TSTP Solution File: SCT030-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SCT030-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 : 600s
% DateTime : Mon Jul 18 22:13:06 EDT 2022
% Result : Unsatisfiable 143.27s 143.50s
% Output : Refutation 153.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SCT030-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.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 : 600
% 0.13/0.34 % DateTime : Sat Jul 2 00:56:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 143.27/143.50
% 143.27/143.50 SPASS V 3.9
% 143.27/143.50 SPASS beiseite: Proof found.
% 143.27/143.50 % SZS status Theorem
% 143.27/143.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 143.27/143.50 SPASS derived 65190 clauses, backtracked 55078 clauses, performed 12 splits and kept 55842 clauses.
% 143.27/143.50 SPASS allocated 157301 KBytes.
% 143.27/143.50 SPASS spent 0:2:23.03 on the problem.
% 143.27/143.50 0:00:00.07 for the input.
% 143.27/143.50 0:00:00.00 for the FLOTTER CNF translation.
% 143.27/143.50 0:00:00.37 for inferences.
% 143.27/143.50 0:00:05.25 for the backtracking.
% 143.27/143.50 0:2:16.92 for the reduction.
% 143.27/143.50
% 143.27/143.50
% 143.27/143.50 Here is a proof with depth 14, length 674 :
% 143.27/143.50 % SZS output start Refutation
% 143.27/143.50 2[0:Inp] class_Orderings_Oorder(u) || c_lessequals(v,w,u)*+ c_lessequals(x,v,u)* -> c_lessequals(x,w,u)*.
% 143.27/143.50 8[0:Inp] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),w),x,u)* -> c_lessequals(v,x,u).
% 143.27/143.50 16[0:Inp] || -> c_lessequals(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 143.27/143.50 26[0:Inp] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w),w,u)*.
% 143.27/143.50 27[0:Inp] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w),v,u)*.
% 143.27/143.50 34[0:Inp] || -> equal(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v),w)**.
% 143.27/143.50 35[0:Inp] || -> equal(c_Fun_Ofun__upd(u,v,hAPP(u,v),w,x),u)**.
% 143.27/143.50 44[0:Inp] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),w),w)** -> c_lessequals(v,w,u).
% 143.27/143.50 45[0:Inp] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(w,u),v),w)**.
% 143.27/143.50 50[0:Inp] class_Lattices_Olattice(u) || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),w)),v)**.
% 143.27/143.50 53[0:Inp] class_Orderings_Oorder(u) || c_lessequals(v,w,u)*+ c_lessequals(w,v,u)* -> equal(v,w).
% 143.27/143.50 56[0:Inp] class_Lattices_Olattice(u) || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w)),v)**.
% 143.27/143.50 64[0:Inp] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(u),u),v),v)**.
% 143.27/143.51 68[0:Inp] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_fun(v,tc_bool)),w),x))* -> hBOOL(hAPP(u,x)) hBOOL(hAPP(w,x)).
% 143.27/143.51 73[0:Inp] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),u),tc_fun(w,tc_bool))*.
% 143.27/143.51 77[0:Inp] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 143.27/143.51 79[0:Inp] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))*.
% 143.27/143.51 96[0:Inp] || -> equal(hAPP(c_COMBB(u,v,w,x,y),z),hAPP(u,hAPP(v,z)))**.
% 143.27/143.51 147[0:Inp] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),x)).
% 143.27/143.51 157[0:Inp] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(u,v),w))**.
% 143.27/143.51 192[0:Inp] || c_lessequals(u,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool))* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 143.27/143.51 193[0:Inp] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),c_Collect(v,u)),c_Collect(c_COMBB(c_Not,v,tc_bool,tc_bool,u),u))**.
% 143.27/143.51 194[0:Inp] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Collect(x,w)),c_Collect(c_COMBB(x,u,w,tc_bool,v),v))*.
% 143.27/143.51 199[0:Inp] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),v),tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 143.27/143.51 215[0:Inp] class_Lattices_Olower__semilattice(u) || equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w),v)** -> c_lessequals(v,w,u).
% 143.27/143.51 216[0:Inp] class_Lattices_Olower__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(w,u),v),v)**.
% 143.27/143.51 219[0:Inp] || -> c_lessequals(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_fun(v,tc_bool)),w),tc_fun(v,tc_bool))*.
% 143.27/143.51 226[0:Inp] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(w,u),v),u)*.
% 143.27/143.51 227[0:Inp] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),w),u)*.
% 143.27/143.51 250[0:Inp] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(w,tc_fun(v,tc_bool)),u))*.
% 143.27/143.51 251[0:Inp] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(w,u),v))*.
% 143.27/143.51 252[0:Inp] class_Lattices_Olattice(u) || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(w,u),v))*.
% 143.27/143.51 260[0:Inp] || c_Fun_Oinj__on(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,tc_fun(w,tc_bool)),x),w,y)* -> c_Fun_Oinj__on(u,v,w,y).
% 143.27/143.51 265[0:Inp] class_HOL_Oord(u) || c_lessequals(v,w,tc_fun(x,u))* -> c_lessequals(hAPP(v,y),hAPP(w,y),u)*.
% 143.27/143.51 308[0:Inp] || -> equal(c_Collect(u,v),u)**.
% 143.27/143.51 309[0:Inp] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 143.27/143.51 312[0:Inp] || equal(hAPP(c_Set_Oinsert(u,v),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> .
% 143.27/143.51 315[0:Inp] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),w)),hAPP(c_Set_Oinsert(u,v),w))**.
% 143.27/143.51 327[0:Inp] || -> equal(hAPP(c_HOL_Ominus__class_Ominus(u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),u)**.
% 143.27/143.51 328[0:Inp] || -> equal(hAPP(c_HOL_Ominus__class_Ominus(u,tc_fun(v,tc_bool)),u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 143.27/143.51 330[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),y)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u)* -> hBOOL(hAPP(hAPP(c_in(x),w),y)).
% 143.27/143.51 375[0:Inp] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),x),w,y)* -> c_Fun_Oinj__on(u,x,w,y).
% 143.27/143.51 389[0:Inp] || -> equal(hAPP(hAPP(c_COMBC(u,v,w,x),y),z),hAPP(hAPP(u,z),y))**.
% 143.27/143.51 390[0:Inp] || -> equal(hAPP(c_COMBK(u,v,w),x),u)**.
% 143.27/143.51 392[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 143.27/143.51 398[0:Inp] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),hAPP(c_HOL_Ouminus__class_Ouminus(u),w)),hAPP(c_HOL_Ominus__class_Ominus(v,u),w))**.
% 143.27/143.51 399[0:Inp] || -> c_Fun_Oinj__on(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v,w)*.
% 143.27/143.51 401[0:Inp] class_Lattices_Olower__semilattice(u) || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w),hAPP(c_Lattices_Olower__semilattice__class_Oinf(w,u),v))*.
% 143.27/143.51 402[0:Inp] class_Lattices_Olattice(u) || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w),hAPP(c_Lattices_Olower__semilattice__class_Oinf(w,u),v))*.
% 143.27/143.51 406[0:Inp] || equal(hAPP(u,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(u,v)),hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(u,v),v))* -> c_Arrow__Order__Mirabelle_Odictator(u,v).
% 143.27/143.51 425[0:Inp] || hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(u,tc_fun(v,tc_bool)),w),x))* -> hBOOL(hAPP(w,x)).
% 143.27/143.51 429[0:Inp] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),v)),v)**.
% 143.27/143.51 441[0:Inp] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbspec__1__1(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),v))* -> hBOOL(hAPP(u,x))*.
% 143.27/143.51 463[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)) equal(v,w).
% 143.27/143.51 477[0:Inp] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Obot__class_Obot(u))**.
% 143.27/143.51 478[0:Inp] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))**.
% 143.27/143.51 479[0:Inp] || hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v))* -> .
% 143.27/143.51 489[0:Inp] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),v),v)**.
% 143.27/143.51 490[0:Inp] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(u,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),u)**.
% 143.27/143.51 497[0:Inp] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,v)),w),c_FuncSet_Oextensional(x,u,v)))* hBOOL(hAPP(hAPP(c_in(tc_fun(u,v)),y),c_FuncSet_Oextensional(x,u,v)))* equal(hAPP(w,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(x,w,y,u,v)),hAPP(y,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(x,w,y,u,v)))* -> equal(w,y).
% 143.27/143.51 498[0:Inp] || -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v))*.
% 143.27/143.51 514[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),w),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))**.
% 143.27/143.51 519[0:Inp] || equal(hAPP(c_Set_Oinsert(u,v),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> .
% 143.27/143.51 529[0:Inp] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),u))*.
% 143.27/143.51 530[0:Inp] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(u))**.
% 143.27/143.51 557[0:Inp] || -> equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Collect(hAPP(c_fequal(v),u),v))**.
% 143.27/143.51 560[0:Inp] || -> equal(c_Collect(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),u),v)**.
% 143.27/143.51 575[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XbexI__1__1(x,u,w)))*.
% 143.27/143.51 579[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),w)))*.
% 143.27/143.51 580[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),w)))* -> .
% 143.27/143.51 588[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(w,x,u)))* hBOOL(hAPP(y,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(w,y,u)))* -> hBOOL(hAPP(x,v))*.
% 143.27/143.51 612[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(w,y,x,u)),w))*.
% 143.27/143.51 613[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(w,x,y,u)),w))*.
% 143.27/143.51 614[0:Inp] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XballE__1__1(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),v))* -> hBOOL(hAPP(u,x))*.
% 143.27/143.51 616[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XbexI__1__1(x,u,w)),x))*.
% 143.27/143.51 632[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,u,w)))*.
% 143.27/143.51 634[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(v,u),w),w).
% 143.27/143.51 644[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(x,u,w)))*.
% 143.27/143.51 649[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),c_FuncSet_Osko__FuncSet__XPi__I__1__1(v,w,x,u,y)),v))* hBOOL(hAPP(hAPP(c_in(tc_fun(u,y)),x),c_FuncSet_OPi(v,w,u,y)))*.
% 143.27/143.51 650[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(v,w,x,u,y)),v))* hBOOL(hAPP(hAPP(c_in(tc_fun(u,y)),x),c_FuncSet_OPi(v,w,u,y)))*.
% 143.27/143.51 658[0:Inp] || -> 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))),v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(u,v)),c_Arrow__Order__Mirabelle_OProf))* c_Arrow__Order__Mirabelle_Odictator(u,v).
% 143.27/143.51 662[0:Inp] || 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))),u),c_Arrow__Order__Mirabelle_OProf))* c_Arrow__Order__Mirabelle_Odictator(v,w)* -> equal(hAPP(v,u),hAPP(u,w))*.
% 143.27/143.51 663[0:Inp] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),v),u))*.
% 143.27/143.51 664[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(w,v)).
% 143.27/143.51 665[0:Inp] || -> 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))),v_P____),c_Arrow__Order__Mirabelle_OProf))*.
% 143.27/143.51 666[0:Inp] class_Complete__Lattice_Ocomplete__lattice(u) || -> class_Complete__Lattice_Ocomplete__lattice(tc_fun(v,u))*.
% 143.27/143.51 667[0:Inp] class_Lattices_Olattice(u) || -> class_Lattices_Oupper__semilattice(tc_fun(v,u))*.
% 143.27/143.51 668[0:Inp] class_Lattices_Olattice(u) || -> class_Lattices_Olower__semilattice(tc_fun(v,u))*.
% 143.27/143.51 669[0:Inp] class_Lattices_Odistrib__lattice(u) || -> class_Lattices_Odistrib__lattice(tc_fun(v,u))*.
% 143.27/143.51 670[0:Inp] class_Lattices_Obounded__lattice(u) || -> class_Lattices_Obounded__lattice(tc_fun(v,u))*.
% 143.27/143.51 671[0:Inp] class_Lattices_Oboolean__algebra(u) || -> class_Lattices_Oboolean__algebra(tc_fun(v,u))*.
% 143.27/143.51 672[0:Inp] class_Orderings_Opreorder(u) || -> class_Orderings_Opreorder(tc_fun(v,u))*.
% 143.27/143.51 673[0:Inp] class_Lattices_Olattice(u) || -> class_Lattices_Olattice(tc_fun(v,u))*.
% 143.27/143.51 674[0:Inp] class_Orderings_Oorder(u) || -> class_Orderings_Oorder(tc_fun(v,u))*.
% 143.27/143.51 675[0:Inp] class_Orderings_Otop(u) || -> class_Orderings_Otop(tc_fun(v,u))*.
% 143.27/143.51 676[0:Inp] class_Orderings_Obot(u) || -> class_Orderings_Obot(tc_fun(v,u))*.
% 143.27/143.51 677[0:Inp] class_HOL_Oord(u) || -> class_HOL_Oord(tc_fun(v,u))*.
% 143.27/143.51 679[0:Inp] || -> class_Lattices_Olower__semilattice(tc_nat)*.
% 143.27/143.51 687[0:Inp] || -> class_Complete__Lattice_Ocomplete__lattice(tc_bool)*.
% 143.27/143.51 688[0:Inp] || -> class_Lattices_Oupper__semilattice(tc_bool)*.
