%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SCT083-1 : 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 : n031.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 08:34:21 PM UTC 2025
% Result : Unsatisfiable 195.18s 136.54s
% Output : CNFRefutation 195.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 17 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-9 aty)
% Number of functors : 85 ( 85 usr; 9 con; 0-6 aty)
% Number of variables : 53 ( 53 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Complete__Lattice_Ocomplete__lattice > c_Finite__Set_Ofold__graph > c_Fun_Obij__betw > c_Record_Oiso__tuple__update__accessor__cong__assist > c_Fun_Oinj__on > c_Equiv__Relations_Oequiv > hBOOL > 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_Oupper__semilattice > class_Lattices_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Odistrib__lattice > class_Lattices_Obounded__lattice > class_HOL_Oord > class_Complete__Lattice_Ocomplete__lattice > c_Arrow__Order__Mirabelle_Ounanimity > c_Arrow__Order__Mirabelle_OIIA > v_sko__local__Xpairwise__neutrality__1 > v_sko__local__X2__1 > c_FuncSet_Ocompose > v_sko__local__X4__1 > c_SetInterval_Oord_OatLeastLessThan > c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1 > c_FuncSet_Osko__FuncSet__XrestrictI__1__1 > c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 > c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 > c_FuncSet_Osko__FuncSet__XPi__I__1__1 > c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 > c_Fun_Ofun__upd > c_COMBB > c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 > c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 > v_sko__local__X3__1 > v_sko__Arrow__Order__Mirabelle__XIIA__def__1 > c_Set_Ovimage > c_Set_Oimage > c_SetInterval_Oord_OgreaterThanLessThan > c_SetInterval_Oord_OatLeastAtMost > c_Relation_OImage > c_Product__Type_OSigma > c_Pair > c_List_Osko__Equiv__Relations__XquotientE__1__1 > c_Hilbert__Choice_Oinv__into > c_FuncSet_Orestrict > c_FuncSet_OPi > c_Finite__Set_Osetsum > c_Complete__Lattice_Ocomplete__lattice__class_OSUPR > c_COMBC > c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 > c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 > c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 > c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 > v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 > c_Set_Oinsert > c_SetInterval_Oord_OlessThan > c_SetInterval_Oord_OgreaterThan > c_SetInterval_Oord_OatMost > c_Relation_Oconverse > c_HOL_Ominus__class_Ominus > c_FuncSet_Oextensional > c_Equiv__Relations_Oquotient > c_COMBK > c_Arrow__Order__Mirabelle_Obelow > c_Arrow__Order__Mirabelle_Oabove > c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 > c_ATP__Linkup_Osko__Set__XbexI__1__1 > c_ATP__Linkup_Osko__Set__XbexE__1__1 > c_ATP__Linkup_Osko__Set__XbexCI__1__1 > c_ATP__Linkup_Osko__Set__XballE__1__1 > c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 > c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 > c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 > v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 > tc_prod > tc_fun > hAPP > c_Set_OPow > c_Inductive_Ocomplete__lattice__class_Olfp > c_Collect > c_Arrow__Order__Mirabelle_Omktop > c_Arrow__Order__Mirabelle_Omkbot > #nlpp > c_lessequals > c_in > c_fequal > c_Orderings_Otop__class_Otop > c_Orderings_Obot__class_Obot > c_Lattices_Oupper__semilattice__class_Osup > c_Lattices_Olower__semilattice__class_Oinf > c_HOL_Oundefined > c_HOL_Oord__class_Oless > c_Complete__Lattice_OSup__class_OSup > c_Complete__Lattice_OInf__class_OInf > c_COMBI > v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 > v_Lab____ > v_F > tc_nat > tc_bool > tc_Arrow__Order__Mirabelle_Oindi > tc_Arrow__Order__Mirabelle_Oalt > c_Arrow__Order__Mirabelle_OProf > c_Arrow__Order__Mirabelle_OLin
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_COMBI,type,
c_COMBI: $i > $i ).
tff(c_Set_Oinsert,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(v_sko__Arrow__Order__Mirabelle__XIIA__def__1,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__1: ( $i * $i * $i * $i ) > $i ).
