%------------------------------------------------------------------------------ % File : Etableau---0.67 % Problem : LCL802-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 12:02:02 PM UTC 2026 % Result : Unsatisfiable 0.11s 0.40s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL802-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.04 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s % 0.11/0.36 % Computer : n016.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Sat Sep 5 19:24:45 UTC 2026 % 0.11/0.36 % CPUTime : % 0.11/0.40 # No SInE strategy applied % 0.11/0.40 # Auto-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y % 0.11/0.40 # and selection function SelectMaxLComplexAvoidPosPred. % 0.11/0.40 # % 0.11/0.40 # Presaturation interreduction done % 0.11/0.40 # Number of axioms: 328 Number of unprocessed: 275 % 0.11/0.40 # Tableaux proof search. % 0.11/0.40 # APR header successfully linked. % 0.11/0.40 # Hello from C++ % 0.11/0.40 # The folding up rule is enabled... % 0.11/0.40 # Local unification is enabled... % 0.11/0.40 # Any saturation attempts will use folding labels... % 0.11/0.40 # 275 beginning clauses after preprocessing and clausification % 0.11/0.40 # Creating start rules for all 1 conjectures. % 0.11/0.40 # There are 1 start rule candidates: % 0.11/0.40 # Found 80 unit axioms. % 0.11/0.40 # 1 start rule tableaux created. % 0.11/0.40 # 195 extension rule candidate clauses % 0.11/0.40 # 80 unit axiom clauses % 0.11/0.40 % 0.11/0.40 # Requested 8, 32 cores available to the main process. % 0.11/0.40 # There are not enough tableaux to fork, creating more from the initial 1 % 0.11/0.40 # Closed tableau found in foldup close cycle with 0 folds and 1 closures done. % 0.11/0.40 # There were 0 total branch saturation attempts. % 0.11/0.40 # There were 0 of these attempts blocked. % 0.11/0.40 # There were 0 deferred branch saturation attempts. % 0.11/0.40 # There were 0 free duplicated saturations. % 0.11/0.40 # There were 0 total successful branch saturations. % 0.11/0.40 # There were 0 successful branch saturations in interreduction. % 0.11/0.40 # There were 0 successful branch saturations on the branch. % 0.11/0.40 # There were 0 successful branch saturations after the branch. % 0.11/0.40 # SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.11/0.40 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.11/0.40 # Begin clausification derivation % 0.11/0.40 % 0.11/0.40 # End clausification derivation % 0.11/0.40 # Begin listing active clauses obtained from FOF to CNF conversion % 0.11/0.40 cnf(i_0_614, plain, (v_n____=v_i____)). % 0.11/0.40 cnf(i_0_651, plain, (class_Lattices_Olower__semilattice(tc_bool))). % 0.11/0.40 cnf(i_0_653, plain, (class_Lattices_Olattice(tc_bool))). % 0.11/0.40 cnf(i_0_654, plain, (class_Orderings_Oorder(tc_bool))). % 0.11/0.40 cnf(i_0_652, plain, (class_Orderings_Opreorder(tc_bool))). % 0.11/0.40 cnf(i_0_636, plain, (class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat))). % 0.11/0.40 cnf(i_0_637, plain, (class_OrderedGroup_Ocancel__semigroup__add(tc_nat))). % 0.11/0.40 cnf(i_0_639, plain, (class_Ring__and__Field_Ocomm__semiring__1(tc_nat))). % 0.11/0.40 cnf(i_0_641, plain, (class_OrderedGroup_Ocomm__monoid__add(tc_nat))). % 0.11/0.40 cnf(i_0_645, plain, (class_OrderedGroup_Omonoid__add(tc_nat))). % 0.11/0.40 cnf(i_0_640, plain, (class_OrderedGroup_Oab__semigroup__add(tc_nat))). % 0.11/0.40 cnf(i_0_642, plain, (class_OrderedGroup_Osemigroup__add(tc_nat))). % 0.11/0.40 cnf(i_0_646, plain, (class_Nat_Osemiring__char__0(tc_nat))). % 0.11/0.40 cnf(i_0_633, plain, (class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat))). % 0.11/0.40 cnf(i_0_634, plain, (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat))). % 0.11/0.40 cnf(i_0_638, plain, (class_Ring__and__Field_Oordered__semidom(tc_nat))). % 0.11/0.40 cnf(i_0_635, plain, (class_OrderedGroup_Opordered__comm__monoid__add(tc_nat))). % 0.11/0.40 cnf(i_0_644, plain, (class_Ring__and__Field_Osemiring__1(tc_nat))). % 0.11/0.40 cnf(i_0_643, plain, (class_Lattices_Olower__semilattice(tc_nat))). % 0.11/0.40 cnf(i_0_649, plain, (class_Lattices_Olattice(tc_nat))). % 0.11/0.40 cnf(i_0_650, plain, (class_Orderings_Oorder(tc_nat))). % 0.11/0.40 cnf(i_0_647, plain, (class_Orderings_Opreorder(tc_nat))). % 0.11/0.40 cnf(i_0_648, plain, (class_Orderings_Olinorder(tc_nat))). % 0.11/0.40 cnf(i_0_618, plain, (c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____))). % 0.11/0.40 cnf(i_0_480, plain, (c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB)=v_rs____)). % 0.11/0.40 cnf(i_0_461, plain, (hBOOL(hAPP(c_InductTermi_OIT,v_u____)))). % 0.11/0.40 cnf(i_0_509, plain, (hBOOL(hAPP(c_InductTermi_OIT,v_ua______)))). % 0.11/0.40 cnf(i_0_620, plain, (c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2))). % 0.11/0.40 cnf(i_0_521, plain, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))))). % 0.11/0.40 