% 143.27/143.51 689[0:Inp] || -> class_Lattices_Olower__semilattice(tc_bool)*.
% 143.27/143.51 690[0:Inp] || -> class_Lattices_Odistrib__lattice(tc_bool)*.
% 143.27/143.51 691[0:Inp] || -> class_Lattices_Obounded__lattice(tc_bool)*.
% 143.27/143.51 692[0:Inp] || -> class_Lattices_Oboolean__algebra(tc_bool)*.
% 143.27/143.51 693[0:Inp] || -> class_Orderings_Opreorder(tc_bool)*.
% 143.27/143.51 694[0:Inp] || -> class_Lattices_Olattice(tc_bool)*.
% 143.27/143.51 695[0:Inp] || -> class_Orderings_Oorder(tc_bool)*.
% 143.27/143.51 696[0:Inp] || -> class_Orderings_Otop(tc_bool)*.
% 143.27/143.51 697[0:Inp] || -> class_Orderings_Obot(tc_bool)*.
% 143.27/143.51 698[0:Inp] || -> class_HOL_Oord(tc_bool)*.
% 143.27/143.51 701[0:Inp] || 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))),v_Q____),c_Arrow__Order__Mirabelle_OProf))* -> .
% 143.27/143.51 704[0:Rew:308.0,560.0] || -> equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),v)**.
% 143.27/143.51 707[0:Rew:308.0,557.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_fequal(v),u))**.
% 143.27/143.51 710[0:Rew:250.0,199.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_fun(v,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(v,tc_bool)),u)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 143.27/143.51 711[0:Rew:308.0,194.0,308.0,194.0] || -> equal(c_COMBB(u,v,w,tc_bool,x),hAPP(c_Set_Ovimage(v,x,w),u))**.
% 143.27/143.51 712[0:Rew:308.0,193.0,308.0,193.0,711.0,193.0] || -> equal(hAPP(c_Set_Ovimage(u,v,tc_bool),c_Not),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(v,tc_bool)),u))**.
% 143.27/143.51 717[0:Rew:707.0,157.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(u),v),tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(v,u),w))**.
% 143.27/143.51 747[0:Con:588.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),v))* -> hBOOL(hAPP(u,x))*.
% 143.27/143.51 807[0:Res:663.1,701.0] || hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____))* -> .
% 143.27/143.51 814[0:Res:330.2,701.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,v_Q____)),hAPP(c_Set_Oimage(v,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),u),c_Arrow__Order__Mirabelle_OProf)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(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_bool)),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),u)* -> .
% 143.27/143.51 846[0:Res:463.1,701.0] || 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))),v_Q____),hAPP(c_Set_Oinsert(u,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OProf)))* -> equal(v_Q____,u).
% 143.27/143.51 1091[0:Res:665.0,664.0] || -> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____))*.
% 143.27/143.51 1110[0:SpL:707.0,519.0] || equal(hAPP(c_fequal(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 143.27/143.51 1527[0:SpR:402.1,56.1] class_Lattices_Olattice(u) class_Lattices_Olattice(u) || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),hAPP(c_Lattices_Olower__semilattice__class_Oinf(w,u),v)),v)**.
% 143.27/143.51 1570[0:Obv:1527.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),hAPP(c_Lattices_Olower__semilattice__class_Oinf(w,u),v)),v)**.
% 143.27/143.51 1865[0:SpR:711.0,96.0] || -> equal(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y),hAPP(x,hAPP(u,y)))**.
% 143.27/143.51 1870[0:SpR:712.0,1865.0] || -> equal(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),v),w),hAPP(c_Not,hAPP(v,w)))**.
% 143.27/143.51 1879[0:SpR:429.0,1870.0] || -> equal(hAPP(c_Not,hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),v),w)),hAPP(v,w))**.
% 143.27/143.51 1881[0:SpR:478.0,1870.0] || -> equal(hAPP(c_Not,hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v)),hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v))**.
% 143.27/143.51 1882[0:Rew:1870.0,1879.0] || -> equal(hAPP(c_Not,hAPP(c_Not,hAPP(u,v))),hAPP(u,v))**.
% 143.27/143.51 1893[0:SpR:489.0,1882.0] || -> equal(hAPP(c_Not,hAPP(c_Not,u)),u)**.
% 143.27/143.51 1952[0:SpR:1893.0,35.0] || -> equal(c_Fun_Ofun__upd(c_Not,hAPP(c_Not,u),u,v,w),c_Not)**.
% 143.27/143.51 2494[0:Res:663.1,634.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(c_Set_Oinsert(v,w),u),u)**.
% 143.27/143.51 2495[0:Res:665.0,634.0] || -> equal(hAPP(c_Set_Oinsert(v_P____,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 2511[0:SpL:2495.0,519.0] || equal(c_Orderings_Obot__class_Obot(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_bool)),c_Arrow__Order__Mirabelle_OProf)** -> .
% 143.27/143.51 2695[0:SpL:251.1,44.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),w),v)** -> c_lessequals(w,v,u).
% 143.27/143.51 2723[0:Obv:2695.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v,u),w),v)** -> c_lessequals(w,v,u).
% 143.27/143.51 2822[0:SpR:45.2,64.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> equal(c_Orderings_Obot__class_Obot(u),v).
% 143.27/143.51 2850[0:SpR:45.2,77.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(v,c_Orderings_Otop__class_Otop(u)).
% 143.27/143.51 3028[0:SpR:704.0,389.0] || -> equal(hAPP(hAPP(c_in(u),v),w),hAPP(w,v))**.
% 143.27/143.51 3041[0:Rew:3028.0,662.0] || hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,u))*+ c_Arrow__Order__Mirabelle_Odictator(v,w)* -> equal(hAPP(v,u),hAPP(u,w))*.
% 143.27/143.51 3042[0:Rew:3028.0,658.0] || -> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(u,v)))* c_Arrow__Order__Mirabelle_Odictator(u,v).
% 143.27/143.51 3062[0:Rew:3028.0,846.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OProf),v_Q____))* -> equal(v_Q____,u).
% 143.27/143.51 3076[0:Rew:3028.0,814.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v),c_Arrow__Order__Mirabelle_OProf),hAPP(u,v_Q____)))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(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_bool)),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v)* -> .
% 143.27/143.51 3077[0:Rew:3028.0,392.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(u,x)))*.
% 143.27/143.51 3086[0:Rew:3028.0,580.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),w),v))* -> .
% 143.27/143.51 3087[0:Rew:3028.0,579.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),w),v))*.
% 143.27/143.51 3098[0:Rew:3028.0,649.0] || -> hBOOL(hAPP(u,c_FuncSet_Osko__FuncSet__XPi__I__1__1(u,v,w,x,y)))* hBOOL(hAPP(hAPP(c_in(tc_fun(x,y)),w),c_FuncSet_OPi(u,v,x,y)))*.
% 143.27/143.51 3099[0:Rew:3028.0,650.0] || -> hBOOL(hAPP(u,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(u,v,w,x,y)))* hBOOL(hAPP(hAPP(c_in(tc_fun(x,y)),w),c_FuncSet_OPi(u,v,x,y)))*.
% 143.27/143.51 3103[0:Rew:3028.0,441.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbspec__1__1(v,u,w)))*+ hBOOL(hAPP(v,x))* -> hBOOL(hAPP(u,x))*.
% 143.27/143.51 3104[0:Rew:3028.0,614.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XballE__1__1(v,u,w)))*+ hBOOL(hAPP(v,x))* -> hBOOL(hAPP(u,x))*.
% 143.27/143.51 3105[0:Rew:3028.0,747.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(v,u,w)))*+ hBOOL(hAPP(v,x))* -> hBOOL(hAPP(u,x))*.
% 143.27/143.51 3111[0:Rew:3028.0,612.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(w,y,x,u)))*.
% 143.27/143.51 3112[0:Rew:3028.0,613.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(w,x,y,u)))*.
% 143.27/143.51 3140[0:Rew:3028.0,616.2] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__XbexI__1__1(x,u,w)))*.
% 143.27/143.51 3144[0:Rew:3028.0,147.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(x,u)).
% 143.27/143.51 3149[0:Rew:3028.0,632.1] || hBOOL(hAPP(u,v))*+ hBOOL(hAPP(w,v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,x,u,y)))*.
% 143.27/143.51 3150[0:Rew:3028.0,575.1] || hBOOL(hAPP(u,v))*+ hBOOL(hAPP(w,v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XbexI__1__1(w,u,x)))*.
% 143.27/143.51 3153[0:Rew:3028.0,644.1] || hBOOL(hAPP(u,v))*+ hBOOL(hAPP(w,v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(w,u,x)))*.
% 143.27/143.51 3169[0:Rew:3028.0,497.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,v)),w),c_FuncSet_Oextensional(x,u,v)))* hBOOL(hAPP(c_FuncSet_Oextensional(x,u,v),y)) equal(hAPP(w,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(x,w,y,u,v)),hAPP(y,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(x,w,y,u,v)))* -> equal(w,y).
% 143.27/143.51 3203[0:Rew:3028.0,514.0] || -> hBOOL(hAPP(u,v)) equal(hAPP(c_Set_Ovimage(c_COMBK(v,w,x),x,w),u),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))**.
% 143.27/143.51 3210[0:Rew:1870.0,3087.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(c_Not,hAPP(w,v))).
% 143.27/143.51 3211[0:Rew:3028.0,3210.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(c_Not,hAPP(u,v)))*.
% 143.27/143.51 3219[0:Rew:1870.0,3086.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(c_Not,hAPP(w,v))) -> .
% 143.27/143.51 3220[0:Rew:3028.0,3219.0] || hBOOL(hAPP(u,v)) hBOOL(hAPP(c_Not,hAPP(u,v)))* -> .
% 143.27/143.51 3233[0:Rew:3028.0,3111.0] || hBOOL(hAPP(u,v))*+ -> hBOOL(hAPP(w,v))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(u,x,w,y)))*.
% 143.27/143.51 3234[0:Rew:3028.0,3112.0] || hBOOL(hAPP(u,v))*+ -> hBOOL(hAPP(w,v))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(u,w,x,y)))*.
% 143.27/143.51 3236[0:Rew:3028.0,3140.1] || hBOOL(hAPP(u,v))*+ hBOOL(hAPP(w,v))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__XbexI__1__1(w,u,x)))*.
% 143.27/143.51 3239[0:Rew:3028.0,3098.1] || -> hBOOL(hAPP(u,c_FuncSet_Osko__FuncSet__XPi__I__1__1(u,v,w,x,y)))* hBOOL(hAPP(c_FuncSet_OPi(u,v,x,y),w)).
% 143.27/143.51 3240[0:Rew:3028.0,3099.1] || -> hBOOL(hAPP(u,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(u,v,w,x,y)))* hBOOL(hAPP(c_FuncSet_OPi(u,v,x,y),w)).
% 143.27/143.51 3268[0:Rew:3028.0,3169.0] || hBOOL(hAPP(c_FuncSet_Oextensional(u,v,w),x)) hBOOL(hAPP(c_FuncSet_Oextensional(u,v,w),y)) equal(hAPP(x,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(u,x,y,v,w)),hAPP(y,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(u,x,y,v,w)))* -> equal(x,y).
% 143.27/143.51 3363[0:SpR:1893.0,3211.1] || -> hBOOL(hAPP(c_Not,u))* hBOOL(u).
% 143.27/143.51 3498[0:SpL:401.1,3220.1] class_Lattices_Olower__semilattice(u) || hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w)) hBOOL(hAPP(c_Not,hAPP(c_Lattices_Olower__semilattice__class_Oinf(w,u),v)))* -> .
% 143.27/143.51 3546[0:SpL:1893.0,3220.1] || hBOOL(hAPP(c_Not,u))* hBOOL(u) -> .
% 143.27/143.51 3701[0:SpR:216.2,3077.0] class_Lattices_Olower__semilattice(u) || c_lessequals(v,w,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Lattices_Olower__semilattice__class_Oinf(w,u),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v))*.
% 143.27/143.51 3721[0:SpR:327.0,3077.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(u,tc_fun(v,tc_bool)),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u))*.
% 143.27/143.51 3764[0:Res:73.0,3144.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),w))*.
% 143.27/143.51 3792[0:SpR:2495.0,3764.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OProf),v_P____))*.
% 143.27/143.51 4049[0:SpR:717.0,219.0] || -> c_lessequals(hAPP(c_fequal(u),v),hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool))*.
% 143.27/143.51 4090[0:SpR:2494.1,4049.0] || hBOOL(hAPP(u,v)) -> c_lessequals(hAPP(c_fequal(w),v),u,tc_fun(w,tc_bool))*.
% 143.27/143.51 4730[0:Res:1091.0,3041.0] || c_Arrow__Order__Mirabelle_Odictator(u,v)* -> equal(hAPP(u,v_P____),hAPP(v_P____,v))*.
% 143.27/143.51 7685[0:SpL:398.1,425.0] class_Lattices_Oboolean__algebra(tc_fun(u,tc_bool)) || hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(v,tc_fun(u,tc_bool)),w),x))* -> hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),w),x)).