tff(c_SetInterval_Oord_OatLeastLessThan,type,
c_SetInterval_Oord_OatLeastLessThan: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_COMBK,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(c_SetInterval_Oord_OgreaterThanLessThan,type,
c_SetInterval_Oord_OgreaterThanLessThan: ( $i * $i * $i * $i ) > $i ).
tff(c_Fun_Obij__betw,type,
c_Fun_Obij__betw: ( $i * $i * $i * $i * $i ) > $o ).
tff(c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1,type,
c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1: ( $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_ATP__Linkup_Osko__Set__XbexCI__1__1,type,
c_ATP__Linkup_Osko__Set__XbexCI__1__1: ( $i * $i * $i ) > $i ).
tff(c_fequal,type,
c_fequal: $i > $i ).
tff(c_Set_OPow,type,
c_Set_OPow: ( $i * $i ) > $i ).
tff(c_Arrow__Order__Mirabelle_OIIA,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
tff(c_SetInterval_Oord_OlessThan,type,
c_SetInterval_Oord_OlessThan: ( $i * $i * $i ) > $i ).
tff(c_List_Osko__Equiv__Relations__XquotientE__1__1,type,
c_List_Osko__Equiv__Relations__XquotientE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3,type,
c_ATP__Linkup_Osko__Set__Xbex__Un__1__3: ( $i * $i * $i * $i ) > $i ).
tff(class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1,type,
v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1: ( $i * $i * $i ) > $i ).
tff(class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
tff(c_Arrow__Order__Mirabelle_Oabove,type,
c_Arrow__Order__Mirabelle_Oabove: ( $i * $i * $i ) > $i ).
tff(c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1,type,
c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1: ( $i * $i * $i * $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_COMBB,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1,type,
c_FuncSet_Osko__FuncSet__XfuncsetI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
tff(c_FuncSet_Osko__FuncSet__XrestrictI__1__1,type,
c_FuncSet_Osko__FuncSet__XrestrictI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Fun_Oinj__on,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(v_sko__local__Xpairwise__neutrality__1,type,
v_sko__local__Xpairwise__neutrality__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
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_Lab____,type,
v_Lab____: $i ).
tff(tc_prod,type,
tc_prod: ( $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1,type,
c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oundefined,type,
c_HOL_Oundefined: $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(c_Equiv__Relations_Oquotient,type,
c_Equiv__Relations_Oquotient: ( $i * $i * $i ) > $i ).
tff(c_Finite__Set_Ofold__graph,type,
c_Finite__Set_Ofold__graph: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,type,
v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1: $i ).
tff(class_Orderings_Otop,type,
class_Orderings_Otop: $i > $o ).
tff(c_SetInterval_Oord_OatMost,type,
c_SetInterval_Oord_OatMost: ( $i * $i * $i ) > $i ).
tff(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1,type,
v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: ( $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1: ( $i * $i * $i ) > $i ).
tff(c_FuncSet_Orestrict,type,
c_FuncSet_Orestrict: ( $i * $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $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(c_Arrow__Order__Mirabelle_OProf,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
tff(c_Complete__Lattice_OInf__class_OInf,type,
c_Complete__Lattice_OInf__class_OInf: $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_SetInterval_Oord_OgreaterThan,type,
c_SetInterval_Oord_OgreaterThan: ( $i * $i * $i ) > $i ).
tff(c_Fun_Ofun__upd,type,
c_Fun_Ofun__upd: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Product__Type_OSigma,type,
c_Product__Type_OSigma: ( $i * $i * $i * $i ) > $i ).
tff(tc_Arrow__Order__Mirabelle_Oindi,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
tff(c_FuncSet_Osko__FuncSet__XPi__I__1__1,type,
c_FuncSet_Osko__FuncSet__XPi__I__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_lessequals,type,
c_lessequals: $i > $i ).
tff(class_Lattices_Oupper__semilattice,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1,type,
c_FuncSet_Osko__FuncSet__XPi__I_H__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_sko__local__X2__1,type,
v_sko__local__X2__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(c_Arrow__Order__Mirabelle_Omktop,type,
c_Arrow__Order__Mirabelle_Omktop: ( $i * $i ) > $i ).
tff(c_Complete__Lattice_OSup__class_OSup,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i ).