cnf(i_0_601, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(v_e____),v_u____),v_T____)))). % 0.11/0.40 cnf(i_0_433, plain, (c_Nat_Osize__class_Osize(c_List_Olist_ONil(X1),tc_List_Olist(X1))=c_HOL_Ozero__class_Ozero(tc_nat))). % 0.11/0.40 cnf(i_0_516, plain, (c_List_Oappend(X1,c_List_Olist_ONil(X2),X2)=X1)). % 0.11/0.40 cnf(i_0_515, plain, (c_List_Oappend(c_List_Olist_ONil(X1),X2,X1)=X2)). % 0.11/0.40 cnf(i_0_581, plain, (c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool))=X1)). % 0.11/0.40 cnf(i_0_619, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(v_ea______),v_ua______),v_T____)))). % 0.11/0.40 cnf(i_0_582, plain, (c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1)=X2)). % 0.11/0.40 cnf(i_0_399, plain, (c_Predicate_Oconversep(c_fequal(X1),X1,X1)=c_fequal(X1))). % 0.11/0.40 cnf(i_0_462, plain, (c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2)=X1)). % 0.11/0.40 cnf(i_0_609, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),v_a____),v_T_H_H____)))). % 0.11/0.40 cnf(i_0_345, plain, (c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2)=c_Transitive__Closure_Ortranclp(X1,X2))). % 0.11/0.40 cnf(i_0_612, plain, (hAPP(c_Type_Oshift(X1,X2,X3,X4),X2)=X3)). % 0.11/0.40 cnf(i_0_657, plain, (hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)))). % 0.11/0.40 cnf(i_0_405, plain, (c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2)=X1)). % 0.11/0.40 cnf(i_0_524, plain, (c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3)=X2)). % 0.11/0.40 cnf(i_0_502, plain, (c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4)=X3)). % 0.11/0.40 cnf(i_0_381, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)))). % 0.11/0.40 cnf(i_0_501, plain, (hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))=v_T____)). % 0.11/0.40 cnf(i_0_625, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_Lambda_OdB_OVar(X2)),hAPP(X1,X2))))). % 0.11/0.40 cnf(i_0_623, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)))). % 0.11/0.40 cnf(i_0_571, plain, (c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)))). % 0.11/0.40 cnf(i_0_624, plain, (hAPP(c_COMBB(X1,X2,X3,X4,X5),X6)=hAPP(X1,hAPP(X2,X6)))). % 0.11/0.40 cnf(i_0_336, plain, (c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4)=c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4))). % 0.11/0.40 cnf(i_0_593, plain, (c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3)=c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3))). % 0.11/0.40 cnf(i_0_475, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)))). % 0.11/0.40 cnf(i_0_519, plain, (hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X1,X2)),c_Lambda_Olift(X3,X2))=c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3),X2))). % 0.11/0.40 cnf(i_0_531, plain, (c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)))). % 0.11/0.40 cnf(i_0_547, plain, (hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)))))). % 0.11/0.40 cnf(i_0_617, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))))). % 0.11/0.40 cnf(i_0_616, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_Lambda_OdB_OVar(v_i____)),v_T____)))). % 0.11/0.40 cnf(i_0_589, plain, (hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,X3)),c_Lambda_Osubst(X4,X2,X3))=c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X4),X2,X3))). % 0.11/0.40 cnf(i_0_471, plain, (c_List_Ofoldl(X1,c_List_Ofoldl(X1,X2,X3,X4,X5),X6,X4,X5)=c_List_Ofoldl(X1,X2,c_List_Oappend(X3,X6,X5),X4,X5))). % 0.11/0.40 cnf(i_0_520, plain, (c_List_Ofoldr(X1,X2,c_List_Ofoldr(X1,X3,X4,X5,X6),X5,X6)=c_List_Ofoldr(X1,c_List_Oappend(X2,X3,X5),X4,X5,X6))). % 0.11/0.40 cnf(i_0_500, plain, (c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)))). % 0.11/0.40 cnf(i_0_532, plain, (c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)))). % 0.11/0.40 cnf(i_0_604, plain, (c_Set_Oimage(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6)=c_Set_Oimage(c_COMBB(X1,X2,X5,X6,X4),X3,X4,X6))). % 0.11/0.40 cnf(i_0_357, plain, (c_List_Ofoldl(X1,X2,c_List_Olist_OCons(X3,X4,X5),X6,X5)=c_List_Ofoldl(X1,hAPP(hAPP(X1,X2),X3),X4,X6,X5))). % 0.11/0.40 cnf(i_0_404, plain, (c_List_Ofoldr(X1,c_List_Olist_OCons(X2,X3,X4),X5,X4,X6)=hAPP(hAPP(X1,X2),c_List_Ofoldr(X1,X3,X5,X4,X6)))). % 0.11/0.40 cnf(i_0_628, negated_conjecture, (~c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_588, plain, (c_Lambda_OdB_OVar(X1)!=c_Lambda_OdB_OAbs(X2))). % 0.11/0.40 cnf(i_0_542, plain, (~c_HOL_Oord__class_Oless(X1,X1,tc_nat))). % 0.11/0.40 cnf(i_0_343, plain, (c_List_Olist_OCons(X1,X2,X3)!=X2)). % 0.11/0.40 cnf(i_0_504, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))). % 0.11/0.40 cnf(i_0_402, plain, (c_List_Olist_OCons(X1,X2,X3)!=c_List_Olist_ONil(X3))). % 0.11/0.40 cnf(i_0_398, plain, (~c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3))). % 0.11/0.40 cnf(i_0_397, plain, (~c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2))). % 0.11/0.40 cnf(i_0_566, plain, (~hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)))). % 0.11/0.40 cnf(i_0_585, plain, (c_Lambda_OdB_OAbs(X1)!=hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))). % 0.11/0.40 cnf(i_0_538, plain, (c_Lambda_OdB_OVar(X1)!=hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))). % 0.11/0.40 cnf(i_0_469, plain, (hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_526, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_535, plain, (X1=X2|c_Lambda_OdB_OAbs(X1)!=c_Lambda_OdB_OAbs(X2))). % 0.11/0.40 cnf(i_0_586, plain, (X1=X2|c_Lambda_OdB_OVar(X1)!=c_Lambda_OdB_OVar(X2))). % 0.11/0.40 cnf(i_0_544, plain, (~class_Orderings_Oorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1))). % 0.11/0.40 cnf(i_0_629, plain, (class_Lattices_Olower__semilattice(tc_fun(X1,X2))|~class_Lattices_Olattice(X2))). % 0.11/0.40 cnf(i_0_631, plain, (class_Lattices_Olattice(tc_fun(X1,X2))|~class_Lattices_Olattice(X2))). % 0.11/0.40 cnf(i_0_430, plain, (c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1)=c_HOL_Ozero__class_Ozero(X1)|~class_Ring__and__Field_Osemiring__1(X1))). % 0.11/0.40 cnf(i_0_546, plain, (~class_Orderings_Opreorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1))). % 0.11/0.40 cnf(i_0_545, plain, (~class_Orderings_Olinorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1))). % 0.11/0.40 cnf(i_0_632, plain, (class_Orderings_Oorder(tc_fun(X1,X2))|~class_Orderings_Oorder(X2))). % 0.11/0.40 cnf(i_0_630, plain, (class_Orderings_Opreorder(tc_fun(X1,X2))|~class_Orderings_Opreorder(X2))). % 0.11/0.40 cnf(i_0_422, plain, (~class_Ring__and__Field_Oordered__semidom(X1)|~c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1))). % 0.11/0.40 cnf(i_0_596, plain, (~class_Orderings_Oorder(X1)|~c_HOL_Oord__class_Oless(X2,X3,X1)|~c_HOL_Oord__class_Oless(X3,X2,X1))). % 0.11/0.40 cnf(i_0_491, plain, (X1=c_List_Olist_ONil(tc_Lambda_OdB)|c_Lambda_OdB_OAbs(X2)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_490, plain, (X1=c_List_Olist_ONil(tc_Lambda_OdB)|c_Lambda_OdB_OVar(X2)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_434, plain, (X1=c_List_Olist_ONil(X2)|c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2))!=c_HOL_Ozero__class_Ozero(tc_nat))). % 0.11/0.40 cnf(i_0_598, plain, (~class_Orderings_Opreorder(X1)|~c_HOL_Oord__class_Oless(X2,X3,X1)|~c_HOL_Oord__class_Oless(X3,X2,X1))). % 0.11/0.40 cnf(i_0_597, plain, (~class_Orderings_Olinorder(X1)|~c_HOL_Oord__class_Oless(X2,X3,X1)|~c_HOL_Oord__class_Oless(X3,X2,X1))). % 0.11/0.40 cnf(i_0_658, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2)))). % 0.11/0.40 cnf(i_0_387, plain, (hBOOL(hAPP(c_InductTermi_OIT,X1))|~c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_393, plain, (X1=X2|c_Nat_Osemiring__1__class_Oof__nat(X1,X3)!=c_Nat_Osemiring__1__class_Oof__nat(X2,X3)|~class_Nat_Osemiring__char__0(X3))). % 0.11/0.40 cnf(i_0_534, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olist_ONil(X2)!=c_List_Oappend(X3,X1,X2))). % 0.11/0.40 cnf(i_0_533, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olist_ONil(X2)!=c_List_Oappend(X1,X3,X2))). % 0.11/0.40 cnf(i_0_603, plain, (c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(X1),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),X2,tc_Lambda_OdB)|~c_Type_Otypings(X1,X2,X3))). % 0.11/0.40 cnf(i_0_580, plain, (c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2)=X1|~class_Lattices_Olower__semilattice(X2))). % 0.11/0.40 cnf(i_0_577, plain, (X1=c_List_Olist_ONil(X2)|c_List_Oappend(X1,X3,X2)!=X3)). % 0.11/0.40 cnf(i_0_413, plain, (X1=X2|c_List_Olist_OCons(X3,X1,X4)!=c_List_Olist_OCons(X5,X2,X4))). % 0.11/0.40 cnf(i_0_513, plain, (X1=X2|c_List_Oappend(X3,X1,X4)!=c_List_Oappend(X3,X2,X4))). % 0.11/0.40 cnf(i_0_412, plain, (X1=X2|c_List_Olist_OCons(X1,X3,X4)!=c_List_Olist_OCons(X2,X5,X4))). % 0.11/0.40 cnf(i_0_512, plain, (X1=X2|c_List_Oappend(X1,X3,X4)!=c_List_Oappend(X2,X3,X4))). % 0.11/0.40 cnf(i_0_567, plain, (X1=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat))). % 0.11/0.40 cnf(i_0_575, plain, (X1=c_List_Olist_ONil(X2)|c_List_Oappend(X3,X1,X2)!=X3)). % 0.11/0.40 cnf(i_0_564, plain, (X1=c_Lambda_OdB_OAbs(X2)|c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(X2))). % 0.11/0.40 cnf(i_0_352, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))=X2|~class_Ring__and__Field_Ocomm__semiring__1(X1))). % 0.11/0.40 cnf(i_0_621, plain, (c_List_Olistsp(X1,X2,X3)|~c_List_Olistsp(X1,c_List_Oappend(X4,X2,X3),X3))). % 0.11/0.40 cnf(i_0_622, plain, (c_List_Olistsp(X1,X2,X3)|~c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3))). % 0.11/0.40 cnf(i_0_607, plain, (c_List_Olistsp(X1,X2,X3)|~hBOOL(hAPP(X1,c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3))))). % 0.11/0.40 cnf(i_0_458, plain, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.11/0.40 cnf(i_0_539, plain, (c_Lambda_OdB_OVar(X1)=X2|c_Lambda_OdB_OVar(X1)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_386, plain, (c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.11/0.40 cnf(i_0_349, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))=X2|~class_OrderedGroup_Ocomm__monoid__add(X1))). % 0.11/0.40 cnf(i_0_463, plain, (c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2)=c_Lambda_OdB_OVar(X1)|~c_HOL_Oord__class_Oless(X1,X2,tc_nat))). % 0.11/0.40 cnf(i_0_557, plain, (X1=X2|hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)!=hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2))). % 0.11/0.40 cnf(i_0_578, plain, (X1=X2|hAPP(hAPP(c_Type_Otype_OFun,X3),X1)!=hAPP(hAPP(c_Type_Otype_OFun,X4),X2))). % 0.11/0.40 cnf(i_0_457, plain, (X1=X2|c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_351, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))=X2|~class_OrderedGroup_Omonoid__add(X1))). % 0.11/0.40 cnf(i_0_558, plain, (X1=X2|hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)!=hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4))). % 0.11/0.40 cnf(i_0_579, plain, (X1=X2|hAPP(hAPP(c_Type_Otype_OFun,X1),X3)!=hAPP(hAPP(c_Type_Otype_OFun,X2),X4))). % 0.11/0.40 cnf(i_0_615, plain, (hAPP(X1,X2)=X3|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_Lambda_OdB_OVar(X2)),X3)))). % 0.11/0.40 cnf(i_0_467, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2)))). % 0.11/0.40 cnf(i_0_468, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)))). % 0.11/0.40 cnf(i_0_525, plain, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.11/0.40 cnf(i_0_346, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2)=X2|~class_Ring__and__Field_Ocomm__semiring__1(X1))). % 0.11/0.40 cnf(i_0_432, plain, (c_HOL_Oord__class_Oless(X1,X2,tc_nat)|~class_Ring__and__Field_Oordered__semidom(X3)|~c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3))). % 0.11/0.40 cnf(i_0_484, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)|~class_Ring__and__Field_Oordered__semidom(X2)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2))). % 0.11/0.40 cnf(i_0_395, plain, (X1=c_HOL_Ozero__class_Ozero(X2)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1)!=c_HOL_Ozero__class_Ozero(X2)|~class_OrderedGroup_Olordered__ab__group__add(X2))). % 0.11/0.40 cnf(i_0_572, plain, (c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3)=c_Lambda_OdB_OVar(X1)|~c_HOL_Oord__class_Oless(X1,X3,tc_nat))). % 0.11/0.40 cnf(i_0_562, plain, (X1=X2|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_583, plain, (X1=X2|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_563, plain, (X1=X2|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_584, plain, (X1=X2|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_363, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)))). % 0.11/0.40 cnf(i_0_394, plain, (X1=c_HOL_Ozero__class_Ozero(X2)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1)!=X3|~class_Int_Onumber__ring(X2)|~class_Ring__and__Field_Oidom(X2))). % 0.11/0.40 cnf(i_0_379, plain, (X1=X2|X3=X4|~c_ListOrder_Ostep1(X5,c_List_Olist_OCons(X2,X4,X6),c_List_Olist_OCons(X1,X3,X6),X6))). % 0.11/0.40 cnf(i_0_347, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2)=X2|~class_OrderedGroup_Ocomm__monoid__add(X1))). % 0.11/0.40 cnf(i_0_606, plain, (c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)|~c_List_Olistsp(X1,X3,X4)|~c_List_Olistsp(X1,X2,X4))). % 0.11/0.40 cnf(i_0_350, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2)=X2|~class_OrderedGroup_Omonoid__add(X1))). % 0.11/0.40 cnf(i_0_608, plain, (c_List_Olistsp(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,X3)|~c_List_Olistsp(X2,X4,X3)|~c_List_Olistsp(X1,X4,X3))). % 0.11/0.40 cnf(i_0_348, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))=X2|~class_Int_Onumber__ring(X1)|~class_Ring__and__Field_Oidom(X1))). % 0.11/0.40 cnf(i_0_550, plain, (X1=X2|c_HOL_Oord__class_Oless(X1,X2,tc_nat)|c_HOL_Oord__class_Oless(X2,X1,tc_nat))). % 0.11/0.40 cnf(i_0_333, plain, (X1=X2|hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)|~class_OrderedGroup_Ocancel__ab__semigroup__add(X3))). % 0.11/0.40 cnf(i_0_334, plain, (X1=X2|hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)|~class_OrderedGroup_Ocancel__semigroup__add(X3))). % 0.11/0.40 cnf(i_0_335, plain, (X1=X2|hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)|~class_OrderedGroup_Ocancel__semigroup__add(X3))). % 0.11/0.40 cnf(i_0_506, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X3)|~c_HOL_Oord__class_Oless(X4,X2,X3)|~c_HOL_Oord__class_Oless(X1,X4,X3))). % 0.11/0.40 cnf(i_0_559, plain, (hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))|~c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_454, plain, (c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)=c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)|~class_Lattices_Olower__semilattice(X3))). % 0.11/0.40 cnf(i_0_455, plain, (c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)=c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)|~class_Lattices_Olattice(X3))). % 0.11/0.40 cnf(i_0_376, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))=c_HOL_Ozero__class_Ozero(X1)|~class_OrderedGroup_Olordered__ab__group__add(X1))). % 