% 143.27/143.51 7706[0:Rew:1870.0,7685.2] class_Lattices_Oboolean__algebra(tc_fun(u,tc_bool)) || hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(v,tc_fun(u,tc_bool)),w),x))* -> hBOOL(hAPP(c_Not,hAPP(w,x))).
% 143.27/143.51 7707[0:SSi:7706.0,675.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1,676.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1,666.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1,677.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1,669.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1,674.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1,672.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1,671.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1,670.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1,668.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1,667.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1,673.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.1] || hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(u,tc_fun(v,tc_bool)),w),x))* -> hBOOL(hAPP(c_Not,hAPP(w,x))).
% 143.27/143.51 9616[0:Res:3363.0,3103.0] || hBOOL(hAPP(u,v))*+ -> hBOOL(c_ATP__Linkup_Osko__Set__Xbspec__1__1(u,c_Not,w))* hBOOL(hAPP(c_Not,v))*.
% 143.27/143.51 9759[0:Res:1091.0,9616.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbspec__1__1(c_Arrow__Order__Mirabelle_OProf,c_Not,u))* hBOOL(hAPP(c_Not,v_P____)).
% 143.27/143.51 9760[0:Res:3042.0,9616.0] || -> c_Arrow__Order__Mirabelle_Odictator(u,v) hBOOL(c_ATP__Linkup_Osko__Set__Xbspec__1__1(c_Arrow__Order__Mirabelle_OProf,c_Not,w))* hBOOL(hAPP(c_Not,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(u,v)))*.
% 143.27/143.51 9764[0:Res:498.0,9616.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbspec__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Not,v))* hBOOL(hAPP(c_Not,w))*.
% 143.27/143.51 9871[1:Spt:9759.1] || -> hBOOL(hAPP(c_Not,v_P____))*.
% 143.27/143.51 9876[1:Res:9871.0,3546.0] || hBOOL(v_P____)* -> .
% 143.27/143.51 9934[0:Res:3363.0,3104.0] || hBOOL(hAPP(u,v))*+ -> hBOOL(c_ATP__Linkup_Osko__Set__XballE__1__1(u,c_Not,w))* hBOOL(hAPP(c_Not,v))*.
% 143.27/143.51 10028[0:Res:3363.0,3105.0] || hBOOL(hAPP(u,v))*+ -> hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(u,c_Not,w))* hBOOL(hAPP(c_Not,v))*.
% 143.27/143.51 10059[2:Spt:9764.1] || -> hBOOL(hAPP(c_Not,u))*.
% 143.27/143.51 10060[2:MRR:3546.0,10059.0] || hBOOL(u)* -> .
% 143.27/143.51 10067[2:UnC:10060.0,3721.0] || -> .
% 143.27/143.51 10149[2:Spt:10067.0,9764.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbspec__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Not,v))*.
% 143.27/143.51 10275[0:Res:1091.0,3150.0] || hBOOL(hAPP(u,v_P____)) -> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__XbexI__1__1(u,c_Arrow__Order__Mirabelle_OProf,v)))*.
% 143.27/143.51 10809[0:SpL:401.1,3153.0] class_Lattices_Olower__semilattice(u) || hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(w,u),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(x,c_Lattices_Olower__semilattice__class_Oinf(w,u),y)))*.
% 143.27/143.51 11235[0:Res:1091.0,3236.0] || hBOOL(hAPP(u,v_P____)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XbexI__1__1(u,c_Arrow__Order__Mirabelle_OProf,v)))*.
% 143.27/143.51 11709[0:Res:11235.1,3546.0] || hBOOL(hAPP(c_Not,v_P____)) hBOOL(c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Not,c_Arrow__Order__Mirabelle_OProf,u))* -> .
% 143.27/143.51 11719[1:MRR:11709.0,9871.0] || hBOOL(c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Not,c_Arrow__Order__Mirabelle_OProf,u))* -> .
% 143.27/143.51 12519[0:SpL:389.0,3233.0] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_COMBC(u,y,z,x1),w),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(u,y,z,x1),w),x2,x,x3)))*.
% 143.27/143.51 12610[0:Rew:389.0,12519.2] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_COMBC(u,y,z,x1),w),x2,x,x3)),w))*.
% 143.27/143.51 12782[0:Res:529.0,3234.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(hAPP(c_Set_Oinsert(v,w),x),u,y,z)))*.
% 143.27/143.51 14324[0:SpL:710.0,260.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> c_Fun_Oinj__on(u,x,v,w)*.
% 143.27/143.51 14573[0:SpR:390.0,3239.0] || -> hBOOL(u) hBOOL(hAPP(c_FuncSet_OPi(c_COMBK(u,v,w),x,y,z),x1))*.
% 143.27/143.51 15028[0:Res:4090.1,192.0] || hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(u,tc_bool)),hAPP(c_fequal(u),v)),v))* -> equal(hAPP(c_fequal(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 143.27/143.51 15042[0:Rew:1870.0,15028.0] || hBOOL(hAPP(c_Not,hAPP(hAPP(c_fequal(u),v),v)))* -> equal(hAPP(c_fequal(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 143.27/143.51 15043[0:MRR:15042.1,1110.0] || hBOOL(hAPP(c_Not,hAPP(hAPP(c_fequal(u),v),v)))* -> .
% 143.27/143.51 15240[0:Res:498.0,9934.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__XballE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Not,v))* hBOOL(hAPP(c_Not,w))*.
% 143.27/143.51 15367[3:Spt:15240.1] || -> hBOOL(hAPP(c_Not,u))*.
% 143.27/143.51 15368[3:UnC:15367.0,15043.0] || -> .
% 143.27/143.51 15369[3:Spt:15368.0,15240.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__XballE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Not,v))*.
% 143.27/143.51 15710[0:Res:498.0,10028.0] || -> hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Not,v))* hBOOL(hAPP(c_Not,w))*.
% 143.27/143.51 15838[4:Spt:15710.1] || -> hBOOL(hAPP(c_Not,u))*.
% 143.27/143.51 15839[4:UnC:15838.0,15043.0] || -> .
% 143.27/143.51 15840[4:Spt:15839.0,15710.0] || -> hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Not,v))*.
% 143.27/143.51 16093[5:Spt:9760.0,9760.2] || -> c_Arrow__Order__Mirabelle_Odictator(u,v) hBOOL(hAPP(c_Not,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(u,v)))*.
% 143.27/143.51 16110[5:Res:16093.1,3546.0] || hBOOL(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(u,v))* -> c_Arrow__Order__Mirabelle_Odictator(u,v).
% 143.27/143.51 18735[0:SpL:389.0,3149.0] || hBOOL(hAPP(hAPP(u,v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_COMBC(u,y,z,x1),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,x2,hAPP(c_COMBC(u,y,z,x1),w),x3)))*.
% 143.27/143.51 18772[0:Res:529.0,3149.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,y,hAPP(c_Set_Oinsert(v,w),x),z)))*.
% 143.27/143.51 18922[0:Rew:389.0,18735.2] || hBOOL(hAPP(hAPP(u,v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,hAPP(c_COMBC(u,z,x1,x2),w),x3)),w))*.
% 143.27/143.51 18986[0:SpR:3203.1,1865.0] || -> hBOOL(hAPP(u,v)) equal(hAPP(u,hAPP(c_COMBK(v,w,x),y)),hAPP(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y))**.
% 143.27/143.51 19029[0:Rew:390.0,18986.1] || -> hBOOL(hAPP(u,v))* equal(hAPP(u,v),hAPP(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x))*.
% 143.27/143.51 19725[0:Res:16.0,265.1] class_HOL_Oord(tc_bool) || -> c_lessequals(hAPP(u,v),hAPP(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v),tc_bool)*.
% 143.27/143.51 19731[0:Res:79.0,265.1] class_HOL_Oord(tc_bool) || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),hAPP(w,v),tc_bool)*.
% 143.27/143.51 19783[0:SSi:19725.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> c_lessequals(hAPP(u,v),hAPP(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v),tc_bool)*.
% 143.27/143.51 19784[0:SSi:19731.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),hAPP(w,v),tc_bool)*.
% 143.27/143.51 20095[0:SpR:34.0,19783.0] || -> c_lessequals(u,hAPP(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w),tc_bool)*.
% 143.27/143.51 20210[0:Res:20095.0,2850.2] class_Lattices_Oupper__semilattice(tc_bool) class_Lattices_Obounded__lattice(tc_bool) || -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 20216[0:Res:20095.0,53.1] class_Orderings_Oorder(tc_bool) || c_lessequals(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),w,tc_bool)* -> equal(w,hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v)).
% 143.27/143.51 20220[0:SSi:20210.1,20210.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 20222[0:Rew:20220.0,20095.0] || -> c_lessequals(u,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)*.
% 143.27/143.51 20223[0:Rew:20220.0,498.0] || -> hBOOL(c_Orderings_Otop__class_Otop(tc_bool))*.
% 143.27/143.51 20225[0:Rew:20220.0,1881.0] || -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),hAPP(c_Not,c_Orderings_Otop__class_Otop(tc_bool)))**.
% 143.27/143.51 20241[0:Rew:20225.0,479.0] || hBOOL(hAPP(c_Not,c_Orderings_Otop__class_Otop(tc_bool)))* -> .
% 143.27/143.51 20245[0:Rew:20225.0,19029.1] || -> hBOOL(hAPP(u,v))* equal(hAPP(u,v),hAPP(c_Not,c_Orderings_Otop__class_Otop(tc_bool)))*.
% 143.27/143.51 20263[0:Rew:20225.0,19784.0] || -> c_lessequals(hAPP(c_Not,c_Orderings_Otop__class_Otop(tc_bool)),hAPP(u,v),tc_bool)*.
% 143.27/143.51 20278[0:Rew:20220.0,20216.2,20220.0,20216.1] class_Orderings_Oorder(tc_bool) || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* -> equal(u,c_Orderings_Otop__class_Otop(tc_bool)).
% 143.27/143.51 20279[0:SSi:20278.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* -> equal(u,c_Orderings_Otop__class_Otop(tc_bool)).
% 143.27/143.51 20365[0:SpR:489.0,20263.0] || -> c_lessequals(hAPP(c_Not,c_Orderings_Otop__class_Otop(tc_bool)),u,tc_bool)*.
% 143.27/143.51 20631[0:Res:20365.0,53.1] class_Orderings_Oorder(tc_bool) || c_lessequals(u,hAPP(c_Not,c_Orderings_Otop__class_Otop(tc_bool)),tc_bool)* -> equal(hAPP(c_Not,c_Orderings_Otop__class_Otop(tc_bool)),u).
% 143.27/143.51 20632[0:Res:20365.0,2822.2] class_Lattices_Oupper__semilattice(tc_bool) class_Lattices_Obounded__lattice(tc_bool) || -> equal(hAPP(c_Not,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 20634[0:SSi:20632.1,20632.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_Not,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 20635[0:Rew:20634.0,20241.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_bool))* -> .
% 143.27/143.51 20636[0:Rew:20634.0,20365.0] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),u,tc_bool)*.
% 143.27/143.51 20637[0:Rew:20634.0,20225.0] || -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 20638[0:Rew:20634.0,20245.1] || -> hBOOL(hAPP(u,v))* equal(hAPP(u,v),c_Orderings_Obot__class_Obot(tc_bool)).
% 143.27/143.51 20675[0:Rew:20634.0,20631.2,20634.0,20631.1] class_Orderings_Oorder(tc_bool) || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)* -> equal(c_Orderings_Obot__class_Obot(tc_bool),u).
% 143.27/143.51 20676[0:SSi:20675.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)* -> equal(c_Orderings_Obot__class_Obot(tc_bool),u).
% 143.27/143.51 20826[0:SpR:20634.0,1893.0] || -> equal(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 20970[0:Res:226.1,20279.0] class_Lattices_Olattice(tc_bool) || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 20973[0:Res:227.1,20279.0] class_Lattices_Olattice(tc_bool) || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 20981[0:SSi:20970.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 20982[0:SSi:20973.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 21072[0:SpR:20981.0,50.1] class_Lattices_Olattice(tc_bool) || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u)**.
% 143.27/143.51 21108[0:SpL:20981.0,2723.1] class_Lattices_Oupper__semilattice(tc_bool) || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)*.
% 143.27/143.51 21113[0:SSi:21072.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u)**.
% 143.27/143.51 21114[0:SSi:21108.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)*.
% 143.27/143.51 21464[0:SpR:21113.0,402.1] class_Lattices_Olattice(tc_bool) || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),u),u)**.
% 143.27/143.51 21511[0:SSi:21464.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),u),u)**.
% 143.27/143.51 21993[0:Res:27.1,20676.0] class_Lattices_Olattice(tc_bool) || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),u),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 22003[0:Res:26.1,20676.0] class_Lattices_Olattice(tc_bool) || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 22011[0:SSi:21993.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),u),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 22012[0:SSi:22003.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 22046[0:SpR:22011.0,1570.1] class_Lattices_Olattice(tc_bool) || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u)**.
% 143.27/143.51 22110[0:SSi:22046.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u)**.
