),T_a_1804) ),
inference(demodulation,[status(thm),theory(equality)],[c_950,c_1022]) ).
tff(c_89371,plain,
! [V_G_3939,V_t_3940,T_a_3941,V_ts_3942] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_3939,c_fequal(V_t_3940,tc_Hoare__Mirabelle_Otriple(T_a_3941)),T_a_3941)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_3939,V_ts_3942,T_a_3941)
| c_Hoare__Mirabelle_Ohoare__derivs(V_G_3939,c_Set_Oinsert(V_t_3940,V_ts_3942,tc_Hoare__Mirabelle_Otriple(T_a_3941)),T_a_3941) ),
inference(demodulation,[status(thm),theory(equality)],[c_818,c_1210]) ).
tff(c_1116,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(v_t,v_tsa,tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(cnfTransformation,[status(thm)],[f_3499]) ).
tff(c_89378,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_fequal(v_t,tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,v_tsa,t_a) ),
inference(resolution,[status(thm)],[c_89371,c_1116]) ).
tff(c_89440,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1114,c_1236,c_89378]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV836-1 : TPTP v9.0.0. Released v4.1.0.
% 0.10/0.13 % 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 : n020.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 : Wed Apr 9 04:48:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 34.24/16.86 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.24/16.86
% 34.24/16.86 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------