%------------------------------------------------------------------------------ % File : Etableau---0.67 % Problem : LCL763-1 : 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 : n007.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 12:01:56 PM UTC 2026 % Result : Unsatisfiable 0.21s 0.56s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.03 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s % 0.08/0.36 % Computer : n007.cluster.edu % 0.08/0.36 % Model : x86_64 x86_64 % 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.36 % Memory : 8046.5625MB % 0.08/0.36 % OS : Linux 6.8.0-71-generic % 0.08/0.36 % CPULimit : 300 % 0.08/0.36 % WCLimit : 300 % 0.08/0.36 % DateTime : Sun Sep 6 00:30:25 UTC 2026 % 0.08/0.36 % CPUTime : % 0.12/0.44 # No SInE strategy applied % 0.12/0.44 # Auto-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y % 0.12/0.44 # and selection function SelectMaxLComplexAvoidPosPred. % 0.12/0.44 # % 0.12/0.44 # Presaturation interreduction done % 0.12/0.44 # Number of axioms: 419 Number of unprocessed: 332 % 0.12/0.44 # Tableaux proof search. % 0.12/0.44 # APR header successfully linked. % 0.12/0.44 # Hello from C++ % 0.12/0.45 # The folding up rule is enabled... % 0.12/0.45 # Local unification is enabled... % 0.12/0.45 # Any saturation attempts will use folding labels... % 0.12/0.45 # 332 beginning clauses after preprocessing and clausification % 0.12/0.45 # Creating start rules for all 1 conjectures. % 0.12/0.45 # There are 1 start rule candidates: % 0.12/0.45 # Found 101 unit axioms. % 0.12/0.45 # 1 start rule tableaux created. % 0.12/0.45 # 231 extension rule candidate clauses % 0.12/0.45 # 101 unit axiom clauses % 0.12/0.45 % 0.12/0.45 # Requested 8, 32 cores available to the main process. % 0.12/0.45 # There are not enough tableaux to fork, creating more from the initial 1 % 0.12/0.45 # Returning from population with 23 new_tableaux and 0 remaining starting tableaux. % 0.12/0.45 # We now have 23 tableaux to operate on % 0.21/0.56 # There were 2 total branch saturation attempts. % 0.21/0.56 # There were 0 of these attempts blocked. % 0.21/0.56 # There were 0 deferred branch saturation attempts. % 0.21/0.56 # There were 0 free duplicated saturations. % 0.21/0.56 # There were 2 total successful branch saturations. % 0.21/0.56 # There were 0 successful branch saturations in interreduction. % 0.21/0.56 # There were 0 successful branch saturations on the branch. % 0.21/0.56 # There were 2 successful branch saturations after the branch. % 0.21/0.56 # SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.21/0.56 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.21/0.56 # Begin clausification derivation % 0.21/0.56 % 0.21/0.56 # End clausification derivation % 0.21/0.56 # Begin listing active clauses obtained from FOF to CNF conversion % 0.21/0.56 cnf(i_0_835, plain, (class_OrderedGroup_Omonoid__add(tc_nat))). % 0.21/0.56 cnf(i_0_838, plain, (class_Orderings_Oorder(tc_nat))). % 0.21/0.56 cnf(i_0_840, plain, (class_Orderings_Oorder(tc_bool))). % 0.21/0.56 cnf(i_0_836, plain, (class_Orderings_Opreorder(tc_nat))). % 0.21/0.56 cnf(i_0_839, plain, (class_Orderings_Opreorder(tc_bool))). % 0.21/0.56 cnf(i_0_837, plain, (class_Orderings_Olinorder(tc_nat))). % 0.21/0.56 cnf(i_0_825, plain, (class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat))). % 0.21/0.56 cnf(i_0_826, plain, (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat))). % 0.21/0.56 cnf(i_0_827, plain, (class_OrderedGroup_Opordered__comm__monoid__add(tc_nat))). % 0.21/0.56 cnf(i_0_830, plain, (class_Ring__and__Field_Oordered__semidom(tc_nat))). % 0.21/0.56 cnf(i_0_832, plain, (class_OrderedGroup_Oab__semigroup__add(tc_nat))). % 0.21/0.56 cnf(i_0_828, plain, (class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat))). % 0.21/0.56 cnf(i_0_829, plain, (class_OrderedGroup_Ocancel__semigroup__add(tc_nat))). % 0.21/0.56 cnf(i_0_831, plain, (class_Ring__and__Field_Ocomm__semiring__1(tc_nat))). % 0.21/0.56 cnf(i_0_833, plain, (class_OrderedGroup_Ocomm__monoid__add(tc_nat))). % 0.21/0.56 cnf(i_0_834, plain, (class_OrderedGroup_Osemigroup__add(tc_nat))). % 0.21/0.56 cnf(i_0_597, plain, (c_List_Oremdups(c_List_Olist_ONil(X1),X1)=c_List_Olist_ONil(X1))). % 0.21/0.56 cnf(i_0_596, plain, (c_List_Orev(c_List_Olist_ONil(X1),X1)=c_List_Olist_ONil(X1))). % 0.21/0.56 cnf(i_0_619, plain, (c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2))). % 0.21/0.56 cnf(i_0_616, plain, (c_List_Oappend(X1,c_List_Olist_ONil(X2),X2)=X1)). % 0.21/0.56 cnf(i_0_614, plain, (c_List_Oappend(c_List_Olist_ONil(X1),X2,X1)=X2)). % 0.21/0.56 cnf(i_0_505, plain, (c_Nat_Osize__class_Osize(c_List_Olist_ONil(X1),tc_List_Olist(X1))=c_HOL_Ozero__class_Ozero(tc_nat))). % 0.21/0.56 cnf(i_0_779, plain, (c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1)=X2)). % 0.21/0.56 cnf(i_0_727, plain, (c_List_Ofilter(X1,c_List_Olist_ONil(X2),X2)=c_List_Olist_ONil(X2))). % 0.21/0.56 cnf(i_0_841, plain, (hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)))). % 0.21/0.56 cnf(i_0_665, plain, (c_List_Orev(c_List_Orev(X1,X2),X2)=X1)). % 0.21/0.56 cnf(i_0_741, plain, (c_List_Orotate(X1,c_List_Olist_ONil(X2),X2)=c_List_Olist_ONil(X2))). % 0.21/0.56 cnf(i_0_734, plain, (c_List_Oremove1(X1,c_List_Olist_ONil(X2),X2)=c_List_Olist_ONil(X2))). % 0.21/0.56 cnf(i_0_693, plain, (c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2)=X1)). % 0.21/0.56 