0.02/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.10 % Command : do_CVC4 %s %d 0.10/0.28 % Computer : n003.cluster.edu 0.10/0.28 % Model : x86_64 x86_64 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.28 % Memory : 8042.1875MB 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.29 % CPULimit : 960 0.10/0.29 % WCLimit : 120 0.10/0.29 % DateTime : Thu Jul 2 09:04:11 EDT 2020 0.10/0.29 % CPUTime : 0.14/0.39 %----Proving TF0_NAR, FOF, or CNF 0.14/0.39 ------- cvc4-fof casc j10 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 960... 0.14/0.39 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 0.60/0.78 % SZS status Theorem for theBenchmark 0.60/0.78 % SZS output start Proof for theBenchmark 0.60/0.78 (skolem (forall ((B_L $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) B_L) c_Arrow__Order__Mirabelle_OLin))) ) 0.60/0.78 ( skv_1 ) 0.60/0.78 ) 0.60/0.78 (skolem (forall ((B_x $$unsorted)) (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member tc_Arrow__Order__Mirabelle_Oindi) B_x) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_member _let_1) (hAPP (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L) B_x)) c_Arrow__Order__Mirabelle_OLin))))) ) 0.60/0.78 ( skv_2 ) 0.60/0.78 ) 0.60/0.78 (skolem (forall ((B_x $$unsorted)) (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member tc_Arrow__Order__Mirabelle_Oindi) B_x) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_member _let_1) (hAPP (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L) B_x)) (hAPP (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin) B_x)))))) ) 0.60/0.78 ( skv_3 ) 0.60/0.78 ) 0.60/0.78 (skolem (forall ((B_x $$unsorted)) (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member tc_Arrow__Order__Mirabelle_Oindi) B_x) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))))) (not (= (c_Orderings_Obot__class_Obot _let_2) (hAPP (c_COMBK _let_2 tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin) B_x))))))) ) 0.60/0.78 ( skv_4 ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) (c_Orderings_Otop__class_Otop (tc_fun T_a tc_HOL_Obool)))) ) 0.60/0.78 ( v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_2, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_3, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_3), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_4, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_c_2))) (= (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus (tc_fun T_a tc_HOL_Obool)) V_A_2) V_B_2))) (and (hBOOL (hAPP _let_1 V_A_2)) (not (hBOOL (hAPP _let_1 V_B_2))))))) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (c_Orderings_Oord__class_Oless__eq _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2) V_B_2)) ) 0.60/0.78 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (c_Relation_Orefl__on T_a V_A_2 (c_Relation_OId__on T_a V_A_2)) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((T_a $$unsorted)) (c_Relation_Orefl__on T_a (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_a T_a) tc_HOL_Obool))) ) 0.60/0.78 ( tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)))) (= (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) _let_0)) (hBOOL (hAPP _let_0 V_x_2)))) ) 0.60/0.78 ( v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_2, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_3, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_3), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_4, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_A_2)) (hBOOL (hAPP V_A_2 V_x_2))) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OLin, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OLin, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OLin, (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OProf, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_2, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_3, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_4, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (hAPP (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin) skv_3), (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_3), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (c_Orderings_Oord__class_Oless__eq _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) V_B_2) V_A_2)) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) skv_1) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) skv_1) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (= (or (= V_x_2 V_y_2) (hBOOL (hAPP V_A_2 V_x_2))) (hBOOL (hAPP (hAPP (hAPP (c_Set_Oinsert T_a) V_y_2) V_A_2) V_x_2))) ) 0.60/0.78 ( v_L, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_1, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) (c_FuncSet_Ocompose T_a T_c T_b V_A_2 V_f_2 V_g_2)) (c_FuncSet_Oextensional T_a T_b V_A_2))) ) 0.60/0.78 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Orestrict _let_1 _let_1 (c_COMBI _let_1) c_Arrow__Order__Mirabelle_OLin))), (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (c_FuncSet_Orestrict tc_Arrow__Order__Mirabelle_Oindi tc_Arrow__Order__Mirabelle_Oindi (c_COMBI tc_Arrow__Order__Mirabelle_Oindi) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (c_Orderings_Oord__class_Oless__eq _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2) V_A_2)) ) 0.60/0.78 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (c_Relation_Osingle__valued T_a T_a (c_Relation_OId__on T_a V_A_2)) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) _let_1) V_B_2)))) ) 0.60/0.78 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun T_a tc_HOL_Obool)) V_A_2) V_A_2)) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (= V_x_2 (c_Set_Othe__elem T_a (hAPP (hAPP (c_Set_Oinsert T_a) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool))))) ) 