% 143.27/143.51 22142[0:SpR:22110.0,252.1] class_Lattices_Olattice(tc_bool) || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),u),u)**.
% 143.27/143.51 22200[0:SSi:22142.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),u),u)**.
% 143.27/143.51 23005[0:Res:3239.0,68.0] || -> hBOOL(hAPP(c_FuncSet_OPi(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_fun(v,tc_bool)),w),x,y,z),x1)) hBOOL(hAPP(u,c_FuncSet_Osko__FuncSet__XPi__I__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_fun(v,tc_bool)),w),x,x1,y,z)))* hBOOL(hAPP(w,c_FuncSet_Osko__FuncSet__XPi__I__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_fun(v,tc_bool)),w),x,x1,y,z)))*.
% 143.27/143.51 23006[0:Res:3240.0,68.0] || -> hBOOL(hAPP(c_FuncSet_OPi(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_fun(v,tc_bool)),w),x,y,z),x1)) hBOOL(hAPP(u,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_fun(v,tc_bool)),w),x,x1,y,z)))* hBOOL(hAPP(w,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_fun(v,tc_bool)),w),x,x1,y,z)))*.
% 143.27/143.51 23112[0:Res:21114.1,2.1] class_Orderings_Oorder(tc_bool) || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_lessequals(v,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)* -> c_lessequals(v,u,tc_bool)*.
% 143.27/143.51 23123[0:SSi:23112.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_lessequals(v,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)* -> c_lessequals(v,u,tc_bool)*.
% 143.27/143.51 23124[0:MRR:23123.1,20222.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> c_lessequals(v,u,tc_bool)*.
% 143.27/143.51 23293[0:Res:23124.1,20676.0] || equal(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Obot__class_Obot(tc_bool),u)*.
% 143.27/143.51 23295[0:AED:312.0,23293.1] || equal(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 143.27/143.51 24011[0:SpR:401.1,20638.0] class_Lattices_Olower__semilattice(u) || -> hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w))* equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(w,u),v),c_Orderings_Obot__class_Obot(tc_bool)).
% 143.27/143.51 24056[0:SpR:1893.0,20638.0] || -> hBOOL(u) equal(hAPP(c_Not,hAPP(c_Not,u)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 24080[0:Res:20638.0,807.0] || -> equal(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 24114[0:Res:20638.0,3546.0] || hBOOL(u) -> equal(hAPP(c_Not,u),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 24152[0:Rew:1893.0,24056.1] || -> hBOOL(u)* equal(u,c_Orderings_Obot__class_Obot(tc_bool))*.
% 143.27/143.51 24379[0:SpR:24080.0,35.0] || -> equal(c_Fun_Ofun__upd(c_Arrow__Order__Mirabelle_OProf,v_Q____,c_Orderings_Obot__class_Obot(tc_bool),u,v),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 24416[0:SpR:24152.1,20636.0] || -> hBOOL(u) c_lessequals(u,v,tc_bool)*.
% 143.27/143.51 24417[0:SpR:24152.1,20826.0] || -> hBOOL(u) equal(hAPP(c_Not,u),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 24423[0:SpR:24152.1,22200.0] || -> hBOOL(u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),v),v)**.
% 143.27/143.51 24434[0:SpR:24152.1,24152.1] || -> hBOOL(u)* hBOOL(v)* equal(v,u)*.
% 143.27/143.51 24446[0:SpL:24152.1,20676.0] || c_lessequals(u,v,tc_bool)* -> hBOOL(v) equal(c_Orderings_Obot__class_Obot(tc_bool),u).
% 143.27/143.51 24551[1:Res:24152.0,11719.0] || -> equal(c_ATP__Linkup_Osko__Set__XbexI__1__1(c_Not,c_Arrow__Order__Mirabelle_OProf,u),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 24574[5:Res:24152.0,16110.0] || -> equal(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(u,v),c_Orderings_Obot__class_Obot(tc_bool))** c_Arrow__Order__Mirabelle_Odictator(u,v).
% 143.27/143.51 25443[5:Rew:24574.0,406.0] || equal(hAPP(u,c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Orderings_Obot__class_Obot(tc_bool),v))*+ -> c_Arrow__Order__Mirabelle_Odictator(u,v)*.
% 143.27/143.51 28861[0:Res:24416.1,8.1] class_Lattices_Oupper__semilattice(tc_bool) || -> hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),v))* c_lessequals(u,w,tc_bool)*.
% 143.27/143.51 28873[0:SSi:28861.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),v))* c_lessequals(u,w,tc_bool)*.
% 143.27/143.51 28876[1:SpR:24551.0,10275.1] || hBOOL(hAPP(c_Not,v_P____)) -> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool)))*.
% 143.27/143.51 28879[1:MRR:28876.0,9871.0] || -> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool)))*.
% 143.27/143.51 28880[5:EqR:25443.0] || -> c_Arrow__Order__Mirabelle_Odictator(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))*.
% 143.27/143.51 28967[1:SpR:24152.1,28879.0] || -> hBOOL(u) hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,u))*.
% 143.27/143.51 28969[5:SpR:24152.1,28880.0] || -> hBOOL(u) c_Arrow__Order__Mirabelle_Odictator(u,u)*.
% 143.27/143.51 28973[5:Res:28969.1,4730.0] || -> hBOOL(u) equal(hAPP(u,v_P____),hAPP(v_P____,u))*.
% 143.27/143.51 28974[1:SpR:24080.0,28967.1] || -> hBOOL(v_Q____) hBOOL(c_Orderings_Obot__class_Obot(tc_bool))*.
% 143.27/143.51 28975[1:MRR:28974.1,20635.0] || -> hBOOL(v_Q____)*.
% 143.27/143.51 29836[0:SpR:24434.2,22012.0] || -> hBOOL(u) hBOOL(c_Lattices_Olower__semilattice__class_Oinf(v,tc_bool))* equal(hAPP(u,c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 29841[0:SpR:24434.2,22011.0] || -> hBOOL(u) hBOOL(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),tc_bool))* equal(hAPP(u,v),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 29909[0:SpR:24434.2,22200.0] || -> hBOOL(u) hBOOL(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),tc_bool))* equal(hAPP(u,v),v)**.
% 143.27/143.51 30062[0:SpR:24434.2,14573.1] || -> hBOOL(u) hBOOL(c_FuncSet_OPi(c_COMBK(v,w,x),y,z,x1))* hBOOL(v) hBOOL(hAPP(u,x2))*.
% 143.27/143.51 31334[1:Res:24434.0,9876.0] || -> hBOOL(u)* equal(u,v_P____).
% 143.27/143.51 32042[1:Res:31334.0,20635.0] || -> equal(c_Orderings_Obot__class_Obot(tc_bool),v_P____)**.
% 143.27/143.51 32047[1:Rew:32042.0,20826.0] || -> equal(hAPP(c_Not,v_P____),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 32048[1:Rew:32042.0,20637.0] || -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),v_P____)**.
% 143.27/143.51 32053[1:Rew:32042.0,22011.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_P____,tc_bool),u),v_P____)**.
% 143.27/143.51 32054[1:Rew:32042.0,22110.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),v_P____),u)**.
% 143.27/143.51 32055[1:Rew:32042.0,22200.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_P____,tc_bool),u),u)**.
% 143.27/143.51 32056[1:Rew:32042.0,22012.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),v_P____),v_P____)**.
% 143.27/143.51 32060[1:Rew:32042.0,23295.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_P____)** -> .
% 143.27/143.51 32211[1:Rew:32042.0,24446.2] || c_lessequals(u,v,tc_bool)* -> hBOOL(v) equal(v_P____,u).
% 143.27/143.51 32272[1:Rew:32042.0,24114.1] || hBOOL(u) -> equal(hAPP(c_Not,u),v_P____)**.
% 143.27/143.51 32277[1:Rew:32042.0,29841.1] || -> hBOOL(u) hBOOL(c_Lattices_Olower__semilattice__class_Oinf(v_P____,tc_bool))* equal(hAPP(u,v),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 32316[1:Rew:32042.0,29909.1] || -> hBOOL(u) hBOOL(c_Lattices_Oupper__semilattice__class_Osup(v_P____,tc_bool))* equal(hAPP(u,v),v)**.
% 143.27/143.51 32718[1:Rew:32042.0,29836.2] || -> hBOOL(u) hBOOL(c_Lattices_Olower__semilattice__class_Oinf(v,tc_bool))* equal(hAPP(u,v_P____),v_P____)**.
% 143.27/143.51 32742[1:Rew:32042.0,32277.2] || -> hBOOL(u) hBOOL(c_Lattices_Olower__semilattice__class_Oinf(v_P____,tc_bool))* equal(hAPP(u,v),v_P____)**.
% 143.27/143.51 32939[1:SpR:32042.0,530.1] class_Lattices_Oboolean__algebra(tc_bool) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_P____),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 32964[1:SSi:32939.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_P____),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 33532[1:SpR:32272.1,1893.0] || hBOOL(u)* -> equal(hAPP(c_Not,v_P____),u)*.
% 143.27/143.51 33553[1:Rew:32047.0,33532.1] || hBOOL(u)*+ -> equal(c_Orderings_Otop__class_Otop(tc_bool),u)*.
% 143.27/143.51 33729[1:Res:1091.0,33553.0] || -> equal(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 33744[1:Res:529.0,33553.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),w),u),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 33747[1:Res:3792.0,33553.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OProf),v_P____),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 33781[1:Res:14573.1,33553.0] || -> hBOOL(u) equal(hAPP(c_FuncSet_OPi(c_COMBK(u,v,w),x,y,z),x1),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 33782[1:Res:31334.0,33553.0] || -> equal(u,v_P____) equal(c_Orderings_Otop__class_Otop(tc_bool),u)*.
% 143.27/143.51 33783[1:Res:24434.0,33553.0] || -> hBOOL(u)* equal(u,v)* equal(c_Orderings_Otop__class_Otop(tc_bool),v)*.
% 143.27/143.51 33818[1:Res:28975.0,33553.0] || -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_Q____)**.
% 143.27/143.51 33827[1:Rew:33818.0,20981.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),v_Q____),v_Q____)**.
% 143.27/143.51 33829[1:Rew:33818.0,21511.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_Q____,tc_bool),u),u)**.
% 143.27/143.51 33831[1:Rew:33818.0,33553.1] || hBOOL(u)* -> equal(v_Q____,u).
% 143.27/143.51 33836[1:Rew:33818.0,32060.0] || equal(v_Q____,v_P____)** -> .
% 143.27/143.51 33838[1:Rew:33818.0,32047.0] || -> equal(hAPP(c_Not,v_P____),v_Q____)**.
% 143.27/143.51 33839[1:Rew:33818.0,32964.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_P____),v_Q____)**.
% 143.27/143.51 33840[1:Rew:33818.0,24417.1] || -> hBOOL(u) equal(hAPP(c_Not,u),v_Q____)**.
% 143.27/143.51 34280[1:Rew:33818.0,33729.0] || -> equal(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),v_Q____)**.
% 143.27/143.51 34365[1:Rew:33818.0,33782.1] || -> equal(u,v_P____) equal(v_Q____,u)*.
% 143.27/143.51 34373[1:Rew:33818.0,33783.2] || -> hBOOL(u)* equal(u,v)* equal(v_Q____,v)*.
% 143.27/143.51 34382[1:Rew:33818.0,33744.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),w),u),v_Q____)**.
% 143.27/143.51 34449[1:Rew:33818.0,33781.1] || -> hBOOL(u) equal(hAPP(c_FuncSet_OPi(c_COMBK(u,v,w),x,y,z),x1),v_Q____)**.
% 143.27/143.51 34484[1:Rew:33818.0,33747.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OProf),v_P____),v_Q____)**.
% 143.27/143.51 34653[1:SpR:33818.0,477.1] class_Lattices_Oboolean__algebra(tc_bool) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_Q____),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 34678[1:Rew:32042.0,34653.1] class_Lattices_Oboolean__algebra(tc_bool) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_Q____),v_P____)**.
% 143.27/143.51 34679[1:SSi:34678.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_Q____),v_P____)**.
% 143.27/143.51 34968[1:SpR:34365.1,3028.0] || -> equal(hAPP(c_in(u),v),v_P____)** equal(hAPP(v_Q____,w),hAPP(w,v))*.
% 143.27/143.51 35137[1:SpR:34365.1,2495.0] || -> equal(hAPP(c_Set_Oinsert(v_P____,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OProf),v_P____)** equal(v_Q____,c_Arrow__Order__Mirabelle_OProf).
% 143.27/143.51 35153[1:SpR:34365.1,490.0] || -> equal(tc_fun(u,tc_bool),v_P____)** equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,v_Q____),c_Orderings_Otop__class_Otop(v_Q____)),v)**.
% 143.27/143.51 35160[1:SpR:34365.1,327.0] || -> equal(tc_fun(u,tc_bool),v_P____)** equal(hAPP(c_HOL_Ominus__class_Ominus(v,v_Q____),c_Orderings_Obot__class_Obot(v_Q____)),v)**.