0.11/0.40 cnf(i_0_498, plain, (X1=c_List_Olist_ONil(X2)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat))). % 0.11/0.40 cnf(i_0_507, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Opreorder(X3)|~c_HOL_Oord__class_Oless(X4,X2,X3)|~c_HOL_Oord__class_Oless(X1,X4,X3))). % 0.11/0.40 cnf(i_0_418, plain, (c_Wellfounded_Oaccp(X1,X2,X3)|~c_Wellfounded_Oaccp(X1,X4,X3)|~hBOOL(hAPP(hAPP(X1,X2),X4)))). % 0.11/0.40 cnf(i_0_485, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)|~class_Ring__and__Field_Oordered__semidom(X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))). % 0.11/0.40 cnf(i_0_510, plain, (c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3)=c_Lambda_OdB_OVar(X1)|X1=X3|c_HOL_Oord__class_Oless(X3,X1,tc_nat))). % 0.11/0.40 cnf(i_0_573, plain, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.11/0.40 cnf(i_0_605, plain, (hAPP(c_Type_Oshift(X1,X2,X3,X4),X5)=hAPP(X1,X5)|~c_HOL_Oord__class_Oless(X5,X2,tc_nat))). % 0.11/0.40 cnf(i_0_388, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)|~class_Ring__and__Field_Ocomm__semiring__1(X1))). % 0.11/0.40 cnf(i_0_560, plain, (c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)|~class_Lattices_Olower__semilattice(X3)|~c_HOL_Oord__class_Oless(X2,X4,X3))). % 0.11/0.40 cnf(i_0_561, plain, (c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)|~class_Lattices_Olower__semilattice(X3)|~c_HOL_Oord__class_Oless(X1,X4,X3))). % 0.11/0.40 cnf(i_0_425, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)|~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)|~class_OrderedGroup_Olordered__ab__group__add(X2))). % 0.11/0.40 cnf(i_0_426, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)|~class_Ring__and__Field_Oordered__idom(X2)|~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2))). % 0.11/0.40 cnf(i_0_470, plain, (hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)))). % 0.11/0.40 cnf(i_0_396, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))|~hBOOL(hAPP(hAPP(X1,X3),X4)))). % 0.11/0.40 cnf(i_0_421, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)|~class_OrderedGroup_Olordered__ab__group__add(X1))). % 0.11/0.40 cnf(i_0_332, plain, (X1=X2|hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)|~class_Int_Onumber__ring(X3)|~class_Ring__and__Field_Oidom(X3))). % 0.11/0.40 cnf(i_0_439, plain, (X1=X2|c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4)!=c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4))). % 0.11/0.40 cnf(i_0_438, plain, (X1=X2|c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4)!=c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4))). % 0.11/0.40 cnf(i_0_431, plain, (c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)|~class_Ring__and__Field_Oordered__semidom(X2)|~c_HOL_Oord__class_Oless(X1,X3,tc_nat))). % 0.11/0.40 cnf(i_0_548, plain, (X1=X2|c_HOL_Oord__class_Oless(X1,X2,X3)|c_HOL_Oord__class_Oless(X2,X1,X3)|~class_Ring__and__Field_Oordered__idom(X3))). % 0.11/0.40 cnf(i_0_549, plain, (X1=X2|c_HOL_Oord__class_Oless(X1,X2,X3)|c_HOL_Oord__class_Oless(X2,X1,X3)|~class_Orderings_Olinorder(X3))). % 0.11/0.40 cnf(i_0_389, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)|~class_OrderedGroup_Ocomm__monoid__add(X1))). % 0.11/0.40 cnf(i_0_383, plain, (c_Wellfounded_Oaccp(X1,X2,X3)|~c_Wellfounded_Oaccp(X1,X4,X3)|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X4)))). % 0.11/0.40 cnf(i_0_465, plain, (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.11/0.40 cnf(i_0_570, plain, (c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)=c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)|~class_Lattices_Olower__semilattice(X3))). % 0.11/0.40 cnf(i_0_590, plain, (hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))|~hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(X1,X4)))). % 0.11/0.40 cnf(i_0_569, plain, (c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3)=c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)|~class_Lattices_Olattice(X3))). % 0.11/0.40 cnf(i_0_400, plain, (X1=X2|c_ListOrder_Ostep1(X3,X1,X2,X4)|~c_ListOrder_Ostep1(X3,c_List_Olist_OCons(X5,X1,X4),c_List_Olist_OCons(X6,X2,X4),X4))). % 0.11/0.40 cnf(i_0_411, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)|~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3))). % 0.11/0.40 cnf(i_0_408, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)|~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3))). % 0.11/0.40 cnf(i_0_356, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3)))). % 0.11/0.40 cnf(i_0_364, plain, (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))|~hBOOL(hAPP(hAPP(X1,X5),X4)))). % 0.11/0.40 cnf(i_0_340, plain, (X1=X2|hBOOL(hAPP(hAPP(X3,X2),X1))|~c_ListOrder_Ostep1(X3,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X1,X6,X5),X5))). % 0.11/0.40 cnf(i_0_530, plain, (c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)=c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)|~class_Lattices_Olower__semilattice(X3))). % 