0.60/0.78 ( v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 0.60/0.78 ( (c_COMBK tc_HOL_Obool tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_Q $$unsorted) (V_P $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= V_P (hAPP (c_COMBK T_a T_b V_P) V_Q)) ) 0.60/0.78 ( skv_2, v_L, tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_3, c_Arrow__Order__Mirabelle_OLin, tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 0.60/0.78 ( skv_3, v_L, tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_4, c_Arrow__Order__Mirabelle_OLin, tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= V_A_2 (c_Relation_ORange T_a T_a (c_Relation_OId__on T_a V_A_2))) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (tc_prod T_a T_a))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (= _let_1 (c_Transitive__Closure_Otrancl T_a _let_1)))) ) 0.60/0.78 ( tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) (c_FuncSet_Orestrict T_a T_b V_f_2 V_A_2)) (c_FuncSet_Oextensional T_a T_b V_A_2))) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OLin, (c_COMBI (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_COMBI tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= V_A_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (c_Orderings_Obot__class_Obot _let_0)))) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_c_2 $$unsorted) (T_a $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member T_a) V_c_2) (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool))))) ) 0.60/0.78 ( v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_2, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_3, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_3), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( skv_4, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_a_2))) (= (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Set_Oinsert T_a) V_b_2) V_A_2))) (or (hBOOL (hAPP _let_1 V_A_2)) (= V_b_2 V_a_2))))) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Ominus__class_Ominus (tc_fun T_a tc_HOL_Obool)))) (let ((_let_1 (hAPP _let_0 V_A_2))) (let ((_let_2 (hAPP _let_1 V_B_2))) (= _let_2 (hAPP (hAPP _let_0 _let_2) V_B_2))))) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_a))) (let ((_let_1 (hAPP _let_0 V_x_2))) (let ((_let_2 (hAPP _let_1 V_A_2))) (= _let_2 (hAPP _let_1 _let_2))))) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot _let_2)))))), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_M_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool))) (= V_M_2 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a T_b) V_A_2) (c_COMBK T_b T_a V_M_2)))) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OLin, tc_Arrow__Order__Mirabelle_Oindi, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 0.60/0.78 ( v_L, tc_Arrow__Order__Mirabelle_Oindi, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a T_b))) (= (c_FuncSet_Oextensional T_a T_b (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_0) (c_COMBK T_b T_a (c_HOL_Oundefined T_b))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))) ) 0.60/0.78 ( tc_HOL_Obool, tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.78 ( tc_HOL_Obool, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 0.60/0.78 ( tc_HOL_Obool, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( tc_HOL_Obool, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( tc_HOL_Obool, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( tc_HOL_Obool, (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 0.60/0.78 ( tc_HOL_Obool, (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool) ) 0.60/0.78 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (let ((_let_1 (c_Set_Oinsert T_a))) (let ((_let_2 (hAPP _let_1 V_x_2))) (or (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_A_2)) (= V_A_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) (hAPP _let_2 V_A_2)) (hAPP _let_2 (c_Orderings_Obot__class_Obot _let_0)))))))) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OLin, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OLin, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OLin, (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OProf, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_2, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_3, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_4, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_3) c_Arrow__Order__Mirabelle_OProf) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot _let_3))))))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot _let_2)))))), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ( (hAPP (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin) skv_3), (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_3), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_x))) ) 0.60/0.78 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.78 ) 0.60/0.78 (instantiation (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (or (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP V_f_2 B_x)) V_B_2))) )) (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_OPi T_a T_b V_A_2 (c_COMBK (tc_fun T_b tc_HOL_Obool) T_a V_B_2))))) ) 0.60/0.78 ( c_Arrow__Order__Mirabelle_OLin, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.78 ) 0.60/0.79 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) V_A_2))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) skv_1) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_a))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)))) (or (not (= (hAPP (hAPP _let_0 V_b_2) _let_1) (hAPP (hAPP _let_0 V_a_2) _let_1))) (= V_b_2 V_a_2)))) ) 0.60/0.79 ( v_L, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( v_L, (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( skv_1, (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 0.60/0.79 ( (c_COMBK tc_HOL_Obool tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_r_2 $$unsorted) (V_S_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_Oconverse T_b T_a))) (let ((_let_1 (tc_prod T_b T_a))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_3 (tc_prod T_a T_b))) (let ((_let_4 (tc_fun _let_3 tc_HOL_Obool))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_4) V_S_2) (hAPP (hAPP (c_COMBB _let_2 _let_4 T_c) _let_0) V_r_2)) (hAPP _let_0 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_2) V_S_2) V_r_2)))))))) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) V_A_2))) (= (hAPP V_B_2 B_x) (c_Orderings_Otop__class_Otop _let_0))) ) (= (c_Orderings_Otop__class_Otop _let_0) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_0) V_A_2) V_B_2)))) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_x_2 $$unsorted) (V_T_2 $$unsorted) (V_S_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_Oextensional__funcset T_a T_b V_S_2 V_T_2)))) (not (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_S_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP V_f_2 V_x_2)) V_T_2))) ) 0.60/0.79 ( skv_2, c_Arrow__Order__Mirabelle_OLin, (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_OPi T_a T_b V_A_2 (c_COMBK (tc_fun T_b tc_HOL_Obool) T_a V_B_2))))) (not (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP V_f_2 V_x_2)) V_B_2))) ) 0.60/0.79 ( skv_2, c_Arrow__Order__Mirabelle_OLin, (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_g_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_fun T_a T_b)))) (let ((_let_1 (c_FuncSet_Oextensional T_a T_b V_A_2))) (or (not (hBOOL (hAPP (hAPP _let_0 V_f_2) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_g_2) _let_1))) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (= (hAPP V_g_2 B_x) (hAPP V_f_2 B_x))) )) (= V_g_2 V_f_2)))) ) 0.60/0.79 ( v_L, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_L, tc_HOL_Obool, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( skv_1, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_L, tc_HOL_Obool, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Otop T_1)) (class_Orderings_Otop (tc_fun T_2 T_1))) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 0.60/0.79 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_0) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) V_B_2) (c_Orderings_Otop__class_Otop _let_0))) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Obot__class_Obot T_a))) (or (not (class_Lattices_Obounded__lattice__bot T_a)) (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) _let_0)))) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((BOUND_VARIABLE_11130 $$unsorted) (BOUND_VARIABLE_11131 $$unsorted) (BOUND_VARIABLE_11132 $$unsorted) (BOUND_VARIABLE_11133 $$unsorted)) (let ((_let_0 (tc_fun BOUND_VARIABLE_11131 tc_HOL_Obool))) (or (= BOUND_VARIABLE_11133 (c_Orderings_Obot__class_Obot (tc_fun BOUND_VARIABLE_11132 tc_HOL_Obool))) (= BOUND_VARIABLE_11130 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR BOUND_VARIABLE_11132 _let_0) BOUND_VARIABLE_11133) (c_COMBK _let_0 BOUND_VARIABLE_11132 BOUND_VARIABLE_11130))))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) ) 0.60/0.79 ( v_L, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_Arrow__Order__Mirabelle_Oindi, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((BOUND_VARIABLE_11112 $$unsorted) (BOUND_VARIABLE_11113 $$unsorted) (BOUND_VARIABLE_11114 $$unsorted)) (let ((_let_0 (tc_fun BOUND_VARIABLE_11113 tc_HOL_Obool))) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR BOUND_VARIABLE_11114 _let_0) (c_Orderings_Obot__class_Obot (tc_fun BOUND_VARIABLE_11114 tc_HOL_Obool))) (c_COMBK _let_0 BOUND_VARIABLE_11114 BOUND_VARIABLE_11112)))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( v_L, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( (c_HOL_Oundefined (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (or (not (c_Orderings_Oord__class_Oless__eq _let_0 V_B_2 V_A_2)) (= V_B_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2)))) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (hAPP (c_Relation_OImage T_a T_a (c_Relation_OId__on T_a V_A_2)) V_B_2) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun T_a tc_HOL_Obool)) V_A_2) V_B_2)) ) 0.60/0.79 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_B_2) V_A_2)))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OProf, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) skv_1) c_Arrow__Order__Mirabelle_OLin), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) skv_1) c_Arrow__Order__Mirabelle_OLin), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop T_a))) (or (not (class_Lattices_Obounded__lattice__top T_a)) (= (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x_2) V_y_2) _let_0) (and (= V_x_2 _let_0) (= V_y_2 _let_0))))) ) 0.60/0.79 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_a))) (let ((_let_1 (hAPP _let_0 V_a_2))) (let ((_let_2 (tc_fun T_a tc_HOL_Obool))) (= (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) V_A_2) (hAPP _let_1 (c_Orderings_Obot__class_Obot _let_2)))) (hAPP _let_1 V_A_2))))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OProf, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) skv_1) c_Arrow__Order__Mirabelle_OLin), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) skv_1) c_Arrow__Order__Mirabelle_OLin), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_c_2))) (or (not (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus (tc_fun T_a tc_HOL_Obool)) V_A_2) V_B_2)))) (not (hBOOL (hAPP _let_1 V_B_2)))))) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Opreorder