tff(class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
tff(c_Record_Oiso__tuple__update__accessor__cong__assist,type,
c_Record_Oiso__tuple__update__accessor__cong__assist: ( $i * $i * $i * $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_SetInterval_Oord_OatLeastAtMost,type,
c_SetInterval_Oord_OatLeastAtMost: ( $i * $i * $i * $i ) > $i ).
tff(c_in,type,
c_in: $i > $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i ).
tff(c_Arrow__Order__Mirabelle_Omkbot,type,
c_Arrow__Order__Mirabelle_Omkbot: ( $i * $i ) > $i ).
tff(c_Inductive_Ocomplete__lattice__class_Olfp,type,
c_Inductive_Ocomplete__lattice__class_Olfp: ( $i * $i ) > $i ).
tff(class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(c_Pair,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1,type,
c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_FuncSet_Oextensional,type,
c_FuncSet_Oextensional: ( $i * $i * $i ) > $i ).
tff(c_Equiv__Relations_Oequiv,type,
c_Equiv__Relations_Oequiv: ( $i * $i * $i ) > $o ).
tff(v_F,type,
v_F: $i ).
tff(class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(c_FuncSet_Osko__FuncSet__XextensionalityI__1__1,type,
c_FuncSet_Osko__FuncSet__XextensionalityI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Set__XbexI__1__1,type,
c_ATP__Linkup_Osko__Set__XbexI__1__1: ( $i * $i * $i ) > $i ).
tff(c_FuncSet_Ocompose,type,
c_FuncSet_Ocompose: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1: ( $i * $i * $i * $i ) > $i ).
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(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_Arrow__Order__Mirabelle_Ounanimity,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
tff(v_sko__local__X4__1,type,
v_sko__local__X4__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Set__XbexE__1__1,type,
c_ATP__Linkup_Osko__Set__XbexE__1__1: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2,type,
c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_sko__local__X3__1,type,
v_sko__local__X3__1: ( $i * $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1,type,
c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1: ( $i * $i * $i ) > $i ).
tff(c_Set_Oimage,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(c_FuncSet_OPi,type,
c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i ).
tff(c_COMBC,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Set__XballE__1__1,type,
c_ATP__Linkup_Osko__Set__XballE__1__1: ( $i * $i * $i ) > $i ).
tff(c_Arrow__Order__Mirabelle_Obelow,type,
c_Arrow__Order__Mirabelle_Obelow: ( $i * $i * $i ) > $i ).
tff(f_4730,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
file(unknown,unknown) ).
tff(f_4727,axiom,
! [V_S,V_x,T_a] :
( hBOOL(hAPP(V_S,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S)) ),
file(unknown,unknown) ).
tff(f_4082,axiom,
! [T_a,V_A] : ( c_Collect(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_A),T_a) = V_A ),
file(unknown,unknown) ).
tff(f_2792,axiom,
! [V_P,T_a] : ( c_Collect(V_P,T_a) = V_P ),
file(unknown,unknown) ).
tff(f_2866,axiom,
! [T_a,V_Q,V_P,T_c,T_b,V_R] : ( hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ),
file(unknown,unknown) ).
tff(f_4709,axiom,
! [V_L] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ),
file(unknown,unknown) ).
tff(f_4731,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
file(unknown,unknown) ).
tff(f_4717,axiom,
! [V_B,T_a,V_A,V_f,T_b,V_x] :
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) ),
file(unknown,unknown) ).
tff(f_4733,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)),
file(unknown,unknown) ).
tff(c_1430,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
inference(cnfTransformation,[status(thm)],[f_4730]) ).
tff(c_2395,plain,
! [T_a_3144,V_x_3145,V_S_3146] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a_3144),V_x_3145),V_S_3146))
| hBOOL(hAPP(V_S_3146,V_x_3145)) ),
inference(cnfTransformation,[status(thm)],[f_4727]) ).
tff(c_2414,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),
inference(resolution,[status(thm)],[c_1430,c_2395]) ).
tff(c_4030,plain,
! [T_a_3344,V_A_3345] : ( c_Collect(hAPP(c_COMBC(c_in(T_a_3344),T_a_3344,tc_fun(T_a_3344,tc_bool),tc_bool),V_A_3345),T_a_3344) = V_A_3345 ),
inference(cnfTransformation,[status(thm)],[f_4082]) ).