0.11/0.40 cnf(i_0_527, plain, (c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)=c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)|~class_Lattices_Olattice(X3))). % 0.11/0.40 cnf(i_0_453, plain, (c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)|~class_OrderedGroup_Oab__semigroup__add(X1))). % 0.11/0.40 cnf(i_0_449, plain, (c_ListOrder_Ostep1(c_Lambda_Obeta,X1,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X1,X3),tc_Lambda_OdB)|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X3)))). % 0.11/0.40 cnf(i_0_482, plain, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)))). % 0.11/0.40 cnf(i_0_481, plain, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)))). % 0.11/0.40 cnf(i_0_420, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)|~class_OrderedGroup_Olordered__ab__group__add(X1))). % 0.11/0.40 cnf(i_0_464, plain, (hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X2)),c_Lambda_Olift(X3,X2)))|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)))). % 0.11/0.40 cnf(i_0_478, plain, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)))). % 0.11/0.40 cnf(i_0_424, plain, (c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)|~c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)|~class_OrderedGroup_Olordered__ab__group__add(X1))). % 0.11/0.40 cnf(i_0_427, plain, (c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)|~class_Ring__and__Field_Oordered__idom(X1)|~c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1))). % 0.11/0.40 cnf(i_0_415, plain, (c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X2,X5,X4),X4)|~c_ListOrder_Ostep1(X1,X3,X5,X4))). % 0.11/0.40 cnf(i_0_443, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)))). % 0.11/0.40 cnf(i_0_600, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype)),c_Lambda_Olift(X4,X2)),X5))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X4),X5)))). % 0.11/0.40 cnf(i_0_377, plain, (c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)|~c_ListOrder_Ostep1(X1,X2,X5,X4))). % 0.11/0.40 cnf(i_0_378, plain, (c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X2,X5,X4),X4)|~c_ListOrder_Ostep1(X1,X3,X5,X4))). % 0.11/0.40 cnf(i_0_368, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))|~class_Ring__and__Field_Ocomm__semiring__1(X1))). % 0.11/0.40 cnf(i_0_487, plain, (c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1)|~class_OrderedGroup_Omonoid__add(X1))). % 0.11/0.40 cnf(i_0_414, plain, (c_ListOrder_Ostep1(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(X1,X5),X6))|~c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X6,X3,X4),X4))). % 0.11/0.40 cnf(i_0_403, plain, (X1=X2|X3=X4|~c_ListOrder_Ostep1(X5,c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X6),X6),X6),c_List_Oappend(X2,c_List_Olist_OCons(X4,c_List_Olist_ONil(X6),X6),X6),X6))). % 0.11/0.40 cnf(i_0_380, plain, (c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)|~hBOOL(hAPP(hAPP(X1,X2),X5)))). % 0.11/0.40 cnf(i_0_602, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X4),X2)))). % 0.11/0.40 cnf(i_0_483, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB)=X3|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)))). % 0.11/0.40 cnf(i_0_613, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_Lambda_OdB_OAbs(X2)),hAPP(hAPP(c_Type_Otype_OFun,X3),X4)))|~hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_Type_Otype)),X2),X4)))). % 0.11/0.40 cnf(i_0_372, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))|~class_OrderedGroup_Ocomm__monoid__add(X1))). % 0.11/0.40 cnf(i_0_529, plain, (c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)=c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)|~class_Lattices_Olower__semilattice(X4))). % 0.11/0.40 cnf(i_0_355, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3)))). % 0.11/0.40 cnf(i_0_429, plain, (c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)|~class_Ring__and__Field_Oordered__semidom(X2)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)|~c_HOL_Oord__class_Oless(X1,X4,X2))). % 0.11/0.40 cnf(i_0_511, plain, (hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X2,X3)),c_Lambda_Osubst(X4,X2,X3)))|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X4)))). % 0.11/0.40 cnf(i_0_428, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)|~class_OrderedGroup_Opordered__comm__monoid__add(X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1))). % 0.11/0.40 cnf(i_0_528, plain, (c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)=c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)|~class_Lattices_Olattice(X4))). % 0.11/0.40 cnf(i_0_496, plain, (hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)))|~c_ListOrder_Ostep1(c_Lambda_Obeta,X2,X3,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_452, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X2)),c_Lambda_Olift(X3,X2)))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)))). % 0.11/0.40 