T_1)) (class_Orderings_Opreorder (tc_fun T_2 T_1))) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 0.60/0.79 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((T_b $$unsorted) (T_a $$unsorted)) (= (c_Relation_ODomain T_a T_b (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_a T_b) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool))) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_c_2))) (or (not (hBOOL (hAPP _let_1 V_A_2))) (hBOOL (hAPP _let_1 V_B_2)) (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus (tc_fun T_a tc_HOL_Obool)) V_A_2) V_B_2)))))) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_prod T_a T_a))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) V_A_2) (hAPP (hAPP (c_COMBC T_a _let_1 _let_1) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_1 _let_1) T_a) (c_Set_Oinsert _let_0)) (hAPP (hAPP (c_COMBS T_a T_a _let_0) (c_Product__Type_OPair T_a T_a)) (c_COMBI T_a)))) (c_Orderings_Obot__class_Obot _let_1))) (c_Relation_OId__on T_a V_A_2)))) ) 0.60/0.79 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((T_b $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) V_a_2) V_A_2))) (not (hBOOL (hAPP (hAPP V_B_2 V_a_2) V_b_2))) (hBOOL (hAPP (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2) V_b_2))) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oalt, (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), c_Arrow__Order__Mirabelle_OLin, (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt 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tc_Arrow__Order__Mirabelle_Oindi, (c_Orderings_Otop__class_Otop (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool))), (c_Orderings_Otop__class_Otop (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool), (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_1)) (class_Complete__Lattice_Ocomplete__lattice (tc_fun T_2 T_1))) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 0.60/0.79 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) 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tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot _let_2)))))), v_L, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), v_L, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member T_a) V_b_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tc_fun T_a tc_HOL_Obool)) V_A_2) V_B_2))) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_a) V_b_2) (hAPP V_B_2 B_x))))) ))) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2)) (forall ((B_x $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 B_x))) (or (not (hBOOL (hAPP _let_1 V_A_2))) (not (hBOOL (hAPP _let_1 V_B_2)))))) ))) ) 0.60/0.79 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Olattice T_a)) (c_Orderings_Oord__class_Oless__eq T_a (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_y)) ) 0.60/0.79 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((T_a $$unsorted) (T_b $$unsorted)) (= (c_Relation_ORange T_b T_a (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_a) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool))) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Oorder T_1)) (class_Orderings_Oorder (tc_fun T_2 T_1))) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 0.60/0.79 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (= _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_0) V_A_2) (c_COMBK _let_0 T_b _let_1))))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OProf, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Olattice T_a)) (c_Orderings_Oord__class_Oless__eq T_a (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_x)) ) 0.60/0.79 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((T_a $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_a T_a) tc_HOL_Obool)) (c_Relation_OId__on T_a (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)))) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (let ((_let_1 (c_Groups_Ominus__class_Ominus _let_0))) (let ((_let_2 (hAPP _let_1 V_A_2))) (let ((_let_3 (c_Set_Oinsert T_a))) (let ((_let_4 (hAPP _let_3 V_a_2))) (= (hAPP (hAPP _let_1 (hAPP _let_2 V_B_2)) (hAPP _let_4 (c_Orderings_Obot__class_Obot _let_0))) (hAPP _let_2 (hAPP _let_4 V_B_2)))))))) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((BOUND_VARIABLE_11887 $$unsorted) (BOUND_VARIABLE_11888 $$unsorted) (BOUND_VARIABLE_11889 $$unsorted) (BOUND_VARIABLE_11890 $$unsorted)) (let ((_let_0 (tc_fun BOUND_VARIABLE_11888 tc_HOL_Obool))) (or (= BOUND_VARIABLE_11890 (c_Orderings_Obot__class_Obot (tc_fun BOUND_VARIABLE_11889 tc_HOL_Obool))) (= BOUND_VARIABLE_11887 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI BOUND_VARIABLE_11889 _let_0) BOUND_VARIABLE_11890) (c_COMBK _let_0 BOUND_VARIABLE_11889 BOUND_VARIABLE_11887))))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) ) 0.60/0.79 ( v_L, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_Arrow__Order__Mirabelle_Oindi, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((BOUND_VARIABLE_11869 $$unsorted) (BOUND_VARIABLE_11870 $$unsorted) (BOUND_VARIABLE_11871 $$unsorted)) (let ((_let_0 (tc_fun BOUND_VARIABLE_11870 tc_HOL_Obool))) (= (c_Orderings_Otop__class_Otop _let_0) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI BOUND_VARIABLE_11871 _let_0) (c_Orderings_Obot__class_Obot (tc_fun BOUND_VARIABLE_11871 tc_HOL_Obool))) (c_COMBK _let_0 BOUND_VARIABLE_11871 BOUND_VARIABLE_11869)))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( v_L, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( (c_HOL_Oundefined (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_r_2 $$unsorted) (V_S_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_Oconverse T_b T_a))) (let ((_let_1 (tc_prod T_b