cnf(i_0_579, plain, (c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2)=c_Transitive__Closure_Ortranclp(X1,X2))). % 0.21/0.56 cnf(i_0_506, plain, (c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2)=c_List_Olist_ONil(X2))). % 0.21/0.56 cnf(i_0_456, plain, (c_Predicate_Oconversep(c_fequal(X1),X1,X1)=c_fequal(X1))). % 0.21/0.56 cnf(i_0_785, plain, (c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)))). % 0.21/0.56 cnf(i_0_763, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X1),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)=X1)). % 0.21/0.56 cnf(i_0_488, plain, (c_Nat_Osize__class_Osize(c_List_Orev(X1,X2),tc_List_Olist(X2))=c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)))). % 0.21/0.56 cnf(i_0_745, plain, (c_List_Olistrelp(X1,c_List_Olist_ONil(X2),c_List_Olist_ONil(X2),X2))). % 0.21/0.56 cnf(i_0_743, plain, (c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3)=c_List_Olist_ONil(X3))). % 0.21/0.56 cnf(i_0_658, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)))). % 0.21/0.56 cnf(i_0_725, plain, (c_List_Ofiltermap(X1,c_List_Olist_ONil(X2),X2,X3)=c_List_Olist_ONil(X3))). % 0.21/0.56 cnf(i_0_728, plain, (c_List_Olist__update(c_List_Olist_ONil(X1),X2,X3,X1)=c_List_Olist_ONil(X1))). % 0.21/0.56 cnf(i_0_569, plain, (c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2)=X1)). % 0.21/0.56 cnf(i_0_817, plain, (c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3)=X2)). % 0.21/0.56 cnf(i_0_736, plain, (c_Map_Omap__upds(X1,X2,c_List_Olist_ONil(X3),X4,X3)=X1)). % 0.21/0.56 cnf(i_0_739, plain, (c_List_Olist_Olist__case(X1,X2,c_List_Olist_ONil(X3),X4,X3)=X1)). % 0.21/0.56 cnf(i_0_425, plain, (c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4)=X3)). % 0.21/0.56 cnf(i_0_477, plain, (c_Nat_Osize__class_Osize(c_List_Oreplicate(X1,X2,X3),tc_List_Olist(X3))=X1)). % 0.21/0.56 cnf(i_0_556, plain, (c_List_Oremove1(X1,c_List_Olist_OCons(X1,X2,X3),X3)=X2)). % 0.21/0.56 cnf(i_0_479, plain, (c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2)=X1)). % 0.21/0.56 cnf(i_0_737, plain, (c_Map_Omap__upds(X1,c_List_Olist_ONil(X2),X3,X2,X4)=X1)). % 0.21/0.56 cnf(i_0_784, plain, (c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5)=hAPP(X1,X4))). % 0.21/0.56 cnf(i_0_452, plain, (c_List_Orev(c_List_Oreplicate(X1,X2,X3),X3)=c_List_Oreplicate(X1,X2,X3))). % 0.21/0.56 cnf(i_0_781, plain, (c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5)=hAPP(X1,X4))). % 0.21/0.56 cnf(i_0_651, plain, (c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5)=hAPP(X3,X4))). % 0.21/0.56 cnf(i_0_576, plain, (c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2)=c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2))). % 0.21/0.56 cnf(i_0_459, plain, (c_Nat_Osize__class_Osize(c_List_Orotate(X1,X2,X3),tc_List_Olist(X3))=c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)))). % 0.21/0.56 cnf(i_0_641, plain, (c_List_Oremdups(c_List_Ofilter(X1,X2,X3),X3)=c_List_Ofilter(X1,c_List_Oremdups(X2,X3),X3))). % 0.21/0.56 cnf(i_0_709, plain, (c_List_Ofilter(X1,c_List_Orev(X2,X3),X3)=c_List_Orev(c_List_Ofilter(X1,X2,X3),X3))). % 0.21/0.56 cnf(i_0_791, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))). % 0.21/0.56 cnf(i_0_429, plain, (c_Nat_Osize__class_Osize(c_List_Olist__update(X1,X2,X3,X4),tc_List_Olist(X4))=c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)))). % 0.21/0.56 cnf(i_0_450, plain, (c_Nat_Osize__class_Osize(c_List_Omap(X1,X2,X3,X4),tc_List_Olist(X4))=c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)))). % 0.21/0.56 cnf(i_0_754, 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))). % 0.21/0.56 cnf(i_0_755, plain, (c_Lambda_OdB_OdB__case(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6)=hAPP(hAPP(X2,X4),X5))). % 0.21/0.56 cnf(i_0_716, plain, (c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3)=c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3))). % 0.21/0.57 cnf(i_0_561, plain, (c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3)=c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3))). % 0.21/0.57 cnf(i_0_573, plain, (c_List_Olist__update(c_List_Olist_OCons(X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_nat),X4,X3)=c_List_Olist_OCons(X4,X2,X3))). % 0.21/0.57 cnf(i_0_683, 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)))))). % 0.21/0.57 cnf(i_0_589, plain, (c_List_Oappend(c_List_Orev(X1,X2),c_List_Orev(X3,X2),X2)=c_List_Orev(c_List_Oappend(X3,X1,X2),X2))). % 0.21/0.57 cnf(i_0_451, plain, (c_List_Omap(X1,c_List_Oreplicate(X2,X3,X4),X4,X5)=c_List_Oreplicate(X2,hAPP(X1,X3),X5))). % 0.21/0.57 cnf(i_0_555, plain, (c_List_Olist_Olist__case(X1,X2,c_List_Olist_OCons(X3,X4,X5),X6,X5)=hAPP(hAPP(X2,X3),X4))). % 0.21/0.57 cnf(i_0_714, plain, (c_List_Olist__update(c_List_Olist__update(X1,X2,X3,X4),X2,X5,X4)=c_List_Olist__update(X1,X2,X5,X4))). % 0.21/0.57 cnf(i_0_629, plain, (c_List_Oappend(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2),X2)=c_List_Orev(c_List_Olist_OCons(X3,X1,X2),X2))). % 0.21/0.57 cnf(i_0_759, plain, (hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X1,X2,X3)),c_Lambda_Oliftn(X1,X4,X3))=c_Lambda_Oliftn(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4),X3))). % 0.21/0.57 cnf(i_0_749, 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))). % 0.21/0.57 cnf(i_0_592, plain, (c_List_Oappend(c_List_Ofilter(X1,X2,X3),c_List_Ofilter(X1,X4,X3),X3)=c_List_Ofilter(X1,c_List_Oappend(X2,X4,X3),X3))). % 