cnf(i_0_450, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2)))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2)),X3)))). % 0.11/0.40 cnf(i_0_374, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))|~class_OrderedGroup_Oab__group__add(X1))). % 0.11/0.40 cnf(i_0_423, plain, (c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)|~class_OrderedGroup_Opordered__comm__monoid__add(X1)|~c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)|~c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1))). % 0.11/0.40 cnf(i_0_451, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X4),X2))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X4),X3)))). % 0.11/0.40 cnf(i_0_344, plain, (X1=X2|c_ListOrder_Ostep1(X3,X1,X2,X4)|~c_ListOrder_Ostep1(X3,c_List_Oappend(X1,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4))). % 0.11/0.40 cnf(i_0_362, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)=X4|hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)|~class_OrderedGroup_Oab__group__add(X1))). % 0.11/0.40 cnf(i_0_540, plain, (hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)))). % 0.11/0.40 cnf(i_0_552, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Type_Otyping(X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X2))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X1)))). % 0.11/0.40 cnf(i_0_446, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X2,X3)),c_Lambda_Osubst(X1,X4,X3)))|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)))). % 0.11/0.40 cnf(i_0_447, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X2,X3)),c_Lambda_Osubst(X4,X2,X3)))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X4)))). % 0.11/0.40 cnf(i_0_406, plain, (c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)|~c_HOL_Oord__class_Oless(X2,X4,X1)|~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1))). % 0.11/0.40 cnf(i_0_417, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))|~hBOOL(hAPP(hAPP(X1,X5),X4)))). % 0.11/0.40 cnf(i_0_416, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X5),X4))|~hBOOL(hAPP(hAPP(X1,X3),X5)))). % 0.11/0.40 cnf(i_0_392, plain, (X1=X2|hBOOL(hAPP(hAPP(X3,X1),X2))|~c_ListOrder_Ostep1(X3,c_List_Oappend(X4,c_List_Olist_OCons(X1,c_List_Olist_ONil(X5),X5),X5),c_List_Oappend(X6,c_List_Olist_OCons(X2,c_List_Olist_ONil(X5),X5),X5),X5))). % 0.11/0.40 cnf(i_0_460, plain, (hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)))). % 0.11/0.40 cnf(i_0_448, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X2,X3)),c_Lambda_Osubst(X1,X4,X3)))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X4)))). % 0.11/0.40 cnf(i_0_495, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)))). % 0.11/0.40 cnf(i_0_459, plain, (hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)))|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X3)))). % 0.11/0.40 cnf(i_0_407, plain, (c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)|~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)|~c_HOL_Oord__class_Oless(X2,X4,X1))). % 0.11/0.40 cnf(i_0_409, plain, (c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)|~c_HOL_Oord__class_Oless(X3,X4,X1)|~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1))). % 0.11/0.40 cnf(i_0_385, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X5),X4))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)))). % 0.11/0.40 cnf(i_0_410, plain, (c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)|~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)|~c_HOL_Oord__class_Oless(X3,X4,X1))). % 0.11/0.40 cnf(i_0_354, plain, (c_ListOrder_Ostep1(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(X1,X5),X6))|~c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X3,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4))). % 0.11/0.40 cnf(i_0_523, plain, (hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))|~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))|~hBOOL(hAPP(c_InductTermi_OIT,X2)))). % 0.11/0.40 cnf(i_0_476, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)))). % 0.11/0.40 cnf(i_0_477, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)))). % 0.11/0.40 cnf(i_0_497, plain, (c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)|~c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)|~c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB))). % 0.11/0.40 cnf(i_0_508, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))|~c_Type_Otypings(X1,X3,X5)|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype))))). % 0.11/0.40 cnf(i_0_370, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))|~class_Ring__and__Field_Ocomm__semiring__1(X1))). % 0.11/0.40 cnf(i_0_488, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)|~class_OrderedGroup_Omonoid__add(X1))). % 0.11/0.40 cnf(i_0_401, plain, (c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)|~c_HOL_Oord__class_Oless(X3,X5,X1)|~c_HOL_Oord__class_Oless(X2,X4,X1)|~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1))). % 0.11/0.40 