% 143.27/143.51 35227[1:SpR:34365.1,2495.0] || -> equal(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_P____)** equal(hAPP(c_Set_Oinsert(v_P____,v_Q____),c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf).
% 143.27/143.51 35278[1:SpR:34365.1,32048.0] || -> equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_P____)** equal(hAPP(v_Q____,v),v_P____)**.
% 143.27/143.51 35318[1:SpR:34365.1,315.0] || -> equal(c_Set_Oinsert(u,v),v_P____)** equal(hAPP(v_Q____,hAPP(v_Q____,w)),hAPP(v_Q____,w))**.
% 143.27/143.51 35322[1:SpR:34365.1,2494.1] || hBOOL(hAPP(u,v))* -> equal(c_Set_Oinsert(v,w),v_P____)** equal(hAPP(v_Q____,u),u).
% 143.27/143.51 35388[1:SpR:34365.1,32056.0] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),v_P____)** equal(hAPP(v_Q____,v_P____),v_P____)**.
% 143.27/143.51 35444[1:SpR:34365.1,32055.0] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(v_P____,tc_bool),v_P____) equal(hAPP(v_Q____,u),u)**.
% 143.27/143.51 35459[1:SpR:34365.1,1952.0] || -> equal(c_Fun_Ofun__upd(c_Not,hAPP(c_Not,u),u,v,w),v_P____)** equal(v_Q____,c_Not).
% 143.27/143.51 35485[1:SpR:34365.1,33839.0] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),v_P____) equal(hAPP(v_Q____,v_P____),v_Q____)**.
% 143.27/143.51 35486[1:SpR:34365.1,34679.0] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),v_P____) equal(hAPP(v_Q____,v_Q____),v_P____)**.
% 143.27/143.51 35693[1:SpL:34365.1,519.0] || equal(hAPP(v_Q____,u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Set_Oinsert(w,v),v_P____)**.
% 143.27/143.51 35766[1:Rew:1952.0,35459.0] || -> equal(v_P____,c_Not) equal(v_Q____,c_Not)**.
% 143.27/143.51 35804[1:Rew:2495.0,35137.0] || -> equal(v_P____,c_Arrow__Order__Mirabelle_OProf) equal(v_Q____,c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 35888[6:Spt:35766.0] || -> equal(v_P____,c_Not)**.
% 143.27/143.51 35892[6:Rew:35888.0,9876.0] || hBOOL(c_Not)* -> .
% 143.27/143.51 35908[6:Rew:35888.0,32053.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Not,tc_bool),u),c_Not)**.
% 143.27/143.51 35911[6:Rew:35888.0,32054.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Not),u)**.
% 143.27/143.51 35912[6:Rew:35888.0,32055.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Not,tc_bool),u),u)**.
% 143.27/143.51 35925[6:Rew:35888.0,33836.0] || equal(v_Q____,c_Not)** -> .
% 143.27/143.51 36537[6:Rew:35888.0,28973.1] || -> hBOOL(u) equal(hAPP(u,c_Not),hAPP(c_Not,u))*.
% 143.27/143.51 36769[6:Rew:35888.0,32316.1] || -> hBOOL(u) hBOOL(c_Lattices_Oupper__semilattice__class_Osup(c_Not,tc_bool))* equal(hAPP(u,v),v)**.
% 143.27/143.51 36895[6:Rew:35888.0,32718.2] || -> hBOOL(u) hBOOL(c_Lattices_Olower__semilattice__class_Oinf(v,tc_bool))* equal(hAPP(u,c_Not),c_Not)**.
% 143.27/143.51 37290[6:Rew:35888.0,35444.0] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(c_Not,tc_bool),c_Not) equal(hAPP(v_Q____,u),u)**.
% 143.27/143.51 37359[6:Rew:35888.0,34968.0] || -> equal(hAPP(c_in(u),v),c_Not)** equal(hAPP(v_Q____,w),hAPP(w,v))*.
% 143.27/143.51 37821[6:Rew:33840.1,36537.1] || -> hBOOL(u) equal(hAPP(u,c_Not),v_Q____)**.
% 143.27/143.51 37848[6:Rew:37821.1,36895.2] || -> hBOOL(u)* hBOOL(c_Lattices_Olower__semilattice__class_Oinf(v,tc_bool))* equal(v_Q____,c_Not).
% 143.27/143.51 37849[6:Con:37848.0] || -> hBOOL(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool))* equal(v_Q____,c_Not).
% 143.27/143.51 37850[6:MRR:37849.1,35925.0] || -> hBOOL(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool))*.
% 143.27/143.51 38148[6:Res:37850.0,33831.0] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),v_Q____)**.
% 143.27/143.51 38150[6:Rew:38148.0,35908.0] || -> equal(hAPP(v_Q____,u),c_Not)**.
% 143.27/143.51 38339[6:Rew:38150.0,37290.1] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(c_Not,tc_bool),c_Not)** equal(c_Not,u)*.
% 143.27/143.51 38362[6:Rew:38150.0,37359.1] || -> equal(hAPP(c_in(u),v),c_Not)** equal(hAPP(w,v),c_Not)**.
% 143.27/143.51 38540[6:AED:312.0,38339.1] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(c_Not,tc_bool),c_Not)**.
% 143.27/143.51 38541[6:Rew:38540.0,35912.0] || -> equal(hAPP(c_Not,u),u)**.
% 143.27/143.51 38548[6:Rew:38540.0,36769.1] || -> hBOOL(u) hBOOL(c_Not) equal(hAPP(u,v),v)**.
% 143.27/143.51 40285[6:MRR:38548.1,35892.0] || -> hBOOL(u) equal(hAPP(u,v),v)**.
% 143.27/143.51 40375[6:Rew:40285.1,30062.3] || -> hBOOL(u)* hBOOL(c_FuncSet_OPi(c_COMBK(v,w,x),y,z,x1))* hBOOL(v) hBOOL(x2)*.
% 143.27/143.51 41452[6:Con:38362.1] || -> equal(hAPP(c_in(u),v),c_Not)**.
% 143.27/143.51 41453[6:Rew:41452.0,3028.0] || -> equal(hAPP(c_Not,u),hAPP(u,v))*.
% 143.27/143.51 41484[6:Rew:38541.0,41453.0] || -> equal(hAPP(u,v),u)**.
% 143.27/143.51 41984[6:Rew:41484.0,18922.2] || hBOOL(hAPP(hAPP(u,v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(u,w)).
% 143.27/143.51 42065[6:Rew:41484.0,18772.1] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(c_Set_Oinsert(v,w),x))*.
% 143.27/143.51 42281[6:Rew:41484.0,12610.2] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(u,w)).
% 143.27/143.51 42368[6:Rew:41484.0,12782.1] || -> hBOOL(hAPP(u,v))* hBOOL(hAPP(c_Set_Oinsert(v,w),x))*.
% 143.27/143.51 43638[6:Rew:41484.0,34449.1] || -> hBOOL(u) equal(c_FuncSet_OPi(c_COMBK(u,v,w),x,y,z),v_Q____)**.
% 143.27/143.51 43694[6:Rew:41484.0,35911.0] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),u)**.
% 143.27/143.51 43696[6:Rew:41484.0,33827.0] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),v_Q____)**.
% 143.27/143.51 43900[6:Rew:41484.0,3076.0] || hBOOL(hAPP(c_Set_Oimage(u,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v),hAPP(u,v_Q____)))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(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_bool)),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v)* -> .
% 143.27/143.51 43902[6:Rew:41484.0,3062.0] || hBOOL(hAPP(c_Set_Oinsert(u,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____))* -> equal(v_Q____,u).
% 143.27/143.51 45089[6:Rew:41484.0,38150.0] || -> equal(v_Q____,c_Not)**.
% 143.27/143.51 45953[6:Rew:43694.0,43696.0,45089.0,43696.0] || -> equal(u,c_Not)*.
% 143.27/143.51 45979[6:Rew:45953.0,399.0] || -> c_Fun_Oinj__on(u,c_Not,v,w)*.
% 143.27/143.51 46228[6:Rew:45953.0,14324.0] || c_Fun_Oinj__on(u,c_Not,v,w)* -> c_Fun_Oinj__on(u,x,v,w)*.
% 143.27/143.51 46535[6:MRR:42065.0,42368.0] || -> hBOOL(hAPP(c_Set_Oinsert(u,v),w))*.
% 143.27/143.51 46558[6:MRR:46228.0,45979.0] || -> c_Fun_Oinj__on(u,v,w,x)*.
% 143.27/143.51 47013[6:Con:40375.0] || -> hBOOL(c_FuncSet_OPi(c_COMBK(u,v,w),x,y,z))* hBOOL(u).
% 143.27/143.51 47014[6:Rew:43638.1,47013.0] || -> hBOOL(v_Q____)* hBOOL(u)*.
% 143.27/143.51 47015[6:Con:47014.1] || -> hBOOL(v_Q____)*.
% 143.27/143.51 47256[6:MRR:41984.1,42281.1] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(u,w)).
% 143.27/143.51 47314[6:MRR:43902.0,46535.0] || -> equal(v_Q____,u)*.
% 143.27/143.51 47744[6:Rew:47314.0,47256.0] || hBOOL(v_Q____) -> hBOOL(hAPP(u,v))*.
% 143.27/143.51 48048[6:MRR:47744.0,47015.0] || -> hBOOL(hAPP(u,v))*.
% 143.27/143.51 50085[6:MRR:43900.0,43900.1,48048.0,46558.0] || -> .
% 143.27/143.51 50089[6:Spt:50085.0,35766.0,35888.0] || equal(v_P____,c_Not)** -> .
% 143.27/143.51 50090[6:Spt:50085.0,35766.1] || -> equal(v_Q____,c_Not)**.
% 143.27/143.51 50091[6:Rew:50090.0,28975.0] || -> hBOOL(c_Not)*.
% 143.27/143.51 50092[6:Rew:50090.0,33836.0] || equal(v_P____,c_Not)** -> .
% 143.27/143.51 50096[6:Rew:50090.0,33838.0] || -> equal(hAPP(c_Not,v_P____),c_Not)**.
% 143.27/143.51 50102[6:Rew:50090.0,35804.1] || -> equal(v_P____,c_Arrow__Order__Mirabelle_OProf)** equal(c_Arrow__Order__Mirabelle_OProf,c_Not).
% 143.27/143.51 50107[6:Rew:50090.0,33829.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Not,tc_bool),u),u)**.
% 143.27/143.51 50135[6:Rew:50090.0,34382.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),w),u),c_Not)**.
% 143.27/143.51 50147[6:Rew:50096.0,35388.1,50090.0,35388.1] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),v_P____)** equal(v_P____,c_Not).
% 143.27/143.51 50148[6:MRR:50147.1,50092.0] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),v_P____)**.
% 143.27/143.51 50150[6:Rew:50148.0,50107.0] || -> equal(hAPP(v_P____,u),u)**.
% 143.27/143.51 50328[6:Rew:50090.0,35160.1] || -> equal(tc_fun(u,tc_bool),v_P____)** equal(hAPP(c_HOL_Ominus__class_Ominus(v,c_Not),c_Orderings_Obot__class_Obot(c_Not)),v)**.
% 143.27/143.51 50373[6:Rew:50090.0,35693.0] || equal(hAPP(c_Not,u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Set_Oinsert(w,v),v_P____)**.
% 143.27/143.51 50408[6:Rew:1893.0,35318.1,50090.0,35318.1] || -> equal(c_Set_Oinsert(u,v),v_P____)** equal(hAPP(c_Not,w),w)**.
% 143.27/143.51 50410[6:Rew:50408.1,50373.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Set_Oinsert(w,v),v_P____)**.
% 143.27/143.51 50412[6:AED:312.0,50410.0] || -> equal(c_Set_Oinsert(u,v),v_P____)**.
% 143.27/143.51 50428[6:Rew:50412.0,50135.0] || -> equal(hAPP(hAPP(v_P____,u),v),c_Not)**.
% 143.27/143.51 50469[6:Rew:50150.0,50428.0] || -> equal(hAPP(u,v),c_Not)**.
% 143.27/143.51 50471[6:Rew:50469.0,50328.1] || -> equal(tc_fun(u,tc_bool),v_P____)** equal(c_Not,v)*.
% 143.27/143.51 50611[6:Rew:50469.0,328.0] || -> equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Not)**.
% 143.27/143.51 50683[6:Rew:50611.0,2511.0] || equal(c_Arrow__Order__Mirabelle_OProf,c_Not)** -> .
% 143.27/143.51 50687[6:Rew:50611.0,399.0] || -> c_Fun_Oinj__on(u,c_Not,v,w)*.
% 143.27/143.51 50709[6:MRR:50102.1,50683.0] || -> equal(v_P____,c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 50887[6:AED:312.0,50471.1] || -> equal(tc_fun(u,tc_bool),v_P____)**.
% 143.27/143.51 50888[6:Rew:50709.0,50887.0] || -> equal(tc_fun(u,tc_bool),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 51635[6:Rew:50469.0,375.0] || c_Fun_Oinj__on(u,c_Not,v,w)* -> c_Fun_Oinj__on(u,x,v,w)*.