0.21/0.57 cnf(i_0_768, 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))). % 0.21/0.57 cnf(i_0_510, plain, (c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,X4,X3),X3)=c_List_Olist_OCons(X2,c_List_Oappend(c_List_Oreplicate(X1,X2,X3),X4,X3),X3))). % 0.21/0.57 cnf(i_0_453, 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))). % 0.21/0.57 cnf(i_0_687, plain, (c_List_Oappend(c_List_Omap(X1,X2,X3,X4),c_List_Omap(X1,X5,X3,X4),X4)=c_List_Omap(X1,c_List_Oappend(X2,X5,X3),X3,X4))). % 0.21/0.57 cnf(i_0_526, plain, (c_List_Olist__update(c_List_Oappend(X1,c_List_Olist_OCons(X2,X3,X4),X4),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),X5,X4)=c_List_Oappend(X1,c_List_Olist_OCons(X5,X3,X4),X4))). % 0.21/0.57 cnf(i_0_756, plain, (hAPP(hAPP(hAPP(hAPP(X1,X2),X3),c_Lambda_OdB_OdB__rec(X4,X1,X5,X2,X6)),c_Lambda_OdB_OdB__rec(X4,X1,X5,X3,X6))=c_Lambda_OdB_OdB__rec(X4,X1,X5,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X6))). % 0.21/0.57 cnf(i_0_655, plain, (c_List_Orev(c_List_Omap(X1,X2,X3,X4),X4)=c_List_Omap(X1,c_List_Orev(X2,X3),X3,X4))). % 0.21/0.57 cnf(i_0_663, plain, (c_List_Orotate(X1,c_List_Omap(X2,X3,X4,X5),X5)=c_List_Omap(X2,c_List_Orotate(X1,X3,X4),X4,X5))). % 0.21/0.57 cnf(i_0_692, plain, (c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5)=hAPP(hAPP(X3,X4),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X5)))). % 0.21/0.57 cnf(i_0_767, 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))). % 0.21/0.57 cnf(i_0_471, plain, (c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Oreplicate(X4,X2,X3),X3)=c_List_Oappend(c_List_Oreplicate(X4,X2,X3),c_List_Oreplicate(X1,X2,X3),X3))). % 0.21/0.57 cnf(i_0_552, plain, (c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5)=c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5))). % 0.21/0.57 cnf(i_0_478, 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)))). % 0.21/0.57 cnf(i_0_575, plain, (c_List_Omap(X1,c_List_Olist__update(X2,X3,X4,X5),X5,X6)=c_List_Olist__update(c_List_Omap(X1,X2,X5,X6),X3,hAPP(X1,X4),X6))). % 0.21/0.57 cnf(i_0_460, plain, (~c_HOL_Oord__class_Oless(X1,X1,tc_nat))). % 0.21/0.57 cnf(i_0_782, plain, (c_Lambda_OdB_OAbs(X1)!=c_Lambda_OdB_OVar(X2))). % 0.21/0.57 cnf(i_0_816, plain, (c_Lambda_OdB_OVar(X1)!=hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))). % 0.21/0.57 cnf(i_0_780, plain, (~hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)))). % 0.21/0.57 cnf(i_0_572, plain, (c_List_Olist_OCons(X1,X2,X3)!=X2)). % 0.21/0.57 cnf(i_0_438, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))). % 0.21/0.57 cnf(i_0_751, plain, (c_Lambda_OdB_OAbs(X1)!=hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))). % 0.21/0.57 cnf(i_0_605, plain, (c_List_Olist_OCons(X1,X2,X3)!=c_List_Olist_ONil(X3))). % 0.21/0.57 cnf(i_0_610, plain, (~c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3))). % 0.21/0.57 cnf(i_0_611, plain, (~c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2))). % 0.21/0.57 cnf(i_0_801, 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))). % 0.21/0.57 cnf(i_0_800, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.21/0.57 cnf(i_0_822, negated_conjecture, (~hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))))). % 0.21/0.57 cnf(i_0_809, plain, (X1=X2|c_Lambda_OdB_OVar(X1)!=c_Lambda_OdB_OVar(X2))). % 0.21/0.57 cnf(i_0_680, plain, (X1=X2|c_Lambda_OdB_OAbs(X1)!=c_Lambda_OdB_OAbs(X2))). % 0.21/0.57 cnf(i_0_788, plain, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_820, 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))). % 0.21/0.57 cnf(i_0_802, 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))). % 0.21/0.57 cnf(i_0_724, plain, (c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X1),X1)|~class_Orderings_Olinorder(X1))). % 0.21/0.57 cnf(i_0_462, plain, (~class_Orderings_Oorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1))). % 0.21/0.57 cnf(i_0_464, plain, (~class_Orderings_Opreorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1))). % 0.21/0.57 cnf(i_0_463, plain, (~class_Orderings_Olinorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1))). % 0.21/0.57 cnf(i_0_815, 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))). % 0.21/0.57 cnf(i_0_447, 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))). % 0.21/0.57 cnf(i_0_807, 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))). % 0.21/0.57 cnf(i_0_694, plain, (c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)|~class_OrderedGroup_Osemigroup__add(X1))). % 0.21/0.57 cnf(i_0_726, plain, (X1=c_List_Olist_ONil(X2)|c_List_Oremdups(X1,X2)!=c_List_Olist_ONil(X2))). % 0.21/0.57 cnf(i_0_604, plain, (X1=c_List_Olist_ONil(X2)|c_List_Orev(X1,X2)!=c_List_Olist_ONil(X2))). % 0.21/0.57 cnf(i_0_787, plain, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_824, plain, (class_Orderings_Oorder(tc_fun(X1,X2))|~class_Orderings_Oorder(X2))). % 0.21/0.57 cnf(i_0_823, plain, (class_Orderings_Opreorder(tc_fun(X1,X2))|~class_Orderings_Opreorder(X2))). % 0.21/0.57 cnf(i_0_598, plain, (X1=c_List_Olist_ONil(X2)|c_List_Oappend(X1,X3,X2)!=X3)). % 0.21/0.57 cnf(i_0_600, plain, (X1=c_List_Olist_ONil(X2)|c_List_Oappend(X3,X1,X2)!=X3)). % 0.21/0.57 cnf(i_0_842, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2)))). % 0.21/0.57 cnf(i_0_814, plain, (X1=X2|hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)!=hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2))). % 0.21/0.57 cnf(i_0_813, plain, (X1=X2|hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)!=hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4))). % 0.21/0.57 cnf(i_0_689, plain, (X1=X2|c_List_Orev(X1,X3)!=c_List_Orev(X2,X3))). % 0.21/0.57 cnf(i_0_489, plain, (~class_Orderings_Oorder(X1)|~c_HOL_Oord__class_Oless(X2,X3,X1)|~c_HOL_Oord__class_Oless(X3,X2,X1))). % 0.21/0.57 cnf(i_0_819, 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))). % 0.21/0.57 cnf(i_0_608, plain, (X1=c_List_Olist_ONil(X2)|c_List_Oappend(X3,X1,X2)!=c_List_Olist_ONil(X2))). % 0.21/0.57 cnf(i_0_609, plain, (X1=c_List_Olist_ONil(X2)|c_List_Oappend(X1,X3,X2)!=c_List_Olist_ONil(X2))). % 0.21/0.57 cnf(i_0_492, plain, (~class_Orderings_Opreorder(X1)|~c_HOL_Oord__class_Oless(X2,X3,X1)|~c_HOL_Oord__class_Oless(X3,X2,X1))). % 0.21/0.57 cnf(i_0_490, plain, (~class_Orderings_Olinorder(X1)|~c_HOL_Oord__class_Oless(X2,X3,X1)|~c_HOL_Oord__class_Oless(X3,X2,X1))). % 0.21/0.57 cnf(i_0_509, plain, (X1=c_List_Olist_ONil(X2)|c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2))!=c_HOL_Ozero__class_Ozero(tc_nat))). % 0.21/0.57 cnf(i_0_603, plain, (X1=c_List_Olist_ONil(X2)|c_List_Orotate(X3,X1,X2)!=c_List_Olist_ONil(X2))). % 0.21/0.57 cnf(i_0_811, 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))). % 0.21/0.57 cnf(i_0_508, plain, (X1=c_HOL_Ozero__class_Ozero(tc_nat)|c_List_Oreplicate(X1,X2,X3)!=c_List_Olist_ONil(X3))). % 0.21/0.57 cnf(i_0_783, plain, (hAPP(X1,X2)=X3|~c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3))). % 0.21/0.57 cnf(i_0_613, plain, (X1=c_List_Olist_ONil(X2)|c_List_Omap(X3,X1,X2,X4)!=c_List_Olist_ONil(X4))). % 0.21/0.57 cnf(i_0_810, 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))). % 0.21/0.57 cnf(i_0_475, plain, (X1=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat))). % 0.21/0.57 cnf(i_0_748, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olist__update(X1,X3,X4,X2)!=c_List_Olist_ONil(X2))). % 0.21/0.57 cnf(i_0_705, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(c_List_Oappend(X3,X1,X2),X2)|~class_Orderings_Olinorder(X2))). % 0.21/0.57 cnf(i_0_704, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(c_List_Oappend(X1,X3,X2),X2)|~class_Orderings_Olinorder(X2))). % 0.21/0.57 cnf(i_0_793, 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))). % 0.21/0.57 cnf(i_0_446, 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)))). % 0.21/0.57 cnf(i_0_564, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X3,X1,X2),X2)|~class_Orderings_Olinorder(X2))). % 0.21/0.57 cnf(i_0_700, plain, (X1=X2|c_List_Olist_OCons(X3,X1,X4)!=c_List_Olist_OCons(X5,X2,X4))). % 0.21/0.57 cnf(i_0_657, plain, (X1=X2|c_List_Oappend(X3,X1,X4)!=c_List_Oappend(X3,X2,X4))). % 0.21/0.57 cnf(i_0_442, plain, (X1=X2|c_List_Oreplicate(X1,X3,X4)!=c_List_Oreplicate(X2,X5,X4))). % 0.21/0.57 cnf(i_0_798, plain, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_480, plain, (X1=X2|hAPP(hAPP(c_Type_Otype_OFun,X3),X1)!=hAPP(hAPP(c_Type_Otype_OFun,X4),X2))). % 0.21/0.57 cnf(i_0_585, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))=X2|~class_OrderedGroup_Omonoid__add(X1))). % 0.21/0.57 cnf(i_0_656, plain, (X1=X2|c_List_Oappend(X1,X3,X4)!=c_List_Oappend(X2,X3,X4))). % 0.21/0.57 cnf(i_0_699, plain, (X1=X2|c_List_Olist_OCons(X1,X3,X4)!=c_List_Olist_OCons(X2,X5,X4))). % 0.21/0.57 cnf(i_0_650, plain, (c_List_Olistsp(X1,X2,X3)|~c_List_Olistsp(X1,c_List_Oappend(X4,X2,X3),X3))). % 0.21/0.57 cnf(i_0_649, plain, (c_List_Olistsp(X1,X2,X3)|~c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3))). % 0.21/0.57 cnf(i_0_481, plain, (X1=X2|hAPP(hAPP(c_Type_Otype_OFun,X1),X3)!=hAPP(hAPP(c_Type_Otype_OFun,X2),X4))). % 0.21/0.57 cnf(i_0_520, plain, (c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2)=c_Lambda_OdB_OVar(X1)|~c_HOL_Oord__class_Oless(X1,X2,tc_nat))). % 0.21/0.57 cnf(i_0_586, 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))). % 0.21/0.57 cnf(i_0_707, plain, (c_List_Olinorder__class_Osorted(c_List_Oremdups(X1,X2),X2)|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X2))). % 0.21/0.57 cnf(i_0_448, plain, (c_List_Oremdups(X1,X2)=X1|c_Nat_Osize__class_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2))!=c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)))). % 0.21/0.57 cnf(i_0_676, 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))). % 0.21/0.57 cnf(i_0_795, 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))). % 0.21/0.57 cnf(i_0_794, 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))). % 0.21/0.57 cnf(i_0_434, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)))). % 0.21/0.57 cnf(i_0_583, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))=X2|~class_OrderedGroup_Ocomm__monoid__add(X1))). % 0.21/0.57 cnf(i_0_578, plain, (c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2)|~class_Orderings_Olinorder(X2))). % 0.21/0.57 cnf(i_0_719, plain, (c_List_Olinorder__class_Osorted(c_List_Oremove1(X1,X2,X3),X3)|~c_List_Olinorder__class_Osorted(X2,X3)|~class_Orderings_Olinorder(X3))). % 0.21/0.57 cnf(i_0_521, plain, (c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X3)=c_Lambda_OdB_OVar(X2)|~c_HOL_Oord__class_Oless(X2,X3,tc_nat))). % 0.21/0.57 cnf(i_0_516, 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))). % 0.21/0.57 cnf(i_0_591, plain, (hAPP(hAPP(X1,X2),X3)=X3|~c_OrderedGroup_Omonoid__add(X2,X1,X4))). % 0.21/0.57 cnf(i_0_590, plain, (hAPP(hAPP(X1,X2),X3)=X2|~c_OrderedGroup_Omonoid__add(X3,X1,X4))). % 