T_a))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_3 (tc_prod T_a T_b))) (let ((_let_4 (tc_fun _let_3 tc_HOL_Obool))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_4) V_S_2) (hAPP (hAPP (c_COMBB _let_2 _let_4 T_c) _let_0) V_r_2)) (hAPP _let_0 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_2) V_S_2) V_r_2)))))))) ) 0.60/0.79 ( (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool))), c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (c_Relation_ORange T_a T_a (c_Transitive__Closure_Otrancl T_a V_r_2)) (c_Relation_ORange T_a T_a V_r_2)) ) 0.60/0.79 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Ominus__class_Ominus (tc_fun T_a tc_HOL_Obool)))) (let ((_let_1 (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun T_a tc_HOL_Obool)))) (= (hAPP (hAPP _let_1 (hAPP (hAPP _let_0 V_A_2) V_B_2)) V_C_2) (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_A_2) V_C_2)) (hAPP (hAPP _let_1 V_B_2) V_C_2))))) ) 0.60/0.79 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_M_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun 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(instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (c_Relation_ODomain T_a T_b V_r_2) (c_Relation_ORange T_b T_a (hAPP (c_Relation_Oconverse T_a T_b) V_r_2))) ) 0.60/0.79 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_OPi T_a T_b V_A_2 V_B_2)))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP V_f_2 V_x_2)) (hAPP V_B_2 V_x_2))) (not (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_A_2)))) ) 0.60/0.79 ( skv_2, (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi 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(let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_Oextensional T_a T_b V_A_2)))) (= V_f_2 (c_FuncSet_Orestrict T_a T_b V_f_2 V_A_2))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (c_COMBI (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_COMBI tc_Arrow__Order__Mirabelle_Oindi), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (= (= V_x_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x_2) V_y_2)) (c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2))) ) 0.60/0.79 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Obot T_a)) (= (hAPP (c_Orderings_Obot__class_Obot (tc_fun T_b T_a)) V_x_2) (c_Orderings_Obot__class_Obot T_a))) ) 0.60/0.79 ( v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.79 ( skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Groups_Ominus T_1)) (class_Groups_Ominus (tc_fun T_2 T_1))) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 0.60/0.79 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf T_a))) (or (not (class_Lattices_Osemilattice__inf T_a)) (= (hAPP (hAPP _let_0 V_a) V_b) (hAPP (hAPP _let_0 V_b) V_a)))) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.79 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Obounded__lattice T_1)) (class_Lattices_Obounded__lattice__bot (tc_fun T_2 T_1))) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 0.60/0.79 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_c_2))) (or (not (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus (tc_fun T_a tc_HOL_Obool)) V_A_2) V_B_2)))) (and (hBOOL (hAPP _let_1 V_A_2)) (not (hBOOL (hAPP _let_1 V_B_2))))))) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (not (hBOOL (hAPP (hAPP V_B_2 B_x) V_b_2)))) )) (hBOOL (hAPP (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2) V_b_2))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OProf, (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool))), c_Arrow__Order__Mirabelle_OProf, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( v_L, (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( skv_1, (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_a_2))) (or (not (hBOOL (hAPP _let_1 V_B_2))) (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Set_Oinsert T_a) V_b_2) V_B_2)))))) ) 0.60/0.79 ( skv_1, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( skv_1, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( skv_1, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (or (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP V_f_2 B_x)) (hAPP V_B_2 B_x)))) )) (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_OPi T_a T_b V_A_2 V_B_2)))) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_a_2))) (or (not (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Set_Oinsert T_a) V_b_2) V_A_2)))) (= V_b_2 V_a_2) (hBOOL (hAPP _let_1 V_A_2))))) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot _let_2)))))), v_L, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) V_A_2))) (= (hAPP V_B_2 B_x) (c_Orderings_Obot__class_Obot _let_0))) ) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_0) V_A_2) V_B_2)))) ) 0.60/0.79 ( (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool))), c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2) V_b_2))) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (not (hBOOL (hAPP (hAPP V_B_2 B_x) V_b_2)))) ))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OProf, (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool))), c_Arrow__Order__Mirabelle_OProf, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( v_L, (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( skv_1, (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_c_2))) (or (not (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus (tc_fun T_a tc_HOL_Obool)) V_A_2) V_B_2)))) (hBOOL (hAPP _let_1 V_A_2))))) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (= (c_Relation_ORange T_b T_a V_r_2) (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool))) (= V_r_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_a) tc_HOL_Obool)))) ) 0.60/0.79 