tff(c_788,plain,
! [V_P_1574,T_a_1575] : ( c_Collect(V_P_1574,T_a_1575) = V_P_1574 ),
inference(cnfTransformation,[status(thm)],[f_2792]) ).
tff(c_4036,plain,
! [T_a_3344,V_A_3345] : ( hAPP(c_COMBC(c_in(T_a_3344),T_a_3344,tc_fun(T_a_3344,tc_bool),tc_bool),V_A_3345) = V_A_3345 ),
inference(superposition,[status(thm),theory(equality)],[c_4030,c_788]) ).
tff(c_5586,plain,
! [T_a_3466,V_R_3469,T_b_3471,V_P_3470,V_Q_3468,T_c_3467] : ( hAPP(hAPP(c_COMBC(V_P_3470,T_b_3471,T_c_3467,T_a_3466),V_Q_3468),V_R_3469) = hAPP(hAPP(V_P_3470,V_R_3469),V_Q_3468) ),
inference(cnfTransformation,[status(thm)],[f_2866]) ).
tff(c_5605,plain,
! [T_a_3344,V_R_3469,V_A_3345] : ( hAPP(hAPP(c_in(T_a_3344),V_R_3469),V_A_3345) = hAPP(V_A_3345,V_R_3469) ),
inference(superposition,[status(thm),theory(equality)],[c_4036,c_5586]) ).
tff(c_1420,plain,
! [V_L_2894] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L_2894),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L_2894,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(cnfTransformation,[status(thm)],[f_4709]) ).
tff(c_251076,plain,
! [V_L_2894] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,V_L_2894))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(V_L_2894,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))) ),
inference(demodulation,[status(thm),theory(equality)],[c_5605,c_5605,c_1420]) ).
tff(c_1432,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
inference(cnfTransformation,[status(thm)],[f_4731]) ).
tff(c_302277,plain,
hBOOL(hAPP(c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F)),
inference(demodulation,[status(thm),theory(equality)],[c_5605,c_1432]) ).
tff(c_1422,plain,
! [V_f_2898,V_A_2897,T_a_2896,T_b_2899,V_x_2900,V_B_2895] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a_2896,T_b_2899)),V_f_2898),c_FuncSet_OPi(V_A_2897,c_COMBK(V_B_2895,tc_fun(T_b_2899,tc_bool),T_a_2896),T_a_2896,T_b_2899)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a_2896),V_x_2900),V_A_2897))
| hBOOL(hAPP(hAPP(c_in(T_b_2899),hAPP(V_f_2898,V_x_2900)),V_B_2895)) ),
inference(cnfTransformation,[status(thm)],[f_4717]) ).
tff(c_260880,plain,
! [V_f_2898,V_A_2897,T_a_2896,T_b_2899,V_x_2900,V_B_2895] :
( ~ hBOOL(hAPP(c_FuncSet_OPi(V_A_2897,c_COMBK(V_B_2895,tc_fun(T_b_2899,tc_bool),T_a_2896),T_a_2896,T_b_2899),V_f_2898))
| ~ hBOOL(hAPP(V_A_2897,V_x_2900))
| hBOOL(hAPP(V_B_2895,hAPP(V_f_2898,V_x_2900))) ),
inference(demodulation,[status(thm),theory(equality)],[c_5605,c_5605,c_5605,c_1422]) ).
tff(c_302419,plain,
! [V_x_8722] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,V_x_8722))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,V_x_8722))) ),
inference(resolution,[status(thm)],[c_302277,c_260880]) ).
tff(c_1434,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)),
inference(cnfTransformation,[status(thm)],[f_4733]) ).
tff(c_69216,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)))),
inference(demodulation,[status(thm),theory(equality)],[c_5605,c_1434]) ).
tff(c_302547,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),
inference(resolution,[status(thm)],[c_302419,c_69216]) ).
tff(c_302566,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),
inference(resolution,[status(thm)],[c_251076,c_302547]) ).
tff(c_302583,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2414,c_302566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SCT083-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.14 % 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
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 19:12:52 EDT 2025
% 0.13/0.35 % CPUTime :
% 195.18/136.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 195.18/136.54
% 195.18/136.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------