0.21/0.57 cnf(i_0_731, plain, (hBOOL(hAPP(X1,v_sko__List__Xconcat__Xinduct__2(X1)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_584, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2)=X2|~class_OrderedGroup_Omonoid__add(X1))). % 0.21/0.57 cnf(i_0_723, plain, (hBOOL(hAPP(X1,v_sko__List__Xtake__Xinduct__2(X1)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_746, plain, (hBOOL(hAPP(X1,v_sko__List__Xmap__Xinduct__2(X1)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_742, plain, (hBOOL(hAPP(X1,v_sko__List__Xlist__Xinduct__2(X1)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_722, plain, (hBOOL(hAPP(X1,v_sko__List__XdropWhile__Xinduct__2(X1)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_580, 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))). % 0.21/0.57 cnf(i_0_427, plain, (X1=c_HOL_Ozero__class_Ozero(tc_nat)|X2=X3|c_List_Oreplicate(X1,X2,X4)!=c_List_Oreplicate(X5,X3,X4))). % 0.21/0.57 cnf(i_0_630, plain, (hBOOL(hAPP(X1,X2))|c_List_Olist_OCons(X2,X3,X4)!=c_List_Ofilter(X1,X5,X4))). % 0.21/0.57 cnf(i_0_738, plain, (hBOOL(hAPP(X1,v_sko__List__Xremove1__Xinduct__2(X1)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_735, plain, (hBOOL(hAPP(X1,v_sko__List__Xdistinct__Xinduct__2(X1)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_588, 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)))). % 0.21/0.57 cnf(i_0_677, plain, (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))|~hBOOL(hAPP(hAPP(X1,X3),X4)))). % 0.21/0.57 cnf(i_0_672, plain, (X1=c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3)|c_List_Orev(X1,X3)!=c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3))). % 0.21/0.57 cnf(i_0_673, 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))). % 0.21/0.57 cnf(i_0_653, plain, (X1=X2|X3=X4|~c_ListOrder_Ostep1(X5,c_List_Olist_OCons(X2,X4,X6),c_List_Olist_OCons(X1,X3,X6),X6))). % 0.21/0.57 cnf(i_0_581, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2)=X2|~class_OrderedGroup_Ocomm__monoid__add(X1))). % 0.21/0.57 cnf(i_0_682, plain, (c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_758, 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)))). % 0.21/0.57 cnf(i_0_582, 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))). % 0.21/0.57 cnf(i_0_558, 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))). % 0.21/0.57 cnf(i_0_559, 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))). % 0.21/0.57 cnf(i_0_560, 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))). % 0.21/0.57 cnf(i_0_440, 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))). % 0.21/0.57 cnf(i_0_757, 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)))). % 0.21/0.57 cnf(i_0_796, 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)))). % 0.21/0.57 cnf(i_0_642, 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))). % 0.21/0.57 cnf(i_0_441, 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))). % 0.21/0.57 cnf(i_0_701, plain, (c_Type_Otyping(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X4),X2))|~c_Type_Otyping(X1,X4,X3))). % 0.21/0.57 cnf(i_0_491, plain, (c_Wellfounded_Oaccp(X1,X2,X3)|~c_Wellfounded_Oaccp(X1,X4,X3)|~hBOOL(hAPP(hAPP(X1,X2),X4)))). % 0.21/0.57 cnf(i_0_515, 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))). % 0.21/0.57 cnf(i_0_435, plain, (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))|~hBOOL(hAPP(hAPP(X1,X5),X4)))). % 0.21/0.57 cnf(i_0_662, plain, (c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))=X1|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_762, 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))). % 0.21/0.57 cnf(i_0_431, 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))). % 0.21/0.57 cnf(i_0_467, plain, (X1=X2|c_HOL_Oord__class_Oless(X1,X2,tc_nat)|c_HOL_Oord__class_Oless(X2,X1,tc_nat))). % 0.21/0.57 cnf(i_0_499, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)|~class_OrderedGroup_Olordered__ab__group__add(X2)|~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2))). % 0.21/0.57 cnf(i_0_496, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)|~class_OrderedGroup_Olordered__ab__group__add(X1)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1))). % 0.21/0.57 cnf(i_0_500, 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))). % 0.21/0.57 cnf(i_0_529, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xconcat__Xinduct__1(X1),v_sko__List__Xconcat__Xinduct__2(X1),t_a)))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_530, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xtake__Xinduct__1(X1),v_sko__List__Xtake__Xinduct__2(X1),t_a)))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_531, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xmap__Xinduct__1(X1),v_sko__List__Xmap__Xinduct__2(X1),t_a)))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_532, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(X1),v_sko__List__Xlist__Xinduct__2(X1),t_a)))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_668, 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))). % 0.21/0.57 cnf(i_0_557, 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))). % 0.21/0.57 cnf(i_0_691, plain, (c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)|~c_List_Olistsp(X1,X3,X4)|~c_List_Olistsp(X1,X2,X4))). % 0.21/0.57 