% 143.27/143.51 51636[6:MRR:51635.0,50687.0] || -> c_Fun_Oinj__on(u,v,w,x)*.
% 143.27/143.51 51770[6:Rew:50469.0,35227.1,50888.0,35227.0,50709.0,35227.0] || -> equal(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf)** equal(c_Arrow__Order__Mirabelle_OProf,c_Not).
% 143.27/143.51 51771[6:MRR:51770.1,50683.0] || -> equal(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 59760[6:Rew:50888.0,3076.1,51771.0,3076.1,50888.0,3076.1,50469.0,3076.0] || hBOOL(c_Not) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf,v)* -> .
% 143.27/143.51 59761[6:MRR:59760.0,59760.1,50091.0,51636.0] || -> .
% 143.27/143.51 59794[5:Spt:59761.0,9760.1] || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbspec__1__1(c_Arrow__Order__Mirabelle_OProf,c_Not,u))*.
% 143.27/143.51 59835[6:Spt:35804.0] || -> equal(v_P____,c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 59836[6:Rew:59835.0,9876.0] || hBOOL(c_Arrow__Order__Mirabelle_OProf)* -> .
% 143.27/143.51 59837[6:Rew:59835.0,33836.0] || equal(v_Q____,c_Arrow__Order__Mirabelle_OProf)** -> .
% 143.27/143.51 59840[6:Rew:59835.0,34280.0] || -> equal(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf),v_Q____)**.
% 143.27/143.51 59841[6:Rew:59835.0,33838.0] || -> equal(hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf),v_Q____)**.
% 143.27/143.51 59845[6:Rew:59835.0,34679.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_Q____),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 59856[6:Rew:59835.0,34365.0] || -> equal(u,c_Arrow__Order__Mirabelle_OProf) equal(v_Q____,u)*.
% 143.27/143.51 59865[6:Rew:59835.0,35766.0] || -> equal(c_Arrow__Order__Mirabelle_OProf,c_Not) equal(v_Q____,c_Not)**.
% 143.27/143.51 59875[6:Rew:59835.0,32053.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Arrow__Order__Mirabelle_OProf,tc_bool),u),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 59929[6:Rew:59835.0,32211.2] || c_lessequals(u,v,tc_bool)* -> hBOOL(v) equal(c_Arrow__Order__Mirabelle_OProf,u).
% 143.27/143.51 59959[6:Rew:59835.0,35486.0] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf) equal(hAPP(v_Q____,v_Q____),v_P____)**.
% 143.27/143.51 59960[6:Rew:59835.0,35485.0] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf) equal(hAPP(v_Q____,v_P____),v_Q____)**.
% 143.27/143.51 60012[6:Rew:59835.0,35153.0] || -> equal(tc_fun(u,tc_bool),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,v_Q____),c_Orderings_Otop__class_Otop(v_Q____)),v)**.
% 143.27/143.51 60073[6:Rew:59835.0,35388.0] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(v_Q____,v_P____),v_P____)**.
% 143.27/143.51 60522[6:Rew:59835.0,35278.0] || -> equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(v_Q____,v),v_P____)**.
% 143.27/143.51 60860[6:Rew:59835.0,35318.0] || -> equal(c_Set_Oinsert(u,v),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(v_Q____,hAPP(v_Q____,w)),hAPP(v_Q____,w))**.
% 143.27/143.51 60875[6:Rew:59835.0,34968.0] || -> equal(hAPP(c_in(u),v),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(v_Q____,w),hAPP(w,v))*.
% 143.27/143.51 60943[6:Rew:59835.0,35693.1] || equal(hAPP(v_Q____,u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Set_Oinsert(w,v),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 61078[6:Rew:59835.0,35322.1] || hBOOL(hAPP(u,v))* -> equal(c_Set_Oinsert(v,w),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(v_Q____,u),u).
% 143.27/143.51 61107[6:Rew:59835.0,34484.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf),v_Q____)**.
% 143.27/143.51 61147[6:Rew:59835.0,35227.0] || -> equal(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(c_Set_Oinsert(v_P____,v_Q____),c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf).
% 143.27/143.51 61683[6:Rew:59835.0,59959.1] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf) equal(hAPP(v_Q____,v_Q____),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 61684[6:Rew:59835.0,59960.1] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf) equal(hAPP(v_Q____,c_Arrow__Order__Mirabelle_OProf),v_Q____)**.
% 143.27/143.51 61689[6:Rew:59835.0,60073.1] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(v_Q____,c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 61710[6:Rew:59835.0,60522.1] || -> equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(v_Q____,v),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 61734[6:Rew:59835.0,61147.1] || -> equal(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(c_Set_Oinsert(c_Arrow__Order__Mirabelle_OProf,v_Q____),c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf).
% 143.27/143.51 61776[7:Spt:59865.0] || -> equal(c_Arrow__Order__Mirabelle_OProf,c_Not)**.
% 143.27/143.51 61780[7:Rew:61776.0,59837.0] || equal(v_Q____,c_Not)** -> .
% 143.27/143.51 61783[7:Rew:61776.0,59840.0] || -> equal(hAPP(c_Not,c_Not),v_Q____)**.
% 143.27/143.51 61788[7:Rew:61776.0,59845.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_Q____),c_Not)**.
% 143.27/143.51 62246[7:Rew:61776.0,59856.0] || -> equal(u,c_Not) equal(v_Q____,u)*.
% 143.27/143.51 62373[7:Rew:61776.0,3076.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v),c_Not),hAPP(u,v_Q____)))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(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_bool)),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v)* -> .
% 143.27/143.51 62392[7:Rew:61776.0,59929.2] || c_lessequals(u,v,tc_bool)* -> hBOOL(v) equal(c_Not,u).
% 143.27/143.51 62487[7:Rew:61776.0,61684.0] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Not) equal(hAPP(v_Q____,c_Arrow__Order__Mirabelle_OProf),v_Q____)**.
% 143.27/143.51 62488[7:Rew:61776.0,61683.0] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Not) equal(hAPP(v_Q____,v_Q____),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 62525[7:Rew:61776.0,60012.0] || -> equal(tc_fun(u,tc_bool),c_Not)** equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,v_Q____),c_Orderings_Otop__class_Otop(v_Q____)),v)**.
% 143.27/143.51 62590[7:Rew:61776.0,61689.0] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Not)** equal(hAPP(v_Q____,c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 62952[7:Rew:61776.0,60943.1] || equal(hAPP(v_Q____,u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Set_Oinsert(w,v),c_Not)**.
% 143.27/143.51 63075[7:Rew:61776.0,61078.1] || hBOOL(hAPP(u,v))* -> equal(c_Set_Oinsert(v,w),c_Not)** equal(hAPP(v_Q____,u),u).
% 143.27/143.51 63104[7:Rew:61776.0,61107.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Not),c_Not),v_Q____)**.
% 143.27/143.51 63160[7:Rew:61776.0,61734.0] || -> equal(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Not)** equal(hAPP(c_Set_Oinsert(c_Arrow__Order__Mirabelle_OProf,v_Q____),c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf).
% 143.27/143.51 63666[7:Rew:61776.0,62487.1] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Not) equal(hAPP(v_Q____,c_Not),v_Q____)**.
% 143.27/143.51 63667[7:Rew:61776.0,62488.1] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Not) equal(hAPP(v_Q____,v_Q____),c_Not)**.
% 143.27/143.51 63675[7:Rew:61776.0,62590.1] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Not)** equal(hAPP(v_Q____,c_Not),c_Not)**.
% 143.27/143.51 63752[7:Rew:61776.0,63160.1] || -> equal(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Not)** equal(hAPP(c_Set_Oinsert(c_Not,v_Q____),c_Not),c_Not).
% 143.27/143.51 64398[7:SpR:62246.1,33827.0] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Not)** equal(hAPP(v_Q____,v_Q____),v_Q____)**.
% 143.27/143.51 65196[7:SpR:34373.1,61788.0] || -> hBOOL(u) equal(c_HOL_Ouminus__class_Ouminus(tc_bool),v_Q____) equal(hAPP(u,v_Q____),c_Not)**.
% 143.27/143.51 65211[1:SpR:34373.1,33827.0] || -> hBOOL(u) equal(c_Lattices_Oupper__semilattice__class_Osup(v,tc_bool),v_Q____)** equal(hAPP(u,v_Q____),v_Q____)**.
% 143.27/143.51 65652[8:Spt:63666.0] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Not)**.
% 143.27/143.51 65698[8:Rew:65652.0,65196.1] || -> hBOOL(u) equal(v_Q____,c_Not) equal(hAPP(u,v_Q____),c_Not)**.
% 143.27/143.51 65718[8:MRR:65698.1,61780.0] || -> hBOOL(u) equal(hAPP(u,v_Q____),c_Not)**.
% 143.27/143.51 65719[8:Rew:65718.1,65211.2] || -> hBOOL(u)* equal(c_Lattices_Oupper__semilattice__class_Osup(v,tc_bool),v_Q____)** equal(v_Q____,c_Not).
% 143.27/143.51 65763[8:MRR:65719.2,61780.0] || -> hBOOL(u)* equal(c_Lattices_Oupper__semilattice__class_Osup(v,tc_bool),v_Q____)**.
% 143.27/143.51 65784[8:Rew:65763.1,24423.1] || -> hBOOL(u)* equal(hAPP(v_Q____,v),v)**.
% 143.27/143.51 65798[8:MRR:63075.0,65784.0] || -> equal(c_Set_Oinsert(u,v),c_Not)** equal(hAPP(v_Q____,w),w)**.
% 143.27/143.51 65827[8:Rew:65798.1,62952.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Set_Oinsert(w,v),c_Not)**.
% 143.27/143.51 65849[8:AED:312.0,65827.0] || -> equal(c_Set_Oinsert(u,v),c_Not)**.
% 143.27/143.51 66531[8:Rew:65849.0,63104.0] || -> equal(hAPP(hAPP(c_Not,c_Not),c_Not),v_Q____)**.
% 143.27/143.51 66538[8:Rew:65849.0,34382.0] || -> equal(hAPP(hAPP(c_Not,u),v),v_Q____)**.
% 143.27/143.51 66734[8:Rew:61783.0,66531.0] || -> equal(hAPP(v_Q____,c_Not),v_Q____)**.
% 143.27/143.51 66737[8:Rew:66734.0,63675.1] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Not)** equal(v_Q____,c_Not).
% 143.27/143.51 66743[8:MRR:66737.1,61780.0] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Not)**.
% 143.27/143.51 66744[8:Rew:66743.0,33829.0] || -> equal(hAPP(c_Not,u),u)**.
% 143.27/143.51 68005[8:Rew:66744.0,66538.0] || -> equal(hAPP(u,v),v_Q____)**.
% 143.27/143.51 68182[8:Rew:68005.0,3268.2] || hBOOL(hAPP(c_FuncSet_Oextensional(u,v,w),x)) hBOOL(hAPP(c_FuncSet_Oextensional(u,v,w),y)) equal(hAPP(x,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(u,x,y,v,w)),v_Q____)** -> equal(x,y).
% 143.27/143.51 77949[8:Rew:68005.0,68182.2,68005.0,68182.1,68005.0,68182.0] || hBOOL(v_Q____)* hBOOL(v_Q____)* equal(v_Q____,v_Q____) -> equal(u,v)*.
% 143.27/143.51 77950[8:Obv:77949.2] || hBOOL(v_Q____)* -> equal(u,v)*.
% 143.27/143.51 77951[8:MRR:77950.0,28975.0] || -> equal(u,v)*.
% 143.27/143.51 77952[8:UnC:77951.0,61780.0] || -> .
% 143.27/143.51 77973[8:Spt:77952.0,63666.0,65652.0] || equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Not)** -> .
% 143.27/143.51 77974[8:Spt:77952.0,63666.1] || -> equal(hAPP(v_Q____,c_Not),v_Q____)**.
% 143.27/143.51 77975[8:MRR:63667.0,77973.0] || -> equal(hAPP(v_Q____,v_Q____),c_Not)**.
% 143.27/143.51 77976[8:Rew:77974.0,63675.1] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Not)** equal(v_Q____,c_Not).
% 143.27/143.51 77977[8:MRR:77976.1,61780.0] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Not)**.
% 143.27/143.51 77979[8:Rew:77977.0,33829.0] || -> equal(hAPP(c_Not,u),u)**.
% 143.27/143.51 78035[8:Rew:77975.0,64398.1] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Not)** equal(v_Q____,c_Not).
% 143.27/143.51 78036[8:MRR:78035.1,61780.0] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Not)**.
% 143.27/143.51 78083[8:Rew:77979.0,28873.0,78036.0,28873.0] || -> hBOOL(u)* c_lessequals(v,w,tc_bool)*.
% 143.27/143.51 78084[8:MRR:62392.0,78083.1] || -> hBOOL(u)* equal(c_Not,v)*.
% 143.27/143.51 78328[8:MRR:63075.0,78084.0] || -> equal(c_Set_Oinsert(u,v),c_Not)** equal(hAPP(v_Q____,w),w)**.
