%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n012.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 11:24:03 AM UTC 2026 % Result : Unsatisfiable 0.16s 0.44s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.01 % Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.05/0.30 % Computer : n012.cluster.edu % 0.05/0.30 % Model : x86_64 x86_64 % 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.05/0.30 % Memory : 8046.5625MB % 0.05/0.30 % OS : Linux 6.8.0-71-generic % 0.05/0.30 % CPULimit : 300 % 0.05/0.30 % WCLimit : 300 % 0.05/0.30 % DateTime : Sat Sep 5 03:18:57 UTC 2026 % 0.05/0.30 % CPUTime : % 0.07/0.36 %----Proving TF0_NAR, FOF, or CNF % 0.07/0.37 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.16/0.44 % SZS status Unsatisfiable % 0.16/0.44 % SZS output start Proof % 0.16/0.44 ( % 0.16/0.44 (declare-sort $$unsorted 0) % 0.16/0.44 (declare-const tptp.v_T $$unsorted) % 0.16/0.44 (declare-const tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.v_sko__Wellfounded__Xaccp__Xinducts__1 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.t_a $$unsorted) % 0.16/0.44 (declare-const tptp.c_Predicate_Oconversep (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_Wellfounded_OwfP (-> $$unsorted $$unsorted Bool)) % 0.16/0.44 (declare-const tptp.c_Predicate_Opred__comp (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_Wellfounded_Oaccp (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.44 (declare-const tptp.class_Lattices_Odistrib__lattice (-> $$unsorted Bool)) % 0.16/0.44 (declare-const tptp.class_Lattices_Olower__semilattice (-> $$unsorted Bool)) % 0.16/0.44 (declare-const tptp.hBOOL (-> $$unsorted Bool)) % 0.16/0.44 (declare-const tptp.v_e $$unsorted) % 0.16/0.44 (declare-const tptp.tc_fun (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_Lambda_Osubst (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.hAPP (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.tc_Lambda_OdB $$unsorted) % 0.16/0.44 (declare-const tptp.tc_Type_Otype $$unsorted) % 0.16/0.44 (declare-const tptp.c_Lambda_OdB_OApp $$unsorted) % 0.16/0.44 (declare-const tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_HOL_Ozero__class_Ozero (-> $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_List_Olist_ONil (-> $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_Type_Oshift (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_Lambda_OdB_OVar (-> $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_Transitive__Closure_Ortranclp (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_fequal (-> $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_Type_Otyping (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.44 (declare-const tptp.c_Lambda_Olift (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_Lambda_OdB_OAbs (-> $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_InductTermi_OIT $$unsorted) % 0.16/0.44 (declare-const tptp.c_ListOrder_Ostep1 (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.44 (declare-const tptp.v_sko__Wellfounded__Xaccp__Xinduct__1 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.tc_nat $$unsorted) % 0.16/0.44 (declare-const tptp.c_Type_Otype_OFun (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.tc_bool $$unsorted) % 0.16/0.44 (declare-const tptp.v_t $$unsorted) % 0.16/0.44 (declare-const tptp.class_Lattices_Oupper__semilattice (-> $$unsorted Bool)) % 0.16/0.44 (declare-const tptp.c_Lambda_Obeta $$unsorted) % 0.16/0.44 (declare-const tptp.c_Lattices_Olower__semilattice__class_Oinf (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_List_Ofoldl (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_List_Olistsp (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.44 (declare-const tptp.c_Transitive__Closure_Otranclp (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_Lattices_Oupper__semilattice__class_Osup (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.44 (declare-const tptp.class_Lattices_Olattice (-> $$unsorted Bool)) % 0.16/0.44 (define @t1 () (@var "T_a" $$unsorted)) % 0.16/0.44 (define @t2 () (@var "V_xs" $$unsorted)) % 0.16/0.44 (define @t3 () (tptp.c_List_Olist_ONil @t1)) % 0.16/0.44 (define @t4 () (@var "V_r" $$unsorted)) % 0.16/0.44 (define @t5 () (@var "V_type2_H" $$unsorted)) % 0.16/0.44 (define @t6 () (@var "V_type2" $$unsorted)) % 0.16/0.44 (define @t7 () (@var "V_type1_H" $$unsorted)) % 0.16/0.44 (define @t8 () (@var "V_type1" $$unsorted)) % 0.16/0.44 (define @t9 () (not (= (tptp.c_Type_Otype_OFun @t8 @t6) (tptp.c_Type_Otype_OFun @t7 @t5)))) % 0.16/0.44 (define @t10 () (@list @t8 @t6 @t7 @t5)) % 0.16/0.44 (define @t11 () (@var "V_U" $$unsorted)) % 0.16/0.44 (define @t12 () (@var "V_T" $$unsorted)) % 0.16/0.44 (define @t13 () (tptp.c_Type_Otype_OFun @t12 @t11)) % 0.16/0.44 (define @t14 () (@var "V_s" $$unsorted)) % 0.16/0.44 (define @t15 () (@var "V_env" $$unsorted)) % 0.16/0.44 (define @t16 () (@var "V_t" $$unsorted)) % 0.16/0.44 (define @t17 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t14)) % 0.16/0.44 (define @t18 () (tptp.hAPP @t17 @t16)) % 0.16/0.44 (define @t19 () (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t20 () (@var "V_ss" $$unsorted)) % 0.16/0.44 (define @t21 () (= @t20 @t19)) % 0.16/0.44 (define @t22 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t14 @t20 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t23 () (tptp.c_Lambda_OdB_OAbs @t4)) % 0.16/0.44 (define @t24 () (not (= @t23 @t22))) % 0.16/0.44 (define @t25 () (@list @t4 @t14 @t20)) % 0.16/0.44 (define @t26 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t23 @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t27 () (@list @t4)) % 0.16/0.44 (define @t28 () (not (= @t22 @t23))) % 0.16/0.44 (define @t29 () (@list @t14 @t20 @t4)) % 0.16/0.44 (define @t30 () (@var "V_rs" $$unsorted)) % 0.16/0.44 (define @t31 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t4 @t20 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t32 () (@var "V_e" $$unsorted)) % 0.16/0.44 (define @t33 () (not (tptp.c_Type_Otyping @t32 @t16 @t12))) % 0.16/0.44 (define @t34 () (@var "V_i" $$unsorted)) % 0.16/0.44 (define @t35 () (tptp.c_Lambda_Olift @t16 @t34)) % 0.16/0.44 (define @t36 () (tptp.c_Type_Oshift @t32 @t34 @t11 tptp.tc_Type_Otype)) % 0.16/0.44 (define @t37 () (@var "V_u" $$unsorted)) % 0.16/0.44 (define @t38 () (tptp.c_Lambda_Osubst @t16 @t37 @t34)) % 0.16/0.44 (define @t39 () (@var "V_e_H" $$unsorted)) % 0.16/0.44 (define @t40 () (@var "V_v" $$unsorted)) % 0.16/0.44 (define @t41 () (@var "V_n" $$unsorted)) % 0.16/0.44 (define @t42 () (tptp.c_Lambda_OdB_OVar @t41)) % 0.16/0.44 (define @t43 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t42 @t30 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t44 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t43) @t40)))) % 0.16/0.44 (define @t45 () (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @t41 @t30 @t40)) % 0.16/0.44 (define @t46 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t4) @t14)) % 0.16/0.44 (define @t47 () (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) % 0.16/0.44 (define @t48 () (tptp.c_Lambda_OdB_OAbs @t16)) % 0.16/0.44 (define @t49 () (@var "V_x" $$unsorted)) % 0.16/0.44 (define @t50 () (@var "V_a" $$unsorted)) % 0.16/0.44 (define @t51 () (@var "T_b" $$unsorted)) % 0.16/0.44 (define @t52 () (@var "V_f" $$unsorted)) % 0.16/0.44 (define @t53 () (@var "V_A" $$unsorted)) % 0.16/0.44 (define @t54 () (@var "V_ts" $$unsorted)) % 0.16/0.44 (define @t55 () (@var "V_m" $$unsorted)) % 0.16/0.44 (define @t56 () (tptp.c_Lambda_OdB_OVar @t55)) % 0.16/0.44 (define @t57 () (not (= @t56 @t22))) % 0.16/0.44 (define @t58 () (@list @t55 @t14 @t20)) % 0.16/0.44 (define @t59 () (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t16))) % 0.16/0.44 (define @t60 () (not @t59)) % 0.16/0.44 (define @t61 () (@var "V_nat" $$unsorted)) % 0.16/0.44 (define @t62 () (tptp.c_Lambda_OdB_OVar @t61)) % 0.16/0.44 (define @t63 () (@var "V_dB2_H" $$unsorted)) % 0.16/0.44 (define @t64 () (@var "V_dB1_H" $$unsorted)) % 0.16/0.44 (define @t65 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t64) @t63)) % 0.16/0.44 (define @t66 () (tptp.c_Transitive__Closure_Ortranclp @t4 @t1)) % 0.16/0.44 (define @t67 () (@list @t4 @t1)) % 0.16/0.44 (define @t68 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t42 @t20 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t69 () (tptp.c_Lambda_OdB_OAbs @t14)) % 0.16/0.44 (define @t70 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t69) @t16)) % 0.16/0.44 (define @t71 () (@var "V_y" $$unsorted)) % 0.16/0.44 (define @t72 () (tptp.tc_fun @t1 (tptp.tc_fun @t51 tptp.tc_bool))) % 0.16/0.44 (define @t73 () (@var "V_B" $$unsorted)) % 0.16/0.44 (define @t74 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf @t53 @t73 @t72) @t49) @t71))) % 0.16/0.44 (define @t75 () (not @t74)) % 0.16/0.44 (define @t76 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t53 @t49) @t71))) % 0.16/0.44 (define @t77 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t73 @t49) @t71))) % 0.16/0.44 (define @t78 () (@list @t73 @t49 @t71 @t53 @t1 @t51)) % 0.16/0.44 (define @t79 () (tptp.c_Lambda_OdB_OVar @t34)) % 0.16/0.44 (define @t80 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t16)) % 0.16/0.44 (define @t81 () (@list @t16 @t34)) % 0.16/0.44 (define @t82 () (@var "V_k" $$unsorted)) % 0.16/0.44 (define @t83 () (tptp.c_Lambda_Olift @t16 @t82)) % 0.16/0.44 (define @t84 () (@var "V_b" $$unsorted)) % 0.16/0.44 (define @t85 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t4 @t50) @t84)))) % 0.16/0.44 (define @t86 () (tptp.c_Transitive__Closure_Otranclp @t4 @t1)) % 0.16/0.44 (define @t87 () (tptp.hAPP @t86 @t50)) % 0.16/0.44 (define @t88 () (tptp.hBOOL (tptp.hAPP @t87 @t84))) % 0.16/0.44 (define @t89 () (@list @t4 @t1 @t50 @t84)) % 0.16/0.44 (define @t90 () (tptp.c_Lattices_Oupper__semilattice__class_Osup @t49 @t71 @t1)) % 0.16/0.44 (define @t91 () (= (tptp.c_Lattices_Oupper__semilattice__class_Osup @t49 @t90 @t1) @t90)) % 0.16/0.44 (define @t92 () (not (tptp.class_Lattices_Olattice @t1))) % 0.16/0.44 (define @t93 () (@list @t1 @t49 @t71)) % 0.16/0.44 (define @t94 () (not (tptp.class_Lattices_Oupper__semilattice @t1))) % 0.16/0.44 (define @t95 () (tptp.c_Lattices_Oupper__semilattice__class_Osup @t71 @t49 @t1)) % 0.16/0.44 (define @t96 () (= @t90 @t95)) % 0.16/0.44 (define @t97 () (@var "V_s_H" $$unsorted)) % 0.16/0.44 (define @t98 () (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t99 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t98 @t14) @t97)))) % 0.16/0.44 (define @t100 () (@var "V_t_H" $$unsorted)) % 0.16/0.44 (define @t101 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t98 @t16) @t100)))) % 0.16/0.44 (define @t102 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t97)) % 0.16/0.44 (define @t103 () (tptp.hAPP @t98 @t18)) % 0.16/0.44 (define @t104 () (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t4))) % 0.16/0.44 (define @t105 () (not @t104)) % 0.16/0.44 (define @t106 () (= @t4 @t14)) % 0.16/0.44 (define @t107 () (tptp.c_Lattices_Olower__semilattice__class_Oinf @t71 @t49 @t1)) % 0.16/0.44 (define @t108 () (tptp.c_Lattices_Olower__semilattice__class_Oinf @t49 @t71 @t1)) % 0.16/0.44 (define @t109 () (= @t108 @t107)) % 0.16/0.44 (define @t110 () (not (tptp.class_Lattices_Olower__semilattice @t1))) % 0.16/0.44 (define @t111 () (@var "V_z" $$unsorted)) % 0.16/0.44 (define @t112 () (tptp.c_Lattices_Oupper__semilattice__class_Osup @t71 @t111 @t1)) % 0.16/0.44 (define @t113 () (tptp.c_Lattices_Oupper__semilattice__class_Osup @t49 @t112 @t1)) % 0.16/0.44 (define @t114 () (= (tptp.c_Lattices_Oupper__semilattice__class_Osup @t90 @t111 @t1) @t113)) % 0.16/0.44 (define @t115 () (@list @t1 @t49 @t71 @t111)) % 0.16/0.44 (define @t116 () (tptp.c_Lattices_Oupper__semilattice__class_Osup @t49 @t111 @t1)) % 0.16/0.44 (define @t117 () (= @t113 (tptp.c_Lattices_Oupper__semilattice__class_Osup @t71 @t116 @t1))) % 0.16/0.44 (define @t118 () (@list @t1 @t49)) % 0.16/0.44 (define @t119 () (not (tptp.class_Lattices_Odistrib__lattice @t1))) % 0.16/0.44 (define @t120 () (@list @t1 @t71 @t111 @t49)) % 0.16/0.44 (define @t121 () (tptp.c_Lattices_Olower__semilattice__class_Oinf @t49 @t111 @t1)) % 0.16/0.44 (define @t122 () (@var "V_c" $$unsorted)) % 0.16/0.44 (define @t123 () (@var "T_c" $$unsorted)) % 0.16/0.44 (define @t124 () (not @t88)) % 0.16/0.44 (define @t125 () (tptp.hAPP @t66 @t84)) % 0.16/0.44 (define @t126 () (not (tptp.hBOOL (tptp.hAPP @t125 @t122)))) % 0.16/0.44 (define @t127 () (tptp.hBOOL (tptp.hAPP @t87 @t122))) % 0.16/0.44 (define @t128 () (@list @t4 @t1 @t50 @t122 @t84)) % 0.16/0.44 (define @t129 () (tptp.hAPP @t66 @t49)) % 0.16/0.44 (define @t130 () (tptp.hBOOL (tptp.hAPP @t129 @t71))) % 0.16/0.44 (define @t131 () (not @t130)) % 0.16/0.44 (define @t132 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t86 @t71) @t111)))) % 0.16/0.44 (define @t133 () (tptp.hAPP @t86 @t49)) % 0.16/0.44 (define @t134 () (tptp.hBOOL (tptp.hAPP @t133 @t111))) % 0.16/0.44 (define @t135 () (@list @t4 @t1 @t49 @t111 @t71)) % 0.16/0.44 (define @t136 () (tptp.hAPP @t66 @t50)) % 0.16/0.44 (define @t137 () (tptp.hAPP @t66 @t71)) % 0.16/0.44 (define @t138 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t4) @t14)))) % 0.16/0.44 (define @t139 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t98 (tptp.c_Lambda_Osubst @t16 @t4 @t34)) (tptp.c_Lambda_Osubst @t16 @t14 @t34)))) % 0.16/0.44 (define @t140 () (@list @t16 @t4 @t34 @t14)) % 0.16/0.44 (define @t141 () (tptp.hBOOL (tptp.hAPP @t136 @t84))) % 0.16/0.44 (define @t142 () (not @t141)) % 0.16/0.44 (define @t143 () (tptp.hAPP @t4 @t84)) % 0.16/0.44 (define @t144 () (not (tptp.hBOOL (tptp.hAPP @t143 @t122)))) % 0.16/0.44 (define @t145 () (not (tptp.c_Wellfounded_OwfP @t4 @t1))) % 0.16/0.44 (define @t146 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t98 @t4) @t14)))) % 0.16/0.44 (define @t147 () (tptp.c_Lambda_Osubst @t14 @t16 @t34)) % 0.16/0.44 (define @t148 () (tptp.c_Lambda_Osubst @t4 @t16 @t34)) % 0.16/0.44 (define @t149 () (@list @t4 @t16 @t34 @t14)) % 0.16/0.44 (define @t150 () (@var "V_dB_H" $$unsorted)) % 0.16/0.44 (define @t151 () (tptp.c_Lambda_OdB_OAbs @t150)) % 0.16/0.44 (define @t152 () (@list @t4 @t1 @t49 @t71)) % 0.16/0.44 (define @t153 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup @t53 @t73 @t72) @t49) @t71))) % 0.16/0.44 (define @t154 () (not @t77)) % 0.16/0.44 (define @t155 () (@list @t53 @t73 @t1 @t51 @t49 @t71)) % 0.16/0.44 (define @t156 () (not @t76)) % 0.16/0.44 (define @t157 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst @t4 @t14 @t47) @t20 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t158 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t23) @t14) @t20 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t159 () (tptp.c_Lattices_Olower__semilattice__class_Oinf @t71 @t111 @t1)) % 0.16/0.44 (define @t160 () (tptp.c_Lattices_Olower__semilattice__class_Oinf @t49 @t159 @t1)) % 0.16/0.44 (define @t161 () (= (tptp.c_Lattices_Olower__semilattice__class_Oinf @t108 @t111 @t1) @t160)) % 0.16/0.44 (define @t162 () (= @t160 (tptp.c_Lattices_Olower__semilattice__class_Oinf @t71 @t121 @t1))) % 0.16/0.44 (define @t163 () (@var "V_dB" $$unsorted)) % 0.16/0.44 (define @t164 () (@list @t4 @t20 @t14)) % 0.16/0.44 (define @t165 () (@list @t14 @t16)) % 0.16/0.44 (define @t166 () (tptp.c_Lambda_Olift @t14 @t34)) % 0.16/0.44 (define @t167 () (tptp.c_Lambda_Olift @t4 @t34)) % 0.16/0.44 (define @t168 () (@list @t4 @t34 @t14)) % 0.16/0.44 (define @t169 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t79 @t54 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t170 () (@var "V_dB2" $$unsorted)) % 0.16/0.44 (define @t171 () (@var "V_dB1" $$unsorted)) % 0.16/0.44 (define @t172 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t171) @t170)) % 0.16/0.44 (define @t173 () (not (= @t172 @t65))) % 0.16/0.44 (define @t174 () (@list @t171 @t170 @t64 @t63)) % 0.16/0.44 (define @t175 () (= @t30 @t20)) % 0.16/0.44 (define @t176 () (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t23 @t30 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t69 @t20 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.16/0.44 (define @t177 () (@list @t4 @t30 @t14 @t20)) % 0.16/0.44 (define @t178 () (@var "V_R" $$unsorted)) % 0.16/0.44 (define @t179 () (tptp.c_Transitive__Closure_Ortranclp @t178 @t1)) % 0.16/0.44 (define @t180 () (tptp.tc_fun @t1 tptp.tc_bool)) % 0.16/0.44 (define @t181 () (tptp.tc_fun @t1 @t180)) % 0.16/0.44 (define @t182 () (tptp.c_fequal @t1)) % 0.16/0.44 (define @t183 () (= @t50 @t84)) % 0.16/0.44 (define @t184 () (@var "V_S" $$unsorted)) % 0.16/0.44 (define @t185 () (= (tptp.c_Lattices_Olower__semilattice__class_Oinf @t49 @t108 @t1) @t108)) % 0.16/0.44 (define @t186 () (@var "V_j" $$unsorted)) % 0.16/0.44 (define @t187 () (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t56 @t30 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) @t68))) % 0.16/0.44 (define @t188 () (@list @t55 @t30 @t41 @t20)) % 0.16/0.44 (define @t189 () (@var "V_nat_H" $$unsorted)) % 0.16/0.44 (define @t190 () (tptp.hAPP @t80 @t37)) % 0.16/0.44 (define @t191 () (tptp.hBOOL (tptp.hAPP @t136 @t122))) % 0.16/0.44 (define @t192 () (tptp.c_Wellfounded_Oaccp @t4 @t84 @t1)) % 0.16/0.44 (define @t193 () (tptp.c_Wellfounded_Oaccp @t4 @t50 @t1)) % 0.16/0.44 (define @t194 () (not @t193)) % 0.16/0.44 (define @t195 () (tptp.hAPP @t4 @t71)) % 0.16/0.44 (define @t196 () (@var "V_P" $$unsorted)) % 0.16/0.44 (define @t197 () (tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @t196 @t4 @t1)) % 0.16/0.44 (define @t198 () (tptp.hBOOL (tptp.hAPP @t196 @t50))) % 0.16/0.44 (define @t199 () (@list @t196 @t50 @t4 @t1)) % 0.16/0.44 (define @t200 () (tptp.hBOOL (tptp.hAPP @t196 @t71))) % 0.16/0.44 (define @t201 () (@list @t196 @t50 @t71 @t4 @t1)) % 0.16/0.44 (define @t202 () (tptp.c_Wellfounded_Oaccp @t178 @t49 @t1)) % 0.16/0.44 (define @t203 () (tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @t178 @t49 @t1)) % 0.16/0.44 (define @t204 () (@list @t178 @t49 @t1)) % 0.16/0.44 (define @t205 () (tptp.c_Type_Otyping @t32 @t100 @t12)) % 0.16/0.44 (define @t206 () (@list @t32 @t100 @t12 @t16)) % 0.16/0.44 (define @t207 () (tptp.c_Wellfounded_Oaccp @t4 @t49 @t1)) % 0.16/0.44 (define @t208 () (@list @t4 @t49 @t1)) % 0.16/0.44 (define @t209 () (tptp.c_Predicate_Oconversep @t4 @t1 @t51)) % 0.16/0.44 (define @t210 () (tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @t4 @t49 @t1)) % 0.16/0.44 (define @t211 () (tptp.c_Predicate_Oconversep @t4 @t1 @t1)) % 0.16/0.44 (define @t212 () (tptp.c_Transitive__Closure_Otranclp @t211 @t1)) % 0.16/0.44 (define @t213 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t212 @t49) @t71))) % 0.16/0.44 (define @t214 () (tptp.c_Predicate_Oconversep @t86 @t1 @t1)) % 0.16/0.44 (define @t215 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t214 @t49) @t71))) % 0.16/0.44 (define @t216 () (tptp.c_Predicate_Oconversep tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t217 () (not (tptp.hBOOL (tptp.hAPP @t125 @t50)))) % 0.16/0.44 (define @t218 () (@list @t4 @t84 @t1 @t50)) % 0.16/0.44 (define @t219 () (not (tptp.c_Wellfounded_Oaccp @t4 @t49 tptp.t_a))) % 0.16/0.44 (define @t220 () (tptp.v_sko__Wellfounded__Xaccp__Xinducts__1 @t196 @t4)) % 0.16/0.44 (define @t221 () (tptp.hBOOL (tptp.hAPP @t196 @t49))) % 0.16/0.44 (define @t222 () (@list @t196 @t49 @t4)) % 0.16/0.44 (define @t223 () (@list @t196 @t49 @t71 @t4)) % 0.16/0.44 (define @t224 () (tptp.v_sko__Wellfounded__Xaccp__Xinduct__1 @t196 @t4)) % 0.16/0.44 (define @t225 () (@var "V_a2" $$unsorted)) % 0.16/0.44 (define @t226 () (@var "V_a1" $$unsorted)) % 0.16/0.44 (define @t227 () (tptp.hBOOL (tptp.hAPP @t143 @t50))) % 0.16/0.44 (define @t228 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t209 @t50) @t84))) % 0.16/0.44 (define @t229 () (@var "V_ya" $$unsorted)) % 0.16/0.44 (define @t230 () (tptp.hAPP @t4 @t229)) % 0.16/0.44 (define @t231 () (tptp.c_Wellfounded_Oaccp @t4 @t229 tptp.t_a)) % 0.16/0.44 (define @t232 () (@list @t196 @t49 @t4 @t229)) % 0.16/0.44 (define @t233 () (tptp.c_Predicate_Oconversep @t14 @t51 @t1)) % 0.16/0.44 (define @t234 () (tptp.c_Predicate_Oconversep @t4 @t51 @t1)) % 0.16/0.44 (define @t235 () (tptp.tc_fun @t51 @t180)) % 0.16/0.44 (define @t236 () (@list @t4 @t14 @t51 @t1)) % 0.16/0.44 (define @t237 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp @t211 @t1) @t49) @t71))) % 0.16/0.44 (define @t238 () (tptp.hBOOL (tptp.hAPP @t137 @t49))) % 0.16/0.44 (define @t239 () (tptp.c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @t4 @t49 @t1)) % 0.16/0.44 (define @t240 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t14) @t16)))) % 0.16/0.44 (define @t241 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t37)) % 0.16/0.44 (define @t242 () (tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @t196 @t4 @t1)) % 0.16/0.44 (define @t243 () (tptp.c_Type_Otyping tptp.v_e tptp.v_t tptp.v_T)) % 0.16/0.44 (define @t244 () (tptp.c_Wellfounded_Oaccp @t216 tptp.v_t tptp.tc_Lambda_OdB)) % 0.16/0.44 (define @t245 () (@var "T_1" $$unsorted)) % 0.16/0.44 (define @t246 () (not (tptp.class_Lattices_Olattice @t245))) % 0.16/0.44 (define @t247 () (@var "T_2" $$unsorted)) % 0.16/0.44 (define @t248 () (tptp.tc_fun @t247 @t245)) % 0.16/0.44 (define @t249 () (@list @t247 @t245)) % 0.16/0.44 (define @t250 () (@var "V_Y" $$unsorted)) % 0.16/0.44 (define @t251 () (@var "V_X" $$unsorted)) % 0.16/0.44 (define @t252 () (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_t))) % 0.16/0.44 (define @t253 () (not @t252)) % 0.16/0.44 (define @t254 () (or @t244 @t253)) % 0.16/0.44 (define @t255 () (not @t243)) % 0.16/0.44 (define @t256 () (or @t252 @t255)) % 0.16/0.44 (assume @p1 (forall (@list @t4 @t1 @t2) (not (tptp.c_ListOrder_Ostep1 @t4 @t3 @t2 @t1)))) % 0.16/0.44 (assume @p2 (forall (@list @t4 @t2 @t1) (not (tptp.c_ListOrder_Ostep1 @t4 @t2 @t3 @t1)))) % 0.16/0.44 (assume @p3 (forall @t10 (or @t9 (= @t6 @t5)))) % 0.16/0.44 (assume @p4 (forall @t10 (or @t9 (= @t8 @t7)))) % 0.16/0.44 (assume @p5 (forall (@list @t15 @t14 @t16 @t11 @t12) (or (tptp.c_Type_Otyping @t15 @t18 @t11) (not (tptp.c_Type_Otyping @t15 @t16 @t12)) (not (tptp.c_Type_Otyping @t15 @t14 @t13))))) % 0.16/0.44 (assume @p6 (forall @t25 (or @t24 @t21))) % 0.16/0.44 (assume @p7 (forall @t27 (= @t23 @t26))) % 0.16/0.44 (assume @p8 (forall @t29 (or @t28 @t21))) % 0.16/0.44 (assume @p9 (forall @t27 (= @t26 @t23))) % 0.16/0.44 (assume @p10 (forall (@list @t4 @t30 @t20) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t4 @t30 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) @t31)) (not (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta @t30 @t20 tptp.tc_Lambda_OdB))))) % 0.16/0.44 (assume @p11 (forall (@list @t32 @t34 @t11 @t16 @t12) (or (tptp.c_Type_Otyping @t36 @t35 @t12) @t33))) % 0.16/0.44 (assume @p12 (forall (@list @t39 @t37 @t11 @t34 @t16 @t12) (or (not (tptp.c_Type_Otyping @t39 @t37 @t11)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift @t39 @t34 @t11 tptp.tc_Type_Otype) @t16 @t12)) (tptp.c_Type_Otyping @t39 @t38 @t12)))) % 0.16/0.44 (assume @p13 (forall (@list @t30 @t41 @t40) (or (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta @t30 @t45 tptp.tc_Lambda_OdB) @t44))) % 0.16/0.44 (assume @p14 (forall (@list @t4 @t14) (= @t46 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t46 @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.16/0.44 (assume @p15 (forall (@list @t4 @t14 @t16) (or (not (= @t46 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t16 @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= @t46 @t16)))) % 0.16/0.44 (assume @p16 (forall (@list @t15 @t16 @t12 @t11) (or (tptp.c_Type_Otyping @t15 @t48 @t13) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift @t15 @t47 @t12 tptp.tc_Type_Otype) @t16 @t11))))) % 0.16/0.44 (assume @p17 (forall (@list @t32 @t49 @t12 @t1) (= (tptp.hAPP (tptp.c_Type_Oshift @t32 @t49 @t12 @t1) @t49) @t12))) % 0.16/0.44 (assume @p18 (forall (@list @t52 @t50 @t51 @t1) (= (tptp.c_List_Ofoldl @t52 @t50 (tptp.c_List_Olist_ONil @t51) @t1 @t51) @t50))) % 0.16/0.44 (assume @p19 (forall (@list @t53 @t1) (tptp.c_List_Olistsp @t53 @t3 @t1))) % 0.16/0.44 (assume @p20 (forall (@list @t4 @t14 @t16 @t54) (or (not (= @t46 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t16 @t54 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= @t4 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t16 (tptp.c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @t4 @t14 @t16 @t54) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (= @t54 @t19)))) % 0.16/0.44 (assume @p21 (forall @t58 (or @t57 @t21))) % 0.16/0.44 (assume @p22 (forall (@list @t55) (= @t56 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t56 @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.16/0.44 (assume @p23 (forall (@list @t16 @t37 @t34 @t32 @t11 @t12) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t38)) (not (tptp.c_Type_Otyping @t32 @t37 @t11)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t37))) (not (tptp.c_Type_Otyping @t36 @t16 @t12)) @t60))) % 0.16/0.44 (assume @p24 (forall (@list @t40 @t41 @t30) (or (= @t40 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t42 @t45 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) @t44))) % 0.16/0.44 (assume @p25 (forall (@list @t41 @t30) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t43)) (not (tptp.c_List_Olistsp tptp.c_InductTermi_OIT @t30 tptp.tc_Lambda_OdB))))) % 0.16/0.44 (assume @p26 (forall (@list @t64 @t63 @t61) (not (= @t65 @t62)))) % 0.16/0.44 (assume @p27 (forall @t67 (= (tptp.c_Transitive__Closure_Ortranclp @t66 @t1) @t66))) % 0.16/0.44 (assume @p28 (forall (@list @t14 @t16 @t41 @t20) (not (= @t70 @t68)))) % 0.16/0.44 (assume @p29 (forall (@list @t53 @t49 @t71 @t73 @t1 @t51) (or @t76 @t75))) % 0.16/0.44 (assume @p30 (forall @t78 (or @t77 @t75))) % 0.16/0.44 (assume @p31 (forall @t81 (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP @t80 @t79))) @t60))) % 0.16/0.44 (assume @p32 (forall (@list @t16 @t82 @t14) (= (tptp.c_Lambda_Osubst @t83 @t14 @t82) @t16))) % 0.16/0.44 (assume @p33 (forall @t89 (or @t88 @t85))) % 0.16/0.44 (assume @p34 (forall @t93 (or @t92 @t91))) % 0.16/0.44 (assume @p35 (forall @t93 (or @t94 @t91))) % 0.16/0.44 (assume @p36 (forall @t93 (or @t92 @t96))) % 0.16/0.44 (assume @p37 (forall @t93 (or @t94 @t96))) % 0.16/0.44 (assume @p38 (forall (@list @t14 @t16 @t97 @t100) (or (tptp.hBOOL (tptp.hAPP @t103 (tptp.hAPP @t102 @t100))) @t101 @t99))) % 0.16/0.44 (assume @p39 (forall @t27 (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t23)) @t105))) % 0.16/0.44 (assume @p40 (forall (@list @t4 @t54 @t14) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t4 @t54 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t14 @t54 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) @t106))) % 0.16/0.44 (assume @p41 (forall (@list @t14 @t16 @t97) (or (tptp.hBOOL (tptp.hAPP @t103 (tptp.hAPP @t102 @t16))) @t99))) % 0.16/0.44 (assume @p42 (forall (@list @t14 @t16 @t100) (or (tptp.hBOOL (tptp.hAPP @t103 (tptp.hAPP @t17 @t100))) @t101))) % 0.16/0.44 (assume @p43 (forall @t25 (or @t24 (= @t23 @t14)))) % 0.16/0.44 (assume @p44 (forall @t93 (or @t92 @t109))) % 0.16/0.44 (assume @p45 (forall @t93 (or @t110 @t109))) % 0.16/0.44 (assume @p46 (forall @t115 (or @t92 @t114))) % 0.16/0.44 (assume @p47 (forall @t115 (or @t92 @t117))) % 0.16/0.44 (assume @p48 (forall @t115 (or @t94 @t117))) % 0.16/0.44 (assume @p49 (forall @t115 (or @t94 @t114))) % 0.16/0.44 (assume @p50 (forall @t118 (or @t94 (= (tptp.c_Lattices_Oupper__semilattice__class_Osup @t49 @t49 @t1) @t49)))) % 0.16/0.44 (assume @p51 (forall @t120 (or @t119 (= (tptp.c_Lattices_Olower__semilattice__class_Oinf @t112 @t49 @t1) (tptp.c_Lattices_Oupper__semilattice__class_Osup @t107 (tptp.c_Lattices_Olower__semilattice__class_Oinf @t111 @t49 @t1) @t1))))) % 0.16/0.44 (assume @p52 (forall @t115 (or @t119 (= (tptp.c_Lattices_Olower__semilattice__class_Oinf @t49 @t112 @t1) (tptp.c_Lattices_Oupper__semilattice__class_Osup @t108 @t121 @t1))))) % 0.16/0.44 (assume @p53 (forall (@list @t14 @t97) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t98 @t69) (tptp.c_Lambda_OdB_OAbs @t97))) @t99))) % 0.16/0.44 (assume @p54 (forall (@list @t4 @t14 @t1 @t51 @t123 @t50 @t122 @t84) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Opred__comp @t4 @t14 @t1 @t51 @t123) @t50) @t122)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t14 @t84) @t122))) @t85))) % 0.16/0.44 (assume @p55 (forall @t128 (or @t127 @t126 @t124))) % 0.16/0.44 (assume @p56 (forall @t135 (or @t134 @t132 @t131))) % 0.16/0.44 (assume @p57 (forall (@list @t4 @t1 @t50) (tptp.hBOOL (tptp.hAPP @t136 @t50)))) % 0.16/0.44 (assume @p58 (forall (@list @t4 @t1 @t49) (tptp.hBOOL (tptp.hAPP @t129 @t49)))) % 0.16/0.44 (assume @p59 (forall @t135 (or (tptp.hBOOL (tptp.hAPP @t129 @t111)) (not (tptp.hBOOL (tptp.hAPP @t137 @t111))) @t131))) % 0.16/0.44 (assume @p60 (forall @t140 (or @t139 @t138))) % 0.16/0.44 (assume @p61 (forall @t128 (or @t127 @t126 @t85))) % 0.16/0.44 (assume @p62 (forall @t128 (or @t127 @t144 @t142))) % 0.16/0.44 (assume @p63 (forall (@list @t14 @t16 @t82) (= (tptp.c_Lambda_Olift @t18 @t82) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Olift @t14 @t82)) @t83)))) % 0.16/0.44 (assume @p64 (forall @t67 (or (tptp.c_Wellfounded_OwfP @t86 @t1) @t145))) % 0.16/0.44 (assume @p65 (forall @t89 (or @t141 @t124))) % 0.16/0.44 (assume @p66 (forall @t149 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t98 @t148) @t147)) @t146))) % 0.16/0.44 (assume @p67 (forall @t140 (or @t139 @t146))) % 0.16/0.44 (assume @p68 (forall (@list @t41) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t42)))) % 0.16/0.44 (assume @p69 (forall (@list @t61 @t150) (not (= @t62 @t151)))) % 0.16/0.44 (assume @p70 (forall @t152 (or @t130 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t4 @t49) @t71)))))) % 0.16/0.44 (assume @p71 (forall @t78 (or @t77 @t76 (not @t153)))) % 0.16/0.44 (assume @p72 (forall @t155 (or @t153 @t154))) % 0.16/0.44 (assume @p73 (forall @t155 (or @t153 @t156))) % 0.16/0.44 (assume @p74 (forall @t25 (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t158)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t14))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t157)))))) % 0.16/0.44 (assume @p75 (forall @t81 (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t35)) @t60))) % 0.16/0.44 (assume @p76 (forall (@list @t41 @t54 @t4 @t20) (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t42 @t54 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t23 @t20 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))) % 0.16/0.44 (assume @p77 (forall @t115 (or @t92 @t161))) % 0.16/0.44 (assume @p78 (forall @t115 (or @t92 @t162))) % 0.16/0.44 (assume @p79 (forall @t115 (or @t110 @t162))) % 0.16/0.44 (assume @p80 (forall @t115 (or @t110 @t161))) % 0.16/0.44 (assume @p81 (forall (@list @t163 @t150) (or (not (= (tptp.c_Lambda_OdB_OAbs @t163) @t151)) (= @t163 @t150)))) % 0.16/0.44 (assume @p82 (forall (@list @t61 @t64 @t63) (not (= @t62 @t65)))) % 0.16/0.44 (assume @p83 (forall @t58 (or @t57 (= @t56 @t14)))) % 0.16/0.44 (assume @p84 (forall @t164 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t31) @t22)) @t138))) % 0.16/0.44 (assume @p85 (forall @t93 (or @t92 (= (tptp.c_Lattices_Oupper__semilattice__class_Osup @t49 @t108 @t1) @t49)))) % 0.16/0.44 (assume @p86 (forall @t165 (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t70) (tptp.c_Lambda_Osubst @t14 @t16 @t47))))) % 0.16/0.44 (assume @p87 (forall @t168 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t98 @t167) @t166)) @t146))) % 0.16/0.44 (assume @p88 (forall (@list @t12 @t11 @t32 @t34 @t54) (or (= @t12 @t11) (not (tptp.c_Type_Otyping @t32 @t169 @t11)) (not (tptp.c_Type_Otyping @t32 @t169 @t12))))) % 0.16/0.44 (assume @p89 (forall @t174 (or @t173 (= @t170 @t63)))) % 0.16/0.44 (assume @p90 (forall @t174 (or @t173 (= @t171 @t64)))) % 0.16/0.44 (assume @p91 (forall @t93 (or @t92 (= (tptp.c_Lattices_Olower__semilattice__class_Oinf @t49 @t90 @t1) @t49)))) % 0.16/0.44 (assume @p92 (forall @t177 (or @t176 @t175))) % 0.16/0.44 (assume @p93 (forall @t177 (or @t176 @t106))) % 0.16/0.44 (assume @p94 (forall @t29 (or @t28 (= @t14 @t23)))) % 0.16/0.44 (assume @p95 (forall (@list @t178 @t1) (= (tptp.c_Transitive__Closure_Ortranclp (tptp.c_Lattices_Oupper__semilattice__class_Osup @t178 @t182 @t181) @t1) @t179))) % 0.16/0.44 (assume @p96 (forall @t89 (or @t88 @t183 @t142))) % 0.16/0.44 (assume @p97 (forall (@list @t178 @t1 @t50 @t84) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp @t178 @t1) @t50) @t84)) @t183 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t179 @t50) @t84)))))) % 0.16/0.44 (assume @p98 (forall @t164 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t98 @t31) @t22)) @t146))) % 0.16/0.44 (assume @p99 (forall (@list @t178 @t1 @t184) (= (tptp.c_Transitive__Closure_Ortranclp (tptp.c_Lattices_Oupper__semilattice__class_Osup @t179 (tptp.c_Transitive__Closure_Ortranclp @t184 @t1) @t181) @t1) (tptp.c_Transitive__Closure_Ortranclp (tptp.c_Lattices_Oupper__semilattice__class_Osup @t178 @t184 @t181) @t1)))) % 0.16/0.44 (assume @p100 (forall @t120 (or @t119 (= (tptp.c_Lattices_Oupper__semilattice__class_Osup @t159 @t49 @t1) (tptp.c_Lattices_Olower__semilattice__class_Oinf @t95 (tptp.c_Lattices_Oupper__semilattice__class_Osup @t111 @t49 @t1) @t1))))) % 0.16/0.44 (assume @p101 (forall @t115 (or @t119 (= (tptp.c_Lattices_Oupper__semilattice__class_Osup @t49 @t159 @t1) (tptp.c_Lattices_Olower__semilattice__class_Oinf @t90 @t116 @t1))))) % 0.16/0.44 (assume @p102 (forall @t93 (or @t92 @t185))) % 0.16/0.44 (assume @p103 (forall @t93 (or @t110 @t185))) % 0.16/0.44 (assume @p104 (forall (@list @t4 @t34 @t186) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst @t4 @t79 @t186))) @t105))) % 0.16/0.44 (assume @p105 (forall @t67 (= (tptp.c_Lattices_Oupper__semilattice__class_Osup @t86 @t182 @t181) @t66))) % 0.16/0.44 (assume @p106 (forall @t118 (or @t110 (= (tptp.c_Lattices_Olower__semilattice__class_Oinf @t49 @t49 @t1) @t49)))) % 0.16/0.44 (assume @p107 (forall (@list @t82 @t37) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar @t82) @t37 @t82) @t37))) % 0.16/0.44 (assume @p108 (forall @t188 (or @t187 @t175))) % 0.16/0.44 (assume @p109 (forall @t188 (or @t187 (= @t55 @t41)))) % 0.16/0.44 (assume @p110 (forall (@list @t150 @t171 @t170) (not (= @t151 @t172)))) % 0.16/0.44 (assume @p111 (forall @t135 (or @t134 @t132 (not (tptp.hBOOL (tptp.hAPP @t133 @t71)))))) % 0.16/0.44 (assume @p112 (forall (@list @t61 @t189) (or (not (= @t62 (tptp.c_Lambda_OdB_OVar @t189))) (= @t61 @t189)))) % 0.16/0.44 (assume @p113 (forall (@list @t171 @t170 @t150) (not (= @t172 @t151)))) % 0.16/0.44 (assume @p114 (forall (@list @t150 @t61) (not (= @t151 @t62)))) % 0.16/0.44 (assume @p115 (forall (@list @t16 @t37 @t14 @t82) (= (tptp.c_Lambda_Osubst @t190 @t14 @t82) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst @t16 @t14 @t82)) (tptp.c_Lambda_Osubst @t37 @t14 @t82))))) % 0.16/0.44 (assume @p116 (forall @t155 (or @t74 @t154 @t156))) % 0.16/0.44 (assume @p117 (forall @t128 (or @t191 @t126 @t85))) % 0.16/0.44 (assume @p118 (forall @t128 (or @t191 @t144 @t142))) % 0.16/0.44 (assume @p119 (forall @t128 (or @t127 @t144 @t124))) % 0.16/0.44 (assume @p120 (forall @t128 (or @t127 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t86 @t84) @t122))) @t85))) % 0.16/0.44 (assume @p121 (forall (@list @t4 @t50 @t1 @t84) (or @t193 @t85 (not @t192)))) % 0.16/0.44 (assume @p122 (forall (@list @t4 @t71 @t1 @t50) (or (tptp.c_Wellfounded_Oaccp @t4 @t71 @t1) (not (tptp.hBOOL (tptp.hAPP @t195 @t50))) @t194))) % 0.16/0.44 (assume @p123 (forall @t199 (or @t198 (not (tptp.hBOOL (tptp.hAPP @t196 @t197))) @t194))) % 0.16/0.44 (assume @p124 (forall @t201 (or @t198 @t200 (not (tptp.hBOOL (tptp.hAPP @t195 @t197))) @t194))) % 0.16/0.44 (assume @p125 (forall @t204 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t178 @t203) @t49)) @t202))) % 0.16/0.44 (assume @p126 (forall @t206 (or @t205 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t16) @t100))) @t33))) % 0.16/0.44 (assume @p127 (forall @t208 (or @t207 @t145))) % 0.16/0.44 (assume @p128 (forall (@list @t4 @t1 @t51) (= (tptp.c_Predicate_Oconversep @t209 @t51 @t1) @t4))) % 0.16/0.44 (assume @p129 (forall (@list @t34 @t16) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t79) @t16))))) % 0.16/0.44 (assume @p130 (forall @t208 (or @t207 (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t4 @t210) @t49))))) % 0.16/0.44 (assume @p131 (forall (@list @t1) (= (tptp.c_Predicate_Oconversep @t182 @t1 @t1) @t182))) % 0.16/0.44 (assume @p132 (forall @t152 (or @t215 (not @t213)))) % 0.16/0.44 (assume @p133 (forall @t152 (or @t213 (not @t215)))) % 0.16/0.44 (assume @p134 (forall (@list @t32 @t34 @t12) (or (= (tptp.hAPP @t32 @t34) @t12) (not (tptp.c_Type_Otyping @t32 @t79 @t12))))) % 0.16/0.44 (assume @p135 (forall @t204 (or (not (tptp.c_Wellfounded_Oaccp @t178 @t203 @t1)) @t202))) % 0.16/0.44 (assume @p136 (forall @t67 (= @t212 @t214))) % 0.16/0.44 (assume @p137 (forall @t27 (or @t104 (not (tptp.c_Wellfounded_Oaccp @t216 @t4 tptp.tc_Lambda_OdB))))) % 0.16/0.44 (assume @p138 (forall (@list @t16) (or (tptp.c_Wellfounded_Oaccp @t216 @t16 tptp.tc_Lambda_OdB) @t60))) % 0.16/0.44 (assume @p139 (forall @t218 (or @t192 @t194 @t217))) % 0.16/0.44 (assume @p140 (forall @t218 (or @t192 @t217 @t194))) % 0.16/0.44 (assume @p141 (forall @t149 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t148) @t147)) @t138))) % 0.16/0.44 (assume @p142 (forall @t222 (or @t221 (not (tptp.hBOOL (tptp.hAPP @t196 @t220))) @t219))) % 0.16/0.44 (assume @p143 (forall @t223 (or @t221 @t200 (not (tptp.hBOOL (tptp.hAPP @t195 @t220))) @t219))) % 0.16/0.44 (assume @p144 (forall @t25 (or (not (tptp.c_Wellfounded_Oaccp @t216 @t157 tptp.tc_Lambda_OdB)) (not (tptp.c_Wellfounded_Oaccp @t216 @t14 tptp.tc_Lambda_OdB)) (tptp.c_Wellfounded_Oaccp @t216 @t158 tptp.tc_Lambda_OdB)))) % 0.16/0.44 (assume @p145 (forall @t222 (or @t221 (not (tptp.hBOOL (tptp.hAPP @t196 @t224))) @t219))) % 0.16/0.44 (assume @p146 (forall @t223 (or @t221 @t200 (not (tptp.hBOOL (tptp.hAPP @t195 @t224))) @t219))) % 0.16/0.44 (assume @p147 (forall (@list @t4 @t1 @t51 @t84 @t50) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t209 @t84) @t50)) @t85))) % 0.16/0.44 (assume @p148 (forall (@list @t4 @t225 @t226 @t1 @t51) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t4 @t225) @t226)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t209 @t226) @t225)))))) % 0.16/0.44 (assume @p149 (forall (@list @t4 @t1 @t51 @t50 @t84) (or @t228 (not @t227)))) % 0.16/0.44 (assume @p150 (forall (@list @t4 @t84 @t50 @t1 @t51) (or @t227 (not @t228)))) % 0.16/0.44 (assume @p151 (forall @t232 (or @t221 @t231 (not (tptp.hBOOL (tptp.hAPP @t230 @t220))) @t219))) % 0.16/0.44 (assume @p152 (forall @t232 (or @t221 @t231 (not (tptp.hBOOL (tptp.hAPP @t230 @t224))) @t219))) % 0.16/0.44 (assume @p153 (forall @t236 (= (tptp.c_Predicate_Oconversep (tptp.c_Lattices_Oupper__semilattice__class_Osup @t4 @t14 @t235) @t51 @t1) (tptp.c_Lattices_Oupper__semilattice__class_Osup @t234 @t233 @t72)))) % 0.16/0.44 (assume @p154 (forall (@list @t4 @t1 @t71 @t49) (or @t238 (not @t237)))) % 0.16/0.44 (assume @p155 (forall @t152 (or @t237 (not @t238)))) % 0.16/0.44 (assume @p156 (forall @t199 (or @t198 (tptp.c_Wellfounded_Oaccp @t4 @t197 @t1) @t194))) % 0.16/0.44 (assume @p157 (forall (@list @t15 @t49) (tptp.c_Type_Otyping @t15 (tptp.c_Lambda_OdB_OVar @t49) (tptp.hAPP @t15 @t49)))) % 0.16/0.44 (assume @p158 (forall @t236 (= (tptp.c_Predicate_Oconversep (tptp.c_Lattices_Olower__semilattice__class_Oinf @t4 @t14 @t235) @t51 @t1) (tptp.c_Lattices_Olower__semilattice__class_Oinf @t234 @t233 @t72)))) % 0.16/0.44 (assume @p159 (forall @t208 (or @t207 (not (tptp.c_Wellfounded_Oaccp @t4 @t210 @t1))))) % 0.16/0.44 (assume @p160 (forall @t208 (or @t207 (not (tptp.c_Wellfounded_Oaccp @t4 @t239 @t1))))) % 0.16/0.44 (assume @p161 (forall @t208 (or @t207 (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t4 @t239) @t49))))) % 0.16/0.44 (assume @p162 (forall (@list @t37 @t14 @t16) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP @t241 @t14)) (tptp.hAPP @t241 @t16))) @t240))) % 0.16/0.44 (assume @p163 (forall (@list @t14 @t37 @t16) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP @t17 @t37)) @t190)) @t240))) % 0.16/0.44 (assume @p164 (forall @t199 (or @t198 (tptp.c_Wellfounded_Oaccp @t4 @t242 @t1) @t194))) % 0.16/0.44 (assume @p165 (forall @t206 (or @t205 @t33 @t101))) % 0.16/0.44 (assume @p166 (forall @t168 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t167) @t166)) @t138))) % 0.16/0.44 (assume @p167 (forall @t199 (or @t198 (not (tptp.hBOOL (tptp.hAPP @t196 @t242))) @t194))) % 0.16/0.44 (assume @p168 (forall @t201 (or @t198 @t200 (not (tptp.hBOOL (tptp.hAPP @t195 @t242))) @t194))) % 0.16/0.44 (assume @p169 (forall (@list @t4 @t14 @t51 @t123 @t1) (= (tptp.c_Predicate_Oconversep (tptp.c_Predicate_Opred__comp @t4 @t14 @t51 @t123 @t1) @t51 @t1) (tptp.c_Predicate_Opred__comp (tptp.c_Predicate_Oconversep @t14 @t123 @t1) (tptp.c_Predicate_Oconversep @t4 @t51 @t123) @t1 @t123 @t51)))) % 0.16/0.44 (assume @p170 (forall (@list @t16 @t32 @t12) (or @t59 @t33))) % 0.16/0.44 (assume @p171 (forall @t165 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t69) @t48)) @t240))) % 0.16/0.44 (assume @p172 @t243) % 0.16/0.44 (assume @p173 (not @t244)) % 0.16/0.44 (assume @p174 (forall @t249 (or (tptp.class_Lattices_Oupper__semilattice @t248) @t246))) % 0.16/0.44 (assume @p175 (forall @t249 (or (tptp.class_Lattices_Olower__semilattice @t248) @t246))) % 0.16/0.44 (assume @p176 (forall @t249 (or (tptp.class_Lattices_Odistrib__lattice @t248) (not (tptp.class_Lattices_Odistrib__lattice @t245))))) % 0.16/0.44 (assume @p177 (forall @t249 (or (tptp.class_Lattices_Olattice @t248) @t246))) % 0.16/0.44 (assume @p178 (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat)) % 0.16/0.44 (assume @p179 (tptp.class_Lattices_Olower__semilattice tptp.tc_nat)) % 0.16/0.44 (assume @p180 (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat)) % 0.16/0.44 (assume @p181 (tptp.class_Lattices_Olattice tptp.tc_nat)) % 0.16/0.44 (assume @p182 (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool)) % 0.16/0.44 (assume @p183 (tptp.class_Lattices_Olower__semilattice tptp.tc_bool)) % 0.16/0.44 (assume @p184 (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool)) % 0.16/0.44 (assume @p185 (tptp.class_Lattices_Olattice tptp.tc_bool)) % 0.16/0.44 (assume @p186 (forall @t118 (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t182 @t49) @t49)))) % 0.16/0.44 (assume @p187 (forall (@list @t251 @t250 @t1) (or (= @t251 @t250) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t182 @t251) @t250)))))) % 0.16/0.44 (step @p188 :rule instantiate :premises (@p170) :args ((@list tptp.v_t tptp.v_e tptp.v_T))) % 0.16/0.44 (step @p189 :rule instantiate :premises (@p138) :args ((@list tptp.v_t))) % 0.16/0.44 (step @p190 :rule cnf_or_pos :args (@t254)) % 0.16/0.44 (step @p191 :rule reordering :premises (@p190) :args ((or @t244 @t253 (not @t254)))) % 0.16/0.44 (step @p192 :rule chain_m_resolution :premises (@p191 @p173 @p189) :args (@t253 (@list true false) (@list @t244 @t254))) % 0.16/0.44 (step @p193 :rule cnf_or_pos :args (@t256)) % 0.16/0.44 (step @p194 :rule reordering :premises (@p193) :args ((or @t255 @t252 (not @t256)))) % 0.16/0.44 (step @p195 false :rule chain_m_resolution :premises (@p194 @p192 @p188 @p172) :args (false (@list true false false) (@list @t252 @t256 @t243))) % 0.16/0.44 ) % 0.16/0.45 % SZS output end Proof % 0.16/0.45 % cvc5 exiting %------------------------------------------------------------------------------