cnf(i_0_373, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))|~class_OrderedGroup_Ocomm__monoid__add(X1))). % 0.11/0.40 cnf(i_0_435, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)|~class_OrderedGroup_Omonoid__add(X1))). % 0.11/0.40 cnf(i_0_441, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)))). % 0.11/0.40 cnf(i_0_442, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X3)))). % 0.11/0.40 cnf(i_0_486, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3)))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)),X3)))). % 0.11/0.40 cnf(i_0_626, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_Lambda_Osubst(X2,X3,X4)),X5))|~hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype)),X2),X5))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X3),X6)))). % 0.11/0.40 cnf(i_0_371, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))|~class_OrderedGroup_Oab__semigroup__add(X1))). % 0.11/0.40 cnf(i_0_359, plain, (c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1))|~class_OrderedGroup_Olordered__ab__group__add(X1))). % 0.11/0.40 cnf(i_0_391, plain, (c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))|~class_OrderedGroup_Osemigroup__add(X1))). % 0.11/0.40 cnf(i_0_361, plain, (c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1))|~class_OrderedGroup_Olordered__ab__group__add__meet(X1))). % 0.11/0.40 cnf(i_0_358, plain, (c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1)),X3)|~class_OrderedGroup_Olordered__ab__group__add(X1))). % 0.11/0.40 cnf(i_0_360, plain, (c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1)),X3)|~class_OrderedGroup_Olordered__ab__group__add__meet(X1))). % 0.11/0.40 cnf(i_0_474, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_Lambda_OdB_OVar(X2)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)))). % 0.11/0.40 cnf(i_0_565, plain, (hBOOL(hAPP(hAPP(c_Type_Otyping(X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),hAPP(hAPP(c_Type_Otype_OFun,X5),X4)))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X3),X5)))). % 0.11/0.40 cnf(i_0_440, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4)))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X4))|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)))). % 0.11/0.40 cnf(i_0_369, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Ring__and__Field_Ocomm__semiring__1(X1))). % 0.11/0.40 cnf(i_0_610, plain, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X2,X3)))|hAPP(hAPP(c_Type_Otype_OFun,X4),X5)!=v_T____|~hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(X6,X3,X5,tc_Type_Otype)),X1),X7))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X6),X2),X5))|~hBOOL(hAPP(c_InductTermi_OIT,X2))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.11/0.40 cnf(i_0_341, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))|~class_Ring__and__Field_Ocomm__semiring__1(X1))). % 0.11/0.40 cnf(i_0_611, plain, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X2,X3)))|hAPP(hAPP(c_Type_Otype_OFun,X4),X5)!=v_T____|~hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(X6,X3,X4,tc_Type_Otype)),X1),X7))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X6),X2),X4))|~hBOOL(hAPP(c_InductTermi_OIT,X2))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.11/0.40 cnf(i_0_479, plain, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))|~c_Type_Otypings(X1,X5,X6)|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),c_List_Oappend(X5,X2,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),X3))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X4)))). % 0.11/0.40 cnf(i_0_473, plain, (c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X1,X2,X3,X4),X1,tc_Type_Otype,tc_Type_Otype)=X2|~c_Type_Otypings(X3,X5,X6)|~hBOOL(hAPP(hAPP(c_Type_Otyping(X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),c_List_Oappend(X5,X4,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),X1))|~hBOOL(hAPP(hAPP(c_Type_Otyping(X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X2)))). % 0.11/0.40 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.11/0.40 # Begin printing tableau % 0.11/0.40 # Found 3 steps % 0.11/0.40 cnf(i_0_628, negated_conjecture, (~c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB)), inference(start_rule)). % 0.11/0.40 cnf(i_0_659, plain, (~c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_as____,tc_Lambda_OdB)), inference(extension_rule, [i_0_603])). % 0.11/0.40 cnf(i_0_709, plain, (~c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____)), inference(closure_rule, [i_0_618])). % 0.11/0.40 # End printing tableau % 0.11/0.40 # SZS output end % 0.11/0.40 # Branches closed with saturation will be marked with an "s" % 0.11/0.40 # Returning from population with 1 new_tableaux and 0 remaining starting tableaux. % 0.11/0.40 # We now have 1 tableaux to operate on % 0.11/0.40 # Found closed tableau during pool population. % 0.11/0.40 # Proof search is over... % 0.11/0.40 # Freeing feature tree %------------------------------------------------------------------------------