cnf(i_0_533, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(X1),v_sko__List__XdropWhile__Xinduct__2(X1),t_a)))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_534, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(X1),v_sko__List__Xremove1__Xinduct__2(X1),t_a)))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_535, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(X1),v_sko__List__Xdistinct__Xinduct__2(X1),t_a)))|~hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))))). % 0.21/0.57 cnf(i_0_711, 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))). % 0.21/0.57 cnf(i_0_710, 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))). % 0.21/0.57 cnf(i_0_568, plain, (c_Type_Otyping(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X4),X2))|~c_Type_Otyping(X1,X4,X3))). % 0.21/0.57 cnf(i_0_443, plain, (c_Wellfounded_Oaccp(X1,X2,X3)|~c_Wellfounded_Oaccp(X1,X4,X3)|~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X4)))). % 0.21/0.57 cnf(i_0_512, plain, (c_List_Ofilter(X1,c_List_Oreplicate(X2,X3,X4),X4)=c_List_Olist_ONil(X4)|hBOOL(hAPP(X1,X3)))). % 0.21/0.57 cnf(i_0_769, plain, (hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))))). % 0.21/0.57 cnf(i_0_771, plain, (hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))))). % 0.21/0.57 cnf(i_0_789, 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)))). % 0.21/0.57 cnf(i_0_648, 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)))). % 0.21/0.57 cnf(i_0_669, 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))). % 0.21/0.57 cnf(i_0_487, 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))). % 0.21/0.57 cnf(i_0_484, 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))). % 0.21/0.57 cnf(i_0_774, 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)))). % 0.21/0.57 cnf(i_0_570, 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)))). % 0.21/0.57 cnf(i_0_466, plain, (X1=X2|c_HOL_Oord__class_Oless(X1,X2,X3)|c_HOL_Oord__class_Oless(X2,X1,X3)|~class_Orderings_Olinorder(X3))). % 0.21/0.57 cnf(i_0_685, 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))). % 0.21/0.57 cnf(i_0_775, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)=X1|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_551, 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)))). % 0.21/0.57 cnf(i_0_622, 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)))). % 0.21/0.57 cnf(i_0_433, 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)))). % 0.21/0.57 cnf(i_0_465, 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))). % 0.21/0.57 cnf(i_0_454, plain, (c_List_Ofilter(X1,c_List_Oreplicate(X2,X3,X4),X4)=c_List_Oreplicate(X2,X3,X4)|~hBOOL(hAPP(X1,X3)))). % 0.21/0.57 cnf(i_0_761, 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)))). % 0.21/0.57 cnf(i_0_549, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))|~hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))))). % 0.21/0.57 cnf(i_0_550, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))|~hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))))). % 0.21/0.57 cnf(i_0_773, 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)))). % 0.21/0.57 cnf(i_0_536, plain, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))|~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3))). % 0.21/0.57 cnf(i_0_537, plain, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))|~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3))). % 0.21/0.57 cnf(i_0_563, 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))). % 0.21/0.57 cnf(i_0_799, plain, (X1=X2|~c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2)|~c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X1))). % 0.21/0.57 cnf(i_0_593, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)=X1|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))=X1|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_770, plain, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))|~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3))). % 0.21/0.57 cnf(i_0_547, plain, (c_Type_Otyping(X1,X2,c_Type_Osko__Type__Xtypes__snocE__1__2(X3,X1,X2,X4))|~c_Type_Otypings(X1,c_List_Oappend(X4,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X3))). % 0.21/0.57 cnf(i_0_541, plain, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xtypes__snocE__1__1(X3,X1,X4,X2))|~c_Type_Otypings(X1,c_List_Oappend(X2,c_List_Olist_OCons(X4,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X3))). % 0.21/0.57 cnf(i_0_804, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X3,X1,X4),tc_Lambda_OdB,tc_Lambda_OdB)=X2|X4=c_List_Olist_ONil(tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X4,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.21/0.57 cnf(i_0_684, 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)))). % 0.21/0.57 cnf(i_0_432, 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)))). % 0.21/0.57 cnf(i_0_708, plain, (c_List_Ofilter(X1,c_List_Olist_OCons(X2,X3,X4),X4)=c_List_Ofilter(X1,X3,X4)|hBOOL(hAPP(X1,X2)))). % 0.21/0.57 cnf(i_0_511, 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))). % 0.21/0.57 cnf(i_0_688, plain, (c_List_Oremove1(X1,c_List_Ofilter(X2,X3,X4),X4)=c_List_Ofilter(X2,X3,X4)|hBOOL(hAPP(X2,X1)))). % 0.21/0.57 cnf(i_0_495, plain, (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)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1))). % 0.21/0.57 cnf(i_0_681, plain, (c_List_Oremove1(X1,c_List_Olist_OCons(X2,X3,X4),X4)=c_List_Olist_OCons(X2,c_List_Oremove1(X1,X3,X4),X4)|X1=X2)). % 0.21/0.57 cnf(i_0_652, 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)))). % 