% 143.27/143.51 78330[8:Rew:78328.1,62952.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Set_Oinsert(w,v),c_Not)**.
% 143.27/143.51 78332[8:AED:312.0,78330.0] || -> equal(c_Set_Oinsert(u,v),c_Not)**.
% 143.27/143.51 78357[8:Rew:78332.0,34382.0] || -> equal(hAPP(hAPP(c_Not,u),v),v_Q____)**.
% 143.27/143.51 78374[8:Rew:77979.0,78357.0] || -> equal(hAPP(u,v),v_Q____)**.
% 143.27/143.51 78380[8:Rew:78374.0,62525.1] || -> equal(tc_fun(u,tc_bool),c_Not)** equal(v_Q____,v)*.
% 143.27/143.51 78386[8:Rew:78374.0,309.0] || -> equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_Q____)**.
% 143.27/143.51 78388[8:Rew:78374.0,478.0] || -> equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_Q____)**.
% 143.27/143.51 78658[8:Rew:78386.0,14324.0] || c_Fun_Oinj__on(u,v_Q____,v,w)* -> c_Fun_Oinj__on(u,x,v,w)*.
% 143.27/143.51 78679[8:Rew:78388.0,399.0] || -> c_Fun_Oinj__on(u,v_Q____,v,w)*.
% 143.27/143.51 78796[8:AED:312.0,78380.1] || -> equal(tc_fun(u,tc_bool),c_Not)**.
% 143.27/143.51 78809[8:Rew:78796.0,78386.0] || -> equal(c_Orderings_Otop__class_Otop(c_Not),v_Q____)**.
% 143.27/143.51 79002[8:MRR:78658.0,78679.0] || -> c_Fun_Oinj__on(u,v,w,x)*.
% 143.27/143.51 79469[8:Rew:78374.0,63752.1,78796.0,63752.0] || -> equal(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,c_Not),c_Not)** equal(v_Q____,c_Not).
% 143.27/143.51 79470[8:MRR:79469.1,61780.0] || -> equal(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,c_Not),c_Not)**.
% 143.27/143.51 86299[8:Rew:78809.0,62373.1,78796.0,62373.1,79470.0,62373.1,78796.0,62373.1,78374.0,62373.0] || hBOOL(v_Q____) c_Fun_Oinj__on(u,v_Q____,c_Not,v)* -> .
% 143.27/143.51 86300[8:MRR:86299.0,28975.0] || c_Fun_Oinj__on(u,v_Q____,c_Not,v)* -> .
% 143.27/143.51 86301[8:MRR:86300.0,79002.0] || -> .
% 143.27/143.51 86333[7:Spt:86301.0,59865.0,61776.0] || equal(c_Arrow__Order__Mirabelle_OProf,c_Not)** -> .
% 143.27/143.51 86334[7:Spt:86301.0,59865.1] || -> equal(v_Q____,c_Not)**.
% 143.27/143.51 86343[7:Rew:86334.0,59837.0] || equal(c_Arrow__Order__Mirabelle_OProf,c_Not)** -> .
% 143.27/143.51 86346[7:Rew:86334.0,59841.0] || -> equal(hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf),c_Not)**.
% 143.27/143.51 86412[7:Rew:86346.0,61689.1,86334.0,61689.1] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Arrow__Order__Mirabelle_OProf)** equal(c_Arrow__Order__Mirabelle_OProf,c_Not).
% 143.27/143.51 86413[7:MRR:86412.1,86343.0] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 86415[7:Rew:86413.0,59875.0] || -> equal(hAPP(c_Arrow__Order__Mirabelle_OProf,u),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 86539[7:Rew:86334.0,61710.1] || -> equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(c_Not,v),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 86714[7:Rew:86334.0,60875.1] || -> equal(hAPP(c_in(u),v),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(c_Not,w),hAPP(w,v))*.
% 143.27/143.51 86908[7:Rew:86334.0,60943.0] || equal(hAPP(c_Not,u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Set_Oinsert(w,v),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 86910[7:Rew:1893.0,60860.1,86334.0,60860.1] || -> equal(c_Set_Oinsert(u,v),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(c_Not,w),w)**.
% 143.27/143.51 86912[7:Rew:86910.1,86908.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Set_Oinsert(w,v),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 86914[7:AED:312.0,86912.0] || -> equal(c_Set_Oinsert(u,v),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 86934[7:Rew:86914.0,519.0] || equal(hAPP(c_Arrow__Order__Mirabelle_OProf,u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 143.27/143.51 86960[7:Rew:86415.0,86934.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Arrow__Order__Mirabelle_OProf)** -> .
% 143.27/143.51 86962[7:MRR:86539.0,86960.0] || -> equal(hAPP(c_Not,u),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 86972[7:Rew:86962.0,86714.1] || -> equal(hAPP(c_in(u),v),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(w,v),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 87148[7:Con:86972.1] || -> equal(hAPP(c_in(u),v),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 87149[7:Rew:87148.0,3028.0] || -> equal(hAPP(c_Arrow__Order__Mirabelle_OProf,u),hAPP(u,v))*.
% 143.27/143.51 87150[7:Rew:86415.0,87149.0] || -> equal(hAPP(u,v),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 93554[7:Rew:87150.0,23006.2,87150.0,23006.1,87150.0,23006.0] || -> hBOOL(c_Arrow__Order__Mirabelle_OProf)* hBOOL(c_Arrow__Order__Mirabelle_OProf)* hBOOL(c_Arrow__Order__Mirabelle_OProf)*.
% 143.27/143.51 93555[7:Obv:93554.1] || -> hBOOL(c_Arrow__Order__Mirabelle_OProf)*.
% 143.27/143.51 93556[7:MRR:93555.0,59836.0] || -> .
% 143.27/143.51 93563[6:Spt:93556.0,35804.0,59835.0] || equal(v_P____,c_Arrow__Order__Mirabelle_OProf)** -> .
% 143.27/143.51 93564[6:Spt:93556.0,35804.1] || -> equal(v_Q____,c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 93568[6:Rew:93564.0,33836.0] || equal(v_P____,c_Arrow__Order__Mirabelle_OProf)** -> .
% 143.27/143.51 93572[6:Rew:93564.0,34280.0] || -> equal(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 93639[6:Rew:93572.0,35388.1,93564.0,35388.1] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),v_P____)** equal(v_P____,c_Arrow__Order__Mirabelle_OProf).
% 143.27/143.51 93640[6:MRR:93639.1,93568.0] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),v_P____)**.
% 143.27/143.51 93642[6:Rew:93640.0,32053.0] || -> equal(hAPP(v_P____,u),v_P____)**.
% 143.27/143.51 93700[6:Rew:93564.0,35278.1] || -> equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_P____)** equal(hAPP(c_Arrow__Order__Mirabelle_OProf,v),v_P____)**.
% 143.27/143.51 93717[6:Rew:93640.0,32742.1] || -> hBOOL(u) hBOOL(v_P____) equal(hAPP(u,v),v_P____)**.
% 143.27/143.51 93718[6:MRR:93717.1,9876.0] || -> hBOOL(u) equal(hAPP(u,v),v_P____)**.
% 143.27/143.51 93730[6:Rew:93718.1,65211.2,93564.0,65211.2,93564.0,65211.1] || -> hBOOL(u)* equal(c_Lattices_Oupper__semilattice__class_Osup(v,tc_bool),c_Arrow__Order__Mirabelle_OProf)** equal(v_P____,c_Arrow__Order__Mirabelle_OProf).
% 143.27/143.51 93731[6:MRR:93730.2,93568.0] || -> hBOOL(u)* equal(c_Lattices_Oupper__semilattice__class_Osup(v,tc_bool),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 93733[6:Rew:93731.1,24423.1] || -> hBOOL(u)* equal(hAPP(c_Arrow__Order__Mirabelle_OProf,v),v)**.
% 143.27/143.51 93895[6:Rew:93564.0,34968.1] || -> equal(hAPP(c_in(u),v),v_P____)** equal(hAPP(c_Arrow__Order__Mirabelle_OProf,w),hAPP(w,v))*.
% 143.27/143.51 94057[6:Rew:93564.0,35693.0] || equal(hAPP(c_Arrow__Order__Mirabelle_OProf,u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Set_Oinsert(w,v),v_P____)**.
% 143.27/143.51 94205[6:Rew:93564.0,35322.2] || hBOOL(hAPP(u,v))* -> equal(c_Set_Oinsert(v,w),v_P____)** equal(hAPP(c_Arrow__Order__Mirabelle_OProf,u),u).
% 143.27/143.51 94206[6:MRR:94205.0,93733.0] || -> equal(c_Set_Oinsert(u,v),v_P____)** equal(hAPP(c_Arrow__Order__Mirabelle_OProf,w),w)**.
% 143.27/143.51 94208[6:Rew:94206.1,94057.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Set_Oinsert(w,v),v_P____)**.
% 143.27/143.51 94210[6:AED:312.0,94208.0] || -> equal(c_Set_Oinsert(u,v),v_P____)**.
% 143.27/143.51 94246[6:Rew:94210.0,519.0] || equal(hAPP(v_P____,u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 143.27/143.51 94286[6:Rew:93642.0,94246.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_P____)** -> .
% 143.27/143.51 94287[6:MRR:93700.0,94286.0] || -> equal(hAPP(c_Arrow__Order__Mirabelle_OProf,u),v_P____)**.
% 143.27/143.51 94309[6:Rew:94287.0,93895.1] || -> equal(hAPP(c_in(u),v),v_P____)** equal(hAPP(w,v),v_P____)**.
% 143.27/143.51 94616[6:Con:94309.1] || -> equal(hAPP(c_in(u),v),v_P____)**.
% 143.27/143.51 94617[6:Rew:94616.0,3028.0] || -> equal(hAPP(v_P____,u),hAPP(u,v))*.
% 143.27/143.51 94618[6:Rew:93642.0,94617.0] || -> equal(hAPP(u,v),v_P____)**.
% 143.27/143.51 101127[6:Rew:94618.0,23005.2,94618.0,23005.1,94618.0,23005.0] || -> hBOOL(v_P____)* hBOOL(v_P____)* hBOOL(v_P____)*.
% 143.27/143.51 101128[6:Obv:101127.1] || -> hBOOL(v_P____)*.
% 143.27/143.51 101129[6:MRR:101128.0,9876.0] || -> .
% 143.27/143.51 101136[1:Spt:101129.0,9759.1,9871.0] || hBOOL(hAPP(c_Not,v_P____))* -> .
% 143.27/143.51 101137[1:Spt:101129.0,9759.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbspec__1__1(c_Arrow__Order__Mirabelle_OProf,c_Not,u))*.
% 143.27/143.51 101267[1:Res:24152.0,101136.0] || -> equal(hAPP(c_Not,v_P____),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 101279[1:SpR:101267.0,1893.0] || -> equal(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),v_P____)**.
% 143.27/143.51 101282[1:Rew:20826.0,101279.0] || -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_P____)**.
% 143.27/143.51 101283[1:Rew:101282.0,20223.0] || -> hBOOL(v_P____)*.
% 143.27/143.51 101285[1:Rew:101282.0,23295.0] || equal(c_Orderings_Obot__class_Obot(tc_bool),v_P____)** -> .
% 143.27/143.51 101286[1:Rew:101282.0,20826.0] || -> equal(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),v_P____)**.
% 143.27/143.51 101345[1:Rew:101282.0,21113.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),v_P____),u)**.
% 143.27/143.51 101355[1:Rew:101282.0,20982.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_P____,tc_bool),u),v_P____)**.
% 143.27/143.51 101356[1:Rew:101282.0,20981.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),v_P____),v_P____)**.
% 143.27/143.51 102051[0:SpR:24114.1,1893.0] || hBOOL(u)* -> equal(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),u)*.
% 143.27/143.51 102059[1:Rew:101286.0,102051.1] || hBOOL(u)* -> equal(v_P____,u).
% 143.27/143.51 102345[1:Res:1091.0,102059.0] || -> equal(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),v_P____)**.
% 143.27/143.51 102354[1:Res:24434.0,102059.0] || -> hBOOL(u)* equal(u,v)* equal(v_P____,v)*.
% 143.27/143.51 102356[1:Res:24152.0,102059.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_bool))* equal(v_P____,u).
% 143.27/143.51 102480[1:SpR:102356.0,101356.0] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),v_P____)** equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_P____),v_P____)**.
% 143.27/143.51 102488[1:SpR:102356.0,101345.0] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),v_P____)** equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_P____),u)*.
% 143.27/143.51 102494[1:SpR:102356.0,24379.0] || -> equal(c_Fun_Ofun__upd(c_Arrow__Order__Mirabelle_OProf,v_Q____,c_Orderings_Obot__class_Obot(tc_bool),u,v),v_P____)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OProf).
% 143.27/143.51 102528[1:Rew:24379.0,102494.0] || -> equal(v_P____,c_Arrow__Order__Mirabelle_OProf) equal(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 102530[2:Spt:102528.0] || -> equal(v_P____,c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 102532[2:Rew:102530.0,101283.0] || -> hBOOL(c_Arrow__Order__Mirabelle_OProf)*.