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_x_2 $$unsorted) (V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_a)) (= (hAPP (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tc_fun T_c T_a)) V_A_2) V_f_2) V_x_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b T_a) V_A_2) (hAPP (hAPP (c_COMBC T_b T_c T_a) V_f_2) V_x_2)))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OProf, (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool))), c_Arrow__Order__Mirabelle_OProf, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.79 ( v_L, (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.79 ( skv_1, (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (not (= (c_Orderings_Obot__class_Obot _let_0) (c_Orderings_Otop__class_Otop _let_0)))) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.79 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 0.60/0.79 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 0.60/0.79 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (or (not (c_Orderings_Oord__class_Oless__eq _let_0 V_A_2 V_B_2)) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2)))) ) 0.60/0.79 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (let ((_let_1 (c_Groups_Ominus__class_Ominus _let_0))) (let ((_let_2 (hAPP _let_1 V_A_2))) (let ((_let_3 (c_Set_Oinsert T_a))) (let ((_let_4 (hAPP _let_3 V_a_2))) (= (hAPP _let_2 (hAPP _let_4 V_B_2)) (hAPP (hAPP _let_1 (hAPP _let_2 (hAPP _let_4 (c_Orderings_Obot__class_Obot _let_0)))) V_B_2))))))) ) 0.60/0.79 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), v_L, (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), skv_1, (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (not (c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (= V_y (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y))) ) 0.60/0.79 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (c_Orderings_Oord__class_Oless__eq T_a (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_y)) ) 0.60/0.79 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member T_a) V_b_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b (tc_fun T_a tc_HOL_Obool)) V_A_2) V_B_2))) (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_a) V_b_2) (hAPP V_B_2 B_x)))) )) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ) 0.60/0.79 (instantiation (forall ((V_B_2 $$unsorted) (T_b $$unsorted) (V_g_2 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$$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) V_a_2) V_A_2))) (= V_A_2 (hAPP (hAPP (c_Set_Oinsert T_a) V_a_2) V_A_2))) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OLin, (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.79 ( c_Arrow__Order__Mirabelle_OProf, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod 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tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (hAPP (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin) skv_3), (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_3), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (c_Relation_ODomain T_a T_a (c_Transitive__Closure_Otrancl T_a V_r_2)) (c_Relation_ODomain T_a T_a V_r_2)) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)) (c_Relation_ODomain T_a T_b V_r_2)) (= V_r_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_a T_b) tc_HOL_Obool)))) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Osemilattice__inf (tc_fun T_2 T_1))) ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 0.60/0.80 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (c_Orderings_Otop__class_Otop _let_0)))) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_x_2))) (let ((_let_2 (c_Set_Oinsert T_a))) (let ((_let_3 (hAPP _let_2 V_x_2))) (or (hBOOL (hAPP _let_1 V_A_2)) (hBOOL (hAPP _let_1 V_B_2)) (= (= (hAPP _let_3 V_A_2) (hAPP _let_3 V_B_2)) (= V_B_2 V_A_2))))))) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OLin, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OLin, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OLin, (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OProf, c_Arrow__Order__Mirabelle_OProf, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OProf, (c_Orderings_Otop__class_Otop (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_2, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_3, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_4, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OProf, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (hAPP (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin) skv_3), (hAPP (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin) skv_3), (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_3), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (c_Orderings_Oord__class_Oless__eq T_a (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_x)) ) 0.60/0.80 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((BOUND_VARIABLE_13164 $$unsorted) (BOUND_VARIABLE_13165 $$unsorted) (BOUND_VARIABLE_13166 $$unsorted) (BOUND_VARIABLE_13167 $$unsorted) (BOUND_VARIABLE_13168 $$unsorted)) (let ((_let_0 (tc_fun BOUND_VARIABLE_13166 tc_HOL_Obool))) (let ((_let_1 (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR BOUND_VARIABLE_13167 _let_0))) (let ((_let_2 (hAPP _let_1 BOUND_VARIABLE_13168))) (let ((_let_3 (c_Set_Oinsert BOUND_VARIABLE_13166))) (let ((_let_4 (hAPP _let_3 BOUND_VARIABLE_13165))) (or (= BOUND_VARIABLE_13168 (c_Orderings_Obot__class_Obot (tc_fun BOUND_VARIABLE_13167 tc_HOL_Obool))) (= (hAPP _let_2 (hAPP (hAPP (c_COMBB _let_0 _let_0 BOUND_VARIABLE_13167) _let_4) BOUND_VARIABLE_13164)) (hAPP _let_4 (hAPP _let_2 BOUND_VARIABLE_13164))))))))) ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (= _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) _let_1) V_A_2)))) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (or (not (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2))) (= V_A_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) V_B_2)))) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Obounded__lattice T_1)) (class_Lattices_Obounded__lattice__top (tc_fun T_2 T_1))) ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 0.60/0.80 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Obounded__lattice T_1)) (class_Lattices_Obounded__lattice (tc_fun T_2 T_1))) ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 0.60/0.80 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (c_Orderings_Obot__class_Obot (tc_fun (tc_fun T_a T_b) tc_HOL_Obool)) (c_FuncSet_OPi T_a T_b V_A_2 V_B_2)) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (not (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP V_B_2 B_x)))) ))) ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (c_Transitive__Closure_Ortrancl T_a (c_Transitive__Closure_Otrancl T_a V_R_2)) (c_Transitive__Closure_Ortrancl T_a V_R_2)) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (not (c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y))) ) 0.60/0.80 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((BOUND_VARIABLE_13361 $$unsorted) (BOUND_VARIABLE_13362 $$unsorted) (BOUND_VARIABLE_13363 $$unsorted)) (hBOOL (hAPP (hAPP (c_member BOUND_VARIABLE_13363) BOUND_VARIABLE_13362) (hAPP (hAPP (c_Set_Oinsert BOUND_VARIABLE_13363) BOUND_VARIABLE_13362) BOUND_VARIABLE_13361))) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_3) c_Arrow__Order__Mirabelle_OProf) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot _let_3))))))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot _let_2)))))), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf T_a))) (or (not (class_Lattices_Olattice T_a)) (= (hAPP (hAPP _let_0 V_y) V_x) (hAPP (hAPP _let_0 V_x) V_y)))) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.80 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Relation_OId__on T_a V_A_2))) (= _let_0 (hAPP (c_Relation_Oconverse T_a T_a) _let_0))) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= V_A_2 (c_Relation_ODomain T_a T_a (c_Relation_OId__on T_a V_A_2))) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_x_2 $$unsorted) (V_T_2 $$unsorted) (V_S_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_Oextensional__funcset T_a T_b V_S_2 V_T_2)))) (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_S_2)) (= (hAPP V_f_2 V_x_2) (c_HOL_Oundefined T_b))) ) 0.60/0.80 ( skv_2, c_Arrow__Order__Mirabelle_OLin, (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) V_b_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tc_fun T_a tc_HOL_Obool)) V_A_2) V_B_2)))) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_a) V_b_2) (hAPP V_B_2 B_x))))) ))) ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Obot__class_Obot T_a))) (or (not (class_Lattices_Obounded__lattice__bot T_a)) (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) _let_0) V_x)))) ) 0.60/0.80 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((BOUND_VARIABLE_13695 $$unsorted) (BOUND_VARIABLE_13696 $$unsorted) (BOUND_VARIABLE_13697 $$unsorted) (BOUND_VARIABLE_13698 $$unsorted)) (let ((_let_0 (c_Set_Oinsert BOUND_VARIABLE_13697))) (let ((_let_1 (hAPP _let_0 BOUND_VARIABLE_13696))) (let ((_let_2 (tc_fun BOUND_VARIABLE_13697 tc_HOL_Obool))) (= (hAPP _let_1 (c_Orderings_Obot__class_Obot _let_2)) (hAPP _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR BOUND_VARIABLE_13698 _let_2) (c_Orderings_Obot__class_Obot (tc_fun BOUND_VARIABLE_13698 tc_HOL_Obool))) BOUND_VARIABLE_13695)))))) ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_a))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)))) (= (= (hAPP (hAPP _let_0 V_c_2) (hAPP (hAPP _let_0 V_d_2) _let_1)) (hAPP (hAPP _let_0 V_a_2) (hAPP (hAPP _let_0 V_b_2) _let_1))) (or (and (= V_c_2 V_a_2) (= V_d_2 V_b_2)) (and (= V_d_2 V_a_2) (= V_c_2 V_b_2)))))) ) 0.60/0.80 ( v_L, v_L, (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( skv_1, skv_1, skv_1, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), v_L, (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 0.60/0.80 ( (c_COMBK tc_HOL_Obool tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_f_2 $$unsorted) (V_g_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (= (c_FuncSet_Ocompose T_a T_c T_b V_A_2 V_g_2 V_f_2) (c_FuncSet_Orestrict T_a T_b (hAPP (hAPP (c_COMBB T_c T_b T_a) V_g_2) V_f_2) V_A_2)) ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Orestrict _let_1 _let_1 (c_COMBI _let_1) c_Arrow__Order__Mirabelle_OLin))), (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ( (c_FuncSet_Orestrict tc_Arrow__Order__Mirabelle_Oindi tc_Arrow__Order__Mirabelle_Oindi (c_COMBI tc_Arrow__Order__Mirabelle_Oindi) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_g_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_fun T_a T_b)))) (let ((_let_1 (hAPP _let_0 V_g_2))) (or (not (hBOOL (hAPP _let_1 (c_FuncSet_OPi T_a T_b V_A_2 (c_COMBK (tc_fun T_b tc_HOL_Obool) T_a V_B_2))))) (not (hBOOL (hAPP _let_1 (c_FuncSet_Oextensional T_a T_b V_A_2)))) (= V_g_2 (c_FuncSet_Ocompose T_a T_a T_b V_A_2 V_g_2 (c_FuncSet_Orestrict T_a T_a (c_COMBI T_a) V_A_2)))))) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Ominus__class_Ominus (tc_fun T_a tc_HOL_Obool)))) (or (not (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_B_2))) (= (hAPP (hAPP _let_0 V_A_2) V_B_2) (hAPP (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_a) V_x_2) V_A_2)) V_B_2)))) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_a_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_b_2))) (or (not (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b (tc_fun T_a tc_HOL_Obool)) V_A_2) V_B_2)))) (hBOOL (hAPP _let_1 (hAPP V_B_2 V_a_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2)))))) ) 0.60/0.80 ( skv_4, (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= V_A_2 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_a _let_0 _let_0) (c_Set_Oinsert T_a)) (c_Orderings_Obot__class_Obot _let_0))))) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((BOUND_VARIABLE_13883 $$unsorted) (BOUND_VARIABLE_13884 $$unsorted) (BOUND_VARIABLE_13885 $$unsorted) (BOUND_VARIABLE_13886 $$unsorted)) (let ((_let_0 (c_Groups_Ominus__class_Ominus (tc_fun BOUND_VARIABLE_13886 tc_HOL_Obool)))) (let ((_let_1 (c_Set_Oinsert BOUND_VARIABLE_13886))) (let ((_let_2 (hAPP _let_1 BOUND_VARIABLE_13885))) (or (hBOOL (hAPP (hAPP (c_member BOUND_VARIABLE_13886) BOUND_VARIABLE_13885) BOUND_VARIABLE_13884)) (= (hAPP (hAPP _let_0 (hAPP _let_2 BOUND_VARIABLE_13883)) BOUND_VARIABLE_13884) (hAPP _let_2 (hAPP (hAPP _let_0 BOUND_VARIABLE_13883) BOUND_VARIABLE_13884))))))) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OProf, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_2) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot _let_2)))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_1) skv_1) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) _let_1)))) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Oord T_1)) (class_Orderings_Oord (tc_fun T_2 T_1))) ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 0.60/0.80 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_B_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (or (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_b_2) (hAPP V_B_2 B_x)))) )) (hBOOL (hAPP (hAPP (c_member T_b) V_b_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2)))) ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ( (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) (c_Orderings_Otop__class_Otop _let_0)))) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun T_a tc_HOL_Obool)))) (= (hAPP (hAPP _let_0 V_A_2) V_B_2) (hAPP (hAPP _let_0 V_B_2) V_A_2))) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_OPi tc_Arrow__Order__Mirabelle_Oindi _let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) V_a_2) V_A_2))) (not (hBOOL (hAPP (hAPP (hAPP V_B_2 V_a_2) V_b_2) V_c_2))) (hBOOL (hAPP (hAPP (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tc_fun T_b (tc_fun T_c tc_HOL_Obool))) V_A_2) V_B_2) V_b_2) V_c_2))) ) 0.60/0.80 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_Arrow__Order__Mirabelle_Oindi, v_L, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) c_Arrow__Order__Mirabelle_OLin) (hAPP (hAPP (c_Set_Oinsert _let_1) v_L) (c_Orderings_Obot__class_Obot _let_2)))))), (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OLin, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_Oextensional T_a T_b V_A_2)))) (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_A_2)) (= (c_HOL_Oundefined T_b) (hAPP V_f_2 V_x_2))) ) 0.60/0.80 ( skv_2, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_a))) (let ((_let_1 (hAPP _let_0 V_a_2))) (let ((_let_2 (tc_fun T_a tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member T_a) V_a_2) V_A_2))) (= V_A_2 (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) V_A_2) (hAPP _let_1 (c_Orderings_Obot__class_Obot _let_2))))))))) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OProf, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_2, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_3, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), skv_4, tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi v_L)) c_Arrow__Order__Mirabelle_OProf))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), v_L, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (hAPP (hAPP (c_Set_Oinsert (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) v_L) c_Arrow__Order__Mirabelle_OLin), skv_1, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (c_FuncSet_Oextensional tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool))), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 0.60/0.80 ( (hAPP (c_COMBK (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi c_Arrow__Order__Mirabelle_OLin) skv_3), (hAPP (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L) skv_3), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_T_2 $$unsorted) (V_S_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (c_FuncSet_Oextensional__funcset T_a T_b V_S_2 V_T_2) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun (tc_fun T_a T_b) tc_HOL_Obool)) (c_FuncSet_OPi T_a T_b V_S_2 (c_COMBK (tc_fun T_b tc_HOL_Obool) T_a V_T_2))) (c_FuncSet_Oextensional T_a T_b V_S_2))) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Olattice (tc_fun T_2 T_1))) ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 0.60/0.80 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 0.60/0.80 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 0.60/0.80 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool), tc_HOL_Obool ) 0.60/0.80 ) 0.60/0.80 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_fun T_a T_b)))) (let ((_let_1 (hAPP _let_0 V_f_2))) (or (not (hBOOL (hAPP _let_1 (c_FuncSet_OPi T_a T_b V_A_2 (c_COMBK (tc_fun T_b tc_HOL_Obool) T_a V_B_2))))) (not (hBOOL (hAPP _let_1 (c_FuncSet_Oextensional T_a T_b V_A_2)))) (= V_f_2 (c_FuncSet_Ocompose T_a T_b T_b V_A_2 (c_FuncSet_Orestrict T_b T_b (c_COMBI T_b) V_B_2) V_f_2))))) ) 0.60/0.80 ( c_Arrow__Order__Mirabelle_OLin, (c_Orderings_Otop__class_Otop (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi v_L), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 0.60/0.80 ) 0.60/0.80 % SZS output end Proof for theBenchmark 0.60/0.81 EOF