0.21/0.57 cnf(i_0_566, 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)))). % 0.21/0.57 cnf(i_0_686, plain, (hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4)=hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))|~c_OrderedGroup_Osemigroup__add(X1,X5))). % 0.21/0.57 cnf(i_0_721, 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)))). % 0.21/0.57 cnf(i_0_498, plain, (c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)|~class_OrderedGroup_Olordered__ab__group__add(X1)|~c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1))). % 0.21/0.57 cnf(i_0_643, plain, (c_List_Ofilter(X1,c_List_Olist_OCons(X2,X3,X4),X4)=c_List_Olist_OCons(X2,c_List_Ofilter(X1,X3,X4),X4)|~hBOOL(hAPP(X1,X2)))). % 0.21/0.57 cnf(i_0_501, 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))). % 0.21/0.57 cnf(i_0_646, 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))). % 0.21/0.57 cnf(i_0_720, 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)))). % 0.21/0.57 cnf(i_0_786, plain, (c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X1,X2,X3,X4),c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)=X4|X4=c_List_Olist_ONil(tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X4,tc_Lambda_OdB,tc_Lambda_OdB))). % 0.21/0.57 cnf(i_0_647, 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))). % 0.21/0.57 cnf(i_0_703, 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))). % 0.21/0.57 cnf(i_0_702, 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))). % 0.21/0.57 cnf(i_0_690, 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))). % 0.21/0.57 cnf(i_0_664, 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)))). % 0.21/0.57 cnf(i_0_513, plain, (c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)|~c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X5),X4))|~c_Type_Otyping(X1,X3,X5))). % 0.21/0.57 cnf(i_0_674, 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)))). % 0.21/0.57 cnf(i_0_675, 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)))). % 0.21/0.57 cnf(i_0_626, plain, (X1=c_List_Orev(c_List_Olist_OCons(X2,X3,X4),X4)|c_List_Orev(X1,X4)!=c_List_Olist_OCons(X2,X3,X4))). % 0.21/0.57 cnf(i_0_654, 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)))). % 0.21/0.57 cnf(i_0_423, 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))). % 0.21/0.57 cnf(i_0_455, plain, (c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2))=c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2))|c_List_Omap(X4,X1,X2,X5)!=c_List_Omap(X4,X3,X2,X5))). % 0.21/0.57 cnf(i_0_503, 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))). % 0.21/0.57 cnf(i_0_660, 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)))). % 0.21/0.57 cnf(i_0_631, 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))). % 0.21/0.57 cnf(i_0_539, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)=X1|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_483, 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))). % 0.21/0.57 cnf(i_0_633, 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))). % 0.21/0.57 cnf(i_0_502, 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))). % 0.21/0.57 cnf(i_0_497, 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))). % 0.21/0.57 cnf(i_0_577, 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))). % 0.21/0.57 cnf(i_0_679, plain, (c_List_Olistrelp(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)|~c_List_Olistrelp(X1,X3,X6,X4)|~hBOOL(hAPP(hAPP(X1,X2),X5)))). % 0.21/0.57 cnf(i_0_486, 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))). % 0.21/0.57 cnf(i_0_766, plain, (hAPP(hAPP(X1,X2),c_List_Ofoldl(X1,X3,X4,X5,X5))=c_List_Ofoldl(X1,X2,X4,X5,X5)|~c_OrderedGroup_Omonoid__add(X3,X1,X5))). % 0.21/0.57 cnf(i_0_540, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)=X1|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))=X1|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_482, 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__cancel__ab__semigroup__add(X1)|~c_HOL_Oord__class_Oless(X2,X4,X1))). % 0.21/0.57 cnf(i_0_637, 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))). % 0.21/0.57 cnf(i_0_671, 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))). % 0.21/0.57 cnf(i_0_519, plain, (c_Map_Omap__upds(X1,X2,c_List_Oappend(X3,X4,X5),X6,X5)=c_Map_Omap__upds(X1,X2,X3,X6,X5)|c_Nat_Osize__class_Osize(X2,tc_List_Olist(X6))!=c_Nat_Osize__class_Osize(X3,tc_List_Olist(X5)))). % 0.21/0.57 cnf(i_0_518, plain, (c_Map_Omap__upds(X1,c_List_Oappend(X2,X3,X4),X5,X4,X6)=c_Map_Omap__upds(X1,X2,X5,X4,X6)|c_Nat_Osize__class_Osize(X2,tc_List_Olist(X4))!=c_Nat_Osize__class_Osize(X5,tc_List_Olist(X6)))). % 0.21/0.57 cnf(i_0_485, 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__cancel__ab__semigroup__add(X1)|~c_HOL_Oord__class_Oless(X3,X4,X1))). % 0.21/0.57 cnf(i_0_635, 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))). % 0.21/0.57 cnf(i_0_636, 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))). % 0.21/0.57 cnf(i_0_639, 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))). % 0.21/0.57 cnf(i_0_517, plain, (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)|~c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype)))). % 0.21/0.57 cnf(i_0_457, plain, (c_List_Olist__update(c_List_Oappend(X1,X2,X3),X4,X5,X3)=c_List_Oappend(c_List_Olist__update(X1,X4,X5,X3),X2,X3)|~c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat))). % 0.21/0.57 