% 143.27/143.51 102533[2:Rew:102530.0,101282.0] || -> equal(c_Orderings_Otop__class_Otop(tc_bool),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 102535[2:Rew:102530.0,101285.0] || equal(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OProf)** -> .
% 143.27/143.51 102542[2:Rew:102530.0,101355.0] || -> equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Arrow__Order__Mirabelle_OProf,tc_bool),u),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 102555[2:Rew:102530.0,102345.0] || -> equal(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 103666[2:Rew:102530.0,102354.2] || -> hBOOL(u)* equal(u,v)* equal(c_Arrow__Order__Mirabelle_OProf,v)*.
% 143.27/143.51 103702[2:Rew:102530.0,102480.0] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_P____),v_P____)**.
% 143.27/143.51 103730[2:Rew:102530.0,103702.1] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 104863[2:SpR:102533.0,477.1] class_Lattices_Oboolean__algebra(tc_bool) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 104871[2:SSi:104863.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 104881[2:SpR:103666.2,104871.0] || -> hBOOL(u)* equal(u,c_HOL_Ouminus__class_Ouminus(tc_bool))* equal(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 104884[2:Rew:102555.0,104881.2] || -> hBOOL(u)* equal(u,c_HOL_Ouminus__class_Ouminus(tc_bool))* equal(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 104885[2:MRR:104884.2,102535.0] || -> hBOOL(u)* equal(u,c_HOL_Ouminus__class_Ouminus(tc_bool))*.
% 143.27/143.51 104934[2:Res:104885.0,20635.0] || -> equal(c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ouminus__class_Ouminus(tc_bool))**.
% 143.27/143.51 104936[2:Rew:104934.0,20635.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))* -> .
% 143.27/143.51 104954[2:Rew:104934.0,102535.0] || equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf)** -> .
% 143.27/143.51 104962[2:Rew:104934.0,104871.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf),c_HOL_Ouminus__class_Ouminus(tc_bool))**.
% 143.27/143.51 105237[2:Rew:104934.0,24011.2] class_Lattices_Olower__semilattice(u) || -> hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w))* equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(w,u),v),c_HOL_Ouminus__class_Ouminus(tc_bool)).
% 143.27/143.51 105354[2:Rew:104934.0,103730.1] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Arrow__Order__Mirabelle_OProf)** equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 105457[2:Rew:104962.0,105354.1] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Arrow__Order__Mirabelle_OProf)** equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf).
% 143.27/143.51 105458[2:MRR:105457.1,104954.0] || -> equal(c_Lattices_Oupper__semilattice__class_Osup(u,tc_bool),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 105459[2:Rew:105458.0,102542.0] || -> equal(hAPP(c_Arrow__Order__Mirabelle_OProf,u),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 105516[2:Rew:105458.0,24423.1] || -> hBOOL(u)* equal(hAPP(c_Arrow__Order__Mirabelle_OProf,v),v)**.
% 143.27/143.51 105755[2:Rew:105459.0,105516.1] || -> hBOOL(u)* equal(c_Arrow__Order__Mirabelle_OProf,v)*.
% 143.27/143.51 107413[2:Rew:105755.1,7707.0] || hBOOL(hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,u),v))* -> hBOOL(hAPP(c_Not,hAPP(u,v))).
% 143.27/143.51 109558[2:Rew:105755.1,10809.1] class_Lattices_Olower__semilattice(u) || hBOOL(c_Arrow__Order__Mirabelle_OProf) hBOOL(hAPP(v,w))* -> hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(x,u),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(v,c_Lattices_Olower__semilattice__class_Oinf(x,u),y)))*.
% 143.27/143.51 110455[2:Rew:105459.0,107413.0,105459.0,107413.0] || hBOOL(c_Arrow__Order__Mirabelle_OProf) -> hBOOL(hAPP(c_Not,hAPP(u,v)))*.
% 143.27/143.51 110456[2:MRR:110455.0,102532.0] || -> hBOOL(hAPP(c_Not,hAPP(u,v)))*.
% 143.27/143.51 110459[2:MRR:3498.2,110456.0] class_Lattices_Olower__semilattice(u) || hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w))* -> .
% 143.27/143.51 111014[2:MRR:105237.1,110459.1] class_Lattices_Olower__semilattice(u) || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v,u),w),c_HOL_Ouminus__class_Ouminus(tc_bool))**.
% 143.27/143.51 111053[2:Rew:111014.1,215.1] class_Lattices_Olower__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(tc_bool),v) -> c_lessequals(v,w,u)*.
% 143.27/143.51 112977[2:Rew:111014.1,109558.3] class_Lattices_Olower__semilattice(u) || hBOOL(c_Arrow__Order__Mirabelle_OProf) hBOOL(hAPP(v,w))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)).
% 143.27/143.51 112978[2:MRR:112977.1,102532.0] class_Lattices_Olower__semilattice(u) || hBOOL(hAPP(v,w))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)).
% 143.27/143.51 112979[2:MRR:112978.2,104936.0] class_Lattices_Olower__semilattice(u) || hBOOL(hAPP(v,w))* -> .
% 143.27/143.51 112981[2:MRR:3701.2,112979.1] class_Lattices_Olower__semilattice(u) || c_lessequals(v,w,u)* -> .
% 143.27/143.51 113006[2:MRR:111053.2,112981.1] class_Lattices_Olower__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(tc_bool),v)* -> .
% 143.27/143.51 113022[2:AED:312.0,113006.1] class_Lattices_Olower__semilattice(u) || -> .
% 143.27/143.51 113023[2:UnC:113022.0,679.0] || -> .
% 143.27/143.51 113450[2:Spt:113023.0,102528.0,102530.0] || equal(v_P____,c_Arrow__Order__Mirabelle_OProf)** -> .
% 143.27/143.51 113451[2:Spt:113023.0,102528.1] || -> equal(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 113459[2:Rew:113451.0,102356.0] || -> equal(u,c_Arrow__Order__Mirabelle_OProf) equal(v_P____,u)*.
% 143.27/143.51 113479[2:Rew:113451.0,22012.0] || -> equal(hAPP(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 113508[2:Rew:102345.0,102488.1,113451.0,102488.1] || -> equal(c_Lattices_Olower__semilattice__class_Oinf(u,tc_bool),v_P____)** equal(v_P____,u).
% 143.27/143.51 113886[2:SpR:113451.0,530.1] class_Lattices_Oboolean__algebra(tc_bool) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf),c_Orderings_Otop__class_Otop(tc_bool))**.
% 143.27/143.51 113888[2:Rew:101282.0,113886.1] class_Lattices_Oboolean__algebra(tc_bool) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf),v_P____)**.
% 143.27/143.51 113889[2:SSi:113888.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf),v_P____)**.
% 143.27/143.51 113894[1:SpR:101282.0,477.1] class_Lattices_Oboolean__algebra(tc_bool) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_P____),c_Orderings_Obot__class_Obot(tc_bool))**.
% 143.27/143.51 113896[2:Rew:113451.0,113894.1] class_Lattices_Oboolean__algebra(tc_bool) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_P____),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 113897[2:SSi:113896.0,696.0,697.0,687.0,698.0,690.0,695.0,693.0,692.0,691.0,689.0,688.0,694.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),v_P____),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 113963[2:SpR:113459.1,102345.0] || -> equal(u,c_Arrow__Order__Mirabelle_OProf) equal(hAPP(c_Arrow__Order__Mirabelle_OProf,u),u)**.
% 143.27/143.51 113965[2:SpR:113459.1,113897.0] || -> equal(u,c_Arrow__Order__Mirabelle_OProf) equal(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),u),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 114032[2:SpR:113459.1,113889.0] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf) equal(hAPP(v_P____,c_Arrow__Order__Mirabelle_OProf),v_P____)**.
% 143.27/143.51 114660[2:SpR:113508.0,113479.0] || -> equal(v_P____,u)* equal(hAPP(v_P____,c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf)**.
% 143.27/143.51 114671[2:AED:312.0,114660.0] || -> equal(hAPP(v_P____,c_Arrow__Order__Mirabelle_OProf),c_Arrow__Order__Mirabelle_OProf)**.
% 153.92/154.19 114672[2:Rew:114671.0,114032.1] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf)** equal(v_P____,c_Arrow__Order__Mirabelle_OProf).
% 153.92/154.19 114674[2:MRR:114672.1,113450.0] || -> equal(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf)**.
% 153.92/154.19 114682[2:Rew:114674.0,113965.1] || -> equal(u,c_Arrow__Order__Mirabelle_OProf) equal(hAPP(c_Arrow__Order__Mirabelle_OProf,u),c_Arrow__Order__Mirabelle_OProf)**.
% 153.92/154.19 114715[2:Rew:113963.1,114682.1] || -> equal(u,c_Arrow__Order__Mirabelle_OProf)* equal(u,c_Arrow__Order__Mirabelle_OProf)*.
% 153.92/154.19 114716[2:Obv:114715.0] || -> equal(u,c_Arrow__Order__Mirabelle_OProf)*.
% 153.92/154.19 114717[2:UnC:114716.0,113450.0] || -> .
% 153.92/154.19 % SZS output end Refutation
% 153.92/154.19 Formulae used in the proof : cls_xt1_I6_J_0 cls_le__sup__iff_0 cls_subset__UNIV_0 cls_inf__sup__ord_I2_J_0 cls_inf__sup__ord_I1_J_0 cls_fun__upd__same_0 cls_fun__upd__idem_0 cls_le__iff__sup_1 cls_sup__absorb1_0 cls_inf__sup__absorb_0 cls_order__eq__iff_2 cls_sup__inf__absorb_0 cls_sup__bot__left_0 cls_sup1E_0 cls_subset__insertI_0 cls_sup__top__right_0 cls_empty__subsetI_0 cls_COMBB__def_0 cls_insert__subset_0 cls_insert__is__Un_0 cls_subset__Compl__self__eq_0 cls_Collect__neg__eq_0 cls_vimage__Collect__eq_0 cls_Compl__partition2_0 cls_le__iff__inf_1 cls_inf__absorb2_0 cls_Un__upper1_0 cls_inf__sup__ord_I4_J_0 cls_inf__sup__ord_I3_J_0 cls_Un__commute_0 cls_sup__commute_0 cls_inf__sup__aci_I5_J_0 cls_inj__on__Un_0 cls_le__funD_0 cls_Collect__def_0 cls_vimage__UNIV_0 cls_insert__not__empty_0 cls_insert__absorb2_0 cls_Diff__empty_0 cls_Diff__cancel_0 cls_inj__image__mem__iff_0 cls_inj__on__insert_0 cls_COMBC__def_0 cls_COMBK__def_0 cls_rangeI_0 cls_diff__eq_0 cls_inj__on__empty_0 cls_inf__commute_0 cls_inf__sup__aci_I1_J_0 cls_dictator__def_2 cls_inf1E_1 cls_double__complement_0 cls_bspec_1 cls_insertE_0 cls_compl__top__eq_0 cls_Compl__UNIV__eq_0 cls_bot1E_0 cls_Int__UNIV__left_0 cls_Int__UNIV__right_0 cls_extensionalityI_1 cls_top1I_0 cls_vimage__const_1 cls_empty__not__insert_0 cls_insert__code_1 cls_compl__bot__eq_0 cls_singleton__conv2_0 cls_Collect__mem__eq_0 cls_bexI_1 cls_ComplI_0 cls_ComplD_0 cls_ball__conj__distrib_11 cls_ball__conj__distrib_1 cls_ball__conj__distrib_0 cls_ballE_1 cls_bexI_0 cls_bex__Un_5 cls_insert__absorb_0 cls_rev__bexI_1 cls_Pi__I_0 cls_Pi__I_H_0 cls_dictator__def_1 cls_dictator__def_0 cls_mem__def_1 cls_mem__def_0 cls_CHAINED_0 clsarity_fun__Complete__Lattice_Ocomplete__lattice clsarity_fun__Lattices_Oupper__semilattice clsarity_fun__Lattices_Olower__semilattice clsarity_fun__Lattices_Odistrib__lattice clsarity_fun__Lattices_Obounded__lattice clsarity_fun__Lattices_Oboolean__algebra clsarity_fun__Orderings_Opreorder clsarity_fun__Lattices_Olattice clsarity_fun__Orderings_Oorder clsarity_fun__Orderings_Otop clsarity_fun__Orderings_Obot clsarity_fun__HOL_Oord clsarity_nat__Lattices_Olower__semilattice clsarity_bool__Complete__Lattice_Ocomplete__lattice clsarity_bool__Lattices_Oupper__semilattice clsarity_bool__Lattices_Olower__semilattice clsarity_bool__Lattices_Odistrib__lattice clsarity_bool__Lattices_Obounded__lattice clsarity_bool__Lattices_Oboolean__algebra clsarity_bool__Orderings_Opreorder clsarity_bool__Lattices_Olattice clsarity_bool__Orderings_Oorder clsarity_bool__Orderings_Otop clsarity_bool__Orderings_Obot clsarity_bool__HOL_Oord cls_conjecture_0
% 153.92/154.19
%------------------------------------------------------------------------------