cnf(i_0_428, plain, (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))|~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3))). % 0.21/0.57 cnf(i_0_638, 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))). % 0.21/0.57 cnf(i_0_525, 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))). % 0.21/0.57 cnf(i_0_544, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)=X1|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)=X1|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_542, plain, (c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)|hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_474, 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)|~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)|~c_HOL_Oord__class_Oless(X3,X5,X1)|~c_HOL_Oord__class_Oless(X2,X4,X1))). % 0.21/0.57 cnf(i_0_445, plain, (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))|~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3))). % 0.21/0.57 cnf(i_0_628, 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))). % 0.21/0.57 cnf(i_0_764, plain, (c_List_Ofoldl(X1,hAPP(hAPP(X1,X2),X3),X4,X5,X5)=hAPP(hAPP(X1,X2),c_List_Ofoldl(X1,X3,X4,X5,X5))|~c_OrderedGroup_Osemigroup__add(X1,X5))). % 0.21/0.57 cnf(i_0_527, plain, (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))|~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB),X3))). % 0.21/0.57 cnf(i_0_678, 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))). % 0.21/0.57 cnf(i_0_543, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)=X1|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)=X1|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))=X1|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_545, plain, (c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))=X1|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)|hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_546, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)=X1|hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_634, 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))). % 0.21/0.57 cnf(i_0_548, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)=X1|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))=X1|hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))|~hBOOL(hAPP(c_InductTermi_OIT,X1)))). % 0.21/0.57 cnf(i_0_765, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,c_List_Olist_OCons(X3,X4,X1),X1,X1)|~class_OrderedGroup_Osemigroup__add(X1))). % 0.21/0.57 cnf(i_0_772, 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)|~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)|~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X5,tc_Lambda_OdB,tc_Lambda_OdB),X4))). % 0.21/0.57 cnf(i_0_565, 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))). % 0.21/0.57 cnf(i_0_706, plain, (c_List_Olist__update(c_List_Olist__update(X1,X2,X3,X4),X5,X6,X4)=c_List_Olist__update(c_List_Olist__update(X1,X5,X6,X4),X2,X3,X4)|X2=X5)). % 0.21/0.57 cnf(i_0_523, plain, (c_List_Ofilter(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,X4,X5),X5),X5)=c_List_Olist_OCons(X3,c_List_Ofilter(X1,X4,X5),X5)|hBOOL(hAPP(X1,c_List_Osko__List__XCons__eq__filter__iff__1__3(X1,X2,X5)))|~hBOOL(hAPP(X1,X3)))). % 0.21/0.57 cnf(i_0_524, plain, (c_List_Ofilter(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,X4,X5),X5),X5)=c_List_Olist_OCons(X3,c_List_Ofilter(X1,X4,X5),X5)|hBOOL(hAPP(X1,c_List_Osko__List__Xfilter__eq__Cons__iff__1__3(X1,X2,X5)))|~hBOOL(hAPP(X1,X3)))). % 0.21/0.57 cnf(i_0_528, 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)|~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)|~c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2))). % 0.21/0.57 cnf(i_0_422, plain, (c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),c_List_Olist_OCons(X2,X3,X1),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))). % 0.21/0.57 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.21/0.57 # Begin printing tableau % 0.21/0.57 # Found 5 steps % 0.21/0.57 cnf(i_0_822, negated_conjecture, (~hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n)))), inference(start_rule)). % 0.21/0.57 cnf(i_0_843, plain, (~hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n)))), inference(extension_rule, [i_0_549])). % 0.21/0.57 cnf(i_0_1192, plain, (~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(c_InductTermi_OIT)),c_ListApplication_Osko__ListApplication__Xlem__1__2(c_InductTermi_OIT),tc_Lambda_OdB,tc_Lambda_OdB)))), inference(extension_rule, [i_0_447])). % 0.21/0.57 cnf(i_0_1193, plain, (~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(c_InductTermi_OIT)),c_ListApplication_Osko__ListApplication__Xlem__1__4(c_InductTermi_OIT),tc_Lambda_OdB,tc_Lambda_OdB)))), inference(etableau_closure_rule, [i_0_1193, ...])). % 0.21/0.57 cnf(i_0_1449, plain, (~c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(c_InductTermi_OIT)),c_ListApplication_Osko__ListApplication__Xlem__1__2(c_InductTermi_OIT),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)), inference(etableau_closure_rule, [i_0_1449, ...])). % 0.21/0.57 # End printing tableau % 0.21/0.57 # SZS output end % 0.21/0.57 # Branches closed with saturation will be marked with an "s" % 0.21/0.57 # Child (1208945) has found a proof. % 0.21/0.57 % 0.21/0.57 # Proof search is over... % 0.21/0.57 # Freeing feature tree %------------------------------------------------------------------------------